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Absorption in cocurrent gas liquid flow in horizontal tubes Hayduk, Walter 1964

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ABSORPTION IN COCURRENT GAS-LIQUID FLOW IN HORIZONTAL TUBES by WALTER HAYDUK B.A.Sc, University o f British Columbia, 1954 M.A.Sc, University o f British Columbia, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1964 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia,, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study, I f u r t h e r agree that per m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission^ Department of (^ 2^ L^ ^^  x < £ ^ - _ t J 2 ^ ? ^ The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, -Canada Date /7", /9S 4-y O' f  The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of WALTER HAYDUK B.A.Sc, The Univ e r s i t y of British. Columbia, 1954 M.A.Sc., The University of B r i t i s h Columbia, 1956 IN ROOM 207, CHEMICAL ENGINEERING BUILDING THURSDAY, JULY 9, 1964, at 1:30 P.M. COMMITTEE IN CHARGE Chairman; W„ H. Gage External Examiner; G; Govier Deputy Chairman, O i l and Gas Conservation Board S,D. Cavers J.S. Forsyth J , Lielmezs E, Peters K.L..Pinder l.T. Warren Calgary ABSORPTION IN GAS-LIQUID HORIZONTAL FLOW ABSTRACT Gas ab s o r p t i o n r a t e s were experimentally determined f o r a number of tworphase g a s - l i q u i d systems i n co- current h o r i z o n t a l flow through c i r c u l a r tubes. S p a r i n g l y s o l u b l e gases were used i n order to determine the l i q u i d phase r e s i s t a n c e to mass t r a n s f e r . A s e r i e s of experiments was ..designed to separate the e f f e c t s of gas density,, l i q u i d r p h a s e d i f f u s i v i t y , v i s c o s i t y , sur face t e n s i o n , and tub.e diameter, on the mass t r a n s f e r r a t e s . The g a s - l i q u i d systems employed, i n a s i n g l e tube 1.757 cm. i n diameter, were C02 _water, He-water, C02-ethanol, and C02-ethylene g l y c o l . Two a d d i t i o n a l tube s i z e s , 1.228 and 2.504.cm. i n diameter were em ployed w i t h the C02-water system to determine the e f f e c t of tube diameter. The.gas and l i q u i d flow r a t e s used produced four d i f f e r e n t flow regions, bubble, plug, s l u g , and annular flow". The, gas, and l i q u i d , super f i c i a l v e l o c i t i e s ranged from 0.1 to 40 fps, and 0.5 to 3.6 fps, r e s p e c t i v e l y . Two c o r r e l a t i o n s were developed f o r p r e d i c t i n g mass t r a n s f e r r a t e s i n two-phase flow. The f i r s t , based on a theory that each bubble represents a "mixing stage", i s a p p l i c a b l e to the bubble and plug regions of flow, and c o r r e l a t e s the experimental' data f o r a wide range of l i q u i d p h y s i c a l p r o p e r t i e s , as w e l l as gas and l i q u i d flow r a t e s , w i t h a probable e r r o r of approxi mately 15%. The second c o r r e l a t i o n , a p p l i c a b l e to slug flow, e m p i r i c a l l y c o r r e l a t e s the data f o r t h i s region, over the same wide range of p h y s i c a l p r o p e r t i e s and flow r a t e s , w i t h a probable.error of approximately 10%. The surface renewal or " p e n e t r a t i o n theory" mechanism of t r a n s f e r i s shown to be c o n s i s t e n t w i t h the experimental r e s u l t s obtained i n the bubble and plug regions. In the s l u g region, on the other hand, evidence i s a v a i l a b l e to i n d i c a t e that another mechanism (probably that proposed by K i s h i n e v s k i i ) , becomes i n c r e a s i n g l y important as the degree of turbulence i n c r e a s e s . GRADUATE STUDIES F i e l d of Study; Chemical Engineering I n d u s t r i a l Chemical Reactions Engineering Calculations F l u i d Flow Heat Transfer Chemical Engineering Thermodynamic s Advanced Chemical Reactor Design Momentum, Heat and Mass Transfer Related Studies: D„S„ Scott N. Epstein N. Epstein L„W. Shemilt L.W. Shemilt D.S. Scott S.D. Cavers Topics i n Organic Chemistry Production Techniques Theory of Measurements Computer Programming Mathematical S t a t i s t i c s Heat Transfer A. Rosenthal H,C. Wilkinson A.M. Crooker C. Froese L. Schwartz W. Wolfe ABSTRACT Gas absorption rates were experimentally determined for a number of two-phase gas-liquid systems in cocurrent horizontal flow through circular tubes. Sparingly soluble gases were used in order to determine the liquid phase resistance t o mass t r a n s  fer. A series of experiments was designed to separate t h e effects of gas density, liquid-phase di f f u s i v i t y , viscosity, surface tension, and tube diameter, on the mass transfer rates. The gas-liquid systems employed, in a single tube 1.757 cm in diameter, were CC^-water, He-water, CC^-ethanol, and GO^- ethylene glycol. Two additional tube sizes, 1.228 and 2 . 5 0 4 cm in diameter were employed with the CC^-water system to determine the effect of tube diameter. The gas and liquid flow rates used produced four different flow regions, bubble, plug, slug, and annular flow. The gas and liquid superficial velocities ranged from 0.1 to 40 fps, and.0.5 to 3.6 fps, respectively. Two correlations were developed for predicting mass transfer rates in two-phase flow. The f i r s t , based on a theory that each bubble represents a "mixing stage", is applicable to the bubble and plug regions of flow,- and correlates with experi mental data for a wide range of liquid physical properties, as well as gas and liquid flow rates, with a probable error of i i i approximately 15%. The second c o r r e l a t i o n , applicable to slug flow, empirically correlates the data for t h i s region, over the same wide range of physical properties and flow rates, with a probable error of approximately 10%. The surface renewal or "penetration theory 1 8 mechanism of transfer i s shown to be consistent with the experimental r e s u l t s obtained i n the bubble and plug regions. In the slug region, on the other hand, evidence i s avail a b l e to indicate that another mechanism (probably that proposed by K i s h i n e v s k i i ) , becomes increasingly important as the degree of turbulence increases. iv TABLE OF CONTENTS Page INTRODUCTION . 1 SCOPE OF RESEARCH 6 DESIGN OF EXPERIMENTS 14 THEORETICAL ASPECTS „ 27 Factors Affecting Absorption Rate 27 Mass Transfer Mechanism for Bubble Region 35 Proposed Velocity Profile in Bubble Flow Region . .38 Proposed Mechanism for Mass Transfer in Bubble Flow .44 Proposed Mechanism for Mass Transfer in Slug Region. • .57 SPECIFICATIONS AND PROPERTIES OF TEST FLUIDS 67 Specifications 67 Fluid Properties, Literature Data 68 Solubility 68 Viscosity and Density 69 Surface Tension 69 Liquid Phase Diffusivity 70 Fluid Properties, Experimental Data for Ethylene Glycol ...71 Solubility of C02 71 Surface Tension 72 Viscosity 73 APPARATUS .84 Liquid System 86 Gas System 89 Absorption Tubes .92 Materials of Construction 98 PROCEDURE 100 Liquid System 100 V Pa&e Water as the Test Liquid 100 Ethanol as the Test Liquid <>.... 102 Ethylene Glycol as the Test Liquid 104 Calibration of the Liquid Rotameters 106 Gas System 108 Calibration of the Gas Rotameters . . . . . . . . 109 Gas Flow Measurement and Control. I l l Gas Humidification and Saturation • 113 Measurement of Pressure in the Absorption Tube. . 115 SAMPLING AND ANALYSIS 118 Sampling 118 C02-Water and C02~Ethanol 122 C02-Ethylene Glycol . . . . 124 He-Water 129 Analysis • 130 C02-Water . . 131 C02~Ethanol and C02-Ethylene Glycol ..<>.... 133 He-Water 134 Preparation and Maintenance of Standard Solutions . 141 TREATMENT OF DATA . . . . . . . . . . 144 EXPERIMENTAL RESULTS 151 Effect of Gas Density 152 Absorption Curves of Three Liquid Superficial Velocities 152 Effect of Increased Liquid Flow Rate 153 Effect of Entrance Type 158 Effect of Temperature on Absorption Rate. . . . . 158 DEVELOPMENT OF CORRELATIONS . . . . . 161 Bubble Region 162 Slug Region 173 DISCUSSION AND CONCLUSIONS. „ 188 Bubble Flow e 190 Slug Region 201 REFERENCES APPENDICES I . PROCESS EQUIPMENT SPECIFICATIONS II. CALIBRATION OF GAS AND LIQUID ROTAMETERS III. SAMPLING AND ANALYSIS IV. IBM-1620 FORTRAN PROGRAMS USED IN CALCULATIONS OF EXPERIMENTAL RESULTS V. LISTS OF EXPERIMENTAL DATA, CALCULATED VALUES OF CORRELATION VARIABLES, AND RELATED CALCULATED RESULTS v i i LIST OF FIGURES 1. Effect of Gas Pressure and Liquid Phase Diffusivity on Absorption Rate 19 2. Proposed Velocity Profile for Horizontal Bubble Flow . .43 3. Graphs of Tensiometer Calibration, Surface Tension Measurements for Ethylene Glycol 74 4. Process Flow Diagram of Apparatus. 85 5. Dimensions of Absorption Tubes and Entrance Tees . . . .94 6. Viscosities of Ethylene Glycol~Water Solutions . . . . 107 7. Concentration Profiles for C0£'*Water and C02~Glycol. • 119 8. Methods of Sampling for Absorption Rate Determinations 121 9. Induced Turbulence in Ethylene Glycol by Ink Injection Tests 125 10. pH Curves for Carbonate Titration in Solutions of Water and Ethanol and Titration Volumes for Solutions of Water and Glycol 135 11. Flow Diagram for Helium Analyzers 136 12. Helium Analyzer Calibration Curve 139 13. Quantity of Absorption for Varying Inlet Concentrations and Logarithmic Mean Driving Force 147 14. NTU vs Gas Superficial Velocity, for Liquid Super ficial Velocity of 0.5 fps 154 15. NTU vs Gas Superficial Velocity, for Liquid Super- ficial Velocity of 0.9 fps 155 16. NTU vs Gas Superficial Velocity, for Liquid Super ficial Velocity of 1.8 fps 156 v i i i £§&§, 17. Effect of Gas and Liquid Flow Rates for the C O 2 " Water System . . 157 18. Effect of Entrance Type on the Absorption Rate for the C02-Water System 159 19. Effect of Liquid Flow Rate, at Low Gas Rates, on the Rate of Absorption, Using the CO^ Htfater System . . . . 168 20. Correlation of Two-Phase Flow Absorption Rates for the Bubble and Plug Regions. • 172 21. Absorption Rate vs Gas Superficial Velocity for Slug Region at a Liquid Superficial Velocity of 0.53 fps. • 175 22. Absorption Rate vs Gas Superficial Velocity for Slug Region at a Liquid Superficial Velocity of 0.91 fps. . 176 23. Absorption Rate vs Gas Superficial Velocity for Slug Region at a Liquid Superficial Velocity of 1.79 fps. . 177 24. Values of "b" and "c" vs Liquid Superficial Velocity to be Used in Equation (21). 181 25. Exponents for Dimensionless Ratios in Equation (24) as Functions of Liquid Superficial Velocity 184 26. Graph of NTU vs Gas Superficial Velocity for the C 0 2 ~ Water System at Liquid Superficial Velocities Exceeding 2 fps 186 27. Correlation for Slug Region, Calculated vs Observed Values of NTU 187 28. Application of the Bubble Flow Correlation to CO2" Water System Data at Various Temperatures 192 29. Application of Slug Flow Correlation to C0£-Water Absorption Data at Various Temperatures 205 ix LIST OF TABLES 1. Solubilities of CO2 in Water and Ethanol 2. Solubility of He in Water . . .77 3. Viscosity of Water and Ethanol . .78 4. Surface Tension of Water and Ethanol i n Contact with Saturated Air 79 5. Liquid Phase Diffusion Coefficients 80 6. Solubility of C 0 2 in Ethylene Glycol ,81 7. Surface Tension of Ethylene Glycol 82 8. Ethylene Glycol Viscosity Determinations 83 9. Amount of C 0 2 Absorbed and Logarithmic Mean Driving Force » . . 146 10. Exponents for Dimensionless Ratios in Equation Variable with Liquid Superficial Velocity. . . . . . . 185 X ACKNOWLEDGEMENT The author wishes to express his acknowledgement to Dr. D. S. Scott, under whose supervision this work was under taken, for his assistance and guidance. Appreciation is also extended to Drs. N. Epstein, and J, S. Forsyth for their helpful suggestions and encouragement which expedited the completion of this project, in Dr. Scott's absence. A particular indebtedness Is expressed to Mr. E. Rudischer for his willing assistance in the construction and assembling of equipment. Financial support for this research was contributed by the Standard Oil Company of British Columbia in the form of their Postgraduate Fellowship for two consecutive years (1961-2 and 1962-3). Additional financial support was provided by the National Research Council of Canada from grants made available to the Chemical Engineering Department at this university. INTRODUCTION A study of gas absorption i n two-phase cocurrent flow w i l l include at lea s t two major areas of chemical engineering enquiry: the mechanism of inter-phase mass transfer, and the hydrodynamic processes which produce the i n t e r f a c i a l areas involved. An adequate explanation of the mechanism of mass transfer i s dependent on a,, r e a l i s t i c picture of the f l u i d dynamics. The f l u i d behaviour of one type of bubble flow i n v e r t i c a l tubes has been explained i n some d e t a i l (1), and con siderable e f f o r t has been expended on the analysis of the flow c h a r a c t e r i s t i c s of upward annular g a s - l i q u i d flow ( 2 S 3 ) . For many of the two-phase flow regions i n both v e r t i c a l and h o r i  zontal tubes, however, studies of the f l u i d dynamics have not yet been p a r t i c u l a r l y successful. Reports i n the l i t e r a t u r e of the rates of mass transfer i n two-phase cocurrent flow (horizontal and v e r t i c a l ) have been extremely sparse (4,5,6) and i n none of these a r t i c l e s has the actual mechanism of mass transfer been brought to l i g h t . In t h i s research experiments designed to improve present knowledge about mass transfer processes i n horizontal two~plm&e gas-l i q u i d flow, have been performed. For the bubble and plug, flow regions an attempt was made to postulate from the observed 2 shape and behaviour of the g a s - l i q u i d interface, which of several possible mechanisms might be operative i n the flowing f l u i d s . For these regions-, therefore, i t was possible to put forward an explanation for the observed variat i o n s i n rates of mass transfer. For the slug and annular regions of flow, however, a more empirical approach was necessary. Some c h a r a c t e r i s t i c s peculiar to horizontal g a s - l i q u i d tubular flow set i t apart from single-phase flow. A knowledge of the volumetric rates of input for both the gas and l i q u i d does not d i r e c t l y a f f o r d a.,, knowledge of the actual average v e l o c i t i e s of either of the phases i n the tube. The volume f r a c t i o n of each of the flowing phases usually d i f f e r s from that at the i n l e t . For horizontal two-phase flow, therefore, a. number of correlations are to be found i n the l i t e r a t u r e (7,8,9) which predict the volume f r a c t i o n of one of the phases i n the tube. The lack of more success, with these correlations has been ascribed, i n part, to an apparent disregard of the method of bringing the two phases together at the tube entrance. For single-phases flow, the mass or heat transfer c o e f f i c i e n t s nearly always depend on the f l u i d v e l o c i t y to a power less than unity. For mass transfer i n two-phase slug, however, t h i s does not seem to be the case. Occurrences of two-phase flow are r e l a t i v e l y frequent; - 3 these include transporting of petroleum products i n g a s - o i l p i p e l i n e s , processing equipment such as condensers and r e b o i l e r s , and also steam generating u n i t s . In these s i t u a t i o n s , the occurrence of two-phase flow i s usually a consequence of the processing operation rather than of a purposeful a p p l i c a t i o n . The a p p l i c a t i o n of two-phase flow to v e r t i c a l tube vaporizers, u t i l i z i n g the g a s - l i f t e f f e c t for increasing the turbulence at the heat transfer surfaces, i s becoming more prevalent because of the r e s u l t i n g unusually high heat transfer c o e f f i  c ients. Cocurrent g a s - l i q u i d tubular contactors have a number of possible applications as mass transfer devices. Because the gas and l i q u i d flow i n the same d i r e c t i o n , however, they have the p o t e n t i a l disadvantages of any cocurrent contacting scheme. For some p a r t i c u l a r a p p l i c a t i o n s such as the absorption of a pure gas by a l i q u i d , or the absorption of a gas which reacts i r r e v e r s i b l y with the l i q u i d , cocurrent contacting i s essen t i a l l y equivalent to countercurrent contacting. For these situations two-phase cocurrent contactors have a p o t e n t i a l advantage when compared to more common contacting equipment such as packed towers. Application of tubular contactors to.gas™- l i q u i d heterogeneous systems, such as the oxidation of s l u r r i e s , appears possible. The presence of the s o l i d p a r t i c l e s i n the 4 l i q u i d p r ohibits the use of packed towers, but would not a f f e c t the performance of tubular contactors. A s p e c i f i c a p p l i c a t i o n i n the pulp and paper industry which has been recently patented, employs a pi p e l i n e contactor for the oxidation of black liquor (10). Reported mass transfer studies with two-phase flow contac tors are very l i m i t e d indeed. Varlamov (4,5) u t i l i z e d the gas- l i f t p r i n c i p l e i n v e r t i c a l tubes for absorption and reaction of. gas i n the l i q u i d phase. The c a l c u l a t i o n of o v e r a l l mass transfer c o e f f i c i e n t s was based on the i n t e r n a l wetted area of the tube. Mass transfer controlled by d i f f u s i o n i n the gas phase (ammonia, a i r , and water) has been studied by Anderson (6) for horizontal annular flow. Overall mass transfer co e f f i c i e n t s were also based-on the tube i n t e r n a l wetted area. I t was shown that the amount of transfer could be correlated by the same rela t i o n s h i p s as those used for wetted wall columns provided that an a d d i t i o n a l contributing factor d i r e c t l y pro por t i o n a l to the l i q u i d s u p e r f i c i a l Reynolds number was included. The s p e c i f i c objective of t h i s research was to investigate the l i q u i d phase resistance to mass transfer for two-phase gas- l i q u i d flow i n horizontal tubes. The range of the investiga tion was to include a s u f f i c i e n t number of g a s - l i q u i d systems, and several flow regions, to permit the development of generalized 5 correlations which would allow the prediction of absorption rates for most g a s - l i q u i d systems. An experimental program was designed to permit the separate evaluation of the molecular ef f e c t s of l i q u i d phase d i f fusiv-ity, i n t e r f a c i a l tension and v i s c o s i t y , as well as geometric e f f e c t s such as tube diameter, and i n l e t arrangements. No guidance was a v a i l a b l e from previous research to indicate the r e l a t i v e importance on the absorption rates of the host of variables associated with two-phase flow. As a r e s u l t some variables-appreciably a f f e c t i n g the absorption rate may have been altogether omitted from t h i s study (such as l i q u i d density), some variables which probably should have been studied more thoroughly (such as type of entrance) were only s u p e r f i c i a l l y investigated, while other variables (such as the l i q u i d flow rate) perhaps need not have been investigated so completely. This research must be considered somewhat exploratory, therefore, defining areas of i n t e r e s t which i n the future w i l l undoubtedly be more in t e n s i v e l y investigated, and consequently better understood. 6 SCOPE OF RESEARCH The se l e c t i o n of gases and l i q u i d s to be used i n the absorption tests was based on a choice of experimentally desirable conditions. To permit the determination of the l i q u i d phase resistance to mass transfer only, the use of pure gases was desirable to eliminate any gas phase resistance. So that the properties of the l i q u i d would remain e s s e n t i a l l y unchanged by the absorption of the gas, the use of only spar ingly soluble gases was indicated. In addition, for the sake of safety, the gases as w e l l as the vapours of the l i q u i d s , needed to be non-toxic, and non-explosive with a i r , because large quantities were to be used and contamination of the work area with the gases and vapours appeared unavoidable. The gases chosen were carbon dioxide (CO2) and helium (He), and the l i q u i d s , water, ethanol, and ethylene g l y c o l . Ethanol was used because of i t s low surface tension when compared with that for water. Ethylene g l y c o l was chosen because of i t s r e l a t i v e l y high v i s c o s i t y . For the pure l i q u i d s and gases, s o l u b i l i t y and d i f f u s i v i t y data were av a i l a b l e from the l i t e r a r ture, except for the CO2 s o l u b i l i t y i n ethylene g l y c o l which was experimentally obtained. The absorption tubes were constructed af glass to permit 7 the visual inspection of the two-phase flow patterns. The glass walls of the tubes were wetted by the liquids used. The wetting characteristics of the tubes were, therefore, comparable to those for most metallic surfaces such as iron and copper, but unlike those for many plastic materials such as tygon and polyethylene. A typical absorption tube installation consisted of an entrance tee, an entrance section, a test sec tion, a short exit section, and a cyclone separator. The gas and liquid, initially brought together in the entrance tee, formed a consistent flow pattern in the entrance section which was then maintained along the rest of the tube. Liquid phase concentration measurements were made at the inlet and outlet of that section of the tube designated as the test section. The two phases were separated in the outlet cyclone. Three tube sizes were used for the absorption experiments, 1.228, 1.757 and 2.504 cm in internal diameter. Each tube was fitted with the same type of entrance tee, for which geometric simi larity was maintained in scaling up from one tube size to the next:. The entrance tee was mounted so that the liquid flowed upward and the gas downward, and then on mixing the two phases flowed horizontally into the absorption tube. The test method consisted of contacting the gas and liquid isothermally in one of the absorption tubes. Liquid phase 8 concentrations were measured at both eods of the test section by withdrawing and analyzing l i q u i d samples. The l i q u i d was continuously c i r c u l a t e d through the absorption tube and a desorption apparatus. This process permitted the repeated use of the same l i q u i d for many absorption experiments. The gas, on the other hand, supplied from high pressure cylinders, was discarded a f t e r a single pass through the absorption tube. The range of l i q u i d flow rates was more li m i t e d than the much wider range of gas flow rates investigated. The approximate l i q u i d s u p e r f i c i a l v e l o c i t i e s ranged- between 0.5 and 3.6 fps, and the approximate gas s u p e r f i c i a l v e l o c i t i e s between 0.1 and 40 fps. This combination of gas- and l i q u i d flow rates and tube sizes produced four d i f f e r e n t types of flow: bubble, plug, slug and annular. I t should be noted that the c l a s s i f i c a t i o n of two- phase flow patterns i s somewhat a r b i t r a r y , and that the t r a n s i  t i o n between flow patterns i s usually i n d i s t i n c t . The flow regions as l i s t e d above conform to a c l a s s i f i c a t i o n introduced by Alves (11) for horizontal two-phase flow. The flow regions can be generally described as follows: (a) Bubble flow: In t h i s flow region discrete gas bubbles move along the upper surface of the tube at roughly the same average v e l o c i t y as the average l i q u i d v e l o c i t y . (b) Plug flow: The difference between bubble and plug flow 9 i s l a r g e l y concerned with the length of the "bubbles" with respect to t h e i r depth. When the length exceeds the depth by a factor of between 10 and 15, then the flow i s considered to be plug flow. (c) Slug flow: In th i s flow region the average v e l o c i t y of the gas which flows along the top portion of the tube i s much higher than the average l i q u i d v e l o c i t y . Intermittent waves of highly agitated l i q u i d frequently r i s e to seal the tube as they are c a r r i e d by the rapidly moving gas. (d) Annular flow: The gas moves at a high v e l o c i t y i n the core of the tube carrying with i t some of the l i q u i d as a spray. Most of the l i q u i d i s d i s t r i b u t e d as a f i l m around the tube w a l l with the greatest f i l m thickness occurring at the bottom of the tube. The r a p i d l y moving gas produces many waves and r i p p l e s on the l i q u i d surface making the ga s - l i q u i d interface extremely i r r e g u l a r . In analyzing mass transfer i n horizontal two-phase flow i t w i l l be usefu l to separate a l l the pertinent variables into l o g i c a l categories. A l l the variables can f i r s t be separated into two categories, one consisting of the primary variables and the other of the secondary vari a b l e s . The primary variables would include those which are fundamental properties such as density and v i s c o s i t y . The secondary variables would include 'those which are some function of one or more of the primary variables. Secondary variables would include pressure drop, i n t e r f a c i a l area, and the actual average l i q u i d or gas v e l o c i  t i e s . The primary variables are l i s t e d under subheadings as follows: (a) Gas phase: density, v i s c o s i t y , volumetric flow rate, and concentration ( i n t h i s research, pure gas). (b) L i q u i d phase: density, v i s c o s i t y , volumetric flow rate,, and concentration of dissolved gas. (c) Both gas and l i q u i d phases: s o l u b i l i t y , i n t e r f a c i a l tension, and l i q u i d phase d i f f u s i v i t y . (d) Tube geometry: tube diameter, tube length, and entrance type. The primary variables for the gas and l i q u i d phases are commonly used properties and are usually r e a d i l y a v a i l a b l e , measureable, or predictable, The tube dimensions and entrance type are variables which would be l o g i c a l l y considered from experience with single-phase flow. The secondary variables, on the other hand, are often d i f f i c u l t i f not impossible to evalu ate because of the present lack of knowledge of the processes involved. Some of the more common secondary variables are l i s t e d below: 11 (a) Fraction of the tube volume f i l l e d with l i q u i d (or gas). (b) The actual average v e l o c i t y i n the tube of the l i q u i d (or gas). (c) Two-phase pressure drop over an i n t e r v a l of tube length. (d) Number of transfer u n i t s , length of transfer u n i t , or some other measure of the mass transfer c h a r a c t e r i s t i c s . (e) I n t e r f a c i a l area for an i n t e r v a l of tube length. (f) Surface conditions such as surface tension, and surface v i s c o s i t y . The intent of t h i s research was to determine i f the primary variables could be used to express the mass transfer rates i n horizontal two-phase flow by r e l a t i v e l y simple, and l o g i c a l r e l a t i o n s h i p s . The absorption-rate expressed as the number of transfer units (NTU) was considered a useful concept for the tubular type of contactor, p a r t i c u l a r l y because t h i s v a r i a ble was independent of the l i q u i d phase concentration which was expected to vary i n a wide range, between e s s e n t i a l l y zero and the saturated value. The e f f e c t s on the mass transfer rates of most of the primary variables l i s t e d above were investigated. It was desirable to c a r e f u l l y choose only those variables which on investigation were most l i k e l y to give useful information. For example, the study of the e f f e c t of gas-phase concentration on two-phase mass transfer would involve the gas-phase 12 coefficient combined with that in the liquid phase. It appeared prudent to limit the investigations to the behaviour of the liquid phase. Further, as discussed in some detail in a subse quent chapter, the shear forces in the gas phase, except perhaps in the annular flow region, were most probably small with respect to the shear forces in the liquid phase. Consequently, the gas phase viscosity was considered to have a relatively small effect on the mass transfer rates and was omitted from this study. The effect of the liquid phase density was also omitted, from this study. Unless the effect of density on the absorption rate is very pronounced, its omission should not seriously affect the results of this investigation. The densities of most liquids that are likely to be used for the absorption of gases lie in a relatively narrow range. The specificogravities of the liquids used in this research varied between 0.8 (for ethanol) and 1.1 (for ethylene glycol), and the assumption was made that provided the superficial velocities of the liquids were the same all other effects of density could be ignored. Partial justification for this assumption is outlined in a following chapter. The primary variables, the liquid phase con centration and the gas solubility, were both involved in the calculation for the number of transfer units. A number of experiments with different entrance types were included to show 13 whether or not the absorption rate was independent of the type of entrance. A l l the remaining experiments, however, were con ducted with only one type of entrance. In summary, the primary variables which were investigated, and the maximum ranges encountered in this research, are as follows: (a) QQ, gas volumetric flow rate, 1.4 to 220 cfh. QL, liquid volumetric flow rate, 0.6 to 4.2 gpm. PQ, gas density, 6.18 to 2.6 gm 1 \ (b) (c) , liquid phase di f f u s i v i t y , o.l4 (10~ ) to 3.69 (10" ) 2 -1 cm sec (e) CT, interfacial tension, 22 to 74 dynes cm -1 (f) liquid phase viscosity, 0.4 to 26 cp. (S) D, T ' tube diameter, 1.23 to 2.50 cm. 14 DESIGN OF EXPERIMENTS In studying the rates of absorption i n horizontal two- phase flow no p r i o r knowledge was assumed about the system. I t appeared advisable to measure the e f f e c t s , on the absorption rates, of variati o n s i n the primary variables such as surface tension and v i s c o s i t y rather than of changes i n such dimension less groups as the Schmidt number, Weber number, Froude number, and Reynolds number. Each of these dimensionless numbers could be legitimately expected to play a r o l e i n mass transfer processes i n horizontal two-phase flow because the viscous, i n e r t i a l , surface tension, and buoyancy forces were a l l i n v o l  ved; however, at the present state of knowledge, the correct d e f i n i t i o n for the terms which comprise each of the dimension less groups was d i f f i c u l t , i£ not impossible, to ascertain for the two-phase system. For example, a number of d i f f e r e n t d e f i n i t i o n s of Reynolds number applying to two-phase flow have been proposed, as discussed by Govier (12), none of which can be unequivocally supported. The reasons for the d i f f i c u l t y i n defining a Reynolds number can be r e a d i l y appreciated. They are associated with the determination of the true v e l o c i t i e s of the two phases, and also of the mixing ef f e c t s r e s u l t i n g from the fact that the flow channel for each phase has an e f f e c t i v e l y 15 variable cross-section. The d i f f i c u l t y i n defining a true Reynolds number for each phase was appreciated i n t h i s work, but since t h i s project was not directed toward the study of the hydrodynamics of horizontal two-phase flow, no enlightened method i s proposed. Somewhat similar problems of d e f i n i t i o n and application e x i s t for the other three dimensionless groups. The use of the Schmidt number for mass transfer situations where the penetration theory i s applicable has been questioned (13). The surface tension and buoyancy forces might well play two d i f f e r e n t roles i n two d i f f e r e n t locations, f i r s t at the entrance tee, and next i n the tube during flow. For these reasons, i t appeared necessary to investigate the o v e r a l l e f f e c t s of the primary variables i n a contacting apparatus which included a p a r t i c u l a r type of entrance section. In t h i s way, correlations for the mass transfer rates by meaningless dimensionless groups were avoided, but, of necessity, a c e r t a i n amount of empiricism was introduced by considering only the o v e r a l l e f f e c t s of the various primary varia b l e s . The determination of the e f f e c t s of a number of variables could be t h e o r e t i c a l l y resolved to a s t a t i s t i c a l experiment but for one consideration. The primary variables could not be independently varied. Because of the nature of chemical compounds some properties such as v i s c o s i t y and d i f f u s i v i t y 16 are c l o s e l y related, preventing the v a r i a t i o n of one without a f f e c t i n g the other. The choice of g a s - l i q u i d systems suitable for i nvestigating the effects of the variables was, therefore, l i m i t e d to those which permitted the separation of the various e f f e c t s . The general method for determining the e f f e c t s of the d i f  ferent primary variables was to choose one system, the CC^-water system, and to e s t a b l i s h the r e l a t i o n s h i p between the absorption rate (expressed as NTU) and the gas and l i q u i d s u p e r f i c i a l v e l o c i t i e s (VQ and v £ ). The method then consisted of changing one variable while keeping a l l the others constant and observing o o the e f f e c t on the NTU, V G , and V L r e l a t i o n s h i p s . The change i n the absorption rates was assumed to be caused by the i n t e n t i o n a l change of the p a r t i c u l a r v a r i a b l e . When two primary variables were simultaneously changed and the e f f e c t of one had already been determined, the t o t a l e f f e c t on the absorption rate was adjusted to compensate for the known eff e c t of the f i r s t v a r i a b l e . The net e f f e c t was then att r i b u t e d to the second va r i a b l e . I t i s apparent that the investigation of a combination, of three variables and the adjustment of the o v e r a l l e f f e c t on the absorption rate for two of them to obtain the net e f f e c t of the t h i r d , could introduce a large error i n the measurement of the t h i r d e f f e c t . The p a r t i c u l a r g a s - l i q u i d systems were chosen 17 to minimize the possible error in the measurement of the "third order" effects. The primary variable whose effect was to be measured, was changed as much as possible when compared with that for the CC^ -water system, while the other two primary variables for which adjustments were required, were changed as little as possible. The actual gas-liquid system and experi mental conditions used to measure the effect of each of the primary variables will be described in detail in subsequent paragraphs. The effect of gas density was determined by using the same system (CO^ -water) at the same temperature (15°C), the same absorption tube (1.757 cm in internal diameter), and the same entrance section, and by measuring the absorption rates at two different pressures in the absorption tube. Because the absorption temperature was the same, the liquid phase viscosity, the liquid phase (CC^ ) diffusivity, and the interfacial tension were assumed to be the same regardless of pressure. Absorption rate measurements were obtained at approximately 10 and 20 psia, thereby varying the gas density by an approximate factor of two without changing any of the other variables. The calculation of NTU involved the gas solubility which did change with pressure, but was assumed to depend on pressure according to Henry's law. The effect of gas density was, therefore, obtained by comparing density gas, He, a !8 the absorption rates at the two pressures. The absorption rate was found to be a function of the gas volumetric flow rate and that, for a p a r t i c u l a r l i q u i d flow, the curves of NTU vs the gas flow rate were coincident for the two pressures provided that the gas flow rate was expressed i n volumetric units (or as the gas s u p e r f i c i a l v e l o c i t y ) . The coincident curves of NTU and gas s u p e r f i c i a l v e l o c i t y at a constant l i q u i d flow rate for the two pressures, 10 and 20 psia, are shown on a log-log plot i n Figure 1. In order to permit the use of the low knowledge of the e f f e c t of gas density over a much wider range than that obtained by changing the pressure of absorption with the C02 -water system was required. The absorption curve for the He-water system was obtained at the same l i q u i d temperature and s u p e r f i c i a l v e l o c i t y as for the CO^water system. I t i s also shown i n Figure 1. The fact that the i n f l e c t i o n s i n the NTU, vs VQ curves for the He-water and CO2-water systems occurred at e s s e n t i a l l y the same values of VQ, was taken as a p a r t i a l con firmation that the e f f e c t of gas- density was lar g e l y compensated for by the use of the gas s u p e r f i c i a l v e l o c i t y , VQ. Referring again to Figure 1, the displacement of the NTU vs VQ curve for the He-water system when compared with that of the CO2- water system was, therefore, at t r i b u t e d to the difference 0.01 0.1 1.0 « ? , S U P E R F I C I A L G A S V E L O C I T Y , F T . / S E C . 10.0 Figure 1. E f f e c t of Gas Pressure and L i q u i d Phase D i f f u s i v i t y on Absorption Rate 20 in the l i q u i d phase d i f f u s i v i t y . When changing from the C^-water system to the C02~ ethanol and CX^-ethylene g l y c o l systems a problem arose as to the basis for obtaining an equivalent l i q u i d flow rate for the three systems. Was a mass flow rate of ethanol equivalent to the same mass flow rate of water or ethylene g l y c o l i n i t s e f f e c t on the absorption rate? Or would the same Reynolds number, using the s u p e r f i c i a l v e l o c i t y i n i t s c a l c u l a t i o n , y i e l d an equivalent flow for the three liquids? I t was neces sary to make a decision on the method for obtaining comparable l i q u i d flow rates before any effects of such variables as l i q u i d v i s c o s i t y , or i n t e r f a c i a l tension, could be ascertained. I t was f i n a l l y assumed that comparable l i q u i d flow rates would be obtained for the three l i q u i d s , provided that the s u p e r f i c i a l v e l o c i t i e s were kept the same. There were three reasons why this basis for comparison was adopted. F i r s t , i n spite of the big density difference of He compared to that of CO2, the shape of the absorption curves (NTU vs VQ) remained the same for the two gases at the same s u p e r f i c i a l v e l o c i t i e s . This suggested that the volumetric throughput was of more consequence in two- phase flow than the mass throughput. The shape of the absorp tion curves (NTU vs VQ) for the same volumetric flow rates of the three l i q u i d s were nearly the same, and also the i n f l e c t i o n 21 points corresponded roughly to the same gas s u p e r f i c i a l velo c i t i e s , even for ethylene g l y c o l , many times as viscous as water or ethanol. F i n a l l y , the appearance of the bubbles, plugs, and slugs (as well as regions of tran s i t i o n ) was approxi mately the same at equal gas s u p e r f i c i a l v e l o c i t i e s , for the same l i q u i d s u p e r f i c i a l v e l o c i t i e s . For these reasons i d e n t i c a l l i q u i d s u p e r f i c i a l v e l o c i t i e s were considered to produce i d e n t i c a l types of flow. Any change i n the absorption rates when compared with the CO2-water system was attributed, there fore, to changes of the other variables involved. As indicated e a r l i e r , the e f f e c t of d i f f u s i v i t y was ob tained by comparing the absorption rate curves for the He-water system with that for the CC^-water system at the same l i q u i d s u p e r f i c i a l v e l o c i t i e s . During the experiments with both of these systems the l i q u i d temperature and hence v i s c o s i t y and density were i d e n t i c a l . The i n t e r f a c i a l tension was also considered to remain e s s e n t i a l l y the same for the two ga s - l i q u i d systems. The influence of the gas composition on the i n t e r - f a c i a l tension i s discussed i n more d e t a i l i n the chapter on Specifications and Properties of the Test F l u i d s . The same tube and entrance tee were likewise used for the He-water and CO^-water systems. The eff e c t of the l i q u i d phase d i f f u s i  v i t y was, therefore, d i r e c t l y observable from the absorption 22 curves of NTU vs VQ for the two systems. The l i q u i d phase d i f f u s i v i t y was increased by a factor of 2.5 by changing from the CC^-water to the He-water system. The effect of i n t e r f a c i a l tension was investigated by using the CO2-ethanol system and comparing the absorption rate curves with those of the CC^-water system at the same super f i c i a l v e l o c i t i e s . Ethanol was chosen for t h i s study because of i t s unusually low i n t e r f a c i a l tension compared with water. I t i s less than one t h i r d that for water, and represents a value somewhat lower than that for most common i n d u s t r i a l solvents. The intention i n using ethanol had been to pick an absorption temperature for which the v i s c o s i t y of ethanol would be iden t i c a l to that of water at 15°C. Due to an oversight the temperature f i n a l l y chosen, 13.5°C, corresponded to a v i s c o s i t y of ethanol s l i g h t l y greater than that for water at 15°C. At t h i s temperature the s p e c i f i c gravity of ethanol was very nearly 0.8. The d i f f u s i v i t y of CO2 i n ethanol at 13.5°C was between that of CO2 i n water and He i n water. Although the variables, density, d i f f u s i v i t y , and v i s c o s i t y , were not held constant when determining the effect of i n t e r f a c i a l tension, the changes i n these variables with ethanol as the l i q u i d were r e l a t i v e l y small when compared to the change i n the i n t e r f a c i a l tension. The effect of v i s c o s i t y was investigated by using the 23 CO^-ethylene glycol system. To obtain the effect of viscosity at two different values, the absorption experiments were per formed at two different temperatures, 30°C and 15°C. At these temperatures the viscosity of ethylene glycol was a factor of 12.2, and 23.2, times as great, respectively, as that of water at 15°C, The absorption experiments were performed with the identical tube and entrance tee that were used for the CG^ -water, He-water, and CG^-ethanol experiments, and at the same liquid superficial velocities. The specific gravity of the ethylene glycol was 1.1. The interfacial tension was only slightly lower than that for water. The CG"2 diffusivity was much lower in ethylene glycol than that of CO2 in water at 15°C, however. The C0 2 diffusivity in ethylene glycol at 30°C and 15°C was approximately one fifth, and one tenth, respectively, of that in water at 15°C. It is apparent that the diffusivity effects as measured by the He-water system had to be extrapolated con siderably for application to the CC^-ethylene glycol system. However, no way of avoiding such an extrapolation could be devised since all viscous liquids exhibit a low diffusivity. Even though the change in diffusivity was large, the change in viscosity for the CC^-ethylene glycol system was even greater, so that a reasonably good measure of the effect of viscosity should have resulted from the use of this system. 24 The effect of tube diameter was investigated using the CC^ -water system, by conducting absorption experiments with two tube sizes, one larger and one smaller than the one used for all the previous experiments. The internal diameters of the tubes were 2.504 cm and 1.228 cm compared with 1.757 cm for the most frequently used tube. The entrance tees were all geometrically similar. Absorption experiments were conducted at similar values of liquid superficial velocity for all the tube sizes. The conditions for absorption were likewise the same, 15°C, and essentially atmospheric pressure. The effect of tube diameter was very pronounced, so that the concen trations of CO2 in the water were very low at some gas flow rates for the largest tube size, and approached saturated values for some gas flow rates for the smallest tube size. All the primary variables were identical for the experiments with the three tube sizes, and the changes in absorption rate could only be ascribed to the effect of the size of the absorp tion tube (and entrance tee). The following summary lists the type and number of experi ments that were employed in attempting to separate the effects of the various primary variables. 25 (a) The effect of gas and liquid flow rates was obtained with the C02~water system at 15°C and the 1.757-cm tube. Six liquid flow rates corresponding to superficial velocities of 0.5, 0.9, 1.3, 1.8, 2.6 and 3.6 fps were used in con junction with a range of corresponding gas superficial velocities from 0.1 to 20 fps for each liquid rate. (b) The effect of gas density was obtained with the (X^-water system at 15°C and the 1.757-cm tube using absorption pressures of 10 and 20 psia. One liquid flow rate corres ponding to 0.9 fps, and gas superficial velocities from 0.2 to 10 fps were used at reach pressure. (c) The effect of liquid phase diffusivity was obtained with the He-water system at 15°C and the 1.757-cm tube. Three liquid flow rates were investigated corresponding to super ficial velocities of 0.5, 0.9, and 1.8 fps. Gas super ficial velocities for each liquid rate ranged from 0.1 to 20 fps. (d) The effect of inter facial.', tension was obtained with the C02~ethanol system at 13.5°C using the 1.757-cm tube. Liquid superficial velocities were 0.5, and 0.9, and 1.8 fps, while the gas superficial velocities ranged from 0.1 to 20 fps for each liquid rate. (e) The effect of liquid viscosity was obtained using the 26 o C(>2-ethylene glycol system at two temperatures, 15 C and 30°C, and the 1.757 -cm tube. For both temperatures three liquid flow rates corresponding to superficial velocities of 0.5, 0.9, and 1.8 fps were used. The gas superficial velocities ranged from 0.1 to 20 fps for each liquid rate,. The effect of tube diameter was obtained by using two addi tional tube sizes, 2.504 and 1.228 cm, with the (X^-water system at 15°C. Three liquid superficial velocities were investigated in each tube, again approximately 0.5, 0.9, and 1.8 fps. Gas superficial velocities ranged from 0.1 to 10 fps in the large tube and from 0.2 to 40 fps in the small tube. The effect of absorption temperature was investigated with the C02~water system using the 1.757-cm tube. Two additional temperatures were used, 30°C and 45°C. The same liquid superficial velocity was used at both tempera tures, 0.9 fps, while the gas superficial velocities ranged from 0.1 to 20 fps for each liquid rate. 27 THEORETICAL ASPECTS In t h i s chapter, the t h e o r e t i c a l aspects of gas absorption i n horizontal g a s - l i q u i d flow are discussed i n three sections. In the f i r s t section, the general considerations which a f f e c t a l l absorption processes are discussed. In the second section,, a postulated mechanism for mass transfer i n the bubble flow region i s developed, and, i n the t h i r d section, the problems o£~ developing a t h e o r e t i c a l model for the slug region of flow are considered. Factors A f f e c t i n g Absorption Rate The rate at which a pure gas w i l l dissolve i n a l i q u i d in. a p a r t i c u l a r contacting apparatus w i l l depend on the gas solu b i l i t y , the i n t e r f a c i a l area., the concentration of the gas i n the l i q u i d , the condition of the interface, and f i n a l l y the degree of mixing i n the l i q u i d phase. The degree to which the above mentioned variables influence the rate of absorption, comprises the study of absorption i n general. The gas s o l u b i l i t y represents the maximum quantity of gas that w i l l dissolve i n a cer t a i n quantity of l i q u i d at any given temperature and pressure. The s o l u b i l i t y can also be considered to represent the maximum d r i v i n g force f o r absorption. I t i s 28 usually highly dependent on temperature, and in this respect, is not unlike the vapour pressure of liquids. The solubility is also influenced by pressure, the effect of which is given by Henry's law for sparingly soluble gases. The determination of the. interfacial area i s usually diff i  cult for most gas-liquid transfer processes. It i s essential , to know the interfacial area i£ the effects of the interfacial, area and the liquid phase resistance to mass transfer are to be separated. Except for a few specially designed systems such as laminar jets (14), and short wetted-wall columns (15), indirect methods for measuring the interfacial area are required. It,is sometimes possible to determine the interfacial area by the use of a combination of experiments for the same contacting system, which entails first, the measurement of the simple rates of absorption and next, the measurement of the rates of absorp-;i tion with chemical reaction of the absorbed gas. Provided . » that the liquid properties are not significantly affected by , the chemical reaction, and that the reaction kinetics have been established for the conditions of the experiment, the interfacial area can be calculated. A knowledge of the true interfacial area for absorption does not necessarily afford a knowledge of the transport mechanism in the liquid phase, although i t does permit the calculation of an average liquid phase coefficient. Whether the mechanism of transport is by diffusion through a thin film at the interface, by unsteady- state diffusion into "packets" of liquid brought to the inter face and rapidly carried away, or by agitation sufficiently great to cause a velocity component away from the interface, can only be postulated. These mechanisms, and combinations of them, have been put forward for essentially a l l absorption systems (16). The influence on the absorption rate of the concentration of absorbed gas in the liquid phase is largely due to its effect on the concentration driving force. If the liquid is saturated no additional transfer will take place, and i f the liquid contains no gas, the rate of solution will be the maxi mum for any particular method of contacting. It is generally considered that the rate of absorption of a pure gas by a liquid is directly proportional to the concentration driving force for any one particular contacting system and set of absorption conditions. This latter statement is true only i f the properties of the liquid remain the same for a l l the gas concentrations obtained in the liquid. For slightly soluble gases the assumption is frequently made that the liquid pro- perties remain unchanged by the-presence of the gas. For highly soluble gases the change in properties of the absorbing 30 liquid cannot be neglected. It i s usually assumed- that the resistance to mass transfer of the gas-liquid interface i t s e l f (perhaps 10 % thick) i s negligible (17). Impurities, which concentrate at the interface affecting the conditions at the interface, are generally known as surface active agents. A layer of a surface active agent as l i t t l e as one molecule i n thickness at the interface can have an appreciable resistance and hence reduce the rate of mass transfer (18,19). The presence of a monolayer can also have a calming effect on the interface by virtue of i t s surface vis-, cosity and resistance to local compression, reducing the extent of surface agitation and rippling (20). The condition of the interface, therefore, can influence the rate of absorption in two ways, by introducing an additional interfacial resistance, and by decreasing the agitation of the interface. The discussion of the degree of mixing w i l l be limited to i t s effect on absorption. If a-pure gas i s absorbed by a completely stagnant liquid, i n f i n i t e i n extent, the rate w i l l be a decreasing function of time because the distance in the. liquid phase across which the gas molecules diffuse, i s increasing. The solution of the appropriate differential equation (21) indicates that for this situation the dependence of the mass transfer rate on the liq u i d phase diffusion coefficient is to the 0,5 power. If turbulent stirring main tains the concentration of the bulk of the liquid during the absorption of a pure gas at a constant value, it has been pro posed by Lewis and Whitman (22) that a certain thickness of liquid at the interface is in laminar flow and that the direc tion of this flow is parallel to* the interface. Through this , "laminar film" mass transfer occurs at a constant rate, as i f the layer were stagnant. For. this situation, the rate of transfer depends on the liquid phase diffusion coefficient to the first power. It is perhaps:significant that few absorption studies have, in fact, shown a dependence of the mass transfer rate on the liquid phase diffusivity to a power greater than 0.7. If a pure gas is absorbed.Jay contact with a turbulent liquid in which the average times of contact for portions of; liquid continually brought to the interface are short, the steady-state theory of Lewis and Whitman cannot be valid. Instead, as proposed by Higbie (23), the rate of mass transfer would be of an unsteady-state type, depending inversely on the square root of the average exposure time and directly on the square root of the liquid phase-diffusivity, In this mass transfer model, it is assumed that the penetration of the absorbed molecules at each exposure does not exceed the depth of liquid for which the velocity is essentially the same as Chat at the interface, and hence this development is known as the "penetration theory". It has been proposed as an explana tion for the absorption in packed columns. The flow of liquid over the individual pieces of packing may be. laminar, exposing the liquid for only short periods of time, while at the junc tion of one piece of packing and the next complete mixing may occur. The dependence of the rate of transfer on diffusivity and exposure times according to the Higbie model has in fact been observed in packed towers (24). In the limit of extreme turbulence when eddies of liquid are swept in and out of the interface with extreme rapidity, neither a laminar surface film, nor a momentarily stationary interface can be physically realistic, according to Kishinevskii (25). For this situation it is proposed that the rate of transfer is completely indepen dent of liquid phase diffusivity and depends instead on the mean velocity of the liquid normal to the interface. This limit of extreme turbulence is seldom reached in any absorp tion operations. Kishinevskii was able to show by actual experiments (25) for the absorption of H2, N2, and 0 2 into water stirred at an extremely high rate, that the rate of transfer for this high degree of turbulence was indeed inde pendent of the liquid phase diffusivity. For intermediate stirring speeds however, the influence of diffusivity was 33 again significant. In reviewing the proposed mechanisms for mass transfer for different situations, several observations can be made. Except for unsteady-state absorptioninto an infinite stagnant liquid, which is not a practical situation, a l l the proposed mechanisms suggest a certain type of dependence between the transfer rate9 the degree of mixing, and the liquid phase diffusion coeffi - t n . ciento As the turbulence 4xtcreases the dependence of the ^ transfer rate on the liquid, diffusivity decreases. Further, it appears likely that the mechanisms as proposed are suitable for specific situations only, and that combinations of these,,, mechanisms perhaps most accurately describe many other practical absorption processes. The absorption rate could then depend directly on the liquid phase.diffusivity to a power anywhere between zero and one, depending.on the degree of turbulence and method of transfer. A closer inspection o£ the ^ 'penetration theory" as a trans,-? port mechanism, and its application to real processes will perhaps be useful. There .are at least two types of mass transfer processes (27) fo^wMch the "penetration theory" has been used as a model. One is the absorption of gas into a stirred liquid, for which one of the assumptions normally made is that complete mixing occurs in the bulk of the liquid due to 34 turbulence. Another assumption,.is that portions of the inter face and adjacent liquid are frequently, and randomly, replaced by means of turbulent eddies. The other type of transfer process occurs in packed columns. The assumptions made for this latter situation include that the liquid is in laminar flow while passing over a particular piece of packing, and that complete mixing occurs at the junctions of flow between pieces of packing. It i s perhaps important to emphasize the dif ference between these two very similar transfer processes. In the first instance the bulk of the liquid is turbulent, and in the second, the flow is essentially laminar with mixing occurring only at fixed positions. The distinction to be made is that unless mixing such as that caused by the liquids flowing from different directions toward a single point is defined as turbulence, the liquid is not turbulent during the transfer of mass over packing. In order that the "penetration theory" will be applicable, the liquid needs to be neither turbulent (as commonly understood) nor even well mixed, provided that some method exists for renewing the interface, and for dissi pating into the bulk of the liquid absorbed molecules which have been concentrated in the interfacial region during the period of absorption. Further, the degree of mixing in the bulk of the liquid needs to be only sufficiently great so as 3 5 not to s i g n i f i c a n t l y l i m i t the transfer process through the bulk of the l i q u i d . As a consequence, then, the major portion of the resistance to mass transport w i l l be retained i n the v i c i n i t y of the ga s - l i q u i d interface. Mass Transfer Mechanism for Bubble Region There are a number of r e a d i l y observable facts i n horizon^ t a l g a s - l i q u i d flow i n the bubble and plug regions which help to give some insight into the f l u i d hydrodynamics. F i r s t of a l l , the bubbles or plugs of gas^ moving along the top of the tube are much less dense than the l i q u i d s . At a constant l i q u i d s u p e r f i c i a l v e l o c i t y , very tiny bubbles (2 mm i n diameter) t r a v e l much slower than large ones (8 ram ) 0 This i s observable even i f both s i z e s of bubbles are i n the tube at one time, and therefore, cannot be explained by supposing that the net volumetric throughput of. the gas phase i s greater i n the case of the larger bubbles.; The explanation would appear to be that a v e l o c i t y p r o f l i e f o r the two phases e x i s t s i n the tube, and that a maximum v e l o c i t y occurs i n some po s i t i o n along a v e r t i c a l l i n e through the centre of the tube. The l i q u i d v e l o c i t y must vary from zero to the maximum from positions a t the w a l l to the p o s i t i o n of the maximum. The v e l o c i t y of a bubble would appear to depend i n some way on the average, 36 or maximum, velocity to which i t was subjected. That is, small bubbles with a small vertical dimension, and flowing near the tube wall, would be subjected to a lower liquid velocity and hence would travel at a slower rate than larger bubbles having a larger vertical dimension. Because the small bubbles move slower than large ones, the void fraction (fraction of tube filled with gas) would be dependent on the bubble size for equivalent gas and liquid throughput rates. The higher velocities of the larger bubbles- appear to be a result of their deeper penetration into the tube, and hence into regions of higher liquid velocities* ; Further, i f i t is accepted that by the use of special entrances-or nozzles, bubbles of various sizes can be produced for -any particular gas flow rate, then it can be readily seen that for ^ bubble flow the void fraction is dependent on the type of entrance used. An expression for the- gas void fraction in terms of the gas and liquid volumetric flow rates has been proposed by Nicklin, Wilkes, and Davidson (28) for vertical gas-liquid slug flow. This equation has been shown by Scott (29) to also apply in a modified version for horizontal flow, by comparison with actual void fraction data. This latter expression applies for superficial liquid Reynolds numbers exceeding 8000, for which the liquid velocity profile might well be expected to be 37 relatively flat. The expression for horizontal flow is: RG = 0;833 QA: (1) where: R„ » void fraction QQ» 13 gas, liquid volumetric flow rates Equation (1) would be expected to apply for the bubble and plug flow regions. The successof such an expression, which in no way accounts for the entrance conditions, is attributed to the fact that most investigations in the bubble flow region have been carried out using relatively large bubbles which would have penetrated well into the core of the liquid where the velocity profile was relatively.flat. Bubble velocities calcu lated by use of equation (1) indicate that the velocities would be 1.2 times the sum of the superficial velocities of both fluids, based on the inlet volumetric flow rates, or equival- ently 1.2 times the true average liquid velocity. Tiny bubbles subjected only to the liquid velocity very close to the tube wall could not be expected to flow at the same velocity as those subjected to the velocity aof the liquid at a more central location in the tube. For- situations when relatively large bubbles are produced, however.,, and for the conditions of its development, equation (1) would be expected to give good results. 38 Proposed Velocity Profile in Bubble Flow Region It is possible to deduce qualitatively the shape of the velocity profile for the bubble flow region of horizontal gas-liquid flow based on readily- observable phenomena as well as on an analysis of the various forces involved. One type of behaviour in bubble flow to which no reference in the literature has been found is tne particular "crawler type" of film circula tion which occurs around bubbles during horizontal flow. When water, ethanol, or ethylene glycol is allowed to flow through a horizontal glass tube dusted with talc powder, and air is injected into i t at-a rate sufficient to produce bubble flow, the circulation oJf the liquid film around each bubble can be readily seen. The film circulation can best be described by considering a single bubble. As a bubble moves forward along the top of the tube, a particle of talc is picked up at the rear of the bubble and carried forward in the direction of flow along the interface and eventually deposited on the tube wall at the front of the bubble. For a short period of time, until the rear of the bubble reaches i t , this particular particle deposited on the top surface of the tube is completely stationary. It is then again swept off the tube wall and circulated by the movement 3 9 of the interface from the rear of the bubble to the front. The bubbles discussed here can be generally refer r e d to as "large", having a v e r t i c a l dimension of more than one quarter that of the tube diameter, and a length of at least three or four times the depth. From observation of the movement of a p a r t i c l e on the bubble int e r f a c e i t i s apparent that the interface moves at a v e l o c i t y greater than the average bubble v e l o c i t y . This must be true otherwise s. v e l o c i t y of a p a r t i c l e at the i n t e r f a c e r e l a t i v e to the bubble i t s e l f ; ; could not be observed. The various forces operative i n the gas and l i q u i d phase during horizontal bubble flow i n a region of the tube distant from the entrance w i l l now be considered* Three types of forces can be exerted by the gas phase on the tube wall and on the g a s - l i q u i d interface., These, are a pressure force, acting at r i g h t angles to a l l surfaces contacted, a shear force due to a v e l o c i t y p r o f i l e adjacent t o the tube w a l l or i n t e r f a c e , and a k i n e t i c energy force. Both the shear and k i n e t i c energy forces would appear to be n e g l i g i b l e i n comparison to the equivalent forces i n the l i q u i d phase. Far from the tube entrance the maximum v e l o c i t i e s possible i n the gas phase would be equal to those of the l i q u i d with which-it was i n contact, because there i s no energy source within the gas. The shear force, and k i n e t i c energy force i n the gas, would be d i r e c t l y proportional to the 40 gas viscosity, and gas density, respectively, in the common expressions for shear and,kinetic energy. A typical ratio of gas to liquid viscosity is.0*01, and of gas to liquid density is in the order of,0.001. The shear and kinetic energy forces for gases and.liquids flowing at the same velocity would likewise va^y roughly in the same proportions. It is assumed, therefore, that $he major force exerted by the gas in bubble flow is one <of pressure. Except those of gas pr assure 9 a l l the forces which deter mined the shape of the bubblesand their velocity during flow are assumed to occur in the liquid phase. Obviously, i f a con stant pressure is assumed at a l l locations within a particular bubble, and al l the gas pressure forces are exactly counter balanced, then there is no* net pressure force on the bubble to cause its motion. For the^situation where (liquid-solid) interfacial forces confine,^, bubble against the tube wall, some motion of al l or part of the confining interfaces is essential, therefore, to cause any motion whatsoever of the gas bubble. Motion of the gas-liquid interface around bubbles causing their flow was in fact observed as discussed earlier. The top of the tube exposed to the gas in the bubble is presumed to be wetted by the liquid at a l l times. Under these conditions the bubble is confined completely by a liquid film, 41 albeit a thin one at the Cop of the tube. Interfacial (or surface tension) forces act to reduce the total interfacial area, and attempt to impose a spherical shape on the bubble. The interfacial tension forces, therefore, act to cause the bubble to penetrate deeper into.the tube. The buoyancy forces tend to maintain the bubble at the top of the Cube. In addi tion, these forces tend to, elongate the bubble opposing the effect of interfacial tension. Inasmuch as motion of*, the gas-liquid interface in the direc tion of flow was observed, some force must have been available to Cause this motion. The obvious force that can be considered is one of viscous shear in-, the - |»iquid phase. If a velocity gradient adjacent to the gas-liquid interface causes its motion in the direction of flow, It is necessary for a maximum (local) velocity to exist at some position below the interface. If the force required to move the gas-liquid interface is small relative to the shearing forces*at the tube wall, then the posi tion of the maximum velocity could be close to the interface itself. That is, only a small velocity gradient would be required to cause a small force-at the interface. It has already been assumed* that the shear caused by any gas velocity in the bubbles can be considered negligible. It will also be assumed that the liquid-solid interfacial 42 tension at the periphery of the .bubbles is small in comparison to the shear at the wall in the liquid phase. Then, i f the tube is cut in half lengthwise by-an^imaginary plane, the area of the tube exposed to liquid is .much smaller in the top half of the tube than that exposed in the bottom half. It is a necessary condition for two-phase flow.that the overall pressure drop due to flow across a finite length of conduit should be the same for a l l positions i n a given cross-section of the conduit. It is therefore assumed that the pressure drop across a finite length of tube (containing many>bubbles) would be the same whether measured in the top, half, or the bottom half of the tube. For this to be possible,-it is apparent that the shear force (per unit area) must necessarily be greater in the top half than in the bottom half. For the shear force to be greater in the top half the mean velocity of liquid must be greater in the top half of7the tube. Alternately, the top portion of the tube can be considered as offering less resis tance to flow than the bottom half because a fraction of the wall area contacts gas. Consequently, a higher fluid velocity would result in the top portion, of the tube. Figure 2 shows a proposed velocity profile for horizontal bubble flow. The mean gas velocity as shown in Figure 2 is greater than the mean liquid velocity. A velocity gradient i s shown adjacent to the g a s - l i q u i d interface. The maximum l i q u i d v e l o c i t y i n a portion of,tube between the bubbles i s shown displaced upwards from the centre-line p o s i t i o n . The v e l o c i t y p r o f i l e has been drawn for a turbulent l i q u i d , but the shape of the p r o f i l e would not be expected to change a great deal for viscous flow, since the same observations and arguments would s t i l l apply- Proposed Mechanism for Mass Transfer i n Bubble Flow Two mechanisms w i l l be considered, both based on the surface-renewal or "penetration theory" model. The f i r s t one i s based on the assumption that the surface-renewal occurs by the motion of the interface from the rear to the front of the bubbles. The second mechanism postulates the superimposed frequent renewal of portions of ; H the interface during the c i r c u  l a t i n g motion around bubbles, as a r e s u l t of eddying or mixing within the bulk of the l i q u i d . Although a stagnant f i l m i s known not to ex i s t i n bubble flow, for the sake of comparison the absorption rate assuming a f i l m theory model w i l l also be estimated and compared with the observed rat e . In any consideration of the rate of mass transfer i n h o r i  zontal bubble flow, the r e l a t i o n between the gas flow rate and bubble frequency i s of considerable importance. The measurement 45 of bubble frequency, as we l l as the production of uniform bubbles by means of sp e c i a l nozzles, was outside the scope of t h i s research. An attempt was made instead to simulate a p r a c t i c a l s i t u a t i o n by using a simple tee for introducing the gas and l i q u i d phases into the contacting tube. For t h i s type of entrance, the bubbles were not completely uniform i n s i z e or shape, although approximate uniformity was achieved for many of the gas and l i q u i d flow rates. The r e l a t i o n between the gas flow rate and bubble frequency at a constant l i q u i d rate was only q u a l i t a t i v e l y observed. The frequency remained roughly constant for a p a r t i c u l a r l i q u i d flow while the gas flow rate was increased; the volume of gas contained i n each bubble increased accordingly. This-behaviour i s consistent with that reported by Johnson (30) for bubbles formed at an o r i f i c e at r e l a t i v e l y high gas flow rates.•* A q u a l i t a t i v e estimate o f the e f f e c t on mass transfer of gas flow rate at a constant l i q u i d rate can be made by using the following approximate model. Its w i l l be assumed that the large bubbles are geometrically s i m i l a r to the small ones, and that the shape of each of them-can be approximated by a right-angled p a r a l l e l e p i p e d . Then the surface area i s d i r e c t l y proportional to the volume of a para l l e l e p i p e d to the 2/3 power. I f i t i s also assumed that the portion o f each bubble i n contact with 46 the tube wall is ineffective for mass transfer, and that a simi lar fraction of each bubble is made ineffective in this manner regardless of size, then the.effective Interfacial area of each bubble will s t i l l be directly proportional to the bubble volume to the 2/3 power. Consider.a length of contacting tube contain ing many bubbles. Even though the frequency of the bubbles (at a constant liquid rate)....is the same with an increasing gas volumetric flow rate, the number of bubbles in a fixed length of tube will decrease with an increased gas rate, because the total fluid volumetric flow is increased. When the volumetric flow of liquid greatly exceeds the gas volumetric flow (as in bubble flow) the effect on the fluid velocity caused by variations in gas flow only, is not large. This effect will be ignored, therefore, in the qualitative arguments concerning the gas flow rate and interfacial area.^ Using the simplified model?of parallelepiped-shaped bubbles of constant frequency, the total interfacial area in a fixed length of contacting tube, at a fixed liquid rate, is approxi mately proportional to the gas volumetric flow rate to the 2/3 power. For a l l models of mass.transfer, the transfer rate would be expected to be directly-proportional to the effective inter facial area, and hence directly proportional to the gas flow rate to the 2/3 power for the simplified model. For the mechanism 47 of surface renewal solely by the motion of the interface from the rear to the front of the bubble, however, the transfer rate is also involved with, the mean contact time, or surface age. If it is assumed that the velocity of the interface rela tive to that of the bubble is constant for a l l the sizes of bubbles, then the net dependence of the mass transfer rate on volumetric gas flow rate can be-estimated. For this situation, the transfer rate would be*directly proportional to the effec tive interfacial area, and inversely proportional to the square root of the mean contact time a ,-If the relative velocity of the interface is constant, then the,dependence of the contact time on any particular length dimension of a bubble would be to the 1/3 power, so that the net mass transfer rate for this mechanism might be expected to depend on the gas volumetric flow rate to the 1/2 power. The assumption, that the bubble dimensions increase proportionately in a l l directions with an increased gas rate is somewhat in error. The dimension of length pro bably increases more than the width for the sizes of bubbles actually investigated. In the extreme case of long "plug" flow, when the bubble length.greatly exceeds its depth, bubbles tend to grow longitudinally only. In this limit of one dimensional growth, the interfacial area is directly pro portional to the gas flow rate ( s t i l l assuming constant bubble , 48 frequency), and so is the contact time. Hence, the net rate of mass transfer again depends on the gas volumetric flow rate to the 1/2 power. From these two extreme cases, i t may he concluded that in bubble flow the net.mass transfer rate must depend on the volumetric gas flow rate to Tsome power of 0.5 or greater, with a maximum possible value of-unity for long plugs and assuming a stagnant film model. Referring to Figure L (p.1ft), in which two typical absorp tion rate curves are shown (NTU^ vs V^), i t is found that in the bubble region of flow the slope,on the log-log plot is nearly 2/3. Most of the absorption rate curves do in fact show a dependence on the gas volumetric flow rate, at a constant liquid rate, to an approximate power of 2/3 (but not of 1/2). Since i t is known that a stagnant film does not exist at the bubble interface, the mechanism.of transfer suggested, there fore, is that of the frequent renewal of portions of the inter face by eddying and mixing. Subsequently much more conclusive evidence will be brought forth to indicate that in al l probabi lity this is the mechanism of mass transfer operative in bubble flow. r An actual experimental run.for which a good estimate of the interfacial area can be made will be used as an illustra tion for comparing postulated mass transfer rates to those 49 experimentally measured. Run number 793 was made with the CC^9 water system at 15°C, using the small tube 1.228 cm in internal diameter. This particular run is used as an illustration because the bubbles produced,were unusually uniform, and represented the smallest size of bubbles studied in this research. The size of bubbles was approximately 1.7 cm in overall length, and 0.6 cm- i n depth (almost half the tube diameter), The mean gas volumetric flow rate i n the test section (between the sample-points) of the absorption tube was also known. The gas input flow rate was corrected for the amount absorbed in the,-tube-,, as well as for the temperature and pressure in the tube to give a true mean value as calcu- lated by means of an IBM-1620 computer. For this particular run the mean volumetric gas.flow was 2.80 cfh which was equi valent to a superficial velocity of 0.610 fps, while the liquid flow rate was equivalent to a superficial velocity of 1.783 fps. The true bubble velocity was calculated by using the relation for void fraction given by Scott, equation (1), discussed earlier in this chapter. The conditions for the use of equation (1) included a liquid superficial Reynolds number exceeding 8000. The liquid superficial Reynolds number for run number 793 was approximately 6000, and the application of equation (1) was, therefore, not strictly justified. Since 50 any probable error was considered to be small in comparison to the major effect that was to be illustrated, i t was used nonethe less. In essence equation (1) states that the gas (bubble) velocity is 1.2 times the true average liquid velocity. From the true bubble velocity the residence time of the bubbles in the test section could be calculated. From diagrams of the bubbles in the tube drawn to scale, i t was possible to estimate the bubble cross-section area, volume, total surface area, as well as the average length: of the longitudinal film surrounding each bubble. These dimensions were subsequently used to calcu late the bubble frequency,: number of bubbles in the test section, and the total interfacial area in the test section. To estimate the transfer rate for the assumption of a stagnant film at the interface,-a knowledge of the film thick ness was required. The limit of the laminar sublayer adjacent to the wall for turbulent flow in circular channels is given by Knudsen and Katz (31). It,was assumed that i f the stagnant layer existed, it would have been of the same order of thickness at the bubble interface as at the tube wall. Further the liquid superficial Reynolds number was-used (6000) in the evaluation of the film thickness because a»true characteristic Reynolds number for two-phase flow was unknown and the film thickness was not highly dependent on Reynolds number. The thickness 51 obtained for the laminar sublayer was 0*0172 cm. To test the rate of transfer for a stagnant film the most common type of engineering rate equation was used; ~ C o } N - ° (2) A x 2 where; A =» 162 cm 1.465 (10"5) cm2 sec" 1 -3 C* » 0.0455 millimoles cm C • - 0 o * x » 0.0172 cm The mass- transfer rate in the test-section for a stagnant film at the interface was calculated by equation (2) to be 0.0063 millimoles per second* A maximum possible driving force was used although the driving farce for run number 793 was actually closer to 90 per cent of the maximum. A linear concen tration profile was also assumed to exist in the film prior to i t s a r r i v a l in the test section* To estimate the transfer rate for the moving interface model, i t was necessary to know-the rate of surface renewal, or contact time. To determine the contact time the velocity of the interface relative to jthat of the bubble was required. Referring to Figure 2 (p.43), which shows the proposed velocity profile for bubble flow, i t appears unlikely that the interface 52 velocity exceeds the mean bubble velocity by more than a factor of 1.3. The relative velocity of the interface, therefore, would be 0»3 times the mean.bubble velocity. It is noted that the choice of the interface relative velocity was somewhat arbi trary, but it will be subsequently shown that this did not significantly alter the result of this illustration. The mean contact time was determined by dividing the interface length by the interface relative velocityand found to be for this situation, 0 .132 sec. The penetration depth was calculated by the expression derived by Danckwerts ( 2 7 ) : The penetration depth as calculated by equation (3) was 0.0050 cm which is considerably smaller than the thickness of a laminar sublayer calculated earlier. The penetration depth, as defined by Danckwerts, is the depth at which the rise in concen tration due to unsteady-state absorption is 0.01 times that at the interface. To calculate the rate of mass transfer in the test section the total area exposed to the liquid was assumed to have been renewed every 0.132 seconds. To calculate the (3) where: PD = penetration depth, cm (P^ —5 2 cfQ = liquid phase,diffusivity, 1.465 (10" ) cm sec & = mean contact time,,sec -1 53 actual quantity of gas absorbed,by the film at every exposure, i t was necessary to know the concentration profile within the penetrated depth of liq u i d . This involved the integration of the relatively complex expression for the time dependence of the concentration and the distance from the interface. The expression for the unsteady-state absorption into a stagnant film i s also given by Danckwerts (27)% C - C . C* - C 0 — • erfc — ( 4 ) wheres C «• concentration at distance, x (cm), from the inter- -3 face, millimoles cm C q « concentration in the bulk of the liquid C* « saturated concentration, at< the interface 0 a mean contact time, sec c •••• For application to this problem i f the maximum driving force i s assumed, the bulk l i q u i d concentration w i l l be zero. The appro priate integration of equation (4). for the mass transfer rate, N A, has been performed by Bird, Stewart, and Lightfoot (32). 2 where: A » 162 cm 6 » 0.132 sec c 54 $ « 1.465 (IO"5) cm2 sec"1 C* ° 0.0455 millimoles, cm"3 C - 0 o = average mass transfer rate for time interval Qc, millimoles sec'V The mass transfer rate for the soiling film model as calculated from expression (5) was 0.^3 millimoles per second. Again the maximum possible driving farce was applied. The actual transfer rate for run number 793 was calculated from the liquid flow rate and the CO2 analysis at the inlet and outlet of the test section, was .0*. 344 millimoles per second. It is of interest to note the difference in rates for the stagnant film, the rolling film, and. the,experimentally observed rate, 0.0063, 0.088, and 0.344 millimoles per second, respectively. It is obvious that the stagnant-film theory cannot explain the mass transfer that actually occurred. The rate calculated for the rolling film, on the other hand, was about one quarter that actually observed and was, therefore, at least of the right order of magnitude. Further, i t is of interest to calculate the frequency of the surface renewal required to explain the high mass transfer rate that was experimentally observed. The frequency is the inverse of the contact time which can be solved for by using equation (5) and substituting the experi-55 mentally observed mass transfer;rate for N^ , the transfer rate. It can be seen from equation (5) that the rate of transfer Is inversely proportional to>the square root of the contact time, so that to obtain a transfer rate 4 times as great would require a contact time approximately 16 times as short. The calculated values of contact time, and penetration depth, are, respectively, 0.0085 sec, and 0.0013 cm. In summary, i t is apparent .that the rate of surface renewal must be about 16 times as great as that accounted for by the longitudinal motion of the interfacial film surrounding the bubbles. Even i f the estimate of the velocity of the inter facial film relative to the bubble was incorrect by a factor of two or three, the rolling film model could not explain the rate of transfer that was experimentally observed. It is, therefore, proposed that the mechanism of transfer;was the process of surface renewal caused by turbulent eddies and mixing within the liquid. A further argument-in support of the application of the penetration theory to bubble flow is the fact that the dependence of the transfer- rate-on the liquid phase diffusivity was found to be to the 1/2 power in accordance with the pene tration theory model. If the relative velocity between bubble and fluid were very small, as might occur for very small bubbles, it is possible to imagine a mechanism of mass transfer depending 56 on the complete absence of normal v e l o c i t y components i n the v i c i n i t y of the bubble during the residence time of bubble i n the test section. This model would correspond approximately to flow past a r i g i d body at low Reynolds numbers and a t h e o r e t i c a l solution for t h i s case has been reported by Friedlander (33). This solution predicts that; .-the^transfer c o e f f i c i e n t w i l l be a function only of the Feclet number, with a dependence on the d i f f u s i v i t y to t h e 2/3 power. .Thus, t h e inference of the pro posed mechanism of t r a n s f e r .4s>.that the transfer rate for horizontal bubble flow i s l a r g e l y a function of the rate of surface renewal r e s u l t i n g from turbulent eddies or mixing i n the l i q u i d phase. The degree of- turbulence or mixing i s expect ed to be some function of the true l i q u i d v e l o c i t y . Further, i n general the transfer rate should: be d i r e c t l y proportional to the surface area exposed to-the>liquid. For bubbles separated by distances equal to about one -tube diameter, eddying would be promoted between the bubbles, whereas for bubbles very c l o s e l y spaced (less than 3 mm) turbulent eddies for the con fined spaces between them .would not be expected. The dependence of the rate of transfer, therefore, must be somewhat influenced by the shape, s i z e , and spacing ,of the bubbles, as w e l l as on the actual i n t e r f a c i a l area. E f f e c t s of surface tension and v i s c o s i t y , i n addition to 57 that of d i f f u s i v i t y , can be considered i n the l i g h t of the proposed mass transfer mechanism* A v a r i a t i o n of surface tension should a f f e c t the s i z e of the i n t e r f a c i a l area, and only i n d i r e c t l y , by v i r t u e o f the smaller i n t e r f a c i a l forces, the degree of mixing i n the bulk of the l i q u i d . One might expect, therefore s that with l i q u i d s of lower surface tension, longer bubbles would be produced, having comparatively larger i n t e r f a c i a l areas. A v a r i a t i o n - i n v i s c o s i t y would be expected to greatly a f f e c t the degree-of ••turbulence, and hence the rate of surface renewal. I t is,.,expeeted that the e f f e c t of d i f f u s i  v i t y associated with changes i n v i s c o s i t y would be accounted fo r by the usual dependence of the transfer rate f o r a penetra t i o n theory model, to the 1/2 power. Proposed Mechanism for Mass Transfer i n Slug Region The pronounced difference between bubble and slug flow i s most s t r i k i n g . In bubble flow the interface i s smooth i n appearance, wavering slowly- with, changing forces within the bulk of the l i q u i d . In slug, flow the in t e r f a c e i s very rough, p a r t i c u l a r l y i n the region of the slugs themselves. Tongues of l i q u i d are v i s i b l y thrown out. of the l i q u i d , r i p p l e s are extensively produced, and t i n y bubbles of gas are churned into the l i q u i d . The speed of the motion of the interface 58 i n the region of the slugs i s f a r too rapid to be v i s u a l l y followed. For the portions of l i q u i d between the highly a g i  tated slugs, the r i p p l i n g and agitat i o n are greatly diminished. The mass transfer rate i n the slug flow region i s gene r a l l y much higher than i n the bubble flow region. The transfer rate increases with gas flow rate at a constant l i q u i d rate, t y p i c a l l y as shown i n Figure 1 (p.19). At a constant l i q u i d rate, and for high gas rates i n the slug flow region, the transfer rates are as much as 10 times as great as the maximum values obtained for bubble flow. An accurate picture of the physical processes may be of assistance i n the analysis of possible mass transfer mechanisms for slug flow. The t r a n s i t i o n between plug and slug flow i s gradual. For a constant l i q u i d flow rate, as the gas rate i s increased the plug v e l o c i t y also increases. The inte r f a c e of each plug becomes r i p p l e d p a r t i c u l a r l y near the front, the inter f a c e takes on a d e f i n i t e slope with the thickness or height of the plug increasing from front to rear, and the int e r f a c e at the rear of the plug becomes highly agitated as i f by the turbulent wake. As the gas rate i s increased further, the amount of r i p p l i n g increases, and the turbulence at the rear i s more intense, entraining t i n y bubbles which tend to c i r c u l a t e behind the plugs. Within the elongated plugs 59 small slugs or waves of l i q u i d are propelled forward, with the c h a r a c t e r i s t i c high degree of ag i t a t i o n at the c r e s t . As the gas rate i s further increased, the cre s t i n g flow predominatesj however, most of the crests or slugs continue to f i l l the tube. At higher gas flows s t i l l , the l i q u i d i s propelled by the gas so r a p i d l y that the tube contains an i n s u f f i c i e n t amount of l i q u i d , even at the crests, to f i l l i t s cross-section. The turbulent crests t r a v e l along the tube at a high v e l o c i t y and at a high frequency. The quantity of l i q u i d tends to accumu l a t e at the slug crests while the amount remaining i n the tube between the slugs becomes only a small f r a c t i o n of the t o t a l amount flowing. At extremely high gas rates the l i q u i d tends to become more evenly d i s t r i b u t e d along the tube, annular rings, moving i n the d i r e c t i o n of flow, begin to appear i n addition to the slugs, while the slugs increase i n frequency and decrease in s i z e . Some further observations about slug flow can be made. At any instant the actual average l i q u i d v e l o c i t y i s most l i k e l y very considerably d i f f e r e n t at d i f f e r e n t positions along the length of the tube. S i m i l a r l y , at any instant at any one cross-sectional position of the tube, the v e l o c i t y of the l i q u i d at the inte r f a c e i s undoubtedly d i f f e r e n t from that of the average at that p o s i t i o n , e s p e c i a l l y i f the po s i t i o n corresponds 60 to a crest. Because in slug flow the liquid undergoes accelera tion and deccelerat ion, and because the agitation of the liquid at the crests is so severe, it appears hopeless to attempt to relate the condition of the liquid to a simple mean liquid velocity component in the direction of flow. Void fraction correlations are available, as indicated earlier, for predict ing average phase velocities. To successfully relate the overall average liquid velocity to that of the interface,' or to the degree of agitation at the slug crests, would be extremely difficult, and at the present state of knowledge, appears impossible. However, a more qualitative approach to mass transfer in the slug region is s t i l l available. Mass transfer rates in the slug region compared to those in the bubble region can easily be a factor of 10 greater. If a surface renewal theory is assumed for the slug region similar to the one proposed for the bubble region, some further compari son can be made. Although the interface is highly agitated i t is probable that the interfacial area in slug flow may be only a factor of two or perhaps three times as great as that in the bubble flow region. For run number 793 the estimated contact time was 0.0085 sec and the penetration depth was 0.0013 cm. For an increase in mass transfer rate of a factor of five, the contact time would need to be reduced by an approximate factor 61 of twenty-five (assuming an interfacial area twice as great). The order of magnitude of the contact time would then be 0.0003 sec. Such a short contact time (or even shorter) might well be possible in the region of the slug crests. In the region between the slugsa however, where the liquid interface is comparable in calmness to that for bubble flow, extremely short contact times of the order of 0.0003 seconds appear unlikely. If transfer rates for portions of the interface between the slugs are assumed to be comparable to those of bubble flow, it is obvious that in the region of the slugs themselves extremely high transfer rates would be required to account for the high overall mass transfer rates experimentally observed. Further, from the extremely turbulent appearance of the slug crests, i t seems entirely possible that the condition described earlier as the "limit of turbulence" might well be reached. For such extreme turbulence the mechanism of mass transfer by means of a velocity component in the liquid normal to the inter face, as proposed by Kishinevskii (25,26), might be expected to apply. It is proposed that for the extreme agitation in the slug crests themselves, the theory of transfer as proposed by Kishinevskii applies, and that for positions in the liquid between the slugs, the surface renewal or "penetration theory" 62 applies. The mass transfer rate expression according to the Kishinevskii theory is: N •- A (C* - C ) V (6) A o n v ' 2 where: A = interfacial area, cm C* =» interfacial concentration, millimoles cm -3 C = bulk concentration, millimoles cm o = mean velocity of liquid normal to the interface, -1 cm sec For this situation, the transfer is independent of the liquid phase diffusivity. Further, i t is apparent that the two trans fer processes can be considered to operate in one location with the two postulated resistances occurring in parallel or in series, as discussed by Davies (34). For the model that would appear to fit the slug flow region most closely, a cer tain varying fraction of the interfacial area can be considered in extreme turbulence, while the remaining portion is subjected to surface renewal by eddying and mixing. The two processes would operate independently in different portions of the tube. The rate equation that would apply would be a combination of equations (5) and (6) with each equation applying to a certain fraction of the interfacial area. It is apparent that neither the total interfacial area, nor 63 the portions thereof, to which the K i s h i n e v s k i i theory or the penetration theory would apply, can be obtained by d i r e c t estimate or measurement. I f they could be obtained, the r e l a t i o n between the mean surface age as well as of the mean v e l o c i t y normal to the in t e r f a c e , and the o v e r a l l mean l i q u i d v e l o c i t y i n the tube would s t i l l be unknown. No d i r e c t check of the proposed mechanisms i s , therefore, possible. Again, however, some s i g n i f i c a n t q u a l i t a t i v e statements concerning the e f f e c t s of the various variables on the rates of absorption can be made in the l i g h t of the proposed mass transfer mechanisms. At one l i q u i d rate ( i n the slug region) with increasing gas rates, the number of slugs, and extent of a g i t a t i o n i n them, would be expected to increase. The transfer mechanism would probably change from transfer by surface replacement only at r e l a t i v e l y low gas rates, to that of a combination of both mechanisms at higher gas rates. The l i q u i d phase d i f f u s i v i t y would have a deereasingly smaller e f f e c t on the rate of transfer, therefore, at increasing gas rates. I t should be possible to compare the absorption rate curves (NTU vs V°.) f o r the CO^-water and He-water systems, and to observe a decreas ing difference between the two curves at increasing gas rates. That i s , the e f f e c t of d i f f u s i v i t y should be diminished i f the e f f e c t of the K i s h i n e v s k i i theory mechanism becomes appreciable. Further, i t can be qualitatively stated that from actual observation, for identical gas rates, the degree of agitation ih slug flow appeared to be noticeably increased by increases in the rate of liquid flow. Following the same line of argu ment as previously, the difference between the CC^ -water and He-water absorption rate curves should be smallest, therefore, for the highest liquid rate. That is, the effect of diffusi vity would be least for the liquid flow rate at which the highest degree of turbulence was achieved. Again, i f the mechanisms proposed do in fact apply, the experimental data should display the corresponding qualitative characteristics. The effect of the surface tension on the absorption rates is qualitatively considered small. The kinetic energy of the liquid would most likely surpass in magnitude the interfacial forces during turbulence. The effect of interfacial tension would be expected to become less significant when the intensity of the turbulence increased. The effect of viscosity on the other hand would be expected to increase with an increase in turbulence because of the higher shear forces involved. The magnitude, and direction of such effects can be adequately determined only by experimentation. One assumption which was made for the bubble region of flow, and thus far tacitly assumed for the slug region, may 65 appear to be no longer valid. It is that at the same gas volumetric flow rates, the liquid turbulence or interfacial area is unaffected by gas density. For much of the slug region, the absorption tube as completely filled by consecutive slug crests, and, as a result, portions of gas were trapped in the tube as elongated, turbulent "plugs", by liquid completely filling the tube at either end. For this situation, as for the bubble region, it would appear that kinetic energy effects in the gas phase would not be of appreciable consequence on the interfacial conditions, compared to those in the liquid phase. For higher gas flow rates, when annular flow was approached, and the top portion of the tube was completely void of liquid, the mean gas velocity would, of necessity, be considerably greater than that of the liquid to produce the same rate of shear at the tube wall. For this latter condition, gas kinetic energy effects would most likely pro duce an increasing gas-liquid interaction (such as increases in interfacial area, droplet entrainment, or emulsification), for increases in gas density. For the conditions of this work, however, the assumption that the interfacial conditions are independent of the gas density appears to be valid for most of the slug region of flow. The possibility of variations in interfacial area, or other 66 gas-liquid interactions due to gas density for conditions of extreme turbulence, however, cannot be discounted until the Rishinevskli theory has been adequately confirmed. Conditions of such extreme turbulence as proposed by Kishinevskii may sel dom be reached in any practical contacting equipment, and hence difficulty may be encountered in obtaining irrefutable experi mental evidence to support or disprove his theory. Partial con firmation of the decreasing effect of diffusivity with increas ed turbulence is available from the reported work of Hutchinson and Sherwood (35) who found a dependence on diffusivity to the 0.25 power. Such a decreased dependence on diffusivity can be explained without the aid of the Kishinevskii theory, however, by assuming that one of the basic conditions for the use of the penetration theory becomes invalid for certain highly turbulent contacting systems. It concerns the lack of any velocity compo nent at right-angles to the interface within the penetration depth during the period of absorption. For highly turbulent systems, i f eddying or mixing occurred within the penetration depth, then the transfer rate would depend not only on the rate of unsteady-state diffusion, but also on the rate of mixing in the liquid, which would result in a decreased dependence on diffusivity, and an increased dependence on the rate of mixing for conditions of increased turbulence in the liquid. 67 SPECIFICATIONS AND PROPERTIES OF TEST FLUIDS Specifications The minimum specified purities are listed for the test fluids along with the supplier, grade, and size of purchase-lot for each. Carbon dioxides The CO^  used in this research was supplied as a liquid in pressure cylinders by the Canadian Liquid Air Company and was of a commercial welding grade purity, specified at a minimum COg content of 99.5 volume per cent. Heliums The He gas was also supplied by the Canadian Liquid Air Company and was of a minimum specified purity of 99.99 volume per cent He. He was supplied as a gas in high pressure cylinders, at approximately 2200 psig, in amounts approximately 200 scf per cylinder. Water; Vancouver city tap water was used as one of the liquids for the absorption studies. Ethanol; The ethanol (not denatured) was purchased from the British Columbia Liquor Control Board in 10 Imperial gallon drums and specified as absolute ethanol for research use only, with a minimum purity of 99.5 volume per cent ethyl alcohol. Ethylene glycol; The ethylene glycol was purchased as one 45 U.S. gallon lot from the Dow Chemical Company, and was of an 68 anti-freeze grade with a minimum purity specification of 99.5 volume per cent. Fluid Properties, Literature Data Except for the solubility of CO^ in ethylene glycol, the viscosity, and the surface tension of ethylene glycol, a l l the fluid properties used in the calculations of the results were obtained from published sources. The density of the gases, CO^  and He, was required for the calculation of the gas super ficial velocities in the absorption tubes. The perfect gas law was used in obtaining the correct volumetric flow at the absorp tion conditions. Since the pressures used were close to atmos pheric and the temperature close to room temperature, no signi ficant deviation from perfect gas behaviour was expected. The presence of liquid vapour in the gas phase was accounted for by applying Dalton's law. The liquid properties and their sources are discussed further under separate headings. Solubility The solubility data for CO^  in water and ethanol were obtained from the most recent review of solubilities by Linke (36). The solubilities expressed as the Bunsen coefficients are given in Table 1. The solubility data for He and water were obtained from the Handbook of Chemistry and Physics (37). The He solubilities expressed as the Henry's law constants are listed in Table 2. Viscosity and Density The viscosity data for water and ethanol, given in Table 3, were obtained from the Handbook of Chemistry and Physics (38). The densities of water, ethanol, and ethylene glycol were also obtained from the Handbook of Chemistry and Physics (39) and these values are also listed in Table 3. Surface Tension Interfacial tension is the consequence of intermolecular forces between two immiscible fluids. When one of the fluids is a gas and the other a liquid, a change in the nature of the gas usually does not appreciably change the interfacial tension. Hence, for gas-liquid systems, the interfacial tension is fre quently referred to as surface tension and usually treated as a property of the liquid only (40). Surface tension data avail able with saturated air, therefore, are considered to apply equally well for either CO2 or He as the gas. Surface tension data for the air-water and air-ethanol systems were obtained from Perry (41) and are listed in Table 4. 70 Liquid Phase Diffusivity The accurate experimental determination of gas-liquid dif fusion coefficients is extremely difficult and is undoubtedly subject to greater errors than the measurement of any of the other physical properties. Lack of adequate precautions to completely eliminate all sources of motion within the liquid in the diffusion path during the measurement of the diffusivities is frequently the cause of the resulting measurements being too high. The diffusivity for (X^ in water was obtained from a reference by Davidson and Cullen in which a number of indepen dent evaluations were compared (42) . The value experimentally obtained, and used in this research, compared favourably with other values reported. The C02"ethanol diffusion coefficient was obtained from the International Critical Tables (43). The diffusivity of CO^  in ethylene glycol reported by Calder- bank (44) was used in this research. The diffusivity of He in water as obtained by Gertz and Loeschcfce (45) was used because it was the lowest value reported. A second reason for its use was that a value calculated by means of the Wilke correlation (46) checked with the Gertz and Loeschcke value within a tolerable limit. The Wilke correlation, particularly for water, is considered by Reid and Sherwood (47) to give diffusivities 71 accurate to within 10 per cent. Diffusivity values were extra polated to temperatures other than at which they were obtained by means of the Nernst-Einstein equation (48) when required. The values of diffusivity as reported in the literature, extra polated values, and sources are given in Table 5. Fluid Properties, Experimental Data for Ethylene Glycol Solubility of C02 In his experiments with C02 and ethylene glycol Calderbank (44) reported the solubility at 25°C. Since in this research absorption studies were performed at 15°C and 30°C, solubility data at these temperatures were required. The solubility was determined by bubbling C02 for a prolonged period of time through the ethylene glycol which was maintained at a constant temperature. Samples of the glycol were analyzed for C02 by injecting known volumes into standardized excess alkali, and back-titrating with standard hydrochloric acid. A 2000-ml 3-necked round flask was used for the solubility determinations. Approximately 1000 ml of glycol was poured into the flask which was then immersed in a water bath whose tempera- ture was controlled by a mercury thermoregulator to within 0.05°C. A fritted-glass bubbler as well as a thermometer were supported by a rubber stopper in the centre opening of the flask. A second opening was equipped with a glass tube and tygon connector for withdrawing samples into a pipette. The third opening was left open so that CO^  rising through the glycol would be at essentially atmospheric pressure in the flask. Bubbling was continued for at least three hours before samples were withdrawn for analysis. Samples were taken by means of a 100-ml pipette, and were withdrawn by raising the flask out of the bath momentarily and draining the glycol into the pipette. A volume of glycol (about 50 ml) was flushed through the pipette prior to disconnecting the pipette from the flask. Exactly 100 ml of glycol was drained from the pipette into an erlenmeyer flask containing the excess caustic. The 100-ml samples were injected into 50 ml of 0.1 N caustic and back titrated with 0,1 N hydrochloric acid. This analysis was identical to that used for the regular absorption samples and is discussed in more detail in a later section. The results of the solubility determinations are shown in Table 6. Surface Tension The surface tension of ethylene glycol in contact with saturated air was measured by means of a duNouy tensiometer 73 (model number 10402), manufactured by the Central Scientific Company of Chicago. The procedure described fpr gas-liquid sur face tension measurements in the tensiometer technical bulletin (49) was closely followed. The tensiometer was calibrated using laboratory balance weights. Surface tension readings were taken at a number of ethylene glycol temperatures and extrapolated to 15°C and 30°C. The calibration measurements and surface tension readings are listed in Table 7. Graphs of the tensiometer calibration, as well as the surface tension measurements taken at various temperatures, are shown In Figure 3. Viscosity The viscosity of pure ethylene glycol was measured at the two temperatures, 15°C and 30°C. In addition, the viscosities at 15°C of glycol-water solutions containing increasing quanti ties of water were determined. The viscosity-water content relationship was used as a test for the contamination of the glycol with water and is discussed in more detail in a later section. The viscosities were measured by Cannon-Fenske type viscometers, following the procedure recommended in the ASTM report D445-53T. The calibrations of the viscometers, C-8 and C-3, as obtained by De Verteuil(50), were accepted. The viscosimeter, H-69, was calibrated by comparison with the TEMPERATURE. °C Figure 3. Graphs of Tensiometer C a l i b r a t i o n , Surface Tension Measurements for Ethylene Glycol 75 viscosity readings obtained with viscometers C-8, C-3, and H-69. The data for a l l the viscosity measurements are shown in Table 8. 76 TABLE 1 SOLUBILITIES OF C02 IN WATER AND ETHANOL Data from Linke (36) (A) C02~Water Temperature, °C j£ , Bun sen coefficient 5 1.424 5.3 1.41 (a) 10 1.194 15 1.019 20 0.878 25 0.759 30 0.664 40 0.530 45 0.480 (B) C0o-Ethanol 5 3.899 10 3.510 13.5 3.280 (a) 15 3.194 20 2.938 interpolated values ml C02 (0°C, 760 mm) dissolved in 1 ml liquid at a CO. partial pressure of 760 mm 77 TABLE 2 SOLUBILITY OF He IN WATER Data from the Handbook of Chemistry and Physics (37) Temperature, °C K (107) 0 10.0 10 10.5 15 10.71 (a) 20 10.9 30 11.1 40 10.9 50 10.5 (a) interpolated value K » Henry's law constant K = * x p = partial pressure in mm of mercury x • mole fraction in liquid 78 TABLE 3 VISCOSITY OF WATER AND ETHANOL Data from the Handbook of Chemistry and Physics (38) (A) Water o -3 Temperature, C Viscosity, cps Density, gm cm 0 1.792 5 1.519 0.9999 10 1.308 15 1.140 0.9991 20 1.005 25 0.894 30 0.801 0.9957 45 0.599 0.9903 50 0.549 (B) Ethanol 0 1.773 10 1.466 0.7979 13.5 1.360 (a) 0.7949 20 1.200 0.7895 30 1.003 (a) interpolated 79 TABLE 4 SURFACE TENSION OF WATER AND ETHANOL IN CONTACT WITH SATURATED AIR Data from Perry (40) -1 (A) Water rature, °C Surface tension, dynes 0 75.6 5 o J 75.1 (a) 15 73.5 (a) 20 72.8 30 71.2 (a) 40 69.6 45 68.8 (a) 60 66.2 (B) Ethanol 0 24.1 13.5 23.4 (a) 20 22.3 40 20.6 60 19.0 (a) interpolated values 80 TABLE 5 LIQUID PHASE DIFFUSION COEFFICIENTS (A) C02-Water (42) Diffusivity, Temperature, C times ( 1 0 ) cm sec 5.3 1.072 (a) 15.0 1.465 (a) 25 1.92. 30 2.190 (a) 45 3.08 (a) (B) C02°Ethanol (43) 13.5 2.95 (a) 17 3.20 (C) CO2-Ethylene glycol (44) 15 0.142 (a) 25 0.229 30 0.285 (a) (D) He-Water (45) 15 3.69 (a) 15 3.02 (b) 37 6.30 (a) extrapolated using Nernst-Einstein equation (47) (b) calculated using Wilke correlation (46) 81 TABLE 6 SOLUBILITY OF C02 IN ETHYLENE GLYCOL (A) Temperature, 15.0°C Barometric pressure: 758.1 mm mercury Sample size: 100 ml Partial pressure less than 0.1 mm mercury Volume Volume Solubility, 0.1 N NaOH 0.1 N HC1 millimoles per litre 50.0 2.80 47.20 50.0 2.90 47.10 50.0 2.80 47.20 50.0 2.90 47.10 mean •= 47.15 Solubility at 15.0°C, 760 mm « 47.27 millimoles per litre (B) Temperature, 30.0°C Barometric pressure: 758.1 mm mercury Sample size: 100 ml Partial pressure less than 0.1 mm mercury 38.0 1.95 36.05 38.0 2.10 35.90 38.0 2.00 36.00 38.0 2.05 35.95 mean 35.97 Solubility at 30.0°C, 760 mm « 36.07 millimoles per litre (C) Solubility by Calderbank at 25.0°C, 760 mm » 39.7 millimoles per litre. TABLE 7 SURFACE TENSION OF ETHYLENE GLYCOL (A) Calibration of Tensiometer Force on ring, gm 31 131 431 631 831 931 1031 Tensiometer Reading 1.1 5.2 9.2 17.3 25.8 34.1 38.2 42.5 Surface tension, , -1 dynes cm 2.4 10.1 17.8 33.2 48.6 64.0 71.7 79.4 (B) Surface Tension Measurements Tensiometer Surface tension, Temperature, °C 15.4 19.7 24.2 24.2 15.8 30.4 15.0 30.0 Reading 26.3 26.1 25.9 25.9 26.2 25.6 dynes cm 49.3 49.0 48.5 48.5 49.1 47.9 49.3 (a) 47.9 (a) Read from graph of surface tension and temperature, Figure 3 (p.74). TABLE 8 ETHYLENE GLYCOL VISCOSITY DETERMINATIONS (A) Calibration of H-60 at 15.0°C Liquid Visco- Time, minutes Viscosity meter (a) (b) (c) mean cs cps glycol H-69 12.237 12.233 12.233 12.234 glycol C-3 3.605 3.608 3.602 3.605 23.636 26.47 1.0 H-69 11.780 11.782 11.777 11.780 1.0 C-8 3.493 3.492 3.496 3.494 22.770 25.50 Calibration constant H-69, from C-3: 1.9320 from C-8: 1.9329 mean: 1.9324 (B) Viscosity of Glycol at 15.0°C glycol C-3 3.605 3.608 3.602 3.605 23.636 26.47 (C) Viscosity of Glycol at 30°C glycol H-69 6.477 6.476 6.477 6.4767 12.516 13.90 (D) Viscosity of Water-Glycol solutions at 15.0°C 0.05 C-8 3.618 3.621 3.620 3.620 23.59 26.42 0.15 C--3 3.587 3.588 3.588 3.588 23.50 26.32 0.50 Cr 3 3.542 3.543 3.545 3.544 23.22 26.01 0.75 C= 8 3.522 3.530 3.529 3.527 22.98 25.74 1.5 C-3 3.411 3.412 3.416 3.413 22.36 25.04 2.0 C-8 3.370 3.366 3.369 3.368 21.95 24.58 Note: numbers in liquid column represent volume per cent of water in ethylene glycol. Calibration constants: C-3, 6.551, cs min ^  C-8, 6.516, cs min"1 H-69, 1.932, cs rain"1 APPARATUS An apparatus was designed and b u i l t for continuously con tac t i n g various gases and l i q u i d s i n a horizontal, tubular, cocurrent absorber. A c i r c u l a t i n g system was incorporated for the test l i q u i d s , thereby permitting the storage and reuse of any one of the l i q u i d s . Provision was made for the contin uous s t r i p p i n g of ehe absorbed gas, for the cooling of the l i q u i d to a c o n t r o l l e d temperature, and f o r measuring the flow rate by means of one of two rotameters. The gases used i n a l l the experiments, He and CO^, were supplied i n the compressed, and l i q u i f i e d , forms respectively, from high pressure cyl i n d e r s . Provision was also made to measure the gas flow rate, again with one of two rotameters, to saturate the gas with the test l i q u i d , and to cool i t to a con t r o l l e d temperature p r i o r to contacting i n the absorption tube. After contacting, the excess gas was vented in t o the room or to the b u i l d i n g exhaust system. A d e t a i l e d flow diagram of the apparatus i s shown i n Figure 4 . In the description of the apparatus following, reference i s made to equipment numbers shown on t h i s diagram, and to drawings of i n d i v i d u a l pieces of equipment included i n Appendix I. Figure 4. Process Flow Diagram of Apparatus 00 86 A d e t a i l e d l i s t of s p e c i f i c a t i o n s f o r each item of equip ment i s also included i n Appendix I. L i q u i d System The l i q u i d processing apparatus was used for the s t r i p p i n g of gas absorbed i n the test section, as w e l l as for the measure ment and control of the l i q u i d flow rate and temperature. The apparatus and i t s function w i l l be b r i e f l y described by following an imaginary "packet" of l i q u i d from the e x i t of the absorbed test section through the cycle that was normally followed by the l i q u i d , back to the entrance of the test section. A f t e r passing through the test section, the gas and l i q u i d phases were separated i n a glass cyclone. From there the l i q u i d was allowed to drain by gravity to an accumulating drum, D- l . The l i q u i d temperature was measured by a thermometer, T-2, mounted i n the drain l i n e . The p a r t i a l l y saturated l i q u i d flowed from the accumulating drum to the stripper because of the vacuum i n the l a t t e r v e s s e l . The rate of flow was auto matically c o n t r o l l e d by an on-off l e v e l - c o n t r o l device which maintained a constant l i q u i d l e v e l i n the s t r i p p e r . The l e v e l c o n t r o l l e r , LC-1, consisted of a m e r c u r y - f i l l e d glass manometer with one leg of the manometer being completely f i l l e d with l i q u i d 87 and forming a continuous column of liquid from the top of the mercury to the top of the liquid in the stripper. The other leg was open to the vapour at the top of the stripper. In this way, the mercury in the manometer always assumed a level corres ponding to the liquid level in the stripper, regardless of the pressure (or vacuum) in that vessel. The side of the manometer exposed to the vapour contained two wire contacts, one immersed in the mercury, and the other placed in such a position that contact with the mercury would just be made when the desired liquid level was obtained. The two wires were connected in series with two dry cells, a switch, and the low voltage side of a relay. The relay in turn was used to operate the solenoid valve, LCV-1, which controlled the flow of partially saturated liquid into the vacuum stripper. A drawing of the vacuum stripper showing internal details is included in Figure 1-1 of Appendix I. The vacuum stripper was supported at an elevation of about 7 feet above the intake of the adjoining circulating pump, P-l, to ensure that a suffi cient liquid head was provided for good operation of the pump. The stripper vacuum was maintained by means of a large-sized water ejector, J - l , while the liquid in the lower portion of the vessel was heated by a steam coil. By means of the centri fugal pump, P-l, the liquid was circulated at a rate of about 88 6 gpra from the bottom of the stripper to the top and through a large spray-nozzle. The circulating rate was adjusted by means of the pressure regulator, PCV-1, which also maintained constant the pressure of a side-stream of the liquid withdrawn to the test section. During the degasification of the liquid, the rate of boiling was controlled by adjusting the steam pressure regulator, PCV-2. The resulting temperature of the liquid varied from about 18°C to 55°C depending on the amount of saturation, the liquid throughput, and on which of the three liquids, ethanol, water, or glycol, was being processed* The pressure likewise varied widely, for the same reasons, from about 20 to 29 inches of mercury vacuum, as did the degree of saturation of the liquid leaving the vacuum stripper. The amount of gas remaining in the liquid after stripping varied anywhere from 2 to 40 per cent of the saturation value based on the absorption conditions. A shell-and-tube heat exchanger, E-l, was provided for cooling the degassed liquid prior to its use in the test section. For a constant liquid flow rate through the test section, the temperature of the liquid was controlled within * 0.3°C of the absorption test temperature. This control was achieved by accurately regulating the flow of the cooling water through the exchanger, by adjusting the supply pressure 89 of the cooling water at the pressure regulator, PCV-1, as w e l l as by t h r o t t l i n g the flow of cooling water by means of the valve, F-3. In addition an exchanger by-pass valve, F -4 , was provided for occasions when the heat duty was unusually low. For maximum cooling, to obtain temperatures of process l i q u i d approaching cooling water temperatures, or while cooling the viscous ethylene g l y c o l , i t was necessary to replace the water ef f l u e n t valve, F -3 , with one of a•larger s i z e . Two c a l i b r a t e d rotameters, R - l , and R-1A, with, s l i g h t l y overlapping ranges, were used to measure the flow rate of the degassed l i q u i d to the absorption tube. When a constant temperature of the degassed l i q u i d had been reached, no d i f f i  c u l t y was encountered i n also maintaining a constant flow through one or the other of the l i q u i d rotameters. Gas System The function of the gas processing apparatus was to supply a continuous stream of gas, at a known flow rate, saturated with the vapour of the t e s t l i q u i d , and at the temperature at which the absorption was to take place. When CO^ was the t e s t gas, two cylinders were required to supply high gas flow rates (up to 220 cfh) because of the l i m i t a t i o n on the amount of gas that could be continuously 90 withdrawn from one cylinder. Without special precautions, at withdrawal rates from a single cylinder exceeding 50 cfh, icing of the pressure regulator and adjacent equipment would occur. For flow rates from both cylinders exceeding a total of 100 cfh, an infra-red heat lamp was directed towards the pressure regu lators. In addition, small steam-heated double-pipe exchangers mounted adjacent to the pressure regulators were used to ensure that any CO2 leaving the cylinders in the liquid, form, would be completely vaporized. No similar problem was encountered with the He gas which could be withdrawn at all the required flow rates from a single cylinder. The dry gas from the cylinders was metered prior to humidi- fication. Two calibrated rotameters, R-2, and R-2A, were used to measure the gas flow rates, one for flow rates from about 1.5 to 20 cfh of the CO2 and the other for flow rates from about 20 to 220 cfh. The same rotameters were used for He. Pressure measurements were obtained at the gas supply header by means of a 30-inch mercury-filled Merlan manometer, P-l, and the corres ponding temperature measurements, downstream of the rotameter by a thermometer, T-2, mounted in the piping. The gas was saturated with the liquid with which it was to be contacted, in a two stage process. The gas was first par tially saturated in a humidifier at a temperature above that 91 used for the experimental runs. The partially saturated gas was subsequently cooled in a double-pipe exchanger, E-3, to the temperature of the experimental runs. At this latter temperature the gas was fully saturated at al l times as evi denced by the presence of droplets of liquid in the gas flowing into the entrance tee. In this way, saturation was readily attained for all gas flow rates, and the small amount of liquid usually condensed during cooling added only negligibly to the total liquid flow in the test section. A detailed drawing of the gas humidifier is shown in Figure 1-2 of the Appendix I. The humidifier consisted of a 2-inch diameter pyrex glass column 24 inches long with provi sion for circulating liquid from the bottom through a series of four spray nozzles into the top portion of the column. The gas was bubbled through the liquid in the bottom and then through the spray from the four nozzles. Sufficient heat was normally supplied by the circulating pump, F-2, to raise the temperature of the liquid somewhat above room temperature for all the gas flow rates. A steam line was provided for inject ing live steam into the humidifier for the series of runs using and water at temperatures of 30°C and 45°C. The flow rate of steam was controlled by a small globe valve, F-24, at a rate sufficient to saturate the gas. 92 The amount of cooling of the p a r t i a l l y saturated gas to be performed i n the exchanger, E-3, was determined from the gas outlet temperature as measured by the thermometer, T-4, Gross changes i n the cooling duty were accomplished by c l o s i n g and opening the appropriate valves, F-22 and F-23, and hence using half of the a v a i l a b l e heat exchange area or a l l of i t as required. Finer, temperature c o n t r o l was achieved by adjusting the cooling water valve, F-24. Absorption Tubes The*gas-liquid contactors employed i n t h i s research con s i s t e d of glass tubes mounted h o r i z o n t a l l y with provisions f o r measuring the pressure and concentration at two locations along the tube near the entrance and e x i t . The combination of one standard type of entrance, the ho r i z o n t a l tee, and an absorp t i o n tube, 1.757 cm ID, was employed i n the majority of the experimental runs. The dimensions of the entrance section for the 1.757 cm tube were used as a basis f o r constructing dimen s i o n a l l y s i m i l a r entrance tees for the smaller (1.228 cm) and larger (2.504 cm) tubes which were used with the C02"water system i n determining the e f f e c t of tube diameter. In a l i m i t e d series of experiments three other tube entrances, having widely d i f f e r i n g c h a r a c t e r i s t i c s , were used with the 93 1.757 cm tube to determine q u a l i t a t i v e l y the e f f e c t of entrance type. In addition to entrance ' type, the entrance length which i s required for the development o f a d e f i n i t e flow pattern i s another important consideration of tubular flow. The entrance length i n the case of single-phase flow i s generally given by a number of pipe diameters, which i n turn i s some function of the Reynolds number. In the case of two-phase flow the depen dence on some modified Reynolds number or any other parameter has not yet been established. On the basis of v i s u a l observa tions,, the entrance length was f i x e d at 12.9 inches for the i n i t i a l series of experimental runs, and l a t e r increased to 31.3 inches f o r the majority of the runs. In a l l the absorp t i o n measurements made, l i t t l e or no quantitative difference was found between the shorter and longer entrance sections. For some t e s t conditions, however, the shorter length seemed, on v i s u a l inspection, to be barely adequate f o r the cl e a r deve lopment of the flow patterns. Hence, the longer entrance length was used for most t e s t s . A t y p i c a l test section with i t s associated equipment i s shown i n Figure 5. Also i n Figure 5 are shown the dimensions of a l l the tubes and entrance types investigated i n t h i s research. GLASS ABSORPTION TUBE AND ASSOCIATED EQUIPMENT TEST SECTION LIQUID INLET- OUTLET CYCLONE O U T L E T P R E S S U R E PO INT - R U B B E R S L E E V E - 12 M M N O M I N A L O.D.- O U T L E T S A M P L E L O C A T I O N ABSORPTION TUBE DIMENSIONS, INCHES S I Z E A B C D E F 0 H M E D I U M 0 . 6 9 2 1.757 C M 1.20 3.8 12.9 9 2 . 3 4.1 2.44 1.07 M E D I U M 0 . 6 9 2 I . 75TCM. 1.20 3 .8 31.3 9 2 . 3 4.1 2.44 1.07 S M A L L 0 . 4 8 3 1.228 C M . 0.81 3.2 31.3 9 2 . 3 4 . 6 1.82 0 . 83 L A R G E 0 . 9 6 6 2 8 0 4 C M L6I 5.4 31.3 9 2 . 3 5.8 3.10 1.31 N O T E - ( I ) A L L D I M E N S I O N S NOT T O S C A L E (2 ) D I M E N S I O N S IN I N C H E S U N L E S S O T H E R W I S E S T A T E D Figure 5 . Dimensions of Absorption Tubes and Entrances Used 95 Since the absorption tubes played a key role in this work the construction, mounting, and related procedures will be described in some detail. Each absorption tube was constructed from two sections of pyrex glass tube both having the same internal diameter when measured by callipers, and a length of approximately 4 feet. After the two sections had been joined by glass blowing, glass nipples were installed diametrically opposite to one another at two positions 92.25 inches apart along the tube, corresponding to inlet and outlet sampling loca tions. The average internal diameter for each absorption tube was subsequently obtained to a high degree of accuracy by measuring the internal volume of a portion of the tube. One end of the tube was sealed with a cork, the sampling and pressure nipples were carefully sealed with plasticine, and water from a volumetric flask was poured into the tube. The height of the column of water with the tube in the vertical position, along with the known volume, was used to calculate the average internal diameter. The entrance tees were blown f r o m standard sizes o f pyrex glass tubing, while the outlet cyclone separators were blown from round-bottomed pyrex flasks of a suitable size. The portions of entrance tee and outlet cyclone directly adjoining the absorption tubes were carefully matched in size, in each 96 case, to that of the absorption tube itself. In preparation for a series of experimental runs one of the absorption tubes, as well as the associated entrance tee and outlet cyclone, was supported on a metal framework by means of laboratory clamps. The sections of the entrance tee, absorption tube, and outlet cyclone were butted together and held by means of tightly-fitting tygon sleeves. The gas and liquid supply lines were connected to the entrance tee by tygon tubing. The outlet tube of the cyclone was connected to the liquid drain line by means of a rubber hose held in place by hose-clamps. Precautions were taken to ensure that the absorption tube was mounted horizontally and that the entrance and exit sections were properly aligned. It was estimated that the maximum devia tion from a horizontal position was less than 0.1 inch in the full length of the tube of over 100 inches. When the absorption tube was in operation, the liquid phase was sampled at the entrance and outlet sample locations by means of the sampling nipples provided. A detailed descrip tion of the sampling procedure is given in the section on Sampling and Analysis. The pressure corresponding to the sampling locations was obtained in the gas phase at the top of the absorption tube by means of two 30-inch Merian mano meters, M-2 and M-3. The manometers were filled with water, 9 7 carbon tetrachloride, or mercury, depending on the range of pressures to be measured. The glass pressure nipples were connected to the manometers with transparent tygon tubing, so that any liquid carried into the tubing could be readily observed. A gas supply line and valve connected to each mano meter line permitted a small amount of gas to be passed through the line and into the absorption tube prior to taking a pressure reading. The gas used for this purpose was the same as that used in the absorption experiment, hence i t did not con stitute an impurity. The flow was always small and infrequent, hence i t added to the measured gas flow rate in the absorption only negligible. The manometers were also provided with small globe valves for damping extreme pressure fluctuations. Especi ally during slug flow, pressure fluctuations were of such a magnitude that, without damping, suitable pressure measurements could not be taken. The test section inlet pressure was measured relative to the atmosphericqpres6ure in all the experi ments. For some experiments the test section outlet pressure was similarly measured. In most runs, however, the second manometer was used to measure the pressure drop in the test section. 98 Materials of Construction As indicated i n Figure 4 (p.85), a l l of the interconnecting l i q u i d flow l i n e s were constructed of standard s t e e l pipe, coated on the inside for added protection against corrosion. A coating was also applied to a l l the other s t e e l surfaces ex posed to the c i r c u l a t i n g l i q u i d including the casing of the pump, P - l , the heads of the exchanger 9 E - l , and the l i q u i d rota meter- entrance and ex i t blocks. For an i n i t i a l s eries.of experi mental runs with CO^ and water, however, the s t e e l surfaces were exposed to the d i l u t e carbonic a c i d solutions without the i n t e r n a l protective coating. I t was found that when a single charge of water was c i r c u l a t e d continuously i n the equipment for a period of about 7 hours, f e r r i c ion was detectable i n the c i r c u l a t i n g l i q u i d . Small amounts of hydroxide p r e c i p i t a t e were observed when samples of the l i q u i d were injected into d i l u t e caustic solutions. Since the equipment was to be used with ethanol and ethylene g l y c o l , l i q u i d s which could not be replaced d a l l y for economic reasons, i t was necessary to prevent the contamination of these l i q u i d s . A l l the appropriate piping and l i q u i d processing equipment was disassembled and subjected to a coating procedure. The Surfaces were washed with soap and water to remove any o i l y f i l m , and scraped free o f rust where necessary. The cleaned surfaces were then dried and coated with a lead-based metal primer. A f t e r the primer~coat had been thoroughly dried, tygon paint, d i l u t e d with acetone to a s u i t  able consistency, was applied, providing a second protective coating. In t h i s way, the s t e e l surfaces were protected by a smooth semi-flexible r e s i s t a n t coating. No s i g n i f i c a n t d e t e r i  oration of the protective coating was observed a f t e r repeated service of the equipment f o r a period of time i n excess of one year. Several of the i n i t i a l runs with CO^ and water were d u p l i  cated a f t e r the l i q u i d processing equipment had been coated, and the results, .indicated that the presence of a small amount of f e r r i c ion i n the. water d i d not s i g n i f i c a n t l y a f f e c t i t s absorption c h a r a c t e r i s t i c s . The remaining portions of the l i q u i d processing equipment were a l l constructed from brass, copper, and glass, a l l three of which were r e s i s t a n t to the l i q u i d solutions used. The gas handling equipment was also constructed from these same three materials, and no corrosion problem was encountered. 100 PROCEDURE The procedure f o r operating the experimental equipment w i l l be described i n two sections, one pertaining to the l i q u i d sys- tern, the other to the gas system. The preparation of the gases, CO and He, was e s s e n t i a l l y i d e n t i c a l ; however, the preparation of the equipment and the test procedures d i f f e r e d somewhat fo r the three liquid®. The operating procedures f o r water, ethanol, and ethylene g l y c o l , therefore, w i l l be described separately. L i q u i d System For a l l three l i q u i d s the general procedure was to esta b l i s h a constant l i q u i d flow r a t e through the test section, and to maintain i t f o r a series of experimental measurements at the varying gas flow rates. The l i q u i d flow and temperature could be kept constant, with a minimum of adjustments to the equipment, for long periods of time and even for widely varying gas flow rates. Water as the t e s t l i q u i d With water as the test l i q u i d , the equipment was recharged d a i l y during a given series of runs. A flow of service water was started into the vacuum st r i p p e r , and also to the water-101 cooled exchangers, E - l and E°3. When a s u f f i c i e n t quantity of water appeared i n the stripp e r , the c i r c u l a t i n g pump, P - l , was started. A water flow was then directed through the test section at approximately the rate desired for the experimental runs, anywhere from 0.6 to 4.2 gpm. The water leaving the tes t section was allowed to accumulate i n the drum, D~l, u n t i l the drum was about one h a l f f u l l , equivalent to about 7 gallons i n quantity. The water ejector was then put into operation, evacu«= atlng. the s t r i p p e r , and causing the water t o flow from the accumulating drum back into the vacuum st r i p p e r completing the cycl e . .Next the fresh water supply l i n e was shut o f f . Subse- quent adjustments were concerned'with achieving a suitable s t r i p p i n g rate, and obtaining the desired l i q u i d flow and temperature i n the test section. A flow of steam was started into the heating c o i l of the vacuum st r i p p e r , which was then adjusted to provide vigorous b o i l i n g , but without bumping, of the water i n the s t r i p p e r . The steam flow r a t e was adjusted by r e s e t t i n g the steam supply pressure as cont r o l l e d by the regulator, PCV-2, to some value between 2 and 20 psi g , depending on the throughput of the process water. The cooling rate of the water leaving the s t r i p  per was regulated to obtain the desired temperature at the absorption tube entrance, usually 15.0°C. I t was adjusted 102 primarily by throttling the cooling water flow out of the exchanger, E-l. When the outlet valve, F-3, was nearly open or closed, however, the pressure regulator, PGV-1, was adjusted to some value between 4 and 30 psig, as required, to maintain control of the temperature at the cooling-water flow valve, F-3. Final small adjustments were made to obtain the exact flow rate of water to the test section, prescribed for that particular series of runs, and to obtain the temperature to within 0.3°C. A small gas flow of approximately 2 cfh was started through the test section about 20 minutes before any measurements were to be taken. This gas flow displaced any air present in the equipment and also aided in deaerating the circulating process water itself• At the completion of a series of experimental runs, the equipment was shut down by first breaking the vacuum in the stripper (opening valve F-ll) and then stopping the circulat ing pump, P-l. The steam and cooling water flows were next stopped, and the equipment was completely drained by means of valves, F-15 and F-16. Ethanol as the test liquid Absolute ethanol was employed as the test liquid for the investigation of the effect of surface tension on the absorption 103 r a t e . Because water had been previously used i n the equipment, a thorough drying of the equipment was necessary to avoid contam ination o f the ethanol with water. F i r s t the equipment was dismantled where necessary to ensure that a l l the water com p l e t e l y drained. The p a r t l y dismantled l i n e s and equipment were allowed to dry overnight. A i r from the b u i l d i n g a i r supply was temporarily connected with rubber tubing to the long sections of piping, and these sections were dr i e d by means of a small flow of a i r again l e f t overnight. A f t e r the dried equipment was assembled, a small amount of ethanol was flushed through the equipment, then approximately 12 U . S . gallons of ethanol was charged into the accumulating drum through the cyclone at the outlet of the test section. The ethanol was allowed to drain into the accumulating drum and stored there between each successive ser i e s of experiments. Because of i t s hygroscopic nature, s p e c i a l precautions were taken to avoid contamination of the ethanol with water from the a i r . When the equipment was i d l e , a l l the outlets opening d i r e c t l y into the room were closed. In t h i s way contact with the room a i r was minimized. Also, i n case of leakage i n the exchanger, E°l, the supply pressure of the cooling water was always maintained at a pressure below that of the ethanol. Frequent additions of fresh ethanol to that i n i t i a l l y 104 charged were required because of the r e l a t i v e l y high evaporation and sampling losses. Apart from those differences already mentioned, the opera- t i o n of the equipment with ethanol was very s i m i l a r to that with water. The i n i t i a l f i l l i n g of the vacuum st r i p p e r before s t a r t  ing the c i r c u l a t i n g pump, was accomplished by f i r s t s t a r t i n g the water ejector and causing ethanol to flow from the accumulating drum to the s t r i p p e r . In a l l other respects the method of opera t i o n was the same as for water. Ethylene g l y c o l as the tes t l i q u i d Ethylene g l y c o l was used as the tes t l i q u i d f or determining the e f f e c t of v i s c o s i t y on the absorption rat e . The experi mental runs using He and water were performed a f t e r C 0 2 and ethanol had been processed i n the equipment; therefore, as f o r ethanol, a thorough drying procedure was required before the g l y c o l could be charged into the equipment without contamina t i o n . Because ethylene g l y c o l i s highly hygroscopic, more r i g i d precautions were taken against i t s contamination with water vapour from the a i r , than were taken with ethanol. In addi t i o n a v i s c o s i t y t e s t was devised and used at frequent i n t e r  vals during the experimentation for determining the water 105 content of the glycol. As measured by the test, at no time during the experimentation did the water content increase more than 0.4 volume per cent above that already present in the newly purchased material. A 15 U.S. gallon plastic carboy was used to charge the ethylene glycol into the equipment. The carboy was equipped with a silica gel dryer for the top opening into which the dryer was installed immediately after filling. An outlet valve at the bottom of the carboy was used to drain the glycol into the equipment. A temporary platform was erected above the absorption tube outlet cyclone to support the carboy while the glycol was being charged into the cyclone. Every outlet of the equipment which could expose the glycol to the room air was subsequently protected by a silica gel air dryer. Silica gel dryers were installed at the outlet cyclone, in the accumulat ing drum vent line, and in the vacuum-breaking line at the valve, F - l l . The dryers did not keep air out of the equipment but were effective in removing the water from the air which entered. When the equipment was being used, however, the silica gel dryer at the outlet cyclone was removed, and later reinstalled at the completion of each series of experiments. The procedure for operating the equipment using ethylene glycol as the test liquid was the same as for ethanol in all 106 other respects. A series of ethylene glycol-water solutions containing from 0 to 2 per cent water by volume, was accurately prepared. The viscosities of these solutions were obtained at 15°C using Cannon°Fenske type viscosimeters, and the procedure described in a previous section. A graph showing the effect of the low concentrations of water on t h e viscosity o f ethylene glycol solutions is shown in Figure 6, and t h e measured values are given in Table 8 (p.83). Because of t h e sensitivity of the viscosity measurements, a water content in the glycol as low as 0.1 volume per cent was detectable. Calibration of the liquid rotameters The liquid rotameters were calibrated by diverting the liquid flow normally passing through the absorber test section, to a 15 U.S. gallon capacity carboy mounted on a platform scale, and recording the time taken to accumulate a measured weight of liquid. A glass tee was installed by means of tygon tubing into the liquid line adjacent to the entrance of the absorption tube. A drain line for diverting the liquid into the carboy, was joined to the temporarily installed tee and provided with a screw clamp. It was therefore possible to circulate liquid through the normal flow channels, to attain 0 . 5 1.0 1.5 WATER CONTENT OF ETHYLENE GLYCOL, VOLUME PERCENT Figure 6. V i s c o s i t i e s of Ethylene Glycol-Water Solutions 108 a desired temperature and flow through the rotameters and absorp tion tube, and then to divert the flow from the absorption' tube to the weigh°tank for calibration. When calibrating the rota meters for ethanol or ethylene glycol, the contents of the car boy were returned into the equipment, by way of the outlet cyclone, when the carboy became about one half full. During calibration, the liquid temperature was maintained to within 0.3°C. The scales could be read within one ounce, and had been recently tested and approved by the Weights and Measures Section of the Department of Trade and Commerce. The accuracy of the calibration, therefore, appeared to be limited primarily by the ability to read the position of the float. The rotameter calibrations are shown in graphical form in Figures II»1, « 2 , =3 and the tabulated data appears in Tables II-l, -2, -3 of Appendix II. Gas System An accuracy of within 3.0 per cent of the true gas flow for a l l flow ranges from 1.5 to 220 cfh was desirable, but difficult to achieve, because of the compressibility of the gas. Such an acceptable accuracy with the gas rotameters was obtained by calibrating the rotameters at specific pressure 109 settings, and thereafter using the rotameters at these pressures only. The control of the gas flow, as well as the humidification of the gas, were relatively simple. The measurement of the pressure at the entrance and exit of the test section, however, was complicated hy the extreme pressure fluctuations which occurred during plug and slug flows. Calibrations of the gas rotameters The gas rotameter, R-2, for use with COg, and covering a flow range from approximately 1.5 to 20 cfh at room conditions, was calibrated using a wet test meter. The wet test meter, manufactured by the Precision Scientific Company of Chicago, had a maximum capacity of 50 cfh and a rated accuracy in the range used, of 0.5 per cent. The rotameter was calibrated at three pressures, 4, 8, and 12 inches of mercury above atmos pheric pressure. This rotameter, when calibrated in the same way for He, gave a range from 1.5 to 50 cfh at room conditions, at pressures of 4, 12, and 24 inches of mercury. The calibration procedure consisted of temporarily divert ing the flow of gas from the absorption tube entrance through the wet test meter. The time taken for a suitable volume of gas to flow through the meter as well as the rotameter pressure, temperature, and float position were recorded. A particular gas 110 flow rate was obtained by alternately adjusting the gas flow valve, F-2, and the gas supply pressure to give the desired rotameter pressure as read by the manometer, M-l, and the desired rotameter float position. The gas temperature at the rotameter was measured by the thermometer, T-3, and remained in the range from 18°C to 25°C for the calibration measurements. The gas rotameter, R»2A, was calibrated for both (X>2 and He by means of a l&rge dry gas displacement meter. The displacement meter, meter number A65630, was manufactured by the Canadian Meter Company of Hamilton, Canada, and had a maximum rated capacity of 900 cfh. The rotameter, R-2A, was calibrated using CO^  for pressures of 4, 8, 12, 16, and 24 inches of mercury above atmospheric pressure, and in the approxi mate range from 20 to 220 cfh. The corresponding calibration pressures for He were 4, 12, and 24 inches of mercury, and the approximate range from 30 to 250 cfh. The procedure for cali bration using the dry gas meter was identical to that using the wet test meter. The calculations associated with the cali bration measurements, and the resulting calibration graphs for CO^  and He are given in Appendix II. The calibrations for the gas rotameters, and all subse quent gas flow measurements, were made in volumetric units, cubic feet per hour, of dry gas at 15°C and 756 mm of mercury I l l absolute pressure. Appropriate corrections for temperature, pressure, liquid vapour pressure, as well as for the quantity of gas absorbed by the liquid, were made when the true volume tric flow rates at the entrance and exit of the test section were required. The calculations involved are discussed in more detail in the chapter on the Treatment of Data. Gas flow measurement and control The procedure for obtaining a particular gas flow rate, as for example 18 cfh of CO^  (at 15°C and 756 mm of mercury pressure), consisted of referring to the gas rotameter calibra tion graphs and choosing the appropriate rotameter, and rota meter settings at a fixed pressure for the desired flow. The actual mechanical procedure of obtaining a particular gas flow consisted of successively adjusting the gas supply pressure, and the position of the flow valve, F-2 (or F-2A). Adjustments to the flow valve changed the gas supply pressure as well as the flow. A number of alternate adjustments to the flow valve and one or both of the cylinder pressure regulators was usually required to obtain a particular float position and, at the same time, a particular rotameter pressure. The method for obtaining any desired flow rate for He was exactly com parable. 112 An approximation was made in measuring the gas flow rates. For the purpose of the calibration, the rotameter temperature was adjusted to 21°C and the barometric pressure to 756 mm of mercury. Gas density corrections were applied to the calibra tion measurements when the actual temperature and barometric pressure differed from 21°C and 756 mm of mercury, as indicated in the Appendix II. For all subsequent flow measurements, however, the rotameter temperature and the barometric pressure were assumed to be 21°C and 756 mm of mercury, respectively, and no correction for the gas density was made. This approxi mation greatly simplified the use of the calibration graphs and introduced only small absolute errors to the flow measure ments. The magnitude of the errors thus introduced can be readily estimated. It is known (51) that for a gas the volumetric flc$» rate through a rotameter, for a particular float position, usually varies inversely as the square root of the gas density. The rotameter temperature and barometric pressure for the majority of the experiments varied in the range 21*4°C and 756*8 mm of mercury, respectively. Since the density varies Inversely as the absolute temperature and directly as the absolute pressure, the assumed value of the gas density could be in error by a maximum of 1.4 per cent because of temperature variations, and 0.93 per cent at the 113 lowest rotameter pressure used, because of barometric pressure variations. The rotameter flow, however, varying inversely as the square root of the gas density, would have a maximum possible error of 0.7, and 0.47 per cent, introduced by ignoring the actual rotameter temperature, and barometric pressure, respec tiv e l y . These errors could be tolerated, since they were usually much less than the maximum values, and since the ab i l i t y to read the float position was li a b l e to errors of a somewhat greater magnitude. Gas humidification and saturation As b r i e f l y described in the section on Apparatus, after being pa r t i a l l y saturated with the vapour of the test liquid in the gas humidifier, the test gas was cooled to the absorp tion temperature and at this temperature was completely satur ated. If Raoult's law was assumed to hold for the three liquids concerned, the molar concentrations of vapour in the gas at saturation would be proportional to the liq u i d vapour pressures. It is evident that the concentration of the ethylene glycol vapour in the gas would be small indeed, while the presence of ethanol vapour i n the gas would significantly increase the gas volume. Prior to start up, the humidifier was charged with approxi-114 raately 500 ml of the test liquid. The operation of the humidi- f i e r consisted only of starting the circulating pump, P-2, and recharging the humidifier when most of the liquid had vaporized. For the majority of the absorption runs the gas temperature was allowed to vary in the range from 1 degree less to 4 degrees more than the prescribed test temperature. Better temperature control was considered unnecessary for two reasons. F i r s t , the total heat content of the gas stream, for a l l the gas and liquid flow rates encountered, was small when compared to that of the liq u i d stream. Temperature differences of the gas of several degrees, therefore, had a negligible effect on the liquid temperature. Next, a considerably amount of contact between the gas and liquid occurred in the entrance tee and entrance section, prior to any concentration measurements. Hence the gas was cooled to the liquid temperature, and the excess vapour simultaneously condensed, because of the direct contact between the two phases. As indicated earlier the temperature rise of the liq u i d was negligible. For these reasons the gas was usually maintained in a temperature range slightly above the absorption temperature. The temperature of the gas flowing into the absorption tube was measured by the thermometer, T~4, mounted i n the piping. The cooling rate in the water-cooled exchanger, E»3j was regulated by adjusting the rate of flow of cooling water and, when necessary, closing and opening the appropriate valves, F-22 and F-23, to double or halve the effective heat exchange area. Measurement of pressure in the absorption tube A number of difficulties are involved in measuring pressures in two-phase flow. The pressure gradient along the tube is not constant, particularly for the bubble, plug, and slug flow regions. The interruption of phases as observed at any one position of the tube, as well as the associated pressure surges, are characteristic of two-phase flow. For this situation some "average" pressure must be measured. Two-phase flow pressure measurements can be made in either the gas phase (at the top of the tube) or the liquid phase (at the bottom of the tube). There is a disadvantage in measuring the liquid phase pressure; a second non-miscible heavier liquid (such as mercury) is usually required as the manometer fluid. With mercury the manometer would become insensitive to the rapid pressure fluctuations due to the inertia of the fluid in the pressure line and manometer. The measurement of pressure in the gas phase was adopted for this work because any desired manometer fluid could be 116 used, and because of the relatively rapid response of this type of system. The two manometers, M«2 and M-3, were mounted adjacent to their respective inlet and outlet sampling locations. The inlet manometer, always measuring the higher pressure, was filled with water, carbon tetrachloride, or mercury, depending on the range of pressures to be measured. The fluids used in the outlet manometer were either water or carbon tetrachloride. The procedure for taking a pressure reading consisted of first clearing the manometer line of any liquid by passing a small amount of test gas through i t . If the manometer fluctuated widely the fluctuations were dampened by partly closing the needle valve in the manometer line. The reading finally taken was a "time-averaged'' one, a pressure reading that persisted for the longest period of time. Because of the nature of the fluctuations, the time-averaged reading did not usually corres pond to the average of the maximum and minimum readings. The method of taking a time-averaged pressure reading was employed whether the particular manometer was used to measure pressure relative to the atmosphere, or to measure the pressure drop between the inlet and outlet sample locations. It should be mentioned that the measurement of two-phase pressures by the method just described was not considered 117 highly accurate. The accuracy of the pressure measurements did not limit the accuracy of the absorption rate determina tions, however. In al l cases, the pressures measured were small relative to the atmospheric pressure, or to the absolute pres sure. The gas solubility and hence driving force for mass transfer depended on the absolute pressure. Any errors in the measurement of pressure above atmospheric, therefore, had little effect on the accuracy of the absolute pressure or on the absorption rate determinations. 118 SAMPLING AND ANALYSIS Sampling In general, i t was desirable to obtain l i q u i d samples which yielded the average or "mixing cup" concentrations. Such samples would be obtained i f a l l the l i q u i d flowing through a given cross-section of tube i n a f i x e d time i n t e r v a l was trapped, removed into a sealed container, and then thoroughly mixed. Although t h i s was not possible i n practice, suitable samples which were equivalent to the mixing cup v a r i e t y could be r e a d i l y obtained, nonetheless. For a l l the experimental runs, the l i q u i d phase was i n either a well mixed, or i n a turbulent, region of flow. The concentration gradient through the bulk of the l i q u i d phase, therefore, could be expected to be i n s i g n i f i c a n t compared to that i n a very small region near the g a s - l i q u i d i n t e r f a c e . Figure 7 shows v e r t i c a l concentration p r o f i l e s for the CO^-water system i n the bubble, and slug flow regions, as w e l l as for the CO^-ethylene g l y c o l system i n the bubble region. The method for obtaining samples at the d i f  ferent v e r t i c a l positions i n the absorption tube i s discussed in a following section. I t i s apparent from Figure 7 that the concentration gradient through the bulk of the l i q u i d was very BUBBLE INTERFACE O E OD UJ co U J 8 8 U i 00 O tr o. i ! f V BOTTOM OF SLUG / i i i d COg-WATER, BUBBLE FLOW O CO-GLYCOL, BUBBLE FLOW 2 9 CO-WATER, SLUG FLOW 2 SATURATE0 CONCENTRATIONS (MILLIMOLE / LITRE) CO-WATER « 45.7 CC-£GLYC0L«47.I 10 15 20 C02 CONCENTRATION, MILLIMOLES/LITRE Figure 7. Concentration P r o f i l e s for C0£-Water and CO2-Glycol VO 120 small r e l a t i v e to the o v e r a l l gradient, from saturation at the interface to the lowest value at the bottom of the tube. I t i s also evident that any concentration chosen i n a f a i r l y wide region between the bottom of the tube and the g a s - l i q u i d i n t e r  face would y i e l d a good approximation to the average or mixing cup concentration, A sample drawn from a p o s i t i o n approximately midway between the bottom of the tube and the minimum gas - l i q u i d i n t e r f a c e , therefore, on analysis would be expected to give a good approximation of the mixing cup concentration. L i q u i d samples were taken at the i n l e t and outlet sample locations to determine the concentration change i n the test section. The method of sampling and analysis for each of the g a s - l i q u i d combinations studied was usually somewhat d i f f e r e n t . When CO2 was absorbed i n any of the three l i q u i d s , water, ethanol, or ethylene g l y c o l , the samples were withdrawn into pipettes, charged into caustic solutions and subsequently analyzed by t i t r a t i o n . For the He-water experimental runs, small water streams were continuously withdrawn at both the i n l e t and outlet locations and passed through stripping columns provided at these two locations. The He was stripped out of the water by a C 0 2 gas stream which was then passed through a thermal c o n d u c t i v i t y - c e l l (TC-cell) for analysis. Details of the sampling apparatus for the four g a s - l i q u i d combinations 121 CARBON DIOXIDE-WATER. CARBON DIOXIDE-ETHANOL Figure 8 . Methods of Sampling for Absorption Rate Determinations 122 are shown in Figure 8. C02-Water and CC^-Ethanol The sampling methods for the CO^ -water and CC^-ethanol systems were almost identical. As indicated in Figure 8, liquid samples were obtained by means of 3 mm OD glass tubes inserted inside the glass sample nipples of the absorption tube. The small diameter sample tubes were held in place by pieces of rubber tubing connected to the glass nipples. Liquid samples could be taken from any vertical position in the absorption tube, at both the inlet and outlet sample locations. During the progress of the experimental runs, the inlet and outlet samples were always taken at the same sample position in the absorption tube, approximately midway between the bottom of the absorption tube and the minimum elevation of the gas-liquid interface. For very turbulent slug or annular flow regions however, when bubbles of gas became entrained in the liquid, precautions were required to prevent withdrawal of the gas bubbles with the liquid samples. For these turbulent flows, the sample tubes were lowered into the sample nipples, with the top of each tube placed 10 to 15 mm below the bottom of the large absorp tion tube. In this way, the sample nipples effectively served as gas-liquid separators, removing entrained bubbles from the 123 liquid samples. The concentration profiles shown in Figure 7 (p.119) were obtained at constant liquid and gas flow rates through the absorption tube, by varying the inlet and outlet sample tube positions simultaneously in measured increments. Because of the low solubilities of in water and ethanol, relatively large samples of these liquids were required for analysis by titration. Samples were accumulated in pipettes mounted below the absorption tube and joined to the sampling tubes with rubber tubing, as shown in Figure 8 (p.121). While the samples were being taken it was important to avoid exposure to the air to prevent loss of the absorbed gas. Each sample pipette was arranged so that, during sampling, the liquid entered at the point of the pipette, and slowly filled it to overflowing. The liquid overflow was diverted to a drain. A volume of liquid approximately equal to the sample volume was normally purged through the pipette to ensure that the sample finally contained in the pipette was a representative one. The pipette size for all the CC^ -water samples was 100 ml. For the CX^-ethanol runs smaller pipettes of 25 and 50 ml were used. The pipettes were clamped in location with the supply and overflow tubes connected at all times except when the samples were actually being transferred to the sample flasks. 124 The sampling rate was normally kept in the range from 10 to 40 ml per minute. Samples were taken simultaneously at the inlet and outlet sample locations for each different combination of gas and liquid flow rates. CO^-Ethylene glycol In addition to the concentration profile measurements, a second qualitative test was performed to determine the extent of mixing in the ethylene glycol phase. Ink was injected with a syringe into the liquid near the entrance of the absorption tube. Sketches of the different visual patterns observed with different and ethylene glycol flows are shown in Figure 9. The mixing in the liquid phase appeared to be good, as already suggested by the flatness of the concentration profile. The superficial Reynolds numbers for the liquids were of the order of 8000 (turbulent) for water and 200 (laminar) for ethylene glycol. Because of the low Reynolds number great care was initially taken in sampling the glycol, and was subsequently found unnecessary. In fact the similarity of the concentration profiles for the two liquids seems anomalous, and this simi larity is discussed further in a later section. The sampling method used for ethylene glycol was a some what elaborate one, chosen to obtain representative samples INK INJECTION 0 NO GAS FLOW MIN. GAS FLOW USED (BUBBLE) SLUG FLOW LIQUID RATE" 1.07 G.RM. ; TUBE DIAMETER' 1.757 CM. Figure 9. Induced Turbulence In Ethylene Glycol by Ink Injection Tests 126 even for large concentration profiles in the liquid phase. Details of the sampling equipment are shown in Figure 8 (p.121). The test section for the CC^-ethylene glycol series of experi ments included the entrance tee, the total length of the absorp tion tube, and the outlet cyclone separator as well. Inlet and outlet samples were taken from the liquid supply line upstream of the entrance tee, and from the outlet cyclone, respectively, to measure the concentration increase i n the test section. Even i f a large concentration gradient existed in the liquid phase of the absorption tube, an average outlet concentration could s t i l l be obtained by utilizing the cyclone action for mixing the liquid in the cyclone separator, and withdrawing a sample from there. The inlet sample was necessarily of a uniform concentration. This method of sampling had the inherent complication of including in the contacting system the entrance tee, an initial tube section where uniform flow may not have been established, and the outlet cyclone. The assumption was made that the flow pattern in the initial section of the absorp tion tube was rapidly established and its contacting effective ness was equivalent to that of any other portion of tube. This appeared to be a good assumption because the visual flow pattern was fully established in most cases within 12 to 18 inches from the entrance tee, and because the entrance length (12 to 18 127 inches) was a small proportion of the total effective tube length of 127.1 inches. Further, it was possible to make measurements of the amount of absorption which occurred in the entrance tee and outlet cyclone for all the ethylene glycol flow rates used, and to correct the overall absorption rates accordingly. Mixing of the ethylene glycol was promoted in the outlet cyclone to achieve a uniform concentration. As indicated in Figure 8 (p.121) a moveable glass stand-pipe was installed inside the cyclone drain line, with very little clearance between the two. Any ethylene glycol flowing into the cyclone filled it to the level of the stand-pipe, and overflowed into the stand-pipe and then through the regular drain line. A small hole was blown in the glass Stand-pipe approximately 5/8-inch below the top edge to serve as a sample point. A sample line consisting of stiff 1/4-inch diameter polyeth ylene tubing was forced through the small hole in the stand- pipe and was held there by a ridge cut around the tubing. The other end of the polyethylene tubing was inserted through a small hole drilled for it in the rubber hose connecting the drain line to the cyclone. In this way, the sample tubing supported the stand-pipe and permitted external adjustment of its position. By adjusting the position of the stand-pipe the 128 outlet cyclone was maintained about one half full for a l l the CO^ - ethylene glycol experimental runs. The liquid in the cyclone appeared to be well mixed by the action of the liquid flowing into the cyclone. In the cyclone most of the surface liquid layer which had been in contact with the CC^  tended to flow radially toward the stand-pipe and then out the drain line. This was a desirable effect since a sample taken from below the liquid surface then showed a CC^  content which largely excluded that resulting from absorption in the cyclone itself. Inlet and outlet samples were taken by means of two 100 ml pipettes. Needle valves were installed in both the inlet sample line,as well as in the polyethylene outlet sample line to regu late the sampling rates. In all other respects the method of sampling was the same as for water and ethanol. An estimate of the amount of absorption occurring in the entrance tee and outlet cyclone was made separately for each different combination of flow rates and temperature that were used during the absorption experiments. The method consisted of passing the ethylene glycol through the absorption tube as a single phase and permitting contact with the CO2 gas only in the entrance tee and outlet cyclone. Prior to each test, CO2 was passed through the entrance tee and absorption tube to ensure that the entrance tee was adequately purged. By means of a temporary l i n e , CG^ was allowed to flow continuously into the outlet cyclone during the test to ensure that the cyclone contained only CC^ gas. I n l e t and outlet samples were taken by the same procedure used for the regular ethylene g l y c o l absorption runs. The only absorption which occurred during these t e s t s , therefore, was that i n the entrance tee and outlet cyclone. I t was assumed that the amount of absorption i n the entrance tee and outlet cyclone remained the same for one ethylene g l y c o l flow and temperature regardless of the gas flow ra t e . In a l l p r o b a b i l i t y t h i s was not a highly accurate assumption, p a r t i c u l a r l y for high gas flow rates, when an increase i n l i q u i d turbulence at both the entrance and outlet was evident. The amount of absorption due to these sections was a very small f r a c t i o n of the t o t a l amount of absorption i n the tube, e s p e c i a l l y at high gas flow rates. The error i n measurement of the o v e r a l l absorption rates would be i n l i t t l e error even i f the amount absorbed i n the entrance tee and outlet cyclone was i n error by a factor of two or more. He-water During the He-water experimental runs the l i q u i d samples were withdrawn from the same two locations i n the absorption tube (92.2 inches apart) that were used for the CO^-water, 130 and CX^-ethanol experiments. The sampling for He-water d i f f e r e d from that of the l a t t e r two systems i n that the samples were continuously withdrawn and continuously analyzed at both the i n l e t and outlet sampling locations. The accuracy of the analy s i s depended on maintaining constant sample flows through small st r i p p i n g columns. Because of the pressure surges character i s t i c of some regions of two-phase flow, maintaining constant sample flows was no simple task. Since the d e t a i l s of the con t r o l of the sample flow rates were so c l o s e l y associated with the He analysis i t s e l f , a more det a i l e d description w i l l be deferred to the next section. Analysis The analysis for dissolved CO^ i n the three l i q u i d s , water, ethanol, and ethylene g l y c o l , was almost i d e n t i c a l . The analysis entailed the reaction of the sample with an ex cess of a known volume of standard sodium hydroxide solution and b a c k - t i t r a t i o n with standard a c i d . The system CX^-water has frequently been used for mass transfer studies because of the r e l a t i v e s i m p l i c i t y of the analysis. An i d e n t i c a l method of analysis was shown to be suitable for solutions of CO 2 i n ethanol and ethylene g l y c o l , as w e l l as i n water. Solutions of He i n water, on the other hand, presented a 131 much greater problem since He i s chemically i n e r t i n solution, and only sparingly soluble. Because of i t s r e l a t i v e l y high gaseous thermal conductivity, however, gas-phase He mixtures could be analyzed by means of a ca l i b r a t e d T O c e l l . A method of s t r i p p i n g He from the water solutions by a c a r r i e r gas was developed for obtaining gas-phase mixtures suitable for analysis by thermal conductivity. C0 2-Water The t i t r a t i o n of carbonates and bicarbonates with a c i d i s usually considered to be a double-indicator t i t r a t i o n , with the f i r s t end point occurring when a l l the carbonate has been con verted to the bicarbonate, and the second, when a l l the b i c a r  bonate has been converted to dissolved CO^. The f i r s t , and second-end points occur at approximate pH values of 9 , and 4, respectively. The analysis of dissolved CO^ was si m i l a r to, but not i d e n t i c a l with, that f o r carbonate solutions. In the i n i t i a l step, the v o l a t i l e CO^ i n the sample was converted to a stable carbonate-bicarbonate mixed solution by i n j e c t i n g the sample into a volume of standard sodium hydroxide s u f f i c i e n t l y large to convert at lea s t some of the CO^ to carbonate. An indicator i n the solution for a pH of 9 , corresponding to the f i r s t end point, confirmed the presence of the carbonate. When titrated with acid to the carbonate-bicarbonate end point (pH 9) the sample solution then contained an amount of bicarbo nate equivalent in number of moles to that amount of C02 origi nally present in the sample. Back-titration with acid to the first end point, therefore, yielded by difference the molar quantity of bicarbonate, or of original C02, in the sample. Titration to the second end point could have been performed as a check on the amount of standard caustic used, but was not required for the determination of the C02 originally present in the sample. The normality of both the sodium hydroxide and the hydro chloric acid solutions used in the volumetric analysis was 0.100. This normality was chosen to provide sufficiently large volumes of titration to ensure a reasonably accurate analysis even for low concentrations of CC^  in the water samples. For the 100 ml sample size used, the maximum volume of sodium hyd roxide required was 45.47 ml, for a water sample completely saturated with C02 at 15°C and 1 atm pressure. The end-point for the carbonate-bicarbonate titration was not expected to be as sharp as for most alkalimetric titra tions (52), but by means of a special mixed indicator an adequate accuracy was obtained for most of the analyses. The mixed indicator chosen was cresol red-thymol blue which, 133 according to Simpson (53), was expected to give a r e l a t i v e l y sharp colour change at the carbonate-bicarbonate end point. The maximum probable error due to analysis was estimated to be equivalent to 0.1 ml of solution for a t i t r a t i o n volume of 5.0 ml, or about 2 per cent. P r i o r to a series of experimental runs, a 250 ml erlen- meyer flask was prepared for each sample that was to be taken. A volume of 0.1 N sodium hydroxide corresponding to the expected CO2 content was drained from a burette into each f l a s k , a few drops of indicator were added, and the flask was then sealed with a stopper. During the sampling, the t i p of the pipette was kept below the caustic surface to avoid loss of CO2. The sample flasks were sealed and set aside for t i t r a  t i o n when the experimental runs had been completed. CO2-Ethanol and (X^-Ethylene g l y c o l For the absorption runs with the CO^-ethanol and CO2- ethylene g l y c o l systems, the method of analysis for the dissolved CO2 was i d e n t i c a l with that outlined above for CO2 dissolved i n water. Before the method was adopted for ethanol and ethylene g l y c o l , however, i t was necessary to show that the reaction of CO2 with sodium hydroxide produced the same reaction i n these two l i q u i d s , and that the mixed indicator 134 changed colour at the carbonate-bicarbonate end point for both liquids. The suitability of the procedure was tested by using solutions of water containing increasing proportions of ethanol (or ethylene glycol). Equal quantities of sodium carbonate were dissolved in pure water, and in a number of ethanol-water solutions with increasing ethanol content, and pH curves for titration with acid were obtained. The same procedure was followed in the preparation of solutions of water and ethylene glycol. Figure 6 (p.107) shows the resulting titration curves for the ethanol solutions, and the titration volumes for the ethylene glycol solutions. In both cases the analysis of the carbonate was independent of the liquid concentration. In fact, the carbonate-bicarbonate end point was somewhat sharper in solutions containing ethanol than in water itself. For the CX^-ethanol experimental runs sample volumes of 25 and 50 ml were taken, because the solubility of (X>2 was considerably higher in ethanol than in water. The solubility of CO2 in the ethylene glycol was much closer to that in water so that 100 ml samples were taken for runs with this system. He-Water For the absorption runs with the He-water system the water was continuously sampled and analyzed at both the inlet and 135 X a. 0.068 GM. Na_C0 DISSOLVED IN Cm O WATER 5 0 % WATER - 5 0 % ETHANOL 6 12 ML. 0.1 N HCI F i g u r e 10. pH C u r v e s f o r C a r b o n a t e T i t r a t i o n i n S o l u t i o n s o f W a t e r a n d E t h a n o l 136 THERMOMETER ABSORPTION TUBE (L -80 ML. BURETTE AS BUBBLE METER SOAP RESERVOIRS 25 ML. GRADUATED CYLINDER- 1 FOR CALIBRATION OF HELIUM ANALYZER -1000 ML. FLASK -FRITTEO-GLASS .BUBBLER - HELIUM-3ATURATE0 WATER -MOORE DIFFERENTIAL FLOW CONTROLLER : NEEDLE VALVE f PRESSURE REGULATORS ' -HOKE I /  T.C.-CELL GO*—MAC TYPE HIS MODEL 9220 S-WAY COCK : SILICA GEL DRIER STRIPPING COLUMN —GLASS TUBING, 5 MM. NOMINAL — CONSTANT-LEVEL OVERFLOW STRIPPING COLUMN SPECIFICATIONS: (1) 12 MM. NOMINAL GLASS TUBING (2) PACKING, 6 MM. GLASS HELICES TO DEPTH OF 20 INCHES IS) CO, RATE APPROX. TS ML./MIN. 14) SAMPLE RATE APPROX. SML./MIM. C0 2 CYLINDER- A 6 ELECTRICAL CIRCUIT FOR TC.-CELL —o o POTENTIOMETER (UP TO I.SMV.) Figure 11. Flow Diagram for Helium Analyzers 137 outlet sample locations by means of two identical specially designed He analyzers. The operation of the analyzers entailed the counter-current stripping of the He from the water in minia ture packed columns using CO^ as a carrier gas. The column effluent water, stripped of its He, was discarded, while the effluent CC^, containing the He, was passed through a calibrated TOcell for analysis. A flow diagram for one of the units is shown in Figure 11. Accurate analysis for He depended on maintaining the flow rates of both the water sample and CCX, stripping gas constant, and then measuring them accurately. To keep the liquid sample flow constant a constant-head overflow tube was installed above the stripping column. A sample flow was continuously withdrawn through a 2 mm diameter plastic sample line. A portion of the stream was passed into the stripping column while the remainder was allowed to overflow by way of the constant-head tube. The rates of both streams were controlled by small Teflon needle valves. The constant-head tube, pro viding a low and constant liquid head, enabled accurate flow control into the stripping column. The column itself was constructed from a 24-inch long 12 mm nominal OD section of glass tubing with enlarged inlet and outlet sections. The column was packed to a depth of 20 inches with 6 mm glass helices. The water level was kept constant in the bottom of the column by an inverted U-tube with a small hole blown at the top of i t to eliminate a siphoning effect. The liquid sample flow was measured at the column effluent line by means of a 25 ml graduated cylinder and a stop watch, and maintained between 7 and 11 ml per minute. A constant flow rate of CO^  to each stripping column was accurately maintained by a Moore constant-differential flow controller, in conjunction with a high quality 40-turn Hoke needle valve. The flow of CC^  to each column was passed through the reference side of the TC-cell then up through the column, through a silica gel dryer, and then through the measuring side of the TOcell. The CC^  flow rates were measured by soap-bubble meters installed downstream of the TC-cells. The flows were maintained in the range from 60 to 75 ml per minute. Good stripping was expected in each of the columns because of the low water flow rates and relatively high gas flow rates. The stripping action was enhanced by keeping the concentration of the He in the CO2 very low, less than 0.01 mole fraction for all analyses, so that the driving force for stripping was always nearly the maximum. Both of the TC-cells were calibrated by using water saturated with He, 139 MV= POTENTIOMETER READING, MILLIVOLTS Figure 12. He Analyzer Calibration Curve 140 and passing various measured flow rates of the He-saturated water through each of the stripping columns. For one column, the calibration was repeated using packing depths in the column of 12.75, 16, and 20 inches. The three resulting cali brations gave a single line. All these calibrations are shown in Figure 12, and supporting data are listed in Table IIX-3 of Appendix III. The fact that the various depths of packing gave identical calibrations for the one column, indicated that the stripping of the He from the water was essentially complete even for the 12.75-inch packing depth. The calibration of the TC-cells with He-saturated water was simplified because of the nearly constant (although small) solubility of He in water with changing temperatures. The electrical circuit for each of the TC-cells shown in Figure 11 (p.136) was a standard one for such detectors. A current of 140 ma was supplied to the heating circuits of both TC-cells. In each case the same milliammeters were used during calibration and subsequent analyses so that any absolute errors in the milliammeter readings were not reflected in the analyses. The TC-cell signals were measured by two Student potentiometers graduated in divisions of 0.1 mv. The zero reading of the TC-cells was taken when the water in the equip ment had been deaerated for a period of at least 1/2-hour. 141 The flow of He was then started through the equipment and the experimental runs were allowed to proceed. Because of the very rapid sampling and the analysis possible with the TC-cells, only 15 to 20 minutes elapsed between successive pairs of concentra tion measurements. At the completion of a series of measure ments the flow was stopped, and the water in the equipment was again circulated for about 1/2-hour for a check on the zero positions of the TC-cells. Any shift of the TC-cell potential readings, usually small, was corrected for by assuming a drift linear with time. The TC-cell method for the analysis of the He in water as employed in this research was considered highly successful in view of the problems normally encountered during analyses of this type. The maximum probable error of analyses was estimated to be about 4 per cent of the measured values. Preparation and Maintenance of Standard Solutions The 0.1 N sodium hydroxide and hydrochloric acid solutions used for the volumetric analysis of CO^  were prepared by diluting commercially prepared sealed ampoules of the concen trated liquids. The solutions were prepared in large quantities of about 8 to 10 liters of the sodium hydroxide and 3 to 4 liters of the acid. To check the normality of the sodium hydroxide solution a standard solution of potassium acid 142 phthalate was prepared. The concentrated liquids, as supplied by The British Drug Houses (Laboratory Chemicals) Company, were specified to have a maximum concentration tolerance on dilution of 0.1 per cent. The concentration of the initial batch of the standard caustic was determined using the potassium acid phthalate standard and was found to be within the 0.1 per cent tolerance specified by the supplier (British Drug Houses Ltd.). The concentration of the diluted acid prepared in the same way as the caustic was within the same limit of accuracy when titrated with the standard sodium hydroxide. Thereafter, when new batches of the 0.1 N acid and base were prepared from ampoules of the concentrated materials, by suitable dilution, they were titrated one against the other. If the titration volumes were within 0.4 per cent of One another (or within 0.1 ml in 25-ml volumes), the concentration of both solutions was assumed to be, therefore, 0.1000 T 0.0004 N. The normal procedures for ensuring that the standard solutions were carbonate-free were followed. The ampoules of concentrated caustic were guaranteed by the suppliers to be carbonate-free, and on testing after dilution with specially prepared C02~free water, a negligible amount of carbonate was found. Special precautions were taken to keep the stock solutions of standard acid and base in a carbonate-free 143 condition. Concentration changes of the standard solutions over a period of three months were n e g l i g i b l e . 144 TREATMENT OF DATA The absorption data were obtained as mean or "mixing cup" concentrations at the extremities of the test section. Pressure measurements were also obtained to permit the c a l c u l a t i o n of absolute pressures at the i n l e t and ou t l e t . In the following section, the methods of c a l c u l a t i n g the NTU (number of transfer u n i t s ) , and the mean volumetric gas flow rate for the absorption tube te s t i n t e r v a l , are presented and discussed. At a constant temperature, pressure, and constant condi tions of contacting, the d r i v i n g force for absorption would be expected to decrease along the absorption tube due to* an increas ed concentration of absorbed gas i n the l i q u i d . For a l l experi mental runs the absorption temperature was measured and found to be e s s e n t i a l l y constant, the pressure change i n the te&fc section, also measured, was found to be small with respect to the absolute pressure, and the volume of gas absorbed when compared with the t o t a l gas flow through the tube was.also usually small. Except for the concentration i n the l i q u i d , therefore, i t appeared that with reasonable accuracy the ; conditions along the tube could be taken as constant at the i r average values. For such a system, where the p o t e n t i a l ( d r i v i n g force) i s l i n e a r i n the v a r i a b l e defining the amount 145 transferred, the logarithmic mean potential applies over the entire tube length (54). If the properties of the liquid were changed appreciably by the presence of the absorbed gas, then the logarithmic mean driving force would be inaccurate. To conclusively determine whether the amount absorbed was, in fact, linearly dependent on the logarithmic mean driving force over the entire concentration range, an experimental test was carried out using the CO^ -water system at constant gas and liquid flow rates but with increasing inlet concentrations of absorbed gas. The variation in inlet concentrations was achieved by changing the boiling rate in the vacuum stripper. Table 9 shows the experimentally obtained values of logarithmic mean concentration driving force and amounts absorbed (as well as the conditions of the experiments). Figure 13 graphically shows the results, which clearly show the linear relationship. The range of concentrations for this test far exceeded those covered in most of the experimental runs, and hence the use of the logarithmic mean driving force for absorption in this work appears to be well justified. It follows from the , definition of NTU that the values of NTU must be independent of the concentration of the entering liquid, when calculated from the quantity of gas absorbed and the logarithmic mean driving force. The calculated values of NTU for the tests 146 TABLE 9 AMOUNT OF C02 ABSORBED AND LOGARITHMIC MEAN DRIVING FORCE Absorption tube: 1.757 cm ID; test section 7.983 ft Sample size: 100 ml; 1.0 ml 0.1 N NaOH equivalent to 1,0 milli moles per litre Flow rates: water, 1.50 gpm; C02» 86.5 cfh (slug flow) Barometric pressure: 764.5 mm mercury Run Amount absorbed millimoles per litre Concentration driving force millimoles per litre LMDF millimoles per litre NTU In Out 901 8.80 42.0 32.4 37.2 0.237 902 8.80 42.1 32.5 37.25 0.236 903 7.15 34.45 26.5 30.47 0.235 904 7.10 34.55 26.65 30.6 0.232 905 4.4 22.1 17.9 20.0 0.220 906 4.75 22.95 17.4 20.2 0.235 907 2.9 13.5 9.8 11.65 0.249 908 2.8 13.4 9.'7 11.60 0.241 147 0 2 4 6 8 10 'C -C . ABSORPTION IN TEST SECTION, MILLIMOLES PER LITRE Figure 13. Quantity of Absorption for Varying Inlet Concentrations and Logarithmic Mean Driving Force 148 described above are also listed in Table 9, and can be seen to be essentially independent of inlet concentration. The defini tion of NTU applicable to this work is then, (C 9 - C-.) k, (A) NTU - — 2- ir — = - L - — (7) (Cf - Cx) - (C% - C 2 ) Qg i n 4 ^ £ l c2 " c2 where C^, C 2 = inlet, and outlet concentrations, millimoles per litre 4e "k C^s C 2 = inlet, and outlet saturated concentrations, millimoles per litre kj^  = mass transfer coefficient, cm sec 1 2 A = interfacial area, cm 3 — 1 - liquid volumetric flow rate, cm sec As stated above, the assumption was made that the conditions for mass transfer along the test section were essentially constant. Some gas was in fact absorbed in the test section, however, as well as in that portion of tube upstream of the test section, teoaeseer, decreasing the total quantity of gas flowing, and, in addition, the pressure along the tube did change, even i f only by a small amount relative to the absolute pressure. These factors were taken into account in calculating the mean gas volumetric flow through the test section. The 149 amount absorbed i n the entrance section was calculated by assuming that the same flow pattern and transfer conditions existed there as i n the remaining portion of the tube, and that, therefore, the NTU per unit length of entrance likewise was the same. From the NTU i n the test section, the amount of absorption therein, and the length, the appropriate con centration d r i v i n g force, and the amount of absorption were calculated for the entrance section. I t can be shown that the amount of absorption i n the entrance section i s c l o s e l y given by the following expression, where C N = tube i n l e t concentration (millimoles per l i t r e ) E = length of entrance, f t L «= length of test section, f t NTU = number of transfer units i n test section The arithmetic mean quantity of gas flowing through the te s t section i s then given by, c l " c 0 g (NTU) (C * - C L ) 1 - ~ f (NTU) (8) = test section i n l e t concentration Ci = test section i n l e t saturated concentration (Q G)m - QQ - f [ ( C T - C 0 ) - h(C2 - Ci)] (9) 150 where (QQ) m mean dry gas flow in test section, cfh at 15 C, 756 mm gas flow at tube inlet, cfh at 15 C, 756 mm conversion factor, from millimoles CO2 per litre o liquid, to gas volumetric units, cfh at 15 C, f 756 mm (depends on liquid rate and gas solubility). The final correction for the mean gas volumetric flow was that for temperature and pressure, which was simply a conversion from cfh at 15°C and 756 mm to the actual absorption temperature and actual mean test section pressure. The above calculations were incorporated in the main IBM 1620 computer programs which were used in processing all the absorption data, and which are listed separately in Appendix IV for the different gas- liquid systems. The experimental data and calculated values for all the runs as listed in Appendix V include the actual quantitative corrections to the gas volumetric flow resulting from transfer into the absorbing liquids, and the test section pressures being different from those at which the flows were originally measured. The magnitude of these corrections was usually small in comparison to the total gas flow rates in the absorption tubes, the maximum occurring for the C^-ethanol system, for which the gas solubility was greatest. 151 EXPERIMENTAL RESULTS In this section the experimental results are shown graphi cally on logarithmic plots of NTU and mean gas superficial velocity (VQ), at constant liquid rates. The range of gas velocities at each liquid rate includes the regions of bubble, plug, slug, and (sometimes) annular flow. A graph showing the effect of entrance type is also included. Lines drawn through the data points on all of these graphs are visually estimated mean representations. The computations of NTU, mean gas superficial velocity, and other information from the raw experimental data were accomplished by means of an IBM 1620 computer. The FORTRAN programs for these computations are given in Appendix IV. In Appendix V are to be found the raw experimental measurements and calculated data for various systems, from which all the values were taken for the plotted graphs. The experimental data for each series of runs (performed in a single day) include the gas and liquid flow rates, flow region, the titra tion volumes, pressures (or pressure drops) for the inlet and outlet locations of the test section, tube diameter, absorption temperature, and barometric pressure. The calcu lated values include the amount of absorption, logarithmic mean concentration dr i v i n g force, NTU, mean gas volumetric flow, gas volumetric correction, and mean gas s u p e r f i c i a l v e l o c i t y . Effect of Gas Density A graph of the absorption curve for the CO^-water system, obtained from measurements taken at a single l i q u i d rate but at two absorption pressures (10 and 20 p s i a ) i s shown i n Figure 1 in the section on Theoretical Aspects. The absorption condi tions were as follows: temperature, 15°C, tube diameter 1.757 cm, and l i q u i d flow rate 1.07 gpm. When the gas s u p e r f i c i a l v e l o c i t y i s used as the ordinate, the data for both pressures f a l l c l o s e l y on a single curve. Absorption Curves at Three L i q u i d S u p e r f i c i a l V e l o c i t i e s Absorption data were obtained at three s u p e r f i c i a l l i q u i d v e l o c i t i e s for each of the four g a s - l i q u i d systems, CX^-water, He-water, C02-ethanol, and C0 2-glycol using the 1.757 cm absorption tube. Absorption data were also obtained using the C02~water system for two additional tube s i z e s , 1.228 and 2.504 cm i n diameter, and at the same three v e l o c i t i e s . To permit comparisons of the absorption behaviour for the dif f e r e n t systems at the same l i q u i d s u p e r f i c i a l v e l o c i t i e s three separate graphs are given. In Figures 14, 15, and 16, absorption curves at s u p e r f i c i a l l i q u i d v e l o c i t i e s of approxi mately 0.5, 0.9, and 1.8 fps, respectively, are shown. The effects of the primary variables cannot be observed d i r e c t l y by an inspection of these graphs since the primary variables could not be independently varied, as discussed i n some detail, i n the section on the Design of Experiments, so that i n most cases combinations of effects only can be observed. The values of l i q u i d phase d i f f u s i v i t y , surface tension, and l i q u i d phase v i s c o s i t y , for each of the ga s - l i q u i d systems corresponding to the absorption curves shown i n Figures 14, 15, and 16, can be obtained from Tables 3, 4 S and 5. Effect of Increased L i q u i d Flow Rate Absorption data for the -water system using the 1.757 cm tube were obtained at three l i q u i d s u p e r f i c i a l v e l o c i t i e s i n addition to the three already mentioned, namely at 1.2, 2.6 and 3.6 fps. The r e s u l t i n g absorption curves, including a r e p e t i t i o n of the one for a l i q u i d s u p e r f i c i a l v e l o c i t y of 0.5 fps, are shown i n Figure 17. 1.0 CT> z z o o.l H o UJ to I-co UJ z 0.01 i r O CO-WATER 2 O HE-WATER O C0-ETHAN0L A CO.-GLYCOL, 30 °C • CO^GLYCOL, 15 • C. } © CO^WATER; 0 CO-WATER i 2 T—r~r >TU8E = 1.757 CM. I.D. TUBE * 1.228 CM. 1.0. TUBE * 2.504 T " i r i i1 • • ' • - i ..-t .t-.J..-a- =L • • • ' • 0.1 1.0 \g, SUPERFICIAL GAS VELOCITY, FT./SEC. 10.0 Figure 14. NTU vs Gas Superficial Velocity, for Liquid Superficial Velocity of 0.5 fps £ I I I I I I I I I I I 1 I — I I I I I 0 01 * 1 ' 1 1 • • • I ' ' . . i . i ' I • 0.1 1.0 10.0 Vf, SUPERFICIAL GAS VELOCITY, FT./SEC. o Figure 15. NTU vs Gas Superficial Velocity, for Liquid Superficial Velocity 0.9 fps CM CM 01 O z z o t-o LU CO CO 0.01 OJ ^ 1.0 10.0 V», SUPERFICIAL GAS VELOCITY, FT/SEC. M Figure 16. NTU vs Gas S u p e r f i c i a l Velocity, for L i q u i d S u p e r f i c i a l V e l o c i t y of 1.8 fps \g SUPERFICIAL GAS VELOCITY, FT./SEC. Figure 17. E f f e c t of Gas and L i q u i d Flow Rates for the CC^-Water System 158 Effect of Entrance Type The effect of the type of entrance was measured using the "Water system and the 1.757-cm tube. In addition to the standard horizontal tee entrance, three other types of entrances were used (please refer to Figure 5). The amount of absorption was determined in the test section for each of the entrances using three particular gas flow rates, a constant liquid rate, and (except for the type of entrance) identical absorption conditions. The entrance types provided widely different mixing characteristics. It was therefore expected that i f the type of entrance in any way affected the absorption rate downstream of the entrance, this would have been readily observable. The resulting amounts of absorption in the test section, correspond ing to the different entrances, are shown in Figure 18 as Values superimposed on the absorption curve for the equivalent conditions of flow and the regular type of entrance. Effect of Temperature on Absorption Rate A number of additional absorption runs were performed using the CX^ -water system, and the 1.757-cm absorption tube, but at three other temperatures, 5.3, 30.0 and 45.0°C* For these experimental runs the liquid rate was held constant at 1.07 V°, SUPERFICIAL GAS VELOCITY, FT./SEC. 6 Figure 18. Effect of Entrance Type on the Absorption Rate for the COo-Water System 160 gpm (equivalent to a superficial liquid velocity of 0.9 fps). The effect of temperature in these experiments should be largely that of the resulting changes in the liquid phase diffusivity, and liquid viscosity, since the corresponding change in surface tension is small. These data were not included when correlations were developed, but were used as a check on the reliability of the correlating expressions for predicting the behaviour of the CC^ -water system. 161 DEVELOPMENT OF CORRELATIONS The extreme differences between the bubble and slug flow regions, i n hydrodynamics, shape of the interface, and mechan isms for mass transfer, suggests the treatment of these two regions as d i s t i n c t i v e l y separate contacting processes. In the following sections two d i f f e r e n t correlations w i l l be presented, one pertaining to the bubble region and extending at least i n part into the plug region of flow, and the other representing slug flow behaviour but including part of the plug region, and extending at lea s t to the slug-annular t r a n s i t i o n . Both correla tions are p a r t i c u l a r l y designed to i l l u s t r a t e , as far as possible, the major flow c h a r a c t e r i s t i c s and probable transport mechanisms of th e i r respective regions, rather than to merely give an empirical description of experimental data. The corre l a t i o n pertaining to the bubble-plug region was obtained by dir e c t deduction from observed q u a l i t a t i v e and quantitative experimental f a c t s . This c o r r e l a t i o n i s more general than that for the slug region and, i n a l l p r o b a b i l i t y , therefore, can be extrapolated without much loss i n accuracy. The co r r e l a t i o n for the slug region, on the other hand, was purposely r e s t r i c t e d to a narrow region of l i q u i d rates for which the r e l a t i o n between NTU and gas s u p e r f i c i a l v e l o c i t y , at constant l i q u i d rates, was 162 l i n e a r on an arithmetic p l o t . Because of t h i s r e s t r i c t i o n , i t was possible to obtain an unusual insight into the mechanisms of mass transfer and support for the theory proposed by Ki s h i n e v s k i i (discussed previously) for highly turbulent trans fer processes. The general c r i t e r i a for extrapolating the slug c o r r e l a t i o n can be q u a l i t a t i v e l y deduced, however, as considered i n the section on Discussion and Conclusions. These develop ments w i l l now b e discussed i n d e t a i l . In the development of a mass transfer c o r r e l a t i o n for the bubble region, a t y p i c a l test section containing many bubbles w i l l be considered. For t h i s transfer process, where the log arithmic mean concentration d r i v i n g force applies, the material balance for C0 o has the form, Bubble Region N A - C£ (C 2 - C X) - k L(A) (10) where: N A = transfer rate, millimoles sec Q£ = l i q u i d s u p e r f i c i a l flow, ml sec -3 C = concentrations millimoles cm A <= i n t e r f a c i a l area i n test section, cm" 163 k^  = transfer coefficient, cm sec 1 To avoid consideration of the actual concentrations and mean con centration driving forces in the test section, expression (10) can be rewritten to a good approximation as, Q° NTU = kL(A) (11) It is recognized that the transfer coefficient in the above expressions i s i n a l l probability dependent on the square root of the product of the liquid diffusivity and surface renewal rate, according to the penetration theory model. The development will first be undertaken for the case for which the volumetric liquid feed rate is constant, and also con siderably greater than that of the gas rate, ( O L ^ ^ O ^ ) * T ^ E absorption curves for such a situation can be observed In Figure 16. Two assumptions will be made concerning the frequen cy and shape of the bubbles produced with varying gas rates, in accordance with the discussion in the section on Theoretical Aspects. First, the frequency of the bubbles remains constant with an increasing gas rate at constant liquid rate and there fore, the increase in bubble volume is directly proportional to the volumetric rate of flow. This assumption is based on qualitative observations that not only for one liquid, but for all liquids tested, at the same superficial liquid velocities, 164 the frequency of the bubbles appeared to be approximately con stant. The second assumption i s that the bubbles maintain geo metric s i m i l a r i t y while increasing i n size with increasing gas rates. As pointed out e a r l i e r , the amount of transfer area would be expected to be proportional to the 2/3 power of the gas volumetric flow rate for bubbles which expand uniformly i n a l l dimensions, or nearly d i r e c t l y proportional to the gas rate for plugs expanding unidimensionally with increased gas flow. The f i r s t s i t u a t i o n corresponds approximately to low r a t i o s of gas to l i q u i d volumetric flow rates, while the plug case corresponds to higher r a t i o s . The values for the NTU for a l l the l i q u i d s used, at a con stant l i q u i d v e l o c i t y , show the same approximate dependence on the s u p e r f i c i a l gas v e l o c i t y . For example, t h i s s i m i l a r i t y for two l i q u i d s of widely d i f f e r i n g v i s c o s i t y i s w e l l shown i n Figure 16 for water and ethylene g l y c o l . Such a s i m i l a r i t y of behaviour with gas v e l o c i t y , together with the observed constant bubble frequency at a constant l i q u i d rate, implies that k^, the transfer c o e f f i c i e n t , must be reasonably constant i n a given gas-liquid system as the gas v e l o c i t y increases, and the observed v a r i a t i o n i n NTU with gas flow i s a consequence largely of changes i n i n t e r f a c i a l transfer area, at least at low gas rates. Additional support for t h i s conclusion may be drawn from 165 experimental observations made concerning the mixing effects in bubble flow. These effects are illustrated in Figure 9 for horizontally flowing bubbles in ethylene glycol. Even in this case, where the superficial liquid Reynolds number was about 200, the mixing and eddying due to "induced turbulence" was rather astoundingly vigorous. Any local concentration differences would be quickly and efficiently dispersed by this action, and the concentration profiles actually measured in the glycol solutions, shown in Figure 8, confirm this conclusion. For any liquid, therefore, flowing at a constant rate, changes in bubble size would be expected to have much less effect on the transfer rate than changes in bubble frequency. Although it is difficult to describe quantitatively the shapes and surface areas of the bubbles as gas flow varies, some useful relationships can be derived. The surface area of n each bubble has already been shown to vary as (QQ) , where n has values between 2/3 and 1. The surface area in a test sec tion of length, L,, and containing a certain number of bubbles, will be proportional to the number of bubbles times the area of each bubble , that is, A Q C ~ (Qg)n (12) B where f is the bubble frequency, sec \ and Vw is the bubble 166 v e l o c i t y . The bubble frequency appears to depend primarily on the l i q u i d flow rate, QL, and so i t can be assumed that f OC m (Q L) . The bubble v e l o c i t y , Vg, i s proportional to the true average l i q u i d v e l o c i t y , (VQ + v £ ), so one can also express o o ^ t h i s p r o p o r t i o n a l i t y as VgQC (QG + \) • Making these substi tutions i n (12), m A eg ( Q l ) L (Qg)" (13) (Q£ + Qg)P The transfer c o e f f i c i e n t , k^, for a submerged object i s known to be generally a function of the degree of turbulence in the ambient f l u i d , and hence for t h i s case of h o r i z o n t a l l y moving bubbles, i t must depend strongly on the number of bubbles per unit length of tube because of the induced turbulence, due to presence of these bubbles, and probably to a rather lesser degree, on the true average l i q u i d v e l o c i t y i t s e l f . On these assumptions, one can write, ( o £ ) q The k^ i s the part of the transfer c o e f f i c i e n t dependent on parameters other than the flow quantitiesv The above relationships are now substituted into equation (11) giving, <£ N T U - ^  OCT 4, <o£> b (QE + Q8>J 167 (Oft)" (15) For the case of Q£ ^ > QQ, that i s , for bubbles approaching spherical or e l l i p t i c a l shapes, "n" i n the above equation should have a value of approximately 2/3. I f the exponent "b" i s assumed to be equal to unity, than equation (15) assumes a p a r t i c u l a r l y simple form, 2/3 Q° NTUock^(Q°) (16) and t h i s expression should apply for a l l l i q u i d rates at low gas rates i n a given system. A logarithmic plot of Q£(NTU) VS QQ* for the CO^-water system i s shown i n Figure 19. Values of Q^(NTU) (which are equal to k^A) can be seen to f a l l on a single l i n e i n the region of low gas rates for a range of l i q u i d volumetric flow rates from 5 to 34 cfh. This provides a good deal of support for the foregoing assumptions i n general, and p a r t i c u l a r l y for the assumption that the exponent, b, can be taken as equal to unity. Equivalent tests for the effect of l i q u i d and gas flow on the mass transfer rate for a l l other gas-liquid systems investigated yielded e s s e n t i a l l y i d e n t i c a l r e s u l t s . In a l l cases the exponent "n" for low gas flow rates had a value approximately equal to 2/3. Figure 19. Effect of Liquid Flow Rate at Low Gas Rates, on the Rate of Absorption Using the CC^ -Water System 169 As the gas flow rate increases relative to the liquid flow, the slope of the k^(A) vs QQ curve should become a decreasing function of QQ as the gas volumetric flow becomes of the same order of magnitude as the liquid flow. If the exponent, a, is sufficiently large, that is, greater than 2/3, then when o o G^'^ L^* maximum values of the quantity kL(A) might be observed. This maximum would show most clearly at low liquid rates. If long plug flow occurred at flows of gas high relative to those of the liquid, (n^l), then it might be possible for k^(A) to become essentially independent of the gas rate. These charac teristics are exactly observed in Figure 19 for the lowest liquid rate. The inference is that the index, a, is greater than 2/3, and has a value between 2/3 and unity. The original equation (15) can be considerably simplified if the exponent, a, is taken as equal to unity, and the final correlating equation then becomes, I S (V£ + V°)NTUcC k^(V°) (17) This expression brings all the data for each of the gas-liquid systems into good agreement over wide ranges of the bubble and plug flow regions. The ability of equation (17) to bring together all the data for each of the gas-liquid systems studied, particularly those for C09-water and CO^-glycol, and for the 170 index, S, to be very nearly the same for a l l systems and between 2/3 and unity, provides considerable evidence that the model for mass transfer chosen for t h i s region of flow i s correct. The effects of the variables, d i f f u s i v i t y , v i s c o s i t y , surface tension, and tube diameter, were introduced into expres sion (17) as simple dimensionless r a t i o s with the basis of comparison being t h e (^-water system a t 15°C and the tube dimension of 1.757 cm i n diameter. Thus i n the bubble region the c o r r e l a t i n g expression for a l l the variables becomes: Z = (V? + V°)NTU i-i G (31 d r c r x i e /^ w x g x D w oC (V°) S (18) where: d i f f u s i v i t y (5 =» surface tension jJi = v i s c o s i t y D = tube diameter V°, V° = gas and l i q u i d s u p e r f i c i a l v e l o c i t i e s , fps G L indices: d - 0.50 e - 0.50 g - 0.14 h - 2.0 171 subscripts: w =» values for CX^water system at 15°C, tube diameter 1.757 cm x 8 3 equivalent property for each of the other gas-liquid systems and conditions. The powers chosen for the dimensionless ratios were those which tended to bring the data into closest agreement with the refer ence system. The experimental data as correlated using equa tion (18) were calculated by means of an IBM 1620 computer, and are graphically represented in Figure 20. A linear rela tionship on the logarithmic plot was. f i t t e d to these data, and the equation of the best straight line was f i t t e d by the method of least squares. The resulting equation is as follows: Z - (0.2024) (V°.)<°-8075> (19) Equation (19) was derived for a range of gas superficial velo c i t i e s from approximately 0.1 to 3.0 fps. This range included bubble flow and was extended well into the plug flow region. The number of transfer units for a length of tube 92.2 i n , can be predicted from equation (19) with a probable error not exceeding 15 per cent. 172 Figure 20. Correlation for Two-Phase Flow Absorption Rates for the Bubble and Plug Regions 173 Slug Region For the turbulent slug region an attempt was made to show quan t i t a t i v e l y that the degree of turbulence i t s e l f affected the extent to which the various system variables, d i f f u s i v i t y , v i s c o s i t y , surface tension, and tube diameter, influenced the rate of mass transfer. That i s to say, for example, that the ef f e c t on the transfer rate of the l i q u i d phase molecular d i f f u  s i v i t y was i n turn affected by the degree of turbulence. Such an i n t e r a c t i o n between the molecular properties, d i f f u s i v i t y , and v i s c o s i t y , at least would be expected i f either the K i s h i  nevskii theory, as discussed e a r l i e r , or some other transfer process i n addition to that of simple surface renewal, were operative i n the slug region of flow. The l i n e a r r e l a t i o n s h i p on an arithmetic plot of the NTU and gas s u p e r f i c i a l v e l o c i t i e s for e s s e n t i a l l y a l l the g a s - l i q u i d systems and conditions, made i t possible to r e a d i l y separate the e f f e c t s of the various v a r i a b l e s . Except for the experimental runs with the CO^-water system at two l i q u i d s u p e r f i c i a l velo c i t i e s exceeding approximately 2 fps, a good l i n e a r NTU-VQ relationship was obtained. The methods and reasoning which were used i n producing the p a r t i c u l a r type of empirical c o r r e l a t i o n developed here 174 are outlined in the following section. Figures 21, 22, and 23 show NTU and Vg data for a l l the gas-liquid systems, plotted on linear coordinates, each graph corresponding to a single superficial liquid velocity, respectively, 0.53, 0.91 and 1.79 fps. The values for these plots were taken directly from the best visually estimated lines through the actual experimental data of Figures 14, 15, and 16. Actual experimental data and appropriate computer programs could have been used for establish ing best straight lines fitted by the method of least mean squares; however, as subsequent analysis will show, the omission of such procedures does not significantly limit the accuracy of the overall results. The major underlying assumption for the slug region (which was also assumed in the bubble region) will be restated here. It is, at equal gas and liquid superficial velocities, the mass transfer rates are directly comparable and any difference in transfer rates that is observed for different systems, therefore, is the consequence of system variables other than flow. It is recognized that such an assumption becomes more dubious as the velocities of both phases increase,- generally increasing the probability of kinetic energy effects and flow interactions. In addition, it is known that the fraction of the tube volume occupied by liquid is governed not only by the flow variables, 175 Figure 21. Absorption Rate vs Gas Superficial Velocity for Slug Region at a Liquid Superficial Velocity of 0.53 fps 176 Figure 22. Absorption Rate vs Gas Superficial Velocity for Slug Region at a Liquid Superficial Velocity of 0.91 fps 177 Figure 23. Absorption Rate vs Gas S u p e r f i c i a l V e l o c i t y for Slug Region at a L i q u i d S u p e r f i c i a l V e l o c i t y of 1.79 fps 178 but to a lesser extent by viscosity and surface tension. An estimate of the effect of these liquid properties on the liquid volume fraction can be obtained from void fraction correlations such as those of Lockhart and M a r t i n e l l i (55), or Hughmark and Pressburg (56). The evidence that specific limits for the slug and slug-annular regions at f i x e d gas rates correspond approxi mately to constant values of the l i q u i d superficial velocity, i s also not completely convincing. Results obtained in these studies, however, indicate that the magnitude of the l i q u i d flow effects themselves, without changes i n any other of the liquid properties or conditions, i s small (but not negligible) in comparison to that caused by these other properties and condi tions. Referring to Figures 21, 22, and 23, for any one gas- l i q u i d system (and temperature), a variation in liquid super ficial velocity by a factor of more than three changes the o slope of the NTU-VQ line somewhat, but changes the magnitude of the actual value of NTU at a specific gas velocity by only a small amount compared to the changes in NTU between different gas-liquid systems. This is particularly evident when comparing the relationships for He-water and CC^-glycol. A further observation can be made from Figures 21, 22, and 23. Increasing slopes invariably correspond to increasing intercepts. An empirical equation suggested for each of the 179 systems, therefore, i s as follows: NTU + k = b c + b VQ = b (c * VQ) (21) where: b c - k = intercept at VQ = 0 NTU = number of transfer units for 7.683 f t of tube o V = gas s u p e r f i c i a l v e l o c i t y , fps G o b = slope of NTU-V-, relationship, and factor which G determines t h e p o s i t i o n o f the intercept; depends on physical properties for each of o the g a s " l i q u i d systems, and also on V^ c = proportionality constant which depends only on V°, for a l l g a s - l i q u i d systems k = single constant for a l l systems and conditions In equation (21) only the va r i a b l e "b" i s a function of the l i q u i d flow rate as well as of the properties of the gas-liquid systems. The variable "c" i s a function of the l i q u i d super f i c i a l v e l o c i t y only, and i s therefore constant for any one l i q u i d rate, while the constant "k" i s completely invariant with flow rates and system properties. The p a r t i c u l a r form of equation (21) was chosen because only the single variable "b" was dependent on the physical properties of the contacting f l u i d s . I t was therefore possible to r e l a t e the slopes of any two NTU-Vp straight l i n e s , corres-ponding to d i f f e r e n t properties but at the same l i q u i d super f i c i a l v e l o c i t y , d i r e c t l y to the e f f e c t of the difference i n the properties concerned. The determination of the constant "k", and va r i a b l e s , "b" and "c", involved an extensive t r i a l - and-error procedure. I t was somewhat s i m p l i f i e d because the value of the constant, "k", necessary to f i t the experimental data was obviously small. Because of the t r i a l - a n d - e r r o r procedure used s i t was easiest to evaluate the v a r i a b l e "c" for the three values of v £ . These values of 1 c", along with the e f f e c t of v£ on the v a r i a b l e "b", are graphically shown i n Figure 24. For the l i m i t e d range of l i q u i d flows, the e f f e c t of V ° on both of the quantities "b" and "c" i s l i n e a r . In the same way as was done for the bubble region, the effects of the d i f f e r e n t system variables were expressed as simple dimensionless r a t i o s , which appeared to best describe the experimental data. Separate exponents for these dimension less r a t i o s were determined, however, for each of the three l i q u i d rates, these rates corresponding to changes i n degree of turbulence. The c o r r e l a t i n g equation for the slug region, obtained by comparing the NTU-VQ slopes for the d i f f e r e n t systems, and based on l i q u i d s u p e r f i c i a l v e l o c i t i e s not exceeding 2 fps, i s then as follows: 182 X • NTU + k = F b (c + Vo) (23) where: k b c V° V° F - 0.014 0.0164 + 0.115(V°) 4.60 - 1.960(V°) liquid and gas superficial velocities, fps 1.0 for the CO2-water system at 15°C, tube diameter 1.757 cm F = P^W CTx .0~w Ac D, w D x g (24) where: diffusivity G- surface tension JU- viscosity D = tube diameter, cm w = values for the CX^ -water system at 15°C, tube diameter 1.757 cm x = equivalent property for each of the other gas- liquid systems and conditions For each liquid flow rate the exponents for the four dimensionless ratios were obtained by the general method out lined in the section on the Design of Experiments. The vari ability in the effects of the molecular properties, viscosity 183 and diffusivity, due to the changes in liquid flow rate, is most pronounced. Figure 25 graphically shows the changes of the exponents with the liquid flow rates, for the effects of the three physical properties and the tube diameter. The data for the values of the exponents which apply to equation (24) are also listed in Table 10. Figure 26 shows a plot of NTU and Vg for the (X^-water system for the two additional liquid superficial velocities exceeding 2 fps. The relationships are no longer linear. If values of the NTU at superficial liquid velocities exceeding 2 fps and for other gas-liquid systems are required, it seems likely that the CG^water curves shown in Figure 26 could be applied, and suitable extrapolated indices for use in equation (24) could be obtained from Figure 25, to give acceptable values for the mass transfer rates in this portion of the slug region. The gas superficial velocities for the proposed correla tion ranged from 2 to 40 fps, while the liquid superficial velocities ranged from 0.53 to 1.79 fps. A test for the pro posed correlation is graphically shown in Figure 27, where the experimental NTU values are plotted against those predicted by equations (23) and (24). The relatively small scatter from the 45° line, with a probable error of approximately 10%, indicates the satisfactory degree of correlation achieved. 0 0L5 1.0 L5 ZD V°, SUPERFICIAL LIQUID VELOCITY, FT./SEC. Figure 25. Exponents for Dimensionless Ratios in Equation (24) as Functions of Liquid Superficial Velocity 185 TABLE 10 EXPONENTS FOR DIMENSIONLESS RATIOS IN EQUATION (24), VARIABLE WITH LIQUID SUPERFICIAL VELOCITY V^  = liquid superficial velocity, fps Ratio Exponent V° - 0.53 V° - 0.91 V » - l . Diffusivity d 0.374 0.307 0.193 Surface tension e 0.151 0.228 0.193 Viscosity f 0.086 -0.028 -0.161 Tube diameter g 1.32 1.063 0.913 186 pi I 1— 1 1 I I I L _ I I 0 4 8 12 16 2 0 V°, SUPERFICIAL GAS VELOCITY, FT./SEC. 6 Figure 26. Graph of NTU vs Gas Superficial Velocity for the C02"-Water System at Liquid Superficial Velocities Exceeding 2 fps N T U , E X P E R I M E N T A L Figure 27. Correlation for Slug Region, Calculated vs Observed Values of NTU M oo 188 DISCUSSION AND CONCLUSIONS One of the major observations from t h e r e s u l t s o f t h i s investigation concerns the r o l e of turbulence with r e s p e c t t o the rates of mass transfer. The mixing a n d e d d y i n g e f f e c t s which have been observed i n ethylene g l y c o l a t s u p e r f i c i a l Reynolds numbers w e l l i n t h e laminar region i n d i c a t e t h a t " i n d u c e d turbulence'" c a u s e d b y c h a n g i n g d i r e c t i o n s of f l o w w i t h i n t h e b u l k o f the l i q u i d can b e a much more s i g n i f i c a n t source of mixing than that due to an a v e r a g e v e l o c i t y v e c t o r i n the d i r e c t i o n o f flow. F o r b o t h . t h e b u b b l e a n d s l u g regions, i t would appear that there are two major c a u s e s o f t h e a c c e n  tuated turbulence which seems to be a c h a r a c t e r i s t i c f e a t u r e of two-phase flow. They are f i r s t , the e f f e c t i v e l y c h a n g i n g cross-sectional area of the flow channel f o r e a c h p h a s e , a n d next the existence of a movable interface w h i c h permits an interaction of forces between the phases. The success of the model for l i q u i d s of widely d i f f e r i n g properties, which relates the source of turbulence i n b u b b l e flow to the presence of the bubbles themselves, suggests t h a t a simple Reynolds number based.on tube dimensions and the flows of one or both phases i s not a s a t i s f a c t o r i l y d e s c r i p t i v e quantity for the flow c h a r a c t e r i s t i c s for the. b u b b l e r e g i o n . 189 S i m i l a r l y i n slug or annular flow, a Reynolds number based on tube dimensions and true l i n e a r v e l o c i t i e s of one or both phases might be very use f u l , but i s again d i f f i c u l t to rel a t e to true two-phase flow c h a r a c t e r i s t i c s . For these reasons, the condi tions of flow have been described simply by phase s u p e r f i c i a l v e l o c i t i e s . I t i s probable that a "bubble" Reynolds number might be a s i g n i f i c a n t parameter i n bubble flow, but such a Reynolds number i s d i f f i c u l t to define e x p l i c i t l y because of the unsymmetrical nature of bubble flow. Because of i t s complexity, and lack of s i m i l a r i t y to that for single-phase flow, the mass transfer process i n two- phase flow would seldom appear to warrant treatment i n a manner simi l a r to that for single-phase flow. Mass transfer i n single- phase flow i s involved with transfer from a s o l i d boundary which i s (normally) immobile. The shear force at the wall i s mani fested as pressure drop and (for single-phase flow) i s well defined by the flow rate, physical properties, and channel dimensions. The transfer of both shear and mass occurs at the same location, at the channel w a l l , and i s governed by related flow c h a r a c t e r i s t i c s , and for t h i s reason relationships between mass and momentum transfer have been successful. In two-phase flow, on the other hand, although the shear at the wall i s also manifested as pressure drop as for single-phase flow (but not 190 so well defined), the mass transfer occurs at another location in the flow channel altogether, at the interface, and i s there fore dependent on the host of variables influencing the condi tions of the i n t e r f a c e . Further, as a r e s u l t of t h i s work, i t appears l i k e l y that the mechanism of transfer changes i n d i f  ferent regions of two-phase flow. Hence, for two-phase flow the relationships between shear at the wall and mass transfer at the i n t e r f a c e s i f they can be determined:, w i l l , i n a l l p r o b a b i l i t y , b e highly complex. The methods of study most l i k e l y to be successful i n two-phase flow are those which are fundamental in nature, and which avoid d i r e c t comparison with the usually completely d i s s i m i l a r phenomena for single-phase flow unless such a comparison i s l o g i c a l l y j u s t i f i e d . Bubble Flow The physical model as developed for bubble flow i n the section on Development of Correlations, and the r e s u l t i n g c o r r e l a t i o n as described by equation (18) w i l l be discussed i n t h i s section. One of the most s i g n i f i c a n t factors i n these results i s the dependence of the transfer rate on the l i q u i d phase d i f f u s i v i t y to the 0.5 power. This gives strong support to the usefulness of the surface renewal or penetration theory models for mass transfer i n t h i s region. The 0.5 exponent for 191 the d i f f u s i v i t y r a t i o i s further substantiated by applying the bubble flow c o r r e l a t i n g equation to the CO^-water res u l t s obtained at various temperatures. As indicated e a r l i e r , absorp t i o n data were obtained at one l i q u i d rate, 1.07 gpm, one tube o si z e , 1.757 cm, and at three temperatures ( i n addition to 15 C), 5.3°C, 30°C, and 45°C. For th i s range of temperatures, the v i s  c o s i ty ranged from 0.60 cp to 1.50 cp, while the l i q u i d d i f f u s - -5 -5 2 -1 i v i t y ranged front 3.08 (10 ) to 1.07 (10 ) cm sec . As would be expected, the temperature v a r i a t i o n had only a small e f f e c t on the surface tension. The exponent on the v i s c o s i t y r a t i o i n the c o r r e l a t i n g equation (0.14) was small, so that the v i s c o s i t y e f f e c t on the absorption rate would be expected to be likewise, small. The approximately three-fold v a r i a t i o n in d i f f u s i v i t y was used as a further check on the e f f e c t of d i f f u s i v i t y on the absorption rate. Figure 28 shows a plot of the least mean squares l i n e and the 15% probable error l i m i t s for the bubble flow c o r r e l a t i o n , and the CX^-water data obtain ed at the various temperatures. The fact that these l a t t e r data f a l l exactly on the same c o r r e l a t i n g l i n e constitutes an independent check of the a p p l i c a b i l i t y of the c o r r e l a t i n g equa tion p a r t i c u l a r l y with respect to the e f f e c t of l i q u i d phase d i f f u s i v i t y on the mass transfer rate i n bubble flow. There i s what appears to be an anomalous e f f e c t of v i s c o s i t y 192 Figure 28. Application of the Bubble Flow Correlation to CC>2-Water System Data at Various Temperatures 193 on the transfer rate in the bubble region. One might expect that the assumption that the degree of turbulence is a result of the number of bubbles or "mixing stages", i f not completely accurate, would err in the direction of reduced turbulence with increased viscosity. From expression (18) it is noted that the index of the viscosity ratio although small ( 0 . 1 4 ) as might be expected, is in the direction which indicates an increased transfer rate with nigher viscosity liquids. The likely explan ation might be that for more viscous liquids a greater fraction of the area of each bubble is exposed to the liquid. For ethylene glycol the assumption that a constant fraction of each bubble supposedly ineffective for mass transfer because of direct contact with the tube wall, may not be accurate. Because of the liquid viscosity, as each bubble moves, more time may elapse for the drainage of liquid down the sides of the tube, in this way effectively increasing the fraction of interfacial area per bubble available for mass transfer. This appeared to be at least qualitatively true from visual observa tion of bubble flow with ethylene glycol. The increase in transfer rate for the more viscous liquids would then be a direct consequence of an increased interfacial area. For large "chain bubbles" rising up through a liquid, two observations which appear pertinent to this work have been 194 reported by Calderbank (57). The f i r s t i s that l i q u i d phase mass transfer c o e f f i c i e n t s for a continuous sequence of bubbles r i s i n g through a depth of l i q u i d are found to be appreciably greater than those for i n d i v i d u a l bubbles, which are equal i n size and under otherwise i d e n t i c a l conditions. The difference i s ascribed to the eff e c t of the bubbles wakes which leave the l i q u i d in a more turbulent state i n the case of the "chain bubbles". This e f f e c t gives more credence to the phenomenon referred to as "induced turbulence" i n horizontal bubble flow. The second observation made by Calderbank i s that the l i q u i d phase c o e f f i c i e n t s of mass transfer for large bubbles r i s i n g in a l i q u i d can be expressed by the common type of relati o n s h i p : ShoC ( S c ) 0 ' 5 (Re) n (25) where: Sh = Sherwood number Sc m Schmidt number Re = Reynolds number n - 0.77 Another explanation for the observed dependence on v i s c o s i t y of the mass transfer rate i n a two-phase bubble flow i s that the i n t e r f a c i a l area remains constant, and that equation (25) is applicable. For such a s i t u a t i o n , whatever the true d e f i n i t i o n 195 of the Reynolds number, the exponent "n" would of necessity have to be less than 0.5 (actually 0.36) i n order for the observed net dependence of the transfer rate to be d i r e c t l y proportional to the l i q u i d v i s c o s i t y to the 0.14 power. Mass transfer c o e f f i c i e n t s increasing with v i s c o s i t y have not been reported i n any of the reviewed l i t e r a t u r e . I t appears most l i k e l y , therefore, that the f i r s t explanation for the e f f e c t of v i s c o s i t y i s the more probable. As indicated i n the section on Theoretical Aspects, one would probably expect that bubbles i n l i q u i d s having lower surface tensions, but otherwise having comparable physical conditions and properties, would be longer and thinner and hence provide a larger i n t e r f a c i a l area per bubble. In comparing the r e s u l t s for the CC^-ethanol and CC^-water systems a s l i g h t l y higher transfer rate for the (^-ethanol systems might be expected, therefore, a f t e r accounting for the difference i n l i q u i d d i f f u s i v i t i e s for these two systems. This behaviour was not observed, however. On the contrary, as indicated by the c o r r e l a t i n g equation (18), the lower surface tension greatly reduced the rate of transfer for comparable conditions. This ef f e c t i s s i m i l a r i n this respect to the damping e f f e c t of monolayers which reduce surface r i p p l i n g , and thereby reduce surface areas and transfer rates. The damping e f f e c t of 196 monolayers has normally been considered a consequence of the "resistance to l o c a l compression". Since the reduction i n transfer rate was observed for pure (absolute) ethanol as the test l i q u i d , the interface was expected to have been free of any monolayer. For a turbulent "clean" interface according to Levich (58), a reduction i n surface tension should enhance the transfer rate. For a number of reasons this writer i s not w i l l  ing to accept that for the experiments with the CC^ethanol system^ the observed reduction i n the transfer rate could have been caused by the presence of a monolayer, even although t h i s would seem to explain the experimentally measured e f f e c t . The reasons are that absolute ethanol was used i n the experi mental equipment, which was i n i t i a l l y flushed with t h i s l i q u i d , and then charged for a series of experiments. After a period of experimentation of several weeks, a noticeable drop i n trans fer rate at equivalent flow conditions occurred, then i n d i c a t i n g the presence of contaminants. After a second flushing and complete recharging with fresh absolute ethanol, o r i g i n a l r e s u l t s were reproduced, and again a f t e r a period of operation a reduction i n transfer rate was observed. The r e s u l t s for the reduced rates of transfer were discarded because of presumed contamination. The r e s u l t s , duplicated for the fresh ethanol, therefore, are considered to r e f l e c t the true e f f e c t of the 197 surface tension of a pure liquid. No completely logical explan ation for this observed effect of surface tension has been found in recent publications, nor have any experiments designed to separate the effects in such dynamic systems as two-phase flow been found in the current literature. Although it is outside the scope of this research, a purely hypothetical reason for the observed effect of surface tension can be suggested i f one makes the following assumptions; (a) The interface can be treated as a membrane which vibrates because of localized eddying. (b) The amplitude of vibration is mainly determined by buoy ancy and other hydrodynamic conditions. (c) A vibrating string represents a one-dimensional view of the two-dimensional situation of a vibrating membrane. (d) The transfer coefficient is directly proportional to the frequency of vibration, at constant amplitude, for the two-dimensional membrane. If the foregoing rather gross assumptions were true, the fre quency of vibration would be directly proportional to the square root of a tension force of a string (59), and equi- valently the mass transfer coefficient would be directly pro portional to the square root of a surface tension force for the interfacial membrane, as obtained in equation (18). The above 198 hypothesis i l l u s t r a t e s that there may be a completely l o g i c a l reason for the dependence of mass transfer on surface tension. A second explanation for the decreasing e f f e c t on the mass transfer rate with l i q u i d s of lower surface tension can be obtained from the work of Baird and Davidson (60). They observed that for large single bubbles immersed i n a "pure" l i q u i d , the mass transfer rates were approximately 50% higher than the rates calculated from surface renewal theory. They att r i b u t e d these high transfer rates to the presence of i n t e r f a c i a l c a p i l l a r y r i p p l e s , which had a marked e f f e c t on the transfer rate exceed ing the contribution of the r i p p l e s to the i n t e r f a c i a l area, by providing a source of mixing i n the i n t e r f a c i a l region. The i n t e r f a c i a l r i p p l e s were eliminated by the addition of a low concentration of n-hexanol. While th i s additive was expected to lower the surface tension, and hence reduce r i p p l i n g , i t was not considered to otherwise a f f e c t the surface renewal rate. Baird and Davidson continued t h e i r experiments with "Lissapol", which was more strongly adsorbed, forming a continuous monolayer at the interface, and reduced the transfer rate even further. The r e l a t i o n between the work of Baird and Davidson and t h i s research i s that i f one assumes that c a p i l l a r y r i p p l i n g was present at the interface with water i n bubble flow, then the absence of such r i p p l i n g could be expected with ethanol, having 199 a much lower surface tension. Any s l i g h t increase i n surface area with ethanol, due to bubble elongation, would appear to be more than o f f s e t by the absence of r i p p l i n g , which might well be the cause of the observed reduction in the mass transfer rate i n t h i s work, as i n that of Baird and Davidson. The r o l e of the horizontal tee entrance as a bubble form ing device i s of considerable i n t e r e s t i n estimating the e f f e c t of tube diameter on the rates of mass transfer i n bubble flow. I f t h i s type o f entrance i s likened t o an o r i f i c e i n a horizon t a l plate, use can be made of the work on bubble formation of Van Krevelin and H o f t i j z e r (61). For the occurrence of "chain- bubbling" , equivalent to high gas rates, the bubble volume was found to be independent of v i s c o s i t y e f f e c t s , surface tension, and even of o r i f i c e diameter. The proposed equation r e l a t i n g bubble diameter and the other variables was as follows: where: DT, = diameter of equivalent spherical bubble, f t p^, = l i q u i d and gas densities This equation supports the previously mentioned observation that in t h i s work the bubble frequency appeared to be independent of (26) QG volumetric gas flow rate per o r i f i c e , cfh 200 viscosity and surface tension. Measurements were not made to test the effect of 'the density ratio, which must approach unity closely for the gas-liquid systems used in this work. A signif- icent conclusion of equation (26), i f the analogy to the hori zontal orifice is s t i l l maintained, is that the bubble frequency would also be expected to be independent of the tube entrance size for the two-phase absorber. If this were true, then equation (17) would s t i l l be expected to express the relation ship between the transfer rate and the variables V° and V°, the liquid and gas superficial velocities. The parallel between the vertical rising chain-bubbles and bubbles formed in a horizontal tee must break down, however, since the bubble frequency was visually observed to be much higher In the small diameter (1.228 cm) absorption tube than in the larger ones. The large exponent of 2.0 for the diameter ratio in equation (18) is indicative of the high dependence of the absorption rate on tube diameter. Particularly for the large (2.504 cm) tube, and at the lowest liquid rate, a considerable deviation from the proposed correlation is noted, probably due to the bubbles in the larger tube flowing proportionately nearer to the top of the tube, and hence affecting the degree of agita tion in the bulk of the liquid to a lesser extent. This behaviour suggests that the ratio of bubble diameter to tube 201 diameter would be a necessary parameter of a correlation, for smaller values of this ratio. Slug Region As discussed in the section on Theoretical Aspects, two effects were to be expected with regard to the mass transfer rates in the turbulent slug region of flow if the Kishinevskii theory was applicable to portions on the gas-liquid interface. The first was that at a constant liquid rate, increasing gas rates might be expected to increase the fraction of the extremely turbulent "slug crest" area in the test section and, therefore, cause a decreased dependence on diffusivity at the higher gas o rates. As can be observed from the NTU-V lines in Figures 21, 22, and 23 for the CO^-water and He-water systems at any one liquid rate, if such a decreased dependence on diffusivity was obtained at a l l , it was small indeed. Further consideration of the mass transfer process at any one liquid rate, suggests that the accelerating effect of the increased gas flow on the liquid phase may be significant. The consequence of this acceleration is that less liquid is present in the tube at higher gas velocities, and the liquid, slug crests included, travels at a much higher velocity through the tube. The total amount of liquid in the tube at any one time is obviously less 202 at higher gas rates (that is, the void fraction increases), and, therefore, the number of slug crests present in the test section is probably smaller. The velocity of the liquid as well as the number of slug crests present in the test section are assumed to be comparable for equivalent gas (C02 and He) superficial velocities. In consequence, a comparison of the absorption rate curves at any one liquid rate is not useful in either supporting or disproving the theory of Kishinevskii, The second effect expected in the slug region was that at constant gas rates, increased liquid rates would decrease the effect of molecular diffusivity. It was qualitatively observed during experimentation that the quantity of liquid in the tube increased with increasing liquid rates, and in addition the degree of agitation increased also to a pronounced degree. By a comparison of the slopes of the NTU-Vg lines in Figures 21, 22 and 23, it is evident that the slope for the He-water system approaches that for the C02-water system at the highest liquid rate (1.792 fps). This indicates that the effect of the molecular liquid phase diffusivity appears to be decreas ing in its influence on the rates of mass transfer at higher degrees of turbulence. The magnitude of this effect is quanti tatively shown by the indices to be used in conjunction with equation (24), in Figure 25 and Table 10. The exponents of 203 the v i s c o s i t y r a t i o s appear to give further q u a l i t a t i v e c o n f i r  mation of the Ki s h i n e v s k i i theory, showing that v i s c o s i t y plays an increasingly important r o l e i n the rates of mass transfer as the turbulence increases. Recent work by Davies, K i l n e r , and R a t c l i f f (62) d i s c r e d i t s the work of Ki s h i n e v s k i i on the grounds that i n t h e i r experiments i n a s t i r r e d vessel, the transfer rates, i n the absence of  splashing and emuIsification, were dependent on the square root of the l i q u i d phase d i f f u s i v i t y f or comparable conditions, regardless of the s t i r r i n g rate. Although i t i s unfortunate that the experiments of K i s h i n e v s k i i were not described i n enough d e t a i l to indicate the extent of the ag i t a t i o n , and condition of the interface, i t appears l i k e l y that the condition of the interface for his work was not comparable to that of Davies et a l . The application of the Ki s h i n e v s k i i theory to th i s present research was made because of the obvious extremely turbulent behaviour of the l i q u i d which included splashing and emulsification at the interface. Because of the successful application of the p r i n c i p l e s of the Ki s h i n e v s k i i theory to thi s work, i t appears that the K i s h i n e v s k i i theory i s an e n t i r e l y possible explanation for the observed absorption phenomena i n two-phase flow. The dependence of the mass transfer c o e f f i c i e n t s on 204 diffusivity to an exponent of less than 0.5 can be independently observed by the use of the experimental C^-water data obtained in the slug region of flow, at various temperatures. As indi cated earlier, absorption data were obtained at one liquid rate, 1,07 gpm, with one tube size, 1.757 cm, and at the three temperatures, 5.3°C, 30°C, and 45°C. Also as indicated earlier, the diffusivity range for these temperatures was a factor of three. For this particular l i q u i d volumetric flow rate, the effect of both the surface tension, and viscosity, were very small because the former was only slightly tempera ture dependent, and the latter had an exponent for the viscosity ratio of 0.028. Figure 29 shows a graph of the experimental NTU values plotted against those predicted using the slug flow correlation. It i s noted that although the exponent for the diffusivity ratio is 0.307, theudata for the three temperatures lie along a single straight line parallel and close to the 45° line. The conditions for this series of experiments make it a relatively stringent test of the effect of diffusivity. The comparison of the absorption rates does not depend on the accuracy of independent diffusivity determinations for two systems, one including the gas H2 or He, for which such deter minations are invariably difficult to make with accuracy, but instead on the values of diffusivity frequently measured over 205 N T U . EXPERIMENTAL Figure 29. Application of Slug Flow Correlation to C02"Water Absorption Data at Various Temperatures 206 a wide temperature range for the one gas-liquid system, CC^- water. In addition, the gas density for these experiments can be considered constant i n comparison to the variatio n s between that of He or HA and such gases as CO and 0 o. This provides a second independent check that the exponent for the eff e c t of d i f f u s i v i t y for thi s p a r t i c u l a r condition of turbul ence i s , i n f a c t , less than 0.5, or 0.307. The fact that the data a l l l i e s l i g h t l y above the 45° l i n e suggests t h a t a gas density r a t i o parameter, raised to a small exponent should possibly be introduced into the co r r e l a  tion for higher accuracy. I t i s r e c a l l e d that the ef f e c t of the difference i n gas densities between He and C0 0 was ignored in the determination of the e f f e c t of d i f f u s i v i t y . I t i s obvious from Figure 29 that the ef f e c t of gas density i s small, and may r e s u l t i n predicted values of NTU being approxi mately 5 to 107o too high, depending on the p a r t i c u l a r gas density. The e f f e c t of surface tension i s noted to be smaller i n the slug region than i n the bubble region. The reason for the d i r e c t i o n of the e f f e c t of surface tension i s not immedi ately obvious, decreasing values decreasing the rates of trans f e r . I t might also be expected, i n the l i g h t of the reduction in the e f f e c t of surface tension i n slug flow when compared to 207 bubble flow, that a continuing reduction would be obtained at higher degrees of turbulence in the slug region itself. The effect of surface tension would be expected to be reflected in changes in interfacial area, or in the degree of microscopic turbulence of the interface. In slug flow, the former seems to be the more likely explanation for the decrease in transfer rates with decreasing surface tension, and would possibly be due to the variation in void fraction with a change in this property of the liquid. According to Hughmark and Pressburg (63), the liquid fraction will vary approximately as Q"* N» where G? is the surface tension, and the exponent, n, is esti mated to be of the order of 0.2. Thus, if one assumes the sur face area at equal gas and liquid rates to be directly propor tional to the amount of liquid in the tube, the effect of a decrease in surface tension of the pure liquid will be to decrease the transfer rate. Because both of these effects of interfacial tension on the transfer rate act in the same direc tion, the rather appreciable dependence of the absorption rate on this property in the slug region of flow becomes understand able. The dependence of transfer rates on tube diameter was found to be less in the slug region than in the bubble region, and was consistently reduced with increased liquid turbulence. 208 It would appear logical that tube geometry would be of lesser importance at higher liquid rates. The interaction of the phase velocities in increasing the turbulence, would be decreasingly affected by the tube walls. It is interesting to note that in Figure 25 at the intercept of the d-v£ curve the value of "d" (2.0) obtained for the bubble region falls directly on the extrapolated line determined by the other values of "d" for the slug region. In conclusion, there is a need to conclusively determine for increasingly turbulent two-phase flows whether a different mechanism of mass transfer is beginning to operate, for example, Kishinevskii's theory, or whether the observed results are the consequence of the same process occurring at very different rates at the same time and in different locations, because of a great variation in the amount of transfer area existing per unit volume of fluid. Although the present work does not settle this point, nor was it intended to do so, present evi dence seems to favour the former viewpoint. Now that the pattern of absorption behaviour is known, and the relative impor tance of the system variables, it should be possible to design unique experiments to investigate the rate process under more carefully controlled conditions. 209 REFERENCES 1. Nicklin s D. J., Wilkes, J . 0. and Davidson, J. F., Trans. Inst. Chem. Engrs. 40, 61 (1962). 2. Anderson, G. H. and Mantzouranis, B. G., Chem. Eng. .Sci. 16_, 222 (1961). 3. Collier, J . G. and Hewitt, G. F., Trans. Inst. Chem. Engrs,. 39, 127 (1961). 4. Varlamov, M. L. s Manakin, G. A. and Staroselskii, Ya. I., Zh. E r i k l . OaiM, (USSR) 32, 2504 (1959). 5. Varlamov a A, h , s Manakin, G. A. and Staroselskii, Ya. I., Zh. P r i k l . Khjjn. (USSR) 32., 2511 (1959). 6 . Anderson s J . D., Bol l i n g e r , R. E. and Lamb, D. E., "Mass Transfer i n TWo-Phase Annular Horizontal Flow". Presented at A.I. Che. Eng. Na t l . Meeting, Los Angeles, February, 1962. 7. Martinelli, R. C. and Nelson, D. B., Trans. Am. Soc. Mech. Eng. 70, 695 (1948). 8. Isbin, H. S., Fauske, H., Grace, T. and Gracia, J., "Symposium on Two-Phase Fluid Flow". Paper No. 10, Inst. Mech. Engrs., London, February, 1962. 9. Hughmark, G. A. and Pressburg, B. S., A. I. Ch. E. Journal 7, 677 (1961). 10. Schiel, K., German Patent No. 1,074,391, issued January 28, 1960. 11. Alves, G. E., Chem. Eng. Progr. 50, 449 (1954). 12. Govier, G. W. and Omer, M. M., Can. Chem. Eng. 40, 93 (1962). 13. Harriot, R. J., Can. J. Chem. Eng. 40. 60 (1962). 14. Scriven, L. E. and R. L. Pigford, A.I. Ch. E. Journal 5, 397 (1959). 210 15. Vivien, J. E. and D. W. Peaceraan, A A < S J [ I L Ch, E. Journal 2, 437 (1956). 16. Davies, J.!T. and Rideal, E. K., "Interfacial Phenomena" 2nd Ed. pp.311~313, Academic Press, New York, 1963. 17. Drew, T. B., Hoopes Jr., J. W. and T. Vermeulen, Editors, "Advances in Chemical Engineering1'', Vol, 4, p.l s Academic Press, New York, .1963. 18. Blank, M., J. Phys. Chem. j y j , 1698 (1961). 19. Harvey, G. A. and Smith, W., Chem. Eng. Sci. 10, 274 (1959). 20. Drew, T. B.s Hoopes Jr., J . W. and T. Vermeulen, Editors, "Advances In Chemical Engineering"', Vol. 4 , pp.3, 7, Academic Press, New York, 1963. 21. Ibid, „ p.5« 22. Lewis, W. K., and Whitman, W. G., Ind. Eng. Chem. 16, 1215 (1925). 23. Higbie, R., Tr ans. Am, Inst, Chem. jEngr S., 3JL, 365 (1935). 24. Sherwood, T. K. and PIgford, R. L., "Absorption and Extrac tion", pp.20, 22, 265-267, McGraw-Hill, New York, 1952. 25. Kishinevskii, M. K. and Pamfilov, A. V., Zh. Prikl. Khim. 22, 1173 (1949). 26. Kishinevskii, M. K. and Serebryansky, V. T., Zh. Prikl. Khim. 29, 27 (1956). 27. Danckwerts, P. V., Ind. Eng. Chem. 43, 1450 (1951). 28. Nicklin, D. J., Wilkes, J. 0. and Davidson, J. F., Trans. Inst. Chem. Engrs, 40, 61 (1962). 29. Scott, D. S., Can. J. Chem. Eng. 40, 224 (1962). 30. Bowman, R. L . and Johnson, A. I., Can. J. Chem. Eng. 40. 139 (1962). 31. Knudsen, J. G. and Katz, D. L., "Fluid Dynamics and Heat Transfer", p.214, McGraw-Hill, New York, 1958. , 2 n 32. B i r d s B.» Stewart, W. E. and Lightfoot, E. N.s "Trans port Phenomena", p.541, Wiley, New York, 1960. 33. Friedlander, S. K., A. I . Ch. E. Journal .?..» 347 (1961). 34. Ref. 20, p.10. 35. Hutchinson, M. H. and Sherwood, T. &.,, fad. Eng. Chem. 2.99 836 (1937). 36. Linke, W. F.„ " S o l u b i l i t i e s Inorganic and Metal Organic Compounds",.Vol. 1 , 4th Ed., Van Nostrand, New York, 1958. 37. Hodgman, C. "Handbook of Chemistry and Physics", 44th Ed., p.lJ&Sj, Chemical Rubber- Publishing Company, Cleveland, 1962. 38. I b i d . , pp.2257, 2260. 39. I b i d . , p.2197. 40. Perry, J . H.9 Editor, "Chemical Engineers Handbook, 3rd Ed., p.363, McGraw-Hill, New York, 1950. 41. I b i d . , p.363. 42. Davidson, J . F. and Cullen, E. J . , Trans. Faraday. Soc. 53,, 51 (1957). 43. "International C r i t i c a l Tables", V o l . 5, McGraw-Hill, New York, 1929. 44. Calderbank, P. H., Trans. Inst. Chem. Engrs. 37,, 176 (1959). 45. Gertz, K. H. and Loeschcke, H. H.> Z. Naturf. 9b» 1 (1954). 46. Wilke, C. R., Chem. Eng. Progr. 218 (1949). 47. Reid, R. C. and Sherwood, I . K., "The Properties of Gases and Liquids", p.286, McGraw-Hill, New York, 1958. 48. I b i d . , p.284. 49. B u l l e t i n No. 101, "The Ring Method for Surface and Inter f a c i a l Tensions", Central S c i e n t i f i c Company, Chicago. 212 50. De V e r t e u i l , G. H., "The V i s c o s i t y of Liquids", M.A.Sc. Thesis s University of B r i t i s h Columbia, 1958. 51. Rhodes, T. J. 8 " I n d u s t r i a l Instruments for Measurement and Control", p.303, McGraw-Hill, New York, 1941. 52. Simpson, S. G., Ind. .Eng. Chem. ,16 v 709 (1924). 53. Hamilton, L . F. and Simpson, S. G.» "Quantitative Chemical Analysis", p.170, 10th Ed., Macmllian, New York, 1952. 54. Ref. 24, p.130. 55. Lockhart 9 R. W. and M a r t i n e l l i , R. C . 9 Chem. Eng. Progr. 45. 39 ( 1 9 4 j ) . 56. Hughmarky G. A. and Pressburg, B . S.s k, I.. Ch. E... Journal 57. Ref. 44. 58. Levlch, V. G., "Physicochemical. Hydrodynamics", pp.135, 136, P r e n t i c e - H a l l , Englewood C l i f f s , 1962. 59. Mendenhall, C. E., Eve, A. S., Keys, D. A. and Sutton, R. M.j "College Physics", 4th Ed., p.197, Heath, Boston, 1956. 60. Baird, M. H. I . and Davidson, J . H., Chem. Eng. S c i . 17, 87 (1962). 61. Van Krevelin, D. W. and H o f t i j z e r , P. J . , Chem. Eng. Pros 46, 29 (1950). 62. Davies, J . T., K i l n e r , A. A. and R a t c l i f f , G. A., Chem. Eng. S c i . ( i n press)(1964). 63. Ref. 56. APPENDIX I PROCESS EQUIPMENT SPECIFICATIONS Rotameters R"laR~lA (liquid) Manufacturer: Brooks Rotameter Company Model: R-l, R-8M-25-2; float, 8-RV-14-2 R-1A, P.-9M-25-2; f l o a t , 9-RV-14 Capacities: see calibration curves Appendix II .Rf-_2,R-.2A.X,Rasl Manufacturer: Brooks Rotameter Company Model: R-2, R-6M-25-1; float, pyrex (spherical) R-2A, R-9M-25-2; float, 8-RV-3 Capacities: see calibration curves Appendix II Pumps  P-l Supplier: Pumps and Power, Vancouver Model: MPJS-33-H, deep-well jet self-priming, centrifugal Capacity: 6.1 gpm at NPSH of 6 ft, inlet and discharge pressures, full vacuum and 30 psig (water) Motor: 1/3 hp, 3450 rpm, directly connected Special features: mechanical shaft seal suitable for vacuum Manufacturer: Eastern Industries Company Model: E-l, type 100, laboratory, centrifugal Capacity: approximately 0.25 gpm at heai of 30 ft (water) Motor: 1/15 hp, 5000 rpm, directly connected Heat ...Exchangers E-l Type: shell-atri-tube, single-pass both shell and tube Tubes: approximately 320,5/16-in OD copper tubes, 42 In long, arranged in a triangular pitch, %~In on centres Shell: 6-in OD Baffles: approximately 25% cut, every 6 in Heads: flanged to match shell flanges, steel, coated with primer and tygon paints Area: approximately 50 sq ft, based on tube outside area E-2. E-2A Type: double-tube, internal tube 3/8-in copper, external 5/8-in copper, 4 in long Construction: brass end-pieces silver soldered, inlet and outlet nipples, ^-in also silver soldered E-3 Type: double-tube, internal tube %-in copper, external 3/4-in copper, overall length 30 in 1-3 Construction: brass end-pieces and three % ~ i n copper nipples silver soldered 4. Drum  D-l Sizes 11-in diameter, 26-in length, approximate volume 11 U.S. gallons Material of construction: . stainless steel 5. WAteg_Ejector  J ^ l Manufacturer: Schutte and Roerting Model; 0 Capacity: approximately 1.5 scfh gas at 26 i n mercury vacuum 6. The rmometers T_-l. ,T-2..t T-4 Manufacturer: W. H. Kessler Type: ASTM, solid point, range 0°C to 30°C, 0.1°C divisions T-3. T-5. T-6 Manufacturer: Kimble Glass Range: -10°C to 100°C, 1°C divisions 7. Pressure Gauges  P - l . P-2 Range: 0 to 30 psig P-3 Range: 0 to 50 psig 1-4 From D-l To J - l To d r a i n From P - l j - T / A - i n . brass end-plates Shower head •3/4-in. i r o n pipe, tygon- coated, 12 i n . long,with 40 1/R-in. holes d r i l l e d Q.V.F. s e c t i o n , 6-in. , 36 i n . long Liquid depth, 12 i n . 3/8-in. c o i l e d copper tube, approx. 15 f t . Note: not to scale Steam i n l e t To P-l Figure 1-1. Details of Vacuum Stripper 1-5 From To P-2 1/4-in. brass end-plates •4, 1/R-in. diameter nozzles •1/2-in. brass pipe Q.V.F. section, 2-in., 24 i n . long Note: not to scale T>ry gas i n l e t F i g u r e 1 - 2 . D e t a i l s o f Gas H u m i d i f i e r APPENDIX 11 CALIBRATION OF GAS AND LIQUID ROTAMETERS TABLE II - 1 CALIBRATION OF LIQUID ROTAMETER FOR WATER AND ETHANOL L i q u i d Temperature Weight Time Flow rate Rotameter ° c lb min gpm Reading (15.0) Water 15 e 2 25 2.92 1.027(a) 1,00 14 c 7 25 2.91 1,031 1.00 20 2.92 0,822 0.80 15 e l 15 2 . 9 1 0.619 0.60 15.1 10 2.90 0,414 0,40 15.3 5 2.90 0.207 0.20 (a) c a l c u l a t i o n of flow rate.based on water density of 8.334 lb/ g a l Ethanol 13.4 6.0 0.813 0.608(b) 0.540 13.5 6.0 0.860 0.899 0.797 13.8 6.0 1.01 1.056 0.923 13.6 6.0 1.49 1.117 0.979 calculation of flow rate based on ethanol density of 6.605 lb/gal Water 30.0 15 1.675 1.078(c) 1.04 (c) calculation of flow rate based on water density of 8.307 lb/gal Water 45.2 15 1.69 1.074(d) 1.04 (d) calculation of flow rate based on water density of 8.263 lb/gal 11-2 TABLE IX-2 CALIBRATION OF LIQUID ROTAMETER„ R-lA, FOR WATER AND ETHANOL Li q u i d Temperature Weight Time F l o w rate Rotameter UC l b min gpm Reading (15.0) Water 15.3 10 2.76 0.435(a) 0.40 15.3 15 1.78 1.011 1.00 14.7 25 1.99 1.508 1.50 14.8 25 1.47 2.042 2.00 15.3 25 1.19 2.52 2.50 15. J . 35 1.41 2.98 3.00 (a) c a l c u l a t i o n of flow rate based on water density of 8.334 l b / g a l (13.5) Ethanol 13.7 6.0 0.730 1.24(b) 1.12 13.5 6.0 0.579 1.57 1.43 13.4 6.0 0.419 2.17 1.96 (b) c a l c u l a t i o n of flow 6.605 l b / g a l rate based on ethanol density of II-3 TABLE II-3 CALIBRATION OF LIQUID ROTAMETER, R-lA, FOR ETHYLENE GLYCOL Temperature Weight Time Flow rate Rotameter °C lb min gpm Reading ( 1 5 . 0 ) 1 5 . 0 5 2 . 2 9 0 0 . 2 3 4(a) 0 . 9 7 1 4 . 9 8 1 . 4 9 2 0 . 5 7 4 1 . 6 6 1 5 . 1 1 1 1 . 0 7 0 1 . 1 0 1 2 • 7 tZ 1 5 . 0 1 5 0 . 9 1 5 1 . 7 5 3 . 8 2 1 5 . 1 20 0 . 9 1 4 2 . 3 4 4 . 9 0 c a l c u l a t i o n i&ased on gl y c o l density of 9 . 3 3 7 l b / g a l ( 3 0.0) 2 9 . 9 6 2 . 0 0 4 0 . 3 2 4(b) 0 . 7 9 3 0 . 0 8 1 . 2 4 9 0 . 6 9 2 1 . 4 0 2 9 . 9 11 1 . 0 3 7 1 . 1 4 6 2 . 1 0 3 0 . 0 1 5 0 . 9 8 1 1 . 6 5 2 . 9 0 3 0 . 1 2 0 0 . 9 9 7 2 . 1 7 3 . 7 0 2 9 . 9 3 0 1 . 3 5 9 2 . 3 9 4 . 0 4 c a l c u l a t i o n based on g l y c o l density of 9 . 2 5 3 l b / g a l II-4 Figure I I - l . C a l i b r a t i o n of L i q u i d Rotameter, R - l , for Water and Ethanol 11-5 o o m ro Y-< _j o LU o lO tr. LU d co* 3 O I 2 3 4 5 ROTAMETER READING, WATER AT I5°C., ETHANOL AT 13.5 °C. Figure II-2. C a l i b r a t i o n of L i q u i d Rotameter, R-1A, for Water and Ethanol 11=6 ROTAMETER READING AT I5°C. 8 30°C. Figure II - 3 . C a l i b r a t i o n of L i q u i d Rotameter, R-1A, for Ethylene Glycol I I - 7 TABLE II-4 CALIBRATION OF GAS ROTAMETER, R-2V FOR CO„ FLOW 2 Rotameter Wet Test Meter Flow Rate Reading Temp. Pressure Volume Time cfh cfh °C in Hg cf min 15°C,756mm 15°C,756mm (a) (b) (c) 0.05 2.33 1.218 1.229 0.05 1.97 1.440 1.456 0.10 1.28 4.44 4.49 0.10 1.45 3.92 3.97 0.20 1.26 9.01 9.11 0.20 1.12 10.10 10.10 0.30 1.23 13.76 13.66 0.40 1.56 14.50 14.44 0.40 1.47 15.38 15.27 0.50 1.57 18.00 18.04 0.50 1.49 18.96 19.00 0.50 1.40 20.16 20.10 0.50 1.34 21.06 21.20 0.50 1.27 22.26 22.40 0.50 1.20 23.52 23.72 (a) volume of C0£ at barometric pressure 757 mm, saturated with water at 74°F, using wet test meter Ch.E. 1668. (b) volumetric flow rate of C02, dry basis. 4.0 23.1 4.0 4.0 23.6 12.0 10.0 23.8 12.0 10.0 24.0 4.0 20.0 24.0 4.0 20.0 20.0 12.0 30.0 18.4 4.0 30.0 19.0 8.0 30.0 17.8 12.0 40.0 21.0 4.0 40.0 21.0 8.0 40.0 12.0 48.0 21.5 4.0 48.0 22.2 8.0 48.0 23.2 12.0 (c) volumetric flow rate of COo, dry basis, for rotameter conditions of 21.0 C and 756 mm (nominal) pressure. I I - 8 TABLE II-5 CALIBRATION OF GAS ROTAMETER, R-2A, FOR C02 FLOW Rotameter Displacement Meter FJLgwJRate, Reading Temp • Pressure Volume Time Volume cfh °C in Hg cf min cf 15°C,756mm (a) (*») (is) 20.0 21*3 24.0 0.50 1.00 0.488 29.5 52.0 21.0 *« 2.0 2.19 1.976 54.25 98.0 20.0 I I 2.0 1.30 1.976 91.1 150 16.0 vt 4.0 1.73 3.905 134.2 200 12.5 tv 5.0 1.64 4.88 174. 231 7.6 61 5.0 1.41 4.89 203* 20.0 19.5 16.0 1.0 2.16 0.976 27.0 98.0 15.0 »» 2.0 1.39 1.976 84.1 150 14.0 « i 3.0 1.42 2.976 123.7 200 14.5 5.0 1.79 4.88 160.8 50.0 22.0 «« 1.5 1.82 1.454 48.2 20.0 22.0 12.0 1.0 2.29 0.976 25.7 52.0 21»3 i * 2.0 2.48 1.976 48.1 98.0 21.5 t« 3.0 2.20 2.908 79.6 150 18»8 «t 4.0 2.01 3.91 116.3 178 16.0 IV 5.0 2 • 12 4.89 136.4 20.0 22.0 8.0 1.0 2.46 0.976 24.0 50.0 22.3 i» 1.5 1.99 1.454 44.1 100 22.7 «« 3.0 2.26 2.91 78.0 150 22.0 it 4.0 2.09 3.88 112.2 2.0 22.5 4.0 0.25 1.91 0.244 7.75 7.0 22.7 it 0.50 2.14 0.489 13.83 12.0 22.8 tt 0.50 1.71 0.489 17.92 20.0 23.0 it 1.0 2.64 0.977 22.44 35.0 20.2 I I 2.0 3.63 1.944 32.18 50.0 20.6 it 2.0 2.79 1.940 41.75 75.0 20.8 it 2.0 2.03 1.940 57.4 98.0 23.0 it 2.0 1.65 1.954 71.8 106 20.0 t  3.0 2.24 2.908 78.0 (a) volume of CO2 at barometric pressure of 756 mm and tempera ture of 23°C, passing through dry gas displacement meter. (b) volume of C0 2 at barometric pressure of 756 mm and tempera ture of 15°C (dry basis). (c) volumetric flow rate of C0 2, dry basis, for rotameter condi tions of 21°C and 756 mm (nominal) pressure. II-9 TABLE 11-6 CALIBRATION OF GAS ROTAMETER, R-2, FOR He FLOW Rotameter Wet Test Meter Reading Temp. Pressure Volume Time °C i n Hg cf (a) m m Flow Rate cfm cfh 15°C,756mm (b) (c) 5.3 23 • 3 4 0.050 1.602 0.03121 1.786 8.9 23.3 V* 0.050 1.629 0.07673 4.391 12.5 22.0 II 0.125 1.510 0.1656 9.480 16.6 22.0 11 0.250 0.910 0.2747 15.72 20.0 22.0 HI 0.250 0.684 0.3655 20.92 23.2 22.3 II 0.500 . 1.120 0.4464 25.55 7.0 23.0 tf 0.050 0.999 0.05005 2.864 4.0 22.9 »» 0.050 2 • 130 0.0235 1.343 4.0 21.0 12 0.025 0.890 0.02809 1.608 5.9 21.0 »» 0.050 1.183 0,04227 2.419 10.7 21.5 II 0.125 0.865 0.1445 8.269 17.7 21.0 •« 0.250 0.707 0.3536 20.23 24.8 21.0 II 0.500 0.906 0.5519 31.58 32.1 21.0 i» 0.750 1.006 0.7455 42.66 8.1 23.0 it 0.125 1.507 0.08295 4.747 14.0 23.0 t i 0.250 1.020 0.2451 14.03 40.7 22.5 ti 1.00 1.050 0.9524 54.50 47.9 22.5 «t 1.00 0.906 1.104 63.18 9.3 22.5 24 0.150 1.073 0.1398 8.00 12.9 ti ti 0.250 0.970 0.2577 14.75 17.2 ti 0.375 0.910 0.4121 23.58 22.9 it 0.750 1.263 0.5938 33.98 30.1 ii 1.00 1.228 0.8143 46.60 39.2 I I 1.00 0.938 1.066 61.00 48.1 ii 1.00 0.783 1.277 73.08 (a) volume of He at 753 mm, saturated at 75.0°F, using wet test meter 1668. (b) volumetric flow rate of He, dry basis, at 753 mm pressure and 75.0°F. (c) volumetric flow rate of He, dry basis, at 756 mm pressure and 15.0°C, for rotameter conditions of 21.0°C, and 756 mm (nominal) pressure. 11-10 TABLE II-7 CALIBRATION OF GAS ROTAMETER, R-2A, FOR He FLOW Rotameter Displace. Meter Flow Rate Reading Temp. Pressure Volume °C in Hg cf U ) 8.20 23.5 24 1.00 36.5 it «i 2.50 43.6 i i it 3.00 54.4 it vv 3.5 62.0 it 11 4.0 72.3 ti II 4.0 85.8 i i It 5.0 Time cfm cfh min 15°C,756mm (b) (c) 1.117 10.8784 52.7 1.023 2.398 143.9 1.090 2.700 162.0 1.087 3.160 189.6 1.133 3.446 207.8 1.007 3.898 233.9 1.107 4.432 265.9 3.8 23.3 24 0.50 0.912 0.5380 32.27 6.9 i i • i 1.00 1.288 0.7619 45.71 11.0 it i t 1.00 0.952 1.030 61.80 14.6 t i i i 1.50 1.210 1.217 73.02 21.2 I I «i 1.50 0.925 1.592 95.52 10.7 ti it 1.00 0.978 1.003 60.18 16.6 t i I I 1.50 1.080 1.363 81.78 20.5 i i II 1.50 0.917 1.605 96.30 30.0 i t IV 2.0 0.943 2.081 124.9 3.6 23.2 12 0.50 1.097 0.4473 26.84 6.2 i i II 0.75 1.180 0.6237 37.42 9.0 it II 1.00 1.249 0.7856 47.14 15.6 II I I 1.25 1.063 1.154 69.24 22.6 II I I 1.50 1.007 1.462 87.72 28.8 II i t 1.50 0.849 1.734 104.0 (a) volume of He at 753 mm and 75.0°F, dry basis. (b) volumetric flow rate of He, dry basis, at 756 mm and 15°C. (c) volumetric flow rate of He, dry basis, at 756 mm and 15°C, at rotameter conditions of 21.0°C and 756 mm (nominal) pressure. 11-11 II-4. C a l i b r a t i o n of Rotameter, R-2, for C0 2 11-12 ROTAMETER READING AT 21 °C , PRESSURE AS SHOWN Figure II-5. C a l i b r a t i o n of Rotameter, R-2A, for C09 11-13 20 40 6 0 80 ROTAMETER READING AT 2l°C,t PRESSURE AS SHOWN 100 Figure I I - 6 . C a l i b r a t i o n R - 2 , for He of Rotameter, 11-14 ROTAMETER READING AT 21 °C, PRESSURE AS SHOWN Figure II-7. C a l i b r a t i o n of Rotameter, R-2A S for He m ~ i APPENDIX III SAMPLING AND ANALYSIS TABLE' III-l CONCENTRATION PROFILE IN LIQUID, IN BUBBLE AND SLUG FLOWS WITH C02"WATER SYSTEM 1. Bubble Flow: Probe Concentration • P o s i t i o n (inlet sample point) mm (a) millimoles/1 - 2 4.70 0 4.85 2 4.90 4 4.95 6 5.00 Note: bottom of bubbles approximately 8 mm from tube bottom. 2. Slug Flow: -1 9.85 0 9.90 1 9.90 2 9.90 3 10.00 Note: bottom of slugs approximately 5 mm from tube bottom. (a) probe position measured from inside bottom level of absorption tube 17.57 mm in diameter. Note: saturated concentration approximately 45.7 millimoles per litre. III-2 TABLE III-2 ABSORPTION RATES IN ENTRANCE TEE AND OUTLET CYCLONE FOR ETHYLENE GLYCOL Glycol Flow Rate NTU at 15°C NTU at 30°C 0.62 1.07 2 .1G 0.00386 0.00333 0.00114 0.00421 0.00281 0.00112 Note: NTU values calculated with no gas flowing through the tube, but with the l i q u i d In the tee and cyclone exposed to the gas. I I I - 3 TABLE I II-3 DATA FOR CALIBRATION OF He ANALYZER FOR INLET SAMPLE POINT Ratio of Mole Water c o 2 rates(lO^) fraction rate ml water/ He in Potential ml/min ml /min ml CQ2 c o 2 ( i o 4 ) m i l l i v o l t s 0 . 4 9 5 7 6 . 5 0 . 6 4 7 0 . 6 0 1 0 . 1 2 0 0 . 6 9 6 7 6 . 3 0 . 9 1 2 0 . 8 4 7 0 . 1 8 0 0 . 9 6 0 7 5 . 9 1 .265 1.175 0 . 2 5 5 1 , 4 2 0 7 5 . 6 1 .878 1 .745 0 . 3 7 5 2 . 1 4 : 5.2 2 . 8 4 6 2 . 6 4 4 0 . 5 4 5 2 . 8 5 7 4 . 7 3 .815 3 .546 0 . 7 5 0 3.36 74.4 4 .516 4 . 1 9 6 0 . 8 9 5 0 .178 7 6 . 6 0.232 0«d^XS 0 . 0 3 1 0 . 3 8 7 7 6 , 4 0 . 5 0 6 0 . 4 7 0 0 . 0 7 7 0 . 5 7 6 7 6 . 2 0 . 7 5 6 0 . 7 0 2 0 . 1 2 8 0 . 8 8 5 7 6 . 0 1 .164 1 . 0 8 1 0 . 2 1 4 1 . 9 2 7 5 . 3 2 . 5 5 0 2 . 3 6 8 0 . 5 0 0 2 . 8 0 7 4 . 7 3 . 7 4 8 3 . 4 8 1 0 . 7 3 6 4 . 4 6 7 3 . 5 6 . 0 6 8 5 . 6 3 6 1 .182 0 . 5 6 4 7 5 . 5 0 . 7 4 7 0 . 6 8 1 0 . 1 1 8 1 . 0 4 7 4 . 4 1 . 3 9 8 1 .274 0 . 2 8 0 1 . 9 0 7 3 . 6 2 . 5 8 0 2 . 3 5 1 0 . 5 0 3 3 . 2 8 7 2 , 7 4 . 5 1 0 4 . 1 1 0 0 . 8 7 5 N o t e : c o l u m n l e n g t h I n each c a s e 20 I n o f p a c k i n g . III-4 TABLE III-4 DATA FOR CAL I BRAT ION OF He ANALYZER FOR OUTLET SAMPLE POINT R a t i o M o l e W a t e r C©2 r a t e s ( 1 0 2 ) f r a c t i o n r a t e r a t e m l w a t e r / He i n P o t e n t i a l m l / m i n m l / m i n m l C 0 2 co2(io4) m i l l i v o l t s 0 . 5 2 6 7 7 . 4 0 0 . 6 8 0 0 . 6 1 9 5 0 . 1 1 0 0 . 9 0 9 7 7 . 1 6 1 . 178 1 . 074 0 . 2 1 4 1 .23 7 6 . 9 2 1 .599 1 . 458 0 . 3 0 4 1 . 85 7 6 . 6 9 2 .412 2 .199 0 . 4 5 8 2 . 5 8 7 5 . 6 4 3 a 3 . 1 0 9 0 . 6 4 3 3 . 4 9 7 4 . 7 4 4 . 6 6 9 4 . 2 5 6 0 . 8 9 7 4.25 7 3 . 9 6 5 . 7 4 6 5 . 2 3 8 1 . 092 5.15 7 3 . 2 1 7 . 0 3 5 6 . 4 1 3 1 . 346 6 . 1 2 7 2 . 7 8 8 . 4 0 9 7 . 6 6 5 1 .586 6 . 8 8 7 1 . 8 4 9 . 5 7 7 8 . 7 3 0 1 . 775 7 . 6 9 7 1 . 4 3 1 0 . 7 7 9 . 8 1 7 1 . 980 8 . 2 6 7 1 . 1 2 1 1 . 6 1 1 0 . 5 8 2 . 1 2 9 0 . 2 9 2 7 7 . 9 0 0 . 3 7 5 0 . 3 4 2 0 . 0 7 8 0 . 5 2 1 ' 7 6 . 9 5 0 . 6 7 7 0 . 6 1 7 0 . 1 3 6 0 . 9 9 0 7 6 . 1 6 1 . 300 1 . 185 0 . 2 4 8 1 .77 7 5 . 5 0 2 . 3 4 4 2 . 1 3 7 0 . 4 5 6 2!«32! 7 4 . 9 5 3 . 0 9 5 2 . 8 2 2 0 . 5 6 4 4 . 6 5 7 3 . 4 0 6 . 3 3 5 5 . 7 7 6 1 .216 4 . 8 0 7 2 . 8 4 6 . 5 9 0 6 . 0 0 8 1 . 259 5 . 5 5 7 2 . 1 5 7 . 6 9 2 7 . 0 1 3 1 . 472 6 . 2 0 7 1 . 8 0 8 . 6 3 5 7 . 4 7 3 1 . 614 7 . 3 4 7 1 . 1 6 1 0 . 3 1 9 . 4 0 0 1 .907 1 .19 7 6 . 0 0 1 . 566 1 .427 0 . 2 7 8 2 . 4 5 7 4 . 7 5 3 . 2 7 8 2 . 9 8 7 0 . 6 0 3 3 . 5 3 7 3 . 9 0 4 . 7 7 7 4 . 3 5 4 0 . 8 9 5 6 . 6 4 7 2 . 1 5 9 . 2 0 3 8 . 3 8 7 1 . 703 7 . 6 3 7 1 . 2 0 1 0 . 7 1 6 9 . 7 6 6 1 . 9 5 4 Note: depth of column packing: H, 20 in J, 16 in K s 12-3/4 in IV-1 APPENDIX IV IBM-1620 FORTRAN PROGRAMS USED I N CALCULATIONS OF EXPERIMENTAL RESULTS Programs for Computing NTU Values for the Various Gas-Liquid Systems The general method consisted of c a l c u l a t i n g the absolute pressures, and subsequently the concentration d r i v i n g forces (correcting for the vapour pressure of the l i q u i d ) , at the i n l e t and outlet of the test section. The NTU values were calculated according to equation (7) i n the section on Treatment of Data. The correction for the amount of gaa absorbed i n the entrance section was made by applying equation (8), and the arithmetic mean gas flow rate i n the test section was calculated from equation ( 9 ) . The arithmetic mean gas volumetric flow rate was calculated at the mean test section temperature and pres sure, and from i t , the mean s u p e r f i c i a l gas v e l o c i t y . The length of a transfer uni t (LTU) was also calculated. A coded number system to describe the type of flow (bubble, plug, etc.) was also included f o r reproduction i n the computer print-out of the data and calculated values. The small v a r i a t i o n s i n the programs w i l l be separately described: IV-2 1. ,C0_2"Water; The two values o f E/L In equation (8) were introduced d i r e c t l y into the program. These values corresponded to 0.13964 for the 12.75-in entrance length ( E ) , and t o 0.33947 for the 30-in entrance length. Constants A and B were i n t r o  duced to convert the pressure measurements i n inches o f manometer f l u i d to mm of mercury, 2. COo-Ethanols The calculations followed an i d e n t i c a l pattern to those forv the C02-water s y s t e m . 3. CCJ2rEthylffi.Be_Cllycol: The entrance length was zero for the. C0 2-glycol system. The NTU values were calculated for the entire tube length therefore, and were corrected for the amount of absorption i n the entrance tee and outlet cyclone. The amount of the corrections Is l i s t e d i n Appendix I I I . The NTU values were m u l t i p l i e d by a factor (0.72541) so that the values were then based on a length of tube 92.2 i n , comparable to that used as the test section for a l l the other systems. 4» He-Water; The c a l c u l a t i o n for the concentration d r i v i n g force for the He-water system d i f f e r e d from that for the C02~ water system, because of the difference i n method of analysis. The r a t i o s of water to CO2 flow rates were required, along with the potentiometer reading to give the liquid-phase He concen t r a t i o n s . The equations for the He concentrations vs m i l l i v o l t readings, as shown i n Figure 12, were used d i r e c t l y i n the IV-3 program for the concentration determinations. Program for Computing the Correlation Variables for the Bubble and Plug Regions The program was mainly involved w i t h t h e c a l c u l a t i o n o f the. c o r r e l a t i n g variable according to equations (17, 18). Absorption data for gas s u p e r f i c i a l v e l o c i t i e s exceeding 3.0 fps (slug region) were excluded. A regression l i n e o f the c o r r e l a t i n g o variable on V'p/S, che gas s u p e r f i c i a l v e l o c i t y ) , was o b t a i n e d b y the method of least squares. Program for Computing the Correlation Variables for the Slug Flow Region The program was Involved with the c a l c u l a t i o n of the cor r e l a t i n g variable for the slug region. Absorption data for gas s u p e r f i c i a l v e l o c i t i e s of less than 2 . 0 fps were excluded. The various c o e f f i c i e n t s for the dimensionless r a t i o s , as shown i n Figure 2 5 , were used for the corresponding values of l i q u i d s u p e r f i c i a l v e l o c i t y . PROGRAMS FOR COMPUTATION OF NTU AND CORRELATING V A R I A B L F S FORTRAN 2 COMP! IF, - - C COMPUTATION OF MTU FOR CARBON QIOXinF WATER 60 PRINT 1 1 FORMAT I/53HSYSTFM TUBE CM BP MM nL GPM TFMP C.A SATC ML VP MM) REA02,L IO ,D ,BP ,OL.TFMP,CSAT,VP,A ,R ,C 2 FORMAT t I U , 1 F 7 . 3 , 2 F R . 3 , 2 F 6 . 2 , 3 F R . 3 , > F P . * t "IF " (L IO) 70'. SO". 70 70 PRINT 3 .L IO.0 .9P ,OL.TEMP,CSAT,VP 3 FORMAT ( I 6 .6FR .3 ) AREA - 0 . 0 0 0 8 4 S U » 0 » 0 PRINT »U |_4 F0RMATJ/67H RUN OG_ CFM P IM PD C IN C OUT TYPF OGM VCOR TUN ... - ^ U L - - y p ' ) - • - - SO RE AO 4 , N 0 , O G . P l , P 0 , C l . C 2 , J 4 FORMAT ( I 8 , 5 F » 0 . U , I 4 ) IF (N0)5t ,60,5 1 5 1 PIM - OP+A.P' _P0y_T » PIM-R.PD PMFAN" 6 .5*( P IM+POIlf ) FO - (P IN-POUT1/2.99 PPIN - PIN-VP PPOUT" POUT-VP OF IN • PPIN.CSAT/76C.0-C.1 JDFOUT- P P O y T » C S A T / 7 6 0 . - C 2 • " ~ OF I'M - (WF iN-OFOiit " ) /LOO(OFiN/OF0l lt ) TUN - ( C 2 - O / 0 F L M TUL - 7.6R3/TUN CONCF- 0 . 3 3 9 4 7 » T U N » O F I N / ( 1 . 0 - . ' 6 V 7 U » T U N > TITR » 8 . 0 2 0 3 » O L » C _ _ _ VJ"-f °_I ITR? I C O N C F + 0 . 5 » ( C 2 - C 1 I )•( 2 (5 .2+TFMP1/275.2 .763.0/ (PMFAN-VP OGf.OR- OG*756.0/ (PMFAN-VP ) » ( 2 7 5 ,2+TEMB >/2RR.? OGM - OGCOR-VOLF VELG - OGM/AREA/3600.0 P R W 7.NO.OG.P ' . F O . C ' ,C? . J . OGM,VOLF.TUN,TUL.VELG 7 FORMAT ( I 4 , I F 7 . 2 , U F 6 . 2 . I 3 . ) F 7 . ? . 1 F 6 . 2 , 1 F 7 . 4 . 1 F 6 . ) , ) F 7 . 3 ) 'PUNCH'S,NO , ' J , QRM",¥UN ,TUL,VELG 8 FORMAT ( I U , I 3 , 1 F 7.?.1F7.4 , 1 F 6 . 1 , 1 F 7 . 3 ) GO TO 50 RO STOP 1 FNO F O R T R A N 2 C O M P I L F . C C O M P U T A T I O N OF N T U F O R C A R B O N O I O X I Q E F T H A N O L 6 0 P R I N T I ! — ~ ~ 1 F O R M A T ( / S 3 H S Y S T E M T U B E C M R P M M O L G P M T F M P C S A T C M L V P M M ) R E A 0 2 , L I O . D . R P . O L . T E M P . C . S A T . V P , A , B , C 2 F O R M A T I 1 4 , 1 F 7 . 3 , 2 F 8 . 3 , 2 F 6 . 2 , 3 F R . 3 , 1 F P . 5 ) I F ( L I O ) V 0 , R 0 , 7 0 7 0 PRINT 3 , L I O , D , B P , O L , T E M P , C S A T , V P 3 F O R M A T ( I 6 . 6 F R . 3 ) P R I N T 1U 1 4 F O R M A T ! / 6 ? H R U N O G C F H P I N P n C I N C O U T T Y P F O G M V C O R T U N ' T U L V G ) 5C R E A D U , N O . O G , P 1 , P O , C I , C 2 , . I • U F O R M A T ( m , 5 F 1 0 . 1 i , I U ) I f ( N O 1 5 1 , 6 0 . 5 I 5 1 P I N » b P + A » P ) P O U T = P I N - B » P O P M E A N * 0 . 5 . 1 P I M + P O U T ) P P I N - P I N - V P P P O U T = P O U T - V P O F I N . P P I N » C S A T / 7 6 0 . 0 - C 1 O F O U T - P P O U T . C S A T . / 7 6 0 . - C 2 O F L M - ( O F I N - O F O I l T l / L O G l n F l N / n F O I J T ) T U N .= ( C 2 - C D / O F L M T U L = 7 . 6 R 3 / T U N C O N C F - 0 . 3 3 9 4 7 . T l l N » O F I N / ( ) . 0 - . 1 6 9 / U o T U N ) T I T R > 8.0?03»01 . .C V O L E - TI TR » ( C O N C E * 0 . 5 « ( C 2 - C ) ). | . ( 2 7 3 . 2 + T F M P 1 / 2 7 5 . 2 * 7 6 0 . 0 / ( P M F A N - V P 1 ) O G C 0 R - U G « 7 b 6 . 0 / ( P M E A M - V P ) . ( 2 7 3 . 2 + T E M P ) / 2 8 h . 2 O G M = O G C O R - V O L F V E L G » O G M /3oCC . C / 0 . OCZo lO P R I N T 7 , M O , W G , P ) , P p , C 1 , C 2 . . I . O ( ; M , V O L F , T I ) N , T U L , V F L G 7 F O R M A T ( I U , I F 7 . 2 . 4 F 6 . 2 , 1 3 . I F 7 . 2 . 1 F 6 . 2 , 1 F 7 . U , 1 F 6 . 1 , 1 F 7 . 3 ) P U N C H 8 , N O , J , O G M , T U N . T U L , V F L G 8 F O R M A T ( I U , 1 3 , 1 F 7 . 2 , I F 7 . 4 , 1 F 6 . 1 , 1 F 7 . ^ ) G O T O 5 0 8 0 S T O P PROGRAMS FOR COMPUTATION OF NTU AND CORRELATING VARIABLES FORTRAN! 2 COMPILE. C COMPUTATION! ;)F ,'IT-tJ FOR HFLIU1-WATFR _6 3 PRINT 1 1 F O R M A T (/biMSYSTSM T U B E CM H P M M O L G<*M TEMP C SAT; MF V P M M ) R E A O ? , L I O . n , B P , O L , T e » I P , r . S A T , v ' P , A , B , ( : ?. " F O R M A T , t ! U , lF7. ! l l . 2 e 3 .3,JF5. i . ,J j ; .T. .3. ,3E.8. : i t . ' ja< . . 5 i • IF ( L I O ) " 0 , 9 3 , 7 0 7 0 P R I M T 3 , L I O , 3 , B ? , O L . . T F M P , C S A T , V P _3 F O R M A T ( l f t , A F B , 3 1 . , . A R E A = 3. 333"H.U5I*#O»O P R I M ! ' i n . J J L _ F O R M A T . . . ! rt\H >JD„...„5. C.Fu. „.PJ_.. H I M H OUT T Y P K y _ i „ ; lNTU L T J ' </KI.~V " " '. " S 3 R F A D II , N O ,C )G , P I tfl \|, VOUT ,TG I N , TGCWT , « J I M , WOUT, J U _ F O R M A T ( I _ , J F 7 , 2 , _ _ _ j Z , h F 7 , 3 j In ) : I F l .NIC) js 1 , 6 3 , 5 ! S 1 P I N = 3 3 t s » P I • POUT"= P ! N - 3 » p o - _ _ _ F D • ' " P O / ' i T s ^ i t P M E A M = j . S » ( » I N| + o :».if) P » INI = P I N - V ? . _ p»ouf»''po"riT-vp " • R I M - 5 3 . 3 / T S I N I / W I N I R O J T _ = S j . 3 /TSO . i. l IV W O J I X I N = R IN'I . ( i i . A ? b0*V IM + 3 . 35\'i ) Y F I N . » X [ N I O . ? 1 ? ' . > S » 3 P / 7 6 0 . 3* ' H . 3 A U / 2 2 . M I I_F ( V O U T - 1. SO ) U 13 XOUT = R I ) U T » ( U . 7 5 U 1 » V 0 ' J T + 3 . 3 3 V ) 30 10 12 . ' . . ] X 01IT_ .= R (HI T• < j f j 1 R p » V 3 U T-, L.Z.lbJ. 1. 1 2' YFOUT-XOllT.O.Vi V25»Ht>/7»3 .3«IH,361/22 .U 11 DFTN = P P I N | » C S A T / 7 6 0 . : - Y F I N QJi-UJI- PP3! IT»CS1T / ^ 6 -3-^- YF OU T OFLM • ( DF IM-DFOUT )/l.OG(0FT M/DFOUT) TUM " ( Y F O J T - Y F I M l / O F i M TJL - 7.AH3/TUN TITR = 8 . 3 2 3 3 * O L » C C0NCE = 3. 33VU7»TUM»0F IN / ( 1 .3 -3 .1 AV7U» TUM) VOLE -T I T R » C O N | C F + 0 . 5 » ( YFOJT-YF IM) ) « 9 9 6 . 3 6 / < P M E A N - V P ) 3GC0R = 03«7bA.O/ (PMEAN) ) 03M - Q3C3R-VOLF ; "TT5 : ST/OP FNO VELG -OGM/AREA/3633.3 PRINT 7 , NO," 05 , P l , F n , Y F I N , Y F O U T , J,OGM,VOLE,TUN,TUL,VELG FORMAT U U , 1 F 7 . 2 . U F 6 . 2 , 1 3. 1F7 . ? . 1 F A .P . I F 7 . U . 1 F A . 1 . 1 F 7 . * ) PUNICH 8 ,NI0, J ,OGM, Ttl.M, T j L»' VEL G FORMAT ( IU, 13, 1 F 7 . 2 • 1 F7 .U , 1F«. .1 , 1 F 7 . 3) 30 -TP- 53 • • : FORTRAN 2 C O M P R F . • C COMPUTATION! OF NTU FOR CARBON OIOXIOF ETHYLFNE GLYCOL 63 PR jlvlf I 1 • FORMAT </b3HSYSTFM TURF CM BP M M OL GP" TEMP C SATC ML CYCLO) R E M V . L I O . n . B P , O L , T E M P , C S A T , C Y , A . B , C _2 FORMAT ( I U , l F 7 . 3 , 2 F 8 . 3 . 2 F 6 . 2 , 1 F R . 5 , 2 F n . 3 , l p f l . 5 )  IF (LIO) fi,nt,tt 70 PRINT 3 ,L IO,0 ,BP,QL.TEMP,CSAT,CY _3 FORMAT ( .6 .6FB .3 )  PRINT 1U 1U FORMAT(/AfH RUN OG C F " P IN PO C IN C OUT T Y P F OGM VCOR TUN I TUL VG )  T 3 READ U,N0,0G,P1 ,P0,C1 , C 2 . J U FORMAT ( IB.bFIC .U , IU ) IF(N0)S1 ,63.51 PIN " BP+A»P1 POUT « P I N - H « P D PMEAN- 0.5»( P IN + POLIT ) PR IN • P IN-0 .1 PPOUT= POUT-0.1 OFIM = P P I N » C S A T / 7 A 0 . 0 - C 1 OFOUT- PB0LJT.CSAT/76S .-C? OFLM = (OF 1N-DF0UT )/L0G(OF IN/DFOtlT ) TUN " 0 .725U1M(C2 -C1 l/DFLM-CY) TUL • 7.6B3/TUN TITR » 8 . 0 2 0 3 « O L « C VOLE ' T I T R » 0 . 5 » ( C 2 - C ' ) » ( 2 / - . 2 + T E M P ) / 2 7 3 , 2 » 7 o 3 . 5 / ( P M F AN-C.1J_ OGCOR- 0G»756 .0 / (PMEAN- . 1 ) *(2 73 .2+TFMP 1/2HH .2 OGM = UGCOR-VOLE VELG • HGM/360C.O/0.33261: PRINT 7 ,N0,0G,R I ,P0 ,C1 ,C2 ,J ,OGM.VOLE,TUN,TUL,VELG FORMAT ( IU,1F7 .2.UFA . 2 , 1 3 , ' F 7 . 2 , ' F 6 . 2 , 1 F 7 . u , I F A . l . 1 F 7 . 3 ) PUNCH__B,NO , J ,OGM ,TUN tTlIL . VELG 8 FORMAT ( IU , 1 3 , 1 F 7 . ? , 1 F 7 , u , 1 F A , 1,1F7.3) GO TO 50 BO STOP PROGRAMS FOR COMPUTATION OF NTU AND CORRELATING VARIABLES IV-6 ...... FORTRAN 2 COMP I I F . C CORRELATION OH VARIABLES FOR BUBBLE AND PLUG REGIONS READ l,N,SUMX,SUMY,SUMXX,SUMXY T " FORMAT l i f t ' , U F 1 0 . D - tl READ 2 , I . I 0 , 0 T , 0 L , n i F F , S T , V I S C 2 FORMAT ( I U . 3 F 6 . 3 . 2 F ? . 3 > IF (LIO) 80 ,80 ,5 5 VELL - 0L /7 .U8 1 /60.0 / (0 . OC0PU5U»DT«DT )* PRINT 9 - - 9 — pnRWAT—r/»2H 110 TUBE Clt GP» 01 FF ' S TEWS VI SC VELL PRINT 8 , L I O , D T , Q L , 0 I F F , S T , V I S C , V E L L 8 FORMAT ( I U . 3 F 6 . 3 . 3 F 7 . 3 ) - PRINT 1 1 " - - - 1 1 FORMAT </50H NO J 0 G M NTU LTU VELG FACTOR CORR Y ) F - S O R T F I 1 . U 6 5 / D I F F » 7 3 . 5 3 / S T ) « ( 1. 1 U / V T S C I • • 0 . l U « 0 T / 3 , 0 8 7 6 » D T 6 0 - • REAP S.NO, J.QGM,TUN,TUL,VELG " ~ — - 3 FORMAT ( l i t , 13, 1F7.2 , 1F7 . U , 1F6. 1, 1F7.3) IF (NO) U , K , 7 C 70 IF (VELG - 3.0) 95,9b,AO 9b Z - T U N » F » ( V E L L + VELG) Y • O . U 3 U 2 9 » L O G F ( Z ) X - O . S 3 l t ? 9 » l O G F ( V E L G l " " " ' PRINT 6 ,NO,J .OGM,TUN,TUL,VELG,F ,Z 6 FORMAT ( l i t , 13, 1F7 .2 , l F 7 . l t , IF 7. 2, 1 F 7 . 3 . 2 F 7 . U ) • — PUNCH 1U,N0,J ,OGM,TUN,TUL,VELG,F,Z 1 It FORMAT ( IU, 13, 1F7.2 , 1F7 . U , I F7.2, IF7. 3, 2F7.lt I N - N + l SUMX -SUMX + X SUMY - SUMY + Y SUMXY - SUMXY + X»Y — — - SUMXX - SUMXX • X»X GO TO 60 80 DN -N XB - 5UMX/DN YB « SUMY/ON B - (SUMXY - D N » X B » Y B ) / ( S U M X X - DN«XB»XB) A - YB - B*XB "'" " PRINT 12,N,SUMX,SUMY,SUMXX,SUMXY,A,B FORMAT ( / 1U, UF12. 5,2F7."5) STOP — END IV-7 PROGRAMS FOR COMPUTATION OF NTU AND CORRELATING VARIABLFC F OP TP.AM 2 C O M P I L E . C C O R R E L A T I O N FOR S L U G R E G I O N R E A O 1 , N , S U M X , S U M Y , S U M X X , S U M X Y ' 1 " F O R M A T ( IU.UFIG.U) u R E A O 2 , L I 0 , D T , O L , n i F F , S T , V I S C 2 F O R M A T ( I U . 3 F A . 3 . 2 F 7 . 3 ) I F ( L to ) 8 0 , 8 0 , 5 b V E L L « O L / 7 . U 8 1 / 6 1 . 0 / ( 0 . 0 0 C 8 U 5 U » O T » O T ) * P R I N T . 9 9 F O R M A T T /U2H L I O T U B E OX G P I T 0 I F F 5 TENS V I S C V F L L ) P R I N T 8 , l . I o , n T , 0 L , 0 I F F , S T , V I S C , V E L L 8 F O R M A T . ( I U , 3 F 6 . 3 , 3 F 7 . 3 ) P R I N T i i 1 1 F O R M A T (/5Ch NO J OGM N T U I T U V E L G F A C T O R C O R R Y ) I F (VFI.L-C .7S) 2 0 , 3 0 , 3 0 2 0 F - ( 1 . U A 5 / U I FF ) * » . 37U« ( 7 3 . 5 3 / S T r » » . »5t» 11 ."tU'/V I S C > « « . U 8 6 M 0 T / 1 .757 > 1 » » 1 . 3 2 G O TO 6 0 3C I F ( V E L L - 1 . 3 ) 4 0 , 5 0 , 5 0 UO F - ( l . U A b / D I F F ) » « . 3 0 7 « M 7 3 . 5 3 / S T ) » « . 2 2 8 » ( V I S C / l . I U ) » » 0 0 . 0 2 b » < D T / 1 . 7 b 17 1 . 0 6 3 G O TO 6 1 " " - ' - - 5 0 F - < I . U 6 b / U I F F ) » » . l 9 3 « l 7 3 . 5 3 / S T ) » « . 1 9 3 » ( V I S C / 1 . I U I • • 0 0 . 1 A ) • ( O T / 1 . 7 5 1 7 ) « « C . 9 I 3 6 0 REAO 3 , N O , J , Q G M , T U N , T U I . , V E L G 5 F O P M A T ( I U . I 3 , 1F7.2, D-7.U, 1F6. I, 1 F 7 . 3 ) * I F ' ( N O ) U . U . 7 C rc •- I F ( V F L G - 2.C) 6 0 , 6 0 , 9 5 9b Y = 1 . 0 / F » ( . 0 1 6 U + . 0 1 1 b » V E L L ) » t U . 6 i.4- • , 9 6 » V F L L A + V E L G ) - ' J . O ' U X = T U N P R I N T 6 , M O , J , O G M , T U N , T U L , V E L G , F , Y 6 FOP MAT ( I U . I 3 , 1F7.2, 1I-7.U, 1F7.2 , 1 F 7 .3 .2F7.U) P U N C H I U . N O , J , O G M , T U N , T U L , V E L G , F , Y • " 1 u F O R M A T ( IU, 13, 1F7.2, 1F7.U, 1F7. 2, 1F7. 3, 2F7.U I N » M + 1 S U M X = SUMX + X S U M Y - S U M Y + Y S U M X Y - SUMXY + X » Y S U M X X » S U M X X + X » X G O TO AO so U N -N X B = S U M X / D N Y B - S U M Y / O N R •• ( S U M X Y - U N * X B » Y 8 ) / ( S U M X X - O N » X 8 » X H ) A Y B - ti»XB ' • " " - P R I N T 1 2 , M , S U M X , S U M Y , S U M X X , S U M X Y , A , B 1 2 F O R M A T ( / I U , 1 F H y . U , l F 1 0 . 6 , 1 F I 0 . 3 , I F 1 C . U , 2 F 9 . A ) " S T O P • " - " E N D APPENDIX V LISTS OF EXPERIMENTAL DATA, CALCULATED VALUES OF CORRELATION VARIABLES , AND RELATED CALCULATES RESULTS L i s t s of Experimental Data and Calculated Values of NTU for the Various Systems The experimental runs were a i l numbered so that values from the three separate l i s t s of calculated r e s u l t s could be related, i f desired. Two number-codes were used, the f i r s t r e f e r r i n g to "system'": Number System 1 C02-Water.. 2 He"Water 3 C0 2~Ethanol Tube size., 1.757 cm 4 C0 2-Glycol at 30°C... 5 C0 2~Glycol at 15°C...( 6 C02~Water Tube s i z e , 1.228 cm 7 C02-Water .Tube s i z e , 2.504 cm The second number-code r e f e r r i n g to "type" or flow region i s as follows: Number Type (flow region) 1 bubble 2 bubble-plug t r a n s i t i o n 3 plug 4 plug-slug t r a n s i t i o n 5 slug 6 slug-annular t r a n s i t i o n 7 annular The values for "SATC ML"1 are saturated concentrations at the V-2 absorption temperature and 760 mm pressure, and are given i n the same uni t s as "C IN" and " OUT" for the p a r t i c u l a r series of experiments, usually ml of 0.1 N equivalent base for a 100-ml sample, or millimoles per l i t r e . The units of the various other l i s t e d variables are as follows: Variable QG CFH P IN, PD QGM VCOR TUN TUL VG D e f i n i t i o n and Units gas flow, cfh at 15°C, 756 mm (dry gas) pressure, pressure drop; inches of carbon t e t r a  chloride (at 21°C), unless otherwise noted mean gas flow rate, cfh at absorption temperature and mean test section pressure, saturated the sum of the volume of gas absorbed i n the entrance section and one h a l f that absorbed i n the test section; units same as for QGM NTU, dimensionless LTU, f t gas s u p e r f i c i a l v e l o c i t y , fps L i s t s of Calculated Correlation Variables for the Bubble and Slug Regions The l i s t e d variables not previously defined, and t h e i r u n i t s , are as follows: V-3 Variable D e f i n i t i o n and Units 2 5 DIFF d i f f u s i o n c o e f f i c i e n t , cm /sec (10 ) S TENS surface tension, dynes/cm VISC v i s c o s i t y , cp VELL l i q u i d s u p e r f i c i a l v e l o c i t y , fps J same as "TYPE", defined by second code-number F A C T O R products of a l l dimensionless groups ra i s e d to appropriate exponents, dimensionless CORR Y (a) ordinate for bubble c o r r e l a t i o n ; fps (b) predicted NTU value for slug c o r r e l a t i o n ; dimensionless COMPUTATION OF NTU M TIIBC LM RD MM 01 GPM TP MP C SATC «L VP MM 1 1 .757 754 f\ *> .623 15 .3 0 0 4b .4 70 12.8 00 RUN OG CFM P IN PO C I" C OUT TYP •= UGM VCOR TUN TUL VG it! 1 33 .40 4 .90 1 ,5b 3 .40 17 .20 3 132.74 . ' 0 .4023 19.0 '4.128 " 42 133.'3 3.20 1 .«? 3.60 l i .SC- b 103.24 .95 .341* 22 .4 1 J . " 8 9 43 72.70 2.00 1 .37 4.33 13.00 5 73 .34 .71 .'25Cb 30.6 7 .774 44 36 .93 1 .50 ' .'8 1 .20 7 .20 _ l( .02 .47 .1491 51 .5 3 ,°4 1 45 1 .24 .50 .31 1 .20 3.60 1 1 .07 .18 .057 I '34 .4 .114 46 4.5 2 .55 .29 1 .40 5 .30 1 4 ,29 .30 .0950 80 .8 .4b7 47 8.82 .70 .4 1 1 .60 5.30 2 8 .69 .28 .0903 85 .0 . "24 r 48 12 ,88 .80 .UB 1 .70 b .70 3 12.79 .31 .0982 78.1 1 .36 IS 49 18.38 1 .00 .68 1 .90 6 .60 5 18.02 .36 .1170 6b .6 1 . "18 53 28.23 1 .30 ..°2 2.C? ' 7 .50 .4 2H .23 .43 .1386 55 .'J 3 .00b 5) 47 .00 1 .70 1 .32 1 .70 V.30 5 47.13 .59 .1953 39.3 b . 0 1 7 52 60 .43 1 .90 1 .33 l .70 10.30 b 60 .62 .67 .2239 34 .3 6 . "52 EXECUTE FORTRAN PROGRAM, S YS I FM 1 TUBE CM 8P MM OL uPM TEMP C SATC ML VP MM 1.757 758.200 2 . ' 0 0 lb .000 4b.47Q 12.800 RUN 53 OG CFH 4 .94 P IN 2.50 P0 2.5C C IN 8.60 54 55 56 57 58 59 7 .86 11 .18 13.28 3.05 3.60 3.70 2.9b 3.28 3.38 9 .50 9.90 9.70 C OUT IOj.50 12 .20 13 .70 1b . ' 0 TYPE WGM VCOR _ !__ Jt.38 j 4V ' I " 7 . 16 1 10.25 I I 1 , 0 3 16.71 20 .22 27 .00 4 .00 5.00 5 .00 •3.62 4 .06 3.37 12.20 7 .60 8.4 0 63 61 62 36.60 46 .00 68.60 6.10 O.10 1? .ap 4.28 b.97 7 .86 63 64 6b 93.U0 IbO .03 122.00 9 .60 10.60 1 2 .' 0 16 .30 12 .00 " l 4 .70 17 .0 : 20.30 1 2 .«? 17.00 14.93 h .Oft 1 0 ,ov 10 .02 66 6 7 102 .50 93 .40 12 .90 12 .50 0 .45 .8.24 1 3 .00 1 3 .80 13 .J_0 15.40 13.30 24 .90 29 .60 20 .43 2b .00 24 .20 3 l b , 7 2 3 19.11 i 2 b . 82 5 35.20 b 44,Q3 5 65 .54 5"" 88 ,7 2 6 I 41.08 5_1 1JS_.S6 5 97 .35 b 88.74 .7b .99 ! .42 r."o? 1.14 .20 I i .33 I .67 2 . J 6 "2704 ,33 ,44 ~.W .90 TUN .0538 .0050 .1 148 .1663 , l . i i 6 . .1247 . ' 336 .1542 .20-7 ;?7 9? "".4 20 r .6621 ,498_4 ."lIT9_" .4056 TUL 142 Vo 66 46 61 57 49 .R 3/ .R 27.5 VG ,467> "• .762 ;- 1 .091>: 1 .270-. T .675 2.034 " 2 .748 3 .747 4 .762 6 ,076 1>1.2 1 1 .6 15.4 17 .4 18.9 9 .444 lb .0 16 12 ,300_ TCT3A2 V .445 SYSTEM 1 TUBE CM BP MM 1.57b 7b7.200 OL GPM 1 .500 TFMP C SATC ML VP MM 15.000 45.470 12.800 RUN OG CFH P IN PO C IN C OUT TYPE nGM VCOP TUN TUL VG 74 1 .32 1.10 1.10 2.20 3 .4b 1 1,10 .23 .^29v 256.9 .146 7b 2 .03 1.15 1.15 3.60 b .40 1 1 .Y"2 ,3b .0448 T 7 T . 7 .227 76 3 .58 1 .30 1 .30 b.5 0 7 .4 0 1 3.27 .35 .04 97 154 .4 .U.HSy. 77 5.R5 .1 .45 1 .41 5.30 8.SO 1 b .32 .59 .0647 93.6 .705 78 9.11 1 .95 1 .88 4 .7 0 9 .00 1 8 .4 0 .80 .1 13o " d f ' S 1.1)3 SYSTEM TUBE CM RO >IM OL GPM TEMP C SATC ML VP MM. 1 1.575 759 .600 1 .500 15 00 45 . 4 7 ' 12.800 KUN OG CFH 0 IN PO C IN C OUT TYPE MGM VCOR TUN TUL VG 79 12.29 2.35 2.16 4.10 9.10 1 1 1 .44 .93 .1307 5HT7" 1 .5 1 b 80 15 .84 2 .45 2.23 4.00 8.70 1 15 .06 .88 .1220 62.9 1 .9V6 81 19 .30 2.70 2.44 5.30 9.50 3 18.63 .78 .1 120 6b .5 2 .468 82 28.90 3 .30 2.98 6.R0 1 1 .60 b 28,14 .89 .1343 57.2 3.728 83 36.00 3 .9t 3.39 6 .70 11 .80 b 30 .07 ,°b .1426 b3 .8 4 .778 84 46.30 .4 .80 4 . 0 a 6,00 12,80 5 47 ,2S 1.10 -.167b 45 • R 6.758; ' SYSTEM TUBE CM BO MM OL GPM TFMP C SATC ML VP MM 1 1 ,S7b 758 .200 1 .500 lb .0 00 4b ,47T 12.800 RUN OG C F " P JN ' PO C IN C OUT TYPE OGM VCOR TUN TUL VG 90 3 .57 1 .25 1 .25 4 .00 6 .30 1 S . i b .42 .ObBl 132.3 .42 1 91 4 .7 9 " 1 7 4 3 " 1 .40 4 .90 7 .60 ~ r 4.34 .50 .0702 139.4- ; 5 T T r 92 19.30 2.60 2.50 8.10 12.20 3 18.70 .76 .1 183 64 .9 2.476 93 57.30 b .10 4.59 B.20 16 .80 b 55 .83 1 .63 • ?6b6 28 .0 7.^95" 94 1 15.30 7 .30 6.61 1 1 .4 0 26 .10 b 112.18 2.91 .5708 1 i .4-I U . 8 5 9 x 95 190.70 11 .03 9.6B 12.50 34.40 6 184 ,0b 4 .69 1.0966 7.3 24 .379" SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP MM 1 1 .57b 759.203 .623 15 .030 45 ,470 12 .800 RUN QG CFw P IN PO C IN C OUT TYPE OGM VCOR TUN TUL VG 112 1 .24 .27 .28 1 .70 3.90 1 1 ,0b .16 .0525 146.2 .143 113 2 .48 .34 .35 1 .70 3 .40 1 2 .22 .28 .0900 85.3 .294 114 5.80 .45 .46 1 .90 6.80 2 5,48 .38 .1216 63.1 .727 115 13.39 .63 .63 2 .00 7.50 3 13.08 .4 2 .1378 55.7 1 .335 116 15.30 .73 .70 2.10 7.43 3 15 .06 .4 1 .1327 57.8 1 .994 117 23 .22 . «B .84 2 .40 7.50 3 20 ,34 .39 .1283 59 .8 2 .655 118 30.80 1 .20 1.13 2.30 8.30 5 30 ,64 .46 .1523 50.4 4.0b9 COMPUTATION OF NTU V-5 _ ^ : :.: SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP M M 1 1 .S7-> 7 S 7 .600 .620 15 .0 00 45.470 1 2 ,800 RUN OG CFH o IN PD . C IN C OUT TYPE UG* VCOR TUN TUL VG 119 u i . i o 1 .35 1 .2? 2.20 1 1 .50 5 43 .85 .73 .2470 3 1 .1 5.4 12:: 120 60 .70 1 .60 1 .41 2.7.0, 1 3 .50 5 60.53 .85 .2971 25 .8 3.018 12 1 85 .00 1 .80 1 .58 3 . 30 13.50 3 85 .12 .80 .2826 21 .1 H . 2 C 4 . 122 1 13.50 2 .4 0 2.05 3.5? 1 5 .10 5 1 13.65 .92 .3298 23 .2 >3 .03.3 v 123 144.00 2.95 2 .38 3.60 ' 7 . 5 C 5 144.02 1.11 .li 1 09 1 8 . 6 19 .076 124 169 .00 3.60 2 .84 4 .00 19.90 5 1 6 0 . 7 6 1 .29 .492 1 15 .6 22 .353 SYSTEM TUBE CM 8P MM OL GPM TEMP C SATC ML V P « M 1 1 .575 753.300 2.100 15.000 45.4 70 12. 800 RUN OG CFH P IN PO C IN C OUT TYPE OGM VCOR TUN TUL _ . 125 1 .36 1 .92 2.01 3.10 4.05 1 1 . 1 3 .24 .0232 350 . 6 .150 12 6 2 ,R2 2.12 2 . 1 b 4.10 5.5b 1 2.48 .37 .0365 i l O . l .329 127 14.BO 3.70 3.57 9.43 13.10 I 14.01 .97 .1 1 09 69 .2 1 . P 3 6 128 130.60 14 .60 10.47 16 .00 28 .50 6 12b .05 3 .42 .5456 14.1 16 .564:< 129 1 91 .70 18.60 14 .09 18.20 34 .40 6 "82.33 4 .65 .8747 8.7 24.151 SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP MM 1 1 ,57a 752.500 2 .1Q0 .15.. 000 43.i.470^ 12 .800 RUN OG CFH P IN P O C IN C OUT TYPE UGM VCOR TUN TUL VG 130 1 .91 2.05 2.11 4 .40 3 .53 1 1 .64 .30 .0291 263 .5 .2 17 131 6 . 1 7 2.52 2.52 6 .70 8 .80 1 5 .72 .55 .0571 1 3 4 .3 .757 .-' 132 12 .79 3.42 3.29 10 .20 1 5 .50 1 12.10 .B7 .1009 76.0 1 .6 03,: 133 14.53 3.60 3.41 1 1 .20 14 .60 1 13 .84 ..89 .1 074 71 .5 1 .833 134 19 . 1 4 4.20 3 .88 12.50 15 .90 3 18.48 .89 . 1 1 1 7 68.7 '2;.i'-4"8 135 1 1 .67 3.30 3.20 12 .70 lb .80 1 1 1 .02 .8 1 .1024 75.0 1 .t'60 136 1 .64 1 .98 2.01 4 .50 5 .30 1 1 .4 0 .26 .0252 304.4 . 1 86 137 8.73 2.90 2.90 8.25 1 1 .00 1 8 . 1 4 .72 .0788 97 . 4 1 .079 138 17 .44 3.96 3.64 10.70 14.10 3 1 6 .77 .89 .1056 72.7 2.222 139 23.30 4.90 •3.96 11 .90 15.60. 3 22 .56 .°7 .1 194 64.3 2 .988 143 30 .10 5.80 4.48: 12;10- 16.00 3 2 9 . 3 0 ^ 1 . 3 2 7 T Z 5 6 " 6 3 . 6 . <J-YSrFM T I I R C CM RP MM PL' GPM TEMP C. SATC ML VP MM '•1. 1 .573 753 . 0 0 0 RUN OG C F H P f i . 1 .soo 1 5 . o n e 45.470 1 2 . O Q 0 ' C OUT TYpg OGM »COP TU>f TUL 141 1 .64 I . U 1 . 2 0 5 .20 6 .50 1 1 . 4 2 .24 .0356 228 . 3 .188 142 2 . « 3 1 .20 1 .26 5 .30 7 .40 1 2 ,4H . 3 9 .0550 1 3 9 .5 .328 145 7.8 1 1 . 7 4 1 . 7 b 7 . 6 0 1 1 .20 1 7 .25 .67 .1 024 7 4 . 9 . "60 144 10 .96 2 . 1 2 2 . 0 8 7 . 0 0 12 .30 1 10.28 .83 .1277 60 . 1 1 .362 145 15.03 2 .40 2 . 3 3 H .50 13 .23 1 14 .34 .88 . 1 394 5 3 . 1 1 .OS-) 146 2b .10 2 . 9 4 2'. 81 9 .00 1 3 .40 4 24 .5 8 .82 .1316' bH . 3 3 . 235 147 40.00 4 . 1 4 3 .70 9 .70- lb .00 5 3 9 . 3 7 1 .00 .1 637 46 . 9 5 . ?Tu 148 69 . 0 0 5 .60 4 . 5 3 10.90 19 . 0 0 b 6f .80 1 '.flu .27 15 28 , 2 8 . "ti 1 SYSTEM TUBF CM. BP MM OL GPM TEMP C SATC ML VP MM 1 1 . 7 5 7 7 5 7 . 3 00 . 1 .500 1 5 . 0 0-0 4 5 . 4 7 0 12.80 RUN OG CFH P IN Pn C IM C OUT TYPF OGM VCOR TUN TUL VG 149 2 .34 1 . 1 5 1 . 2 1 3 . 8 0 5 .50 1 2 .05 .31 .0423 ' 8 0 . 6 .218 150 3 .99 1 .27 1 .29 4 .30 6 . 7 i i 1 3 . 5 9 . 4 4 .^61.3 125 . 2 .382 151 2 0 . 1 4 ' 2 . 6 7 2 . 5 5 7 . 1 0 1 1 .30 3 19.<<4 .78 . H a l 65.0 77TR0 152 55 .20. 5 .26 4 .69 8.40 lb .20 5 54 .1 1 1 .28 .2053 3 C . 4 5 . 7 6 ' : 153 107 .50 7 . 5 ? . 3 .62 1 0 .90 2 1 .60 b 1.05 .29 2 . 06 .3735 20 . 5 11 .907 154 151 . 5 3 9 .39 7 .76 12 .40 26 .30 3 147 . 7 7 2 . 7 3 • ^468 14 . 0 15". 7 2"8""" 155 190.60 1 1 . 4 3 9 ,S5 1 3 .80 3 0 . 0 0 6 1 o 5 . 2 4 3 . 26 . 7 1 4 7 IO .7 1 0 .7 1 is SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP MM 1 1 . 7 5 7 750 .300 1 . 5 00 1 5 . 0 00 4 b . 4 7 0 I 2 . n o RUN OG CFH P IN P'n C IN r. O U T TYP E uG« VCOR TUN TUL VG 156 5 .59 1 . 4 3 1 .46 3 .20 0 . 13 1 5 . 1 5 . . 5 5 .0785 97.7 .S48 157 12 .74 2 . 25 2 .25 3 .40 1 0 . 30 1 12.06 . 9 3 . 1 343 5 7 .0 1 .384 158 17 .58 2 . 46 2 ,4D 5 . 5 5 9 . RC 3 1 7 . 1 2 .80 .1 160 AO . 2 1 , « 2 2 159 121.20 7.82 6 . 6 9 . 9 . 0 0 2C .90 5 1 19.70 2 .32 . 1 1 0 5 5 1 9 . 0 12 .741 160 163.80 9 . 8 6 8.48 1 0 .20 24 . 5 0 b 161 . 3 3 2 . " 3 .8294 14 .8 1 7 . 1 7 ? 16 1 194.70 1 1 .70 9 . 8 2 1 1 .30. 2 ( . OO 6 1 9 1 . 09 • 3 . 14 . * 2 5 3 12 . 3 "ZO . T « """ 162 21 .65 2 . 7 9 2 . 63 6.05 1 0 . 2 0 21 .27 . 7 8 . 1 145 6 7 . " 2 .264 SYSTEM TUBE CM 8P MM OL GPM TEMP c -SATC ML VP MM 1 . 1 . 7 5 7 7 5 9 .200 1 .07 0 1 5 . 0 ' - u 43.470 12 .80 RUN OG CFH P IN .C IN C OUT TYPE UGM VCOR TUL l » 3 164 22 .60 1.^.1 1 .70 • .-> 1 1 .64 4 .1 0 0 . t»... 9 . 0 0 *• 4 2 2 . 1 3 ." f. .65 • • f.i ..- . 1 282 39 . 0 1 . / H T 2 . 3 b u 165 31 .50 2.12 1 . 9 3 4.30 1 0 . 0 0 . . 3 3 0 . 0 9 .76 . 1 S ' 4 50 . 7 3 . ' 9 ( i 166 86.40 3 .5 2 3.08 3.10 13 . 0 0 3 83.47 1-. 34 .3833 26 , 0 9.097 167 1 3 7 . 60 4 .«7 4 .24 5 .90 1 8 .90 5 136.0-3. 1 . 7 " .4029 19 . 0 1 4 . 'J i.i 1 168 1 9 8 . 30 7 .03 3 >*6 7 .10 3 4 .30 I, ' 9 b . 13 2 .43 .S983 12 2;. . 7 7 1 V COMPUTATION OF NTU s S Y S T E M T U B F CM RP M M ' O L O P * "TfcMP SATC* *C V P * vfi5' •- - I 1 1 . 7 5 7 7 5 1 . 5 0 0 i . 0 7 : 1 5 . 0 0 0 4 5 , 4 7 0 1 2 . \ ' . R U N O G C F M P I M PO C I M C O U T T Y P E U G M V C O R . T U N T U L V G I 1 6 9 1 . 3 2 . 4 6 , 4 V 1 .oc 3 . 5 0 1 1 . 1 3 . 2 1 . 1 3 8 5 1 9 0 , 4 . 1 2 0 • 1 7 3 3 . 3 2 . 6 5 . 6 6 2 . 4 0 b . 0 0 I 2 . 7 3 . 3 4 . 0 6 4 1 1 1 9 . 7 . 2 9 1 • 7 1 8.77 1 . 1 2 1 . 1 3 3 . 3 0 7 . 9 0 1 H.M . 6 2 . 1 190 6 4 ,b . H H 6 1 7 2 1 1 . 4 3 1 . 2 6 I . 2 6 3.70 0 . 7 3 2 1 0 . 9 5 . 6 7 . 1 3 1 4 5 B . 4 1 . 1 6 6 ' 7 3 1 3 . 6 6 1 . 3 6 ' . 3 6 3 , 4 0 « . 3 0 3 1 b . 2 7 . 6 6 . 1 2 7 5 6 3 . 2 . I . 4 1 3 . 1 7 4 1 6 . 2 7 1 . 4 5 . 1 . 3 9 •3 . 3 0 B . 2 0 3 lb , ° 3 . 6 6 . 1 2 7 1 6 . . 4 1 , A V 6 ! 1 7 5 5 4 . 9 0 3 . 0 3 , 2 . 4 6 u . 2 0 1 1 . o z b 5 4 . 7 2 1 ,0b . 2 1 2 " 3 0 . 2 b . " 2 5 !!• 1 7 6 1 6 7 . 1 0 I n - 1 r\ 6 . 0 2 ——rn— b . 2 6 —7—rr- 3 . B C 2 0 . 5 0. 5 1 6 6 . 6 3 - r m — T T T 2 . 0 7 T 2 - T - . 4 7 4 2 1 6 ; 2 i"9 1 7 . 7 3 5 S Y S T E M T U B E C M B P M M O L G P M T F M P C S A T C M L Vf M M 1 1 . 7 5 7 7 4 9 . 4 0 0 370 15.0i 4b .470 12. HO.' R U N O G C F H P IN P O C IN ( , O U T T Y P F • v!GM V C O R T U C : T U L V G 178 2.07 . 5 9 .62 . 2 .30 4 .30 1 1 . « 5 . .26 .149". 1 5 6 . 7 . . 179 3 . 5 7 .72 . 7 3 2 .40 b .'i0 1 3.25 . 4 . " . ' 746 102.0 .346 . 180 6 .26 .91 .92 3 .30 7 .1.0 1 5 .89 . 5 1 .0976 76 .6 .627 181 V . 7 0 1 . 1 9 1.19 3.30 8.20 1 9.26 • .66 .1277 6 .:•. 1 ,6"H6" 182 12.69 1 .32 1 .30 b.30 8.40 3. 12.29 .60 .1332 5 7 . 6 1 .30o 183 15.84 1 .41 1 . 3 7 3 . 5 0 8.20 3 15 .57 .63 .1227 62 .6 1 .657. S Y S T F M T U R F C M R P M M OL G P M T E M P C S A T C ML V P ' M M 1 1 .757 760 .400 .620 1 5 . 0 0 0 4b.470 12 .R0 RUN OG CFH P IN PO C IN C OUT TYPF U G M VCOR TUN Till. V G 193 1 .32 .27 .38 2.60 4 .65 1 1.12 .20 ."14 VB" 1 5 4 . C .119 194 3.22 . 3 7 . 4 7 2.85 6 .6b 1 2 .86 .39 .OObO 6 3 , R .304 195 5 . 5 3 . .40 .50 2 .90 •7 . 4 b 1 b .1 1 . 4 7 . 1 150 66.7 . 5 4 4 196 B;20 .55 .65 3.40 8.40 1 7.76 .51 . .1 288. b9;6 .B26 197 10.96 .60 .70 3.40 6.40 20 10 .55 ' .51 .1286 b9 .6 1.123 , 198 12.74 .62 .72 3.30 8.30 3 12 . 3 5 .51 .1284 39 . R 1.3 14 199 1 6 . 3 1 . 7 3 .81 3 . 4 b b • 00 3 16 .00 . 4 7 . 1 166 6b .8 ' i . 7 03" 200 19.26 .86 .94 . 3 . 7 5 8. DO 4 19 .00 . 4 3 .1093 70 .2 2 . "23 20 1 31 .20 , "9 1 .26 4 .85 9 . 1 5 5 31 .03 .44 . 1 136 67 .5 3 .303 X SYSTFM I TUBF CM BP MM 1 .757 759.90 0 OL GPM .620 TEMP C lb .000 SATC M L VP M M 45 .470 12.RO0 RUN OG CFH P IN PO 202 42 .50 1 .51 I . 1 9 C , I N C O U T T Y P F O G M V C O R T U N • T U L 3.60 9.55 42 .22 . 6 2 . 1 5 5 7 203 54.30 204 72 .60 205 96.60 I .68 1 .84 2.48 206 1 3 4 . 1 0 20 7 1 7 7 .00 20 8 197.20 1 .27 1 .37 I .66 4 . 15 1 1 . 1 0 4 .55 1 3 . 1 5 b.OC 1 4 . 9 b 3 ,62 5 . 1 4 6.04 2.21 2.54 3.38 5.90 1 7 . 7 5 7 .53 2 1 .60 . 8.30 23.80 b 5 J> 5 ' 33 .03 5 1 7 4 . 7 8 b 194.33 53 .96 72 .20 96 ,03 V G 4 9 .3 _Li_"_!_. u"i".1 5 .746 3 2 . 0 . 7.685 .73 . 1 6 7 1 . 0 2 .23*7 _L'07 .28616 2 6 . 8 1 0 .221 1 . 3 0 " " 3 5 9 6 " 27. 3 ' " i 4.161 1.59 .4651 16.5 16.603 1 .80 .SUOs 1 4 . 2 2C.6n4 SYSTEM 1 TUBE CM BP MM 1 .757 760.200 OL G P M 3.0C0 TEMP C lb .000 SATC ML V P M M 4b.470 12 .800 RUN OG CFH P IN 209 .59 6.88 PO 3.4b C IN C OUT TYPF PGM VCOR TUN TUL 3 ,4b 1 1 .3 1 .26 213 2.87 211 5.81 212 9.Bp 6 .00 7 . 4 7 8 . 5 7 213 IS .58 13.03 214 23 .70 1 1 .7 3 215 33.10 1 3 . 0 5 3.48 3.9 1 4.77 4.20 b . l b 6.00 7.60 10.00 12.10 2 .36 4 .97 8 .65 5.57 13.45 16.OC 1 14.07 6.52 1 3 . 9 0 16.80 3 21.77 7.13 14.50 18.1b 5 30.37 .45 .77 1 .01 7723" 1 .40 1 .77 .0131 DK5.4 702"3l~3"3"T77- ..1411 166.7 .0604 127.1 216 44.70 16.30 B.41 15.55 19 .RC 217 75.40 22.70 11 .69 17.75 24.50 ."BIS .0940 .1209 94 . 1 8 1 .6 63.5 41 .05 .1460 5 2 . 6 68.09 3.35 .2560 30 . . 1 3 9 X . — \ T S "4 . 5 2 0 . 0 2 1 1 .498 2 . 3 1 6 3 . 2 3 ? "4 .369 7 . 2 4 7 218 97 .00 25.50 12.74 I V . 6 0 27 .70 87 .03 4.10 .3356 22.8 9.263 SYSTEM TUBE CM BP MM OL GPM TFMP C SATC ML VP iiM _ 1 1 .757 758.900 3.0C0 15.000 43.470 12."P00 RUN OG CFH P IN PO 219 2.37 3.46 3.57 5 .50 6.35 223 7.57 4.55 4.23. 7.50 8.83 221 11 .49 5.46 4.74 1Q.70 12.QQ C IN C OUT TYPE QGM VCOR 1 1 . 6 6 1 6 . 9 6 1 10.4 1 .41 .63 1 .08 TUN TUL "" ".12 1 7 3b2i .0352 218 . .06b9 H 6 . VG . 1 7 7 . 7 4 0 * .108 " 2 2 - 18.45 6.79 5.47 1 1 .40 14.30 3 16". 9 6 223 65.80 13.76 10.75 16.00 22.00 b 61.45 224 102 .3? IB.30 1 3 . 9 2 1 9 . 1 5 28.10 b 0 4 . 3 6 I .'US .0 8 91 8 6 73" 1 3 . 0 5 .2226 3 4 . 5 6 4 . 7 8 . 3 9 6 7 1 9 . 3 10 R0"5~ S41 0 44^ 10 6 " 528 043 22b 134 .30 21 .80 1 6 . 4 B 22 .00 32.Sb 6 1 2 3 . 1 3 5.93 .Sbb3 13.8 1 3 226 172.03 26.70 20 . 1 3 24 .70 3 7 .60 7 l bb .29 8.10 . "612 8 . 0 16 227 187.40 27.80 20.98 25.00 3 7 . 8 1 7 169 .52 6 . 0 4 .8633 6 . 6 16 COMPUTATION OF NTU V-7 SYSTEM TllbF CM BP M M 1 ' . 7 5 7 7 4 / . 6 0 0 OL GPM 5 . 0 0 0 TFMP r. ' 5 . 0 0 0 SATO. ML VP MM U D . U 7 0 1 2 . H C O RUN OG C F H p J M 2 2 b 5 . OB 4 . 0 V PO C TN C OUT T Y P F OGM VCOR 3.93 7 .35 6.70 IC 4.67 .50 229 , H.72 5.09 230 1 3 . 1 0 0 . 1 3 4 . 6 5 5 . 2 1 8.43 1 0 . 3 0 9,9b 12.4b 6 . 1 7 1 2 . 3 4 . 6 " . 0 3 TUN TUL vr, . 037 1 2 06.6 . i i 97 .o"S2T"T4b .6 "";$•(*" .1749 ' 02 . 8 1 . "« 14 231 2 7 . 2 0 H.21 6.64 1 1 . 1 5 14.35 b 26.23 1.20 . .0V9H 7 6 . 9 2.792 252 5 9 . 3 0 1 3 . 12 10.CS. 1 3 . n o 19 . 1 5 5 . 5 7 .05 2.01 . 'Bs t i 4 ' . 3 6 . "72 233 R9.3.~ I6."4 12.89 15.65 7 5 . 9 5 5 8 4 . 0 3 3 . 1.5 232 93.7 0 . - 4 2 234 '25 .20 20.70 15 .75 1 7 . B" - 9 9 . 235 164.60 24 .BO l u . 9 " 19.30 32.10 i 1 I, 8 0 ' 5 4 . 15 4 .61 . 1 4 3 6 . 6 / 1 3 14.1 ' 2 . 5 3 9 11.4 ' 6 . i ' 0 7 SYSTEM TUBE CM BP MM 1 1 .757 752.4Q0 OL O P M 1 .070' T E M P C " 5 .SOO S A T C ML VP MM 62.010 6.6O0 RUN OG CFH P IN pn C IN C OUT TYPE OGM VCOR TUN TUL VG 236 4.63 .96 .97 6 . 1 5 9 .70 1 3.92 .60 .0658 1 16 .6 .4 17 237 B .48 1.16 1 . 1 5 6 ,R5 12.20 1 7 .36 ,°2 .1022 75 , 1 .783 23H 12.79 1 .37 1 .36 7 .45 12 .90 3 1 1 .55 • °3 .1054 72 , P 1 ,929 239 24 .30 1 .9) 1 .85 8.25 1 2 .'95 5 22 .90 .BO .0915 83 , 0 2.4 37 24.0 "45.70 3 . 1 3 2.0H 9 o" 15.R5 3 43 .28 ' . 1 8 .1380 55 .6 4 .607 ! 24 1 R7 .20 3.BB 3 . 1 3 1 0 . 01 2 1 .00 b 82 .73 1 . 0 6 ,9.St,5 32 ,1) 8.806- i . 242 1 2 2 . ° 0 4 .90. 4.4b •10.90 25.05 5 ' 16 . 1 2 2 .18 .32 17 25 ,« 12.4 02 243 1 64 .70 3.65 b.05 13 . 1 5 29.30 3 156 .31 5.01 • --jTp'y -j" l y ."3"~ 16 .'6 37" SYSTEM 1 " TURF_CM RP_flM " " T . 7 5 7 " T 5 5 . 3 0 0 " SATC ML vp y.» " 2 9 . 6 3 0 " 3 1 .80? R U N O G CFu p I M pn 0. IN 244 4.68 245 8 .44 _246 _ 12 L R3_ 24 7 25".«"6" 246 45.70 249 88.10 . 7 4 . 9 6 1 . 1 8 1 . 71 3 . 2 7 4 . 5 3 .73 -.94 1.16 1 .'68 3.18 4.34 1 , 6 5 I , 0 5 2 , 1 0 2 . 4 5 3 . 1 5 C O U T T Y P E OGM _VC08 4 l 6 4 " '.i"C 4 . 2 5 5 .30 3 .10 b.B-O 7..BO 0 5 11 . 2 5 2b0 125.30 2b l 1 6 5 . R O 5 . 2 6 6 . 4 9 4 . 8 1 5.96 . 7 5 1 . 3 . 2 1 . 1 0 1 5 . 7 5 a .62 1 3 . 4 4 25 . 4 8 49.10 9« 16_B 132 .12" 1 7 8 . 0 1 . 6 5 . 6 6 . 6 5 . 0 2 1,40 2.13 J U N "". if . '3 'T . 1 3 6 1 .1.395 . 1 3 0 2 .7043 .3309 ,4u T6 .5643 TUL .... 7 _ „ . „ . 56 . 2 55,0 55 . 1 5 7 . 6 • 2 1_,-R ""17.3 V3 . 6 VG ,"l!94" •iOl.H. 1 . ' t i3f • 2 . 7 19 5 .32 6 10 . 0 7 7 l'4.1 - 3 18 , ntif, S Y S T F M T U B E CM BP MM OL GPM-. T E M P C s * T C ML VP MM I 1 . 7 5 7 7 5 7 . 0 0 0 1 . 0 7 0 4 5 . 0 0 0 _ 2 . J _ . 4 . 2 0 . 71 .QQ' RUN OG CFH o IN 252 4_.7_3_ ._6B_ 253 8.48 . 0 1 254 12 .65 1 .07 255 23.1Q 1 .60 256 45.30 2b7 86,0 0 258 122 .QQ 2 . 5 3 3 . 3 4 4 , 0 9 259 165.OC b . 6 3 5 . 1 7 pn • C. IN C OUT TYPF WGrt VCO" _ , 6 6 J . 1 5 2 . 7 0 1 5 . 4 3 . 3 3 ,89' 1 . 5 5 3 i " 9 3 1 0 , 7 9 . 5 2 1 . 0 3 1 .15. 3 , 7 5 3 1 4 . 8 9 , 1 ' 7 1 . 5 3 I . 7 5 3 . 8 5 3 7 7 .Sci . 4 5 ^ -T-_ 1 . 2 5 1 . 5 2 2 . 0 2 2 . 2 8 3 . 0 4 3 . 6 7 2 . 1 0 2 . 5 0 3.'b 3 . 0 5 b . 5 0 7 . 0 0 9 . 1 0 "Vi . 0 5 5 54.10 5 102.70 3 146.75 5 ' 96 .36 TUN . ^ 8 9 0 . 1 4 4 8 . 1 3 ' » . 1 208 _ .... , p.^ -. . 3 6 3 7 . 4 9 2 6 . 6 6*31 Till. . . 7 5 3 . 0 58 . 2 6 0 . 5 "3"371"' 2 0 , 0 1 5 . 5 1 5 . 6 2 0 VG . 5 7 7 i . 0 4 2 1 . 5 8 5 2 . " 3 6 y, " 3 " . 7 3 ' ' l i . " 3 i For runs number 260 to 306 inc l u s i v e only, the i n l e t pressure, P IN, given l n inches of mercury; (PD) given i n inches of CCI4 as previously. ; S Y S T F M T U B F CM BP MM 01. Gpy T E M P c S A T C ML VP MM ~ 1 1 1 .757 753 .100 1 .070 1 5 . 0 0 0 . 45 .470 12.80 ' RUN OG . C F H P IM pn r. IM C O U T T Y P F OGM V C O R TUM T U L VG : 26 0 6 .27 9 .95 . 8 1 5 . 1 0 9 .45 1 4 . 1 9 .5 8 .08 56 9 1.8 .44A 26 1 9 .20 9 . 9 0 .96 3 . 2 0 1 1 . 1 0 1 6 . 2 2 . 7 9 .1 155 66 .4 .662 I 26 2 13 .31 9 .95 1 .4 ! 6 . 1 5 12 . 5 5 2 9 .28 .R6 . 1 2«3 59 .P .988 | • 263 28.30 10.03 1 .5 8 7 . C O 12 . 1 0 4 20 . B 5 .68 .1023 75 . 0 2 .219 i 1 264 55 .70 9 ..90 2 .63 9 .80 16 .75 3 4 1 .67 .°b . 1 5 19 50.5 4 . 4 3 5 ; ' ' 263 . 8 6 . 0 0 9 .95' 3 .13 1 1 . l b 2 1 . 4 5 5 64 . 3 3 1 .44 .24 17 31 .7 6 .847 266 1 27 .80-1 0 . 0 0 3 . 10 11.7-0 24..20 b 95 .89 1 .7 9 .3038 23 .1 10 .2 06 ! 267 1 6 3 . 0 0 K'.Ob 4 . 0 0 15.73 2< . 4 0 5 122 . 1 3 1 .91! .3575 2 1 . 4 13 .042 '• S Y S T E M T U B E CM B P MM 0L GPM T E M P c S A T C ML VP MM 1 1 .757 762 .410 4 . 200 1 5 . 0 0 0 45.470 12 .80 J RUN OG C F H P I N PO C IM C OUT T Y P F OGM VCOR T U M T U L VG 268 3 .42 1 .05 5.93 4 . 0 0 5 . 0 0 1 2 .69 . 6 6 .0241 318 . 1 .787 X 269 5.97 1.1.3 6 .56 4 .95 6 . 0 5 1 5 . 1 3 .7? .0271 2 8 2 . 6 .546 ; 270 13.23' 1 .35 .8 . 1 1 6 . 80 8.80 . 1 1 1 . 6 1 1 .34 . .052 1 ' 4 7 . 3 1 .736 271 24.10 1 . 6 1 9 .54 8.35 11 . 1 5 3 21 .58 1 , 8 H .07o4 100.5 2 .297 272 34.50 1 .91 11.12 1 0 .05 13 . 4 5 5 31 .07 2 . 29 .0973 7 8 . 9 3 .3C7 273 54.30 2 .43 ' 1 3 .74 12 .55 18.30 b 4 7 . 0 6 ' 3 .94 . .18 13 4 2 . 3 5.104 274 74.20 2 . 9 9 16.90 15 .65 2 2 . 0 5 3 65 .67 4.42 .7224 3 4 . 1 6 . 9 8 9 . V-8 COMPUTATION OF NTU S Y S T E M T U B F L M RP MM OL GPM T E M P C S A T C ML VP MM ! .757 755.700 4.200 l i . 0 0 0 45 .473" 12.WOO RUN OG CF» 275 2 . ' 2 2/6 IV.P7 277 2h.SP P IN Pn c IN C OUT TYPE OGM VCOR 02 5.7V 1.55 V.16 1.7B 10.62 T U L ' 3.2b 4.00 10.1b 12.10 12.70 15,50 1 .60 I B .22 25 .99 .50 - .017V > .32- .055V 1.91 .0673 428.6 1 3 / . 2 B7.o .170 x 1 . 0 3 0 2 . 7 6 6 X 278 45.20 279 87 .70 280 109.00 2.20 12.63 3.38 16.81 3.79 20.79 14 . 65 18 .65 18 .60 25.15 21 .05 29 .05 41 .06 78.2 V 96.21 T T 7 4 — . t.33 7 4.5V .2547 5.76 ,350V "bTTC" 30 . 1 2 1.8 4.371 8.325 10.240 261 137.60 262 176.10 2o3 180.20 4.33 23.58 5.10 28.52 5.32 30.09 23.65 33.10 20.20 3V.7C 27.20 37.80 6 120,15 6 151.09 7 155.03 7.07 .4782 9.34 .7050 8.50' .6611 1670 IO." 1 1 .6 12.788 16.061 16.501 S A T C ML V P MM 43.470 12.800 SYSTEM TU6E CM RP KM I 1.737 737.700 OL GPM 1 .07 0 T E M P C lb.000 RUN OG CFH P IN PO C IN C OUT TYP •= kiGM VCnR TUN TUL VG 264 2.70 11.18 1 .55 6 .05 9.20 1 ' 1 ,S6 .40 .0383 131.1 -.168 203 5 .86 l l . l a 1 .63 7.50 1 1 .6 J A 1 3.78 .52 . " 7 y i 97 . 1 .405 •', 266 "2.52 11 .IB "•.«!> r .70 14 .43 1 8 .6 3 ,8b .1 343 •>'.'• . 6 IH 287 25 .90 11.19 1 .88 6.R0 14,40 3 16 ,87 .72 .1 12b 66.2 1 .796 .268 31 .no 11.19 1 .93 9.05 14 ,3b 4 22.14 ,68 .1067 7 1 .9 2.3b7 289 47.80 11.19 2.02 1 0 .85 17.63 b- 34 .33 .86 .1433 53.5 3.654 290 85 .5 0 11.19 2.83 10 .50 21 .20 b 61 .62 1 .44 .2365 32.4 6.S36 ' ' 291 155 .60 11 .20 4 .03 14 .65 20 .75 5 " 2 .96 1 .OH .3639 ?' . 2 12.023 2v2 163 .00 11 .22 4.12 14 .R5 29 . 6 5 b 1 \o.2t 2 .09" .3846 i 9. ft 12 .588 SYSTEM .TUBE CM flP itM OL 6PM TFMP C S»TC ML VP -MM 1 1 .757 757 .70C 1 .070 15.0 0 3 4 b .47 3 12.800 RUN OG CFH P IN PO C IN C OUT TYPE OGM VCOR TUN TUL VG M 2 ."08 -8 .30 .68 •z.50 4 .2 J 1 2.52 .l» ' iCbVb l'2b.O .209 294 4 .95 - 8 . 2 9 .91 3.40 6 .20 1 6 .32 .70 .1034 74.2 .*72 2V5 12 .29 -8.14 1 .23 4 .20 7'. Ob 3 16 .61 .70 .1076 71 .2 1.768 ! 296 18.98 - 8 . 1 5 1 .45 4 .95 aTfO b 2b .0-9" .78 .123b 62.T " 2.706 297 26.50 - 7 . 9 1 2.40 7 .80 1 1 .30 b' 3b .99 .87 .1540 49 .8 4.150 298 37 .20 - 8 . 1 5 2.65 12.60 16.15 5 51 ,7b .01 .2329 37.8 5 .508 1 299 4 l .liO -7 1 3 . 5 a 16.65 25 .80 b ••'55 705" 1 .Uf .29 71) 2b .« b . V b b y j S Y S T C M TIIRF r.M RP MM PI GPM T F M P C S A T C _ . M _ L VP MM - - : - - - • - » » 45 .470 12.800 1 1 .757 762.700 1 .070 15 . RUM OG f.FH P IN KO C TM C OUT TYPi= OGM VCOR TUN TUL VG 330 301 302 1 .51 3 . 4 2 7 . 1 9 -8.03. - 8 . 0 6 - 8 . 1 6 .60 .7 2 1 .09 2.45 3 . 1 b 4 .25 3 . 5 5 5 . 3 5 7.50 1 1- 2 1 ,R3 4.2 1 V.24 .26 .5 3 .80 .33 1 1 .0777 . 1 22b 206 .7 V6 .7 62 . 5 .1 94 .HUH ' ,Qa~5 303 304 335 9 .RO 1 5 .R4 23 . 4 0 - 8 . 0 7 - 6 . 1 b - 8.12 1 .20 1 .60 2 .20 3.1b 5 .70 6.10 8 .4 0 8 .35 9 .25 5 4 • 5 12 .83 2 1 .50 3 1 .9b .80 .65 .78 .1265 .1 046 .127V a* .7" 7 3 . 3 6 0.0 1 .'66 2,768 3 . " 0 1 30 3 38.70 -7 .RO 9 . 0 9 1 5 . 3 5 18 .30 • b 5 3 . 5 9 . 7 6 . 1 9 3 3 3 9 .7 5 .7 "4 COMPUTATION OF NTU S Y S T E M 3 T U B E C M B P M M O L G P M T E M P A C S A T C M L V P M M 1 . 7 5 7 7 4 7 . 5 0 0 1 . 0 4 0 1 3 . 5 0 0 3 6 . 6 0 0 2 8 . 7 0 0 R U N O G C F H P I N 3 5 1 1 . 9 8 3 5 2 4 . 0 4 3 5 3 5 . 9 9 3 5 4 8 . 6 8 3 5 5 1 5 . 4 8 , 4 7 .55 . 6 7 . 8 1 . 0 9 P O .77 .88 . 9 9 1 .22 1 . 5 9 C I N C O U T T Y P E Q G M V C O R T U N T U L 1 2.65 3.50 5.05 6.70 7.85 356 2b.BO 1.39 2.06 5.50 8.35 5 24.87 2.03 .1026 74.8 357 34.50 1.85 2.68 6.20 8.75 5 34.12 1.81 .0935 82.1 358 59.60 2.47 3.46 7.35 12.50 5 58.21 3.7B .2077 36.9 9.80 17.10 1 . 4 5 1 . 9 0 2 . 7 0 3 . 9 0 4 . 9 0 1 . 2 2 3 . 0 9 4 . 5 8 7 . 0 6 1 4 . 0 4 , 8 4 1 . 1 2 1 . 6 6 1 . 9 9 2 . 1 1 0 3 6 8 2 0 8 . 6 . 0 5 0 0 1 5 3 . 4 . 0 7 6 3 1 0 0 . 6 . 0 9 5 3 8 0 . 5 . 1 0 4 2 7 3 . 6 3 5 9 1 0 7 . 4 0 3 . 7 2 5 . 0 7 5 1 0 5 . 7 V 5 . 5 8 . 3 4 3 7 2 2 . 3 V G . 1 3 0 . 3 2 9 . 4 8 8 . 7 5 1 1 . 4 9 4 2 . 6 4 7 3 . 6 3 2 X 6 . 1 9 5 1 1 . 2 5 9 S Y S T E M 3 T U B E C M B P M M 1 . 7 5 7 7 5 0 . 7 0 0 O L G P M 1 . 0 4 0 T E M P C 1 3 . 5 0 0 S A T C M L V P M M 3 6 . 6 0 0 2 8 . 7 0 0 R U N O G C F H P I N P O C I N C O U T T Y P E O G M V C O R T U N T U L V G 3 7 5 1 . 6 6 . 4 2 . 7 1 1 . 2 5 2 . 3 5 1 . 9 5 . 7 6 . 0 3 3 3 2 3 0 . 4 . 1 0 2 3 7 6 2 . 9 2 . 5 1 . 7 9 1 . 6 5 2 . 9 5 1 2 . 1 2 . 9 1 . 0 3 9 9 1 9 2 . 0 . 2 2 6 3 7 7 5 . 7 3 . 6 0 . 9 9 2 . 9 5 5 . 0 0 1 4 . 5 1 1 . 4 4 . 0 6 6 5 1 1 5 . 5 . 4 8 0 3 7 8 9 . 0 6 . 8 6 1 . 3 1 4 . 1 5 6 . 8 5 1 7 . 5 0 1 . 9 1 . 0 9 2 1 8 3 . 4 . 7 9 8 3 7 9 1 6 . 6 7 1 . 1 7 1 . 7 0 5 . 4 5 7 . 9 5 3 1 5 . 5 4 1 . 7 7 . 0 8 8 8 8 6 . 4 1 . 6 5 4 X 3 8 0 2 0 . 5 3 1 . 3 0 1 . 9 7 5 . 5 5 8 . 0 5 4 1 9 . 5 5 1 . 7 7 . 0 8 9 1 8 6 . 1 2 . 0 8 0 V 3 8 1 2 7 . 4 0 1 . 5 2 2 . 2 5 6 . 1 5 9 . 7 5 5 2 5 . 8 5 2 . 5 8 . 1 3 3 8 5 7 . 3 2 . 7 5 2 3 8 2 4 3 . 8 0 2 . 0 6 2 . 9 8 7 . 2 0 1 1 . 3 5 5 4 2 . 4 0 3 . 0 0 . 1 6 2 1 4 7 . 3 4 . 5 1 3 3 8 3 8 4 . 4 0 2 . 8 9 4 . 0 7 7 . 7 0 1 3 . 2 5 5 8 3 . 2 4 4 . 0 8 . 2 2 7 3 3 3 . 7 8 . 8 5 9 : : 3 8 4 1 1 5 . 3 0 3 . 7 3 5 . 2 5 9 . 4 0 1 5 . 6 5 5 1 1 4 . 4 0 4 . 6 7 . 2 7 9 2 2 7 . 5 1 2 . 1 7 5 - 3 8 5 1 6 6 . 7 0 5 . B 3 7 . 8 7 1 2 . 4 0 1 8 . 1 0 6 1 6 6 . 9 9 4 . 2 6 . 2 8 7 4 2 6 . 7 1 7 . 7 7 2 3 8 6 1 9 0 . 8 0 6 . 8 9 9 . 2 8 1 2 . 9 5 1 8 . 6 5 6 1 9 1 . 2 5 4 . 2 6 . 2 9 4 4 2 6 . 0 2 0 . 3 5 4 ' . S Y S T E M 3 T U B E C M B P M M O L G P M T E M P C S A T C M L V P M M 1 . 7 5 7 7 5 0 . 7 0 0 1 . 0 4 0 1 3 . 5 0 0 3 6 . 6 0 0 2 8 . 7 0 0 3 8 9 3 8 9 3 9 0 3 9 0 3 9 1 3 9 1 3 9 2 3 9 2 3 9 3 3 9 3 3 9 4 1 4 5 8 8 . 1 0 8 8 . 1 0 1 0 3 9 4 1 4 5 . 1 0 3 9 5 1 9 3 . 0 0 3 9 5 1 9 3 . 0 0 . 5 3 . 5 3 R U N O G C F H P I N 3 8 7 1 . 5 4 . 4 3 3 8 7 . 1 . 5 4 . 4 3 3 . 5 2 3 . 5 2 2 6 . 3 0 2 6 . 3 0 3 8 . 1 0 3 8 . 1 0 5 3 . 6 0 5 3 . 6 0 P D . 7 2 . 7 2 . 8 4 . 8 4 2 . 2 0 , 2 0 , 7 2 , 7 2 , 2 4 . 2 4 , 2 1 , 2 1 , 6 1 , 6 1 , 1 9 , 1 9 : I N 1 . 5 0 1 . 7 5 - 2 . 8 0 2 . 9 5 8 0 0 0 8 0 8 5 9 5 2 0 8 . 9 0 8 . 7 0 1 0 . 8 0 1 1 . 1 5 1 2 . 6 5 1 2 . 7 5 C O U T 2.50 2.60 4.55 4.55 9.30 9.60 1 1.0b 1 1.25 13.30 13. 1 5 15.55 15.80 19.65 19.4b 21 .55 21 .85 T Y P E O G M . 9 0 1 . 0 0 2 . 4 3 2 . 5 3 2 4 . 7 9 2 4 . 7 2 3 6 . 4 4 3 6 . 3 2 5 0 . 8 2 5 1 . 1 4 8 6 . 1 4 8 5 . 7 7 1 4 2 . 4 6 1 4 2 . 9 5 1 9 0 . 6 6 1 9 0 . 4 6 V C O R . 6 9 . 5 9 , 2 3 , 1 2 , 5 1 , 5 8 1 1 2 2 3 . 0 7 , 1 9 , 7 2 , 4 0 . 9 9 , 3 6 9 6 6 . 4 7 7 . 0 9 7 . 2 9 T U N . 0 3 0 4 . 0 2 6 0 . 0 5 6 2 . 0 5 1 5 . 1 2 8 2 . 1 3 3 1 . 1 6 3 9 . 1 7 0 5 . 2 5 7 3 . 2 4 1 4 . 2 9 4 2 . 3 1 4 8 . 4 5 2 3 . 4 2 4 9 . 4 9 9 8 . 5 1 7 6 T U L 2 5 1 . 9 2 9 4 . 8 1 3 6 . 6 1 4 9 . 1 5 9 . 9 5 7 . 6 4 6 . 8 4 5 . 0 2 9 . 8 3 1 2 6 2 4 1 6 1 8 1 5 1 4 V G . 0 9 6 . ' 0 7 . 2 5 8 . 2 7 0 2 . 6 3 9 2 . 6 3 1 3 . 8 7 8 3 . 8 6 6 5 . 4 0 9 X 5 . 4 4 3 9 . 1 6 8 9 . 1 2 9 1 5 . 1 6 2 1 5 . 2 1 4 2 0 . 2 9 2 2 0 . 2 7 0 S Y S T E M 3 T U B E C M B P M M 1 . 7 5 7 7 4 7 . 0 0 0 O L G P M T E M P C S A T C M L V P M M 1 . 0 4 0 1 3 . 5 0 0 3 6 . 6 0 0 2 8 . 7 0 0 R U N O G C F H 3 V 6 1 1 . 4 5 3 9 6 3 9 7 3 9 7 3 9 8 3 9 8 3 9 9 3 9 9 4 0 0 4 0 0 4 0 1 4 0 1 4 0 2 1 1 . 4 5 1 4 . 5 2 1 4 . 5 2 1 9 . 9 7 1 9 . 9 7 2 5 . 6 0 2 5 . 6 0 4 0 . 2 0 4 0 . 2 0 9 1 , 0 0 9 1 . 0 0 1 8 6 . 0 0 IN .88 . 8 8 . 9 5 . 9 5 . I B . 1 8 1 . 3 7 1 . 3 7 1.8 1 1 . B 1 402 186.00 6 . 5 7 6 . 5 7 P 0 1 . 4 7 1 . 4 7 1 . 6 1 1 . 6 1 1 . 8 8 1 . 8 8 2 . 1 7 2 . 1 7 2 . 8 1 2 . R 1 4 . 2 8 4 . 2 8 8 . 9 2 8 . 9 2 C I N 4 . 6 0 5 . 1 5 4 . 9 5 4 . 9 0 5 . 1 5 , 1 5 , 4 0 . 5 0 , 4 0 , 15 10 8.90 13.CO 12.95 C O U T 7 . 4 0 7 . 9 5 7 . 6 0 7 . 7 5 7 . 7 5 1 0 . 4 0 1 0 . 3 5 . 1 5 . 4 0 1 5 . 2 0 2 2 . 2 5 2 2 . 9 0 T Y P E O G M 2 9 . 9 6 9 . 9 6 1 3 . 2 8 1 3 . 1 3 1 9 . 0 0 1 8 . 7 0 2 4 . 6 4 2 4 . 4 6 3 V . 0 2 3 8 . 8 7 8 9 . 9 1 8 9 . 9 2 1 8 4 . 2 0 1 8 3 . 4 8 V C O R 2 . 0 0 2 . 0 0 1 . 8 9 2 . 0 4 . 2 . 9 0 3 . 0 5 4 . 7 4 4 . ti 7 . 5 2 8 . 2 3 T U N . 0 9 7 8 . 0 9 9 7 . 0 9 3 4 . 1 0 0 6 . 0 9 2 1 . 1 0 7 1 . 1 0 4 2 . 1 1 4 2 . 1 5 2 2 . 1 5 9 0 A . 2 8 1 2 . 2 7 8 7 . 5 4 3 5 . 5 9 8 1 T U L 7 8 . 5 7 7 . 0 8 2 . 2 7 6 . 3 8 3 . 3 7 1 . 7 7 3 . 6 6 7 . 2 5 0 . 4 4 8 . 3 2 7 . 3 2 7 . 5 1 4 . 1 1 2 . 8 V G 1 . 0 6 0 1 . 0 6 0 1 . 4 1 3 1 . 3 9 7 2 . 0 2 2 1 . " 9 0 , 6 2 3 , 6 0 3 1 5 3 1 3 7 5 6 9 , 5 7 0 1 9 . 6 0 4 1 9 . 5 2 8 COMPUTATION OF NTU S Y S T F M 3 TUBS CM BP My OL GPM TFMP C SATC ML VP MM 1 .757 7U9.700 2. ICO 13.500 36.600 2b.7CC RUN OG CFH «0 3 403 404 404 405 405 406 406 407 407 40 b 400 409 409 410 1.62 1 .62 3.01 3.01 B. 12 b.12 14.04 14.04 20.02 20.02 33.20 33.20 84.70 84.70 182.BO 410 182.BO P I N 1.45 1.45 1.51 1.51 1.82 1 .82 2.32 2.32 2.83 2.83 3.78 3.78 7.93 7.93 14.20 14.20 PO C IN 2.49 2.05 2.4V 1.90 2.62 2.70 2.62 3.05 3.05 3.76 3.76 4.39 4.39 5.53 5.53 7.90 7 . ° C 17.30 17.30 S Y S T E M 3 T U B E CM 8P MM 1.757 756.300 K U N 41 1 41 1 41 2 412 413 413 414 41 4 415 415 416 416 417 417 O G CFH 2 . 1 7 2.17 5.13 5.13 1 1 .82 1 1 .82 16.71 16.71 26.50 26.50 51.20 51.20 150.20 150.20 P IN 1.48 1.48 1.62 1.62 2. 15 2. 15 2.53 2.53 3 . 1 8 3.18 5.33 5.33 12.70 12.70 65 45 40 60 60 70 80 PO 2.58 2.58 2.73 2.73 3.52 3.52 4.02 4.02 4.89 4.89 6.96 6 . 0 6 15.00 15.00 10.45 10.30 13.70 13.85 17.35 16.90 O L G P M 2. 100 C IN 2.35 2.3C 3.80 3.75 6.00 5.95 7.65 7.5.C 9.40 9.75 1 1.90 12.05 17.35 17.50 r. O U T T Y P E UGM VCOR TUN T U L VG 2.45 1 1.12 .56 .0122 62 5 . 5 . 119 2.40 1 . 0 8 .70 .0 153 501.9 . '04 3 . 5 5 1 1 . 0 3 1. 19 .0268 266.4 .205 3 .50 1 1.93 1 .19 .0267 2b6.'o .205 5 .7C 1 6.66 1.76 .04 19 182.o . 709 5 . 5 5 1 6 . B 1 1.62 .0385 199 . 5 .725 8.05 1 12.51 2.05 .0526 145.0 1 .352 8.05 1 12.51 2.05 .0526 K 5 . 9 1.332 9 . 9 5 3 17.53 3 .22 .0862 89.0 1 .866 9 . 95 3 17.68 3 .07 .0825 93.0 1 .RB 1 12. OC 5 30.81 3 .52 .1051 7 3 . 1 3 .279 13. 15 5 30.22 4 . U .1225 62.6 3 .216 19.10 5 78.30 8.C8 .2850 2 6 . 9 8 . 3 3 3 19.70 5 77.54 8.84 .3155 2 4 . 3 8.253 23.80 6 169.91 14.05 .6117 12 . 5 18 .083 75.8C 6 169.05 14.91 .6360 12.0 17.991 T E M P C S A T C ML VP MM 13.800 36.600 28.700 C. O U T T Y P E OGM V C O R T U N T U L V G 2.75 1 1 .67 .55 .0122 625.8 . 178 f. 2.85 1 1.47 .76 .0168 454.8 .156 4.60 1 4 . 16 1 .1 i .0258 297.2 .443 4.70 1 3.95 1.32 .0307 25C.0 .421 7.65 1 9.84 2.32 .0581 132.0 1 .047 7.45 1 10.05 2. 10 .0526 145.8 1.070 9.65 1 14.35 2.82 .0753 102.0 1.527 9.20 I 14.78 2.39 .0632 121.3 1.573 1 1.85 3 23.71 3.48 .0994 77.2 2.524 11.RO 3 24.30 2.90 .08 37 91.7 2.586 15.70 5 46.73 5.50 . 1757 43 .7 4 .974 15.30 5 47 .57 4.67 . 1493 51 . 4 5.062 24 .60 6 138.82 1 1.47 .4897 15.6 14.774 24 .40 6 139.46 10.83 .4642 16.5 14.843 SYSTFM 3 T U B E CM RP MM 1.757 751.00C OL GPM 2. 100 TEMP C 13.500 SATC ML VP MM 75.200 78.700 RUM or, C F H P IN pn C IN r. O U T T Y P F UGM V C O R T U N T U L VG 41H 1 .60 1.43 2.81 3.75 4 . 65 1 1 .03 .63 .0 137 559.6 . 109 419 3 . o v 1. 55 2 . 69 o.BC H.73 1 2 .76 1 . 37 . 0 3 l « 244 .2 .294 42 0 10.07 I . 0 5 3 .29 10.65 14.55 1 7 . 6 6 2 .77 .068 1 112 . 6 .816V 42 1 17 . 6 6 2 .62 4 . 14 16.63 20.73 1 15 . 36 2 .02 .0800 9 3 . ° 1 . 6 3 4 422 23.30 3 . 10 4 .80 19.CO 24.23 3 2 2 . 3 v 5.77 . 1 3 8 6 70.7 2.38 3 42 5 33.20 3 . 8 5 5.70 2 1 .05 27 .40 5 31 .74 4 .S9 . 1 3 8 5 55 . 4 3.378 42 4 75.8C ' 7.47 8 . 0 3 28.50 3v .70 3 60.03 »•. 4 ft . 3073 2 4 . 0 7. 358 425 152.30 13 .30 15.50 30.20 54.20 5 '59.74 13 .47 . 6498 1 1 .8 14 .872 426 ' 87 .40 16 .00 1 8 . 60 4 3. 30 5 7.00 6 174.64 1 2 . 5 8 .73o2 10.8 18 ,586 S Y S T E M T U H F CM HP MM O L GPM T E M P C S A T C " L VP MM 3 1.757 730 .100 1.070 13.5 0 C 75.200 28 .700 RUN OG C F H P IM nn C IN C O U T T Y P F OGM VCOR T U N T U L VG 42 7 1 .40 .40 . 70 4 .45 6 . 30 1 .79 . 6 6 .0288 266 . 3 .084 428 4 . 10 .50 . ° 1 6 . 3 5 V.7C 1 5.05 1.21 .0344 14 1 .0 .325 429 1 1 .76 .88 1.53 10.60 16.95 2 9.0Q 2 . 3 3 . ' 138 67.4 1.053 430 18.28 1. 12 1 .84 11.80 17. 70 3 16.14 2 . '6 .1076 7 1.3 1 .792 43 1 24 .70 1.32 2 . 19 12.73 19.25 5 23 .28 2 . 39 . 1212 63 . 3 2 . 4 7 8 432 39 .2C 1 . 7 9 2 . "5 14. "0 23; 40 5 37.49 3.71 .1702 4 5 . 1 3 . 0 9 1 43 3 8 1.40 2 .77 4 .28 18.95 3 1 .75 5 7 V . 4 1 4 .94 .2896 26.5 8.431 434 149.80 3.03 7 . 2 2 23.65 4 1 .85 5 147.82 6 .57 .4522 16 . 0 15 .752 4 3 5 182.50 6.61 9.05 28.85 46.65 5 179 .86 7.46 .5590 13.7 19. 142 S Y S T E M 3 T U B E CM RO MM 1 . 7 5 7 751.700 OL GPM .613 T E M P C S A T C ML VP MM 13.533 73 .200 26.700 RUN OG C F H P IN PO C I N C O U T TYPF. OGM V C O R T U N T U L V G 436 1 .5 1 . 12 .32 3 .25 5 .00 1 1 .32 .54 .0407 188.6 .109 437 3.02 . 16 .41 5.45 9.83 1 2 .24 .90 .073 1 109 .4 .738 43d 6.70 .26 .53 5 .68 12. . 0 5 1 5.43 1 .53 .12 10 63 .4 .578 43 9 1 1 .08 .39 .77 6.70 15.35 2 9.75 1.76 .1422 54 .0 1 .338 44 0 17.27 .42 . 0 3 7.50 14.75 3 16 .43 1.52 .1239 61 .0 1.748 4i» 1 25 .30 .71 1 .15 8.70 15 .80 5 24 .76 1 .49 .1256 62 . 1 2.638 44 2 52 .20 1 .13 1 .65 1 1.45 22.33 5 31 .83 2.33 .7057 37 .3 5 .8 16 443 98 .70 1 .79 2.45 14.25 3 1 .55 5 98.33 3.00 .3722 23.6 ' 3 . 4 6 5 44 4 179.30 3.0Q 4. 05 23.45 4 3 . 15 6 183.33 4.67 .8466 14.0 19.163 COMPUTATION OF NTU SYSTEM TUBE CM 8P MM OL GPM TEMP&C SATC ML VP MM 3 1.757 747.400 .610 13 .500 36.603 28.733 RUN OG CFH P IN PD C IN C OUT TYPE QGM VCOR TUN TUL VG 4 4 5 1 . " 9 .20 .1*8 2.05 4 . 0 5 1 1 .25 .83 .0633 121 .2 . 1 3 3 4 4 6 4 . 0 1 * .25 . 5 5 2.65 5.80 1 2 .90 1 .32 .1037 7 4 .0 .308 1)1*7 7.67 . U 5 .69 3 . 0 5 6 . 6 0 2 6 . 5 2 1 .1*9 .1191 6 4 . 4 .693 1*1*8 12 . 7 4 .56 . 9 7 4. 10 7 . 7 0 2 11 . 7 9 1.52 .1253 61 .2 1 .255 1*1*9 2 3 . 8 5 . 7 5 1 ;24 4 . 5 5 8 .U0 3 20. 1 5 1.63 . 1 3 6 8 5 6 . 1 2 ; 1 4 4 U 5 3 U 3 . 3 0 1 .03 1.70 5 . 50 1 1 . 1 5 5 i»2 .76 2 .44 .2152 3 b . 6 4 . 5 5 1 1*5 1 7 9 . 1 * 0 1.69 2.21 6 . 3 0 17.05 5 7 7 . 7 1 5 . 0 3 . 4 7 1 * 8 16 . 1 8 .270 1*5 2 11*6.60 3 . 3 6 4 . 3 5 9 . 8 5 25 . 3 5 5 11*3.63 8 . 5 3 . 0 6 8 4 7 , 9 15.283 . SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP MM 3 1 .767 7.49.900 - 1.070 13.5 00 - 73,200 -28.. 70 3 RUN OG CFH P IN PO C. IN C OUT TYPE OGM. VCOR TUN TUL VG 48 0 1.51 .37 .81 3.80 5.50 1 . .96 .61 .0262 293.. 0. . 102 48 1 2.49 .46 .91 4 .05 7.10 1 1.82 .77 .0338 226'. a . 193 48 2 7.71 .77 1.4Q 6.40 10.95 1 6 .37 1.66 .0747 102. 7 .678 • 48 3 -1.3...66 . J .04... - 1. 7.8 7. 50 13.25 . 3 -12-. . 13—2.10 — .09-7-1. -7.V-.0- 1 .290 48 4 19.83 1.30 2. 13 8.15 13.80 4 18.55 2.06 .0963 7V.7 1 .0 74 486 31 .20 1 .02 2.67 8.90 15 .75 5 29.88 2.52 . 1 194 64 . 3 3. 180 486 6 1.70 2.44 3.39 10.85 21.86 5 59..R2 4.14 .2063. 3.7,2. . 6.3.6.7. _. 48 7 118 .00 4. 17 5.90 15.60 32.40 6 115.23 6.63 .3688 20.8 12.204 488 186.60 7 .28 10.10 2 1 .80 42.05 6 182.90 8.41 .5 378 14 .2 19.465 SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML VP MM 3 1.757 757.200 2.100 13.500 73.200 28.700 KUN OG CFH P IN PO C IN C OUT TYPE' OGM VCOR TUN TUL VG 489 1 .64 1 .61 2.74 3.40 4.25 1 1.09 .59 .0127 601 .5 .116 490. _.. 3.07 1 .69 . 2 . 8 4 4.83 6. 15 1 . 2.21 . ..94. .-..020.7... 36 9.4 .236_ 49 1 ' 7 . 7 6 2. 16 3.65 5.50 8.00 1 6.22 1.74 .0392 195.7 .662 492 16.80 2.88 4. 67 8.00 1 1.90 1 14.4V 2.74 .0643 119.3 1 .542 49 3 27.20 3.65 5.62 V.20 14. 30 3 24.25 3.60 .0865 88.7 2.5.8.1 49.4 47.90 5.03 7.55 10.95 18.80 5 • 43.28 5.62 .1403 54.7 4.606 49 5 73.40 7.45 9.80 15.35 27.45 5 65.53 8.BV .2434 3 1.5 6.974 SYSTEM TUBE CM BP MM QL G P M TEMP C SATC ML VP MM 3 1 .757 751 .900 .610 13.500 7J5..200 2B .70 RUN QG CFH P IN PO C IN C OUT TYPE QGM VCOR TUN TUL VG 47 1 1 .63 . 10 .28 3.50 6 .15 1 1 .15 .54 .0408 187.0 .122 " 472 ' 2 .62 .11 .32 3.95 7.55 1 1 .98 .74 .0563 136.3 .213 473 6.32 .21 .48 5 .15 10.80 1 5.39 1.17 .0916 83.8 .574 474 11 .76 .40 .79 6. 15 1 3.40 2 10.70 1.52 .1211 63.4 1.138 47 5 20.67 .52 1.01 7.25" T4:uo 3 19 "97 1.50 .1215 ' 63.1 2.126 47 6 35.60 .82 1.40 9.65 19.00 5 34.97 1.98 .1690 45.4 3.722 47 7 61 .90 1.20 1.73 1 1.90 24.60 5 61 .43 2.76 .2474 31 .0 6.538 47 8 117 .13 2.18 3.00 16.45 33.70 6 17.24 3.90 .3889 19 .7 12 .478 : . 5 YS TF M T'.IR? CM RP >IM OL C-° M TF MP C £_«£_ MM 2 1.7 57 75T 003 1.07 0 l b , 303 73.0 62 12 . •103 MO or, C f i i 1 _P_3 . H IM '1 OUT TYPF ClfiM J/ULE •MTU I TU VFI G i :C5 1 . 5 4 .49 .48 2.33 7.55 1 1 .84 3.00 .386 1 8V.1 .164 X 63 h 2 .2 3 .53 .6 8 ' .83 8 .4 ; 1 2.23 0 , 0 3 .13 3 3 7 4.6 , r> 3 4 v 53 7 6.24 .78 .7.8 . 2 , Ob 12, R5 1 _.».,26. . 31 .1620 4 7.4 . *,66 '53 » 1.. , U -; ' " ' .20 1 .""15 5.23 1 6 . 5 M " 3 j iii . 1 V6-2 "Ti. 1"' 1 . 5 T i ' 5 0 V 2 1 .90 .52 1 , 4 H 3.37 1 6 . 8 9 4 2 1 .°6 . 3 1 . 1 " 4 9 u1 .5 2 . 33ri 51 3 3V.21 2.4? 2.42 7.46 2 1 .56 5 3V .25 .31 .2586 ?V.6 4 .178 311 66 . 33 3.48 3.47 V.15 2V.50 5 66 .25 .32 , 4 1 4 8 1 8 . 6 7.052 ,v 51 2 M 4 . ° ' j 4.60 ' 4.2b 11.5V 37 ,05 b M4 .53 .33 .6372 12 '6 1 2 , l 87v 61 3 ! 7 4 . 0 3 5.78 0,07. 1 3,_4.1. 4ft . 48 _>. 174.1 1 .04 . "V 19 8.6 18.832s SYSTEM TUBF CM Rp MM OL GPM TFMP C SATC MF VP MM '2 1. 75/ 75 4 '30 1.070 15.030 ..73.062 12 . R.13 : NO OG C E " ? 1 PI) H IN H OUT TYPE OGM VOLE NTU L TU VELG i ; 514 1 .32 .53 .. ...5 ft 3 . 32 o.31 1 1.31 0.30 . 3463 165-.7 .143 51 5 2.08 " ' .55 .58 "3". 85" '/'.hi' .... .... 2 - _ _ " O o . 3632 12 1.3 .221 516 5 .53 .7.8 .78 5 .75 ' 4 . 5 o 1 5 . 4V 0.03 . 1 494 51.3 .585 51 7 13 ,13 1.10 1.58 6.93 18.63 2 10.1? .01 .50 76 36 .9 1 .377 ' 518 1 1 .45 . 14 l . i ? 7.01 l y .1 7 2 11.44 .01 .? l6V 35.4 1.2 17 ; 61 V IV .40 . 39 1. 32 6.81 18.33 4 1 V , 38 .31 .2028 3 7..8 2.062 1 52 0 26. 85 . 8 4 1.66 7, 7.6....l'.9 .4 4 ..5. 26.,7.9_ ,.01 .2096 36 .6 2. "3 2 „ _ .1 4 U . 16 2 . 73 "2.4.7." 9 .8 j ? 4 . 3 8 6 43 .99" ". 3l' .jirvri ~ 2 7 . 5 '4 ."682 ' COMPUTATION OF NTU SYSTEM TURF C BP MM OL GPM TFMP C S"\1X_£'£ -V-K_ MM. 2 1.Y5f 754.600 1 .073 lb .000 70.»&2 12.BOO MO OG CFH P 2 _ _ HO ri IM H OUT TYPF yGM VOI.E .*-!Ti> LTH VELG " " " ' " ' ' ' 5 .24 " ? r . U S i i ,>•/ "37 . V o ; 0 3 4 . ' i A 2 3 b ' . 5 . 1 Bi)' 3 .97 7 . 5 6 1 l . o * O.OO ' .0563 ' 3 6 . 2 . '77. 5 .22 12 . 3 6 1 3 .7B P.O.") . 1 1 rt 0) 6 5 . 1 . H 32 _    1 pn 52 2 " " 1'. 30"" ."b'l " "'.5 5 52 3 1 .67 .53, .58 52 4 3.79 ,70 .70 52 b 9.83 .98 1 .08 52 6 13.6B ' . 07 1 .20 7.28 18.43 1 9.81 .01 .1977 3 8 . 1 1.045 7 .58 .18 .33 3 15.66 .01 .1910 40.2 1.454 52 7 15 .72 1 . 19 1 .25 7.39 1 7.95 3 15 .'(1 ^0J_ 60 4 1 J _ . 1.671 52 8 23.90 1.60 J.53 7.BR 18.04 .5 23 .8b .0.1 . 1802 42 .6 2 .5 59 529 49.23 3.00 2.79 10.34 24.26 5 48 .06 .01 .2675 38.7 5.31) 530 70 .50 3.82 3.34 12 . 5 0 . 3 0 . 1 1 b 70 .01 .01 .3673a 3 0 . ° 7.45? 33 1 159.50 b . 1 5 ' 4.56 1 3.99 Ul .03 5 157.06 . 03 .6605 1 1 ,6 16.113 3^2... 22 7,0? 'S.93 •S.ft.3,,'.>...a!»..'LS.,Ta S 22.U„„6,HL J t t 3Z2.1.-...-9...3. .23-..P.14. SYSTEM TUBE CM 3° OL CPU TFMP C SATC MF VP MM i 1 .737 756.300 1 .370 15.000 7J_«&2 19.800 r y o OG CFH PI pn H IN H OUT-TYPE UGM VOLE MTU LTU VELG 533. 1.30 ,51 .53 2.73 6.29 1 1 .29 0,00 .0547 14J3..2 . 1 37 534 1.62 .53 ' .56 3.88 7.85 1 1.61 0.00 .0624 123. 1 .171 53 b 2.8.4 .59 .61 5.26 10.21 1 2.83 0. 00 .0801 95.8 .301 536 7.39 .95 .93 7.09 17.21 1 7 .36 .01 . 1 76 8 43 .4 .783 53 7 1 1 .97 1 . 16 1.20 6.33 17.89 2 1 1 .92 .01 .2019 38.0 1 . 269 538 18 .50 1.34 1.45 6. 36 16.75 5 18 .43 .01 .1796 42.7 1 .062 53 9 22 .50 1 .54 1 .57 ' 6.73 17.09 5 22 . 4 1 .01 • .1972 38 .9 2 .385 54 0 30 .80 2.07 2. 12 '7.53 19.03 5 30.65 .01 .2031 37 . 4 3.262 54 1 56 .83 3.61 3.22 1 1.36 20.42 5 66.23 .01 .3444 22.3 7. 04 9 54 2 97.00 3.98 3.50 13.04 35 .7 5 5 96.09 .02 .4521 16.9 13.227 54 3 133.43 4. 85 4.25, 14.14 3 7.66 5 131.00 .02 .5455 14.0 14.03 9 54 4 203. 13 5.35 4. 69 14.66 42 .57 5 197.63 .03 .7357 10.9 21.036 SYSTEM TUBE CM BP MM OL GPM TEMP C SATC MF VP MM 2 1.757 752 .000 2. 100 15.30 3 70.962 •12.800 NO OG CFH PI PO H IN H OUT TYPE OGM VOLE NTU L ru "v E'LO 55 5 1.30 1.66 1.80 1.52 4.55 1 1 .29 0.00 .0457 16d .1 .13-1 * 1 : sib 1 .67 1,74 . 1 .88 2.21 5.64 1 1 ;66 a . 03 .0~325 146.2 . 1 7 7 / 1 • 557 2.44 V. 82 1.92 2.27 6.47 • 1 2 .43 •0.03 . 0648 118 .4 . 239 * 55 8 4.13 2.09 2. 16 4.06 8.92 , 1 4.12 0.00 .0774 99.2 .439 55 9 7 .05 2 .55 2.54 5.37 12.03 1 7.03 .01 . 1098 59 .9 55 0 12.00 3.22 3.06 7.05 14.48 1 •1 1 .96 .01 .1267 60.6 1.973 56 1 15.06 3.39 3.25 7.53 15.18 3 15.01 .01- .13 17 58.3 1 .598 55 2 IS .RO 3.87 3.56 7.87 1 3.29 3 18 .72 .01 .1282 59 .9 1 . 093 563 95 .33 4.99 3.94 7.54 16.67 5 24 .81 .01 .1585 48 .4 3 . 64 1 56 4 32.30 3 .85 4.56 7.83 16.57 b 3 1 .99 j 0 2 . .1898 40 .4 3.405 56 5 42 .90 7, 12 5.35 8. 04 20.6R 5' 42 . 35 .02 . 2 12 7 . . . . . . . . . . . . . . . . ""u75"3"H" ' ' " 566 65.23 9 .75 7.00 1 1 .50 2 7.92 5 63 .92 .03 . 3250 95 .6 6.0J5 .SYSTEM TUBE CM RP M«t. fll GPM T£MP C SATC MF_yP MM " 2 1.757 "752.000"""" 2."<00 15.000 70.962 12,800* NO CFH P J : PQ H IN HJ1UT i_TYPE QGM VOLE„ NTU LTU VELG 567 1.30 1.66 1.80" 1.88 U.03" 1 1 .29 0.00 .0325 236 .3 . 138 568 1 .90 1.74 1.88 3.20 6.08 1 1.89 0.00 .0446 172.0 .202 569 2.44 1.82 1.92 3.72 7.03 1 2.43 0.00 .0516 148.6 .259 57 0 4. 13 2 . 09 2. 16 U.38 9.39 1 4.12 0.00 .0802 95.7 .U39 571 7.05 2.55 2.54 5.31 12.22 1 7.03 .01 .11U2A 67.2 .749 572 1 2 . 00 3.22 3.08 6.23 1U.80 1 11.96 .01 .1456 52.7 1.273 57 3 1 5 . 06 3.39 3.25 6.U9 15.28 3 15.01 .01 .1502 5 1 . 1 1.598 57U 18.80 3.87 3.56 7.28 15.77 3 18.72 .01 .1464 52. U 1.993 575 25.00 U.99 3.94 8.07 16.81 5 24.81 .01 .1524 50.3 2.641 57 6 32 . 30 5 . 85 4 .5* 9.52 1 9 . 06 5 31 .99 . 01 . ' 716 UU.7 3.U05 577 42 .90 7. 12 5.35 10.58 21.95 5 42.35 .02 .21 15 36.3 4.508 - 5L!l ^ i ! 0 ?-«7i.._7.;.°.9 1 ?."»2. 28.70 5 63_,92 .03 .3277 23.U .6.803 SYSTEM T±I*Z_S* 1» J l OL G P M XE MP. , C . S A T O . i !L. i'.5._.MM .... 2 C 7 5 f ' T s T . 6 3 3 2 . 130 15. 300 7 0 . ° 6 2 12 .803 M U O G C F H p i pn H I M H O U T . T Y P E O G M V ! ) I F M T U L T U VEI 0 579 1 .67 1 .84 I. op 2.85 3.6! I 1.66 0.30 .0497 179.6 .177 580 5.31 2.31 2.03 3.07 7.50 l 3.30 3.00 .0555 138.0 .352 b8_l_ 7_,07 9.5J( 2.53 5.37 ' 1 .46 L . _ L » 3 A , .f i1. .,?pO* 7.6.7 .7.5.1... "b'-i2 """15.96"" 3. 36 3.24 0.78 14 .75 3 13 .92 .01 .1.356 56.6 1.482 583 21.00 4.'25 3.81 7.52 1 6 . U 3 2.0 .9 1 .01 .1489 51 .8 2 .725 584_ SOjjlO _b,_B7 4.47 6.52 17.63 5 79 .72 .02 .1 924 3_Vj2>_JL,.Ji>.3_ 585 ' 49 .90""" '8.6'8'" '6. W" v763 23.57 \ 5 49 .07 .02 .770 1 2 8 . " 5.723 566 80.03 12 .75 8.01 17,49 32.51 8 77.86 .04 .4 178 18 .3 8.7oH •587 127.20 16.30 10. 36 1 6. 11 4 1 ,28 S '22,47 tOP. 17. ...i.2.,_7 J 3 ,035. "bHB TH'5.00 '19750- 12 . ' 4 19.51 46.82 6 176.58 .06 .7284 13.5 '8 .794 COMPUTATION OF NTU S YS r EM TUe|__CM_RP_jMM OL GPM TEMP C, SATC. ME VP MM 2 ~ 'T ' . ' 7S'f~75~~.63T 2 . 133 15.033" "70 .96 2" 12.833 •MO OG CFM PI pri }{ {\\ 4 QIJT TX°E UG.M VOL F MTU L TU V E L G 53 9 2 .3 i I. 89 1.85 2.87 5.83 1 2 .33 3 . 0 3 .0453 ' 6 9 ' . 2 59 3 5.31. 2.33 2.On 3.35 7 . 1 2 ' . 2. °9 3. 33 .0699 1 3 9 . 8 59 1 J O . ' 3 _ 3.06_ 2 .1d M 5.2 s 13.76 1 13.06 .01 .1I»1S _5U .2 69 2"" 18,03"'' ~U."33 3.64 ~6, 74 ' 5 . 8 2 593. 39.90 7. 18 5. 19 9.28 2 1 .01 594_ 82.23 12.26 _8._3_8 1.1.62 31^05. " 595' T3 07 33" 1 5 ".Tf" fo". 32~1 5 '. 35~Y3 .51 ' 596 182.23 1 9 .33 11 .82 17 .54 4 8 . 1 0 5 173.26 S Y S T E M TUBE CM BP MM OL GPM TEMP C SATO ME VP MM 2 1.757 7 5 0 . 4 0 0 . . 6 2 0 1 5 . 0 3 0 7 3 . 9 6 2 1 2 . 8 3 3 MO. OG C F H P I Pf) H IM H OUT T Y P E OGM V O L E MTU L1" J V E L 3 597 1 .33 . 31 .31 2.8 1 8 .95 1 1.30 0. 30 .0975 78.7 .1 38 598 1 . 6 7 .36 .35 2 .96 10.45 1 1.67 0.00 .1205a 63.7 . 1 7 8 599. 2 . 5 6 . 4 3 .41 2 . 9 8 11 .76 1 2 .67 0.00 . 1 4 2 8 5 3 .7 . .284 6 0 3 4 , 5 6 . 4 5 .46 3.32 1 3 . 6 9 2 4 . 5 8 3 . 0 3 ' . 1 7 1 " 4 4 . 6 .487 _63_1 7.39 _ .61 _ . 5 3 _ 3 _ . 3 3 1 3 . 3 5 2 7.43 3.00 . 1 6 5 5 4 6 . 4 _ . 7 9 0 ' 63 2 " " 1 0 . 9 0 ™ T58~~ .56* "3.'T4T''l'2 ".64~"*3 "'"ibV96''"''o. 00 " i ' i 558"" ' ' "4 9 . T ' )'. 1 6 6 " 6 0 3 15 .98 .72 .71 3.73 1 3 . 3 8 3 1 6 . 0 7 0.00 . 1 6 0 3 48 .3 1 .7 13 S Y S T E M 2 TUBE CM RP MM 1 .757 7 4 6 . 9 0 3 OL GPM .623 TEMP C. 15 .033 SATC MF VP MM 73.062 12.800 MO OG CFH 60 4 1 .30 P I • .30 PD .31 63 5 2.23 63 6 5.00 60 7 1.0 . 30 " W :to~ 53 8 63 9 61 3 27 .00 4 4 . 6 0 . 34 .46 __.60 "."79" .91 1.47 ri I N H OUT T Y P F UGM VOLE 2 . 7 6 6.77 1 1.3 1 3 . 3 3 NTU L T U V E L G .0966 8 3 . 3 . 1 3 9 .36 .48 • 5 " . ""777"' .08 1.32 3.57 11.18 4.27 1 3 . 9 5 4 . 1 3 14 ..06 "il'."5'9'"in',T7"" 4.42 15-. 5 9 6 . 1 3 1 9 . 0 3 5 . 2 . 2 2 5.P6 J 3 . 4 0 1979 0" 2 7 . 2 7 4 4 .OH 3. 33 3.03 0.30 "0700> 0.00 0.00 . 1244 . 1 6 5 0 . 1 6 7 2 Ti'6"2T" . 1 9 1 0 . 2 3 3 3 6 1.7 4 7 . 1 45 .9 "it7 . '3 40 .2 3 5 . 3 . 2 3 6 . 6 5 4 1 . 1 3 7 >;",-Tirt" 2 . " 3 3 4 . 7 8 8 61 1 69 .60 1 .95 1.65 8.48 2 6.26 . 5 70". 1 1 . 3 4 9 0 2 2 T 3 7TK"6"3 S YSTEM TUBE CM BP MM OL GPM TEMP C SATC MF VP MM 1.757 749.4C . 6 2 0 1 5 . 0 0 0 7 3 . 9 6 2 1 2 . 8 0 0 NO OG C FH P I PD H I N H OUT TYPE UGM VOLE: MTU LTU V E L G 61 2 4.56 .44 .47 4,61 1 3 . 9 1 2 4 ,5 '9 0. 30 '. 16"6 4 4 9 . 1 . 4 8 8 61 3 8 . 7 7 .56 .52 4.74 14. 17 2 8 . >1'3 3 . 30 . 1 5 9 1 4 8.2 .9 39 61 4 1 3 . 8 8 .68 .63 6.42 J 4 . 2 6 - J * 1 3 . 0 7 3 . 3 3 . 1 5 3 3 6 1 . 1 1 . ID) 7 " 6 ' i V 214".To" * .04" """ .88" 5. 0 4 ~15 .34 4 ""2"4".'2'5" "o7oo"" " ."16T5" " 4 7.6 "" 2. '•:) i 61 6 35 .00 1 . 2 2 1 . 14 6.8 8 1 7 . 7 5 6 3 3 . 2 1 3.00 . , U 2 6 3 9 . 8 3 , 7 4 7 61 7 8 6.80 2 . 3 0 1.8R_ 9._36 2.9_^32 6 89 .38 .01 .4064 18 .9 9_,482 518 1 4 9 . 1 0 2 . 5 7 2 . 14 1 1.71 3 8 . 3 6 5 1 4 9 . 4 9 .01 .62 3 9 12.3 1 6 . ° 1 2 S YST = M TURF CM BP MM tn GPM TEMP C SATP. MF VP MM 2 1 . 7 5 7 7 4 9 . 4 Q 0 1.070 1 5 . 0 0 0 7 0 . 9 6 2 12 ,800 MO OG C FH P I PD H IM H OUT T Y P F UGM VOLF MTU LTU Vel.G ' 61 9 1.30 .63 .63 2 . 9 3 6.01 1 1 . 3 3 3 . 00 . 0 62 1 1 2 3 . 5 . 1 3 8 52 3 1 . 7 1 .66 . 66 3. 15 7.82 1 1.71 3 . 03 . 0 7 3 6 1 0 4 . 3 .182 62 1 3.23 . 7 7 .76 4.05 1 0 . 7 2 1 3 .24 0.03 . 1 3 8 6 7 3 . 7 .34 6 "." 62 2 3 5.6*"3" 2 . 4 9 2.27 7.9.0 1 9 . 5 9 5 33 .7 3 . 31 .2 119 '36 i 2" "".3.RJ0 S Y S T E M TUBE CM RP MM OL CP"- TEMP ' C SATC MF VP MM 1.767 749.400 VP- J ; " H 82 __P . D _ "623 ' ' l'.33"""TTn"5 l , 9 f 624 2.86 2:05 2.39 2. 133 1 5 . 0 3 3 "70.962 12 . 8 3 3 >l I M "MT TYPF »fi3—ttQ.L£ HIU . VEL ' i 2 . 1 0 4.44 1 1.33 3 . 3 3 . 3 3 5 6 2 1 5 . 8 . 1 3 8 2.82 6.58 1 2 .86 3 . 3 0 . 0 5 8 5 13 1 .2 ."536 62 5 5 . 5 0 2 . 4 6 2 . 4 3 4 . 1 0 9,72 1 5 . 5 3 .31 .09J4i nu , 0 . 8 6 6 COMPUTATION OF NTU V-14 ; SYSTEM TURF CM RP MM OL GPM TEMP C SATC ML CYCLO 5 1 .75 7 7bb .900 1 .070 lb .0 00 47.270 05 RUN or, CFH P IN pn C IN C OUT TYPE MGM • VCOR TUM TUL VG ' 62 6 l .59 . 6 8 5 .87 2.50 3 .80 1 1 . 4 4 .1.3 .0188 407 .4 . 1 5 3 ! 62 7 2 .62 .76 6.39 3 . 1 5 4 .80 1 2 .42 . 1 6 .0250 306.7 .257 628 b .5 3 .R7 7 .34 3.5b 5 .80 2 5.22 .22 .0355 216.0 .556 62v 9 . 7 0 .R9 7 .58 3 .45 5 .5b 3 9.34 .21 .0328 255 .6 . 0 9 4 630 12 .°2 .98 •8.05 3.50 5 .70 4 12.48 .22 .0345 222 .2 1 .328 63 1 Its.12 1 .08 9 . 1 6 5 .75 6 . 1 0 5 ' 17 .56 .23 .0375 205 ,7 1.869 652 26 .70 1 . 1 5 1 0 .60 4 .00 6.70 5 2b .97 .27 .04 37 "T7b . 6 2.764 635 38 ,R0 1 .36 1 1 .60 4 .40 7 .80 5 37 .60 .33 .0564 1 5 6 . 1 4 .002 SYSTEM TURE 9M RP MM OL GPM TEMP C SATC ML CYCLO 5 ' . 757 7b6 .100. 1 .070 lb .000 47.270 03 RUN or, CFH P IN K> C IN C OUT TYPE OGM VCOR TUN TUL VG 654 4 .04 .81 6.58 3.20 5 . 1 5 1 3.78 . 1 9 .0301 255.0 .405 63 b 7 .27 .R6 7 .2b 3 .25 5 .60 3 6 .92 .23 .0370 207 ,5 .73 7 636 12.74 .98 8.62 3.20 5.3b 4 12.32 .21 .0334 229.4 1.311 63 7 65 .10 1 .70 14.10 4 .65 9.5b 5 62 .76 .48 .0639 91 .5 6.680 j. 638 90 .90 2.02 16.80 5 .30 1 l-.Sb 5 R7 .21 .64 .1 167 65.8 9.281 ! 65 9 1 3 5 . 10 2.63 21 .80 6 .30 l b .5b b '28.34 . " 0 . 1 7 4 9 43.0 1 3 .659 64 0 171.20 3 . 1 3 24.60 7.10 18.30 5 160.96 .08 .2207 34 .8 17.130 ...S.YSU=il._.-XUiiE. -UH-RO. MM -Ol GfiiL _IEilP _C S4.IC-.MJ_ C Yf, 1 0 1.757 752 .°O0 .620 lb .000 47 .370 . 00300 Rlhi O G C F H P I M p n r FM r. n i IT T Y P E C l G M Vf.OR T U M Till V G 64 1 1 .59 .4 1 3.49 1.7 0 5 .60 1 ! . 4 7 .1 1 .028 1 7.72 , fl . 156 64 2 2 .5 3 . 4 3 3 .7 « 2.00 4.30 1 2 .38 . 1 3 ,03bl 2 18 .764 .6.45. •.. ,46. .4.7. . 4 . Ch ._2..»15_ ...5_«2b 2 3 . 2 7 ' .04H9 157 • 0 .5 6 1 644 9 . 7 9 .52 4.65 2.40 b.5b 3 9 .56 .18 .03.00 15 3.4 1.018 64 5 1.3 .73 .57 4 . 7 4 2.30 b.3b 4 12 . 9 7 . 1 7 . 04 8 T 159 .6 1.381 64 6.. "_L8,R6 .64 5.50 2.35 b .65 4 '18.54 . 1 0 .0524 146 .4 1 . 0 7 3 64 7 27 .30 .74 6.20 2 .50 6 . 1 0 b ' 26 .86 .21 .0576 132 .0 ?.Rb8 64 8 40 .5 0 .85 7.05 2.70 7.20 b 39 .82 .26 .07 3 9 103 . 8 4.738 SYSTFM TUBF .'CM R P MM OL GPM TEMP C SATC ML CYCLO 3 1.757 7 5 2 . ° 0 C .62C lb . 0 47 .270 .0039 0. KU'M O G C F H P I M p n r. ' I M r. O U T TYPE I ' G M VCOR TUM 1 ni V G 04 9 . 3 .°9 . 4 b 3 .o 1 1.90 4 . 5 5 1 . 3 . " 3 . 1 5 . 04 09 1 8 7 . 6 .406 tbr Z_*Z3_ ...b..Jib... ...5... ... .X..02__ .0499 163 ,6 .747 05 1 70.5 0 1 . 0 2 6.70 . 3 . 1 0 9.50 b 69 .23 .37 . 1 098 69 ,0 7 .368 632 Vi .30 1 . 1 0 9 , 0 0 5 . 7 5 11.45 b 9C.36 . 4 4 . 1 3 0 6 56 . \ .9 .619 . _ 6b 3 ! :••..: . 7 0 -1..5 3-. 12. 1 0 4.30, 14,16 3 129.02 , 5 7 . 1 8 39 4 1 . 7 13 . 7 32 654 i 7 « . 1: 1 .'<2 1 4 . 0 0 4 , h 5 16 . 1 5 b 17 0 , 4 3 ' .67 .3220 34 , 5 1 8 . 1-38 SYS1 E M TUH.E . . C M . HE _ v , . M _ . . _CU LiE.iS -T.E1!!? _ C . S^.TC. M L CYCLO 5 1.7 57 75 0 c. I\ r- 2 , 1 0 ; IS.' 0 0 4 7 . 2 7 0 .00 no .. . .rlUN MG CHli__ E [ i<. .-l'L> C I>i_ r. ni IT T..YK C O R TUM TUL V G ' ; 6 5 5 1.65 1 .58 1 3 .7b 3.05 3.65 1 1 . I 1 6 . 1 1 .0009 » b 6 . 7 . l b 7 65 6 2 . R H 1 .64 14.01 3.5 5 4.40 1 2 .65 .16 .0132 580 , R .282 65 7. . ..3...A.4 .15_I_. 4.15 —5...2S . •-; 5 .30 .21 .0176 436 . 0 .564 63 8 9 .8 9 2 . 03 17 .30 4 .70 b ,Rb 5 9.40 .22 .0186 412 . 6 1 .001 . 659 1.3 .64 2.1b 18.30 4 .or. 6.30 3 12 .06 .77 .0229 3 34 ,4 1.382 . ..660 19 .93 ? .4 1... 2 0.60 3 .25 7.00 3 lo .Ob .33 .0291 26 3 .5 7.117 6 6 1 27 .4 0 2.52 2 1 .40 5.70 7 ,°5 b 26 .05 .41 .0365 2.1 0 2.77.3 i 662 4 1,10 2 . 0 7 2b .40 6.70 V .60 .5 38 .86 .85 .0508 151 . 1 4 . 1 3 8 SYSTFM TUbF CM H P M M OL GP« TEMP C SATC ML CYCLO 5 1 .757 764 .5 00 2.100 1 b . 0 0 47.27C .00110 MIM t)G r,Fn P I M pn r. i»' r. OUT TYPF OGM VCOR TUM . Till. VG .66.3.- U..C4.. _.i_7J_ --U7.2. .„3_Z.0_ . .4.Z.i_ _1_ 3 3 .17 .20. . 0 1 64 465 O .396 664 7.08 .1 , N 9 1 . « 3 4 . 1 5 3 .30 6 .64 .23 . 0 1«2 ii 2 0- . 0 .70 7 .: 665 21 .6(1 Z.5 1 2.47 b . 10 •6.85 5 20.4 1 .33 .02o7 266 . p 2 . 1 7 3 66 6- -63. 4-3— 3^60 --3.5.1- -7..P A J...L..2.0 5 59.04 .77 . 1 7 3 9 105 t 0 6". 7B3 66 7 8 7 ' . « " 4 . 2 1 4.16 9 . 2 0 14.80 5 8 1 . 05 1 . 0 4 .1 062 72 .3 8 .676 66 8 13b.op 5 .62 b .46 1 1 .85 3 0 .05 b 122.61 1.49 . 1 69>; 45 .7 1 3 .049 . ..60 9 . 174.. 6.0 .. . 6 . 6 4 . . . _6...35- .1 3 ..7.C . 25..R.b... ...a...!54...R3_ U_2_ .2250 3 4 . 1 I 6 . l i 7 7 V-15 COMPUTATION OF NTU SYSTEM TUBE CM BP MM 5 1 .757 756 . 2CC OL GPM 2 . 1 C 0- T E M P r. ••to . i n SATC ML CYCI.n 36 .071 .rniio RUN OG CFH p IM -6JX 4-.2J 1 . 19. PD C IM C OUT TYPF OGM VCOP _U-17__Jt_,_-3 5_-3 5 I 4.06 .27 67 1 7.07 672 21.B2 -6.7-3 _-L_!___ .3'U 1.29 ,R9 . 1 .84 .JEih ___8-i_ 4 . 75 5.95 5.U0 7.50 -X .55 1 7.02 2 I . R u _6_i,60_ .24 .SOL TUN TUL VG -_if:33___..2_j2_. £ .h 32 ^ • .0269 284.0 ,747 .0490 156.6 2,520 . 1 158 6 0 . 3 6.67.3 674 88.60 3.39 3.20 9.35 15.30 '5 86.RH I . l o .169U 675 132.30 4 .31 U.08 11,10 19.30 3 127.70 1.60 .260 1 ...ajfr 172 .R0 5.-1- 4,84 l ? u6 ?2.66 5 164.34 I.Pit .3529 U5 .3 9.24? 29.5 13.5V) 21.7 17 . V 1 SYSTEM TUBE CM BP MM OL GPM TEMP C SATC ML CYC1.0 5. 1 .767 756.600 2. 100 30.000 36.070 .001 10* RUM OG CFH P IM >D~ C IM C OUT TYPE OGM VCOR TUN __. 7 7 _J__6.il_ 1 ,-nu B.70 u .16 4.81 . 1 ' .8ft _US .0139 6 3 2.1 . 1 66 678 2.73 1.12 9.44 U . 10 4 . ° 0 1 2 .65 .16 .0172 444 , i .282 67 9 6.22 1.22 10.62 U.30 5.45 2 5 .1 U .23 .1254 301 .3 .6U7 680 9 .ou 1 .47 12,6U 4 . 6 6 6.00 .6 9.92 .27 .0303 253. 1 1 .066 681 13 .82 1 .6U IU .00 5.00 6.65 6 13.80 .33 .0377 20 3.3 1 . U69 682 19.87 1 .83 15.UO 5.U5 7.35 5 19.87 .38 .0UU2 173.4 2 .115 683 27 .7 0 _2-___L 17,0.1 6 .00 8.36 5 27 .6V .^7 .0562 136.5 2 . "47 ' 684 m..90 2 .33 20.10 6.50 9.80 5 Ul .7U • .66' .0816 94 .1 u, U4 3 -ilY_S.L£M TUBE CM BP MM -OL—G.P-M I £ M P C SAIL- Ml, LY£.Lfl_ 1 .757 753.900 1.07 0 3 0.00 36.07C .00280 ..RU£L.i!G_C£H_ 975 1 .59 976 2.5 8 _ L M - - P - J 3 - -IU.L: 3.82 4.35 3.81 U .34 X...M C-.0.U..T. -T.YP.E-UGM— A/COP IUiL. 2.60 3 .»5 1 1.53 .13 .0256 300.0 2.60 4 . 1 5 1 2.63 . 1 6 .0323 237.4 -YG. . 162 .269 977 5.37 4 .99 6.03 3.05 5 . 10 1 5 .39 .21 .0443 173.0 .673 978 9 .74 6.00 5 .95 3.25 3.60 3 9.90 .24 .0616 148 .7 1.054 979 1 3 .28 _____! tu3£l 3 L v 2 £ i*5JS tt i;i.5iJ_„.«^.(l .i-'603_..16_2J6 1 ,446 5 16.58 .27 .0565 130.3 1.977 6 27 . 13 .29 .0626 122.7 2."67 _5 J_0._,R4 .39 .0666 66.6 4 .347 980 16.12 981 26 .40 VM? 30 ,81 7 .02 7 .75. 9.1Q 6 .R7 7.70 v.OC 3.30 3.45 5 .Br. 5 . "5 6 . 25 7.6-5 SYSTEM 5 TUBE CM HP MM 1 .757 764.001 OL GPM — 1 .070 TE"P C -30-.000 SATC Ml. CYCI.O -3.6^.7-. ._01_28C RUM OG CFH P IM 98 5 22.03 7 .4Q P 0 7.42 C IM C .OUT TYPE UGM 2.80. 5 .5a 5 22.61 VCOR T U N .29 .OoOl TUL VG 127 .7 2. 984 62.30 1 1 . 15 1,0.06 3.75 6 . « 5 685 87.20 13 .10 1 2 . P O 4.35 10.95 666 134.30 17.30 16.30 6.41 14135 687 1 75 .30 21 .10 19 .10 5 .°5 17.15 3 63.74 5 .88.92 5 135.7 V .6 3 .69 .1206 . 1 6 3 7 .2401 65.6 6.7tl3 4 6.0 V . I'. 6 3 3 1.° 14.45? 5 175.68 1 .15 , 3 1 9 V 24.0 18.697 1SJ7.-XEM TUBE CM BP MM CD GPM TFMP C SATC MI._f.YCLO 1.757 753.800 .620 30.000 36.07C .C042C RUM nr. CPU p [\| pn r IM r. niiT TYPE UGM .i/XflB... TUN.....;. TUL VG 688 1 .64 2 .09 2.06 ! .75 3.65 1 1 .60 . 11 .0384 199.7 """".170" 669 2.63 2.24 2.26 1 .85 4 .10 1 2.62 .13 .0U65 165. 1 .27 9 6Vfi 5 .07 2.29 2.2V 1 .90 4 .68 1 6.16 .16 .0557 .137.7 .649 6V1 9.80 3.08 3.01 2.05 5.00 3 10.09 .16 .0629 122.1 f .07 4 6V2 1 3 .00 3 .48 3.49 2 .15 5.50 4 13.41 .20 .1725 105 .9 1 .4 27 ... ... ..._i.V3_ 1 H ,70 3 .on 3 .96 2.36 8 .66 5. .....1.9.. 3 7 ,20 .0717 107.0 2.062 6V4 2.7 .00 4 .47 4.35 2.30 6 . 00 5 26 . 00 .22 .0810 94 .7 2.O60 6V5 40.10 5 .22 5.30 2.46 7 .05 5 . 4 1.60 .28 .1036 74 . 2 4 .4 27 . SYSTEM TUBE CM RP MM OL GPM TEMP C. SATC ML f.YCLO 5 1 .757 752 .ROC .620 30 . 0 00 30 .17 3 .01420 RUN OG CFH P IM HO C IM C OUT TYPE UGM VCOR TUN TUL VG 696 6 .07 2.47 2.52 2.10 4.75 2 6.21 .16 .06 6 1 1 36 .7 ,*6 1 6V7 9 ,11 2 .97 2,96 2.30 6 .28 3 9.38 .18 .0636 •20 .OVB 6V8 63 .40 6 .35 6.41 2.75 8.60 6 65 . RO ,36 . 1 366 56 .2 7 .103 699 67 .70 7.45 7.47 3.15 10.18 5 90.89 . 4 3 .1696 46.3 o .673 7.0.0.. J.3.7 .60 -JU2.Z V . 4 tt 5^5,0. .12..P.5- ...5 ...L4..L-8.U. ,37 .7427 • 31,6 13.100 70 1 176.10 12.40 1 1 .20 4 . 00 15 .26 5 1 8 0 . 4 9 .68 ".31,4 6" 25 .2 "19T2 10 V-16 COMPUTATION OF NTU, E F F E C T OF ENTRANCE T X P E J > Y S T E M _ T U B E CM BP MM Q L G P M T E M P C S A T C ML VP MM_ 1 " " 1 . 7 5 7 7 5 4 . 0 0 0 1.675 TSTOOO 4 5 7 4 7 0 T 2 . 8 C 0 RUN QG C F H P IN 7 0 3 " 6 . 2 0 7 0 4 1 2 . 2 9 7 0 5 5 3 . 4 0 7 0 6 7 0 7 7 0 8 7 0 9 7 1 0 7 1 1 6 : 2 0 " 12.29 53.40 6720" 12.29 53.40 1 . 2 6 1 .B7 4 . 5 5 "TT2 6720"" 713 12.29 714 53.40 T7To~ 1 . 5 9 4 . 5 0 " T T 5 7 2 . 3 7 4 . 5 0 . 3 0 . 4 9 1 . 5 8 C IN C O U T T Y P E OGMA "7729" 1.88 4 . 4 8 .24 .44 I .30 ~ 7 7 2 " 1.27 1.30 5.75 9.40 6.30 10.75 8.00 14.30 '373"5 573"5~ 4 . 0 0 7 . 6 0 5 7 5 3 ' 4 . 7 5 7 . 3 5 1 3 . 5 0 " 8 . 7 0 " 8 . 6 0 ~739~ . 6 7 1 . 7 7 8 . 8 5 1 5 . 1 5 " 5 . 1 5 — 9 7 I O " 5.90 10.35 7.35 1 3 . 9 5 3 5.64 3 a l 1.65 5 52.50 S'.7i- 11 .87 52.56 " 5 7 7 2 1 1 .76 52.48 " 5.58 11.65 52.46. VCOR _ A T U N _ . 6 5 . 6 9 8 8 T U L .79 1 . 1 4 " " 7 5 3 " . 5 9 I .06 .56 " .68 1 . 1 4 -.70 .79 1.20 .1233 . 1866 .0756 .086 I . 1715 • 08W7 . 1014 . 19 13 .1056 .1220 .1928 "77.7 62.2 41.1 T0T75 89.1 44 .7 9 0 . 6 " 75.7 40.1 ' 7277 62 .9 39.8 .600 1.240 5.58B . 6 T 3 ™ 1.263 5.595 "" "7609 " 1.251 5.586 " 7 5 W - 1.240 5.566 Runs 703 to 705 i n c l u s i v e , regular entrenee Runs 706 to 708 i n c l u s i v e , l i q u i d through run of tee Runs 709 to 711 Inc l u s i v e , gas through concentric tube Runs 712 to 714 i n c l u s i v e , tee seme diameter as tube COMPUTATION OF NTU FOR VARIOUS ENTRANCE CONCENTRATIONS S Y S T E M TURF CM BP MM OL GPM TFMP "c"' SATC ML MM 1 1 .757 764 .8 00 1 .070 15 .0 00 45 .47 0 12 . RUN OG. C F H P IN 80 C IN C OUT TYPF WGM VCOR TUN TUL VG 90 V 71 .30 6.05 4.6 1 4.00 12.80 5 . 6V .47 1 .17 .2376 32.3 7,395 902 71 .30 6.0b 4 .61 3.90 12.70 b 6V ,47 1.17 . .2369 32,4 7.395 90 3 71 .30 6 ,0b 4 .6 1 11.55 18 . 7 0 b 69 .69 .Ob .2566 32.6 7 . 4 1 a . 904 71 .30 0 . Ob 4 .6 1 11.4b 18.55 b 69.70 • .04 .2330 32.0 7YT> 19 905 7 1 .30 6,05 • 4 .6 1 22.00 27.30 b 70.06 .58 .2153 35 .6 . 7 . 457 906 71 .30 6 .Cb 4.6 1 23 .05 27.80 b 70 .01 .63 • 2564 32.4 7.4 52 V07 71 .30 6.05 4.6 1 32 , 5 0 35 .4 0 b 70 .26 .39 .2501 30 . 7 7 .478 j 90 0 71 .30 6.05 4.61 32.60 35.40 5 70.27 .37 . 2424 3 1.6 7.>>80 1 COMPUTATION OF NTU Vk SYSTE M TUBE CM HP MM Cll GPM TFMP c SATC 11. VP 1 1 .757 750 .300 • 1 .07 0 45 .0 0 0 2 ! .42 ; 7 1 . •>0o RUM OG CFH P IM CO C. IN C OUT TYP S l|GM VCOR TUM TUL VG 715 1 .61 .50 .55 2 , 8 0 5 .65 \ 1 .79 . 1 8 .03 34 14 5 , 8 ,191 716 2 .53 .56 .6U 2 , ° 5 4 . i j 1 2 .86 .24 ,"7 36 104.2 .3 04 717 '4 .5 2 .72 .7 4 5 ,25 4 .85 1 3 .20 .54 .1060 72 .4 .564 715 9 .6 1 1 .01 1 .02 3 . 3 5 5.75 1 1 ' .26 .52 ,1640 46 .6 1 .199 f 719 1 1 .R4 1 .09 I .08 3 .60 3 .80 2 14 ,04 .48 . 1 6 2.6 5 0 .4 1 .493 i 720 15 .02 1 .25 1 .08 3 .7 0 5 ,°3 3 17 ,05 .4 7 .1495 51 . 3 1 .010 72 1 20 .6 8 1 .75 1 .I'O 4 . 05 6 .20 4 2.4 . « 7 .4? .1531 5 0 . 1 2 . 6 4 7 r 722 30 .60 2 . 3 0 2 .27 4 . 03 6 .43 5 36 ,92 .5 2 .1725 44 ,5 3 .030 . 1" SYS! EM TUBE CM HP ilM OL Goe T C M P " £ ' S<\TC. ' L VP v, V, 7 ' 2 .8 04 75 0 Q 00 2.01C 13 .0 4 5 •'-' 7 " 12.R0- i RUM O G CFH o i v PO C r\i C OUT TYP E i i G » VC05 , M TOT i 72 3 2 . 0 5 . 3 5 .34 2 . 7 5 5 .53 1 1 , a l .26 •0 1 94 394 . " 9 5 72'4 3 . 5 2 .37 .36 2,or. 3 . ° 3 1 3 .25 . 5 4 0237 398 . 7 .17" 1 72 3 5 . 3 2 .39 .37 4 . 0 0 5 .36 1 4 . 0 9 . '.-.V ' 3-1' '3 2 4 ' . R: .961 726 6 . 7 8 . 3 8 .30 6 .50 8 .25 1 6 .4 - .56 1 4 75 16 1 .5 . 4 4 J 7 2 7 14 .08 . 4 4 .47 10 . 6 6 12 .60 2 14 .67 . 6 5 05 V K '26 .2 .709 726 3 1 . 3 2 . 8 5 .60 1 1 .35 1 3 . 5 3 2 2 1 , 07 . ' 3 _ 069 r "TTr.'a" —r;r«i! 729 33 .60 . 7 3 .74 1 1 .5 0 13 .80 3 33 .5 9 .77 "7 28 1 05 . 3 1 ,7o0 73 0 5 3 . 0 0 1 . 0 6 .99 1 1 .60 1 4 .1 0 b 53 .32 . 8 4 :796 96 , 1: 7 .794 SYSTEM TUB"1 CM RP ,'|M OL GPM TEMP C SATC 1 L V? 7 2 .5 04 7 5 2 . 3 0 0 1 .150 13 .0 0 0 4 3 . 4 7 ; 12 . | RUM O G CFH P IM PO C I'M C OUT TYP c l,»G M VCOR TUN TUL VG | 73 1 1 . 6 3 • 0 5 . 11 4 .25 ~ 3 . " i b ' ' 1 •" 1 , 4 9 " . 16 "22 7 5 3 7 .5 . " 7 8 7-5 2 2 .72. .06 . 13 4 . 4 6 3 . 4 : 2 . 6 0 .1.7 " 7 4 1 3 17 . O . 1 36 7-S3 5 . 1 1 .07 .15 3 . 2 0 6 ,4b 2 4 .09 .23 03'/:, 236 . 1 .?o 1 754 8 . 0 B .12 .17 5 .23 6 .4b 3 6 ,93 .23 0513 . n .469 75 5 1 4 . 6 7 .74 . .77 5 .00 6 ,2b 3 1" .73 .33 ^323 237 , 4 .773 736 22 . 4 4 .65 . 7 5 4 .95 6 . 13 4 7 2 . 6 0 . 2 2 " 5 09 2u8 , 0 1 .189 75 7 3 6 . 7 0 i .20 1 . " 5 4 .PO 6 ,4b 3 37 .1.5 . 50 " 4 26 18 ' , 1 1 . 0 4 6 73 8 6 0 .00 1 .RO 1 ,RD 5 .00 7 .4 0 3 60 .60 .'•lb 0528 '7.2 . 2 3 .170 75 9 1 1 4 . 7 0 2 . 4 0 2 . 2 0 6 . 5 5 1 1 .40 3 H 5 . 7 1 ,92 1 3 08 3 6 . 1 6 . 064 740 1 81 . 7 0 3 . 1 0 2 . 7 0 7 . " 5 13.53 3 163.34 1 .09 • 1688 43 .5 9 .608 SYSTEM TUBE CM HP MM OL GPM TEMP c SATC Ml. VP -IM 7 2 .504 753.. 1 00 3 .950 15 . 0 46 .47.' 12. RUM OG CFH P IM pn C IM C OUT TYPF WGM VCOR TUM Till. VG 74 1 1 . 6 3 .9 0 .97 4 .20 4 . 6 5 1 1 .37 .29 0112. 6B~T ,0 .071 742 2 . 7 8 .94 1,00 4 . 7 0 3 .30 1 2 .44 .38 0 152 304 . 1 .128 74 3 5.11 .99 1 . 0 6 0 .35 7 .23 1 4 .62 ,58 ' 2 5 9 5 2 " .7 .742 74 4 1 0 . 0 2 1 .17 1 . 2 3 11 .00 12 .10 1 9 . 4 9 .71 0 334 3 3 . 9 .3 ,497 74 5 19 .86 1 .49 1 , 4 0 14.15 15 .70 1 I v .22 1 . " 1 0525 1 4 6 , 1 1 .0 07 746 39 .4 0 2 .35 2 . 1 1 12 . 3 0 14.40 3 36 .64 • 1 .57 .674 1 1 5 ,0 7 .026 74 7 6 7 . 4 0 4 . 1 2 3 . 8 5 1 4 .65 17 .20 5 66 .51'. 1 . 6 7 "8o7 86 .5 3 .467 74 8 1 1 1 .20 6 . 5 0 4 . 0 3 15 .2.3 1 8 . 5 3 5 ' 0 9 .16 3 .37 • 1 / H 6 69 .7 5 .720 SYSTEM- . TUBE -L.U..BO.. -MM-- -CL—OP-M. TEMP - C - -SA IS Ml VI' I M - 7 2 .5 04 7 4 9 . 4 0 3 3 .03C 15.000 43 .470 1 2 . f\ "C RUN OG r. F H P IM v n r pi r nil] TVDC f l G M V.CQB— _...T.U_'! Till VG 749 12 .4 (1 1 .22 1 .25 1 ' .85 13 .25 1 1 ' . " 3 .01 0442 1 7 3 ,5 .621 75 0 3 1 . 1 0 1 . 9 3 1 .7 8 1 1 . 9 5 13 .90 3 3 0 . 5 0 1 .28 0622 123 . 3 1 .59 8 73.1 6 7 . 3 0 7-79 1 9 . O H 1 4 . 4 3 - .5. . . _5J..I.5.- -..1_..0J- Ob 06 152 . 6 2.°952< 75 2 1 1 3 . 8 0 5 . 95 3 . 5 2 15 .30 19 .00 5 1 12 .38 2 .46 1 33 V 57 .3 5 . " 0 9 73 3 139.40 8.10 3 . 7 8 1 6 . 0 5 2 0 . 2 0 b 1.36.79 2 .7b 1537 49 ,0 7 . 1 6 8 764 17 2.30! 8 . 6 0 4 . 1 8 16.76 71 .65 b 1 6 7 . 00 3 .28 1 8 89 40 .6 6 .75 1 SYSTEM TURF CM HP MM - OL GPM TEMP c. SATC ML VP 7 3 .5 0,4 755 5 6.'] 3 . 0 1 . " 15 . 6 0! T; 4 6 .4 7 0 . .12.. H O C RUM OG CFH P IM pn . C IM C O U T TYPE OGM VCOR TUM TUL V G 785 40 .1 n ,09 . " w 6 , 1 6 1 ?.• . 65 "i 39 .RO . 8 5 » 0 7 2o 103 . 8 2 . 0 9 0 736 7 0 .00 1 .45 1.36 6 . 8 0 1 1 ,9b 3 69 .96 1 .05 0921 63 75 7 M 6 . 7 0 1 . O H ' 1 . 5 5 9 . 3 0 1.3 ,7 0 3 . 1 16 .72 1 .4 8 1 329 57 .7 6 . 1 1 6 75 8 146.3 6 7 , 3 9 J . - H 5 - _..ft.it5... .1.4 ...7.0.. 5 146.3_5_ _L..Z.9_ 6 14 4.7..,.5 _ .7_..664_ • 759 ' 8 0 . 1 0 2 , 6 4 2 . 0 3 1 0 . 1 0 16 .15 6 180,05 2 . 0 8 1921 39 .0 9 . 4 3 5 . V-18 COMPUTATION OF NTU s Y S r I.M Fi P MM \, r = « Kh rr. Ml VP -IM r 2 . 6 " 4 7 .5 0 •_. 'j 1 . 13 0 b 00 4 5 . ! ' 7 0 12. BO .UG..CEH.- P...-J.A! .an.... .X.-JJl— ..C~.'iUX... T.Y.P __U£il.. ..V.C0?_. .T..U-M Ti l l VG fa Z « . 7 i - . 1 ? .-' i 2 . 9 3 3 ." 0 1 ".1 .5 8 .15 . 0 2 0 7 3 7 1 0 .0 8 2 7b 1 5 , 2 . 0 4 . 1 2 3 . 00 4 . 03 2 3 ,2>i .19 . 0 2 5 6 2 9 9 '-' .17 2 . .7.6? 7 .B l . ' 2 . 1 .6 ••. OS ii .'J-3 5 7 .611 • . 2 5 . 1 3 4 3 2 2 3 4 . 4 0 2 \ (bi 9 3 . 1 " 1 .30- r.oo D . 05 b. H 0 5 9 3 .7 0 .70 .09 9 6 7 7 1 4 . " 1 0 i Tat ' u 6 . 2 o 2.20 2 . 1 5 6 . 30 1 1 . 8 5 5 1U7.00 1 .06 . 1 5 6 3 ' 4 9 1 7 . 7 0 3 (65 1 8.1 .30. ...2...9..C.... 2..7 0 . ..6.75. ' 2 _ ° 0 3 " 8 2 . 6 2 1 . i B — . 1 7 6 6 U 5 L f) . 5 7 - . . . S YS 1 ? M TUB? C « BP i-IM OL OP'- f E MP C SATC ML VP MM 6 1 .?'26 765 .611 " 6.2.0 16.000 46,470 12 , noc rt'.IM d(4 C F M P i«i Pn C. -I'M C OUT TYP E UGM VC1P TUN TUL VG 76 6 '..•-6 !..--1 .1.34. .. . 2 . 9 5 . .7 .10 1 1 ,09 . 3 6 .1 060 73 , 1 .237 767 2 . 2 1 1 . 3 6 ! .27 3 . 1 0 9 . 1 0 'f 1.7 1 .52 "."1563" 49 . 1 . 3 7 3 76 8 3 .68 1 ,i'-3 1 . 6 4 5 . O b 1 1 . 6 5 ' 1 3 .04 .69 .2 103 36 .5 .6o3 7b9 3.4ft 2.26 2.25 6 .05 14.70 ' 1 • 4 .66 .66 .2793 27 , 4 1.0-17 77 :•• 8.20 2.36.. 2.68 4 . 2 6 10,90 3 7.72 . 5 9 .1600 42 . 6 1 .682 7 7 1 1 1 .96 . 2 . 9 3 .2.77. .4 ..II 0 . .1 D..B5- .11 .5.4,.... . 5 7 .. _OJJi4_ 44 . 0 2,615 7 72 19.84 5 . 0 5 3. "6 6 .25 1 2 . 9 5 3 19 .3 li . 6 0 .2 167 35 . 4 4 . 2.1 4 77 3 6 6 .5 i ; 5 . -' 6 6 • 0 7 6.50 I 7 . n i 3 32 .64 1 .05 . 5 4 64 2 2 .0 7.113 SYSIF-I TUB E _M t-iP iM OL GPM TF.MP r. SATC ML VP MM 6 1 .226 762 . 4 0:' 16 .0 c..; 43 .4 70 12. 8 00 XI I'l Or. CP " P IM P D C I M C OUT TYPF UGM VCOR TUN TUL "VG 774 6 .76 2 . 4 8 2.. 3.7 4 . 6 0 12.66 3- 6 . 1 3 .7 1 .2224 34 .5 1 . 34 1 77 5" '65.5.0 1 ' .15 _7 _S-'- M , 8 0 v s ,? " 3_ 63 .62 1 .64 .6976 12 , 8 13.862 r 7 o 1 1 .". . 1 ". i 5 .3 0 12 .00 1 2 .65 3 3.20 3 106."5 2 . 3 7 .9982 7 . 6 23.301 7 7 7 160.0.', .19.5 0 17.6 0 17 .00 3 0 . 2 0 6 1 4 4 . 1 3 2 . 8 3 1 .3677 3 . 6 3 1 .4 05 Cr b 1 9 4 . : ; 27..50 . 2 4.60 2 1..70 40.70 .. .7. . 184., 04. .. 2. ...7.7 . ! .'.-5-.J.. _____ , 0 4 0 ...101 SYS IF •i TUBF C M B P ,•1M OL GPM TE '- 'P r. SATC M L VP 1 , ? ? M 753 , 30.0 . - .2-9.3 16,1 45 .470.... 12.«,.-;- rt' 1 M or- CFM P JM r n r. iM C OUT TYPE OGM' VCOR TUN TUL VG . 779 1 .5.6 1,6.. .60 . 2 . 9 . 0 . . y . ..1... 1 .26. . .. _.,3.G .1 593 4ti , 1 -.? 60 7 8 0 2.07 .32 . 7 4 3 .46 1 0 . 7 5 1 1 . 7 4 . 3 6 .1 9 6 9 39 , 0 .360 7 8 1 3 . 5 6 .5 0 . 8 4 5 . 8 3 1 5 .05 2 3 .17 . 4 7 • ?67V 29 .7 .692 Lay 5 . 4 V ,61 . 9 5 . i...fir._ 1 ? a" 5,13 ,46 .9511 3 0 ,5 1.119 78 3 8 . 3 4 . «1 1.10 3.9 0 1 1 .36 3 8.12 . 3 7 ,2 036 3 7 .7 1 .7 71 764 ! 1 . « 1 1.08 1 .32. 4 . 00 1 .1 .7 0 5 1 1 . 6 " .33 ,161b 42 . 3 2 .6U7 1 85 .19.1 l ... I .35 .2.1.5 3 . 0 5 . 1.3.1.5 . 5.. ...19...03.... . . . 4 1 ... ...?33 2.. 53 . 3 4.147 786 S l . i - i 2 .75 2.66 5 . 0 0 17.66 3 30 .94 ".62 .3620 2 f , 1 6 . 7 4 3 SYST F .„ T .UBF. . .^ .M_JB.2 •t \i 01 ,•;(>*> T i" *l P r S M C -Ml V P MM 6 1 . 9 2 8 7 6 1 . 6 0 0 .2 9 3 13.0 4 6 .470 1 2 . 8 _ 0. rt.l'i '•!G CFH .P.. I M .P.O. . C. IM .... C OUT T.YP.E ;I.GM. y.c.op... TUN TUL VG . 767 62.81 6 . 8 3 5.65 7.9 0 24.26 3 62 .80 . 9 3 .6919 12 , 6 13 ' , 6 6 b 786 1 .19.30 7 .55 6 . 6 5 1 2 .80 33.65 6 10 6 .66 1 . 37 1 .0474 7 .3 23.653 .... 789- 14 9.1-0 1 7 . 6 1 1 0 . 6 . H i . L _ _ .4-0.-03... 6 1 46 . 3 9 1 ,82 1.6690 4 . 6 31.8 96 790 190 .30 18.00 15.60 24 .«6 42 , '1- 7 183 .1 1 1 . 9 9 2.2241 3 , 4 40 . 3 12 SYSTEM TUBE CM RP rt r-i OL GP>- TE MP C. ...SATC . ML .VP 6 1 .228 751 .600 1,020 15.0 0 0 4 3 . 4 7 0 1 2 . «00 rtU M. o c r p n D [ M r1 £. _C J.:-] C- OU-T T V D P ,-.if;M vrnp T H M . Till VG 79 1 1.36 3 . 4 0 5 . 1 9 2 . 8 3 3 .5 0 1 . 9 3 .44 .1667 1 1 6 . 0 .213 f92 1 .80 3 .86 3 .53 3 . 1 5 6 . 4 5 1 1 .26 .56 .0630 0 '< , 6 .275 79.3 .-.5...6.8._.--4.,,!i2... 4 _3B 4 _ 2 0 9 .55 1 2,80 .92 .14 18 54 ,1 . 6 10 7 9H 6 . 1 7 3 . 6 3 5 . 1 5 5 .30 1 1 .83 1 4.09 1 . 1 3 .1802. • 42 . 6 .89 1 795 6 . 3 9 6.36 6 ,23 6 . 1 5 13.16 3 7 .24 l .22. .200 1 38 . 3 1 .67 8 .. 796.. 1 1 .71 7 .0 0 6 . 1 5 0 . 3 8 11.41 5 1 0 .92 .86 ,1406 64 . 6 2.380 . 9 7 " V v . 6 3 " 1 0 . 1 1 t i . 4 0 7 . 1 5 1 3 , 6 0 5 18.70 l . l i . 1 8 6 7 41 . 3 4.074 798 31.61 15 .40 10,95 6.60 17.40 6 29.67 1.55 .2722 26.2 6 . " 6 5 S Y S T E M T U B E CM. BP M M O L G P M T E M P C S A T C ML vp MM 6 1.22a- 7 51 . 1 CO 1.020 15 .000 43 .470 12 . "00 K ' . I S OG CFM ? IN P D C IM C OUT TYPE OGM VCOR TtlM. TUL VG l i 799 63 .91 20.21 16.91 11. "5 '28. 1 5 6 59 .23 3 .22 .6478 U.8 12. "07 I | 6 OO 0 . 9.1..i.:i..2b..8b..22..!i:__lJi-JJ.-.3.4.-.5.b b...„.8A.-)i ii..66....l... 0.2.09 7 , S I B , ? , , ! , . . 8.M i?0."0 33.40 27.60 17.60 39 ;05 6 109.00 5 .69 1.3569 6.6 23 .751 I CORRELATING V A R I A B L E FOR BUBBLF-PLUG FLOW V~19 LIO TUBE OL OPM DTFE S TENS VISC VELL 1 1.75V .620 l.itftS 73.530 1.140' . 52v VELG FACTOR CORP AY • 111* . 9 0 9 8 .0367 s-trsr—:-9998-—;0936- 1.61b .9998A . 1U3 .9998 294 T 9 V 9 B - - .727 .9998 1.3J5 .9998 66 . 7C 5 9 . 6 C 59.80 65.8o 7CT20- .2862 • C352 •••07U0- . 1527 .2568 -o voy ;-33ir7- 2.655 .9998 .4064 . 1 1 9 .9998 .(1322 riCV TV998 . C79 I" .544 .9998 .1234 .826 .9998 .1746 !TT23-"" 'V9998'—. 2127 1.3I4 .9998A .2366 1.703 .9998 .2602 ~2TC23" -79V98" 27 89~ LIO TUBE OL GPM OIFF S TENS V1SC VELL 1 1 .757 I .CTC—irwyTtttt l -TT4tr-r9-|-3" NO J "T63—4" 164 4 169 1 -TTC- OGM MTU -rr.-3-t—.-T220- 17 1 17 2 173 174 17 8 -179-- IbO la I 182 22. 15 1.13 — 2 Y T 5 ~ 8.33 IC.95 15.27 15.9.3 1 .85 — 3 T 2 5 ' - 5.89 9.26 " 7 2 7 2 9 — .1282 .0385 TC6-4-T .1 190 .13 14 VI275 . 1271 .C49 0 :C74-6" .C976 .1277 7T332 1*13 26 0 • 26 1 26 2 -265 - 284 2b 5 28 6 287 3 288 4 29 3—1 29 4 I 29 5 3 S" 3CC 1 301 1 30 2—2 " 30 3 3 304 4 15.57 — 4 " T T V — 6.22 9.28 - 2 0 T 8 6 — 1 .58 3.78 — 8 T 6 - 3 — 16.87 22. 14 — 2 . 5 2 — 6.32 16.6 ! ™ 2 - b - 9 V — 1.83 4.2 1 — 9 . 2 4 . 12.83 21.5C . 1227 ;CfT36- . 1155 .1283 r l C 2 3 - .05b5 .079 I .-1-34-3- .1125 . 1067 .0595 . 1034 . 1C78 ;-123 S - .0371 .C777 .-T228- . 1265 . 1048 LTU -6 J2.-6tr 59.9C 199.40 T1V-. 64. 50 5b.40 60.20 6C.4C 156.7C TU2.9C- 78.60 6C. 10 57.6C 62.60 ~9lT«e- 66.4 0 59.80 -76vctr 131.10 97. IC -57. tC 6 b . 2C 7 1.90 V2BV9C 74.2C 7 1.20 -6-2-,-lt- 2C6.7C 98.70 62. 5C 6C.7C 75.30 VELG FACTOR CORR Y —IT94V- -,-9<?9b— . 3 4 9 1 — 2.358 .999b .4193 .120 .9998 .0397 T 2 V T - - - . - W 8 — ; 0771 .886 .9998 .2140 1.166 .9998 .2731 - 1 - 4 1 3 — . 9 9 9 8 .2966 1.696 .9998 .3315* .197 .9998 .C544 3 W " 9V9TJ— -.X939— .627 .9998 .1503 .9b6 .9998 .2425 "1. 3 0 8 . 9 9 9 8 .2958 1.657 —vun-6— .662 .968 -2^21 V — . 168 .4C5 .-«•(•« - 1 .796 2.357 - .269 .67 2 1.768 2.766 - . 194 .446 -.983 1.366 2.2b8 .9998 .-990-8 -- .9998 . 9 9 9 6 799W— .9998 .9998 VY9W- .9998 •9998A . - 9 9 9 8 - .9998 . 0 9 9 8 .9998 .9998 . 9 9 9 8 .9998 - .9998 • 9 9 9 U .3153 i l l 36 .1819 .24 39. .-32C3- .0632 .1041 .-2459- .3047 .3486 .0-703 .1639 .2890 .4643 .C410 .10*57 .2328 .2882 .3364 LIO TUBF OL GPM D I FF S TENS v i s e VELL 1 1.757 1.5CC 1.465 7 3.53C 1. 140 1.28 .'* NO J OGM NTU LTU VELG FACTOR CORR Y 74 1 1. 1C .0299 2 56.90 . 146 .9998 .C426 75" —r~- 1.72 VOU'4'tr -1 71.20 - .227- —.-9998 - -.0675 77 1 5.32 .0847 90. 60 .705 .9996 . 1661 78 1 b.40 . 1 136 67 . 5C 1. ! 13 . 9998 .27 18 79 — - 1 — 1 1 .44 -.1-30-7 -5b;-7C 1.515' .9998 - .3663 80 1 15.06 . 1220 62.90' 1. 996 . 9996 .3996 b 1 3 lb .63 . 1-120 68.5C 2.468 .9998 .4 197 ' - 9 t 1 3. lo .056 ! '32.00- - --.421 .9998 -.0988 9 1 1 4.34 .C7C2 ' 09 .40 .574 . 9998 . 130 1 92 3 l b . 70 .118 3 64.90 2.476 .9996 .4443 ll»T - 1.-42 .C336 228.30 . 168 .9998 .0493 142 1 2.4B .C55C 13V.51, . 328 .9996 .0884 143 1 7.25 . 1024 74.90 .960 .9998 .2293 144 — I — 1C.2R .1277 6C. !C 1.362 .9998 .3373 145 1 14.34 .1394 36. IC 1. 9CC .9996 .4432 149 1 2.05 .C425 18C.60 .216 . 9 0 9 6 .0636 I5C 1 3.59 .06 13 125.2C .36 2 . 9998 .1018 15 1 3 19.54 . 1 lb 1 65.00 2.C8C .9998 .3968 16 6- "" 1 5.16 '.0785 97.70 .548 .9998 . 1435 157 1 12.C6 .1345 57. CO 1 .284 . 9998 A . 3 4 4 8 15b 3 17./! 2 . ! I6C .66. 20 1.822 .99 98 .3598 162 ~4" 2 1 .27 . 1 '45 6 7.00 2.264 .9996 .4057 V-20 CORRELATING VARIABLE FOR BUBBLF-PLUG FLOVT L I P TUBE O L G P ^ I) I F F S TENS v i s e V E L L ' * 1 1 . 7 5 7 2. I C G I .H66 7 3 . 5 3 C - 1 . tut: 1 .79i! . . . . .... N O J O G M N T U L T U VEI . G EACTOR CORR Y 5 9 ~ ~ 3 - 25.82 1336' 57.Uf 2.748 - . 9 9 0 8 .6065 1 2 5 1 1 . 1 3 . C 2 3 2 3 3 C . 6 C . I5C .9998 .04 50 . 120 1 2.48 . 0 3 6 5 2 10. K ; .329 . 9 9 9 8 .0774 1 2 T " " ' I — f t — ; - | - 1 C V - 6 V T 2 C - 1 .P56-- -;99 98 • .4 04 6" I5C 1 . 1.64 .029 1 263. 5 C .2 17 . 9998 .0584 155 1 13. 84 .1074 7 1 . 50 1 . 6r>3 . 9998 .3893 1 5 1 - - a — " I H ; 48— '1-7—6 b'. 7tr •2.-448- V9998-- -.4735 155 1 11.02 .1024 7 3 . ( X I .460 .9996 .3550 156 1 l.4i. .0252 3L4.4C . 186 .9996 .C49o ~ - " T 3 T V R . 1 4 - . 0 7 8 8 9 7 . 4 0 ' - 1.079 . 9 9 9 8 .2262 158 3 1 6 . 7 7 . 1036 7 2 . 7 0 - 2.222 . 9 9 9 8 .4238 1 5 9 3 2 2 . 5 6 .1194 64.30 2.966 .9998 .5707 LIO T U B E O L G P M O I F F S T E N S v 1 sr. V E L L 1 1 . 7 5 7 3 .C0O I.U65 7 j . 5 3 ( ; ! .140 2.560* N O J O G " N T U LTU V E L G F A C T O R C O R R Y 2 1 0 1 2 . 3 8 . 0 2 5 1 5 3 ! . 2 C . 2 = 4 . 9 9 9 8 • •J6S-0 2 1 1 — ]••--U .97- -.041 1 1 8 6 ; 7 C . 5 2 9 . 9 9 9 8 . 1 2 6 9 2 1 2 1 8 . 6 5 . C 6 C 4 127 . 1C .92 1 . 9 9 9 8 .2 102 2 1 3 1 1 4 . 0 7 .06 15 9 4 . 1 G 1 .498 .9 .99b .3307 • 21-tf-• - 3 ~ -2 1 . 7 7 . C ' 9 4 0 "8 l ;6C 2.318 V9998 . 4 5 8 5 2 1 9 1 1.66 .0217 3 5 2 . 5 0 . '77 .9998 .0594 2 2 1 1 10.4 1 .0669 116.50 1 . 1 08 .9996 .2417 2 2 2 .. 3 1 6 Y 9 6 .0893 • 8 6 . O C 1 .805 . 9 9 9 8 .3898 22 o 1 0 4 . 6 7 .0371 2 C 6 . 6 C .497 . 9 9 9 8 . I 134 2 2 9 1 8.17 . C 5 2 7 145 .61) . 870 . 9 9 9 6 . 1807 • • Z 3 r — r - 12.34 , i ; 7 4 9 1 0 2 . 5 0 1 . 3 1 4 V999R " . 2 9 0 ! 2 5 I 5 2 6 . 2 3 . 0 9 9 8 7 6 . 9 0 2.792 . 9 9 9 8 . 5 3 4 1 LIO I U R F OL" GPM 0 I FF 5 T E N S v i s e V E L L 1 1 . 7 5 7 4 .200 1 . 4 6 5 7 3 . 5 3 0 ! . 1 4 0 3 . 5 0 5 N O J O G " N T U L T U V E L G F A C T O R C O R P . V 2 6 9 1 3 . 1 3 .0271 2 8 2 . 6 0 . 5 4 6 . 9 9 9 8 . 1 1 1 9 ... . .... 2 7 ? I "VI ".6 1 . 0 5 2 1 147.30 1 .236 . 9 9 9 6 . 2 5 1 1 2 7 1 5 2 1 . 5 8 .0764 100.50 2.297 ' . 9 9 9 8 . 4 4 9 3 2 7 6 1 1 8 . 2 2 . i 5 5 9 1 3 7 .20 1 . 9 3 9 .9998 .30.0 7 99 - 8 . 0 9 4 2 5 - 72 .99438 '6 .8129 I 19 .326 1 5 - . 6 6 9 7 0 .82700 LIO T U R E O L G O M OIFF S A T E N S v i s e VELl. 1 1 . 7 5 7 1 . 0 7 0 1 . 0 7 2 7 5 . I C C 1 . 5 0 5 . 9 1 3 NO J OG" N T U L T U V E L G F A C T O R C O R R A Y 2 3 6 1 3 . 9 2 . 0 6 5 8 1 1 6 . 6 0 . 4 1 7 1 . 1 1 2 4 . 0 9 7 3 ; ~ - 2 3 7 .... , .. 7 . 3 6 . 1 0 2 2 7 5 . 1 0 . 7 8 3 1 . 11 2 4 . 1 9 2 8 2 3 8 3 1 1 . 5 5 . 1 0 5 4 7 2 . 8 0 1 . 2 2 9 1 . 1 1 2 4 . 2 5 1 1 2 3 9 5 2 2 . 9 0 . 0 9 1 5 8 3 . 9 0 2 . 4 3 7 1 . 1 1 2 4 . 3 4 1 0 LIO T U B E OL GPM D I FF S T E N S v i s e V E L L 1 1 . 7 5 7 1 . 0 7 C 2.019 7 1 . 2 C C .BCC . 9 1 3 N O J OGM N T U L T U V E L G F A C T O R C O R R Y 2 4 4 1 4 . 6 4 . 1 0 3 ! 7 4 . 4 0 . 4 9 4 . 9 0 9 4 . 1 3 1 9 2 U 5 1 8 . 6 2 . 1 3 6 6 5 6 . 2 0 . 9 1 8 . 9 0 9 4 4 .22 7 5 2 4 6 3 1 3 . 4 4 . 1 3 9 3 3 5 . 0 0 1 . 4 3 0 . 9 0 9 4 . 2 9 7 3 2 4 7 5 2 5 . 4 8 . 1 3 9 2 5 5 . 1 0 2 . 7 1 2 . 9 0 9 4 . 4 5 8 9 LI 0 T U B E O L GPM OIFF S T E N S VI S C V E L L 1 1 . 7 5 7 1 . 0 7 0 3 . C 8 0 6 8 . 8 0 0 . 5 9 9 . 9 1 3 NO J QGM N T U L T U V E L G F A C T O R C O R R Y 2 5 2 1 5 . 4 2 . 0 8 9 0 8 6 . 2 0 . 5 7 7 . 7 8 0 0 . 1 0 3 4 - - " 2 5 - 3 —1 V . 7 9 - ; 1 4 4 8 5 3 . 0 0 1 . 0 4 2 . 7 B C 0 A . 2 2 0 8 2 5 1 3 1 4 . 8 9 . 1 3 1 8 5 8 . 2 0 1 . 5 8 5 A . 7 8 0 C - A . 2 5 6 8 2 5 5 5 2 7 . 5 8 . 1 2 6 8 6 0 . 5 0 2 . 9 3 6 .7b00a . 3 8 0 7 7 1 5 1 1 . 7 9 . 0 5 3 4 1 4 3 . R C . 1 9 1 ,7b00 . 0 4 6 0 7 1 6 1 2 . 8 6 . 0 7 3 6 1 0 4 . 2 0 . 3 0 4 .7b00 . 0 6 9 8 7 1 7 1 5 . 2 0 . 1 0 6 0 7 2 . 4 0 . 5 5 4 . 7 b 0 0 A . 1 2 1 3 • " 7 1 8 1 1 1 . 2 6 . 1 6 4 6 4 6 . 6 0 1. 1 9 9 .7bCC . 2 7 1 2 71 9 2 1 4 . 0 4 . 1 5 2 3 5 0 . 4 0 1 . 4 9 5 .7bOC . 2 8 6 1 i 7 2 0 3 1 7 . 0 5 . 1 4 9 5 5 1 . 3 0 1 . 9 1 0 . 7 8 C 0 . 3 2 9 2 7 2 1 4 2 4 . 8 7 . 1 5 3 1 5 0 . 1 0 2 . 6 4 7 . 7 8 0 0 . 4 2 6 2 CORRELATING VARIABLE FOR BUBBLE-PLUG FLOW V-21 L I O TUBE OL GPM D I F F S TENS vise V E L L 3 1.757 .610 2 . 9 5 0 2 3 . 4 0 C 1.360 .520* NO J OGM NTU LTU VELG FACTOR CORR Y 43"6 r 1.02 .0407 IBB.60 . 109 1.-2185 .0312 43 7 i 2.24 .0701 109.40 . 238 1.2185 .0648 438 t --5.43- .1210 6 3.40 .57R 1.2185 .1619 439 2 9.75 .1422 54.00 1.038 1.2185 .2700 44 0 3 16.43 .1239 6 1 .90 1 .748 1.2185 .3425 44 1 5 24.7B .1236 62. 10 2.638 1.2185 .4757 47 2 1 1.9B .0563 136.30 .2 10 1.2185 .0501 47 3 1 5.39 .09 16 83.RO .574 1.2185 .1221 474 2 10.70 .1211 63.40 1. 138 1.2 185 .2447 47 5 3 19.97 .1215 63. 10 2. 126 1.2 185 .39 18 LI 0 TUBE OL GPM DIFF S TENS vise VELL 3 1.757 1.070 2.950 23.400 1.360 .913 ' 1M0" J ' • OGM NTU LTU VELG FACTOR CORR Y 35 1 1 1.22 .0368 208.60 . 13C 1.2185 .C467 35 2 1 3.C9 .0500 153.40 • 32V 1.2185 .0756 35 3 1 4.58 .0763 100.60 ,.488 -1.21 85 .1302 35 4 1 7.06 .0953 80. 50 .751 1.21B5 .1932 35 5 3 14.04 .1042 73.60 1.494 1.2185 .3056 356 5 24.87 . IC26 74.ftC 2.647 1.2185 .4451 • -37 5 1 .95 .0333 23C.4C . 102 1.2 185 .0412 i 37 6 1 2.12 .0399 192.CC .226 1.2185 .0553 37 7 1 4.51 .0665 115.50 .480 1.2185 .1 129 • -37 8 1 7.50 .0921 83.40 .798 1.2185 .1920 3B 1 5 25.B5 .1338 57.30 2.752 1.2185 .5975 38 7 1 .90 .0304 251.90 ;096 1.2185 .0373 • 38 7 1 1.00 .0260 294.80 . 107 1.2185 .0323 38 8 1 1 .68 .0404 189.7C . 178 1.2185 .0537 38 8 1 1 .82 .0342 224.20 . 193 1.2185 .0461 38 9 1 2.43 .0562 136.60 .268 1.2185 .0802 38 9 1 2.53 .0515 1 4 9 . 10 .270 1.2185 .0742 39 0 5 24.79 .1282 59.90 2.639 1.2 185A .5549 - - 39 C 5 24.72 .1331 57.60 2.631 1.2185 .5748 39 6 2 9.96 .0978 78.50 1;060 1.2185 .2351 39 6 2 9.96 .0997 77.00 1.060 1.2185 .2397 39 7 3 13.28 .0934 82.20 1.413 1.2185 .2647 39 7 3 13. 13 .1006 76.30 1.397 1.2185 .2832 39 8 ~u -19.00 .0921 83.30 2.022 1.2185 .3294 - -— 39 8 4 I8.7C .1071 7 1.70 1.990 1.2185 .3788 39 9 5 24.64 .1042 73.60 2.623 1.2IB5 .4490 39 9 5 24.46 . 114? 67 .20 2.603 1.2185 .4893 42 7 1 .79 .0288 266.30 .084 1.2185 .0350 428 T 3.05 .0544 141.00 .325 i ;2 I85 .0820 - — 42 9 2 9.90 . 1138 67.40 1 .053 1.2IRS .2726 43 0 3 16.84 .1076 7 1.30 1.792 1.2185 • .3547 43 1 5 23.28 .1212 ' 63.30 2.478 1.2185 .5008 48 0 1 .96 .0262 293.OC . 102 1.2185 .0324 46 1 1 1.82 .0338 226.80 . 193 1.2185 .0455 482 6 . 37 .0747 102.7C .678 1.2IB5 . 1448 —: 48 3 3 12.13 : .0971 79.00 1.290 1.2183 .2606 48 4 4 18.55 .0963 79.7C 1.974 1.2185 .3368 LIO TUBE OL GPM DIFF S TENS VISC VELL 3 1.757 2.100 2.950 23.400 1.360 1.792 - - - - NO J OGM NTU LTU VELG FACTOR CORRAY 403 1 1. 12 .0122 625.50 . 1 19 '.2185 .0284 40 5 1 6.66 .04 19 182.9C .709 -1.2185 . 1277 - - 406 1 12.51 .0526 145.90 1.332 1.2185 .2002 40 7 3 17.53 .0862 89.CC 1.866 1.2185 .3842 -40-7- -s- -17; 68 .C825 93.CC 1. 881 1.2185 .3693 : . 41 1 l 1.47 .C168 454.8C . 156 1.2185 .0398 41 2 1 4. 16 .0258 297.20 .443 1.2165 . .0702 412 1 3.95 .0307 250.CC .42 1 1 .2185 - . 0 8 2 8 : - " 413 I 9.84 .0581 132.00 1.047 1.2185 .2010 41 3 1 10.05 .0526 145.80 1.C70 1.2185 .1834 4t« T - -74.35-- .C753 1C2.CC 1 . 527 1.2183 - . - 3 0 4 5 - . — - — . 414 1 14.78 .0632 12 1.30 1,573 1.2185 .259 1 41 5 3 23.71 .0994 77.2C 2.524 1.2185 .5228 -415 3 24.30 .0837 91.70 2.586 1.2185 • .4466 41 8 1 1.C3 .0137 559.6C . 1C9 1.2185 • C317 42 1 1 15.36 .caco 95.90 1.634 1.2185 .3340 - "42 r —J- 22.39 VI 08'6 •7C.7C "2.383 1.2185 - .5525" - • 489 1 1.09 .0127 601.50 . 116 1.2185 .0295 49 C 1 2.21 .C2C7 369.40 .236 1.2185 • OS 11 49 1 1 6.22 .C392 195.7C .662 1.2185 .1172 - — 49 2 1 14.49 .0643 H 9 . 3 C 1.542 1.2185 .2612 49 3 3 24.25 .0865 8B.70 2.581 1.2185 .4609 88 10.90949 -69.172C6 20.23141 24.36837-.68233 .83654 ' CORRELATING VARIABLE FOR BUBBLE -PLUG FLOW V-22 L I O T U B F ' O L GPM D I FF S A T E M S V I S C . V E L L 2.1 .757 .620 3.690 73.530 .1.11*11 .529 MO J OGM MTU LTU VELG FAf.TUK COPR Y 597 1 1.30 .0975 78.70 .138 .6299 .0409 598 ! rTTfl .1216 63.TL. rm .6299 .('.536 ^ ~ 599 1 2.67 .1428 53.70 .284 .629.9 .073 1 601. 2 4.58 . 17 19 44.60 .467 .6299 . !!0t- 6li I 2 TT4~3 . !635 46.40 TTT!? .6299 7VSV> 602 3 • 10.96 . 1558 49.20 1.166 .6299 . 1663 603 3 c-16.07 .1600 4b . OC 1 .7 10 .6299 .2257  FFu I : T731 ,cV56 BC.5L .139 . o / v « . u n . / 605 1 2.22 .1244 61.70 .236 .6299 .0599 606 2 5.96 .1650 4 7 . H .634 .6299 .1194 — 6 T 7 3 1074- . !6 12 4 6.90 ! . I C7—r6 '29V—TTT23 ' 6C6 3 19.90 .1621 uy . S f 2.118 .6299 .2703 609 4 27.27 .1910 40.20 2.903 .6299 .4129 —BTZ 2 — U.5V . '564 4V. 'C 7WT5 .6299 rlOO? 613 2 6.83 .159 1 4 . . 2 0 .939 .6299 .1u7! 614 3 13.97 . i SOC. b ! .H ' ' i .487. .6299 . I9 . S — r . ' 5 4 24.25 . ' T H ' S — r r r s c — 2 ; 5 8 ' — ; 6 ' 2 ° V . 3 ^ 4 LIO 1U6E UL GP" DIFF 6 TENS V I SC. VELL X I - 7 S 7 3 . h 9 _ '.3.6.M ' . 141. T9-13—~ - " " NO J OGM NTU LTU VELG (-ACTOR COP.P.AY —5tr7 1 fi^m .162? HI.HI-—TTBrns rPZV9~- - . - t t r r i 506 3 14.47 .1962 39. 'C 1 .541 .6299 ..3<"33 bC.9 4 2 1 .96 . 1849 4 1. 5(. 2.338 .6299 .3767 —5TH 1 mn .9463 i6b;TT H U T .SIT?—.f3C7 5 '5 . 1 2.C7 .11632 12I.3C .22 1 .6299 .C;'4s! 516 1 3.49 . 1494 51.31 .586 .6299 . l 4 l r ; —5-17 2 10. 12 .2076 3T>"T°T rr077 r«29V—T2«C3 " 518 2 11.44 .2169 35.40 1.217 .6299 . 2 V ! ' 519 4 19.38 .2028 37.80 2.062 .6299 .38!. ' — 5 Z C 5 27J7T9 .2096 J S T S T T 27H3-2 . " 6 7 7 9 ."UV 72 523 1 1.66 .0663 136.20 .177 .6299 . .386 524 1 3.78 . l l t i C 6 5 . 10 .402 .6299 .0977 —5250 1 9 7 8 - 1 - 7 T 9 7 7 — 3 B T R C rrOVS '."629 V ' - ' . 2439 326 3 13.66 . 191! 40. 20 1.464 .6299 .2848 . -6-2 7 3 — l a . T t - .*oft< s —rtrn—i-vw— to_9v - r:i ? - 3 t i . - - 528 5 23.66 . !8C2 42.61 2.539 .6299 .39 19 533 1 U ? 9 .('547 I4C.2; .137 .6299 .C3oi 554-—I +T6-I r(-fr24 '2 3.10 rtT-i iTrfcW -.-;.-4-26 : — 635 '1 2.83 .C8C1... 95.81; .3(1 .6299 .0612 336 I 7.36 .1768 43.40 .783 .6299 .1689 -5-37 2 1-1-7*2—T2V I V — U t r s v f ' " i T g o ' V — r W f - . 2 7 7b - 636 3 16.43 .1796 42 .7 ! . ' .962 .6299 .3253 339 5 2 2 . U ! .1972 3 e , 9 ! 2.3o6 .6299 .4 (97 TP-TV 1 l T 3 t Jtjp-21—r23TSt r B f i .*29v—.-'-4-I-I - 62(. 1 1.7 1 .1-736 K 4 . ? r . . . 162 .6299 .05v7 • 621 1 3.24 . If.BA 70.71 .346 .6299 .(;86C LIO TUliE OL GPM DIFF S VfcNS VIST. VELL 2 1 .757 2.1.1' 3.69s. 73.63:. l..Ui 1.792 NO J OGV NiU . LTt! VELG l-ACTOR CORK Y 556 i 4.12 .0774 9 9 . 2 0 .459 .6299 . 1 ( 9 1 ; 557—r rvrs—r*v-9ts-~nT:vz—-,-TUV-.-6_-vv- -.-'768 6 6 1 ! 11.96 . 1267 61..60 1 . 273 .6299 / S A . 2446 661 3 15.C1 . 1317 68. 31 ' . 598 ,629V .2813 56-2"—3. IB.72 7+2R2—SVT9'-. 1T993 - ". 62 9 V M ,- 3!; 3 '(•'- • 665 5 24.6 1 . 1565 4o.i'(. 2 .6 " • .629v .4427 667 1 1.29 .0325 256.3 ' .138 .6299. ,_39b 5ffB 1 rmv~-Tt-44-6--IT27 O r " 2 ( ; 2 . - 6 2 9 9 056(*- • 669 1 2.43 .0616 140.61 .269 .6299 .(1666 57(: I 4 . 1 2 .C8C 2 95.71: .439 .6299 . ' 1 2 7 3-7-1 1 TTC3 ." l i '4'2~—6T V2--- ~.-749 .6299 .'62'.! 572 1 11 .96 . ' 4 5 6 52.70 1.275 . 6 * 9 9 . 26 ' 2 573 3 15.01 . 1 5 ( 2 5 ! . 1 0 ' . 5 9 6 .6299 .32. 8. 57V—3— 1 H . 7 2 - V R W — 5 2 _ V f I . - 9 V 3 ; " 6 2 9 v . 3 4 9 ! 676 5 24.61 .1524 5C.3C 2 .641 .6299 .42b6 57V. 1 1.66 .0427 179.6C .177 .6299 .0629 58T3 1 3T3C .0556 l.3o.(:t T352 . 6 2 9 9 7 0 7 5 • 56 1 I 7 . 0 6 . 1 0 ( 1 7 0 . 7 1 • . 7 3 1 .6299 . 16i.li 582 3 13.92 .1336 66.60 1.462 .6299 .2797 583—3"— 2 F79"l .T iny .—5TT5T—-2T2ZS " ~~T6 '2W—.3 79 8 589 I 2 . C O .0453 169.2C ' , 2 ' 2 .6299 .0572 391- I 2 . 0 9 . .C699 1 ( 9 . 6 ! .3 16 .6299 .0929 j^. . , , i - t T r i r - 6 — - . - t i n s —54 . 2 0 - 1 .C7 I . 6 2 0 9 - .26 52 692 3 17.85 ; 1654 49.i iC 1.9S.C. .6299 . 3 6 1 5 T5Z3 1 fTJT Jt357r7157Tfn ; t 3 K — v » — . i n c i r s 624 1 2.H6 .0585 I5! .20 .305 .6209 .0773 626 ! 5.50 .C9C4 ti4.9C .566 .6299 .1334 CORRELATING VARIABLE FOR BUBBLE-PLUG FLOW V-23 L i o TUbE OL GPM DIFF S Tb*'S V1 SC VELL 4 I.757 .620 .285 47.900 13;90C .52V NO J OGM 666 1 1.60 689 ! 2.62 6V0 1 5.16 691 3 lU .09 N T U .0364 .0466 .0557 .0629 LTU VELG F A C T O R C O R R A Y 199.76 . 170' 1.97PV .053 I 165. !f: 1 3 7 .70 122. 10 .279 1.97BV- .549 1.9789 I.074 1.9789 -rm—n—rsTTi—.0725 693 5 19.37 .07 17 694 5 28.CO .0810 6 . 2 1 .066 I ~o"97j- 697 —074 3 . 1 188 .1996 105.9C I.42T ' . 9 T B 9 rftrstr 1C7.CC 2.062 l.'97R9 .3676 94.70 2.980 1 .9789 A . 5 6 2 5 136.7 0 . 6 6 ' 1.9789 Tt-3-ri- 9.38 .C635 120.80 .998 1.9789 . 1 9 19 L U ' IUBL UL GPM Ul FF S TE"'S V I SO 4 1.757 1.C7C .285 4 7 . 9 0 0 '3 .9CC V b L L .913 NO J 975 976 9TT " T O W — 1 1.53 I 2.53 5.39 T7T0 TTT) VETOG nrTTTTR-crrRlr'Y- - .0266 30C.CC i 162 1 .9789 .0544 .0323 237.40 .269 1 .9789 .0755 978 979 96G 98 1 983 9.90 13.58 lb .5b 27. 13 22.61 • C4UJj IT3.(.C .0516 148.70 .0503 152.6C .573 ' .9T89 1.054 1 .9789 1.446 1.9789 rfr5T5~3— I 36 . 3 C '-T977 ' . 9 T H 9 - . 0 6 2 5 122.70 .C6C1 127.70 2.887 1.9789 2.406 i . « 7 8 9 -T*-3T»- .2'.'(.• 8 • 234P -;-32XC- .4 <"0:i . 3947 LIO T1IBF OL GPH T ' l l - F S TENS VISC VtLL 4 1 .757 2. 100 .285 47.900 13.900 l . 7 "2 j NO J PGM NTU LTU VELG FACTOR CORP Y 671 3 7 . C 2 .0269 284.9C .747 1 . 0 7 6 9 . 136 ' ! 6 ( 5 ' 2 ! \ 80 .0490 I56.6C 2T37C TT9T89' .5987 1 67 ? 1 1.56 .0K39 552. IC .166 1.9769 .05 38 1 67 8 1 2.65 .0172 444. if' .282 1 .9789 .07 06 679 ? 5. 14 .0254 " 3 ' c r r r 3 f 7 " —."547 "1".T>789 - .1176 •' 68 0 6 9.92 .C3 l 3 2.5 3. '0 1.066 1 . 9 7 0 9 . 1 7 0 H 68 1 5 IS. no —7vsn~ 2'C3. 30 - 1 .Ufitj T;-o-7nv •--.-2U-3-3 — 68 2 5 19.87 .0442 173.40 2 . 1 1 5 1 .9789 . 34 1 7 663 5 27 .69 .0562. 1 .36 . 5 C 2 . 0 4 7 I . 0 7 M 9 .5271 • 13.00644 - 7 6.444 '4 Iv. 10323 2 4 . 5 3 5 6 9 - . 7 0 6 O 2 .70077 LIO TUBE OL GPM DIFF S TENS VISC VELL 5 1.757 .620 .142 4V.300 26.500 .529 NO 64 1 OGM 1.47 -64-2— r 64 3 644 643 - 64 6 64 7 -64"9" 65 0 — 2 T 3 8 - 5.27 9.56 -I2V97 18.54 26.86 - "3V 8 2 " 7.02 NTU .028 I - 0 3 5 1 .0489 .0500 .0481 .0524 .0578 V 0 W 9 .0499 LTU 272.80 •2T8.-8C 157;00 1 5 3 . 4 0 159.60 146.40 132.90 " 1 8 7 . 6 0 153.60 VELG FACTOR CORR Y .156 2.5247 • • ~ 254 2.524 7 .561 2.5247 1.018 1.38 1 1.973 2.5247 2.5247 2.5247 2.85b 2.5247 " V406 "2i '524T .747 2.5247 .0486 .0694 .1346 .1953 .2319 .3310 .4943 .0965 . 1607 LIO TUBE OL GPM DIFF S TENS VISC V E L L " 5 1.757 1.070 .142 4V.3C0 26.500 .913 — I T O - 3 - - 62 6 1 62 7 628 62 9 630 -H63T - 1 2 3 4 - 5 - 63 2 5 63 4 1 63 5 - '3 636 4 ""OGM 1 .44 2.42 5.22 9.34 12.48 -T7V56-" 25.97 3.78 "6.92 12.32 "NTU" " .0188 .0250 .0355 .0328 .0345 .0373 .0437 .0301 .0370 .0334 "LTU 407.40 306.70 216.00 233.60 222.20 "205.7C 175.60 255.00 207.50 229.40 VELG FACTOR .153 2.5247 .257 .556 .994 .328 2.5247 2.5247 2.5247 2.5247 1.869 2.5247 2.764 2.5247 .403 2.5247 .737 2.5247 1.311 2.5247 CORR Y - .0506 .0738 . 1317 .1579 .1952 .2620 .4057 .1000 .154 I .1875 "nor TUBE OL" GPM DIFF S TENS VISC VELL 5 1.757 2.100 .142 49.300 26.500 1.792 " N O 65 5 65 6 "65 7 65 8 65 9 "660"' ' OGM 1 .48 2.65 " 5 . 3 0 9.40 12.98 18.95 NTU LTU VELG FACTOR CORR Y A .0089 856.70 .0132 580.80 .0176 436.00 .0186 412.60 .0229 334.40 . 157 2.5247 .282 2.5247 .564 2.5247 1.001 2.5247 1.382 2.5247 .0291 263.50 2.017 2.5247 .04 38 .0691 .1047* .131 I .1835 .2798 66 1 5 26.05 •66 3 1 3 . 72 664 3 6.64 665 5 20.41 .0365 210.40 .0164 4 65.90 .0182 420.00 .0287 266.80 2. 773 2. 5247 .396 2.5247 .707 2.5247 2. 173 2.5247 .4207 .0906 . 1 148 .2873 V-24 CORRELATING VARIABLE FOR BUBBLF.-PLUG FLOW LI o TUBF OL HP" OIFF 5 TENS VISC VELL 6 1.228 .293 1 .465 73. 530 I.I4U .512 MO J 0G» NTU LTU VELG FACTOR CORRAY 77 V 1 1.26 .1595 48. 10 .280 .4884 .06 16 76 C 1 1.74 .1969 39.OC .380 .4884 .0857 7B 1 2 3 .17 .2579 29.70 .692 .4884 .1516 7b 2 3 5.13 .25 1 1 30.50 1.119 .4884 .2000 78 3 3 8.12 .2036 37.70 1.771 .4884 .2270 781 3 1 1.69 .1815 42. 3C 2.547 .4884 .2711 LIO TUBF OL GPM DIFF S TENS VISC VELL 6 1.228 .520 1 .465 73.530 l . ' 4 C .9C8 NO J OG" NTU LTU VELG FACTOR CORR Y A 76 6 1 1 .C9 . 1050 7 3 . 10 .237 .4884 .0587 76 7 1 1.71 . 1563 49 . IC .373 .4884 .0978 76 8 1 3.04 .2103 36.50 .663 .4884 .1614 76 0 1 4.66 .2795 27.4C 1.017 . 4 8 8 4 A .2628 77 0 3 7.72 . 1800 42.60 1.6b2 .4884 .2277 77 I 4 1 1.54 .1744 44.00 2.515 .4bb4. A . 2 9 16 77 4 3 6.15 . .2224 34.5C 1.341 .4884 .2443 • LIO TUBE OL GPM DI FF S TENS VISC VELL 6 1.228 1.020 1 .465 7 3.530 I.140 1.782 NO J OGM NTU LTU VELG FACTOR CORR Y 7V 1 1 .93 .0657 116.90 .203 .4884 .0637 79 2 1 1 .26 .0830 92.50 .275 .4884 .0834 79 3 1 2.8C .14)8 64. 10 .6IU .4684 . 1656 79 U 1 4.09 .1802 42.60 .891 .4884 .2352 79 b 3 7.24 • 20C1 38.30 1.578 .4884 .3284 796 3 10.92 .1405 54.60 2.380 .4884 .2856 LIO TUBE OL GPM DIFF S TENS VISC VELL 7 2.504 1.130 1 .465 73.530 1.140 .474 NO J OG" NTU LTU VELG FACTOR CORR Y 73 1 1 1 .49 .0227 337.50 .078 2.0307 .0254 73 2 2 2.60 .024 1 317.9C . 136 2.0307 .0298 733 2 4.99 .0325 236.10 • .261 2.0307A .0485 • 734 3 8.95 .03 12 24b.BC .469 2.0307 .0598 73 5 3 14.75 • C323 237.40 .773 2.P307 .0818 73 6 4 22.69 .0309 248.00A 1 . 189 2.0307 . 1 0 4 4 73 7 5 37.13 .0426 180.10 1.046 2.0307 .2094 76 0 1 1 .58 .0207 37 I.OC .082 2.0307A .0234 76 1 2 3.26 .0256 299.40 . 172 2.C3C7 .0336 76 2 3 7.68 .0343 223.40 .402 2.0307 .061C L i n T O B F CL GPM DIFF S TENS VISC • ' VELL 7 2.5C4 2.010 1.465 73.530 1.140 .844 NO J 0G« NTU LTU VELG FACTOR CORR Y A 723 1 1.81 .0194 394.OC .095 2.1307 .0370 72 4 1 3.25 .0257 296.20 . 170 2.C307 .0529 725 1" 4.99 .034 1 224.BC .261 2.C3C7 .0765 726 1 6.40 .0475 161.50 .440*2 .0307 .1239 72 7 2 14.67 .0598 128.2C .769 2.0307 .1959 728 2 2 1 .07 .0693 110.80 1. 104 2.0307 .2742 72 9 3 33.59 .0728 1C5.3C 1.760 2.0307 .3850 730 5 53.32 .0796 96.40 2.794 2.0307 .5881 75 5 •"3; 3-9.89 .0726 TC5.8C 2.090 2.0307 .4326 LIO TUBE OL GPM DIFF S TENS VISC VELL 7 2.504 3.950 1.46b 73.530 1.140 1.66C NO J OGM NTU LTU VELG FACTOR CORR Y — ' - - 7 m ' ... r - ' 1.37 .0112 681.90 .071 2.C307 .0393 •' - 74 2 1 2.44 .0152 5C4.10 .128 2 .C3C7 .0551 74 3 1 4.62 .0239 320.70 .242 2.0307 .0923 74 4 1 9.49 .0334 229.30 .4V7 2.0307 .1463 74 5 1 19.22 .0525 146. 10 1.0C7 2.C307 .2843 74 6 3 3B.64 .0674 113.9C 2.C25 2.C3C7 • 5C43 749" 1 11.85 .0442 173.5C .621 2.C3C7A .2047 75 0 3 30.50 .0622 123.30 1.59R 2.0307 .4 115 75 -14 .60868 -65 .479C5 17.0 1018 23 .24763- .72875 .74081 PREDICTION OF NTO BY SLUG CORRELATION V-25 LIO TUBF fJL GPM DIFF S TEWS VISC VKLL 1 1.757 .620 ' .465 73.530 I.'40 .529 VELG F A C T O R C O P R Ya 14 . 128 1.0000 . 3 8 3 8 LIO TUBF OL GPM P I FF S TEWS VISC. VfcLL 1 1 .757 1.070 I.HAS 73.530 1.140 .913 N O J 164 4 22. ' ! "loTT- 166 16 7 —lATT 175 17b . - T T T — T 26 3 U 264 5 -265—5" SC. 99 bb.47 136,05 -TV5TT5~ 54.72 160.63 20. fib 4 I .67 64.33 NTU LTU .1202 59.90 ••—T5TA—5O;TO- .2.B53 .4 029 ".5963 .2 120 .1742 •;5i, l F i ' .1023 .16 19 -24:17 " 26 6 26 6 269 95.119 TT2T53" 22. Hi 34. 33 291: 29 1 292 -5"—BTTTTT" 5 1 13.96 5 MR.27 .3056 .-3575— .10*7 . H 3 3 ;'2'5B5-' . 360 9 . 3846 2b.OC I9.rr, " I 2 . 8 C 30.20 '6.20 ' I3'.'90- 7 b. 00 50.50 31.70 25. IB - z r ~ i n r 7 1 , 9 i ! 5 .60 32 - . T 0 - 2 1 . 2 0 IV. 90 VELG FACTOR COR» Y 2,3bB I.COUO .125-0 - j ' i T w n ' t i i r c i ' ! 6 " 3 ' OOOO .3fio3 0 0 0 0 " 9.09 7 14.48I 20 0771 " b.1125 17.735 "2l""."9-96"" 2.219 4.4 35, ' 6 . B U 7 - 206 357 654 , 02 3 ,588 3.9 6 29 7 298 •5 25.99 6 iH.ov 5 3 1.75 r n>3 5 ~ . '54," .2029 -s~<rrro- 49 . H f i 37 .80 , 150 ,508 30 4 30 5 306 Ti 21T5T - 5 31.95 b: 33.59 , I . .4H , ' 279 ' ,1933 TST7T- 6C . 0 0 39.70 -2BT3- 40 1 704 4;, I I 6204 . 00,, . 2 183 .00004 .53o7 nrC0 ' jfr---.«265 •- .00004 . 1 2 12 .0000 .!b09 00-00- .2438 .0000 .336' TOFOTiir—.-4124—- .0000, .1250 .0000 .1399 VOi". r ;2380— .000c .3RS0 .onoi: .4r,v2 .W;..:'g-;-'-36',-- .000,' . '732 •0000A .2097 .COO., r ' 2 3 ' ' .0000 . '530 .0000 .2 '50 LIO TUbh OL G P M DIFF S TEWS VISC VELL 1.1.757 1.500 1.463 7.3.530 1.140 .1.280 VELG F A C T O R C O P . R A Y b 1 3 18.63 . 6 6 . 5 ( 2. 468 1.0000 . '278 62 6 26. 14 . ' ? > u 3 " 57.20' 5 . 728 1. OfcfV •. *6 ' f fT 63 5 36.07 . 1426 3 3 . 80 4.778 1 .TOOL- . 1997 92 3 18.70 . ' 183 64. 0(. 2.476 1 . 0 0 0 0 . '28 1 146 4 24. 58 . 1 i 1 6 56. 3<- 3 . 255 '.oooo . ' 323 147 5 59.37 . 1 6 3 7 46.90 b.2 '4 i . G j t r . .2 ' 3 3 146 5 67.80 .27 lb 28.20 8 . 9 6 1 I.LOOv . 3 3 , 5 lb 1 3 ! V . 34 . 1 1 8 1 6 5 . 0 0 2.1,Hi; 1 , L c v'V .1 rs 8 - " Ib2 5 54. ' 1 .2053 37.40 5 . 7 6 0 1.0000 .2303 133 5 105.29 .3735 20.50 1 ' .207 1 . 0 0 0 0 .39 96 154 b !4 / . n . 5468 1 4 . Oil !b.^28 ! .001 OA .5406 " -• " 156 6 lob.24 . 7 '47 ' 0 . 70 lv.716 i.coc-o .6647 159 5 1 19.70 .4035 19.00 12.741 1.0000 .4476 16K 5 1 6 1 . i'i .5294 14.SO ' t .</V. I .Of . , ! . .-5-633" 16 1 6 191.09. .6233 '2.30 20.339 1 .0000 .0R4' 1 162 4 21 .27 . 1 145 6 7.00 2.264 1.0000 . '213 L io TUBE OL OPM DIFF S TEWS VISC VELL 1 1 . 7 5 7 2.100 1 .465 7 3.531. ' . 140 1.792 MO J OGM NTll LTU VELG FACTOR CORR Ya 69 3 25.82 .1336 57.40 2.748 I.OOOv .1279 60 5 3 S . 2 0 . 1542 49.80 3 . 7 4 7 1.oooo .1*49 6 1 3 44.93 .2027 37.80 4.782 1.OOOw .2032 62 b 65.54 .3.V92 ' 27. 50 6 . 9 7 6 1 .OOo,- . 2 8 4 4 ' 63 5 8 8 . 7 2 .4201 10.20 9.444 1.0000 .3757 64 6 14 1.08 .662 1 1 1 . 60 15.0 1 6 !.00*0 .5820 63 6 1 15.56 • .4984 13.40 !2.3uO 1.00 004 .4613 1 66 5 9 7 . 3 5 .43v2 17.40 10.362 1.0000A .4007 ! 67 5 0 8 . 7 4 .'4056 18.90 9.445 1.0000 .3756 129 6 18 2. 3 3 ,8747 o.K, 24.15 1 1 .CuOC- .92.,' 134 3 18.46 . 1 1 1 7 68.70 2.448 I . U C - C O A . ' I6B 138 3 16.77 .10*56 72.70 2. 222 ' . O O O O .1084 lav i 22. 56 . 1 1.94 «4 . sr. 2. 966 1 .00LO . 1 .ion- 72 20.4396 2 1.42 IP O I 8.026 R.3198 .011826 1.C0O396 PREDICTION OF NTU BY SLUG CORRELATION. - Trro-TU6Tr"T!C-erpp-TirFF---s- T E N S ' v i s e V E L L — 3 1.757 .AU:--2.9M. 23.400 1.36.0 .52C ' N O J or~<— 44 ! 5 .24.78 44 2 5 3 1 . B 3 — 5 98. 33 mv L T T J — T E r r r — F ^ C T O R ' - C O P T O ? — . ' 2 3 6 62.10 2.638 . V i l l i .1404 .2057 37.30 5.5 16 . 9 0 1 ' .2 119 "T3722—20TKtT-T07TO5"—79 tm 7 3 3 W 44 4 UTS 4 7 6 5 U 7 7 5 -nrv—k 6 I6G.C3 .19.97 .5U66 -r'^+5- .1690 .2474 T 3 R B 9 - 14. C O 65. 10 4b.40 31,00 -vrrrtr 19. 160 2. 126 3.722 6.536 12.478 .901 I .901 1 .5509 • 1277 34.97 6 1.43 I ' 7 . 24- . 9 1 1 1 1 . 1 6 7 3 . 9 0 1 1 . 2 3 7 3 . 9 0 1 1 T 3 U 4 - 9 - LIO TURF OL GP1< LUFF S TENS VISC VELL 3-—T.-7S7 I.C7C 2.7b-f 2 . . 4 r t 1 .360 .913 NO -3ST6- 3b b 35 9 "S 24T8T- 5 58.21 5 ICS.79 NTU - 7 0 1 - C 2 O - .2077 .3437 L T U -74T8T- 36.9C 2 2 . 30 VELG -2T6-4-7- 6. 19b 1 1.2b9 FACTOR CO i - rcs -24— I .C524 1.C524 RP Y -.-1254 .2161 .3456 38 1 38 2 39 C "39X- 39 1 39 1 -5 25.85 5 42.4C 5 24.79 -5 24 772 5 3 0 . 4 4 5 36.32 r+SOSH STvSe 2.752 I.CSgTi . 12S1 -37-2- 39 3 39 3 "394- 39 4 •39 5 -S i - i -T l r - 5 66 . 14 5 63.77 5 142.46 5 142.95 6 I9C.66 - 3 V 3 - 39 8 39 9 —3v V " 40 0 UC-<- 40 1 4C2 -Hl-2- 43 I 43 2 6 l9C-.-tro-- 4 IV. C-l: 5 ' 24 .64 -_>—24V46 • 39. r 2 36.87 6 9.9 I - 6 9 . 0 2 1 6 4 . 2 0 •fr—18 3V48 5 23.28 5 37.49 433 434 43 3 -48 5 "S 7 9 . 4 f - 5 147.82 5 179.86 5 29.88 .1621 . 1262 .133 I .1639 .1715 V2<rl4" .2942 .3148 -.-US23- .4249 .4996 -.-fllTB- .1.92 I . >C42 . 1 142" . 1522 . 15VC V28T2 - .2787 .543.8 .598 f .1212 . 17C2 .-21T76" .4522 .5590 .1 194 4 7 . 3C 5V.9C 37.61. 46.80 45.CC 4.513 2.639 2.63 I 3.678 3.666 "3-t.~8f- 2 9 . If 2 4 . U C —TATVr.- ' 1 6 . C L 1 5 . 3 C - 1 4 7 oc- 8 3 . 3 C 7 3 . 6 C " 6 7 . 2 C S C . . 4 C 4 6 . 3 C - 2 7 . - 3 I - 2 7. 5 C ' 4 . H 1 2 . 8 0 " 6 3 . 3 C 4 5 . 1 0 - 2 6 ; - 5 T - I 6 . 9 C 1 3 . 7 C 6 4 . 3 0 -5.44 3- 168 . 129 ; 16-2 ,214 2C.2V2 2C-. 27t 2. (.22 2.623 2.60 3 4. 153 4 . 137 -~9-. 5«9 9.570 I9.6v4 19V528 2.478 3.99 1 ~fl-.-«r_rr 15.732 19.142 3. lac 1.0524 1 .C524 '.-0524 1 .C524 1 .05 24 +.•05 2-4 1 .C624 1.05.4 1.C524 " 1.0524 1.C524 v-.-es-24 - 1.0524 1.0524 1.05 24 1.0524 A I.C5 24 r;-rs"24- - 1 .06244 1 . f524 1.0624 1.f 324 1.C524 T ;C524 - - 1.C524 1.C524 I.C524 .1731 .1252 .125" .1569 . 1566 . IV 69 .292 I .29 1 ! .44 54 .4467 .5765 .-5-760 . ICV3 .1240 ; 124 3 . 1639 .1635 73024" .3.:. 24 .5589 .5570 .121 I . 15V6 V27 3P .4599 .547 I .139 I 466 5 59.82 - T B I b l l b . 2 3 - 46 8 6 18 2.90 .2C63 37.20 6.367 I.C524 .22C6 .5378 14.20 19.465. 1 .C324 .5554 LIO IU8F HL—G-PV~riTF-F"""S TT: N S' VI SC V E L L ' 3 1.757 2 .10I 2.9SC 23.4CC 1.360 ' . 792 M ! J — 40 8 5 40 8 5 • OGM 30.8 I 30.22 TvTTJ . ICS 1 .1225 T T O 73. H.; 62.60 " v r n ; — F A T 3.279 1. 3.216 1. TTJR—nTRfra?— 12 H- .1301 12'Cfl .1280 -4T\7 5" 40 9 5 41C 6 Tb.30 77.54 1 6 V . 9 I .2830 ,31bb .6117 -25-.-9T- 24. 3C 12.50 -"Er.33 3 1 8.25 3 1 18.083 ! " I 2 H : A , 1 2 1 0 A , 1 2 1 C A rz9Tc~ .2943 .6 I89 -TTTT b~ 4l b 3 4 l b 3 I 69.1.5 23.71 24. 3C .6360 .0994 .0837 7-1-76-7- . '493 .4697 - r 2 7 T r r 7 7 . 2 0 9 1 . 7 0 W . W 1 1.12 10 .6 156 .1052 .1072 2.524 1. 2.586 1, 1 2 1 C I 2 1 C - 5 - 416 5 4 1 7 6 •41 7 42 2 3 42 3 5 -42-4- 42 5 42 6 — « r s r T 3 - 47. 57 136.62 +-3-V.-4TT- 22.39 . 3 1.74 —6b;-95- 139.74 174.64 -vrs—3- 49 4 5 49 5 5 -4716—6~ 49 7 6 -24.26- 43.26 65.53 10150.-54- 16b.67 ;-ir6-4_- . 1 C 6 6 . 1 3 6 5 . - 3 C - 7 3 - . 6 4 9 0 .7062 rOBe-S- . 1403 . 2 4 3 4 P O O 44"" . 7 0 2 5 -4-37-tx"- 5 1 .4£ 15.6C -t-firSe- 70. 7C. 55.40 - 2 4 , 9 0 1 1 . hi ' o . P C -4771'fl—'-.-12+p-s—.-+86-'."- 5.06 2 1 14.774 1 -1-47-84-3-- + 2.36 3 1 3.376 1 -77-338 1 14.872 ' 18.586 .1 1 2 I0 1 2 K .1890 .50 96 +g+ta .6 117- 1210 121C +2 ' 0 - 12 'OA 12 10 --mr.Tc- 54.70 3 1.50 l'8 r°TT ' 0 .90 —Z75WT-T 4.616 1 6.974 ,1 11.233 1 17.932 1 rT2-rt~ , 1 2 1 0 • 12 1 0 A ,12 T O A . 1 2 1 0 A , I O c 5 . 1 3 3 4 . 2 6 4 1- . 5 1 2 9 . 6 3 5 5 i+oro— .1739 . 2 5 2 I . 3 9 2 7 - — . 6 1 4 6 T T I 23.T37V~24-.599 19b V.-5T5 ' "9 771 12 ~ ~7C T7T« 3 - - . 9 7 7 715 -HTU BY SLUG CORRELATION FOR C02-RATER AT VARIOUS TEMPERATURES L I O T U B E O L G P « O I F F S T E N S V I S C V E L L 1 ' . 7 5 7 1 .070 1 . 0 7 2 7 5 . 100 1 . 5 0 5 9 ' 3 2 3 9 C IG« " M T U 2 2 . 9 0 T 3 T 2 B - 2 U 1 5 B 2 . 7 3 2 4 2 5 1 1 6 . 5 2 " 2 T 3 — 5 I 5 6 . 3 T " L T U 09 1 5 83.90 T3 _0"~53TKT." V E L G F A C T O R C O R . R Y 2 . 4 3 7 1. " 0 3 6 -UTBT/T-TTT.—•_- .1 I3B . 1 6 6 7 ' . 2 3 6 5 3 2 . 4 0 fl.B0'6 ! . ! 0 ' 3 B . 2 6 9 0 . 3 . 2 1 7 2 3 . 8 0 ' 1 2 . 4 0 2 ' . 1 0 3 8 . 3 5 6 7 . 3 9 7 1 1 9 . 3 0 I 6 . 6 3 7 A I . ICT5B : 4 3 9 9 _ L I O T U B E O L G P M D I F F ' S T E N S V I S C V E L L 1 1.75? 'I.070 2.019 7 1.200 .BOO r ° 7 NO J "247—«r U G M 2 S . 4 6 2 4 8 5 " 4 9 . 1 0 2 4 9 5 9 4 . 6 B -25-0—3 1 3 2 . 5 2 - 2 5 I 5 1 7 8 . 0 ' N T U . 1 3 9 2 - . 2 0 4 3 . 3 5 0 9 ~7<rtrl-ft- . 5 6 4 5 L T U V E L G h A C T O R C O R P . Y r + 5 0 3 5 5 . 1 0 2 . 7 1 2 — . V 0 3 8 3 7 . 6 0 5 . 2 2 6 . 9 0 3 6 . 2 2 5 1 2 1 . 8 0 1 0 . 0 7 7 . 9 . 3 8 . 3 6 9 5 - t T ; - 3 ( f - l a - . - t 0 5 - . 9 0 3 8 A- . U e v u ' 3 . 6 0 I H . 9 4 6 , 9 . ; 3 8 . 6 3 . 5 - n O - T U B 1 = ~ O l . — t > - p M - O T F F — 1 > T E M S - V T S C " V E L L 1 1 . 7 5 7 1 . 0 7 C 3 . 0 8 C 6 6 . 8 0 0 . 5 9 9 . 9 1 3 -tm-3- 2 5 3 3 2 7 . 5 6 2 5 6 5 3 4 . ' 0 - 2 5 7 — s - t e s r T . - "MT_— L'TtI V E I . T — (-A0IOR COPRAYA- . 1 2 6 8 . 2 1 8 5 •"73 8 3 7 2 3 6 5 1 4 6 . 7 5 . 4 9 2 6 2 5 9 5 1 9 6 . 3 6 . 6 6 5 1 -TTI— 4" - 2 4 - . - 8 T — . ' 1 5 3 1 "SOr I 7 2 2 . 5 3 o . 0 2 . 1 7 2 3 4 4 . 5 6 0 . 6 0 2 . 9 3 6 3 5 . 1,- 5 . 7 3 9 2 C . 0 0 ' 0 . P 3 ' 1 5 . 6 0 1 . 5 . 6 2 0 1 1 . 5 0 2 0 . 9 0 0 2 . 6 4 7 3 . 9 3 0 , 7 V 3 7 . 1 8 0 7 , 7 9 3 7 A . 2 7 6 4 , 7 9 3 7 - . 4 5 1 7 - , 7 9 3 7 . 7 9 3 7 , 7 9 3 7 , 7 9 3 7 . 6 I 0 6 . 7 8 9 6 - . 1 7 0 9 " • 2 1 u 4 PREDICTION OF NTU BY SLUG CORRELATION L I O T U B E O L G P « O I F C S T E M S V I S C V E L L 2 1 . 7 5 7 . 6 2 0 3 . 6 9 0 7 3 . 5 3 0 1 . l n l j . 5 2 9 MO J OG" N T U L T U VELG FACTOR CORP.AY 6 0 8 3 19.OC . 1 6 2 1 4 7 . 3 0 2 . 1 1 8 6 0 o u — _ 7 . 2 7 r t - e - l C f — 4 0 . - 2 0 — 2 " . 9 r 3 - . 2 3 0 0 3 3 . 3 0 4 . 7 8 6 . 3 4 9 0 2 2 . 0 0 7 . 4 6 3 i - T 6 " 1 5 — 4 7 T 5 C - — 2 " . - 5 8 •• - 6 1 6 5 3 5 . 2 1 , . 1 9 2 6 3 9 . B l 3 . 7 4 7 6 1 7 6 8 9 . C P . 4 0 6 4 1 8 . 9 0 9 . 4 8 2 - t r l - 8 5 1 4 9 . 4 9 . 6 2 3 9 1 2 . 3 0 1 5 . 9 1 - ? / - 6 1 C 5 4 U . 9 B 6 1 1 5 7 0 . H - t r t t > — 4 — - 2 4 - i - 2 5 — L I O TUBE OL OPM D I F F S T E N S v i se 2—1 . - 7 5 7 -I . " 0 - 7 0 _ 7 ' 6 9 C 7 3 . 5 3 0 1 . 1 4 0 .7076 . 1664 - 7 C 7 H .-1913 . 7070 . 25 1 2 . 7078 .3362 .-•70-7H- —.16 - 1 1 .7078 .2 182 .707B .40C3 .7078 - . 6 0 4 6 V E L L . 9 1 3 . 2 3 6 6 . 1 6 0 0 .-7530A V I 8 B 2 - . 7 5 3 0 . 2 5 3 6 , 1770 G FACTOR CORR Y - 3 3 8 . - 7 5 3 0 " .1699 178 .7530 '062 .7530 P52 682 539 .7530 2-i-t —.-T3W*—.-2T23- 452 .7530A .3526 .7630 .6870 7-75-30—.-9407- .753CA .1715 .7530 .2029 .7530 .75.30 .7530 77530- .7530 7 3 3 8 2 . 4 5 1 7 . 5 8 7 9 . 8 3 7 9 . 2 2 2 1 L I O T U B . O L UP" n iTF S ^ f E W . V I S C T t t T L " — 2 1 . 7 5 7 2 . I O C 3 . 6 9 C 7 3 . 5 3 0 1 . 1 4 0 1 . 7 0 2 ~ VET GO—F.-A C T 0 R - C 0 R K A Y. PREDICTION OF NTU BX SLUG CORRELATION LID TUBE UL GPM U1PF—S TENS VIM. VTTtt 4 1.757 .620 .285 47.9CC 13.900 .529 N C) -J CJGM— 69 3 5 19.37 6V 4 5 28.CC " N T T r T T U - -757-5—s—Tr.-srr- 69 8 5 65 . BC 69 9 5 90.89 1CV—5 141.88 .0717 107.00 .0810 94. 70. " V E L T O — F A C ' I U R — c m n r T — 2.062 1.587 1 .0656 2.O60 1.587 1 .0786 Tress— T r ; 2 t — • v r v r r — r r s m — r o w r .1366 56.20 7.C03 1.567! .1356 .1695 45 .30 9 .673 1.5871 .1735 T2427—3"1 .60 15. 1C0T ! .687 I—T2TCIT" 701 5 180.49 .3C43 25.20 19.210 1.5871 .3086 L i n TUBfc UL OPM Illl-F S I LNS VISC VETZ 4 1.757 2.100 .285 47.900 13.900 1.792 NO J 98 I 5 9b2 5 — 5 22.6 I 984 5 63.74 685 5 88.92 -6B-5—5 136.79 OGM NT 0 LTD VETTO .27. 13 .0625 122.7C 2.867 2.2284 40.84 .0866 68.60 4.347 2.2284 FBrTOR—COP .RAY .05 ! 9 .0762 .0601 127.7 0" 2.406 - 2 T 2 Z 8 * r - 6.783 2.2284 " • C U H T - 63.60 " .1167 46.9C 9.463 2.2284 .1612 TV9F"T4".Tr5-2—-2T22Tr4 .'2rnrcr 6b7 5 175.68 . 3 1 9 9 . 24.CO 18.697 2.2284 .3 !46 LIO TubE OL GPM DIFF S TENS VISC VELL 4 1 .757 1.070 .285 47.9CC- 13.900 .913 NO J 6 7 2 - 6 - 7 - S - OGM 2! .80 62.69 67 4 67 5 676 66 2 66 3 3 - 3 - 5 66.84 5 127.70 6 1 6 4 . 3 4 5 19.87 6 27.69 NTU LTU V E L G F A C T O R C O R R Y .0490 156.60 — +(-38— 60v30- .1694 45.30 .260 1 ;3620 29.51 2 . 3 2 0 1 .0548 -6-.fr7-3-1-.V54o- 9-. 2 4 2 I . 9 3 4 0 I 3 . 5 9 I ' . 9 5 4 8 2 ! . 7i. ' 7 . 4 9 ' T . 9 54 8 ' .0565 .--.-V-F6-5- . ! 5 ! H . .2 ' '7 .2653 .0442 173.40 .0562 136.50 2 . 1 1 5 1 . 9 5 4 8 A . 0 5 3 7 2 : 9 4 7 1 . 9 3 4 8 . 0 6 6 2 6 6 " i r — ' 5 n v 7 t r — V C P t f i - - 94"; C O 4 V 4 4 3 - T . < ; 5 4 8 - . 0 8 5 8 66 1 7 . 8 16! ' 6 .065096 7 . 2 ' 8 5253 .023 178•1 .00966! LIO TUBE OL GPM DIFF S TENS VISC VELL 3 1.757 .620 .142 49.300 26.500 .529 N O J 6 4 7 5 O G " 26.86 ~64T3 5 3V.82 65 ! 5 69.23 65 2 5 90.36 65 3 N T U L T U V E L G F A C T O R C O R R Y A .0578 132.00 2.85b 1.9398 .0604 6 !29.02 3 170.42 . 0 / 3 9 ! I i . HC" . ' 0 9 6 6 9 . 9 0 . ' 3 6 8 6 6 . 1 0 . 1 8 3 9 4 . 2 3 8 1.9396 TOToTT 7.368 1 .9398 .1127 9.619 1.9398 .1367 ' 3 . 732 1 . 9 3 W 4 ! .70 34.50 18.138 1 . 9 3 9 6 A 1864 2375 6 5 4 . 2 2 2 6 Ll fl TUBE UL GPM U1FF S IhNS VISC VTOOt 5 1.757 1.C7C .142 49.300 26.500 .913 —mr-J OS"— 63 2 5 25.97 63 3 5 37.60 -NTU tr .0437 175.60 .0564 ' 36 .10 -VtrtG-—F-At-TfrR C O R R A Y 2 . 7 6 4 2 . 4 4 9 0 . 0 4 7 2 4 . 0 C 2 2 . 4 4 9 0 A . 0 6 0 8 -B3T 5 62.T6 658 5 67.21 63 9 5 128.34 -64-0- 3—1-6tT<Ws- .0839 . 1167 . 1749 Ttt fe 7- V I.5C 6.660 2.4-49C .09C2 65.PC 9.28 I 2 .4490A .1 188 43.90 13.639 2.4490 .1669 - - 3 ^ m r - i T T + 3 t r - 2 T » r t - 0 t ! — r 2 C 3 - c - L I O T U B E O L G P M D I F F S T E N S V I S C V E L L 5 1.T5T 2. I C C r i 4 2 4 9 . 5 0 0 2 6 . 9 6 0 . — 1 . 7 9 2 NO J -WO 5- 66 1 5 66 2 5 • r o  ot" 10.95 2 6 . 0 5 3 8 . 8 0 -2C-.-rrr-T T 6 6 6 5 5 9 . 0 4 6 6 7 3 6 1.05 6 6 8 - - 3 — 1 2 2 V 6 " 1 " 6 6 9 5 ! 5 4 . B 2 MTU LTU VFLG FACTOR CORR Y T C 2 9 T - 7 6 - 3 T 5 T 1 2TirtT--2T8-t2 3 — TC2 oTT .0365 210.40 .0508 1 5 ! . IC rC2R7 266."Btr 2.773 2.8125 4. 136 2.8 123 2. I f3~27 8T25- • C739 1C3.90 6.263 2.8123 .1062 72.3C 8.626 2.8123 .1698 43.-20—1-3-.-C49 2.PI25 .2250 34.10 16.477 2.8125 .0367 .0547 "70288" .0829 .1 138 .1720 .2171 V-29 PREDICTION OF NTU BY SLUG CORRELATION L H ' lUBfc nC-X^"IJTFF~'-S'-TFf;-'VISC 6 1 .228 .293 1.465 73.530 1.140 .512 NO "3 OG" u i u - 7o4 • 3 1 1.69 .16 'b IU 3 b 19.03 .2312 70 6 b 3 C . o « .3626 7b 7 b 62. 80 .59 19 7o!i "" 6" Tt6-."56 1 ~ C 7 i . 769 6 IU6.39 1 .6690 79 r, 7 Ibb.C! 2.2241 "LTU V E L G K AC. 10R" CORRAT" ,20 b 7 -33.30— i r ; - i trY- 21.10 6.743 12.9f 13.66b 7;-sr-2S-«b-«r 4.60 3 ' . 898 -.-623-2 .6232 .3557 .6232 .6040 • 6232A ,0f.r6 .6232 ' . 2 5 5 3 LIO TU6E OL GPP DIFF S TENS VISC VFLL 6 1.228 .520 1.465 73.530 1.140 .908* N O J 77 1 4 OG" 1 1.64 NTU .1744 LTU 44 . 0 0 VELn F A C T O R C . O ' R A Y 2.515 . 6 6 3 3 .1955 — r r z ~ —ti ttT*n~ -3b .4C -4-r?"Hr- 77 3 5 32.64 .3464 2 2 . ro 7 . H 3 • 68 33A .3762 77 5 5 63.62 .5975 12. 8C 13.862 .6633 .6414 - 7 7 - 6 " 5-TU6.-93 -.9962 7.60 23. 30 1 . 6u35 1.0 123 77 7 6 144.13 1 .36/7 5.6C 3 1.41 5 ..66 33 1 .3307 77 6 7 164.C4 I .5506 4.90 4C.-10C ,6c 33 1 .6724 LIO TUbE OL GPM DIFF S TENS V I SC VELL N O J O G V 79 6 3 10 .O2 — 7 V 7 5 18.7C- 796 3 29.67 79 9 b 59.23 "8 f t C 5 " 63.6 I 1 .0209 BC I 6 I 09 . CO ! .3569 1.140 1.782 NTU LTU VELG FACTOR COR R A Y A .1405 54 . 6 0 2.30C .7210 . ' 644 - ; -rra7—4T . -sr—u . -rr4 - - - ;7-2tt—rzvir- .2722 28.20 6.465 .7210 A .3734 .6476 I ',80 12.907 .7210 .7C31 7 . 5 C 16.218 .72 10 .9749 5.6C 2 3 . 7 5 1 .7210 1.258C —trn-Tot i r - r t tsw-rIFF - s-TTf-s -viSC—VFLT— 7 2.5C4 1. 1.31 1.465 75.530 ' . ' 4 0 .474 - N O J • 736 5 VELG FACTOR COPR Y 3. '79 ' . 5962 .1.797 "OGM NTU LTU 6C.66 .0628 122.2:: 739 5 115.71 .1368 66.10 6.064 1.5962 .1193 •70 C—5'"T8-SV34-- ; 166B--'-'45.5C - 9 . 6 0 8 - '-.5962 ;1678 7o3 5 93. 70 .0996 77.10 4.910 1.5962 . 1034 764 5 147.00 .1563 49.10 7.705 1 . 5 9 6 2 4 . 1 4 ' 7 "765 5 182.62' . 1766 43.40 9.570. 1.5962 . 1673 "x 1«! 1 ubf cl -vprirrFF• - s " T E N X \ V I s r v e i l " " 7 2.5C4 2.C10 1.465 73.630 1.140 .844 NO J CTfW 'NTO LTD VEXr." FACTOR C"CJB"R"Y~ 730 5 35.32 .0796 96.40 2.794 1.4573 .C88b 735 3 39.89 .C726 IC5.PC 2.C90 1 . 4 5 7 3 .0762 ~lS7, 5 69 . 0 6 767 . 5 I 16,. 72 75 6 5 146.25 -ret " 7 5 - 9 - ."r6~ . CVT! E37~C 376b~5—T.-h~5~73 nT/ira" .1 .329 67.70 6. 116 1 . 4 5 7 3 .1463 _. 1614 47.50 7.664 1 .4573 . 1760 . r 9 2 T " - 3 V Y 9 T — 9V435" TV4573—."2076" LIO TUBE OL GP1-' UIFF S TENS VISC 7 Z.Seu 3.931 .465 13.630 VELL I . 6 6 C * 1 N O J rrtra—3- OGM 36.64 74 7 74 6 5 60.54 5 ' 09 .16 3 ! l 2 . . t « NTU LTU VELG .0674 1 13.90 FACTOR C.ORR.AY 2.C25 1.3C-T8 T1T725- ,0867 86. 50 3.467 1.38 16 . M i ; I .1266 59.70 5.720 1.3818 .1674 . 1339—STTSt 3.669 ' . 3 6 l B .1718 .1537 49.90 7.168 1.38 16A .2046 .1669 4 C . 6 C P.75 1 1.38 18 .2453 73 3 73 4 5 l 3 o . 7 9 5 167.00 58 19.676 1 19.205037 19.308 !7.1956 . 4 4 2 8 1 . .846422 

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