UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Tube material and augmented surface effects in heat exchanger scaling Sheikholeslami, Roya 1984

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1984_A7 S54.pdf [ 8.74MB ]
Metadata
JSON: 831-1.0058727.json
JSON-LD: 831-1.0058727-ld.json
RDF/XML (Pretty): 831-1.0058727-rdf.xml
RDF/JSON: 831-1.0058727-rdf.json
Turtle: 831-1.0058727-turtle.txt
N-Triples: 831-1.0058727-rdf-ntriples.txt
Original Record: 831-1.0058727-source.json
Full Text
831-1.0058727-fulltext.txt
Citation
831-1.0058727.ris

Full Text

TUBE MATERIAL AND AUGMENTED SURFACE EFFECTS IN HEAT EXCHANGER SCALING By ROYA SHEIKHOLESLAMI B.Sc, The University of Kansas, 1980 A THESIS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Chemical Engineering) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1984 CORoya Sheikholeslami, 1984 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 o f the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t 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 t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f 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 o f my department o r by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying o r 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 g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of / ?Jp^, P„£ /illi tif.fiAi ft The U n i v e r s i t y o f B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 1 Date APA : M A<\%k - i i -ABSTRACT The performance o f stainless s t e e l , copper and mild steel p l a i n heat exchanger tubes and an externally-finned mild steel tube was studied under calcium carbonate scaling conditions at constant heat flu x . A r t i f i c i a l hard waters made up with sodium bicarbonate and calcium s a l t s to a l k a l i n i t i e s up to 350 mg CaCOyi and calcium hardness to 650 mg CaCOyi were recirculated through a steam heated annular test section for periods of 70 hours. The e f f e c t of velo c i t y on the rate o f heat flow, the overall heat transfer c o e f f i c i e n t , the fouling resistance and the fouling rate has been determined. Fouling resistance increased with time in a l i n e a r manner in the majority of runs although f a l l i n g rate and asymptotic behaviour were also observed. I n i t i a l scaling rates were compared with the predictions of Hasson's ionic d i f f u s i o n model. Generally, scaling decreased in extent as the tube material was changed from mild steel to copper to stainless s t e e l , although there were some operating conditions where thi s trend was not followed. No firm conclusion could be drawn concerning i n i t i a l fouling rates f o r these experiments which were done primarily at low levels of water a l k a l i n i t y . The longitudinally finned mild steel tube, having f i n and total surface e f f i c i e n c i e s of 33A and 53A, respectively, was examined under the same operating conditions as for the p l a i n mild steel tube. In addition to higher values of heat flow rate, the former had higher values of both - iii" -the clean and the d i r t y overall heat transfer c o e f f i c i e n t s along with the lower values of fouling resistance, a l l based on the nominal (bare-tube) outside area. The deposits were thicker on the prime surface. The fouling process appeared to be more gradual on the finned tube than on the plain tube. However, the model predictions suggested a s l i g h t l y higher rate f o r the finned tube at the same velocity. For a l l tubes, the clean and the d i r t y overall heat transfer c o e f f i c i e n t s and the predicted fouling rates increased with velocity. Generally, the fouling resistances decreased with increasing velocity except f o r the copper tube at high a l k a l i n i t y . No generalization could be made regarding the relationship between the experimental values of fouling rate and the velocity for either of non-corroding plain tubes. However, for corroding tubes, as the velocity increased, the fouling rate decreased. The finned tube appears to be the most suitable choice in the presence of hard water scaling. In the velocity region tested, the model can be safely applied to predict the scaling rate of the copper and both mild steel tubes at a l k a l i n i t i e s of about 350 since i t over-predicted the experimental values; however i t does not predict the e f f e c t of v e l o c i t y . - iv -TABLE OF CONTENTS Page Abstract i i L i s t of Tables v i i L i s t of Figures v i i i Acknowledgements x i i 1. INTRODUCTION 1 2. THEORY 5 2.1 Types of Fouling 5 2.2 Fouling Behaviour 6 2.3 Prec i p i t a t i o n Fouling 8 2.4 Calcium Carbonate Precipitation 11 2.5 Models Predicting the Rate of CaC03 Precipitation .... 17 2.6 Hasson's Ionic Diffusion Model 23 2.7 Factors Effecting P r e c i p i t a t i o n Fouling 30 2.7.1 Velocity 30 2.7.2 Heating Surface 34 2.7.3 Temperature 35 2.7.4 Water Chemistry 37 2.8 Heat Transfer from Plain Surfaces 43 2.9 Heat Transfer from Extended Surfaces 48 2.10 Comparison Between an Enhanced and a Plain Heat Transfer Surface 55 3. EXPERIMENTAL APPARATUS 59 3.1 Water Flow Loop 59 3.2 Supply Tank 61 3.3 Steam System 61 3.4 Tube Material and Geometry . 63 3.5 Temperature Measurements 67 - v -Page 4. EXPERIMENTAL PROCEDURES 70 4.1 General Approach 70 4.2 Solution Preparation 71 4.3 pH Measurements 72 4.4 A l k a l i n i t y Measurements 72 4.5 Hardness Measurements 73 4.6 Determination of Total Dissolved Solids 74 4.7 Procedure f o r a Scaling Run 76 4.8 Cleaning 80 5. RESULTS AND DISCUSSION 82 5.1 General Outlook 82 5.1.1 Low Concentration Runs . 82 5.1.2 High Concentration Runs 85 5.2 E f f e c t of Reynolds Number on Overall Heat Transfer Coefficient 96 5.2.1 Copper and Stainless Steel Tubes 96 5.2.2 Copper and Plain Mild Steel Tubes 100 5.2.3 Plain and Finned Mild Steel Tubes 104 5.3 Fouling Resistance With Respect to the Time 107 5.4 Effe c t of Reynolds Number on Fouling Resistance 120 5.4.1 Copper and Stainless Steel Tubes 120 5.4.2 Copper and Plain Mild Steel Tubes 122 5.4.3 Plain and Finned Mild Steel Tubes 124 5.5 Determination of the Fouling Rate 126 5.5.1 Measured Fouling Rate 126 5.5.2 Predicted Fouling Rate 126 - vi -Page 5.6 E f f e c t of Reynolds Number on the Measured Fouling Rate. . 128 5.6.1 Copper and Stainless Steel Tubes 128 5.6.2 Copper and Plain Mild Steel Tubes 128 5.6.3 Plain and Finned Mild Steel Tubes 132 5.7 Effec t of Reynolds Number on the Predicted Fouling Rates 134 5.8 Comparison Between the Predicted and Measured Fouling Rates 140 6. CONCLUSION 145 7. NOMENCLATURE 149 8. REFERENCES 156 APPENDIX I. CALIBRATION OF THERMOCOUPLES AND ROTAMETERS .... 165 APPENDIX II. SAMPLE CALCULATIONS 169 11 -1 Determination of Heat Flow Rate 169 11.2 Determination of Heat Transfer Area 170 11.3 Determination of Logarithmic Mean Temperature Difference 170 11.4 Determination of Overall Heat Transfer Coe f f i c i e n t 171 11.5 Determination of the Fouling Resistance. . . 171 11.6 Determination of the Wall Temperature. . . . 174 11.7 Determination of the Equivalent Diameter . . 174 11.8 Determination of the Reynolds Number .... 176 11.9 Determination of the Water Quality Parameters 177 11.10 Numerical Example Using Run 26 178 11.11 Numerical Determination of Fin E f f i c i e n c y and Deposit Thickness 182 APPENDIX III. COMPUTER PROGRAMS 184 APPENDIX IV. FOULING CURVES 193 - v i i -LIST OF TABLES Table Page 2-1 Some Fouling Rate Models for Precipitation Fouling 18 2- 2 Ef f e c t of Temperature and Velocity on Fouling Factor. ... 49 3- 1 Summary of Properties of Tubes 66 5-1 Summary of Results f o r Runs at Low Concentration of Chemicals 86 5-2 Summary of Results for Runs at High Concentration of Chemicals 91 5-3 Summary of Results for Stainless Steel Tube 98 5-4 Summary of Results for the Copper Tube at Low Concentration of Chemicals 99 5-5 Summary of Results for the Copper Tube at High Concentration of Chemicals 102 5-6 Summary of Results for the Plain Mild Steel Tube 103 5-7 Summary of Results f o r the Finned Mild Steel Tube 105 5-8 Summary of Model Calculations 127 5-9 Comparison of Measured Fouling Rates on Copper and Stainless Steel 129 5-10 Comparison of Predicted Fouling Rates on Copper and Stainless Steel 136 5-11 Comparison of Predicted and Measured Fouling Rates on Copper 141 5-12 Comparison of Predicted and Measured Fouling Rates on Stainless Steel 141 5-13 Comparison of Predicted and Measured Fouling Rates for High Concentration Runs 142 APPENDIX I 1-1 Calibration Table for Thermocouples 165 1-2 Constants Corresponding to the Calibration Equation f o r Thermocouples 166 - v i i i -LIST OF FIGURES Figure Page 2-1 Characteristic Fouling Curves 9 2-2 Equilibrium Distribution Fractions of Total Carbon at Various pH Levels 16 2-3 S o l u b i l i t i e s of Hydroxides and Calcium Carbonate With Respect to pH 38 2- 4 Sketch and Nomenclature of a Rectangular Fin 52 3- 1 Flow Diagram of Apparatus 60 3-2 Photograph of Apparatus from the Back 62 3-3 Sketch of a Twelve Longitudinally Finned Tube 64 3-4 Horizontal (a) and Verti c a l (b) Cross Sections of a Finned Tube 65 3-5 C i r c u i t Diagram f o r Datalogger Connection 68 3-6 Photograph of Apparatus from the Front 69 5-1 Run 5 Typical Output 84 5-2 Run 16 Typical Output 88 5-3 Run 24 Typical Output 90 5-4 Photograph of Disassembled Fouled Copper Tube 93 5-5 Photograph of Disassembled Fouled Plain Mild Steel Tube. . 94 5-6 Photograph of Disassembled Fouled Finned Mild Steel Tube . 95 5-7 E f f e c t of Reynolds Number on Clean and Dirty Overall Heat Transfer Coefficients of Copper and Stainless Steel Tubes 97 5-8 Eff e c t of Reynolds Number on Clean and Dirty Overall Heat Transfer Coefficients of Copper and Plain Mild Steel Tubes 101 - ix -Figure Page 5-9 Effe c t of Reynolds Number on Clean and Dirty Overall Heat Transfer Coefficients of Plain and Finned Mild Steel Tubes 106 5-10 Run 2 Fouling Resistance Versus Time 109 5-11 Run 4A Fouling Resistance Versus Time 110 5-12 Run 20 Fouling Resistance Versus Time I l l 5-13 Run 26 Fouling Resistance Versus Time 112 5-14 Run 36 Fouling Resistance Versus Time 113 5-15 Run 1 Fouling Resistance Versus Time 114, 5-16 Run 6 Fouling Resistance Versus Time 115 5-17 Run 23 Fouling Resistance Versus Time 116 5-18 Run 27 Fouling Resistance Versus Time 117 5-19 Run 31 Fouling Resistance Versus Time 118 5-20 Run 38 Fouling Resistance Versus Time 119 5-21 Effe c t of Reynolds Number on Fouling Resistance for Copper and Stainless Steel Tubes 121 5-22 Ef f e c t of Reynolds Number on Fouling Resistance for Copper and Plain Mild Steel Tubes 123 5-23 Effe c t of Both Velocity and Reynolds Number on Fouling Resistance for Plain and Finned Mild Steel Tubes 125 5-24 Effe c t of Reynolds Number on Measured Fouling Rate for Copper and Plain, Mild Steel Tubes 131 5-25 Ef f e c t of Both Velocity and Reynolds Number on Measured Fouling Rate for Plain and Finned Mild Steel Tubes 133 5-26 Effe c t of Reynolds Number on Predicted Fouling Rate for Copper and Stainless Steel Tubes 135 - X -Figure Page 5-27 Ef f e c t of Reynolds Number on Predicted Fouling Rate for Copper and Plain Mild Steel Tubes 138 5-28 Effe c t of Both Velocity and Reynolds Number on Predicted Fouling Rate for Plain and Finned Mild Steel Tubes 139 5-29 Comparison of Measured Scaling Rate With Rate Predicted by the Ionic Diffusion Model 144 APPENDIX I 1-1 Calibration Curve for Large Rotameter 167 1-2 Calibration Curve for Small Rotameter 168 APPENDIX III I I I - l Program to Evaluate Overall Heat Transfer Coefficients and Fouling Resistances 185 111-2 Program to Linearly F i t Fouling Resistances 186 II1-3 Program to Asymptotically F i t Fouling Resistances 187 II1-4 Program to F i t Fouling Resistances to a Polynomial Function 188 111-5 Program to Plot the Fouling Resistance Data and the Best F i t 189 III - 6 Program to Determine the Rates Predicted by the Hasson's Ionic Diffusion Model 191 APPENDIX IV I V-1 Run 1A Fouling Resistance Versus Time 193 IV- 2 Run 2A Fouling Resistance Versus Time 194 IV-3 Run 3A Fouling Resistance Versus Time 195 IV-4 Run 3 Fouling Resistance Versus Time 196 - xi -Figure Page APPENDIX IV IV-5 Run 5A Fouling Resistance Versus Time 197 IV-6 Run 5 Fouling Resistance Versus Time 198 IV-7 Run 6A Fouling Resistance Versus Time 199 IV-8 Run 21 Fouling Resistance Versus Time 200 IV-9 Run 22 Fouling Resistance Versus Time 201 IV-10 Run 24 Fouling Resistance Versus Time 202 IV-l 1 Run 25 Fouling Resistance Versus Time 203 IV-l2 Run 28 Fouling Resistance Versus Time 204 IV-l3 Run 29 Fouling Resistance Versus Time 205 IV-l4 Run 30 Fouling Resistance Versus Time 206 IV-l5 Run 32 Fouling Resistance Versus Time 207 IV-l6 Run 33 Fouling Resistance Versus Time 208 IV-l7 Run 37 Fouling Resistance Versus Time 209 x n ACKNOWLEDGEMENTS I would l i k e to thank Dr. A.P. Watkinson f o r his patience and conscientious supervision during the course of t h i s study. I am also very grateful to the members of my family f o r t h e i r unrelenting support. My special thanks go to Dr. 8.D. Bowen f o r bis valuable technical advice i n computer graphic p l o t t i n g of data. My thanks also go to the personnel o f the workshop, electronic shop and stores, and especially to Mr. H. Lam f o r his assistance in the acquisition of parts and chemicals. 1 . INTRODUCTION During heat transfer operation with most li q u i d s and some gases, an undesirable f i l m gradually builds up at phase interfaces. The accumulation of t h i s s o l i d material can occur both on f l u i d - s o l i d and f l u i d - l i q u i d interfaces. However, t h i s thesis w i l l only deal with the f l u i d - s o l i d interfaces., In cooling systems, the deposition process can be categorized as either scaling or fouling. Scaling refers to the c r y s t a l l i z a t i o n and prec i p i t a t i o n of dissolved s a l t s on the heat exchanger surfaces. Fouling i s a more general term, and i s used here to include deposition of scale or non-scale forming substances. Every s a l t has a s o l u b i l i t y l i m i t at a given temperature. If this l i m i t i s exceeded, p r e c i p i t a t i o n w i l l occur given a favourable s i t e . Most salts have s o l u b i l i t y curves f o r which s o l u b i l i t y increases as temperature r i s e s . However, some sal t s show "inverse" s o l u b i l i t y c h a r a c t e r i s t i c s . For these s a l t s , s o l u b i l i t y decreases with increasing temperature over some range. If water containing such a scale-forming s a l t enters a heat exchanger and i s subsequently heated, frequently the s o l u b i l i t y l i m i t w i l l be exceeded and deposition of the scaling material w i l l take place on the hot heat exchanger surface. In other words, p r e c i p i t a t i o n fouling i s primarily due to presence of supersaturated s a l t s under the process condition. - 2 -The thermal conductivity of the s o l i d deposit residing on the heat exchanger surface i s usually much less than the metal wall. Therefore, t h i s scaling process would increase the total thermal resistance, decrease the overall heat transfer c o e f f i c i e n t , and hence the performance of the heat exchanger w i l l deteriorate. The thermal resistance of the accumulated scale i s c a l l e d the fouling factor or fouling resistance ( R f). Fouling factors f o r tubular heat exchangers can be found i n the Tubular Exchanger Manufacturers Association (TEMA) standards (1). Since fouling resistance increases with time, a period of one year i s usually chosen as a basis for reporting these numerical values. Even though the scaling process i s an unsteady state operation, the fouling factor i s added indiscriminately to the steady state heat transfer resistances to calculate the total resistance of the unit. The following formula i s the design equation for a fouled p l a i n heat exchanger surface. q = (R. + R + R. 1 + R f + R f ) M T m ho w h i f i fo At a given q and A T M additional surface area i s added to compensate for the increased thermal resistance due to fouling. Fouling i s a costly phenomenon i f a l l operating, c a p i t a l , maintenance and production expenses are considered. Due to the insulating e f f e c t of the deposits, more fuel energy may be needed to supply the required - 3 -heat transfer rate. In addition, increased pumping costs due to the reduced cross-sectional area or roughness would increase the operating expenses. There i s also a r i s e i n capital costs i n case of additional heat exchange surface provided in anticipation of fouling. Manual or even chemical cleaning of the equipment results in high maintenance costs. Furthermore, there are production losses during the plant downtime. Despite the d i f f i c u l t y i n obtaining the accurate measurements regarding fouling expenses, Thackery (2) has suggested, in his recent study at AERE Harwell, England, that the fouling cost i s about $0.73 - $1.20 b i l l i o n per year in the United Kingdom. He has estimated that about 41% of th i s amount i s due to the increased operating cost as the result of energy losses. About 21% of the fouling cost i s due to increased capital expenses. About 17% and 21% of the fouling expenses are attributed to maintenance costs and production losses, respectively. Since p r e c i p i t a t i o n fouling i s a major problem in in d u s t r i a l systems, the a b i l i t y to predict the rate and extent of thermal scaling processes can be of a great help in evaluation of the performance of a heat exchanger. In cooling water systems, CaC03 i s one of the major scale-forming s a l t s . The deposition rate of CaC03 based on the radial d i f f u s i o n of C a + + and CO3 ions from the bulk of the f l u i d toward the hot heat exchange interface has been predicted by Hasson et a l . (3). In t h i s thesis, one objective i s to compare experimental scaling rates of CaC.03 on d i f f e r e n t tubes with the predictions of the ionic d i f f u s i o n model of Hasson. To see - 4 -i f the data f o r p l a i n surfaces could be used to predict what would happen on finned surfaces, an attempt i s also made to study the e f f e c t of extended surfaces on both the scaling rate and the scaling resistance. In addition, the e f f e c t of f l u i d velocity on the fouling process i s examined. - 5 -2. THEORY 2.1 Types of Fo u l i n g F o u l i n g has been c l a s s i f i e d i n t o s i x d i f f e r e n t c a t e g o r i e s by Epstein (4). This c l a s s i f i c a t i o n has been c a r r i e d out according to the "immediate cause of the f o u l i n g " . 1. S c a l i n g or P r e c i p i t a t i o n F o u l i n g : the p r e c i p i t a t i o n of inverse s o l u b i l i t y s a l t s which are supersaturated under the process c o n d i t i o n . 2. P a r t i c u l a t e F o u l i n g : the d e p o s i t i o n of suspended s o l i d s present i n a f l u i d onto a heat exchange i n t e r f a c e . This process could be g r a v i t y c o n t r o l l e d and c a l l e d "Sedimentation F o u l i n g " i n case of a ho r i z o n t a l heat t r a n s f e r s u r f a c e . 3. Chemical Reaction F o u l i n g : s o l i d m a t e r i a l s are formed as a r e s u l t of chemical r e a c t i o n s which occur at the heat t r a n s f e r s u r f a c e . The surface material u s u a l l y acts as a c a t a l y s t r a t h e r than as a reactant. This type of f o u l i n g i s often encountered i n petroleum r e f i n e r i e s . 4. Corrosion F o u l i n g : deposits are made of the c o r r o s i o n products r e s u l t i n g from chemical r e a c t i o n of the heat t r a n s f e r surface and the process f l u i d . The fo u l e d l a y e r may a s s i s t the de p o s i t i o n of other f o u l i n g m a t e r i a l . - 6 -5. Biofouling: the accumulation of biological organisms and t h e i r generated slimes onto a heat transfer surface. 6. Freezing Fouling: deposits are formed due to the s o l i d i f i c a t i o n of a pure l i q u i d or components of a l i q u i d solution as a result of sub-cooled heat transfer surface. The f i r s t f i v e types of fouling may be synergistic. In the case of categories 1-5, the fouling process i s enhanced with increasing the temperature. However, freezing fouling can only be accomplished by a temperature drop in the process f l u i d . 2.2 Fouling Behaviour Fouling proceeds by a sequence of six fundamental mechanisms: 1 . I n i t i a t i o n which can be referred to as nucleation, induction, incubation or surface conditioning depending upon the type of fouling involved. This step may produce a delay period before thermal ef f e c t s are manifest. 2. Transport of the foulant from the bulk of process f l u i d toward the heat transfer surface. 3. Adsorption, attachment or adhesion of the fouling material to the surface. - 7 -4. Accumulation of the deposits at the heat transfer interface. 5. Detachment, re-entrainment, scouring, erosion or sloughing-off of the deposits from the surface back into the bulk f l u i d . 6. Aging such as crystal dehydration or chemical degradation of the deposits. The fouling behaviour i s usually represented by the fouling resistance (R^) which i s a function of time. The most common type of fouling curves follow l i n e a r , asymptotic or f a l l i n g rate behaviour. The net rate of fouling should be defined f i r s t i n order to understand any kind of fouling behaviour. Since fouling occurs due to two physico-chemical processes c a l l e d accumulation and re-entrainment of the deposits, the net fouling rate (m) can be specified by the following equation (5, 6). £ = ft = m, - mr ( 2 - 1 ) where rh^ and mr are the gross rates of deposition and removal of the foul ant, respectively. The l i n e a r curve exhibits the fouling behaviour in which there i s no re-entrainment process or the rate of deposition exceeds the rate of removal. In case of asymptotic fouling, the fouling resistance increases up to a point at which the net fouling rate equals zero due to an increase in the removal rate or a decrease in the deposition rate. Asymptotic - 8 -behaviour might result i n i n d e f i n i t e operation of the unit with no need for cleaning. The t h i r d mode of behaviour ( f a l l i n g rate) i s a t r a n s i t i o n between the asymptotic and l i n e a r modes. The three d i f f e r e n t types of fouling curves are shown in Figure 2-1. 2.3 Prec i p i t a t i o n Fouling As was mentioned e a r l i e r , p r e c i p i t a t i o n fouling occurs due to supersaturation of sparingly soluble s a l t s under the process condition. Supersaturation can be achieved as the result of one of the following processes: 1. Evaporation of a solution beyond the s o l u b i l i t y l i m i t of a dissolved s a l t . 2. Mixing of two d i f f e r e n t streams can cause supersaturation as in the case of phosphoric acid preparation. 41.5 - 44.5% phosphoric acid saturated with CaSO^ i s produced by the addition of phosphate rock to the s u l f u r i c acid. The solution i s concentrated in the evaporators, operated at 70°C, to get 70 - 74% H 3P0 4 > Since the s o l u b i l i t y of CaSO^ changes at d i f f e r e n t acid concentrations (decreases in t h i s case), bulk p r e c i p i t a t i o n of the s a l t takes place. Figure 2 - 1 . CHARACTERISTIC FOULING CURVES - 1 0 -3. Cooling down or heating up normal or inverse solubility salts, respectively. Supersaturation can occur during the heat transfer operation with respect to the heat transfer surface, the bulk of the process fluid or both. Following the creation of supersaturation, the ultimate accumulation of the deposits occurs according to the six fundamental mechanisms mentioned earlier. In precipitation fouling, the delay time (e )^ is due to nucleation phenomena. Growth of the crystals follows the nucleation step. Since an increase in temperature would lead to a higher degree of supersaturation, i t is obvious that the delay time would decrease with increasing temperature. This effect was statistically proved by Banchero and Gordon (7). Diffusion of the ionic species and particulate solids, in case of their presence in the bulk f luid, onto the heat exchanger wall will succeed the crystal growth. The deposits will be absorbed by and accumulate at the solid-layer interface. According to Hasson (8), a removal process would take place simultaneously with the deposition process, due to the fluid shear stress. Aging processes can cause the material already deposited on the heat exchange surface to recrystallize and harden due to a temperature increase. Also, as the result of the shedding-off mechanism caused by stresses, the deposits can be weakened with the passage of time. - 1 1 -2.4 Calcium Carbonate Precipitation The common ion e f f e c t determines the saturation concentration of sparingly soluble s a l t s such as CaCCs according to the following formula: where i s the temperature dependent concentration s o l u b i l i t y product. The bracketed parameters are the saturation concentrations, and the a c t i v i t y c o e f f i c i e n t i s unity. Therefore, supersaturation occurs when the concentration of the ion increases beyond i t s saturation concentration with respect to that s a l t : [Ca] [CO"] = s s K sp (2-2) [ C r ] > [Ca +] = - 3 L _ S £C6- 3] S (2-3) or CCO3] > [ C O ^ = (2-4) - 12 -K s p i s s i g n i f i c a n t l y affected by temperature. Larson and Buswall (9) have used the experimental data of other investigators such as Frear and Johnston (1929) to predict the s o l u b i l i t y product of CaC0*3 (10). The following relationship represents the temperature dependency of K between 0°C and 80°C f o r unit a c t i v i t y c o e f f i c i e n t : where T i s in degree centigrade. Considering the above-mentioned equation, i t i s obvious that K decreases with increasing temperature. Hence, pr e c i p i t a t i o n of CaC0 3 in a solution w i l l take place due to either a decrease in K Sp as a result of temperature increase or addition of a common ion (Ca + or C0 3 ). When a soluble s a l t of calcium i s added to a bicarbonate solution, the following reactions would take place: pK c n = 0.01183T + 8.03 (2-5) H + + OH (2-6a) HC0o + H + H 2C0 3 = C02"+ H20 (2-6b) HC0o =- COo + H (2-6c) CO, + Ca ++ CaCO (2-6d) - 13 -Thus, the total carbon concentration (Cj) i s given by: C T = [HCO3] + [ H 2 C 0 3 ] + [ C 0 P ( 2' 7 ) To determine the carbonate s o l u b i l i t y , the chemistry of carbonic acid solution should be f i r s t understood. Since dissociation of strong acids and bases in pure water i s complete, the hydrolysis e f f e c t of water i s negligible and pH can be calculated using the molar mass of the substance added. However, in the case of weak acids or bases, the dissociation i s not complete and the pH cannot be determined by the above-mentioned manner. Therefore, a reference pH i s defined as the equivalence point which i s the pH of an equivalent solution established by adding, say, x moles of a weak acid or base to a l i t r e of pure water. This pH or the equivalence point depends on the amount of substance added to the water. The concept of equivalence point becomes important when mixing of a weak acid or i t s s a l t s with a strong base or strong acid, respectively, takes place. Calcium carbonate i s the s a l t of a diprotic weak acid (HgCO-j). Carbonic acid has three d i f f e r e n t equivalence points with respect to H2CO3, HCO3 anc' ^ 3 " *n a w a t e r sample, i f the pH of solution i s above the HgCO-j, HCO3 or CO3 equivalence points, the concentration of the monoprotic strong base which establishes that observed pH i s c a l l e d total a l k a l i n i t y , phenolphthalein a l k a l i n i t y and caustic a l k a l i n i t y , respectively. - 14 -Therefore, based on the electroneutrality condition through the proton balance equation, the total a l k a l i n i t y (T.A.) of a water with total carbon species (Cy) would be: [T.A.] = [B +] = [HC03] + aCCOg] + C ° R ] " [ H + ] ( 2 _ 8 ) The concentration of a dip r o t i c strong base which s a t i s f i e s the same condition i s : [T.A.] = [B +] = \ [Ca +] (2-9) In a solution containing CaCO^, the d i s t r i b u t i o n of the carbon species i s s i g n i f i c a n t l y affected by the pH. The e f f e c t of pH can be investigated considering the following relationships obtained from the e q u i l i b r i a of carbonic acid. [H +] [HCO3] 1 = LCo 2J (2-10) - 15 -where and l<2 are, respectively, the f i r s t and second molar dissociation constants of carbonic acid. Solving three independent equations 2-8, 2-10 and 2-11, f o r three d i f f e r e n t unknowns would y i e l d : (2-12) [T.A.] + CH+] - [OH] 2<1+ Sf) _ [T.A.] + [H +] - [OH] 2K 9 [H +] [T.A.] + [H +] - [OH] K, 2K 9 (1+ c [H +] [H +] ) [HC0~? - LI.A.J + LH J - LUHJ (2-13) 3 [C0 2] = L . . A . J + L" 1- LUHJ ( 2_ 1 4 ) [CO"] And the d i s t r i b u t i o n fractions of carbon species ( i . e . a^ g- = ) would be: 3 X "CO" = (1 + ([H+]/l< 2) + ([H +]/K 1K 2)) _ 1 (2-15) aHC0 3 = (1 + ([H*]/!^) + (K 2/[H +])) _ 1 (2-16) a C 0 2 = (1 + (K 1/CH +3) + (KjKg/CH*] 2))' 1 (2-17) Thus, i t i s obvious that the d i s t r i b u t i o n of carbon species in water i s very pH dependent as i s shown in Figure 2-2. With regard to equation 2-3, i t i s clear that the degree of supersaturation i s also a function of both the total carbon concentration (C T) and the pH. - 16 -Fiaure 2-2. EQUILIBRIUM DISTRIBUTION FRACTIONS OF TOTAL CARBON AT VARIOUS pH LEVELS (8) - 17 -2.5 Models Predicting the Rate of CaCO^ Precipitation The a b i l i t y to predict the fouling rate i s of great importance regarding both the design and the performance of a heat exchanger. Several predictive models have been presented with respect to both type of fouling and mode of operation. Some of these correlations involving p r e c i p i t a t i o n fouling are shown in Table 2-1 and w i l l be b r i e f l y discussed below. Apparently, the f i r s t analytical study of fouling was carr i e d out by McCabe and Robinson (11). Their experimental work in evaporators under constant AT (two isothermal f l u i d s ) was in a good agreement with t h e i r proposed model (equation 2-19) which predicted a f a l l i n g rate behaviour. The model was based on the proportionality of the quantity of scale deposited with both the amount of l i q u i d evaporated and the total heat transferred f o r accomplishing t h i s process. Removal processes were not taken into consideration by these authors. In 1959, Kern and Seaton (5, 6) presented t h e i r model (equation 2-20) considering both the deposition and removal processes i n determining the net rate of fouling. Their mathematical co r r e l a t i o n was based on the asymptotic behaviour of fouling in indu s t r i a l heat exchangers. The following equation was proposed to approximate the fouling resistance. R Q = R * ( l - i B e ) (2-18) - 18 -Table 2-1. SOME FOULING RATE MODELS FOR PRECIPITATION FOULING Year Authors Fouling rate s (dm) • m de Systems Described 1924 McCabe a Robinson (11) * " «„ * ajU (2-19) In evaporators with constant AT 1959 Kern 3 Seaton (5, 6) * " a2CbV - "1 T *f (2-20) Particulate and other fouling 1962 Hasson (12) m - a3Uf (2-21) Hon Isothermal fluid * - (2-22) CaCOj precipitation 1964 Reltzer (15) It • <(cb-cs)n (2-23a) Precipitation of Inverse solubility salts m = a4Un (2-23b) With constant AT * = a5 (2-23c) With constant heat flux 1968 Hasson et al. (17) id = kgpEjcrj^jcr),] (2-24a) For CaCOj scaling with (2-24b) constant heat flux. 1972 Taborek et al. (18, 19) m . a7P9 a exp'^'-b, 1 xj (2-25) Cooling water 1975 Watklnson » Martinez (20) m • K(cb-cs)n-b3 tx f " K [ a8 l+(hxf/kf) ] " b3 T x f (2-26) CaC03 scaling at constant steam temperature where R i s the asymptotic value of the fouling resistance and B i s a constant i n time"'. The gross deposition rate was considered to be a function of f l u i d flow (V) and the concentration of foulant i n bulk ( c ^ ) . deposition rate = a2c$ The removal rate was proposed to be a function of f l u i d shear stress, x , and thickness of the scale, x^. The mathematical model (equation 2-21) expressed by Hasson (12) involved sensible heating of cooling water. The model results in an i n f i n i t e f ouling resistance buildup due to the lack of removal term. His experimental analysis f o r tube side fouling at low v e l o c i t i e s (v<l m/sec) confirmed the pr e d i c t i v e model using a value of f=2.5. However, at higher v e l o c i t i e s , the c o r r e l a t i o n does not hold since the removal term becomes e f f e c t i v e . In the same paper, Hasson has also formulated a growth rate (equation 2-22) f o r CaC03 p r e c i p i t a t i o n based on the mass transfer p r i n c i p l e s (13). The o v e r a l l mass transfer c o e f f i c i e n t Ko was considered to be a function of the d i f f u s i o n of HCO^ and Ca + ions through the boundary layer and the formation of a c r y s t a l l a t t i c e . 1 1. + 1 (2-27) T7 - 20 -where and are, respectively, the mass transfer c o e f f i c i e n t f o r diff u s i o n and the rate c o e f f i c i e n t f o r surface reaction. K Q can be estimated using the Sherwood equation f o r turbulent flow inside pipes (14): where D i s the hydraulic diameter and D A b i s the d i f f u s i v i t y of HCO^ o r C a + + ions. would be evaluated through the Arrhenius equation as follows: lnK R = J - ^j- (2-29) where R^  i s the gas constant, T g i s the surface temperature, E i s the activation energy and J i s the constant in the Arrhenius equation. Reitzer (15) proposed his model (equation 2-23a) f o r p r e c i p i t a t i o n of inverse s o l u b i l i t y s a l t s based on the degree of supersaturation (16) considering a l i n e a r inverted s o l u b i l i t y curve f o r a r e l a t i v e l y small range of temperature. His model predicted an increasing, non-linear, fouling resistance build up f o r constant operating conditions according to the equation 2-23b. At a constant heat flux, a l i n e a r deposition rate was predicted as i s shown in equation 2-23c. No removal term was involved in formulating t h i s model. - 21 -Hasson et a l . (17) have also studied the CaCO-j scaling using an annular constant heat flux heat exchanger. He suggested that in a d i f f u s i o n controlled process, when the chemical reaction and surface c r y s t a l l i z a t i o n rates are high, the overall growth rate i s a function of C a + + ion driving force f o r d i f f u s i o n (equation 2-24a). Using the J-factor analogy between mass and heat transfer, he derived the net fouling rate as a function of Reynolds number (equation 2-24b). His experimental measurements based on the mass transfer data f o r waters having Reynolds numbers between 13000 and 42000 (24.8 £ v £ 82 cm/sec) provided the following rate equation: iti=a 9(Re)°:^ (2-30) which was in a close agreement with the model presented. However, the practical value of the model might be doubtful at higher v e l o c i t i e s due to the absence of the removal term. It should be mentioned that a more recent model containing both the removal and the deposition terms was formulated by Hasson in 1978. This so-called "Ionic Diffusion Model" has taken into account the e f f e c t of water chemistry on the d i f f u s i o n process and w i l l be discussed separately. The model (equation 2-25) proposed by Taborek et a l . (18, 19) involved both deposition and removal processes. In t h i s study, the effect of water chemistry on the fouling rate has been considered. The gross deposition term was assumed to be reaction controlled and hence a function of c r y s t a l l i z a t i o n process. The e f f e c t of water chemistry was taken into account using the Langelier saturation index and represented by the, fi , - 22 -"water characterization factor". The e f f e c t of residence time of the foul ant in the reaction zone which i s an inverse function of the velocity, was taken into consideration through the, P^, "probability function of velocity". 9 *d = a 7 P d fi e x p ^ " E / R g V The gross removal rate was defined in terms of f l u i d shear stress, T , and the deposit bond resistance, * R^ was expressed as a function of both the deposition thickness, x^, and the deposition structure, Y . \ = b2 7 ( V r In 1975, Watkinson and Martinez (20) presented t h e i r model (equation 2-26) f o r scaling of CaC0 3 inside copper tubes. They used the Kern-Seaton concept of deposition and removal with the Reitzer deposition term, as the basis of t h e i r gross deposition rate. Considering a l i n e a r inverted s o l u b i l i t y curve f o r the range of temperature involved, the gross rate of scale build up can be determined by: md - K ( c b - c s ) n = K a £ ( T s - T b ) n - 23 -writing the scale surface temperature, T s, in terms of the wall temperature, T , they derived: w md = K l + ( h x f / k f ) This model d i f f e r s from those expressed by other investigators in that the gross deposition term i s not constant but varies both with time and the scale thickness. Assuming an Arrhenius function f o r the rate of crystal growth, K, i t shows that the gross rate of deposition i s strongly temperature dependent. The removal term i s considered to be proportional to both the deposit thickness and the f l u i d shear stress which i s , in turn, a function f 2 of f r i c t i o n factor, f l u i d velocity and density ( T = ^ p ). 2.6 Hasson's Ionic Diffusion Model Even though water chemistry i s an important factor in p r e c i p i t a t i o n of CaCO-j, i t hadn't been taken into consideration in the predictive models proposed before 1972. However, the model presented by Taborek et a l . (19) has taken t h i s factor into account. They have used the Langelier saturation index (LSI) as a parameter relating the water chemistry to the fouling rate. Since the index i s rather a qualitative than quantitative measure of the tendency of water to either dissolve or precipitate the CaC0 3, Hasson has (8) c r i t i c i z e d the use of the index and has formulated the ionic d i f f u s i o n model. - 24 -His model (13) i s based on the radial d i f f u s i o n of Ca and CO3 (or HCO^) ions from the bulk of the f l u i d toward the hot heat transfer surface. He has disregarded the deposition by precipitated CaCOg present in the bulk f l u i d and has used the experimental data published by Morse and Knudsen (21) to verify the accuracy of his model. The rate of c r y s t a l l i z a t i o n and gross deposition of CaCO^ per unit area at the interface was expressed, based on the surface controlled mechanism (22, 23), by the following equation: where bracketed parameters are the i n t e r f a c i a l concentrations and K s p i s the s o l u b i l i t y product of CaCO^ at the scale water interface. The rate of crystal growth, KR, i s temperature dependent and assumed to follow the Arrhenius law. As was experimentally shown by Gazit and Hasson (24), i t can be evaluated from the following relationship: w= KR ([Ca ]. [CO"]. - K ) (2-31) lnK R = 38.74 - 20700 (2-32) where R g i s the gas constant in cal/mole °K, T g i s the absolute 3 temperature of the scale surface and K s i s in cm/sec/gr CaCOo/cm . - 25 -The d i s t r i b u t i o n of various carbon species (C0 3, HCO^, CG^) in a carbonate solution i s pH dependent as was shown previously. Since the d i f f u s i o n process depends on the concentration of a l l the d i f f u s i n g species present in the water, f i r s t i t should be determined which one of the species i s predominant. Looking at equations 2-12, 2-13 and 2-14, i t i s obvious that for a given solution, most of the carbon i s in the form of HCO^ ion at low pH values. However, the tendency toward formation of C0 3 ions increases with increasing pH. Therefore, in the case of high pH values, the rate of d i f f u s i o n w i l l be controlled by C0 3 ions concentration as follows: w = K D [ ( C a + ) - ( C a + ) . ] = ^[(CO'MCO^).] (2-33) The c o n t r o l l i n g species are either C0 2 or HC03 ions at low pH values giving ris e to the following rate equation: w = ^ [ ( C r M C r ) . ] = K D[(C0 2)-(C0 2).] = 2^ [(HC0 3)-(HC0 3) .] (2-34) where l<D represents the convective d i f f u s i o n c o e f f i c i e n t and can be considered the same f o r a l l above-mentioned carbon species due to t h e i r close d i f f u s i v i t y values. The numerical value of t h i s parameter, K D, can be approximated using the following relationship (14): ^ S c 2 / 3 = 0.023 Re" 0' 1 7 (2-35) - 26 -where v i s the velocity and Sc and Re are Schmidt and Reynolds numbers, respectively. Having eliminated the i n t e r f a c i a l concentrations from equations 2-31 and 2-33 he obtained the following gross deposition rate f o r CaC03 scaling at high pH values. 4[C0-] K ±- ( i §2 ) K n[Ca +] [CO:] K n / [ C a + + ] [Ca +][C5:] w = D + --—-) (1- 1 ±-) (2-36) 2 [ C a ] K R[Ca +] ./ [CO3] K Q 2 ( l + - ^ + hr) [Ca ] K [Ca ] ++ If the CO^ concentration i s much lower than the Ca concentration, as i s often the case, the following sim p l i f i e d equation would express the gross deposition rate. _sp_ w = KpLT-Op [Ca ] [CO3] 1+ [CO"] (2-37) ++. K R[Ca ] [Ca ] - 27 -At low pH values, equations 2-13, 2-14, 2-31 and 2-34 were used f o r the gross rate of scale build up resulting in the following relationship: K1 w K c n L"C0,J [HCOJ/2 J _ ( w + sp ) ( w + 2_ } = (1_ w ) ( L 3J w _ 4K 2 K R [ C a + ] 2 [ C a + ] 2 l< D[Ca +] [Ca +] K D[Ca +] [Ca +] K D[Ca +] (2-38) Having the above-mentioned condition, Ca + » CO^, the equation w i l l be reduced to: KnL"ca+J k I—717 where: 4K ? K R[Ca ] a = 1- •*-=• . -A? (2-40) K l KD [C0 2] 4K2 IC _ K L b = + — . — . [HCO,] + S P * (2-41) [Ca ] K1 KD 6 K D[Ca ] K« Kp[HC0.] 2 K c n [ C 0 ? ] K R C = -i- . -2 r | S P +. 2 R (2-42) Kx K D[Ca ] [Ca l\ - 28 -Under the condition where the term in the square root i s approximately 1, a further s i m p l i f i c a t i o n r e s u l t s : K_siL [Ca +] [CO"] w = K n[C0:] . - (2-43) D 3" Kp 4[C0 3] K + — + sp_ K R[Ca +] [HC0 3] [Ca +] [COg] Hasson has used the Kern-Seaton type model f o r the overall rate of the scale build up. The removal term was expressed as a function of the f l u i d shear stress, the deposit thickness and mechanical strength of the adhering material. Therefore, the net growth velocity of the layer can be correlated by the following equation: (dx f/de) = (w/ P f) - ( x f T / M ) (2-44) where T i s the f l u i d shear stress, x i s the deposit thickness and M i s a constant representing the mechanical strength of the deposit. Since the fouling resistance i s the difference in the overall resistance of the clean and the fouled heat exchanger, i t can be expressed by: R f = R " Ro = k^ (2-45) - 29 -where i s the thermal conductivity of the foulant. Differentiation of this equation yields: ^ = ^ = J _ ^ I = ^ _ . ! j l = _w_.R _L { 2. 4 6 ) de de k f de P f k f Mkf P f k f f M K C H D ; Integration of the above-mentioned equation with the i n i t i a l condition e=0, Rf=0 results in an asymptotic fouling behaviour represented by: Rf= Rf [1-exp (e/e c)] (2-47) where the adherent term (the time constant, e c) is given by: e_ = M/T (2-48) and the asymptotic fouling resistance is expressed by: substituting equations 2-48 and 2-49 in equation 2-46 yields: dR.p R.p R .p c c - 30 -when the f l u i d shear stress i s low or generally in case of very adherent deposits, e becomes very large and the removal term diminishes resulting in a l i n e a r fouling behaviour as follows: dRj de" w (2-51) 2.7 Factors Affecting P r e c i p i t a t i o n Fouling The fouling process i s best defined by either the time dependence of the thickness of the fouled layer or the thermal fouling rate. Therefore, the e f f e c t of parameters such as velocity, surface material, temperature and water chemistry on the fouling rate w i l l be discussed below. 2.7.1 Velocity A decrease in the fouling rate with increases in velocity was usually considered to be in e f f e c t in design of heat exchangers (25, 26). As was mentioned e a r l i e r , the net rate of fouling i s a function of both the deposition and the removal rates. The importance of velocity e f f e c t s in the removal process has been widely recognized. It has been suggested that the re-entrainment process takes place due to either the f l u i d shear stress (5,6) which i s a function of v e l o c i t y , f r i c t i o n factor and the flow configuration or to turbulent bursts (27, 28). - 31 -According to Cleaver and Yates, removal w i l l occur i f the minimum or c r i t i c a l f r i c t i o n velocity (v*) i s exceeded. The c r i t i c a l f r i c t i o n velocity i s described by: T (2-52) p where t and p are the f l u i d shear stress at the surface and the f l u i d density, respectively. For the occurrence of a removal process, Hasson et a l . (17) have reported the minimum velocity value of 2.6 cm/sec while Watkinson and Martinez (26) have suggested a minimum value of 2.9 cm/sec for v* in CaCOg scaling. Nucleation, d i f f u s i o n and chemical reaction rate processes w i l l determine the gross rate of deposition. In precipitation of CaCO^, the f i r s t scale layer i s deposited on a metal surface followed by subsequent addition of the deposits on the scaled surface. In the case of CaCOg the rate of nucleation i s considered to be constant and independent of the surface material (17); therefore, gross deposition rate i s defined only in terms of s i g n i f i c a n t operating parameters (d i f f u s i o n and chemical reaction). P r e c i p i t a t i o n of CaCG"3 i s i n i t i a t e d by d i f f u s i o n of Ca + and HCO^ ions toward the hot heat transfer surface and followed by the following chemical reaction: k' 2HC03 -—- C0~ + C0 2 + H20 (2-53) - 32 -The subsequent c r y s t a l l i z a t i o n of CaCO^ on the hot surface would take place and be represented by: Ca + + CO3 CaC03 (2-54) (s) The p r e c i p i t a t i o n process would be completed i f the l a t t i c e binding forces of the CaC03 crystal exceeds the shear force exerted by the l i q u i d flow. It should also be mentioned that the dissolved C0 2 produced, according to equation 2-53, would either migrate towards the bulk or be released in gaseous form at the surface. Since the rate c o e f f i c i e n t (k 1) i s r e l a t i v e l y high, the rate of diffus i o n i s controlled by the migration of Ca + and HCO^ ions toward the surface. In addition, assuming that the generated CO2 either escapes rapidly i n gaseous form or diffuses toward the water bulk, the gross rate of deposition, m^ , i s governed by both d i f f u s i o n and c r y s t a l l i z a t i o n processes. Hasson has experimentally shown (12) that d i f f u s i o n i s the ef f e c t i v e factor at low v e l o c i t i e s while the e f f e c t of surface reaction becomes important at re l a t i v e l y higher v e l o c i t i e s . When the process i s di f f u s i o n controlled, velocity enters the gross deposition term via the convective mass transfer c o e f f i c i e n t (equation 2-28). Since there i s not any appreciable removal process at lower velocity values, the net rate of scale - 33 -build up would be constant with no asymptote and can be approximated through equations 2-22 and 2-27 by the following relationship f o r the overall mass transfer c o e f f i c i e n t : K o " KD " v ° ' 8 3 " R e ° ' 8 3 ( 2 _ 5 5 ) thus, m « R e 0 , 8 3 (2-56) where iti i s the net rate of scaling. Since the fouling process i s s p e c i f i c to the operating conditions, the above-mentioned equation holds f o r a constant heat flow system where the scale surface temperature and hence K R are invariant with respect to time. Another theoretical model (equation 2-24b) suggested by Hasson et a l . (17) represents the increase in the fouling rate with the f l u i d velocity. Their experimental results (equation 2-30) were in close agreement with t h e i r predictive model for r e l a t i v e l y low v e l o c i t i e s (v _< 0.82 m/sec) and hence the absence of removal term. The experimental results presented by Watkinson and Martinez (20) showed the positive e f f e c t of velocity on the asymptotic fouling resistance for Reynolds numbers below 12000 (v<0.5 m/sec). However, a decrease in the - 34 -asymptotic fouling resistance with the velocity was both observed (equation 2-57) and predicted (equation 2-58) f o r Reynolds numbers above 12000. * -1 33 R f tt v A"" (2-57) * 9 *2 Rr Bp R f + # R f + -4 = 0 (2-58) where b 2 i s temperature dependent and can be approximated f o r bulk temperatures below 350°k through: B2 = 0.000271Tb - 0.08489 (2-59) It should be mentioned that the system was operating under constant steam temperature. 2.7.2 Heating Surface In CaC0 3 scaling, the heat transfer surface i s neither a reactant nor a c a t a l y s t . The major influence of the heating surface on t h i s kind of fouling process occurs during the induction period. Parameters such as average roughness, surface free energy, wettability and heat of immersion are used to characterize the nature of the s o l i d surface. Corrosion of the surface material can also a f f e c t the fouling process. Some metallic surfaces - 35 -may undergo corrosion and provide roughened areas as nucleation sites f o r deposition to i n i t i a t e (29) or increase the fouling factor by the deposition of corrosion products (30). Nucleation of CaCO-j occurs at the metallic surface. Even though subsequent deposition of CaCO^ w i l l take place on CaCO^ c r y s t a l s , the s o l i d interface continues to e f f e c t fouling process through the adhesion force of the fouled layer. However, experiments have shown (17) that, in the case of CaCO^, the rate of nucleation on a metallic interface i s almost equal to the rate of growth on a fouled CaCOj layer. 2.7.3 Temperature Bulk temperature would e f f e c t the physical properties of the process f l u i d as well as a l l the reactions involved in the fouling phenomena. For an inverse s o l u b i l i t y s a l t the temperature-solubility relationship can be approximated by a l i n e a r relationship (c.-c ) = b'(T -T.) (2-60) D S S D where c i s the concentration, T i s the temperature and subscripts b and s are denoted to the bulk and the scale surface, respectively. The suggested deposition models based on the concentration driving force (equations 2-22, 2-23a, 2-24a and 2-26) show that an increase in the bulk temperature would lower the diffusional driving force, at constant scale surface temperature, due to a decrease in the bulk s o l u b i l i t y l i m i t . However, th i s condition may - 36 -give r i s e to bulk p r e c i p i t a t i o n and hence to particulate fouling. The negative effect of the temperature r i s e on the d i f f u s i o n process i s also c l e a r in equations 2-20 and 2-25 through bulk concentration and water characterization factor, respectively. The convective mass transfer c o e f f i c i e n t (KQ), for which the f l u i d properties w i l l be measured at the f i l m temperature, would also be affected by the bulk temperature. As the scale surface temperature r i s e s , the gross deposition rate increases through an increase i n the concentration gradient (equation 2-60). The e f f e c t of T g on both the convective mass transfer c o e f f i c i e n t (Kg) due to the change in f i l m temperature and the surface rate c o e f f i c i e n t (K R) i s obvious according to equation 2-28 and the Arrhenius law (equation 2-29), respectively. The positive e f f e c t of r a i s i n g the surface temperature i s experimentally shown in the work of Hasson et a l . (17) on CaCO^ scaling. Physical properties of the fouled layer such as adhesion to the s o l i d surface and f r i a b i l i t y are greatly affected by the surface temperature. Under a constant heat flux condition where the scale surface temperature i s constant, the wall temperature r i s e s as the tube scales. The internal temperature of the fouled layer increases with increasing temperature and recrystal1ization of the deposited material i s l i k e l y to occur as the time passes. This i s the so c a l l e d aging process and in t h i s case would tend to strengthen the deposit and weaken the removal process. - 37 -2.7.4 Water Chemistry Water properties such as carbon dioxide content, pH, hardness and total alkalinity play an important role in the deposition of calcium carbonate. The s o l u b i l i t y of CaC0 3 in water, i n the absence of C0 2, i s 14 ppm at 25°C. Addition of carbon dioxide would increase the CaC0 3 s o l u b i l i t y to 300-400 ppm (31) via the following reaction: CaC0 3 + C0 2 + H 2 0 — » - Ca(HC0 3) 2 (2-61) S o l u b i l i t y of CaC03 also changes with respect to pH of the l i q u i d . At high pH values most of the carbon i s in the form of C0 3 ion (equation 2-12). Therefore, for a solution having the total carbon concentration of Cj and temperature of T, the degree of supersaturation increases with increasing pH (equation 2-3). Figure 2-3 shows the decrease in the s o l u b i l i t y of CaC0 3 with increasing pH. The reduction of the asymptotic fouling factor due to a decrease in pH i s experimentally shown in Knudsen and Roy's study of CaC0 3 p r e c i p i t a t i o n on a 90-10 copper-nickel surface (30). The presence of calcium and magnesium sa l t s are usually considered as hardness. Equation 2-3 represents the positive e f f e c t of the hardness, due to Ca + ions, on the degree of supersaturation and hence on the fouling process. A l k a l i n i t y i s a function of HC03, C0 3 and Ofl ions. Looking at both equations 2-8 and 2-4, i t i s obvious that the supersaturation of CaC0 3 - 38 -Figure 2-3. SOLUBILITIES OF HYDROXIDES AND CALCIUM CARBONATE WITH RESPECT TO pH (.8) - 39 -occurs more readily with increasing total a l k a l i n i t y . The positive e f f e c t of a l k a l i n i t y on the fouling resistance i s experimentally shown by Morse and Knudsen (21). Some methods including the e f f e c t of hardness, a l k a l i n i t y and pH were suggested to relate the water chemistry with the fouling process. Langelier (32, 33) has developed a q u a l i t a t i v e formula by which the tendency of water to either p r e c i p i t a t e or dissolve calciun carbonate can be predicted. The equation i s based on the pH, total a l k a l i n i t y , hardness and temperature which are effective in s o l u b i l i t y of calcium carbonate in water. The basis of his prediction involved in the reversible scaling process i s : CaCO, + H + — » » C a + + HC0~ (2-62) The s o l u b i l i t y constant, k, for the above-mentioned reaction can be expressed by: [Ca ] [HC0\] k = T — (2-63) [H +] Therefore, the saturation or equilibrium pH can be written: pH s = pCa + pHC03 - pk (2-64) - 40 -considering both the second s o l u b i l i t y constant, K2, f o r carbonic acid and the CaC03 s o l u b i l i t y product, K s p, y i e l d s : pk = pK 2 - pK s p (2-65) using equation 2-13, PHC63 can be formulated in terms of pH and total al kal i n i t y : 2K pHCfl, = p (T.A. + [H +] - [Off]) + log (1+ - ~ - ) (2-66) 2 [H +] substituting equations 2-65 and 2-66 into equation 2-64 y i e l d s : ++ pCa + (pK 2-pK s p) + p (TA + [H ] - [OH]) + log (1+ 2K, [H +] )(2-67) pH s corresponds to the pH of a solution, with a given calcium carbonate content and total a l k a l i n i t y , at which water i s in equilibrium with CaCO^. Hence, the Langelier Saturation Index, which i s defined as: LSI = pH-pHs (2-68) can be a qual i t a t i v e measure of CaCO^ s o l u b i l i t y i n water. If the index i s positive, CaCO^ tends to deposit. Negative values of the index represent the tendency of water to dissolve CaCO^. The water i s at equilibrium with CaCOg when the index is zero. Watkinson (34, 35) has experimentally shown that the asymptotic fouling resistance increases with increasing saturation index. - 41 -Ryznar (36) has c r i t i c i z e d the use of saturation index as a qualitative measure of CaC0 3 s o l u b i l i t y in the water. He has empirically developed an index which supposedly makes i t possible to predict whether a water i s scale forming or corrosive. This parameter was c a l l e d Ryzner St a b i l i t y Index and can be given by: RSI = 2pHs-pH (2-69) He has experimentally shown that a water having a s t a b i l i t y index of approximately 6.0 or less i s scale forming while a water having an index above 7 tends to be corrosive. The presence of other chemical substances also changes the water chemistry and may in turn influence both the fouling process and the constituents of the scale. It has been shown (21) that the scale strength i s generally proportional to the scale purity; therefore, the higher degree of purity accelerates the fouling rate. The experiments car r i e d out by Heat Transfer Research Corporation, HTRI (37), have supported the purity e f f e c t , showing that in a solution of single s a l t , the c r y s t a l l i n e structures are strongly adhered to each other. The effect of magnesium on the fouling process has very b r i e f l y +2 been studied. Thurston (38) reported that the presence of Mg at concentrations higher than 0.2 C a + + , in waters low in s i l i c a , would weaken the structure of CaCO^ deposit by production of c a l c i t e in the suspension which depresses the supersaturation. Watkinson's experimental work (34) on 2+ 2+ the waters having Mg >0.2 Ca showed a decrease in both the fouling - 42 -rate and asymptotic fouling resistance and resulted i n a deposit containing less than 0.5% Mg + + content. However, in his further study, Watkinson (39) has reported that as the Mg + +/Ca + + increases, both the fouling resistance and the scaling rate would decrease and go through a minimum at ++ ++ ++ Mg /Ca about 0.2. The Mg content of the deposits was about 1.6% by weight in the l a t t e r . The presence of any impurity in a solution may also a l t e r the pre c i p i t a t i o n process. Peters and Stevens (40) have reported that the existence of iron would decrease the crystal growth rate of CaCO^ - MgfOH^ precipitate while enhancing the nucleation rate. Since i t has been observed that the c r y s t a l l i z a t i o n of CaCO^ and MgtOH^ are independent of each other (41), i t can be deduced that the same e f f e c t i s applicable to the CaC0.j pr e c i p i t a t i o n . The increase i n the s o l u b i l i t y of CaCO-j in the presence of strontium was also reported (42). Knudsen and Roy (30) have experimentally shown that i n the absence +2 of Mg the Si^/CuO ra t i o in the scale i s an influencing parameter in the magnitude of the fouling resistance. It has been observed that when thi s r a t i o i s about 3.0, the fouling factor i s high while i t decreases as the rati o becomes unity or les s . The presence of dissolved oxygen and chloride ion might also affect the fouling process since they both enhance the corrosion of some heat transfer surfaces (43, 44, 45). - 43 -2.8 Heat Transfer From Plain Surfaces In a tubular heat exchanger, the transfer of heat between the two streams in the tube and in the annulus would take place due to: the conduction through the tube wall; the p a r a l l e l mechanisms of convection and radiation between the streams and the inner and outer surfaces of the tube. Therefore, the total rate of heat transfer under the steady state condition in the absence of radiation, which i s negligible, would be (46): q = = ( q c ) 0 = q k (2-70) where q i s the total rate of heat flow and subscripts c, k, i and o are denoted to convection, conduction, inner surface and outer surface, respectively. The rates of heat flow f o r three d i f f e r e n t modes of heat transmission are represented by the following equations: t , - V , - | T , - „ - y , 2 - 7 1 ' \ ' V ° ' V T ° ' ( 2 ~ 7 2 1 0 0 0 % • 2kw TS^ ' W ( 2 - 7 3 ) - 44 where: h*c = the average unit thermal conductance for convection k w = the average unit thermal conductance for conduction D,-> = the inside and outside tube diameters i o T«n, T Q = the temperatures of the inner and outer streams T , T = the inside and outside surface temperatures s i so Aj, A 0 = the inner and outer surface areas A -A. the logarithmic mean area = 0 ^ 757 1 substituting equations 2-71 to 2-73 in equation 2-70 yields: 1 • ^ c / ^ n - V = A o B c 0 ( T s 0-V " 2 k w D 7 D 7 ( T s " T < 2 - 7 4 ' which can also be expressed by: T. - T i n 0 (2-75) i D - D . , i _ + _°_L + _ l A h „. T A.h o c Q 2kwA i c. - 45 -The denominator of the above equation represents the ove r a l l resistance of the exchanger. The overall unit thermal resistance, -jj, of the exchanger based on the outside area i s given by: - , (D -D.)A A 1 = 1 + o i o + o _ ( 2. 7 6 ) ^ \ 2kw* V i thus, « • UoVT1n-To> (2"77> Since the streams and the wall temperatures are not constant along the path of the exchanger, equation 2-77 holds f o r an elemental area, dAQ, and can more properly be represented by: d< = U o d A o ( T i n - T o ) = U o d A o A T ( 2" 7 8 ) dividing both sides of the equation 2-78 by daT would y i e l d : dq U dA AT — = 0 0 (2-79) dAT dAT - 46 -Now considering the heat balance equations in the absence of phase change: dq = W. c dT. = W C dT (2-80) in P 1 n in o p Q o where W and c p are the mass flow and the sp e c i f i c heat of the f l u i d , respectively. The above relationships represent that q i s l i n e a r both i n T. and T Q; therefore, i t s l i n e a r i t y i n t h e i r difference i s evident and can be given over the length of the exchanger, L, by: & r a U T ) x = L - q u T ) x = 0 ,2"81> substituting equation 2-81 i n equation 2-79 y i e l d s : U dA AT 7-Ti 9-7-n = - 2 7 i 4 - (2-82) (AT) L - (AT) 0 dAT For a constant overall unit thermal conductance, U o, the integration of the above-mentioned equation along the path of the exchanger y i e l d s : q = U 0A 0AT m (2-83) where AT^ i s the logarithmic mean temperature difference, LMTD, given by: - 47 -The above-mentioned procedure can be carri e d out to f i n d the overall unit thermal conductance based on the inner surface area: q=U.A.AT m (2-85) Equation 2-76 represents the overall unit thermal resistance of a clean tube. To calculate the ove r a l l unit thermal resistance of a fouled exchanger, the unsteady state fouling resistances are indiscriminately added to the steady state heat transfer resistances as follows: , . (D "D.)A A D ry A (1 ) = 1 + 0 1 0 + ° + R f + R f ° (2-86) ^ d \ 2 kw A ° ^ where i s the fouling factor and the subscript d i s denoted to the fouled o r d i r t y exchanger. Using the same analogy as in equation 2-70, the performance of a heat exchanger can be defined by (47): q = * r A ° A T f 0 = * r A ^ T f i ( 2 _ 8 7 ) where ATf i s the temperature drop through the fouling f i l m . Equation 2-87 shows that fouling factor, Rf, i s not the only parameter c o n t r o l l i n g the fouling e f f e c t ; ATf and the heat flux, are equally important. - 48 -Equation 2-76 implies that the o v e r a l l unit heat flow conductance of an exchanger depends on: the geometry; the flow v e l o c i t y ; the s p e c i f i c heat; the thermal conductivity of both the surface material and the stream; and the v i s c o s i t y . It increases with the f i r s t four while i t i s an inverse function of the l a s t parameter. The rate of heat flow and, in turn, the fouling process are also affected by these factors. Table 2-2 shows how fouling factor i s related to temperature and velo c i t y (1). It increases with increasing the temperature and decreasing the ve l o c i t y . 2.9 Heat Transfer From Extended Surfaces To increase the rate of heat transfer per unit volume of the exchanger, extended surfaces as f i n s attached to the heat transfer wall have a wide in d u s t r i a l application. They compensate for the poor rate of heat flow i n the f l u i d with lower heat transfer c o e f f i c i e n t by exposing more surface to i t . Therefore, the t o t a l rate of heat flow would be: q t = q p + q f (2-88) where t, P and f are subscripts denoted to t o t a l , prime and finned areas. Knowing that any extended surface i s less e f f e c t i v e per unit area than a bare one due to the distance from the heat source, the f i n e f f i c i e n c y (n f) i s defined (47, 48) by: - 49 -Table 2-2. EFFECT OF TEMPERATURE AND VELOCITY ON FOULING FACTOR (47) F O U L I N G FACTORS* Temperature of heating medium Up to 240°F 24O-4O0°Ft Temperature of water 125"F or less Over 125°F Water velocity. Water velocity. fi sec /Usee 3/' Over 3/' Over Water and less 3/' and less 3/' Sea water 0.0005 0.0005 0.001 0.001 Brackish water 0.002 0.001 0.003 0.002 Cooling tower and artificial spray pond: Treated make-up 0.001 0.001 0.002 6.002 Untreated 0.003 0.003 0.005 0.004 City or^ well water (such as Great Lakes) 0.001 0.001 0.002 0.002 Great Lakes 0.001 0.001 0.002 0.002 River water: Minimum 0.002 0.001 0.003 0.002 Mississippi 0.003 0.002 0.004 0.003 Delaware, Schuylkill 0.003 0.002 0.004 0.003 East River and New York Bay 0.003 0.002 0.004 0.003 Chicago sanitary canal 0.008 0.006 0.010 0.008 Muddy or silty 0.003 0.002 0.004 0.003 Hard (over IS grains/gal) 0.003 0.003 0.005 0.005 Engine jacket 0.001 0.001 0.001 0.001 Distilled 0.0005 0.0005 0.0005 0.0005 Treated boiler fcedwater 0.001 0.0005 0.001 0.001 Boiler blowdown 0.002 0.002 0.002 0.002 • Standards of Tubular Exchanger Manufacturers Association, 5th ed.. New York, J968. t Ratings in the last two columns are based on a temperature of the heating medium of 240 to 400°F. If the heating medium temperature is over 4O0°F, and the cooling medium is known to scale, these ratings should be modified accordingly. - 50 -actual heat transferred by f i n q n f ~ heat which would have been (2-89) transferred i f entire f i n were at the base temperature where • y f ( Y V (2-90) T = s prime surface temperature or the temperature at the base of the f i n = bulk temperature Substituting equation 2-89 and 2-90 i n the equation 2-88 and applying the same analogy used f o r the finned area, equation 2-89, to the total area y i e l d s : assuming that fi, i s invariant over the total surface would simplify the equation 2-91 to: (2-91) n t \ =(VAf) (2-92) - 51 -where n t A t i s the e f f e c t i v e area ( A g f f ) . F i n e f f i c i e n c y can be estimated making a heat balance f o r a small element of the f i n under steady state condition rate of heat flow rate of heat flow rate of heat flow by conduction into = by conduction out + by convection from element x of element x+dx surface between x and (x+dx) with regard to Figure 2-4. The above-mentioned equation becomes: % - V d x + 2 y »t)dx(T-T b) (2-93) or f o r uniform • k f i n b t £ = - k f 1 n b t - S ( T * a 5 d x ) + 2Fi c(b +t)dx(T-T b) (2-94) fa 2Tr(b+t) C ( T - T J (2-95) dx 2 k f . n b t b - 52 -Figure 2-4. SKETCH AND NOMENCLATURE OF A RECTANGULAR FIN - 53 -The above second order d i f f e r e n t i a l equation can be solved based on following assumptions: Steady state and no heat generation by internal sources. Transverse temperature gradient i s very small that T=T(x). Uniform thermal conductivity f o r both f i n and the tube. Uniform convective heat transfer c o e f f i c i e n t , Fi c, between surface and f l u i d . Uniform f l u i d temperature. Heat loss from the end o f the f i n i s n e g l i g i b l e . Therefore, the actual heat transferred by f i n would be given by: q f = "k f l- nA f ^r= k f l. nA fm(T s-T b)tanh(ml) (2-96) where A r = f i n cross section = bt - 54 -P = perimeter = 2(b+t) . - (V/kfiA' 0.5 (2-97) F i n e f f i c i e n c y can be estimated by substituting equations 2-90 and 2-96 i n equation 2-89: Knowing that (ml) grows more rapidly than Tanh (ml) with increasing (ml), i t can be seen that nf and therefore nt a r e r e c i p r o c a l l y related to Ti c. Thus, f i n s are more e f f e c t i v e when they are placed on the stream side having a lower convective heat transfer c o e f f i c i e n t , B c. As in equation 2-76, the overall unit thermal resistance of a clean externally finned tubular exchanger, based on the t o t a l outside area, can be expressed by: (2-99) - 55 -Adding the fouling resistances results in the overall unit thermal resistance of a d i r t y exchanger as follows: . . VDo-°1» \ \ • \ ° d ' t A 2v \s X O 0 1 When the outer surface i s finned, p a r t i c u l a r consideration should be given to the fouling resistance of the inside of the tube. When the inside fouling resistance, Rf, i s very large, there would be no use i n adding external f i n s i and increasing the outer surface which would, i n turn, increase the to t a l fouling resistance. 2.10 Comparison Between an Enhanced and a Plain Heat Transfer Surface In a tubular heat exchanger, f i n s can be attached either to the inside or to the outside surface area of the tube. There are d i f f e r e n t f i n designs which are generally c l a s s i f i e d into two major categories: longitudinal and r a d i a l . Both the existence and the design of the f i n s a f f e c t the hydrodynamic flow condition and might, i n turn, influence the fouling process which i s a function of the dynamics o f the f l u i d . In a turbulent annular flow, the presence of f i n s would re s u l t i n the formation of eddies and subsequent disturbance of the laminar sublayer as was shown by Knudsen and Katz (49). These investigators showed that the number of eddies and therefore the degree of turbulence increases with increasing the f i n height, 1, to the f i n spacing, Sf, r a t i o . The study of - 56 -Knudsen and McCluer (50) on transverse finned tubes confirmed the results obtained by the previous investigators. They showed that, due to the existence of the transverse f i n s , the rate of calcium sulfate scaling decreases with increasing values of the 1/S^ r a t i o , resulting i n a high turbulence. This gave r i s e to the notion that the fouling factors are less f o r finned tubes than f o r the p l a i n tubes. The experimental data reported both by Katz et a l . (51) and by Webber (52) also indicated a less pronounced fouling process on the finned tubes than on the p l a i n tubes. However, Knudsen and Roy (30) studied the CaC0 3 scaling and reported the same fouli n g factor, based on the projected outside area, f o r both smooth and finned tubes. The e f f e c t of f i n s on the asymptotic scaling of CaCO^ under the constant steam temperature was studied by Watkinson et a l . (53). P l a i n , inner f i n and s p i r a l l y indented heat exchanger tubes were tested. The experimental results showed substantial advantage in heat transfer c o e f f i c i e n t of the enhanced tube over that of the p l a i n tube after fouling. However, the asymptotic fouling resistance was higher f o r the i n n e r - f i n tube than f o r the p l a i n tube in the velocity region (2 < v < 6 ft/sec) tested. For the s p i r a l l y indented tubes at v e l o c i t i e s below 3 f t / s e c , the asymptotic f o u l i n g resistance was above that f o r the p l a i n tube while i t became less than that of the p l a i n tube at v e l o c i t i e s above 3 f t / s e c . To investigate the performance of an enhanced heat transfer surface, i t i s important to know the e f f e c t of fouling on the t o t a l e f f i c i e n c y of the surface, r\.. Epstein and Sandhu (54) presented two mathematical models - 57 -to predict the e f f e c t of uniform fouling on the total e f f i c i e n c y of extended heat transfer surfaces. In the f i r s t model, they treated the fouling deposit on the f i n as a thermal resistance i n series with the adjacent f l u i d , as i t i s normally considered to be. In the second one, the d i r t on the extended surface was treated as a thermal conductor in p a r a l l e l with the f i n . Dirty f i n e f f i c i e n c y , T i f (j, was expressed i n terms of parameter m^  f o r a d i r t y surface in the same manner shown i n equation 2-98 f o r a clean surface. The models suggested that in both cases, the d i r t y f i n e f f i c i e n c y would decrease due to an increase in m^ . Since m^  i n either case i s proportional to m of a clean surface (equation 2-97), any decrease i n m would result i n an enhancement of the fouled f i n e f f i c i e n c y . In the series model, a decrease i n m^  and a subsequent increase in the d i r t y f i n e f f i c i e n c y i s accompanied by a reduced heat transfer due to the insulating e f f e c t of the d i r t and a lower e f f e c t i v e convective heat transfer c o e f f i c i e n t . However, heat transfer and d i r t y f i n e f f i c i e n c y are simultaneously increased due to a higher e f f e c t i v e conductivity i n the p a r a l l e l model. The ratio of the total e f f i c i e n c y of the clean enhanced surface to that of the d i r t y one, n t ^ n t d ' w a s c n o s e n a s a m e a s u r e to see the actual e f f e c t of fouling on an extended surface. Holding a l l the other parameters constant (for 0<Aj;/At<l), t h i s ratio increases with increasing ml f o r the p a r a l l e l model while i t goes through a minimum of ml-2 f o r the series model. In both cases at A f/A t=0, n t / n t ( j i s constant and has a higher value than those with A^./At>0. Therefore, both mathematical models show that an increase i n thermal resistance caused by a uniform fouling deposit on an enhanced heat transfer surface i s less pronounced than that on a p l a i n surface having the same d i r t thickness. With the other parameters constant, - 58 -at higher d i r t y f i n e f f i c i e n c y , r i f ^ , due to the lower m^ the r e s i s t a n c e f a c t o r , n t / n t c | , o f an exchanger i s enhanced according to the s e r i e s model while reduced with regard to the p a r a l l e l model. However, the negative e f f e c t o f the d i r t on the prime surface i n s e r i e s with the f l u i d i n c o n t a c t would reduce the performance o f the exchanger by i n c r e a s i n g n t / n t d , i n the p a r a l l e l model. The models p r e d i c t s i m i l a r r e s u l t s f o r the n t / n t d r a t i o at lower values o f A^/A^, higher values o f ml (lower f i n e f f i c i e n c y ) and lower values o f h/h d. The s e r i e s model g i v e s r i s e to more co n s e r v a t i v e r e s u l t s . I t provides a higher value f o r n t / n t c | r a t i o than the p a r a l l e l model even under the above-mentioned c o n d i t i o n s . - 59 -3. EXPERIMENTAL APPARATUS 3.1 Water Flow Loop A flow diagram of the apparatus i s shown i n Figure 3-1. The a r t i f i c i a l l y hardened water leaves the supply tank v i a a 2 inch pipe and i s pumped around the closed loop using a Cole-Parmer model K-7084-20 centrifugal pump. The pump i s driven by a t o t a l l y enclosed fan cooled (TEFC) 3/4 HP motor. The f l u i d enters and e x i t s the pump via 1-1/2 i n . copper pipes. The flowrate of the r e c i r c u l a t i n g water i s controlled manually and measured by a Brooks Model R-12M-25-4 rotameter (see Appendix I f o r the c a l i b r a t i o n curve). The test f l u i d flows upwardly into the shell side of the heat exchanger which consists of a 1.15 meter long glass tube with an inside diameter of 37 mm. The shell i s flanged from both ends to brass headers and sealed with rubber gaskets. Hard water i s heated by the steam which passes downwards through the central tube. The test f l u i d leaving the shell side of the heat exchanger i s cooled down by passing through a finned h e l i c a l heat exchanger. Cooling water i s supplied v ia the building mains and controlled by a R-9M-25-2 Brooks rotameter (see Appendix I f o r the c a l i b r a t i o n curve). Dr Drain F Filter He Heat exchanger HHE Helical heat exchanger SHC Steam heated coil VTS Valve for sampling P Pressure gauge R Regulator Tc Thermocouple Figure 3-1. FLOW DIAGRAM OF APPARATUS - 61 -Recirculating water which exits the finned hel i c a l heat exchanger can either enter the supply tank d i r e c t l y or f i r s t pass through an i n - l i n e f i l t e r . This f i l t e r i s equipped with an AMF Cuno Mikro-Klean 50 micron cartridge which removes the particulates without affecting the water chemistry (Figure 3-2). 3.2 Supply Tank Water i s recirculated from a 220-liter stainless steel tank. Two holes are d r i l l e d i n the bottom and on the side of the tank and tapped to bulk head f i t t i n g s with 3/4 i n . NPT (National Pipe Tapered) and 2 i n . NPT, respectively. The 3/4 i n . NPT hole i s connected to a 3/4 i n . steel pipe equipped with a valve which i s used as a drain. The 2 i n . NPT hole i s connected to a 2 i n . steel pipe which can either d i r e c t the test f l u i d v ia a 1-1/2 i n . copper pipe to the pump or to the drain v i a a valve. Water samples are taken using t h i s o u t l e t . The tank i s equipped with a steam heating c o i l to heat the test f l u i d up to the i n i t i a l operating temperature. It i s also covered with a piece of wood having an opening f o r introducing the chemicals. 3.3 Steam System The steam i s supplied by the main steam l i n e at a regulated pressure measured by a 100 psig Marsh steam pressure gauge. This regulated steam i s introduced either to the steam heating c o i l in the tank or to the tube side of the shell and tube heat exchanger v i a a 1/2 i n . steel pipe - 62 -Figure 3-2. PHOTOGRAPH OF APPARATUS FROM THE BACK - 63 -(Figure 3-2). In ei t h e r case, the l i n e pressure i s controlled by a valve and measured by a 30 psi Marsh steam pressure gauge. The condensate produced by a downward passage of the steam through the t e s t exchanger i s removed by a Clark No. 60 steam trap located at the base of the heat exchanger. The steam and generated condensate from the c o i l are d i r e c t l y discarded into the drain. 3.4 Tube Material and Geometry On the basis of geometry, the tubes used can be divided into two groups: finned and p l a i n . The 1.5 meter mild steel finned tube having twelve longitudinal f i n s welded to i t s outside surface area, i s supplied by Bas-Tex Corporation (Figure 3-3). Figure 3-4a and Figure 3-4b show horizontal and v e r t i c a l cross-sections of a finned tube. The three d i f f e r e n t 1.5 meter long p l a i n tubes used can be categorized into two groups: f i r s t , the non-corroding stainless steel and copper tubes, and second, the corroding mild steel tube. The properties and geometries of the tubes are summarized and l i s t e d in Table 3-1. Both in case of the p l a i n tubes and the finned tube, the length of the tube in contact with the working f l u i d was 1.33 meters. In either 2 situation, the nominal area - outside diameter (0.0796 m ) i s used to express the heat transfer performance. Use of the nominal area allows a di r e c t measure and comparison of the results i f the finned tube replaces the p l a i n one. Figure 3-3. SKETCH OF A TWELVE LONGITUDINALLY FINNED TUBE Figure 3-4. HORIZONTAL (a) AND VERTICAL (b) CROSS SECTIONS OF A FINNED TUBE Table 3-1. SUMMARY OF THE PROPERTIES OF TUBES Tube Material O.D. I.D. Properties of Fins De Net Free Area x 10 4 (m2) No. (mm) (mm) No. Length Height (m) (mm) Width (mm) (m) 1 S.S. 19.1 15.9 - - - 0.01 791 7.9128 2 Cop 19.1 15.3 - - - 0.01791 7.9128 3 M.S. 19.1 13.3 - - - 0.01 791 7.9128 4 M.S. 19.1 14.7 12 1.2 6 0.5 0.00869 6.9528 S.S. = stainless steel Cop = copper M.S. = mild steel - 67 -3.5 Temperature Measurements Hard water and steam t e m p e r a t u r e s are measured u s i n g i r o n - c o n s t a n t a n t h e r m o c o u p l e s . The temperature o f t h e hot stream i s measured a t t h e i n l e t and o u t l e t o f t h e t u b e . O t h e r t h e r m o c o u p l e s t o measure t h e temperature o f the t e s t f l u i d a re l o c a t e d a t t h e f e e d t a n k e x i t , a t t h e i n l e t and o u t l e t o f the s h e l l and a t t h e e x i t o f t h e h e l i c a l heat exchanger. The t h e r m o c o u p l e s a r e c o n n e c t e d to a s w i t c h , which i s i n t u r n c o n n e c t e d t o t h e F l u k e Model 2240A d a t a l o g g e r ( F i g u r e 3-5). The d a t a l o g g e r measures t h e v o l t a g e w i t h t h e t h e r m o c o u p l e s o u t p u t r e f e r e n c e d to 0°C by p l a c i n g t h e i r c o l d j u n c t i o n s i n an i c e bath ( F i g u r e 3-6). Thermocouples were c a l i b r a t e d u s i n g a H e w l e t t P a c k a r d model 2801A q u a r t z thermometer. eSwitch = ( \ Datalogger CM CO Thermocouple Hot junction Figure 3-5. CIRCUIT DIAGRAM FOR DATALOGGER CONNECTION - 69 -Figure 3-6. PHOTOGRAPH OF APPARATUS FROM THE FRONT - 70 -4. EXPERIMENTAL PROCEDURES 4.1 General Approach A r t i f i c i a l l y hardened water was prepared by adding Ca(N0 3) 2 . 4H20 or C a C l 2 . 2H20 and NaHC03 to 210 l i t e r s of water. To avoid corrosion on mild steel by chloride ion, calcium ni t r a t e was used as a source of calcium. Nitrogen gas was introduced into the water to remove the dissolved oxygen in the supply tank. When s u f f i c i e n t nitrogen had bubbled through the water, the nitrogen gas flow rate was measurably reduced and diverted only to maintain a nitrogen atmosphere above the l i q u i d i n the tank, to prevent further introduction of oxygen into the test f l u i d during the run. It i s important to have both steady temperatures and heat flow. These were to be achieved by keeping the temperature of water entering and leaving the exchanger constant. Where the i n l e t temperature could not be held constant due to l i m i t s on the cooling water temperature and flow rate, the temperature r i s e of the water in the exchanger was nevertheless kept as constant as possible. After being assured, by taking several temperature readings, that the steady state condition was reached, C a C l 2 . 2H20 or Ca(N0 3) 2 . 4H"20 was added. Two or three minutes l a t e r , NaHC03 was added. The f i r s t water sample was taken, allowing time f o r complete mixing to occur i n the tank. The sample was f i l t e r e d using a Gelman magnetic f i l t e r funnel equipped with a - 71 -Whatman GF/B glass microfiber f i l t e r which removes p a r t i c l e s down to 1 micron in s i z e . Several water samples were taken during each run, approximately 8-12 hours apart, and more chemicals were added to keep the water quality constant. It should be mentioned that the addition of chemicals was done during the run with higher concentration of chemicals since the water quality did not vary to a great extent during runs at lower concentration. The i n - l i n e f i l t e r i n the recycle l i n e was used to remove excessive amounts of suspended s o l i d s . However, f o r runs at lower concentration of chemicals, the d i r e c t recycle l i n e was used because the suspended s o l i d s concentrations were ne g l i g i b l e . 4.2 Solution Preparation For the low concentration early runs, 97.35 gr of CaCl 2 • 2H20 and 64.58 gr of NaHCO^ were used to provide an a r t i f i c i a l l y hardened water with the i n i t i a l concentration o f 0.126 g of C a + + and 0.084 g/1 of Na +. In l a t e r runs, Ca(N0 3) 2 . 4H20 was used as a source of calcium to reduce corrosion a r i s i n g from the chloride ion. Since the deposit obtained using the above-mentioned concentrations of chemicals was muddy, the amount of substances was increased by a factor of 2.2 (0.00694 mole/liter of C a + + and 0.00805 mol e / l i t e r of Na +) i n order to get a harder and better constructed scale. In either case, the chemicals were separately dissolved in the water before addition to the supply tank. - 72 -4.3 pH Measurements pH i s measured using an Orion Research D i g i t a l Ionalyzer/501. pH 4.01 + 0.01 (at 25°C) and pH 8.00 + 0.02 (at 25°C) buffer solutions are used to c a l i b r a t e the pH meter. 4.4 A l k a l i n i t y Measurements Total a l k a l i n i t y (T.A.) i s measured by t i t r a t i o n using a bromocresol green-methyl red mixed indicator which i s more suitable f o r a l k a l i n i t i e s below 500 mg/l. Na2S 20 3 i s used as an i n h i b i t o r f o r the removal of residual chlorine that would otherwise impair the indi c a t o r colour changes. 0.2 N HC1 i s used as a t i t r a n t and the end point i s both determined by the indicator color change and by a pH meter (55). 1 drop of Na2S203 and 3 drops of the mixed indicator are added to 50 ml of sample. The blue sample i s t i t r a t e d with 0.02 N HC1 to the appearance of a l i g h t pink which occurs at pH 4.5. Total a l k a l i n i t y i s then calculated using the following formula: Total A l k a l i n i t y = B' x N y* 5 0 0 0 0 where B' = volume of the t i t r a n t (ml) N = normality o f t i t r a n t v' = volume of the sample (ml) - 73 -4.5 Hardness Measurements Hardness i s determined by a complexometery method using Erichrome Black T as an indicator. The presence of magnesium i s required f o r satisfactory determination of the end point in the t i t r a t i o n . Both the sharpness of the end point and the tendency of CaC0 3 and Mg(0H) 2 to precipitate increase with increasing pH; therefore, the pH value of 10.0 + 0.01 i s recommended as a satisfactory compromise. A buffer solution i s prepared by mixing 55 ml concentrated HC1 with 400 ml d i s t i l l e d water, adding 310 ml 2-amino ethanol and 5 g magnesium s a l t of EDTA and d i l u t i n g the whole mixture to 1 l i t r e with d i s t i l l e d water (56). To prevent the i n t e r f e r i n g e f f e c t of some metal ions which cause an i n d i s t i n c t end point, a mixture of 4.5 gr hydroxylamine hydrochloride in 100 ml of 95 percent ethyl-alcohol i s used as an i n h i b i t o r . A solution of 0.01 M disodium ethylenediamine tetraacetate dihydrate (EDTA) i s used as a t i t r a n t . To carry out the t i t r a t i o n , 1 ml of the buffer, 1 ml of the i n h i b i t o r and 2 drops of the indicator are added to 25 ml of sample which i s already diluted to 50 ml. 0.01 M solution of EDTA i s added to the reddish sample until the disappearance of the l a s t reddish tinge. Duration of t i t r a t i o n should not exceed 5 min in order to prevent p r e c i p i t a t i o n of CaC03 at higher pH values. Using the following formula, the hardness (Ca +) can be determined: - 74 -where A' = volume of the t i t r a n t (ml) B " = mg of CaC0 3 equivalent to 1 ml of EDTA v' = volume of the sample (ml) 4.6 Determination of Total Dissolved Solids Since there i s not a high quantity of dissolved solids i n the tap water, i t can be treated as d i s t i l l e d water regarding c a l c u l a t i o n of tota l dissolved solids (TDS). If solutions of x mole/liter of NaHC03 and y mol e / l i t e r of Ca(N03)2 were brought together, the following basic reactions would take place (assuming -| < y < x which i s applicable i n t h i s experiment: x NaHC03 xHC0 3 + xNa + yCa(N0 3) 2 — yCa + + 2yN0 3 xHCD3 £ C0 2 + £ CD 3 + £ H20 |C0 3 + yCa + ; — C a C 0 3 + (y-|) Ca + 2yN03 + xNa -—- xNaN03 + (2y-x) NQ3 (2y-x) NO" + (y-£) C a + -r-*- (y~£) Ca(N0 3) 2 Therefore, summation of the above chemical reactions y i e l d s : xNaHC03 + yCa(N0 3) »- | CaC0 3 + x NaN03 + (y-£)Ca(N0 3) 2 + £ C0 2 + | H 20 - 75 -Thus, following the assumption that the tap water i s treated as d i s t i l l e d water: Total A l k a l i n i t y (mole/liter) = | CaC0 3 Hardness (mole/liter) = (y-£) Ca ( N 0 3 ) 2 + £ CaC0 3 TDS (mole/liter) = \ CaC0 3 + x NaN03 + (y-£) Ca ( N 0 3 ) 2 Therefore, a l l the above-mentioned quantities can be rewritten i n terms of mg/l i t e r of CaC0 3: T.A. = 10 5 | C+a+ = 10 5y C a + - T.A. = 10 5(y-|) TDS = 10 5(x+y) Also, TDS can be evaluated i n terms of tota l weight of solids per volume (mg/l): TDS = (10 5 |) + (85000x) + (164) ( C a 1 Q" T , A- ) TDS = T.A. + 1.7 T.A. + 1.64 (Ca + - T.A.) = 1.06 T.A. + 1.64 Ca + - 76 -Procedure For a Scaling Run (1) I n s t a l l one of the clean test sections in the tube and shell heat exchanger. Connect i t , from the top, to the steam l i n e and, from the bottom, to the steam trap. Insulate the t e s t heat exchanger. (2) F i l l the supply tank to 210 l i t e r l i n e with the tap water. Connect the tap water hose to the cooling water l i n e . (3) Put the cold junctions of the thermocouples i n the thermos bottle already f i l l e d with the ice/water mixture. (4) Turn on the datalogger. Set the time and program the format of a scan sequence. Program the datalogger to give the output in m i l l i v o l t s . (5) Turn on the pump and set the r e c i r c u l a t i n g water flow rate at a desired value. (6) Introduce the nitrogen gas by turning the control valve open. (7) Follow the solution preparation procedure. (8) Reduce the nitrogen gas flow and divert i t from the water to the top of the tank. - 77 -(9) Turn on the steam into the heating c o i l located inside the supply tank. (10) Cut o f f the steam to the tank after reaching the desired operating temperature (25°C f o r most of the runs). (11) Turn the steam on the exchanger at 115.15 kPa absolute pressure (used f o r almost a l l of the runs). (12) Set the cooling water flow rate. (13) Calculate the heat flux by measuring the i n l e t and o u t l e t temperatures of hot and cold streams passing through the test heat exchanger. (14) A f t e r taking several readings and having the steady heat flow rates, add C a C l 2 . 2H20 or Ca(N0 3) 2 . 4H20 (as required) solution. Wait f o r 2-3 minutes until the chemical i s completely mixed, then add NaHCOg solution and note the time. The chemicals are added using a p l a s t i c funnel passing through the hole i n the center of the wooden l i d of the tank. (15) When the mixing process i s judged to be complete (approximately a f t e r 5 minutes), record both the temperature measurements and steam pressure and take the water sample using the side o u t l e t of the supply tank. Register the time. - 78 -(16) Take the temperature readings every 10 minutes during the f i r s t hour and every 30 minutes for the rest of the run. Record the steam pressure as often as possible. (17) Try to keep the exchanger at a steady heat flow by c o n t r o l l i n g both the steam pressure (which r i s e s as the tube scales) and cooling water flow rate. (18) Since the r e c i r c u l a t i n g water flow rate i s not automatically controlled, control i t manually to have a steady water flow rate. (19) Take a water sample every 8-12 hours and determine the water quality following the pH, total a l k a l i n i t y and hardness measurements after f i l t r a t i o n of the water sample through a Whatman GF/B glass microfibre f i l t e r . (20) When there i s a s i g n i f i c a n t change in to t a l a l k a l i n i t y and hardness during the two successive samplings, which usually occurred f o r the runs with higher concentrations of chemicals, addition of more chemicals i s made to keep the water quality e s s e n t i a l l y constant. Assuming that the deposit i s made purely out of CaCOo, the change in both tota l a l k a l i n i t y and - 79 -hardness should be exactly the same (see determination of TDS). Considering the above assumption, the addition process i s car r i e d out according to the following relationships: 2 1 0 1 M C a ( N 0 J 9 . 4H?0 weight of C a ( N 0 J 9 . 4rU0 added gr = £-= =-10 4 2 0 1 MNaHC0 3 weight of NaHCO^ added gas (gr) = P * HT where: Z = the change in a l k a l i n i t y or hardness (the average of the two i n case they are d i f f e r e n t due to experimental e r r o r s ) . (21) Take water samples after addition of make up chemicals and re-evaluate water quality. (22) Calculate the heat flux, the overa l l heat transfer c o e f f i c i e n t and the fouling resistance f o r each reading. (23) After a period of 70 hrs, where there i s not a big change in the fouling resistance for several hours, stop the run. (24) Cut o f f the steam to the tube. Turn o f f the valve to the main steam l i n e and purge the l i n e by turning on the steam valve to the steam heating c o i l . - 80 -(25) Turn o f f the pump, tap water and datalogger. Drain the supply tank through both bottom and side e x i t s . Let the system cool down. Remove the tube from the heat exchanger. Examine the tube's deposit f o r hardness. Measure the thickness of the deposit at several places throughout the length of the tube. Scrape or crack o f f the scale and c o l l e c t i t f o r comparison with the results of other runs. (26) Measure the outside diameter of the bare tube to see i f there has been any change due to corrosion. 4.8 Cleaning The tubes were used several times; therefore, t h e i r outside surface areas required cleaning after each run. I n i t i a l l y , a f t e r removing the tube from the exchanger and scraping o f f the heavier deposit, the tube was replaced in the exchanger and the water containing about 2400 ppm of Oakite 31 (containing phosphoric acid and biodegradable surfactants) was pumped around the system f o r a couple o f hours to remove CaCO^ deposits both on the tube and in the rest of the equipment. Since the s o l u b i l i t y o f CaCO^ in oakite solution increases with increasing temperature, the solution was heated up by turning on the steam to the heating c o i l located in the supply tank. Then the pump was stopped and the cleaning solution was drained out of the system. To remove any oakite from the equipment, pure water was pumped throughout the system f o r - 81 -30 minutes and then drained out v i a the supply tank. This action was repeated 3 to 4 times to clean the tube and the rest of the equipment from any residual oakite. This cleaning procedure was not satisfactory f o r two reasons. F i r s t l y , i t was not possible to clean the tubes well. Secondly, the procedure enhanced the corrosion of mild steel tubes. One alternative was to clean the tubes by hand. F i r s t , the majority of scale was removed by a mild steel wire brush, then remaining deposits were removed by steel wool and emery clo t h . However, t h i s manual cleaning was neither time nor labor e f f i c i e n t and, most importantly, f a i l e d to remove a l l the scale. A second alternative was to remove the deposits by a 20% solution of in h i b i t e d hydrochloric acid. P i c k l i n g i n h i b i t o r , Rodene, was added at concentrations of 0.1% by volume to prevent the corrosive e f f e c t of the acid. The tubes were chemically cleaned under the batch condition using a 120 cm high glass column having an inside diameter of 5 cm. The cleaning procedure was completed using an emery c l o t h . However, a mixture of oakite solution was pumped around the system to clean the rest of the equipment. In t h i s case, two metal rods having the same outside diameter as the tubes were used to block the i n l e t and o u t l e t of the hot stream in the exchanger. As mentioned above, the residual oakite was removed by r e c i r c u l a t i n g pure water. - 82 -5. RESULTS AND DISCUSSION 5.1 General Outlook 5.1.1 Low Concentration Runs Tests were f i r s t done on the stainless steel and copper tubes with ++ + i n i t i a l concentration of Ca = 0.126 g/1 and Na = 0.084 g/1, using CaCl 2 . 2H20 and NaHC03 as sources of calcium and carbonate, respectively. These are termed "low concentration runs". As the i n i t i a l operating condition, the steam was conducted to the tube at 115.15 kPa absolute pressure, after heating up the tank water temperature to 25°C (see Section 4.7). The entrance and e x i t temperatures of both the hot and the cold streams were recorded and used f o r c a l c u l a t i o n of heat flow, q, and overall heat transfer c o e f f i c i e n t , U (see Appendix I I ) . Having obtained the steady state condition with water only, the chemicals were then added. This was followed by subsequent measurement of water quality and c a l c u l a t i o n of q and U. As time passed and the tube scaled, the ove r a l l heat transfer c o e f f i c i e n t dropped and the steam pressure was raised to supply a constant heat flow. The magnitude of the fouling resistance, R^ , was determined by intermittent measurement of U and hence the change in the tota l resistance of the exchanger with respect to time. The e f f e c t of scaling on the water quality was followed using a l k a l i n i t y , hardness and pH measurements. Since - 83 -the i n - l i n e f i l t e r was not used f o r these runs, the suspended solids content of the water sample was determined using the Whatman GF/B glass microfiber f i l t e r to investigate the extent of the bulk p r e c i p i t a t i o n process. Figure 5-1, corresponding to the copper tube at annular flow velocity of 0.503 m/s, shows a typical output f o r a run at low concentration of chemicals. At constant heat flux value of 14.1 kW, the over a l l heat 2 transfer c o e f f i c i e n t decreased with the time, reaching 2.09 kW/m K a f t e r 70 hrs., which corresponded to an 18.4% drop i n U from the clean condition (2.56 kW/rA). As i s evident from t h i s figure, the fou l i n g process was accompanied by a drop both in total a l k a l i n i t y and the hardness. The reductions in the magnitude of these parameters f o r the subsequent water samples were not high enough to require the addition of more chemicals. After 70 hrs., the changes i n the magnitude of total a l k a l i n i t y and hardness were respectively 61 and 63 mg CaCO^/l. Considering the experimental errors, these values were close enough to deduce that the deposits were e s s e n t i a l l y pure CaCO^ (see Section 4.6). The suspended s o l i d s content o f the water f i r s t increased with time and reached a maximum of 3.6 ppm after 24 hours. This suggests that some p r e c i p i t a t i o n occurred both i n the bulk and in the hot f i l m adjacent to the interface. The s l i g h t reduction in the suspended solids content in the l a t t e r part of the run indicates the possible existence of a small extent of parti c u l a t e fouling. X E a. a. cn; a) E 10 O U o o + + o u cn E 10 O O o o a25 7.7 5 3_ 3^ 300 j 280 260 240 I75P 155 135 I 15 2.6 j CVJ E o 3 24 2.2 2.0 10 -a 1 Q-18.3 4 RUN 5 " a — r 1 20 30 40 Time (hrs) 50 60 TI g-ao a H 70 Figure 5-1, RUN 5 TYPICAL OUTPUT - 85 -Each tube was studied under three d i f f e r e n t annular flow v e l o c i t i e s ranging from 0.29 m/s to 0.7 m/s. The results are l i s t e d in Table 5-1. Since heat flow increases with annular mass flow rate, both the heat flow rate and the ove r a l l heat transfer c o e f f i c i e n t of a clean tube increased with increasing v e l o c i t y , as i s shown i n the table. Comparing the non-corroding tubes under approximately identical operating conditions, the st a i n l e s s steel tube has both lower heat flux and lower clean overall heat transfer c o e f f i c i e n t than does the copper tube. This was understandable considering the lower value of unit thermal conductance f o r the stainless steel than f o r the copper. Regarding the d i r t y heat transfer c o e f f i c i e n t , the advantage of the copper tube over the stainless steel one was also evident through the experimental results. The only i r r e g u l a r i t y occurred f o r the stainless steel tube at annular velocity of 0.503 m/s (Run 3) in which there was no change either in the magnitudes of water quality parameters or i n the o v e r a l l heat transfer c o e f f i c i e n t with the passage of time due to an unknown reason. For either tube, the scale thickness on the d i r t y surface decreased with distance from the steam entrance. The deposits could not be cracked o f f . Hence, they were taken out p a r t l y by scraping o f f with a spatula, resulting in a rusty coloured powdery residue. The remainder was removed by chemical cleaning. 5.1.2 High Concentration Runs Tests were carr i e d out on both the p l a i n and the finned mild steel tubes under the above-mentioned operating conditions using low concentrations Table 5-1. SUMMARY OF RESULTS FOR RUNS AT LOW CONCENTRATIONS OF CHEMICALS Stainless Steel Copper v (m/s) T.A. Ca++* U (kW/m2*) T.A.* Ca*+* U ( k W / o A ) Run q pH a v e Run q p H a v e  ( k W ) ( k W ) Start End Start End Start End I Drop S t a r t End Start End Start End % Drop 1A 168 285 7.84 1.16 1 5.3 6A 129 250 7.61 1.74 22.7 0.299 7.9 188 305 1.37 11.5 177 298 2.25 1 148 270 7.86 1.16 15.3 6 105 228 7.60 1.69 24.9 3A 175 302 7.89 1.68 0.0 5A 140 260 8.11 2.17 15.2 0.503 10.4 182 310 1.68 14.1 176 298 2.56 3 175 302 7.93 1.68 0.0 5 115 235 8.11 2.09 18.4 2A 158 280 7.92 1.83 9.9 4A 151 274 8.03 2.73 17.0 0.695 11.5 182 302 2.03 18.0 170 294 3.29 2 125 247 7.95 1.73 14.8 2.55** 22.5** 00 T.A. = t o t a l a l k a l i n i t y Ca** » hardness * Units In mg CaC0 3/l ** Values determined by extrapolation A • runs lasted 48 hours - 87 -o f chemicals. The plots of the o v e r a l l heat transfer c o e f f i c i e n t versus time showed e r r a t i c behaviour especially at higher flow rates (above 2.33 x -4 3 10 m / s ) . The high v e l o c i t y runs resulted in a drop of the overall heat transfer c o e f f i c i e n t during approximately the f i r s t ten hours of the experiment followed by a subsequent r i s e i n the magnitude of the c o e f f i c i e n t even though there was a continuous reduction i n the values of the tot a l a l k a l i n i t y and the hardness throughout the run. A t y p i c a l example for such a run i s shown i n Figure 5-2. The corroding e f f e c t of the mild steel tube was considered to be the major factor responsible f o r t h i s behaviour especially i n the case of the p l a i n tube. Therefore, nitrogen gas was introduced to blanket the l i q u i d in the tank and CafNC^^ . 4^0 replaced CaC^ • 2^0 as the source of calcium to eliminate the corrosive e f f e c t of dissolved oxygen and chloride ion, respectively. The r i s e in the value of o v e r a l l heat transfer c o e f f i c i e n t could be due to the low concentration o f chemicals which might prevent the complete adherence of the scale to the mild steel surface and enhance the p r o b a b i l i t y of removal mechanism at high v e l o c i t i e s o r to roughness e f f e c t s which would be of considerable importance with thin scales. Thus, the concentration of chemicals were raised by a factor of 2.2 to get a more pronounced result since the main objective was the determination of the fouling resistance and i t s variation with the time. These runs are designated "high concentration runs". With the increase in amount of scale deposited, the changes in the magnitude of the total a l k a l i n i t y and hardness f o r two subsequent water samples taken during the run were high enough to require the intermittent addition of make up chemicals to keep the water quality as constant as possible (see Section 4.7). In X Q. 8.3 7.9 e CL 3 7.0 tn to • TT RUN 16 3.C E ^ 300 o 2 280 + + u 260 • • • • 3 • • • • ^1 70 O <^I50 o I 30 ID • • • • E 1.8 1.6 U CD ccP, => 1.4 1 0 10 20 30 40 Time (hrs) 50 60 7 0 Figure 5-2. RUN 16 TYPICAL OUTPUT - 89 -addition, the i n - l i n e f i l t e r was used to eliminate the i n t e r f e r i n g e f f e c t of the suspended s o l i d s i n the bulk. The i n i t i a l absolute steam pressure was 115.15 kPa f o r a l l high concentration runs except f o r Runs 21 and 22 (P=129 kPa). The i n i t i a l tank water temperature was also uniform f o r a l l runs except f o r Run 22 (T=30°C). A ty p i c a l output f o r a high concentration run i s shown in Figure 5-3. At 0.299 m/s annular velocity, as the tube fouled, the overall heat transfer c o e f f i c i e n t of the p l a i n mild steel tube decreased approximately from 1.45 kW/m2K to 1.25 kW/m2K (13.8%) after 70 hours. Figure 5-3 also represents a rapid decrease i n the magnitudes of total a l k a l i n i t y and hardness during the f i r s t four hours (about 20 mg/1 of CaCO-j per hour) followed by a slower one (about 4.5 mg/1 o f CaCO^ per hour). Five d i f f e r e n t annular flow v e l o c i t i e s , ranging from 0.29 m/s to 0.8 m/s (2.33 x 10" 4 to 5.50 x 10~ 4 m 3/s), were used to investigate the e f f e c t o f velocity on the fouling process of the mild steel tubes. The copper tube was also tested under high concentration of chemicals at three d i f f e r e n t annular water flow rates in the above-mentioned region. Table 5-2 summarizes the results of the high concentration runs. The data i n the table indicate an increase i n the overall heat transfer c o e f f i c i e n t with the velocit y f o r ei t h e r tube. Under id e n t i c a l operating conditions, the rate of heat transfer and the clean and the d i r t y heat transfer c o e f f i c i e n t s were higher f o r the copper tube than the p l a i n mild steel one. In the case of mild steel tubes, the finned tube had a higher heat flow rate than the p l a i n one. The reasons f o r the advantage of the copper and the finned mild steel 10 20 30 40 50 60 70 Time (hrs) Figure 5-3. RUN 24 TYPICAL OUTPUT Table 5-2. SUIMARV QF RESULTS FOR RUNS AT HIGH CONCENTRATION OF CHEMICALS Finned HI Id steel Plain Mild steel Capper Vol. Flo. Rate i 10s (•3/«l Run q T.A.* Ca"* PH "o Run o. T.A.' pH U„ tkU/aA) Run i T.A.* Ca"* PH Ho UU) ave ave aw Start End I Drop UN) ave ave ave Start End I Drop IkUl am ave ave Start End I Drop 23.67 27 30 9.8 10.1 371 365 661 650 7.64 7.S4 1.61 1.69 1.54 1.45 4.3 14.2 24 8.4 415 697 7.78 1.45 1.25 13.8 38 9.9 361 659 7.69 1.70 1.48 12.9 32.00 28 11.3 347 633 7.60 2.00 1.78 11.0 29 9.1 351 639 778 1.58 1.32 16.5 39.83 26 12.7 361 648 7.S8 2.24 2.02 9.8 23 33 11.2 9.4 3S8 353 644 640 7.68 7.93 1.84 1.63 1.43 1.48 22.3 9.2 37 12.5 346 642 7.81 2.28 1.80 21.1 47.50 31 13.85 340 626 7.64 2.32 2.10 9.5 25 10.9 356 651 7.45 1.90 1.63 14.2 55.00 32 15.45 318 603 7.68 2.70 2.15 19.6 20 21 22 11.9 13.5 12.0 351 360 348 700 641 639 7.74 7.72 7.63 2.02 2.50 2.18 1.80 2.15 1.85 10.9 14.0 15.1 36 13.4 320 619 7.79 2.4 1.80 25.0 T.A. • total alkalinity Ca** • hardness • Units In »g UCO3/I (1 values based on nominal (bare-tube) outside area. Plain annular cross sectional area • 79.128 * IO-5 o2 Finned annular cross sectional area - 69.528 < IO"6 •? - 92 -tubes over the p l a i n mild steel tube are the higher unit thermal conductance of the metal i n case of the former and the extended surface area i n case of the l a t t e r . The over a l l heat transfer c o e f f i c i e n t of the finned mild steel tube, based on the outside nominal (bare-tube) area (Appendix 11.2), was also shown to be larger than the p l a i n tube c o e f f i c i e n t e i t h e r before or after fouling. The experimentally determined ratio of the clean overall heat transfer of the finned tube to that of the p l a i n tube (Table 5-2) was about 1.25. I f the f i n s were 100% e f f i c i e n t , f o r tubes of the same wall thickness, one would expect the value of t h i s r a t i o to be approximately 3. However, the wall thickness i n the finned tube i s less than that f o r the p l a i n tube and the f i n e f f i c i e n c y and the to t a l surface e f f i c i e n c y of the surface are 33% and 53%, respectively. Therefore, the expected r e s u l t would be i n a close agreement with the experimental value of t h i s ratio (1.25). The value of t h i s ratio was s l i g h t l y higher (1.3) based on the d i r t y overall heat transfer c o e f f i c i e n t s (Table 5-2). The thickness of the deposits formed during the high concentration runs increased with distance from the water entrance. In the case o f the finned tube, the deposits were mostly formed on the prime surface. The formation of the deposits on the f i n s was not uniform and the thickness of the scale decreased with distance from the base of the f i n s . Both the yellow shiny deposits formed on the copper tube and the gray ones on the pl a i n mild steel tube were hard and b r i t t l e , and could be cracked o f f e a s i l y . However, the deposits on the finned mild steel tube had to be scraped o f f with a spatula, providing a l i g h t grayish powder. The photographs of the three disassembled d i r t y copper, p l a i n and finned mild steel tubes are shown i n Figures 5-4, 5-5, and 5-6. - 93 -- 94 -Figure 5-5. PHOTOGRAPH OF DISASSEMBLED FOULED PLAIN MILD STEEL TUBE - 95 -Figure 5 - 6 . PHOTOGRAPH OF DISASSEMBLED FOULED FINNED MILD STEEL TUBE - 96 -5.2 E f f e c t of Reynolds Number on Overall Heat Transfer C o e f f i c i e n t 5.2.1 Copper and Stainless Steel Tubes The test heat exchanger tubes were examined under three d i f f e r e n t annular flow v e l o c i t i e s and the clean and the d i r t y heat transfer c o e f f i c i e n t s after 48 hours and 70 hours were determined i n each case. Water quality parameters and operating conditions f o r each run are summarized i n Tables 5-3 and 5-4. The hot and cold stream temperatures and the factors representing the chemistry of water were a l l averaged throughout a run. The wall temperatures were calculated using the heat flow rates and the average steam temperatures (see Appendix II.6). Figure 5-7 represents the change i n both the clean and the d i r t y overall heat transfer c o e f f i c i e n t s with respect to the Reynolds number based on the f i l m temperature and hence the velocity. The po s i t i v e e f f e c t of Reynolds number on the value of the overall heat transfer c o e f f i c i e n t i s evident from the graphs. In e i t h e r clean or d i r t y conditions, the over a l l heat transfer c o e f f i c i e n t was higher f o r the copper tube than the corresponding one f o r the stainless steel tube. However, the percentage of drop, over the same length of time, in the value of U was higher f o r the copper tube than f o r the stainless steel one. This might have been due to both the smoothness of the stainless steel tube which weakens the adherence of the scale to the surface and the higher bulk and wall temperatures i n the case of the copper tube (Tables 5-3 and 5-4). - 97 -CVJ E C V o 3 E T3 C a> o CVJ E r 2 o in o 8 1 — i — I — r H 1 r 6A o IA V I I I i — r 'o "I 1 1 1 r 5A o 3A V -\ I h Copper O S.S. V 2A V 12 16 20 24 R e f i l m X l ° -3 4 A O 28 Fiaure 5-7. EFFECT OF REYNOLDS NUMBER OM CLEAN AND DIRTY OVERALL HEAT TRANSFER COEFFICIENTS OF COPPER AND STAINLESS STEEL TUBES Table 5-3. SUMMARY OF RESULTS FOR THE STAINLESS STEEL TUBE Vol. Flow Rate x l O ' 5 (m 3/s) Run (m/s) Re b R e f l l r a T.A. ave CA+** ave TDS ave (mg/l) pH ave ave CO ave CO ave CO (kU) U 0 (kW/ra2K) Start End I Drop Rf (ra2K/kU) 23.67 1A 0.299 6271 11136 11194 181 173 298 290 681 659 7.84 7.86 23.0 106.09 95.43 106.80 96.14 7.9 1.37 1.16 15.3 1.16 15.3 0.140 0.140 39.83 3A 3 0.503 10554 18576 18599 177 177 304 304 686 686 7.89 7.93 27.3 103.95 89.91 104.12 90.08 10.4 1.68 1.68 0.0 1.68 0.0 0.000 0.000 55.00 2A 2 0.695 14573 24984 25261 173 161.4 294 283 666 635 7.92 7.95 27.0 102.18 86.66 103.66 88.14 11.5 2.03 1.83 9.9 1.73 14.8 0.052 0.085 T.A. = total a l k a l i n i t y Ca** = hardness TOS » total dissolved solids * Units In mg C a O j y i Table 5-4. SUMMARY OF THE RESULTS FOR THE COPPER TUBE AT LOW CONCENTRATIONS OF CHENICALS Vol. Flow Rate x l O " 5 (m3/s) Run (m/s) R«b R ef11m T.A.* ave CA + +* ave TDS ave (mg/l) pH ave Tb ave CC) Ts ave CC) ave C O (kW) U 0 (kW/m2K) Start End % Drop Rf (m2K/kU) 23.67 6A 6 0.299 6829 12921 12987 154 141 275 262 641 579 7.61 7.60 31.0 109.81 109.01 110.60 109.80 11.5 2.25 1.74 22.7 0.130 1.69 24.9 0.147 39.83 5A 5 0.503 11494 21170 21397 162 150 281 269 633 600 8.11 8.11 30.6 106.42 105.43 107.83 106.84 14.1 2.56 2.17 15.2 2.09 18.4 0.070 0.088 55.00 4A 4 0.695 15870 29506 169 294 661 8.03 31.8 106.80 105.54 18.0 3.29 2.73 17.0 2.55 22.5 0.062 0.088 T.A. = total a l k a l i n i t y Ca +* = hardness TDS = total dissolved solids * Units i n mg CaC0 3/l - 100 -5.2.2 Copper and Plain Mild Steel Tubes The copper tube was tested under high concentrations of chemicals and three d i f f e r e n t flow v e l o c i t i e s to make the comparison between the non-corroding and the corroding (plain mild steel) tubes possible. The summary of results, representing the average water quality, the operating conditions, and the overall heat transfer c o e f f i c i e n t s , are given i n Tables 5-5 and 5-6. As i s shown i n Figure 5-8, the clean o v e r a l l heat transfer c o e f f i c i e n t has a greater value f o r the copper tube than f o r the mild steel tube, and both c o e f f i c i e n t s rose with increasing Reynolds number. However, in the case of the copper tube at high values of the Reynolds number, the po s i t i v e e f f e c t of Reynolds number on the c o e f f i c i e n t decreased f o r the clean condition and vanished f o r the d i r t y one. The r e s u l t was a higher percentage drop i n U at higher v e l o c i t i e s . An increase in the d i r t y c o e f f i c i e n t of the mild steel tube with the Reynolds number was observed, though no s p e c i f i c trend was found considering the percentage of the drop i n the c o e f f i c i e n t . The d i r t y c o e f f i c i e n t of the copper tube was higher than that of the mild steel tube at lower Reynolds numbers. Runs 23 and 33 (Table 5-6) both correspond to the mild steel tube at 0.503 m/s annular flow v e l o c i t y . The clean c o e f f i c i e n t f o r Run 23 was much higher than the one f o r Run 33 due to the higher steam temperature. However, they both had close values o f d i r t y c o e f f i c i e n t s , presumably as a result of a greater wall temperature i n the case of the former. Run 20 was - 101 -CM E C V o E \ -St: CO o ID 2.5 2.0 24 1.0 3.0 2.5 2.0 1.5, i — i — i — i — i — i — i — i — r 38 • 24 O M i l d steel • Copper 37 • 21 O P=l29kPo T » 2 5 ° C 2? 20 o 361 ° P=l29kPa T T« 30°C 2 9 o 3 J 2 3 3 ^—I—hH—i—i i i 21 O 36 37 • 25 23 o 22 O 20 O 29 O 33 €> J I I I 1 I I I I 16 20 24 28 32 R e f i . m * 1 0 ' 3 Figure 5-8. EFFECT OF REYNOLDS NUMBER ON CLEAN AND DIRTY OVERALL HEAT TRANSFER COEFFICIENTS OF COPPER AND PLAIN MILD STEEL TUBES Table 5-5. RESULTS FOR THE COPPER TUUE AT HIGH CONCENTRATION OF CHEMICALS Vol. Flow Rate x IO" 5 (u.3/s) Run (ra/s) Re 0 Refiim T.A.* ave CA++* ave TDS ave pH ave ave Ts ave ave q (kW/m2K) Rf (ra2K/kW) (mg/1) CO CO CC) (kU) Start End % Drop 23.67 38 0.299 6801 12938 361 659 1463 7.69 30.84 110.07 109.38 9.9 1.70 1.48 12.9 0.087 39.63 37 0.503 12101 22488 346 642 1420 7.81 33.29 112.81 111.94 12.5 2.28 1.80 21.1 0.117 55.00 36 0.695 17087 32072 320 619 1354 7.79 34.27 117.06 116.12 13.4 2.40 1.80 25.0 0.139 T.A. = total a l k a l i n i t y Ca +* = hardness TOS = total dissolved solids * Units in mg CaC0 3/l Table 5-6. SUMMARY OF RESULTS FOR THE PLAIN MILD STEEL TUBE Vol. Flow Rate x l O " 5 (m 3/s) Run (m/s) Re b R e f i l r a T.A.* ave CA+ +* ave TDS ave PH ave Tb ave ave Tw ave q "o (kW/ra2K) Rf (m2K/kU) (mg/l) CC) CC) C O (kW) Start End % Drop 23.67 24 0.299 6500 11952 415 697 1583 7.78 28.7 107.75 99.69 8.4 1.45 1.25 13.8 0.110 32.00 29 0.404 8777 16253 351 639 1420 7.78 28.63 109.34 100.60 9.1 1.58 1.32 16.5 0.125 39.83 23 33 0.503 10767 10831 21312 19394 358 353 644 640 1436 1424 7.68 7.93 27.92 28.21 119.77 103.99 109.02 94.97 11.2 9.4 1.84 1.63 1.43 1.48 22.3 9.2 0.156 0.062 47.50 25 0.600 12660 23078 356 651 1445 7.45 27.40 105.94 95.48 10.9 1.90 1.63 14.2 0.087 55.00 20 21 22 0.695 14592 14820 17180 26624 25770 29030 351 360 348 700 642 639 1520 1433 1417 7.74 7.72 7.63 27.00 27.75 34.50 106.78 103.06 111.91 95.36 90.10 100.39 11.9 13.5 12.0 2.02 2.50 2.18 1.80 2.15 1.85 10.9 14.0 15.1 0.061 0.065 0.082 o co T.A. = total a l k a l i n i t y C a + + = hardness TDS = total dissolved solids * Units In mg CaO>3/l - 104 -also repeated, resulting i n higher values of the clean c o e f f i c i e n t (Runs 21 and 22). In the case of Run 22, an increase in both inside and outside convective heat transfer c o e f f i c i e n t s due to higher i n i t i a l steam pressure and higher i n i t i a l tank water temperature, respectively, was responsible f o r the higher magnitude of the overall heat transfer c o e f f i c i e n t . However, in the case of Run 21, the r i s e i n the overall heat transfer c o e f f i c i e n t was inexplicable due to both the lower f i l m temperature and higher temperature difference (T - T ) of the hot stream (Table 5-6). ave ave Amongst these, Run 21 yielded the highest heat flow rate as the result of the greater magnitude of the temperature driving force. Increasing the i n i t i a l value of the steam temperature (Run 21) was accompanied by an increase in the percentage drop i n U which was further enhanced due to the simultaneous r i s e i n the i n i t i a l tank water temperature (Run 22). 5.2.3 Plain and Finned Mild Steel Tubes The operating conditions and the resu l t s of the tests done on the finned mild steel tube under f i v e d i f f e r e n t v e l o c i t i e s are given i n Table 5-7. Figure 5-9 and both Tables 5-6 and 5-7 show the po s i t i v e e f f e c t of velocity on both the clean and the d i r t y c o e f f i c i e n t s of the tubes. The higher value of the clean c o e f f i c i e n t due to the greater heat transfer area i n the case of the finned tube i s evident from the f i g u r e . The beneficial e f f e c t of the enhanced tube over the p l a i n tube remained v a l i d even after the fouling process. However, at Reynolds numbers approximately above Table 5-7. SUMMARY OF RESULTS FOR THE FINNED MILD STEEL TUBE Vol . Flow Rate x l O - 5 ( • 3 / S ) Run (a/s) Ret, Refllm T.A.* ave CA*** ave TDS ave pH ave T b ave Ts ave Tw ave q "o (kU/a2K) Rf (ng/1) CO CC) CC) (kU) Start End X Drop (lA/kU) 23.67 27 30 0.340 3844 3735 6917 6849 371 365 661 650 1477 1453 7.64 7.54 31.88 30.57 108.73 111.73 101.87 104.66 9.80 10.10 1.61 1.69 1.54 1.45 4.3 14.2 0.028 0.098 32.00 28 0.460 4946 8973 347 633 1406 7.60 29.61 107.43 99.52 11.30 2.00 1.78 11.0 0.062 39.83 26 0.573 6170 10904 361 648 1445 7.58 29.70 104.84 95.95 12.70 2.24 2.02 9.8 0.049 47.50 31 0.683 7716 13579 340 626 1387 7.64 31.89 109.74 100.05 13.85 2.32 2.10 9.5 0.045 55.00 32 0.791 9066 15882 318 603 1326 7.68 32.54 111.71 100.90 15.45 2.70 2.15 19.6 0.095 T.A. * total a lka l in i ty Ca** ' hardness TDS = total dissolved sol ids * Units in ag CaC03/1 - 106 -.5h l — i — i — r — i — i — i — i — i — i — i — r 26 A A , . 32 21 31 A O P«l29kPa T»25°C H 2 8 20 A 8 ° 25 27 O A 33 23 A 3 0 2 9 C 9 24 O O 4—1 1 r—I 1 1—I 1 r—r O Plain A Finned 22 O 32 A 31 A 21 O 26 A P = l29kPa 22 T»30°C o 28 20 A 25 ° " 23 O 0) 30 A ? Q 33 27 24 O O J I I I » I I I I I I I 8 12 16 20 24 28 R e f j l m x i o " 3 Figure 5-9. EFFECT OF REYNOLDS NUMBER ON CLEAN AND DIRTY OVERALL HEAT TRANSFER COEFFICIENTS OF PLAIN AND FINNED .MILD STEEL TUBES - 107 -11000, t h i s advantage decreased since the curve (U^ vs. R e f - f i m ^ t e n ( * e d to f l a t t e n out (Figure 5-9). No s p e c i f i c relationship was found between the percentage of the drop in the overall c o e f f i c i e n t and Reynolds number in either case. Due to the e r r a t i c behaviour of the fouling curve, Run 27 was repeated on the finned tube. Considering the experimental errors, both the f i r s t (Run 27) and the second (Run 30) t r i a l s resulted i n reasonable agreement f o r the heat flow rate and the clean c o e f f i c i e n t (Table 5-7). However, the percentage of the drop i n U was much higher f o r Run 30, y i e l d i n g a lower d i r t y c o e f f i c i e n t presumably as a result of higher wall temperature. 5.3 Fouling Resistance With Respect to Time As the fo u l i n g process took place, the ove r a l l heat transfer c o e f f i c i e n t of the exchanger was reduced due to a r i s e i n the ove r a l l resistance of the heat transfer unit as a r e s u l t of the occurrence of the fouling resistance (Rf). Since the scaling solution was not highly concentrated even during the "high concentration" runs, the variation of the fouling resistance with respect to the time was anticipated to be gradual, showing a l i n e a r behaviour. This was the case f o r most of the runs. Figures 5-10 to 5-14 show the typical fouling behaviour. - 108 -The fouling resistance versus time curves f o r Runs 1, 6, 23, 27, 31 and 38 were f a r from l i n e a r , as shown i n Figures 5-15 to 5-20, respectively. Run 27 (Figure 5-18) f o r the finned tube at 0.340 m/s annular velocity showed an inexplicable e r r a t i c behaviour whereas Run 30 under approximately identical operating conditions, resulted in a r e l a t i v e l y l i n e a r behaviour. The asymptotic behaviour of Run 23 (Figure 5-17) on the p l a i n mild steel tube was also inconsistent since l i n e a r i t y was evident during a repeat t r i a l (Run 33). This inconsistency might have been due to the use of a new tube in case of the former. The sawtooth behaviour resulting from Run 31 (Figure 5-19) on the finned tube at 0.683 m/s flow velocity must have been due to the change in the cooling water flow rate. As a consequence of the reduction in the usage of the main supply water at night, the cooling water flow rate increased resulting in a lower i n l e t r e c i r c u l a t i n g water temperature. This situation increased the magnitude of the temperature driving force, the rate of heat flow and the overall heat transfer c o e f f i c i e n t , resulting i n a lower value of the fouling resistance. Runs 1, 6 and 38 (Figures 5-15, 5-16 and 5-20) were a l l carried out on the non-corroding ( s t a i n l e s s steel and copper) tubes at an annular flow velocity of 0.299 m/s. These runs, either under "low concentration" (Runs 1 and 6) or "high concentration" (Run 38) of chemicals, displayed asymptotic behaviour. The i n i t i a l r i s e i n resistance was extremely rapid, occurring usually over the f i r s t three to f i v e hours. The rapid growth of the fouling deposit would usually r e s u l t i n a more porous and less tenacious scale, which has low values of density and thermal conductivity, resulting i n a higher magnitude of fouling resistance than a non-porous tenacious scale f o r - 109 -0.21 0.16 0.12 RUN Q V Re T.A. C V PH 2 11.5 kW 0.695 m/s 25261 I 6 1.4 mg/l '283 mg/l 7.9 5 • • cvj 0.0 8 e 0.04 -0.04 ' 20 30 40 Time (hrs) 50 60 70 Figure 5-10. RUN 2 FOULING RESISTANCE VERSUS TIME - 110 -0.2 0.16 0.12 * 0.0 8 CM E or 0.0 4 0.0 -0 .04 1 RUN 1 1 4A i i 1 Q 18.0 kW — V 0.69 5 m/s — Re 2 9 5 0 6 T.A. 169 mg/1 2 9 4 mg/1 - pH 8.0 3 • 1 i i 1 1 1 10 2 0 30 40 Time (hrs) 50 60 70 Figure 5-11. RUN 4A FOULING RESISTANCE VERSUS TIME - I l l -Figure 5-12. RUN 20 FOULING RESISTANCE VERSUS TIME - 112 -RUN 26 Q l2.7kW V 0.5 7 3 m / s Re 1 0 9 0 4 T.A. 361 mg/l CcT* 6 4 8 mg/l pH 7.5 8 0 10 20 30 4 0 50 60 Time (hrs) Figure 5-13. RUN 26 FOULING RESISTANCE VERSUS TIME - 113 -RUN 36 Q !3 .4kW 0 10 2 0 3 0 4 0 50 6 0 Time (hrs) Figure 5-14. RUN 36 FOULING RESISTANCE VERSUS TIME -114 -Figure 5-15. RUM 1 FOULING RESISTANCE VERSUS TIME - 115 -Figure 5-16. RUN 6 FOULING RESISTANCE VERSUS TIME - 116 -0 10 20 30 4 0 50 60 Time (hrs) Figure 5-17. RUM 23 FOULING RESISTANCE VERSUS TIME - 117 -0.2 0.1 6 h-0.1 2 0.0 8 0.0 4 0.0 -0.04 • RUN Q V Re T.A. C a + * pH 1 27 9.8 kW 0.340 m/s 6 9 1 7 371 mg/ l 66 I m g / l 7.6 4 W ° a r? a «PoB«bPpBa £ _p CD • D • an • • • 1 10 20 30 4 0 Time (hrs) 5 0 60 70 Figure 5-18. RUN 27 FOULING RESISTANCE VERSUS TIME - 118 -0.2 0.16 „ 0.12 °E 0.0 8 0.04 0.0 - 0.04 RUN Q V Re T.A. C a * + pH • l 3 £ 5 k W 0.683 m/s I 3 5 7 9 3 4 0 mg/1 6 26 mg/1 7.6 4 • D • S P • • • • • • • • U CO • • tm • • " f t • • • • • •o _ —I 1 1 20 30 40 Time ( hrs) 50 60 70 Figure 5-19. RUN 31 FOULING RESISTANCE VERSUS TIME - 119 -0.2. T 0.16 0.1 2 RUN Q V Re T.A. C a + * PH 38 9.9 kW 0.299 m/s 12938 361 mg/ I 659 mg/1 7.69 0.0 8 0.04 0.0 -0.041 DriP • 8 l 1 10 20 30 40 Time (hrs) 50 60 ml • 70 Figure 5-20. RUN 38 FOULING RESISTANCE VERSUS TIME - 120 -a s p e c i f i c mass of foul ant. However, the former i s more prone to the removal than the l a t t e r . The asymptotic form of the fouling curve f o r these runs might have been due to the rapid formation of the scale and the absence or negligible e f f e c t of removal as the r e s u l t of the low annular velocity value during the i n i t i a l part of the run, followed by enhancement of the removal mechanism at l a t e r stages due to the deposit weakness. The remainder of the fouling curves are shown i n Appendix IV. 5.4 E f f e c t of Reynolds Number on Fouling Resistance 5.4.1 Copper and Stainless Steel Tubes Figure 5-21 represents the fouling resistance o f the copper and stainless steel tubes under low concentration of chemicals both after 48 and 70 hours plotted versus the Reynolds number. The fouling resistance of both non-corroding tubes decreased with increasing Reynolds number (see Tables 5-3 and 5-4). At low veloc i t y i n e i t h e r case, the majority of the fouling process occurred during the early part of the experiment while at higher annular flow v e l o c i t i e s , the fouling resistance increased gradually throughout the run. This was deduced by comparison between the fouling resistance of each tube after 48 and 70 hours ( i . e . Run 1 and 1A), which showed good agreement with the curves representing the fouling behaviour (see Section 5.3). The stainless steel tube provided a lower fouling resistance than the copper tube over the same length of time. - 121 -CM E 0.16 0.12 h 0.08 h-1 f~6 T " I O i—I—I—r l—r 5 2 4' ^01 \ I 1 I 1 I 1 h OJ 0.15 h 0.11 h-0.07 0.03 8 I A V. 6A w O Copper V S.S. 5A 2A J L J I I J I L 12 16 2 0 2 4 28 R e „ , X I O film -3 Figure 5-21. EFFECT OF REYNOLDS NUMBER ON FOULING RESISTANCE FOR COPPER AND STAINLESS STEEL TUBES - 122 -As i s shown i n Table 5-3, the only inconsistency occurred during the experiment on the stainless steel tube at flow velocity of 0.503 m/s which resulted i n zero fouling resistance due to the inexplicable absence of fouling. 5.4.2 Copper and P l a i n Mild Steel Tubes The fouling resistances pertaining to the tests done under high concentration of chemicals on both the copper and the p l a i n mild steel tubes are given in Tables 5-5 and 5-6. The comparison between these two sets of data was carried out (Figure 5-22) to see the e f f e c t of the surface material on the fouling process with respect to the Reynolds number. As the figure shows, the fouling resistance on the copper tube increases with increasing Reynolds number. However, i n the case of the mild steel tube, the i n i t i a l increase in the fouling factor was followed by a decrease at Reynolds numbers approximately above 18000. This might have been due to the reduction in the s t i c k a b i l i t y of the scale to the mild steel tube and hence enhancement of the removal term at higher v e l o c i t y rates. The only inconsistency involving the mild steel tube occurred during Runs 23 and 33 which resulted i n a very high f o u l i n g factor i n the case of the former, presumably due to the high wall temperature, and a r e l a t i v e l y low fouling resistance i n the case of the l a t t e r f o r an unknown reason. The enhancement of the fouling resistance as a result of either high pressure or both high temperature and pressure (Runs 21 and 22) i s also 0.1 81 0.14 E cr 0.10 0.0 6 T — i — i — T O Mild steel • Copper 24 O 38 • 29 O i—r 33 O 23 37 • 25 O 21 P = l29kPa O T = 25°C T-30°C. P=l29kP0 0 2 2 _ 20 co 0.041 8 J I I I I I I I I I L 12 16 20 24 -3 Re... X l O film 28 32 Figure 5-22. EFFECT OF REYNOLDS NUMBER ON FOULING RESISTANCE FOR COPPER AND PLAIN MILD STEEL TUBES - 124 -evident from the f i g u r e . In general, even though the non-corroding copper tube showed lower fouling resistance than the mild steel one at low Reynolds numbers, i t s e f f i c i e n c y tended to slacken o f f at higher Reynolds numbers. 5.4.3 Plain and Finned Mild Steel Tubes The fouling resistance of the finned tube based on the outside nominal area i s calculated (Table 5-7) and plotted versus both the velocity and the Reynolds number based on the equivalent diameter i n Figure 5-23. Except f o r Run 32, the fouling resistance decreased with increases in the Reynolds number i n the velocity region tested. This could be due to the geometry of the tube and hence higher level of turbulence and enhancement of the removal process at high v e l o c i t y values. The e f f e c t of velocity on the fouling resistance at Reynolds numbers above 16000 could not be investigated due to the limited r e c i r c u l a t i n g water flow rate. In general, i t can be considered that the enhanced tube provided more favorable fouling resistances than the p l a i n one at the corresponding velocity values. I t should also be mentioned that since the fouling resistance of the finned tube i s evaluated based on the prime area, the weight of the deposit per tot a l area and hence the thickness of the deposit i s smaller (about 14%) on the finned tube than that on the p l a i n tube f o r the same magnitude of the fouling resistance based on the prime area (see Appendices II.5 and 11.10). - 125 -l i i i i i FJii—i—i—i—r O.I4[ 29 a i ° f " ° * 2 5 3 2 ^ O 2 5 22 OP=l29kPa 28 3 3 21 T = 3 ° ° C a06r- A C 26 2 0 8 A A 3 I A 0.0 2| 1 1 1 1 1 1 1 1 1 1 | f-0.2 0.3 0.4 0.5 0.6 0.7 V ( m /s ) 0.16 O Plain A Finned 23 O 0.12|- 24 30 ° A 29 O 32 A 25 O 22 0.081- O. 28 33 P-l29kPa 21 0.04 A 26 C T ' 2 5 ° C ° O 2 0 J 1 I I I I I I I I I I 6 10 14 18 22 26 30 R e f i l m x ' 0 " 3 Fiqure 5-23. EFFECT OF BOTH VELOCITY AND REYNOLDS NUMBER ON FOULING RESISTANCE FOR PLAIN AND FINNED MILD STEEL TUBES - 126 -5.5 Determination of the Fouling Rate 5.5.1 Measured Fouling Rate The fouling rate was determined through numerical analysis using the U.B.C. DLQF curve f i t t i n g routine and the experimental fouling resistance data. Linear, asymptotic and 4th order polynomial functions were used f o r f i t t i n g (see Appendix I I I ) . Even though the l i n e a r function provided the most suitable f i t f o r the majority of the runs, the asymptotic one could be considered the best f i t f o r a few others as was evident from the fouling resistance curve versus the time (see Section 5.3). 5.5.2 Predicted Fouling Rate The average water chemistry parameters and the operating condition data such as velocity and temperature were used to calculate the predicted fou l i n g rate based on the ionic d i f f u s i o n model of Hasson (Appendix I I I ) . The average concentrations of the carbon species and calcium ion for each run were determined. The fouling rates were calculated using both Hasson's low and high pH equations. Since the bicarbonate ion concentration was higher than the carbonate one, the fouling rate based on the low pH equation was considered to be the e f f e c t i v e one f o r a l l runs. The results of model calculations are summarized in Table 5-8. Table 5-8. SUMMARY OF MODEL CALCULATIONS Run p H a v e HCO3 x l O 2 * CO3 x 104* C02 x 104* C a + x l O 2 * C a l c u l a t e d * * S c a l i n g Rate x l O 6 1A 7.84 0.1748 0.2687 0.4237 0.2977 0.0914 1 7.86 0.1668 0.2689 0.3860 0.2897 0.0844 3A 7.89 0.1703 0.2944 0.3672 0.3037 0.1353 3 7.93 0.1696 0.3218 0.3337 0.3037 0.1359 2A 7.92 0.1661 0.3032 0.3347 0.2937 0.1586 2 7.95 0.1540 0.3029 0.2895 0.2827 0.1403 6A 7.61 0.1504 0.1422 0.6256 0.2748 0.0853 6 7.60 0.1377 0.1273 0.5868 0.2618 0.0715 5A 8.11 0.1510 0.4488 0.1983 0.2807 0.1415 5 8.11 0.1396 0.4158 0.1835 0.2688 0.1242 4A 8.03 0.1593 0.3961 0.2513 0.2937 0.2075 24 7.78 0.4017 0.6056 1.1068 0.6964 0.4747 29 7.78 0.3397 0.5144 0.9352 0.6384 0.4815 23 7.68 0.3485 0.4240 1.2149 0.6434 0.6327 33 7.93 0.3375 0.7123 0.6565 0.6394 0.5480 25 7.45 0.3505 0.2457 2.0562 0.6504 0.6388 20 7.74 0.3406 0.4781 1.0212 0.6994 0.7281 21 7.72 0.3502 0.4480 1.1040 0.6404 0.7048 22 7.63 0.3397 0.3683 1.3261 0.6384 0.7807 30 7.54 0.3579 0.3145 1.7205 0.6494 0.5233 27 7.64 0.3621 0.4007 1.3800 0.6604 0.5321 28 7.60 0.3394 0.3393 1.4154 0.6324 0.5938 26 7.58 0.3536 0.3352 1.5412 0.6474 0.7316 31 7.64 0.3318 0.3654 1.2634 0.6254 0.8181 32 7.68 0.3096 0.3745 1.0763 0.6025 0.8464 38 7.69 0.3511 0.4413 1.1983 0.6584 0.4289 37 7.81 0.3334 0.5541 0.8679 0.6414 0.6416 36 7.79 0.3086 0.4915 0.8457 0.6184 0.7797 * Units i n mole/1. ** Unit i n m 2K/kJ. - 128 -5.6 E f f e c t of Reynolds Number on the Measured Fouling Rate 5.6.1 Copper and Stainless Steel Tubes The experimental measurements of the fouling rate under low concentration of chemicals on the two non-corroding tubes accompanied by the type of f i t t e d curves are given i n Table 5-9. As i s shown in the table, neither of the tubes showed any s p e c i f i c trend with respect to the Reynolds number. Asymptotic behaviour was the only common e f f e c t of low velocity value on the rate of fouling i n either case, presumably due to the negligible e f f e c t or absence of the removal process i n the early part of the run. 5.6.2 Copper and Plain Mild Steel Tubes The copper tube under high concentration of chemicals also showed asymptotic behaviour at low velo c i t y leading to a very high i n i t i a l f ouling rate i n comparison with the corresponding ones at high velocity values. The high rate of fouling at low Reynolds number (Run 38) might have been due to the absence of a removal process and hence the rapid formation of the scale. However, the strength of the scale might be compromised by the high rate of fo u l i n g . Therefore, the growth i n the deposit thickness and the reduction i n the adherence factor would re s u l t i n the asymptotic behaviour. At high v e l o c i t i e s , both the gross deposition and the removal terms are e f f e c t i v e from the start of the run resulting in both a more gradual increase in the Table 5-9. COMPARISON OF MEASURED FOULING RATES ON COPPER AND STAINLESS STEEL V Copper Stainless Steel (m/s) Run* R e f i l m dR i n 6 de" x 1 0 (m2K/kJ) F i t Run R e f i l m (m2K/kJ) F i t 0.299 6A 6 12921 12987 1.9766 1.9334 Asymp Asymp 1A 1 11136 11194 12.3109 12.7204 Asymp Asymp 0.503 5A 5 21170 21397 0.3545 0.4224 Asymp Asymp 3A 3 18576 18599 -0.0570 -0.0204 Lin Lin 0.695 4A 29506 0.3678 Lin 2A 2 24984 25261 0.0808 0.3138 Lin Lin Note: A = runs lasted 48 hours Lin =1inear Asymp = asymptotic * Low concentration runs - 130 -scale thickness and a stronger deposit. Having a higher fouling rate f o r the run at 0.695 m/s than the one at 0.503 m/s (Figure 5-24) indicated that the e f f e c t of increasing velo c i t y on the removal process was counterbalanced by the high gross deposition rate. The net rate of fouling on the p l a i n mild steel tube was also affected by the velocity (Figure 5-24). No asymptotic behaviour was shown, even at low values of Reynolds numbers. This was attributed to the surface material e f f e c t . The fouling rate was increased with increasing velocity up to a Reynolds number of about 17000 due to the enhancement of the gross deposition rate. However, the e f f e c t of the removal rate became more pronounced at higher Reynolds numbers, resulting in a reduction of the net fouling rate with further increases in the magnitude of the velocity. The simultaneous e f f e c t s of both higher temperature and pressure leading to a higher fouling rate can be seen in comparison between Runs 20 and 22. However, an increase in the fouling rate with an increase only i n the i n i t i a l steam pressure (Run 21) was not evident due to either experimental errors or the curve f i t t i n g procedure which covered a l l data points. With regard to Figure 5-24, i t can be considered that the p l a i n mild steel tube provided lower fouling rates than the corresponding ones on the copper tube, but more data i s needed to confirm t h i s r e s u l t . T — i — i — i — i — i — i — i — i — i — i — i r • 38 • Copper O Plain M.S. 3 6 ^ 29 O 23 33 37 22 ° O C L 2 5 O 20 P'l29kPa-2 | o T « 3 0 ° C O P*I29 kPa T « 2 5 ° C • I I I I I I I I I I I I 8 12 16 20 24 28 32 R * f i . m X , ° -3 FIGURE 5-24. EFFECT OF REYNOLDS NUMBER ON MEASURED FOULING RATE FOR COPPER AND PLAIN MILD STEEL TUBES - 132 -5.6.3 Plain and Finned Mild Steel Tubes Velocity was also one of the e f f e c t i v e factors on the net rate of fouling of the finned tube. Figure 5-25 shows both the velocity and the Reynolds number ef f e c t s on both the p l a i n and the enhanced mild steel tubes. The fouling rate values were determined by f i t t i n g the entire data using a numerical analysis method (see Section 5.5.1). However, i n the case of Run 31, the curve f i t t i n g method could not supply a r e l i a b l e f i t due to the periodic changes in the cooling water flow rate and hence the sawtooth behaviour of the fouling resistance curve (see Section 5.3). For t h i s run, an attempt was made to v i s u a l l y f i t the data points corresponding to the daytime (8:00 a.m. to 8:00 p.m.) cooling water flow rates. Disregarding Run 32, the general outlook provided by the experimental data on the enhanced tube showed a drop in the fouling rate with increasing v e l o c i t y . The reduction might have been due to higher magnitude of the removal term, the c o n t r o l l i n g e f f e c t of the surface reaction mechanism or both at the high velocity rates. The reason f o r rapid growth in the value of fouling rate at 0.791 m/s (Run 32) i s not known. The reduction i n the rate of fouling took place at Reynolds numbers approximately above 16000 (V=0.404 m/s) f o r the p l a i n tube, while at Reynolds numbers about 7000 (V=0.340 m/s) for the finned (Figure 5-25). This might be due to the f a c t that the same degree of turbulence occurs at the lower values of Reynolds number i n case of the enhanced tube as a result - 133 -1 1 1 1 1 1 30 24 A O 29 O 23 O 25 O 32 22 A O 1 1 2 8 A 1 1 26 A 1 2 0 O 021 P=l29kPa , , T = 25°C 3 1 A -1 0.2 0.3 0.4 0.5 V(m/s) 0.6 0.7 A Finned O Plain 30 _ A 24 O 28 29 O 32 A 33 O 25 O 2 2~ P=l29kPaO T» 30°C — A 26 A 31 A O ° * 0 21 -1 1 1 1 1 10 14 18 22 26 30 R e f „ m X I 0 " 3 5-25. EFFECT OF BOTH VELOCITY AND REYNOLDS NUMBER ON MEASURED FOULING RATE FOR PLAIN AND FINNED MILD STEEL TUBES - 134 -of the existence of the f i n s . Generally, the finned tube provided lower and more favourable fouling rates than did the p l a i n one, at equivalent annular flow v e l o c i t y values. 5.7 E f f e c t of Reynolds Number on the Predicted Fouling Rates An increase i n the predicted fouling rate with velo c i t y was expected since the model was based on both the d i f f u s i o n controlled mechanism and the absence of the removal term. Due to the f a c t that the model predicts a l i n e a r behaviour f o r the fouling curve and the rate should increase with an increase i n the Reynolds number, an increase i n the fouling resistance with the velocity i s expected. Figure 5-26 and Table 5-10 both represent the e f f e c t of Reynolds number on the non-corroding tubes under low concentrations of chemicals. Model calculations resulted in a lower magnitude of fouling rate for the copper tube than the stainless steel one under approximately identical operating conditions at Reynolds numbers below 22000. The f a c t that the plot of the predicted fouling rate versus Reynolds number f o r the stainless steel tube had a reduction in i t s slope at higher annular flow velo c i t y value might have been due to the smoothness of the surface which became more e f f e c t i v e i n diminishing the occurrence of the fouling process i n the presence of higher degree of turbulence. The basis of the model, the constancy of the fouling rate with respect to the time, was evident considering the close values of predicted rate corresponding to a run over two d i f f e r e n t periods of time ( i . e . 5 and 5A). A decrease in experimental fouling resistance with velocity (Figure 5-21) was in contradiction with the model's prediction (Figure 5-26). - 135 -T — r " i — i — i — i — i — i — r ~ " I—r - — V 2 0.14 0.10 0.06 0.20 0.16 o'e —^I—I—I—I—I—I 1 1 1 1 V O Copper V SS 4 A O I 2A 5A £ 0.12 0j08r-IA <^6A J I I I I I I I 10 14 18 22 26 30 Re f X 10 r3 5-26. EFFECT OF REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR COPPER AND STAINLESS STEEL TUBES - 136 -T a b l e 5-10. COMPARISON OF PREDICTED FOULING RATES ON COPPER AND STAINLESS STEEL v (m/s) Run"' Copper S t a i n l e s s S t e e l Re f i l m Run R e f i l m (nTK/kJ) (nTK/kJ) 0.299 6A 12921 0.0893 1A 11136 0.0956 6 12987 0.0757 1 11194 0.0886 0.503 5A 21170 0.1497 3A 18576 0.1416 5 21397 0.1323 3 18599 0.1424 0.695 4A 29506 0.2180 2A 24984 0.1666 2 25261 0.1484 Note: A = runs l a s t e d 48 h o u r s . * Low c o n c e n t r a t i o n r u n s . - 137 -The e f f e c t of Reynolds number on predictions f o r both the copper and the plain mild steel tubes under high concentration of chemicals i s shown in Figure 5-27. An increase in the fouling rate with the velocity was also held to be generally in e f f e c t for these tubes. The s l i g h t inconsistency occurred during Run 24, on the plai n mild steel tube, which was presumably due to the r e l a t i v e l y high values of total a l k a l i n i t y and hardness in comparison to the other runs. The single e f f e c t of the i n i t i a l steam pressure and the combined e f f e c t of both the i n l e t water temperature and the i n i t i a l steam pressure are shown by Runs 21 and 22, respectively. Comparing Runs 20 and 21, the lower value of the fouling rate f o r Run 21 i s understandable and can be attributed to i t s lower average wall temperature (Table 5-6). The enhancement of the experimental fouling resistance with the velocity (Figure 5-22) was in good agreement with Hasson 1s model in the case of the copper tube. However, the reverse relationship in the case of the plain mild steel tube (Figure 5-22) was contradictory with the predicted fouling rate results (Figure 5-27), suggesting the ionic d i f f u s i o n plus reaction did not control the fouling rate on mild s t e e l . In general, the predicted rates on both tubes were similar at corresponding annular flow v e l o c i t i e s . As i s shown in Figure 5-28, the predicted fouling rate also increased with increasing velocity in the case of the finned mild steel tube. This trend was opposite to the variation of the fouling resistance with the Reynolds number provided by the experimental data (Figure 5-23). Predicted fouling rate values were indicative of the fact that the plain tube behaved more favourably than the enhanced one i n the velocity region — i 1 n 1 1 r -22 361 O Mild steel *g • Copper * u P-l29kPa 0 ° T-30 °C 23 3rA P"l29kPa 3 t-O T *25°C 25 24 29 ° 38 ° • 33 € 10 14 18 22 26 30 R e f „ m X , ° -3 FIGURE 5-27. EFFECT OF REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR COPPER AND PLAIN MILD STEEL TUBES - 139 -0.8 0.6 26 A 0.4 CM J 0 Ct> ^ 0.91 or T3 24 O _J_ 27 30 29 O _ l _ 23 28 0) _L 25 O 0.2 0.3 0.4 0.5 V (m/s) 0.6 O A Plain Finned 31 A 32 A 0.7 h 26 A 3. 3 2 A | A _ 022 ? n r . P=l29kPa 2 0 8 T=30 8 C_ 21 27 A 0.5 h 3 0 28 A 23 25 3 O 24 O 29 O 33 € I 4 Re film 18 x i o - 3 22 0.7 22 20 ° %° -P=l29kPo T = 25°C 26 30 FIGURE 5-28. EFFECT OF BOTH VELOCITY AND REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR PLAIN AND FINNED MILD STEEL TUBES - 140 -investigated. This i s due to the e f f e c t s of the f i n s on the hydraulic diameter, and hence the Reynolds number. This trend was also i n contradiction with the results based on the f i t t e d value of fouling rates (Figure 5-25). 5.8 Comparison Between the Predicted and the Measured Fouling Rates Tables 5-11, 5-12 and 5-13 represent the ra t i o of the predicted to the measured fouling rates f o r a l l runs. The graphical representation o f the change i n t h i s ra t i o f o r low concentration runs with respect to Reynolds number (Tables 5-11 and 5-12) was not feasible due to the wide range of var i a t i o n in i t s magnitude i n the v e l o c i t y region tested. Data corresponding to the copper tube under low concentration of chemicals suggest that the model underpredicts the fouling rate, p a r t i c u l a r l y at low values of the annular velocity. This i s also the case f o r stainless steel tube at low Reynolds numbers. However, no other conclusion could be drawn regarding the other runs on the s t a i n l e s s steel tube. For the copper and both mild steel tubes under high concentration of chemicals, the model overpredicted the experimental f o u l i n g rates (Table 5-13). The only inconsistency occurred with respect to Run 38 due to the asymptotic behaviour of the fouling curve (see Section 5.3). Figure 5-29 shows the e f f e c t of Reynolds number on the ratio of the measured to the predicted fouling rates f o r these high concentration runs. In the case o f the two mild steel tubes, the consistency between the model and the experimental data decreases with increasing Reynolds number, presumably due - 141 -Table 5-11. COMPARISON OF PREDICTED AND MEASURED FOULING RATES ON COPPER dR St* 10 6 Run* V R e f i l m (m2K/kJ) ( d R / d 6 ) m e a s (m/s) Predicted Measured ( d R / d e ) p r e d 6A 6 0.299 12921 12987 0.0893 0.0757 1.9766 1 .9333 22.134 25.539 5A 5 0.503 21170 21397 0.1497 0.1323 0.3545 0.4224 2.368 3.193 4A 0.695 29506 0.2180 0.3678 1.687 Note: A = runs lasted 48 * Low concentration hours, runs. Table 5-•12. COMPARISON OF PREDICTED AND MEASURED FOULING RATES ON STAINLESS STEEL dR d i x 10 6 Run* V R e f i l m (m2K/kJ) ( d R / d e ) m e a s (m/s) Predicted Measured ( d K / d e ) p r e d 1A 1 0.299 11136 11194 0.0956 0.0886 12.3109 12.7204 128.775 143.57 3A 3 0.503 18576 18599 0.1416 0.1424 -0.0570 -0.0204 -0.403 -0.143 2A 2 0.695 24984 25261 0.1666 0.1484 0.0808 0.3138 0.485 0.473 Note: A = runs lasted 48 hours. * Low concentration runs. - 142 -Table 5-13. COMPARISON OF PREDICTED AND MEASURED FOULING RATES FOR HIGH CONCENTRATION RUNS Run Tube Material and Geometry (m/s) R e f i l m de (m2K/kJ) Predicted Measured ( d R / d e ) m e a s ( d R / d e ) p r e d 38 Cop 0.299 12938 0.4288 3.3839* 7.8897 37 Cop 0.503 22488 0.6423 0.3369 0.6055 36 Cop 0.695 32072 0.7826 0.6442 0.8262 24 P.M.S. 0.299 11952 0.4723 0.3552 0.7483 29 P.M.S. 0.404 16253 0.4818 0.4711 0.9784 33 P.M.S. 0.503 19394 0.5483 0.3453 0.6301 25 P.M.S. 0.600 23078 0.6389 0.3196 0.5003 20 P.M.S. 0.695 26624 0.7286 0.2541 0.3490 21 P.M.S. 0.695 25770 0.7047 0.2156 0.3050 22 P.M.S. 0.695 29030 0.7814 0.3369 0.4315 30 F.M.S. 0.340 6849 0.5230 0.4173 0.7974 28 F.M.S. 0.460 8973 0.5943 0.2415 0.4067 26 F.M.S. 0.573 10904 0.7314 0.1455 0.1989 31 F.M.S. 0.683 13579 0.8194 0.1000** 0.1222 32 F.M.S. 0.791 15882 0.8497 0.3920 0.4631 cop = copper P.M.S. = plain mild steel F.M.S. = finned mild steel * Asymptotic f i t ** Visually f i t t e d - 143 -to the enhancement of removal process at high velocity values. The copper tube provided good agreement between the predicted and experimental value of the fo u l i n g rate at annular flow velocity of 0.695 m/s. No other s p e c i f i c relationship was found between velocity and the magnitude of t h i s r a t i o using the copper tube. In general, f o r either the copper tube or the mild steel ones, the e f f e c t of Reynolds number on the magnitude of t h i s r a t i o followed the same trend as did the value of the corresponding measured fouling rate (see Figures 5-24 and 5-25). 3 8 D • Copper O Plain M.S. A Finned M.S 30 A 24 O 28 A 26 A 29 O 32 A 31 A 33 O 37 • ,25 20 2 l 0 0 P=l29kPa T=25°C 36_ [] 22 O P*l29kPa T»30 °C 6 10 14 18 22 26 30 Re,., X l O " 3 film Fiaure 5-29. COMPARISON OF MEASURED SCALING RATE WITH RATE PREDICTED BY THE IONIC DIFFUSION MODEL - 145 -6. CONCLUSION The e f f e c t of the fouling process on the two non-corroding (copper and stainless steel) tubes and the performance of the exchanger either before or af t e r the deposit accumulation was examined. The copper tube showed higher values of heat flow rate and both clean and d i r t y overall heat transfer c o e f f i c i e n t s than did the stainless steel tube. The same trend was applicable regarding the percentage of drop in the clean overall heat transfer c o e f f i c i e n t , over the same period of time, due to the smoothness of the stainless steel tube and higher bulk and wall temperatures f o r the runs on the copper one. With respect to the Reynolds number, the fouling resistance of the copper tube was also higher than the corresponding one on the stainless steel tube. In e i t h e r case, the fouling resistance was generally l i n e a r in time except f o r the low veloc i t y (0.299 m/s) runs which showed an asymptotic behaviour. The magnitude of the fouling resistance, f o r e i t h e r tube, decreased with increasing velocity, unlike the values of heat flow rate, clean and d i r t y o v e r a l l heat transfer c o e f f i c i e n t s which showed increases with the Reynolds number. Therefore, even though the gain i n performance of the copper tube over the stainless steel one diminished due to the fouling process, the copper tube was more favourable. The predicted rates of fouling were s l i g h t l y lower f o r the copper tube than the corresponding ones on the stainless steel tube at Reynolds numbers below 22000. In either case, the predicted fouling rates increased with increasing Reynolds number. In general, even though the copper tube was more prone to fouling, i t provided a higher degree of performance than the stainless steel one both before and after the scaling process. - 146 -Under high concentration of chemicals, i . e . a l k a l i n i t y ~ 300-400 mg CaCO^/l, the copper tube also had higher values of heat flow rate and both i n i t i a l and f i n a l overall heat transfer c o e f f i c i e n t s than did a p l a i n mild steel tube. In both cases, the magnitude of these parameters increased with the v e l o c i t y . The fouling curves generally followed l i n e a r behaviour. For the copper tube, the magnitudes of fouling resistance and percentage of drop in the clean overall heat transfer c o e f f i c i e n t increased with increasing vel o c i t y . However, for the p l a i n mild steel tube, these values were increased with the velocity only f o r Reynolds numbers approximately below 18000 (v=0.503 m/s). The result was a lower magnitude of fouling resistance f o r the copper tube than the p l a i n mild steel one at low velo c i t y values (v<0.503) followed by a higher value f o r the former than the l a t t e r at Reynolds numbers above 18000 (v>0.503 m/s). For either tube, the experimental values of the fouling rate with respect to the Reynolds number followed the same trend as did the fouling resistance except f o r Run 38. In general, the measured fouling rates indicated lower values f o r the p l a i n mild steel tube than the corresponding ones of the copper tube. Though calculations based on Hasson's ionic d i f f u s i o n model provided close values f o r the corresponding runs on either tube, the model over-predicted the experimental rates of fouling except f o r Run 38. The predicted rates increased with the velocity resulting i n a better agreement with the measured values at high Reynolds numbers i n the case of the copper tube, while giving r i s e to more suitable predictions at low v e l o c i t i e s using the p l a i n mild steel tube. T o t a l l y , i t can be said that the copper tube had always a better performance, regarding the d i r t y heat transfer c o e f f i c i e n t , than the p l a i n mild steel one, especially at low annular flow v e l o c i t i e s . - 147 -In comparison between the two corroding mild steel tubes, the p l a i n tube provided lower values of heat flow rate and both clean and d i r t y heat transfer c o e f f i c i e n t s . In addition, a near l i n e a r increase of these parameters with the velocity was evident. The l i n e a r i t y of the fouling curves with respect to time was also generally evident, except for a run on a new tube. The fouling resistance f o r the finned tube generally decreased with increasing velocity. However, in the case of the p l a i n tube, the fouling resistance reached i t s maximum at Reynolds number of approximately 18000 as was mentioned e a r l i e r . The enhanced tube always gave r i s e to a lower value of fouling rate than did the p l a i n tube in the velocity region investigated. The measured rates of fouling followed the same trend with respect to v e l o c i t y as did the fouling resistances. The predicted rates, i n either case, rose with the velocity. However, unlike the measured values, they were lower f o r the p l a i n tube than the finned one. For both tubes, the model over-predicted the experimental values of fouling rates providing a better agreement with the measured rates at lower v e l o c i t i e s . In general, the finned tube was shown to be more favourable than the p l a i n one regarding both the overall heat transfer c o e f f i c i e n t and the fouling resistance build up over the same period of time. Testing the tubes under low concentration of chemicals ( a l k a l i n i t y ~ 180 mg CaCO-j) resulted in rather soft and powdery deposits, on the copper and s t a i n l e s s steel tubes, and muddy deposits on the mild steel tubes which precluded firm conclusions of on the e f f e c t of the fouling process on the mild steel tube under these conditions. When a more concentrated scaling solution was used, the deposits were much stronger and - 148 -more resistant to removal. The corroding e f f e c t of the mild steel tube which enhanced the fouling process providing a higher magnitude of the fouling resistance f o r the mild steel tube than the copper at low v e l o c i t y was counterbalanced f o r copper by an increase in the strength of the scale at high v e l o c i t y values. Between the two mild steel tubes, the enhanced one had lower values of fouling resistance than the p l a i n one at identical Reynolds numbers. At the same Reynolds number, the v e l o c i t y in the finned tube i s higher than that of the p l a i n tube. Thus, the more favourable behaviour of the finned tube can be attributed either to the higher degree o f turbulence or the soft and powdery structure of the deposits which were more prone to the removal mechanism. The reducing e f f e c t of velocity on the fo u l i n g resistance was also reasonable considering the structure of the deposits formed on the enhanced tube. In conclusion, the greater values of both clean and d i r t y heat transfer c o e f f i c i e n t s along with the lower magnitudes of fouling resistance made the enhanced tube a better choice, where any hard-water scaling i s expected. In addition, even though the ionic d i f f u s i o n model does not y i e l d good agreement with the experimental r e s u l t s , i t can be safely used to predict the magnitude of the fouling rates f o r the copper and both mild steel tubes under high concentration of chemicals i n the velocity region tested. - 149 -7. NOMENCLATURE Symbol Description 9Q» 9 ^ , * • • » <*9 deposition constgnts A surface grea A logarithmic mean area A e f f e f f e c t i v e area A f surface area of the f i n s V APrime prime or unfinned area Ao nominal (bare-tube) outside area A t t o t a l surface area A' volume of the t i t r a n t (EDTA) Asymp asymptotic bj, b 2, bg removal constants b length of the f i n b' degree of supersaturation B' volume of the t i t r a n t (HC1) B " mg of CaCOg equivalent to 1 ml of EDTA C b bulk concentration CP sp e c i f i c heat C s concentration of saturated l i q u i d at the surface C T total carbon species concentration 150 -Description diameter d i f f u s i v i t y equivalent diameter diameter of the shell diameter of the tube activation energy convective heat transfer c o e f f i c i e n t d i r t c o e f f i c i e n t , reciprocal of fouling resistance f o r unit surface area Heat Transfer Research Incorporated constant i n the Arrhenius equation molar s o l u b i l i t y constant of CaCO^ rate c o e f f i c i e n t for bicarbonate decomposition reaction mass transfer c o e f f i c i e n t f o r d i f f u s i o n of Ca(HC0 3) 2 thermal conductivity of deposit thermal conductivity of f i n thermal conductivity of l i q u i d average unit thermal conductance of wall 1 5 1 -Description constant for the Reitzer gross deposition rate f i r s t molar dissociation constant of carbonic acid second molar dissociation constant of carbonic acid mass transfer coefficient for diffusion overall mass transfer coefficient rate constant for surface reaction molar solubility product of CaCO^  height of the f i n length of the tube 1inear Logarithmic Mean Temperature Difference Langelier Saturation Index clean f i n efficiency parameter dirty f i n efficiency parameter mass of deposit per unit area total mass of the deposit net rate of fouling gross rate of deposition rate of removal constant for the mechanical strength of the deposit 152 -Description normality of the t i t r a n t ( H C 1 ) Net Free Area f i n perimeter polynomial probability function of velocity heat flux heat flux by convection rate of heat flow by the finned area rate of heat flow by the p n (unfinned) area total rate of heat flow unit thermal resistance deposit bond resistance fouling resistance gas constant unit thermal resistance at time zero Ryzner S t a b i l i t y Index asymptotic fouling resistance annular cross sectional area f i n spacing thickness of the f i n 153 -Description temperature bulk temperature temperature of cold stream f i l m temperature temperature of hot stream surface temperature steam temperature wall temperature Tubular Exchanger Manufacturers Association Total Wetted Perimeter overall heat transfer c o e f f i c i e n t clean overall heat transfer c o e f f i c i e n t d i r t y overall heat transfer c o e f f i c i e n t velocity volume of the water sample c r i t i c a l f r i c t i o n velocity volumetric flow rate rate of deposition in Hasson ionic d i f f u s i o n model mass flow rate mass flow rate of cold stream mass flow rate of hot stream deposit thickness - 154 -Dimensionless Groups Pr Nu Re Sc Greek Letters 6 2 A m n f n f d \ n t d ¥ e e c eD u p p f Description Prandtl number, Cpn/k Nusselt number, hD/k Reynolds number, PVD/n Schmidt number, u/PD Description d i s t r i b u t i o n f r a c t i o n of carbon species a function dependent on wall, scale surface and bulk temperatures difference between values logarithmic mean temperature difference (LMTD) f i n e f f i c i e n c y d i r t y f i n e f f i c i e n c y total surface e f f i c i e n c y total d i r t y surface e f f i c i e n c y constant = 3.14 time time constant delay time visco s i t y density of the l i q u i d density of the deposit - 155 -Greek Letters Description T liquid shear stress f deposit structure factor ft water characterization factor Subscripts Description ave average b bulk i, in inside k conduction max maximum meas measured o, out outside pred predicted Superscripts Description B exponent f exponent g exponent n exponent r exponent - 156 -8. REFERENCES 1) Standards of Tubular Exchanger Manufacturers Association, 5th Editio n , New York, 1968. 2) Thackery, P.A., "The Cost of Fouling in Heat Exchanger Plant". In: Proceedings of the Conference "Fouling - Science or Artu", Surrey, Guildford, England, March 27-28, 1979. 3) Hasson, D., Sherman, H. and Biton, M., "Prediction of Calcium Carbonate Scaling Rates". Proceedings 6th International Symposium on Fresh Water from the Sea, Vol. 2, p. 193, 1978. 4) Epstein, N., "Fouling in Heat Exchangers". Proceedings of 6th International Heat Transfer Conference, Vol. 6, p. 235-253, August 1978. 5) Kern, D.G. and Seaton, R.E., "A Theoretical Analysis of Thermal Surface Fouling". B r i t i s h Chemical Engineering, Vol. 4, p. 258, May 1959. 6) Kern, D.G. and Seaton, R.E., "Surface Fouling . . . How to Calculate Limits". Chemical Engineering Progress, Vol. 55, p. 71, June 1959. 7) Banchero, J.T. and Gordon, K.F., "Scale Deposition on a Heated Surface". Advances in Chemistry Series, Vol. 27, p. 105, April 1960. - 157 -8) Hasson, D., "Precipitation Fouling". In "Fouling of Heat Transfer Equipment", Somerscales, E. and Knudsen, J.G. (Editors), Hemisphere Publishing Corporation, p. 527-568, 1981. 9) Larson, T.E. and Buswell, A.M., "Calcium Carbonate Saturation Index and A l k a l i n i t y Interpretation". Journal of American Water Work Association, Vol. 34, p. 1667, 1942. 10) Loewenthal, R.E. and Marais, G.V.R., "Carbonate Chemistry of Aquatic Systems: Theory and Application", p. 125, Ann Arbor Science Publishers Incorporation, Ann Arbor, Michigan, 1976. 11) McCabe, W.L. and Robinson, C.S., "Evaporator Scale Formation". Industrial and Engineering Chemistry, Vol. 16, No. 5, p. 478, January 18, 1924. 12) Hasson, D., "Rate of Decrease of Heat Transfer due to Scale Deposition". Dechema-Monographien, Vol. 47, p. 233, 1962. 13) Hixon, A.W. and Knox, K.L., "Effect of Agitation on Rate of Growth of Single Crystals". Industrial and Engineering Chemistry Engineering and Process Development, Vol. 43, No. 9, p. 2144, September 1951. 14) Treybal, R.E., "Mass Transfer Operations", Third Edition, Chemical Engineering Series, McGraw-Hill Book Company, New York, 1980. - 158 -15) Reitzer, B.J., "Rate of Scale Formation in Tubular Heat Exchangers". Industrial and Engineering Chemistry Process Design and Development, Vol. 3, No. 4, p. 345, October 1964. 16) Bransom, S.H., "Factor in Design of Continuous C r y s t a l ! i s e r s " . B r i t i s h Chemical Engineering, Vol. 5, No. 12, p. 838, 1960. 17) Hasson, D., A v r i e l , M., Resnick, W., Razenman, T. and Shlomo, W., "Mechanism of Calcium Carbonate Scale Deposition on Heat-Transfer Surfaces". Industrial and Engineering Chemistry Fundamentals, Vol. 7, No. 1, February 1968. 18) Taborek, J . , Aoki, T., R i t t e r , R.B. and Palen, J.W., "Fouling: the Major Unresolved Problem in Heat Transfer Transfer". Chemical Engineering Progress, Vol. 68, No. 2, February 1972. 19) Taborek, J . , Aoki, T., R i t t e r , R.B. and Palen, J.W., "Predictive Methods for Fouling Behavior". Chemical Engineering Progress, Vol. 68, No. 7, July 1972. 20) Watkinson, A.P. and Martinez, 0., "Scaling of Heat Exchanger Tubes by Calcium Carbonate". Transactions of the American Symposium of Mechanical Engineering, Journal of Heat Transfer, Vol. 97, p. 504, November 1975. - 159 -21) Morse, R.W. and Knudsen, J.G., "Effect of A l k a l i n i t y on the Scaling of Simulated Cooling Tower Water". The Canadian Journal of Chemical Engineering, Vol. 55, p. 272, June 1977. 22) Nancollas, G.H. and Reddy, M.M., "The C r y s t a l l i z a t i o n of Calcium Carbonate: II Calcit e Growth Mechanism". Journal of C o l l o i d and Interface Science, Vol. 37, No. 4, p. 824, December, 1971. 23) Wiechers, H.N.S., Sturrock, P. and Marais, G.V.R., "Calcium Carbonate C r y s t a l l i z a t i o n Kinetics". Water Research, Vol. 9, p. 835, 1975. 24) Hasson, D. and Gazit, E., "Scale Deposition From an Evaporating F a l l i n g Film". Desalination, Vol. 17, p. 339, 1975. 25) Lord, R.C., Minton, P.E. and Slusser, R.P., "Design of Heat Exchangers". Chemical Engineering, p. 96, January 26, 1970. 26) F a n a r i t i s , J.P. and Bevevino, J.W., "Designing Shell and Tube Heat Exchangers". Chemical Engineering, p. 62, July 5, 1976. 27) Cleaver, J.W., Yates, B., "Mechanism of Detachment of Colloidal P a r t i c l e s from a F l a t Substrate i n a Turbulent Flow". Journal of Co l l o i d and Interface Science, Vol. 44, p. 464, September 1973. - 160 -28) Cleaver, J.W. and Yates, B., "The Effe c t of Re-Entrainment on P a r t i c l e Deposition". Chemical Engineering Science, Vol. 31, p. 147, 1976. 29) Suitor, J.W., Marner, W.J. and R i t t e r , R.B., "The History and Status of Research in Fouling of Heat Exchangers i n Cooling Water Service". The Canadian Journal of Chemical Engineering, Vol. 55, p. 374, August 1977. 30) Knudsen, J . and Roy, B.V., "Studies on the Scaling of Cooling Tower Water". International Conference of Heat Exchanger Surfaces, Engineering Foundation, White Haven, November 1982. 31) "Principles of Industrial Water Treatment", Third Edition, Drew Chemical Corporation, New Jersey, 1979. 32) Langelier, W.F., "The Analytical Control of Anti-Corrosion Water Treatment". Journal of the American Water Work Association, Vol. 28, p. 1500, 1936. 33) Langelier, W.F., "Chemical E q u i l i b r i a in Water Treatment". Journal of the American Water Work Association, Vol. 38, No. 2, p. 169, February 1946. 34) Watkinson, A.P., "Effects of Water Quality on Hard Water Scaling". Proceedings of the 30th Canadian Chemical Engineering Conference, National Heat Transfer Symposium, Vol. 2, p. 616, October 1980. - 161 -35) Watkinson, A.P., "Process Heat Transfer: Some Practical Problems". The Canadian Journal of Chemical Engineering, Vol. 58, p. 553, October 1980. 36) Ryznar, J.W., "A New Index f o r Determining Amount of Calcium Carbonate Scale Formed by a Water". Journal of the American Water Work Association, Vol. 36, p. 472, April 1944. 37) HTRI set of Electron Scanning Microscope (ESM) Pictures showing various stages of c r y s t a l l i n e growth and behaviour. Available upon request. 38) Thurston, E.F., "Experimental Plant f o r Studying Methods of Controlling Scale Formation in B o i l e r s " . Chemistry and Industry, p. 1238, July 10, 1965. 39) Watkinson, A.P., Water Quality Effects on Fouling from Hard Waters. In: "Heat Exchangers - Theory and Practice", Taborek, J . , Hewitt, G.F. and Afgan, N. (Editors), Hemisphere Publishing Corporation, 1983. 40) Peters, R.W. and Stevens, J.D., "Effect of Iron as a Trace Impurity on the Water Softening Process". The American Institute of Chemical Engineers Sympsoium Series, p. 46, 1982. - 162 -41) Peters, R.W. and Stevens, J.D., "Additivity of Crystal Size Distributions in the Simultaneous Precipitations of CaCOg and MgtOH)^". Proceedings of the Second World Congress of Chemical Engineering, Vol. 4, 76-81, October, 1981. 42) Kemmer, F.N., "Water: The Universal Solvent". Nelco Water Handbook, Second Edition, p. 58, Nelco Chemical Company, February 1979. 43) Somerscales, E.F.C., Fundamental Ideas in Corrosion Testing in the Presence of Heat Transfer. In: Symposium "Corrosion in Heat Transfer Conditions", Teddington, England, November 3, 1982. 44) "BETZ Handbook of Industrial Water Conditioning", Eighth Edition, BETZ Laboratories Incorporated, Trevose, Pennsylvania, 1980. 45) Uhlig, H.H., "Corrosion and Corrosion Control", 4th Printing, John Wiley 3 Sons Incorporated, New York, 1967. 46) Kreith, F., "Principles of Heat Transfer", Third Ed i t i o n , Harper Row Publishers, Incorporated, New York, 1973. 47) Kern, D.G. and Kraus, A.D., "Extended Surface Heat Transfer". McGraw-Hill Book Company, New York, 1972. 48) Kern, D.G., "Process Heat Transfer". McGraw-Hill Book Company, New York, 1950. - 163 -49) Knudsen, J.G. and Katz, D.L., "Heat Transfer and Pressure Drop in Annuli". Chemical Engineering Progress, Vol. 46, No. 10, p. 490, October 1950. 50) Knudsen, J.G. and McCluer, H.K., "Hard Water Scaling of Finned Tubes at Moderate Temperatures". Chemical Engineering Symposium Series, Vol. 55, No. 29, 1959. 51) Katz, D.L. et a l . , University of Michigan. Engineering Research Institute, Project M592, July 1953. 52) Webber, W.O., "Under Fouling Conditions Finned Tubes Can Save Money". Chemical Engineering, Vol. 67, No. 6, p. 149, March 21, 1960. 53) Watkinson, A.P., Louis, L. and Brent, R., "Scaling of Enhanced Heat Exchanger Tubes". The Canadian Journal of Chemical Engineering, Vol. 52, p. 558, October 1974. 54) Epstein, N. and Sandhu, K., "Effect of Uniform Fouling Deposit on Total E f f i c i e n c y of Extended Heat Transfer Surfaces". In: Sixth International Heat Transfer Conference, Vol. 4, p. 397, Toronto, Ontario, August 1978. - 164 -55) "Standard Methods of Chemical Analysis", Sixth Edition, Vol. 2, p. 2399. Welcher, F.J. (Editor). D. Van Nostrand Company Incorporated, Princeton, N.J., 1963. 56) "Standard Methods for the Examination of Water and Wastewater", Twelfth Edition, APHA, AWWA, WPCF, 1965. 57) "CRC Handbook of Chemistry and Physics", 57th Edition, Weast, R.C. (Edito r ) , CRC Press Incorporated, Cleveland, Ohio, 1976-1977. - 165 -Appendix I. CALIBRATION OF THERMOCOUPLES AND ROTAMETERS Table 1.1 Calibration Table* for Thermocouples (57) (Eltctron&tin Force io Absolute Millivolt*. Tnoprrttum in Dtfreca C (lot. 1943). Rtlntne* Junctiooi tt 0* C.) •PI ° 1 ' i T T T T T - i n -7.e« •7.89 -7 71 -7,73 -7 76 -7 78 -IK -7.40 -7 43 -7 48 -7.49 -7 31 -7.54 -7.M -7 39 -7 61 -7 64 -m -7.13 -7 16 -7.18 -7.21 -7 24 -7.27 -7.30 -7 33 -7 35 -7,38 -160 -1 S3 -8 S3 -6.81 -6.91 -8 94 -6.97 -7.00 -7 03 -7 OS -7.09 -IH -«.» -8 33 -6 66 -6.60 -6 63 -6.66 -6.89 -6 72 -6 76 -6.79 -140 -6.16 -8 19 -6 22 -6.26 -6 29 -6 33 -6.36 -6 40 -6 43 -6.46 — 110 -3.30 -SU -3.87 -5.91 -5 94 -6.98 -6 01 -6 OS -6 08 -6.12 -120 -3.42 -3.48 -5.60 -5 34 -5 58 -5.61 -5.63 -5 69 -5 72 -S 76 -110 -5 03 -5.07 -5 11 -5.15 -3 19 -5.23 -5.37 -5 31 -5 35 -5.31 -100 -(S3 -4.67 -4.71 -4.75 -4 79 -4.53 -4.87 -4 91 -4 93 -4.99 -«0 -4.21 —4.13 -4 30 -4.34 -4 36 -4 43 -4 46 -4 50 -4 55 -4.59 -10 -3.71 -3 32 -3.87 -3.91 -3 96 -4.00 -4 04 -4 08 -4 13 -4.17 -TO -3.34 -1 38 -3.43 -3.47 -3 S3 -3 66 -3.60 -3 63 -3 69 -3.74 — 50 -2.19 -2.94 - 1 9 1 -3 03 -3 07 -3 12 -3 16 -3 21 -3 23 -3 30 -SO -2.43 -3 48 -2.32 -2 67 -2 62 -2.66 -3.71 -2 75 -2 80 -2.M -40 -IK -2.01 -2.06 -3.10 -2 15 -2 20 -3.34 -2 29 -2 34 -2.33 -30 -1 48 -1.33 -1 58 -1.63 -1 67 -1.72 -1.77 -1 82 -1 87 -1.91 -20 -l.OO -1 04 -1 09 — 1.14 -1 19 -1.24 -1.29 -1 34 -1 39 -1.43 -10 -0 JO -0 55 -0 60 -0.65 -0 70 -0.75 -0,60 -0 85 -0 90 -0.85 <-)0 0.00 -0.03 -0 10 -0.15 -0 20 -0 25 -0.30 -0 35 -0 40 -0.45 (+)0 0.00 0 05 0.10 0.15 0 20 0 25 0 SO 0 35 9 40 0.45 10 0 SO 0 58 0.61 0.66 0 71 0.76 0 61 0 86 0 91 0.97 JO 1 02 1.07 111 1.17 1 22 1.28 1 33 1 38 I 43 1.48 JO 1 34 1 59 1 64 1.69 1 74 1 80 1 85 1 90 1 95 2.00 40 2.03 2.11 2.16 2.22 2 27 2 32 2.37 2 42 2 48 2 53 M 2 S3 2 M 2.69 2.74 2 80 2 63 2.90 2 96 3 01 3.06 eo 3.11 3 17 3.33 1.27 3 33 1 38 3 43 3 49 3 54 3.60 70 3 63 3.70 3.76 J 81 3 8f 3.92 3.97 4 02 4 08 4.13 so 4 19 4.24 4.39 4.35 4 40 4 46 4.61 4 56 4 62 4.67 90 4.73 4 71 4 63 4.89 4 94 5.00 6 06 5 10 5 16 5.21 100 3.37 1.32 6.38 5.43 5 43 5.54 5.59 6 65 6 70 3.76 110 3.81 1 (8 6 93 5.97 6 03 6 OS 6.14 6 19 6 25 6.30 1» 3 36 9 41 6.47 6.53 6 58 6.63 6.68 6 74 6 79 6.83 110 in 8.98 7.01 7.07 7 12 7.18 7.13 7 29 7 31 7.40 140 ;.4S 7.31 7.66 7.62 7 67 7.73 7.76 7 M 7 39 7.85 150 3.00 3 OS 1.13 8.17 3 13 8.36 3.34 1 39 8 43 8.SO too 8.to a 31 3.67 8.72 3 76 3 84 8.(9 I 93 9 00 9.08 170 9.11 9 17 9 22 9 28 9 33 9.39 9.44 9 50 9 56 9.61 i n 9.87 9.73 9.78 9.83 9 69 9.95 10.00 10 06 10 11 10.17 ISO 10. r 10 28 10 34 10.39 10 45 10.50 10.56 10 61 10 67 10 72 100 10.78 10.M i o n 10.93 11 00 11.03 11.13 11 17 11 23 11.28 >I0 11 34 11.39 11.45 11.80 11 56 11 81 11.67 11 71 11 73 11.81 B0 11 89 II 95 13.00 12.06 13 13 12 17 11.23 13 38 12 34 12.39 230 12.43 13.60 13 M 13 «3 13 67 12 73 12.73 12.84 12 89 12.95 140 13 01 13 03 11.13 13.17 13 23 13 28 13 34 13 40 13 48 13 51 UO 13 56 13 32 13.67 13 73 13 78 13.64 13.39 13.95 14 00 14.06 M0 14 13 14 17 14 S3 14 28 14 34 14 89 14 45 14.50 14 M 14 61 no 14.87 14.73 •4 78 14 83 14 80 14.94 13.00 13.06 16 11 15.17 no 13 11 18.33 15.33 18.39 15 44 15.50 13.15 15.6) IS 66 15.72 no 15.77 13.33 15 38 15.94 16 00 16 OS 16.11 16.16 16 22 16.27 300 It 33 16 38 16.44 16 49 16 35 16 60 16 66 16 71 16 77 16 82 110 130 1983 It 43 16.99 17 04 17 10 17.15 17.31 17.26 17 31 17.37 17.43 17.48 17 54 17.60 17 65 17 71 17.76 17.62 17 87 17.93 130 17.93 18 04 18 09 18 15 16 20 18 26 18 33 18.37 18 43 18 48 140 18.34 18.69 18 15 18.70 16 76 18.81 16.87 18 92 18 98 19.03 360 19 00 19.14 19.30 19.36 19 31 19.37 19.13 19 49 19 S3 19.39 no 19.34 19.70 19.73 19.81 19 66 19.93 19 97 20 03 20 08 20.14 370 20.20 10.23 10.31 20.36 30 42 30.47 30.63 30.58 20 64 20.69 330 20 75 30.80 30 66 20.91 30 97 31.02 31.03 31 13 21 19 21.24 330 21.30 11.35 31.41 21.48 31 62 31.57 31.63 31.68 21 74 21.79 too 21.33 11.90 81.94 22.02 11 07 13.13 33.18 22.24 22 29 32 35 410 22 40 12 41 22.51 22 57 22 62 22 68 31.73 22 79 22 84 22.90 430 32 «3 23.01 33.03 83 12 23 17 33.23 33.38 23.34 23 39 23 45 430 440 23.30 11.M 23.31 23.67 S3 72 23.71 13 13 23.39 21 94 24.00 24.03 34.11 11.17 24 22 34 21 24 S3 14 39 34 44 24 30 24.55 430 34.31 34 M 14.72 24.77 34 31 24.18 34.94 S3 00 23 05 2S.11 480 23.18 33.21 13.27 25.33 25 IS 25 44 33.49 23 55 35 60 23 66 470 25.72 33.77 35 83 25.88 25 94 25.99 26.05 26 10 26 16 26.22 430 23.27 36.31 16.38 38.44 28 49 26.53 26.61 26.68 26 72 26 77 400 28.83 26.19 36 94 27.00 27 05 27.11 27.17 27.22 27 28 27.33 100 27.39 37.46 77.50 27.56 27 61 27.67 27.73 27.78 27 84 27.90 310 27.93 18 01 28 07 28.12 28 IB 28.23 28.29 38 33 2S 40 28 49 130 29 33 38.67 38 63 26-69 28 74 28 80 28.86 28 91 28 97 29 o: 130 29.08 29.14 19.20 29.23 29 31' 29.37 29.42 29 48 29 54 29 59 340 MO 39 33 29 71 39 33 29 82 39 •8 29.94 19 99 30.OS SO 11 30 16 30.22 30 ta 10.34 30.39 30 43 30.51 30.67 30.63 ao 43 30 71 Bami on UM laurui^ u) Ttapcrtlun 8c*k of IMS. * Used in Runs 1 to 8. - 166 -T a b l e 1.2. CONSTANTS CORRESPONDING TO THE CALIBRATION EQUATION* FOR THERMOCOUPLES L o c a t i o n o f C b a Range Run The Thermocouple CC) CC/mv) (°C?/mv) CC? Tank o u t -1.67865 21.65324 -0.71004 25-50 9-38 E x c h i n 0.25190 19.79763 -0.29185 25-50 9-21 0.37845 19.10536 0.0 20-40 22-38 2.40695 17.71571 0.24891 25-50 9-21 Exch o u t 0.20770 19.34461 0.0 20-40 22 0.15810 19.27142 0.0 20-40 23-26 0.34057 19.12506 0.0 20-40 27-38 Steam i n 9.60230 15.75524 0.18182 100-130 9-21 0.65260 18.80879 0.0 90-130 22-38 Steam o u t 9.97206 15.60082 0.18964 100-130 9-21 0.39281 18.85247 0.0 90-130 22-38 * T = a v 2 + bv + c (T i n °C, v i n m i l l v o l t s ) . E x c h = exchanger. - 167 -Figure 1-1. CALIBRATION CURVE FOR LARGE ROTAMETER - 168 -Figure 1 - 2 . CALIBRATION CURVE FOR SMALL ROTAMETER - 169 -Appendix I I . SAMPLE CALCULATIONS 11 -1 Determination of Heat Flow Rate The rate of heat flow (q) to the r e c i r c u l a t i n g water was calculated by: q = W cc pAT c ( H - l ) where m, c p and AT are the mass flow rate, the s p e c i f i c heat and the temperature change o f the water, respectively. Subscript c i s denoted to the cold stream (water). A T £ was calculated using the c a l i b r a t i o n table or c a l i b r a t i o n equations shown i n Appendix I. Wc was determined using the volumetric flow rate (V) as follows: Wc = PV (11-2) Physical properties (Cp and p) of water were evaluated at the bulk temperature (T^) using: P(kg/m 3) = -0.3269 f 5 + 1005.4 (II-3) c p (k /kg°C) = -0.00108 T 5 + 4.1818 (II-4) where i s in degrees centigrade. - 170 -II.2 Determination of Heat Transfer Area The outside nominal area of the tubes were used as a reference area in c a l c u l a t i o n of the overall heat transfer c o e f f i c i e n t A Q = TrDQL (11-5) where DQ i s the outside diameter (19.1 mm) and L i s the length (1.33 m) of the tubes i n contact with the water. 11.3 Determination of Logarithmic Mean Temperature Difference Following the evaluation of the i n l e t and o u t l e t temperatures of both streams v i a ei t h e r the c a l i b r a t i o n table or equations, the logarithmic mean temperature difference (LMTD) was calculated using: LMTD = ^ ^ (II-6) l n <VTc. ) / ( V T c > i n out where T i s the temperature and subscripts c, h, in and out are denoted to the cold, the hot, the incoming and the outgoing streams. Since the steam (hot stream) did not undergo any sub-cooling, the average of the i n l e t and o u t l e t temperatures, (T^) of that stream, which were s l i g h t l y d i f f e r e n t due to the experimental errors, was used in the determination of LMTD. - 171 -II.4 Determination of Overall Heat Transfer Coefficient The following equation was applied to compute the overall heat transfer coefficient based on the outside nominal area: o~ A O(LVD) (II-7) 11.5 Determination of the Fouling Resistance The change in the magnitude of the overall heat transfer coefficient over the length of the run was due to the fouling resistance (R f) which was calculated through: where Uc and are the clean and the dirty overall heat transfer coefficients evaluated, respectively, at the start and end of a run. It should be noted that the fouling resistance of the finned tube was calculated based on the nominal area (bare-tube) outside diameter (see Appendix II.2). To relate the mass and thickness of the deposit on the finned tube to that of the plain tube, the effective area ( A e f f) should be taken into consideration. The relationship between the fouling resistance based R = 1 - 1  R f TT IT d c (II-8) - 172 -on the prime area (R f ) and the one based on the e f f e c t i v e area (R f ) can T l T2 be expressed by: R f =J^- R f (II-9) r2 % T l The unit thermal resistance (R^), the mass per unit surface area (m^) and the thickness of the deposit (x^), are in t e r - r e l a t e d as: mf = = p f k f R f (11-10) Therefore, the to t a l mass of the deposit on the finned tube would be \ = pfk^fx \ r i m e { I I - U ) or m t „ = p f k f R f „ A e f f ( I I" 1 2 ) Thus, the mass of the deposit per unit prime area (mf ) and per unit tot a l T l area (mf ) would be T2 m^  = p^k^R^ (11-13) p f k f R f 9 A e f f m = j± (11-14) T2 A t m f 2 R f 2 A e f f mT~ Rc A. r l f l t (11-15) - 173 -Considering equation 11-10 and substituting equation 11-9 into equation 11-15 would y i e l d : 2 mf /nu = x* /x* = A;;„/A A. (11-16) 2 1 2 1 A e f f can be evaluated using the f i n e f f i c i e n c y (n f) through: 0.5 m = ( i . A ) (11-17) K f in A f n f = tanMrrnjL ( I I . 1 8 ) Aeff a V t - ( V A f ) + V f ( I I - 1 9 ) where, 1, P, A f and k^. are the height, the perimeter, the surface area and the conductive heat transfer c o e f f i c i e n t of the f i n . The convective heat transfer c o e f f i c i e n t h c was approximately 2.8 kW and evaluated by: K° n no? n 0.8 D 0.333 / T T on\ N u - c . 0.023 Re f l. l m P r f 1 1 m (11-20) K l A sample c a l c u l a t i o n i s given in Section 11-11. - 1 7 4 -11.6 Determination of the Wall Temperature The average wall temperature throughout a run was evaluated using the radial rate of heat flow equations f o r concentric cylinders in the steady state condition. Wall temperatures were required for model calculations only. 2irLk q = irD.Lh.(T -T ) = _ _ " (T -T ) = *D L h ( T -T. ) i i s,..,. w. I nl D /v.) w. w o o w o ave i o i i o o ave ave ave ave ave (11-21) where T i s the temperature and subscripts s, w^  and wQ are denoted to the steam, inside and outside tube wall, respectively. Assuming that the inside wall and the steam temperatures are equal, the following equations can be written: 2* L kw  q " In (DQ/D.) (T ave w_ (11-22) ave w_ = T ave ave q ln(D Q/D.) 2^LlT (II- 23) w 11.7 Determination of the Equivalent Diameter The equivalent diameter (D g) determination of the Reynolds number. (D g) should be evaluated by d i f f e r e n t the tubes. was required f o r the subsequent The magnitude of t h i s parameter means considering the geometry of - 175 -In the case of p l a i n tubes, the following equation was applied: D e = D s - D t (11-24) i o where D and D. are, respectively, the inside diameter of the shell and s i zo the outside diameter of the tube. The equivalent diameter of the enhanced tube was calculated using: n _ A Net Free Area (NFA) , T T 9 C x Ue " 4 Total Wetted Perimeter (TWP) U W b ) where NFA = Inside cross sectional area of the shell Outside cross sectional area o f the tube Cross sectional area of the f i n s = I (D 2 - D 2 ) - 12 t l (11-26) ^ s i zo and TWP - TJ (D + D. ) + 12(2) 1 (11-27) s i zo where t and 1 are, respectively, the thickness and the height of the f i n s . - 176 -11.8 Determination of the Reynolds Number Reynolds numbers were calculated based on both the bulk (T. ) ave and the f i l m (T^) temperatures using the following equation: Re = PvD e/n = PVD e/Sn (11-28) where p, v, V and u are, respectively, the density, the ve l o c i t y , the volumetric flow rate and the v i s c o s i t y of the water passing through the annular cross sectional area, S. To calculate the physical properties (p , \i) o f the water at the average bulk temperature, l i n e a r regression was applied i n the 20°-30°C temperature region y i e l d i n g to equation 11-3 i n case of density, and: u (kg/m.s) = -0.1731 x 10" 4 T + 1.3177 x 10* 3 (11-29) ave where T. i s i n degrees centigrade, ave For the evaluation o f the density and v i s c o s i t y at the average f i l m temperature, the following relationships were applied: P (kg/m3) = 1181.32 - 0.593 T f (11-30) n(kg/m.s.) = 0.1/[2.148 ((T f-281.435) + (8078.4+(T f-281.435) 2) 0 , 5)-120.] (11-31) - 177 -where T f i s in degrees kelvin and evaluated by: + T w )/2 (11-32) ave o ave 11.9 Determination of Water Quality Parameters Total a l k a l i n i t y (T.A.) was evaluated using the following expression: T.A. = B 1 x N [ X 5000 ( n _ 3 3 ) where B', N and v' are the volume of the t i t r a n t (HC1), normality of the t i t r a n t and volume of the sample, respectively. - 178 -Hardness (Ca +) of the water sample was evaluated using: Ca + = fl' x B;,' x 1 0 0 0 (11-34) where A' and v 1 are volumes of the t i t r a n t (EDTA) and of the sample, respectively; B'' i s the weight (mg) of CaC0 3 equivalent to 1 ml of EDTA. The magnitude of t o t a l dissolved solids (TDS) was required f o r model calculations and as explained in Section 4.6, can be approximated by: TDS = 1.06 T.A. + 1.64 Ca + (11-35) The values of tota l a l k a l i n i t y and hardness, obtained from equations 11-21 and 11-22, were averaged throughout a run and used in equation 11-23 f o r evaluation of average tota l dissolved s o l i d s . 11.10 Numerical Example Using Run 26 Run 26 corresponds to the test on the finned tube having rotameter setting o f 50 (V = 39.83 x 10~ 5 m 3/s). Using the c a l i b r a t i o n equations (Table 1.2), the temperature readings f o r the s t a r t of the run are: T = 25.18°C c i n T = 32.80°C c o u t T = 100.07°C s - 179 -T. = 28.99°C D Applying equations 11-3 and 11-4: P b = 995.969 kg/m3 c = 4.1787 kJ/kg°C p c Using equations 11-1 and 11-2: q = (39.83 x 10" 5) (995.969) (4.1787) (32.80-25.18) = 12.68 kW Substituting the temperature values i n equation II-6 y i e l d s : LMTD = 32.80 - 25.18 = 7 0 > 9 7 ° c , 100.07-25.18  l n 100.07-32.80 Applying equation II-5: A Q = Tr(0.0191) (1.33) = 0.0796 m2 Therefore, by plugging the above numerical values i n equation II.7, the clean overall heat transfer c o e f f i c i e n t would be obtained: - 180 -The d i r t y o v e r a l l heat t r a n s f e r c o e f f i c i e n t would be eva lua ted us ing the temperature readings f o r the end of the run f o l l o w e d by the above procedure: II (39.83 x 10~ 5 ) (995.44) (4.1785) (34.35-26.84) _ 9 n 9 ^,,J-V V i (0.07976) (34.35-26.84) 2 ' 0 2 k W / m K a " I (107.78-26.861 l n 107.78-34.35 Then, the f o u l i n g r e s i s t a n c e can be c a l c u l a t e d accord ing to equat ion 11-8 R f = — — - — — = 0.049 m2K/kW T 2.02 2.24 The average steam temperature and the heat f low ra te throughout a run were, r e s p e c t i v e l y , 104.84°C and 16.7 kW. Thus, accord ing to equat ion 11-23 T _ i n . M 12.7 1n(19 .1 /15 .9) _ Q ( - Q , o f ° a v e " ~ 2w(44 .99) ( l . 33 ) " 9 5 ' 9 5 C Having T = 29.70°C y i e l d s : ave T f = 9 5 ' 9 5 \ 2 9 - 7 0 = 62 .32°C P b = 995.74 kg /m 3 n b = 0.0008051 kg/m.s P f = 982.081 kg /m 3 u f = 0.0004484 kg/m.s - 181 -Using equations 11-25, 11-26 and 11-27 y i e l d s : n - 4 TT(0.037 2 - Q.Q1912)/4 - 12(0.006)(0.0005) n n n o, Q m e 4 W0.037 + 0.0191) + 12 (2) (0.006) u.UU»°9 m Therefore, the Reynolds numbers can be calculated knowing S = NFA = 69.528 x 10 _ 5m 2 and using equation 11-28: Re = (995-74) (0.0239) (0.0869) = 6 1 7 Q  b (69.528 x 10" 5) (0.0008035) Re = (982.081) (0.0239) (0.0869) s 1 Q 6 5 2  f (69.528 x 10" 5) (0.0004484) 50 ml of the water sample taken at the s t a r t of the run was t i t r a t e d with 19.1 ml of 0.02 N HC1. Thus, according to equation 11.33: T.A. - (19 .D (0.02) (50000) = 3 8 2 p p m ^ For the hardness determination, 25 ml of the sample was t i t r a t e d with 0.01 M EDTA (1 mg CaC0 3 per 1 ml of EDTA). 16.8 ml of the t i t r a n t was used u n t i l the occurrence of the indicator colour change. Equation 11-34 y i e l d s : c + a + _ (16.8) (1) (1000) = 6 7 2 p p m C a C 0 3 - 182 -Having the average a l k a l i n i t y and hardness values of 361 and 648, respectively, the magnitude of the average t o t a l dissolved solids f o r t h i s ++ high concentration run (0.00805 mole N a V l i t e r and 0.00694 mole Ca / l i t e r ) would be: TDS = 1.06 (361) + 1.64 (648) = 1445 mg/liter 11.11 Numerical Determination of Fin E f f i c i e n c y and Deposit Thickness For a 1.2 m long and 6 mm high and 0.5 mm wide f i n , the f i n e f f i c i e n c y was calculated through equations 11-17 and 11-18: m = r(2.8 X 1Q3) (2) (1.2) -,0'5 _ 4 q a q, m L(44.99) (1.2) (0.0005) J " 4 9 8' 9 4 _ tanh [(498.94) (0.006)] _ n oo n f ~ (498.94) (0.006) U , J J (498.94) (0.006) Therefore, the e f f e c t i v e area and the total e f f i c i e n c y of the finned tube would be evaluated through equation 11-19 having A f = 2 (12) (1.2) (0.006) = 0.1728 m2 and A t = 0.0796 - 12 (1.2) (0.0005) + 0.1728 = 0.2452 m2 - 183 -A e f f = (0.2452 - 0.1728) + 0.1728 (0.33) = 0.1294 m 2 and i t = P- 1 2 9 4 = 0 53 t 0.2452 u ' b J Therefore, using equation 11-16: - 184 -Appendix III. COMPUTER PROGRAMS Four computer programs were used to investigate the results of each run. The f i r s t program (Figure 111.1} converts the raw datalogger data to temperatures and computes the rates of heat flow, the overall heat transfer c o e f f i c i e n t s and the fouling resistances. The second one contains three separate subprograms, each of which f i t s the fouling resistance data to a l i n e a r (Figure III.2), an asymptotic (Figure III.3) or a fourth degree polynomial (Figure 111.4) function. The t h i r d one plots both the fouling resistance data and the best f i t with respect to time (Figure III.5). The l a s t program (Figure III.6) calculates the predicted fouling rates based on the Hasson's ionic d i f f u s i o n model. - 185 -Figure I I I - l . PROGRAM TO EVALUATE OVERALL HEAT TRANSFER COEFFICIENTS AND FOULING RESISTANCES REAL LMTD INTEGER RUN DIMENSION TIME(200),R1(200),R2(200),R3(200),R4( 200) . EI (200) ,E0(200) DIMENSION DT(200),SD(200).SI(200).TS(200) .TW(200).LMTD(200).DE(200) DIMENSION HC(200).OA(200),UA(200),UI(200),RE(200) TT=0. SS=0. AA=0. READ (5.1) RUN,GG,VE,N 1 FORMAT (I5.2F10.5.I5) 2 FORMAT (F6.0.4F6.3) DO 10 1=1.N READ (5.2) TIME(I).R1(I).R2(I).R3(I).R4(I) EI(I)=19. 10536289*R1(I)+0.3784450408 EO(I)=19.125505776*R2(I)+0.3405731389 DT(I)=EO(I)-EI(I) SO(I )=18.8524736*R3(I )+0.39280770 SI(I)=18.80878684«R4(I)+0.6525958763 TS(I)»(S0(I)+SI(I))/2. TW(I)»(E0(I)+EI(I))/2. TT«TT+TW(I) SS«SS+TS(I ) LMTD(I)=0T(I)/ALOG((TS(I)-EI(I))/(TS(I)-E0(I))) DE(1) = (-0.326893 )*TW(I)+1005.445464 HC(I)=(-0.OOO108)*TW(I) + 4. 181817 OA(I ) = (DT(I )*DE(I)*HC(I)*VE)/60. UA(I)=0A(I)/(0.07976*LMTD(I)) U K I )«1/UA(I ) RE(I)=UI(I)-GG AA=AA+OA(I) 10 CONTINUE WRITE (6.3) 3 FORMAT (' EI EO DT 50 SI TS LMTD TIME 0 1 ' U R ' ) 4 FORMAT (1X.3F6.2,4F7.2,F6.0.2F6.2.F7.3) Z=0. DO 7 I = 1 .N WRITE (6.4) E K I ) ,E0( I ) ,DT(I ),S0( I ) ,SI( I ).TS( I ) , LMTD( I ) . TIME ( I ) . OA ( I ) . 1UA(I).RE(I) Z=Z+1. 7 CONTINUE — WA=TT/Z SA=SS/Z FA«AA/Z WRITE (6,5) 5 FORMAT ( ' TW(ave) TS(ave) O(ave) ') 8 FORMAT (1X.2F10.2.F8.2) WRITE (6.8) WA.SA.FA STOP END - 186 -Figure III-2. PROGRAM TO LINEARLY FIT FOULING RESISTANCES DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) . Y F ( 2 0 0 ) , WT(200) . E 1 ( 6 ) . E 2 ( 6 ) . P (6 ) COMMON M 3 READ(5, 1 ) N.M.NI 1 FORMAT(315) READ(5 .2 ) EPS 2 F0RMAT(F1O.5) 12 FORMAT(6F10.5) 11 FORMAT(F10 .1 , F10 .4) READ ( 5 . 1 2 ) (P( I ) .1=1.M) DO 10 1=1.N 10 READ(5 ,11 ) X(I ) . Y ( I ) EXTERNAL AUX CALL L O F ( X , Y , Y F , W T . E 1 . E 2 . P , 0 . 0 . N . M . N I , N D , E P S , A U X ) IF (ND.NE .1 ) STOP WRITE ( 6 , 4 ) 4 FORMAT(' ESTIMATES OF ROOT MEAN SOUARE TOTAL ERROR IN THE PARAMETERS ' ) WRITE ( 6 , 5 ) ( E2 ( I ) ,1=1.M) 5 FORMAT ( 1 X . 8 G 1 5 . 5 ) WRITE ( 6 , 6 ) 6 FORMAT(' VALUES OF X VALUES OF Y FITTED VALUES OF Y ' ) DO 7 1=1,N 7 WRITE ( 6 . 5 ) X( I ) . Y(I ) . YF ( I ) WRITE ( 6 . 8 ) P ( 1 ) , P ( 2 ) 8 FORMAT ! / , ' a= ' . G 1 2 . 5 . ' b= ' . G 1 2 . 5 ) 30 STOP END FUNCTION A U X ( P , D , X , L ) DIMENSION P ( 6 ) , D ( 6 ) COMMON M D( 1 ) = 1 . D(2 ) = X AUX = P( 1 ) + X* (P (2 ) ) RETURN END - 187 -Figure II1-3. PROGRAM TO ASYMPTOTICALLY FIT FOULING RESISTANCES DIMENSION X ( 2 0 0 ) . Y ( 2 0 0 ) . Y F ( 2 0 0 ) . WT(200) . E 1 ( 5 ) , E 2 ( 5 ) , P (5) COMMON M 3 READ(5,1 ) N.M.NI 1 F0RMAT(3I5) READ(5 .2 ) EPS 2 FORMAT(F10.5) 12 FORMAT(3F10.5) 11 FORMAT( F 1 0 . 1 , F 1 0 . 4 ) READ ( 5 . 1 2 ) (P ( I ) ,1 = 1,M) DO 10 1=1,N 10 READ(5 ,11 ) X(I ) , Y ( I ) EXTERNAL AUX CALL L O F ( X , Y , Y F . W T , E 1 , E 2 , P , 0 . 0 , N . M . N I , N D , E P S , A U X ) IF (ND .NE .1 ) GO TO 3 WRITE ( 6 , 4 ) 4 FORMAT(' ESTIMATES OF ROOT MEAN SOUARE TOTAL ERROR IN THE 1 PARAMETERS ' ) WRITE ( 6 , 5 ) ( E2 ( I ) ,1=1.M) 5 FORMAT ( 1 X . 8 G 1 5 . 5 ) WRITE ( 6 . 6 ) 6 FORMAT'( ' VALUES OF X VALUES OF Y FITTED VALUES OF Y' ) DO 7 1=1,N 7 WRITE ( 6 , 5 ) X ( I ) , Y ( I ) . Y F ( I ) WRITE ( 6 . 8 ) P(1 ) , P ( 2 ) , P ( 3 ) 8 FORMAT(/ , ' a= ' .G12 .5.'b= ' . G 1 2 . 5.'c= ' . G 1 2 . 5 ) 30 STOP END FUNCTION A U X ( P , D . X , L ) DIMENSION P (3 ) ,D (3 ) COMMON M D( 1 )=1 . D (2 ) = 1 .-EXP(-P (3 )*X ) D (3 )=P (2 ) *X*EXP (-P (3 ) *X ) AUX=P(1 )+p(2 ) * (1-EXP (-P (3 ) *X ) ) RETURN END - 188 -Fiaure 111-4. PROGRAM TO FIT FOULING RESISTANCES TO A POLYNOMIAL FUNCTION DIMENSION X(200). Y(200), YF(200), WT(200), E 1 ( S ) . E 2 ( 6 ) . P(6) COMMON M 3 READ(5 , 1 ) N.M.NI 1 FORMAT(315) READ(5,2) EPS 2 F0RMAT(F10.5) 12 FORMAT(6F10.5) 11 FORMAT(F10.1.F10.4) READ (5. 12) (P(I),I=1.M) DO 10 1=1,N 10 READ(5, 11) X ( I ) , Y(I ) EXTERNAL AUX CALL LOF(X.Y.YF,WT,E1,E2.P.0.0.N.M.NI,ND,EPS.AUX) IF (ND.NE.1) STOP WRITE (6,4) 4 FORMAT(' ESTIMATES OF ROOT MEAN SOUARE TOTAL ERROR IN THE PARAMETERS ') WRITE (6,5) ( E 2 ( I ) ,I=1,M) 5 FORMAT (1X.8G15.5) WRITE (6,6) 6 FORMAT(' VALUES OF X VALUES OF Y FITTED VALUES OF Y') DO 7 1=1,N 7 WRITE (6,5) X ( I ) . Y ( I ) , Y F ( I ) WRITE (6.8) P( 1 ) , P ( 2 ) . P ( 3 ) , P ( 4 ) , P ( 5 ) 8 FORMAT(/,' a = '.G12.5,' b = '.G12.5,' c = '.G12.5. #/,' d= '.G12.5.' e= '.G12.5 ) 30 STOP END FUNCTION AUX(P,D,X,L) DIMENSION P(6).D(6) COMMON M D(1)=1. D(2)=X D(3)=X*X D(4 ) = X*X*X D(5)=X*X*X*X AUX=P(1)+X*(P(2)+X*(P(3)+X*(P(4)+X*(P(5))))) RETURN END - 189 -Fiqure 111-5. PROGRAM TO PLOT THE FOULING RESISTANCE DATA AND THE BEST FIT INTEGER N DIMENSION X ( 2 0 0 ) . Y ( 2 0 0 ) , Z ( 2 0 0 ) . X X ( 2 0 0 ) READ ( 5 . 3 ) A . B . C . D . E 3 FORMAT (5E12 .9 ) READ ( 5 , 2 ) N,RUN,Q 2 FORMAT ( I 5 . F 5 . 0 . F 5 . 1 . F 6 . 3 . F 7 READ ( 5 . 4 ) M,K,W 4 FORMAT ( 2 I 5 . F 5 . 0 ) READ ( 5 , 1) ( X ( I ) , Y ( I ) , I = 1,N) 1 FORMAT ( F 1 0 . 1 . F 1 0 . 4 ) R E . T A . C A . P H 0 . 2 F 5 . 0 . F 5 . 2 ) CALL AXIS (2 . CALL PLOT (2 . CALL PLOT (2 . CALL PLOT (2 . , 2 . . ' R f ( M * * 2 . K / k W ) ' . 1 4 , 6 . . 9 0 . 0 , - 0 . 0 4 . 0 . 0 4 ) , 2 . , 3 ) , 1 9 . 3 ) , 2 . .2 ) (T .2 ) 9 , 2 ) .3 ) ( 2 . , 2 . , 3 ) T = 3 . DO 5 1=1.7 CALL PLOT (T CALL PLOT (T CALL PLOT T = T+1 5 CONTINUE CALL PLOT XS = 0. CALL NUMBER ( 1 . 975 xs=xs+eoo. CALL NUMBER ( 2 . 8 7 5 , 1 . 7 5 R=3.825 DO 30 1=1.6 XS=XS+600. CALL NUMBER (R, R = R+1 30 CONTINUE CALL PSYM ( 4 . 95 CALL PLOT ( 2 . , 8 F = 3 . DO 40 1=1,7 CALL PLOT ( F . 8 . CALL PLOT ( F , 7 CALL PLOT ( F , 8 F = F+1 40 CONTINUE P = 7 . DO 50 1=1 CALL PLOT 1 . 7 5 , 0 . 1 , X S . O . - 1) 1 .XS .O.- 1) 1 . 7 5 , 0 . 1 . X S . 0 . - 1 ) 1 . 5 5 , 0 . 1 5 , ' T I M E ( m i n ) ' , + 0 . .3 ) 10) .2 ) 9 ,2 ) .3 ) .6 ( 9 . , P , 2 ) •1 ) CALL PLOT ( 8 . 9 . P . 2 ) CALL PLOT ( 9 . , P , 3 ) P = P- 1 . 50 CONTINUE DO 20 I=1.N X ( I ) = 2 . + X ( I ) / 6 0 0 . Y ( I ) « 2 . + ( Y ( I ) + . 0 4 ) / 0 . 0 4 CALL SYMBOL ( X ( I ) , Y ( I ) , O . 0 8 . 0 , 0 . 20 CONTINUE XX (1 )=0 .0 IF ( C . E O . O . ) GO TO 60 IF ( D . E O . O . ) GO TO 70 DO 90 J » 1 ,K Z ( J ) « A + X X ( J ) * ( B + X X ( J ) * ( C + X X ( , J ) * ( D + X X ( J ) » ( E ) ) ) ) X X ( J + 1 ) « X X ( J ) + 3 0 . 90 CONTINUE - 190 -Figure III- 5 . PROGRAM TO PLOT THE FOULING RESISTANCE DATA AND THE BEST FIT (Continued) DO 91 d=1,K XX ( J )=2 .+XX ( J ) /600 . Z( J)=2 . + ( Z ( J ) + 0 . 0 4 ) / 0 . 0 4 91 CONTINUE GO TO 100 70 CONTINUE DO 80 J=1 ,K Z ( J )=A+B*(1-EXP(-C*XX( J ) ) ) XX( J+1)=XX( J )+30. 80 CONTINUE DO 81 J=1,K XX( J )=2.+XX( J )/GOO. Z ( J ) = 2 . + ( Z ( J ) + 0 . 0 4 ) / 0 . 0 4 81 CONTINUE GO TO 100 60 CONTINUE DO 10 J=1,K Z( J )=A+B*XX( J ) XX( J+1)=XX( J )+30. 10 CONTINUE DO 11 J=1,K XX ( J )=2 .+XX ( J ) /600 . Z( J ) = 2. + ( Z ( J ) + 0 . 0 4 ) / 0 . 0 4 11 CONTINUE 100 CONTINUE CALL PLOT ( XX (M ) , Z (M ) .3 ) DO 15 J=M,K CALL PLOT ( X X ( J ) , Z ( J ) , 2 ) 15 CONTINUE WRITE ( 6 , 8 ) X ( N ) . Z ( M ) , Y ( N ) . A , B 8 FORMAT ( / , ' X = ' . G 1 2 . 5 . ' Z = ' , G 1 2 . 5 . ' Y = ' , F 9 . 5 , ' A = ' , G 1 2 . 5 , ' B = ' , G 1 2 . 5 ) CALL SYMBOL ( 3 . 0 . 7 . 4 . 0 . 1 . ' R U N ' . 0 . . 3 ) CALL SYMBOL (3 . 0 , 7 . 2 5 . 0 1. ' 0 ' . 0 . .1 ) CALL SYMBOL (3 . 0 . 7 . 1 , 0 . 1 , ' V , 0 . . 1 ) CALL SYMBOL ( 3 . 0 . 6 . 9 5 , 0 1 . ' R e ' . 0 . . 2 ) CALL SYMBOL (3 . 0 , 6 . 8 , 0 . 1 , ' T . A . ' , 0 . ,4 ) CALL SYMBOL (3 . , 6 . 6 5 . 0 . 1 , ' C a ' . 0 . , 2 ) CALL SYMBOL ( 3 . 1 7 , 6 . 6 9 . 0 . 1 0 . ' + + ' , 0 . , 2 ) CALL SYMBOL ( 3 . . 6 . 5 , 0 . 1 ' P H ' . 0 . . 2 ) CALL NUMBER (3 . 6 . 7 . 4 . 0 . 1 . R U N . O . . - 1) CALL NUMBER ( 3 . 6 . 7 . 2 5 . 0 1 . 0 . 0 . , 1 ) CALL NUMBER ( 3 . 6 . 7 . 1 , 0 . 1 , V , 0 . , 3 ) CALL NUMBER ( 3 . 6 , 6 . 9 5 , 0 1 .RE .0 . ,-1 ) CALL NUMBER (3 . 6 . 6 . 8 . 0 . 1 , T A , 0 . ,- 1 ) CALL NUMBER (3 . 6 , 6 . 6 5 , 0 1 , C A . O . , - 1 ) CALL NUMBER (3 . 6 . 6 . 5 . 0 . 1 . P H . O . . 2 ) CALL PSYM (4 . 1 5 , 7 . 2 5 , 0 . 1 . ' k W ' . + 0 . . 2 ) CALL PSYM (4 . 1 5 , 7 . 1 , 0 . 1 ' m / s ' , + 0 . , 3 ) CALL PSYM (4 . 1 5 , 6 . 8 . 0 . 1 ' m g / 1 ' , + 0 . , 4 ) CALL PSYM (4 . 1 5 . 6 . 6 5 , 0 . 1 , ' m g / 1 ' . + 0 . , 4 ) IF (W .EQ.O. ) GO TO 120 CALL PSYM ( 3 . 7 , 7 . 4 . 0 . 1 . ' A ' . + 0 . , 1 ) 1 2 0 CALL PLOTND STOP END - 191 -Figure 1 1 1-6. PROGRAM TO DETERMINE THE RATES PREDICTED BY THE HASSON"S IONIC DIFFUSION MODEL /COMPILE IMPLICIT REAL (A-Z) INTEGER RUN C INPUT UNITS OF TA,TDS ARE PPM, TEMP=DEG K, V=CM/SEC. D = CM READ ( 5 , 9 9 ) RUN ,V ,D ,TW ,TB ,TDS ,CA ,TA , PH 9 FORMAT ( I 2 , F 6 . 2 , F 6 . 3 , F 7 . 2 , F 6 . 2 , F 6 . 0 , 2 F 5 . 0 , F 5 . 2 ) TW=TW+273.16 TB=TB+273.16 IF (RUN .EO. 0) GO TO 3 TEMP=.5*(TW+TB) PR INT, 'RUN=' ,RUN C FIND LIQUID DENSITY AND VISCOSITY AS A FUNCTION OF TEMP C LIQUID DENSITY=P LIQUID VISCOSITY=U P= (1181 .32-0 .593*TEMP )/1000 . U = 1 . / ( 2 . 1 4 8 * ( ( T E M P - 2 8 1 . 4 3 5 ) + ( 8 0 7 8 . 4 + ( T E M P - 2 8 1 . 4 3 5 ) * * 2 ) * * . 5 ) - 1 2 0 . 0 ) C FIND REYNOLDS NUMBER (RE) AND SCHMIDT NUMBER (SC) RE=V*D*P/U SC=U/(P*1 .E-05) P R I N T , ' P = ' , P , ' U = ' , U , ' R E = ' , R E , ' S C = ' , S C C CALCULATE MASS TRANSFER COEFFICIENT KD K D = 0 . 0 2 3 * R E * * ( - 0 . 1 7 ) * S C * * ( - 0 . 6 6 6 ) *V C CALCULATE KR- REACTION RATE CONSTANT KR=EXP (38 .74-20700 ./ (1 .987*TEMP ) ) C CHANGE UNITS OF KR TO KR1 (CM/S)/(G CAC03/CM**3) TO (CM/S)/(GMOLECA/L)) KR1=KR*2 .497239*40 .08/1000 . KR1=100.*KR1 C DETERMINE IONIC STRENGTH OF THE SOLUTION I = (1 . E-03 ) *TDS/40 . C DETERMINE FI F I = ( I * * . 5 ) / ( 1 + I * * . 5 ) - . 3 * I C CHANGE UNITS OF TA,TDS,AND CA (AS PPM OF CAC03) TO MOLES/L TA = T A / ( 1 0 0 0 . * 100.08935) CA = C A / ( 1 0 0 0 . * 100.08935) PRINT, '1 = ' , 1 , ' T A = ' , T A , 'TDS= ' ,TDS C FIND FM AND FD, ALSO K1 AND K2 AND HENCE K11 AND K21 F M = 1 0 . * * ( - 0 . 5 1 * F I ) F D = 1 0 . * * ( - 2 . 0 4 * F I ) C USE PH TO DETERMINE (H+) AND PKW TO FIND (0H-) H= (10 . * * ( -1 . * PH ) ) / FM 0H=(( 1 0 . * * ( - 4 7 8 7 . 3 / T E M P - 7 . 1321 *ALOG10(TEMP)-0.01037*TEMP+22.801) ) 1/H)/FM P R I N T , ' F M = ' , F M , ' F D = ' , F D K1 = 10.** (-17052/TEMP-215.21*AL0G10(TEMP)+0.12675*TEMP+545 . 56) K2=10.** (-2902 .39/TEMP-0 .02379*TEMP+6.498 ) P R I N T , ' K 1 = ' , K 1 , ' K 2 = ' , K 2 , ' T E M P = ' , T E M P K11=K1/FM**2 K21=K2/FD**2 PRINT, 'K1 1 = ' ,K1 1 , 'K21 = ' ,K21 C NOW USE THE VALUES OF TA ,H ,OH,K11 ,K21 TO DETERMINE (HC03 ) . (COS ) . (C02 ) HC03=(TA+H-0H)/ ( (2 . *K21/H)+1. ) C03=(TA+H-0H)/(2.+H/K21) C02 = (H*(TA+H-0H) )/(K11 + 2 .*K11*K21/H) P R I N T , ' P H = ' , P H , ' H = ' , H P R I N T . ' ( H C 0 3 ) = ' . H C 0 3 , ' ( C 0 3 ) = ' , C 0 3 , ' ( C 0 2 ) = ' , C 0 2 P R I N T , ' ( O H ) = ' , O H , ' K 1 1 = ' , K 1 1 , ' K 2 1 = ' , K 2 1 C NOW WE CALCULATE W USING CA++ CONC. KSPU=10 . * * ( -0 .01183* (TEMP-273 )-8 .03 ) KSP=KSPU/(FD*FD) P R I N T , ' C A + + = ' , C A . ' K D = ' , K D , ' K R = ' , K R , ' K S P 1 = ' , K S P W=(KD*CA/2. )* (1.+C03/CA+KD/(KR1*CA) ) * ( 1 . - ( 1 . - ( ( 4 . * C 0 3 / C A ) * ( 1 . - K S P / - 192 -Figure 111-6. PROGRAM TO DETERMINE THE RATES PREDICTED BY THE HASSON'S IONIC DIFFUSION MODEL (Continued) 1 (CA*C03) ) ) / (1 .+C03/CA+KD/ (KR1*CA) ) * *2 ) * * .5 ) A=1 .-4 . *K21*KR1*CA/ (K11 *KD ) B=C02/CA+4.*K21*KR1*HC03/(K11*KD)+KSP*KR1/(KD*CA) C=K21*KR1*HC03**2/(K1 1 *KD*CA )-KSP*C02*KR1/(CA**2*KD) C C = ( 1 . + 4 . * A * C / B * * 2 ) * * .5- 1 . VV = CC+1 . WLPH=.5*.1*KD*CA*B*CC/A WP=KD*C03*(1 .-KSP/(CA*C03) )/ (KD/(KR1*CA)+4.*C03/HC03+KSP/(CA*C02) ) C CORRECT UNITS OF W FROM CM/S * MOLE/L TO GM/CM**2-S W=(W/1000. )*100.08935 WP=.1*WP PR INT , ' VV= ' ,VV , 'WLPH= ' ,WLPH . 'WHPH= ' ,W . ' IN G/(CM**2-S) ' PRINT, 'W LPH APP=',WP WRITE(6.12) 12 FORMAT(// ) 3 CONTINUE STOP END /EXECUTE - 193 -Appendix IV. FOULING CURVES The remainder of fouling curves with respect to time are shown in Figures IV.1 to IV.17. Figure I V - l . RUN 1A FOULING RESISTANCE VERSUS TIME - 194 -0.2 0.1 6 0.1 2 RUN Q V Re T.A. Ca + * PH I 2 A I 1.5 kW 0.695 m/s 2 4 9 8 4 I 73mg/ l 294 mg/l 7.9 2 0.0 8 0.04 0 0 a? as • • • • - 0 . 0 4 1 1 1 10 20 30 40 Time (hrs) 50 60 70 Figure IV-2. RUN 2A FOULING RESISTANCE VERSUS TIME - 195 -0.2 0.16 0.1 2 RUN Q V Re T.A. C a * + pH 3A 10.4 kW 0.503 m/s 18576 177 mg/l 304 mg/l 7.8 9 0.08 0.0 4 • n ft O.Ofr-- 0 . 0 4 1 • CD -a— • L an ft 10 20 30 40 Time (hrs) 50 60 70 Figure IV-3. RUN 3A FOULING RESISTANCE VERSUS TIME - 196 -0.2, 0 .16 0.1 2 RUN Q V Re T.A. C a " pH I 0.4 kW 0.503 m/s I 8 599 I 77mg/l 3 0 4 mg/l 7.93 0.0 8 0.04 0.0 8= -0.04 20 30 4 0 Time (hrs) 50 60 70 Figure IV-4. RUN 3 FOULING RESISTANCE VERSUS TIME - 197 -0.21 T 0.16 0.12 Run Q V Re T.A. C a " PH 5A 14.1 kW 0.50 3 m/s 2 1170 I 62 mg / I 281 mg/1 8.1 I 0.0 8 0.0 4 0 0 - 0.04 1 10 20 30 4 0 Time (hrs) 50 60 70 Figure IV-5. RUN 5A FOULING RESISTANCE VERSUS TIME - 198 -14.1 kW 0.503 m/s 21 397 I 50mg/l 269 mg/l 8.1 I 0 10 20 30 40 50 60 Time (hrs) Figure IV - 6 . RUN 5 FOULING RESISTANCE VERSUS TIME 0.1 6 0.1 2 RUN Q V Re T.A. C o ~ PH - 199 -Figure IV-7. RUN 6A FOULING RESISTANCE VERSUS TIME - 200 -Figure IV-8. RUN 21 FOULING RESISTANCE VERSUS TIME - 201 -0.21 0.16 0.1 2 RUN Q V Re T.A. Co** PH 22 I 2.0 kW 0.695 m/s 2 9 0 3 0 3 4 8 mg/l 6 3 9 mg/l 7.6 3 0.08 0.04 rSj DU eg • • H D i f • • • cp -0 .04' 10 20 30 40 Time (hrs) 50 60 70 Figure IV-9. RUM 22 FOULING RESISTANCE VERSUS TIME - 202 -0.21 0.16 5 O.I2| 0.08 0.04 RUN 24 Q 8.4 kW V 0.2 99 m/s Re 1 1 952 T.A. 4 1 5 mg/1 C a + + 6 97 mg/1 pH 7.7 8 • •1 • • • —I -0.04 10 20 30 40 Time (hrs) 50 60 70 Figure IV-10. RUN 24 FOULING RESISTANCE VERSUS TIME - 203 -0.2 O.I 6 O.I 2 RUN Q V Re T.A. C o " pH 25 1 0.9 kW 0.600 m/s 2 3078 3 56 mg / I 6 5 1 m g / l 7.4 5 W E 0.0 8 or 0.04 o - 0 . 0 4 1 10 20 30 40 Time (hrs) 50 60 70 Figure IV-11. RUN 25 FOULING RESISTANCE VERSUS TIME - 204 -0.2i 5 0.16 0.1 2r— RUN Q V Re T.A. Co** pH 28 I 1.3 kW 0.460 m/s 8 9 7 3 3 4 7 mg /I 6 3 3 mg/1 7.6 0 CM 0.0 8 r-0.04 0.0 0.04 1 1 10 20 30 40 Time (hrs) 50 60 70 Figure IV-12. RUN 28 FOULING RESISTANCE VERSUS TIME - 205 -CVJ E *#-or O.I 6 r -O.l 2 h-0.0 8 r — -0.04 0.04 Figure IV-13. RUN 29 FOULING RESISTANCE VERSUS TIME - 206 -RUN 30 V 0.3 40 m/s Re 6 8 4 9 J - A ; + 36 5 mg/| C a + + 6 5 0 mg/| PH 7.5 4 Time (hrs) Figure IV-14. RUN 30 FOULING RESISTANCE VERSUS TIME 0.1 6 - 207 -40 50 T ime (hrs) 70 Figure IV-15. RUN 32 FOULING RESISTANCE VERSUS TIME - 208 -0.2 O.I 6 ^ O.I 2 CM E 0.0 8 0.04 - 0.0 4 RUN Q V Re T.A. C a + + PH 33 9.4 kW 0.503 m/s I 9 3 9 4 353 mg/ I 6 4 0 mg/1 7.9 3 0 2 0 30 4 0 Time (hrs ) 50 60 70 Figure IV-16. RUN 33 FOULING RESISTANCE VERSUS TIME - 209 -O.I 6 h 0.1 2 H <? 0.08 or 0.0 4 0.0 Q>--0 .04 30 40 Time (hrs) Figure IV-17. RUN 37 FOULING RESISTANCE VERSUS TIME 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0058727/manifest

Comment

Related Items