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 this 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 requirements  this thesis  British  it  freely available  for  fulfilment of the  f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y  of  Columbia,  agree t h a t  i n partial  I agree that f o rreference  permission  the Library  shall  and s t u d y .  I  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my  understood  that  copying or p u b l i c a t i o n  f i n a n c i a l gain  shall  of this  / Jp^, P„£  Department o f  /illi  ?  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  APA  :  M  It i s thesis  n o t be a l l o w e d w i t h o u t my  permission.  Date  further  f o rextensive copying o f t h i s  department o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  tif.fiAi  Columbia  A<\%k  ft  1  written  - iiABSTRACT The performance o f stainless steel, copper and mild steel  plain  heat exchanger tubes and an externally-finned mild steel tube was studied under calcium carbonate scaling conditions at constant heat flux.  Artificial  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  recirculated through a steam  calcium  hardness  to  650 mg  CaCOyi  were  heated annular test section f o r periods o f  70 hours. The e f f e c t o f velocity 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 i n a linear manner i n  the majority o f runs although f a l l i n g rate and asymptotic behaviour were also observed.  Initial  scaling rates were compared with the predictions o f  Hasson's ionic d i f f u s i o n model. Generally, scaling decreased i n extent as the tube material was changed from mild steel to copper to stainless steel, although there were some operating conditions where this trend was conclusion could  be drawn concerning i n i t i a l  not followed. fouling  No  firm  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 o f 33A and 53A, respectively, was examined under the same operating conditions as f o r the p l a i n mild steel tube.  In addition to  higher values o f heat flow rate, the former had higher values o f 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, coefficients  and  the  the clean and predicted  the d i r t y overall heat transfer  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 and the velocity for either of non-corroding  values of fouling rate  plain tubes.  However, for  corroding tubes, as the velocity increased, the fouling rate decreased. The finned tube appears to be the most suitable choice presence of hard water scaling.  in the  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 experimental  values; however i t does not predict the e f f e c t of v e l o c i t y .  the  - iv TABLE OF CONTENTS Page Abstract L i s t of Tables L i s t of Figures Acknowledgements  ii vii viii xii  1. INTRODUCTION  1  2. THEORY  5  2.1 Types of Fouling  5  2.2 Fouling Behaviour  6  2.3 Precipitation 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 Precipitation Fouling  30  2.7.1 2.7.2 2.7.3 2.7.4  Velocity Heating Surface Temperature Water Chemistry  30 34 35 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 3.5 Temperature Measurements  .  63 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  5.1.1 Low Concentration Runs 5.1.2 High Concentration Runs 5.2 E f f e c t of Reynolds Number on Overall Heat Transfer Coefficient 5.2.1 Copper and Stainless Steel Tubes 5.2.2 Copper and Plain Mild Steel Tubes 5.2.3 Plain and Finned Mild Steel Tubes  82 .  82 85 96 96 100 104  5.3  Fouling Resistance With Respect to the Time  107  5.4  Effect of Reynolds Number on Fouling Resistance  120  5.4.1 5.4.2  Copper and Stainless Steel Tubes Copper and Plain Mild Steel Tubes  120 122  5.4.3  Plain and Finned Mild Steel Tubes  124  5.5  Determination of the Fouling Rate 5.5.1 5.5.2  Measured Fouling Rate Predicted Fouling Rate  126 126 126  - 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 5.6.2 Copper and Plain Mild Steel Tubes 5.6.3 Plain and Finned Mild Steel Tubes  128 128 132  5.7 Effect of Reynolds Number on the Predicted Fouling Rates 5.8 Comparison Between the Predicted and Measured  134  Fouling Rates  140  6. CONCLUSION  145  7. NOMENCLATURE  149  8. REFERENCES  156  APPENDIX I.  CALIBRATION OF THERMOCOUPLES AND ROTAMETERS . . . .  165  APPENDIX I I .  SAMPLE CALCULATIONS  169  11 -1 11.2 11.3  169 170  11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11  Determination of Heat Flow Rate Determination of Heat Transfer Area Determination of Logarithmic Mean Temperature Difference Determination of Overall Heat Transfer Coefficient Determination of the Fouling Resistance. . . Determination of the Wall Temperature. . . . Determination of the Equivalent Diameter . . Determination of the Reynolds Number .... Determination of the Water Quality Parameters Numerical Example Using Run 26 Numerical Determination of F i n E f f i c i e n c y and Deposit Thickness  170 171 171 174 174 176 177 178 182  APPENDIX I I I . COMPUTER PROGRAMS  184  APPENDIX IV.  193  FOULING CURVES  - vii LIST OF TABLES Table  Page  2-1  Some Fouling Rate Models f o r P r e c i p i t a t i o n Fouling  18  2- 2  E f 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 Summary of Results f o r Runs at High Concentration  86  of Chemicals  91  5-3  Summary of Results f o r Stainless Steel Tube  98  5-4  Summary of Results f o r the Copper Tube at Low Concentration of Chemicals Summary of Results f o r the Copper Tube at High  99  5-2  5-5  Concentration of Chemicals  102  5-6  Summary of Results f o r 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 Comparison of Predicted Fouling Rates on Copper and Stainless Steel Comparison of Predicted and Measured Fouling Rates on Copper Comparison of Predicted and Measured Fouling Rates on Stainless Steel Comparison of Predicted and Measured Fouling Rates  5-10 5-11 5-12 5-13  for High Concentration Runs  129 136 141 141 142  APPENDIX I 1-1  Calibration Table f o r Thermocouples  165  1-2  Constants Corresponding to the Calibration Equation f o r Thermocouples  166  - viii LIST OF FIGURES Figure  Page  2-1  Characteristic Fouling Curves  2-2  Equilibrium Distribution Fractions of Total Carbon at Various pH Levels S o l u b i l i t i e s of Hydroxides and Calcium Carbonate  16  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 Vertical (b) Cross Sections  2-3  9  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 5-7  Photograph of Disassembled Fouled Finned Mild Steel Tube . E f f e c t of Reynolds Number on Clean and Dirty Overall Heat Transfer Coefficients of Copper and Stainless Steel Tubes Effect of Reynolds Number on Clean and Dirty Overall Heat Transfer Coefficients of Copper and Plain Mild Steel Tubes  95  5-8  97 101  - ix Figure 5-9  Page E f f e 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  Ill  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  E f f e c t of Reynolds Number on Fouling Resistance for Copper and Stainless Steel Tubes E f f e c t of Reynolds Number on Fouling Resistance for Copper and Plain Mild Steel Tubes E f f e c t of Both Velocity and Reynolds Number on Fouling Resistance for Plain and Finned Mild Steel Tubes E f f e c t of Reynolds Number on Measured Fouling Rate for Copper and Plain, Mild Steel Tubes E f f e c t of Both Velocity and Reynolds Number on Measured Fouling Rate for Plain and Finned Mild Steel Tubes  5-22 5-23 5-24 5-25 5-26  E f f e c t of Reynolds Number on Predicted Fouling Rate for Copper and Stainless Steel Tubes  121 123  125 131 133 135  - X  -  Figure 5-27 5-28 5-29  Page E f f e c t of Reynolds Number on Predicted Fouling Rate for Copper and Plain Mild Steel Tubes E f f e c t of Both Velocity and Reynolds Number on Predicted Fouling Rate f o r Plain and Finned Mild Steel Tubes Comparison of Measured Scaling Rate With Rate Predicted by the Ionic Diffusion Model  138  139 144  APPENDIX I 1-1  Calibration Curve f o r Large Rotameter  167  1-2  C a l i b r a t i o n Curve f o r Small Rotameter  168  APPENDIX III III-l  Program to Evaluate Overall Heat Transfer C o e f f i c i e n t s 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 Program to Plot the Fouling Resistance Data and the Best F i t Program to Determine the Rates Predicted by the Hasson's Ionic Diffusion Model  111-5 III- 6  188 189 191  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  xn  ACKNOWLEDGEMENTS I would l i k e to thank Dr. A.P. Watkinson f o r his patience and conscientious supervision during the course o f t h i s study. I am also very grateful to the members o f 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 o f data. My thanks also go to the personnel o f the workshop, electronic shop and  stores, and e s p e c i a l l y to Mr. H. Lam f o r his assistance  acquisition of parts and chemicals.  i n the  1.  INTRODUCTION During heat transfer operation with most liquids 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  precipitation of dissolved salts 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 rises.  However, some salts 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 range.  over some  I f 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 salts 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 ) . Fouling factors f o r tubular f  heat exchangers can be found Association (TEMA) standards  i n the Tubular  Exchanger  Manufacturers  (1). Since fouling resistance increases  with  time, a period of one year i s usually chosen as a basis f o r 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. + R + R ) o i i o 1  h  w  h  f  f  f  M T  f  m  At a given q and A T additional surface area i s added to compensate f o r M  the increased thermal resistance due to fouling. Fouling  is a  costly  phenomenon  i f a l l operating,  maintenance and production expenses are considered.  capital,  Due to the insulating  effect 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 rise i n capital costs i n case of additional heat exchange surface provided  i n a n t i c i p a t i o n of f o u l i n g .  Manual or even  cleaning of the equipment results in high maintenance costs.  chemical  Furthermore,  there are production losses during the plant downtime. Despite  the  difficulty  i n obtaining the  accurate  measurements  regarding f o u l i n g expenses, Thackery (2) has suggested, i n his recent study at AERE Harwell, England,  that the f o u l i n g cost i s about $0.73 -  b i l l i o n per year in the United Kingdom.  $1.20  He has estimated that about 41% of  this amount i s due to the increased operating cost as the r e s u l t of energy losses. About 21% of the f o u l i n g cost i s due to increased c a p i t a l 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  industrial  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 i n evaluation of the performance of a heat exchanger. In cooling water systems, CaC03 i s one of the major scaleforming s a l t s . of C a  + +  The deposition rate of CaC03 based on the radial d i f f u s i o n  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). objective i s to compare experimental  In t h i s t h e s i s , one  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. the e f f e c t of f l u i d velocity on the fouling process i s examined.  In addition,  - 5 -  2. THEORY  2.1  Types of F o u l i n g  Fouling Epstein  has been  classified  (4). T h i s c l a s s i f i c a t i o n  into  s i x d i f f e r e n t categories  has been c a r r i e d out according  by  t o the  "immediate cause o f the f o u l i n g " .  1.  Scaling or Precipitation Fouling:  the p r e c i p i t a t i o n o f inverse  s o l u b i l i t y s a l t s which are supersaturated  under the process  condition.  2.  Particulate Fouling: present  in a fluid  the d e p o s i t i o n onto a heat  o f suspended  exchange i n t e r f a c e .  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  solids This  "Sedimentation  F o u l i n g " i n case o f a h o 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 r e s u l t o f chemical surface.  4.  r e a c t i o n s which occur a t the heat t r a n s f e r  as a reactant.  usually acts  This type  as a c a t a l y s t  o f f o u l i n g i s often  i n petroleum r e f i n e r i e s .  Corrosion F o u l i n g :  deposits a r e made o f the c o r r o s i o n products  r e s u l t i n g from chemical and  s o l i d m a t e r i a l s are formed as a  The surface material  r a t h e r than encountered  Fouling:  the process  fluid.  r e a c t i o n o f the heat t r a n s f e r surface The f o u l e d  d e p o s i t i o n o f other f o u l i n g m a t e r i a l .  l a y e r may a s s i s t the  - 6 5.  B i o f o u l i n g : the accumulation of biological organisms and their 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. categories temperature.  1-5, the fouling  process  i s enhanced with  In the case of increasing the  However, freezing fouling can only be accomplished  by a  temperature drop i n 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 effects 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  resistance (R^) which i s a function of time.  the  fouling  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, - m  r  (2-1)  where rh^ and m are the gross rates of deposition and removal of the r  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 f o r 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 different types of  fouling curves are shown i n Figure 2-1. 2.3 Precipitation Fouling As was mentioned  e a r l i e r , precipitation fouling occurs due to  supersaturation of sparingly soluble salts 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  solution  i s concentrated i n the evaporators, operated at  70°C,  rock to the s u l f u r i c acid.  to get 70 - 74% H P0 3  4>  The  Since the s o l u b i l i t y of  CaSO^ changes at different acid concentrations (decreases in t h i s case), bulk precipitation of the s a l t takes place.  Figure 2-1.  CHARACTERISTIC FOULING CURVES  -  Cooling down or  3.  salts,  10  -  heating up normal  respectively.  or  inverse  solubility  Supersaturation can occur during the  heat transfer operation with respect to the heat transfer surface, the bulk of the process fluid or both.  Following accumulation of  the  the  creation  deposits  mechanisms mentioned earlier. (e^)  occurs  degree  of  supersaturation, according to  the  the six  In precipitation fouling,  is due to nucleation phenomena.  nucleation step.  of  ultimate fundamental  the delay time  Growth of the crystals follows the  Since an increase in temperature would lead to a higher  supersaturation,  it  is  decrease with increasing temperature.  obvious  that  the  delay  time  would  This effect was statistically proved  by Banchero and Gordon (7).  Diffusion of the ionic species and particulate  solids,  presence in  in case  exchanger wall  of  will  their  succeed the crystal  absorbed by and accumulate at the  the  bulk  growth.  solid-layer  fluid,  onto the  The deposits will  interface.  heat be  According to  Hasson (8), a removal process would take place simultaneously with the deposition process, due to the fluid shear stress. cause the material recrystallize  already  deposited on the  and harden due to a temperature  Aging processes can  heat exchange surface increase.  Also,  to  as the  result of the shedding-off mechanism caused by stresses, the deposits can be weakened with the passage of time.  -  11  -  2.4 Calcium Carbonate Precipitation The common ion e f f e c t determines  the saturation concentration of  sparingly soluble salts such as CaCCs according to the following formula:  [Ca]  [CO"]  s where  s  = K  (2-2)  sp  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 :  [ C r ] > [Ca ] = - 3 L _ £C6- ] +  S  3  (2-3)  S  or  CCO3] > [ C O ^  =  (2-4)  - 12 K  i s s i g n i f i c a n t l y affected by temperature.  sp  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 :  pK  (2-5)  = 0.01183T + 8.03  cn  where T i s i n degree centigrade. Considering the above-mentioned i t i s obvious that K  decreases with increasing temperature.  equation, Hence,  p r e c i p i t a t i o n of CaC0 i n a solution w i l l take place due to either a 3  decrease i n K p as a result of temperature increase or addition of a S  common ion ( C a or C 0 ). +  3  When a soluble salt of calcium i s added to a bicarbonate solution, the following reactions would take place:  H + OH +  (2-6a)  HC0 + H  +  HC0  =- COo + H  o  o  H C0 = C0 "+ H 0 2  CO, + Ca++  3  CaCO  2  2  (2-6b) (2-6c) (2-6d)  - 13 Thus, the total carbon concentration (Cj) i s given by:  C = [HCO3]  +  T  To determine  [ H  2 3 C 0  ] +  [  C  0  P  the carbonate  (2  '  7)  s o l u b i l i t y , the chemistry of carbonic  acid solution should be f i r s t understood. and bases i n pure water i s complete,  Since d i s s o c i a t i o n of strong acids 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, i n the case of weak acids or bases, the d i s s o c i a t i o n 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 o r 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 d i p r o t i c weak acid (HgCO-j). Carbonic acid has three d i f f e r e n t equivalence points with respect to H2CO3, HCO3 ' ^ 3 " * anc  na 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 e l e c t r o n e u t r a l i t y 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 ] = [HC0 ] + aCCOg] +  3  The  concentration  +  C  °  R ]  "  of a d i p r o t i c strong  [ H + ]  (2_8)  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 J 2  (2-10)  - 15 where  l<  and  dissociation  are,  2  constants  respectively,  of  carbonic  the  acid.  first Solving  and  second  three  molar  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 :  [T.A.] + CH ] - [OH] +  2  <  (2-12)  Sf)  1+  [HC0~? _- [T.A.] LI.A.J ++ [H LH ]J -- [OH] LUHJ 2K 3 +  (2-13)  9  [H ] +  [C0 ] = L[T.A.] . . A . J + [H L" ]1- - [OH] LUHJ K, 2K (1+ ) [H ] [H ] +  2  +  c  +  (2  _  +  And the d i s t r i b u t i o n fractions of carbon species ( i . e . a^g- = 3  "CO" = a  HC0 = 3  a  C0 = 2  (1 +  14)  9  ([H ]/l< ) +  2  + ([H ]/K K )) +  1  +  (1 + (K /CH 3) + (KjKg/CH*] ))' +  2  ) would be:  (2-16)  _1  2  1  X  (2-15)  _1  2  (1 + ([H*]/!^) + (K /[H ]))  [CO"]  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 i n water i s very pH dependent as i s shown i n 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 ) and the pH. T  - 16 -  F i a u r e 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  regarding both the design and the performance of a heat exchanger.  importance Several  predictive models have been presented with respect to both type of fouling and mode of operation. Some of these c o r r e l a t i o n s involving p r e c i p i t a t i o n fouling are shown i n 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 carried out by McCabe and Robinson (11).  Their experimental work i n evaporators under  constant AT (two isothermal f l u i d s ) was i n 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 p r o p o r t i o n a l i t y of the quantity of scale  deposited with both the amount of l i q u i d evaporated and the total transferred f o r accomplishing this process.  heat  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  correlation was based on the  asymptotic behaviour of fouling i n industrial heat exchangers.  The following  equation was proposed to approximate the fouling resistance.  R  = R*(l-i ) B e  Q  (2-18)  - 18 -  Table 2-1. SOME FOULING RATE MODELS FOR PRECIPITATION FOULING Year 1924  Authors McCabe a Robinson (11)  Fouling rate  (dm) • m de  s  Systems Described  * " «„ * ajU  (2-19)  In evaporators with constant AT  1959 Kern 3 Seaton (5, 6)  * " 2 b - "1 *f  (2-20)  Particulate and other fouling  1962  m - aU  (2-21)  Hon Isothermal fluid  *-  (2-22)  CaCOj precipitation  It • <(c -c )  (2-23a)  Precipitation of Inverse solubility salts  m = aU  (2-23b)  With constant AT  * = a  (2-23c)  With constant heat flux  id = kgpEjcrj^jcr),]  (2-24a) (2-24b)  For CaCOj scaling with constant heat flux.  Cooling water  1964  Hasson (12)  Reltzer (15)  a  C  V  T  f  3  b  s  n  n  4  5  1968  Hasson et al. (17)  1972 Taborek et al. (18, 19)  m . aP9 a exp'^'-b, 1 xj  (2-25)  1975 Watklnson » Martinez (20)  m • K(c -c ) -b  (2-26)  7  b  s  n  tx  3  f  CaC0 scaling at constant steam temperature 3  "  K  [a  8 l+(hx /k ) f  f  ]  " 3 b  T x  f  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 =  a2 $ c  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 fouling 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  predictive 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  overall 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  T7  1.  +  1  (2-27)  - 20 where  and  diffusion  and  are, the  respectively, the mass transfer c o e f f i c i e n t f o r  rate c o e f f i c i e n t f o r surface  reaction.  K  can  Q  be  estimated using the Sherwood equation f o r turbulent flow inside pipes (14):  where D i s the hydraulic diameter and D b i s the d i f f u s i v i t y of HCO^  or  A  Ca  + +  ions.  would be evaluated through the Arrhenius equation as follows:  lnK = J - ^j-  (2-29)  R  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 equation 2-23b.  operating conditions according  to the  At a constant heat f l u x , a l i n e a r deposition rate  predicted as i s shown in equation 2-23c. No removal term was involved in formulating t h i s model.  was  - 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 diffusion  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 force f o r d i f f u s i o n (equation 2-24a).  ion driving  + +  Using the J - f a c t o r 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 t r a n s f e r 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 (Re)°:^  (2-30)  9  which was i n 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 D i f f u s i o n 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 will be discussed separately. The model (equation 2-25)  proposed  by Taborek  involved both deposition and removal processes.  et a l . (18,  19)  In this study, the effect  of water chemistry on the fouling rate has been considered.  The  gross  deposition term was assumed to be reaction c o n t r o l l e d 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 d P  fi  ^"  exp  E / R  gV  The gross removal rate was defined in terms of f l u i d shear stress, the deposit  bond resistance,  * R^ was  expressed  T  , and  as a function  of  both the deposition thickness, x^, and the deposition structure, Y .  \=  b  2  7 V (  In  1975,  (equation 2-26)  r  Watkinson  and  Martinez  (20)  presented  f o r scaling of CaC0 inside copper tubes. 3  t h e i r model 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 linear  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:  m - K(c -c ) = Ka£(T -T ) n  d  b  s  s  b  n  - 23 writing the scale surface temperature, T , in terms of the wall s  temperature, T w , they derived:  m = K d  l +  (hx /k ) f  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  scale thickness.  Assuming an Arrhenius  the  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 of f r i c t i o n factor, f l u i d velocity and density ( 2.6  T  f = ^  2 p  ).  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 f a c t o r 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 , Hasson has 3  (8) c r i t i c i z e d the use of the index and has formulated model.  the ionic d i f f u s i o n  - 24 His model (13) i s based on the radial diffusion of Ca and  CO3  (or HCO^) ions from the bulk of the f l u i d toward the hot heat t r a n s f e r surface. He has disregarded the deposition by p r e c i p i t a t e d CaCOg present in the bulk f l u i d and has used the experimental data published by Morse and Knudsen  (21)  crystallization  to  verify  and  gross  the  accuracy  of  his model.  deposition of CaCO^ per  The  unit area  rate  of  at  the  interface was expressed, based on the surface c o n t r o l l e d mechanism (22, 23), by the following equation:  w=  K  R  ([Ca ]. [CO"]. - K  where bracketed parameters  )  (2-31)  are the interfacial concentrations and K  sp  is  the s o l u b i l i t y product of CaCO^ at the scale water i n t e r f a c e . The rate of crystal growth, Arrhenius law.  K, R  i s temperature  dependent and assumed to follow the  As was experimentally shown by Gazit and Hasson (24), i t can  be evaluated from the following r e l a t i o n s h i p : lnK = 38.74 - 20700  (2-32)  R  where R  g  i s the  gas  constant  in cal/mole  °K,  T  g  i s the 3  temperature of the scale surface and K i s i n cm/sec/gr CaCOo/cm . s  absolute  - 25 The d i s t r i b u t i o n of various carbon species (C0 , HCO^, CG^) in a 3  carbonate  solution i s pH dependent as was  shown previously.  Since  the  diffusion 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 ions increases with 3  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 [(Ca )-(Ca ).] = ^[(CO'MCO^).] +  (2-33)  +  D  The c o n t r o l l i n g species are either C0 or HC0 ions at low pH values giving 2  3  rise to the following rate equation:  w = ^[(CrMCr).]  where l<  D  represents  = K [ ( C 0 ) - ( C 0 ) . ] = 2^ [(HC0 )-(HC0 ) .] D  the  2  2  convective  3  (2-34)  3  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  approximated using the following relationship (14):  ^Sc  2 / 3  = 0.023 R e " ' 0  17  (2-35)  can  be  - 26 where v i s the v e l o c i t y 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  CaC0  3  scaling  at high pH values.  4[C0-]  K [Ca ] D  [CO:]  +  n  w =  K +  [Ca]  2  n  --—-) (1K [Ca ] ./  / 1  ±[Ca ] ++  +  R  (i  ( l  +  [CO3] - ^  [Ca ]  K  §2 ) [Ca ][C5:] ±-) (2-36) 2 K +  +  Q  hr)  K [Ca ]  ++  If the CO^ concentration i s much lower than the Ca concentration, as i s often the case, the following simplified equation would express the gross deposition rate.  _sp_  [Ca ]  w = KpLT-Op 1+  [CO3]  [CO"] K [Ca ] R  ++.  [Ca ]  (2-37)  - 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 i n the following r e l a t i o n s h i p :  K  1  w  J_( w 4K K [ C a ] +  2  sp [Ca ]  + 2  +  R  L"C0,J  cn  K  )  w l< [Ca ]  (  2_ _ [Ca ]  +  2  }  +  =  (1  +  D  w K [Ca ] L  )  (  +  D  [HCOJ/2 3 [Ca ] J  +  w_ K [Ca ]  (2-38)  Having the above-mentioned condition, Ca » CO^, the equation w i l l be +  reduced to:  k  nL" a J  K  c  +  I—717  where:  4K  K [Ca ] -A?  ?  R  (2-40)  a = 1- •*-=• . l D K  b =  K  [C0 ]  4K IC _ K L + — . — . [HCO,] + P * [Ca ] K K K [Ca ] 2  2  S  6  1  D  K« Kp[HC0.] C = - i - . -2 r | K K [Ca ] 2  x  D  (2-41)  D  K [C0 ]K . [Ca l\ cn SP  ? 2  +  R  R  (2-42)  +  D  -  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 D[C0:] 3" n  .  Kp  4[C0 ]  -  3  K [Ca ] +  R  +  —  [HC0 ] 3  +  (2-43)  K sp_ [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 /de) = (w/ ) - ( x f  Pf  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 by:  R  f  = R  " o k^ R  =  (2-45)  expressed  - 29 where  i s the thermal conductivity of the foulant.  Differentiation of  this equation y i e l d s :  ^  =  de  ^ =J _ ^ I de  k  f  ^ _ . ! j l  =  de  P f  k  f  =  Mk  f  _w_.  _L  R  P f  k  f  f M  { 2  .  K C  4 6 ) 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:  R = Rf [1-exp (e/e )] f  (2-47)  c  where the adherent term (the time constant, e ) i s given by: c  e_ = M/T  (2-48)  and the asymptotic fouling resistance i s expressed by:  substituting equations 2-48 and 2-49 in equation 2-46 y i e l d s :  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"  2.7  w  (2-51)  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 will be discussed below. 2.7.1  Velocity  A decrease in the fouling rate with increases usually considered  in velocity  to be in e f f e c t in design of heat exchangers (25,  was 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 is described by: T p where t  (2-52)  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 v e l o c i t y value of 2.6 cm/sec while Watkinson and Martinez (26) have suggested a minimum value of 2.9 cm/sec f o r v* i n CaCOg s c a l i n g . Nucleation, d i f f u s i o n and chemical determine  the gross rate of deposition.  f i r s t scale layer i s deposited on a metal  reaction rate processes  will  In p r e c i p i t a t i o n of CaCO^, the 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 i n 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).  Precipitation 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 C a and HCO^ +  ions toward the hot heat transfer surface and followed by the following chemical reaction: k' 2HC0 -—- C0~ + C0 + H 0 3  2  2  (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  CaC0  (2-54)  3  (s) The precipitation process would be completed i f the l a t t i c e binding forces of the  CaC0  3  crystal exceeds the shear force exerted by the l i q u i d flow. I t  should also be mentioned that the dissolved C0 produced, 2  according to  equation 2-53, would e i t h e r migrate towards the bulk o r be released i n gaseous form at the surface. Since the rate c o e f f i c i e n t ( k ) i s r e l a t i v e l y high, the rate of 1  diffusion i s c o n t r o l l e d by the migration of C a and HCO^ ions toward the +  surface.  In addition, assuming that the generated CO2 e i t h e r 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 e f f e c t i v e factor a t 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 relatively higher v e l o c i t i e s .  When the process i s d i f f u s i o n  controlled, velocity enters the gross deposition term v i a 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 a t 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 " D K  " °' v  8 3  "  R e  °'  8 3  ( 2 _ 5 5 )  thus,  m « Re  (2-56)  0 , 8 3  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 f o r 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 for Reynolds numbers below 12000 (v<0.5 m/sec).  resistance  However, a decrease i n 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  *  R  33  v ""  tt  (2-57)  A  f  *  9 *2 Rr R + # R + -4 f  where b  Bp  = 0  f  2  i s temperature  dependent and  (2-58)  can  be  approximated  for  bulk  temperatures below 350°k through: B = 0.000271T - 0.08489 2  (2-59)  b  It should be mentioned that the system was operating under constant steam temperature. 2.7.2  Heating Surface  In CaC0 scaling, the heat transfer surface i s neither a reactant 3  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, w e t t a b i l i t y and heat of immersion are used to characterize the nature of the s o l i d surface. surface material can also a f f e c t the fouling process.  Corrosion of the  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. subsequent deposition  of CaCO^ w i l l  s o l i d interface continues  Even though  take place on CaCO^ c r y s t a l s , the  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  solubility  salt  the  temperature-solubility  relationship can  be  approximated by a l i n e a r relationship (c.-c ) = b'(T -T.) D  S  S  (2-60)  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 2-23a, 2-24a and 2-26)  2-22,  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, t h i s condition may  - 36 give rise to bulk p r e c i p i t a t i o n and hence to p a r t i c u l a t e f o u l i n g . negative effect of the temperature c l e a r i n equations characterization  r i s e on the d i f f u s i o n process i s also  2-20 and 2-25 through  factor,  The  respectively.  bulk concentration and water  The  convective  mass  transfer  c o e f f i c i e n t (KQ), f o r 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 As the scale surface temperature  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 i n film 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^ s c a l i n g . 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  temperature  r i s e s as the tube scales.  The internal  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 i n 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  carbonate. 14 ppm  important  The s o l u b i l i t y of CaC0  at 25°C.  role in the deposition of 3  calcium  in water, i n the absence of C0 ,  is  2  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 + C0 + H 0 — » - Ca(HC0 ) 3  2  2  3  (2-61)  2  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 (equation  2-12).  Therefore,  for a  concentration of Cj and temperature  solution having  3  with  ion the  total  carbon  of T, the degree of supersaturation  increases with increasing pH (equation 2-3). in the s o l u b i l i t y of CaC0  3  Figure 2-3 shows the decrease  increasing pH.  The  reduction of  the  asymptotic fouling f a c t o r due to a decrease i n pH i s experimentally shown in Knudsen and Roy's study of CaC0 p r e c i p i t a t i o n on a 90-10 3  copper-nickel  surface (30). The presence of calcium and magnesium s a 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. equations  A l k a l i n i t y i s a function of HC0 , C0 and Ofl ions. Looking at both 3  2-8 and 2-4,  3  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 qualitative formula by which the tendency of water predicted.  to either  precipitate  or dissolve  calciun  carbonate  can  be  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 i n 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, f o r the above-mentioned  reaction can be expressed  by:  k =  [Ca ] [HC0\] T — [H ]  (2-63)  +  Therefore, the saturation or equilibrium pH can be written: pH = pCa s  + pHC0 - pk 3  (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 , y i e l d s : sp  pk = pK - p K 2  (2-65)  sp  using equation 2-13, PHC63 can be formulated i n terms of pH and total al kal i n i t y : 2K  pHCfl, = p (T.A. + [ H ] - [Off]) + log (1+ - ~ - ) [H ] +  2  (2-66)  +  substituting equations 2-65 and 2-66 into equation 2-64 y i e l d s : 2K, ++ pCa + (pK -pK ) + p (TA + [H ] - [OH]) + log (1+ )(2-67) [H ] 2  sp  +  pH corresponds to the pH of a s o l u t i o n , with a given calcium carbonate s  content and total a l k a l i n i t y , at which water i s i n equilibrium with CaCO^. Hence, the Langelier Saturation Index, which i s defined as: LSI = pH-pH  (2-68)  s  can be a qualitative measure of CaCO^ s o l u b i l i t y i n water. positive, CaCO^ tends to deposit.  If the index i s  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.  (34, 35) has experimentally shown  Watkinson  that the asymptotic fouling resistance increases with increasing saturation index.  - 41 Ryznar (36)  has  criticized  the  use  of saturation  qualitative measure of CaC0 s o l u b i l i t y in the water. 3  index  as a  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  Stability Index and can be given by: RSI = 2pH -pH  (2-69)  s  He  has experimentally  approximately  shown that a water having  a stability  index  6.0 or less i s scale forming while a water having an  of index  above 7 tends to be corrosive. The presence of other chemical chemistry  and may  substances also changes the water  in turn influence both the fouling process  constituents of the scale.  and  the  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 c a r 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 been  studied.  Thurston  (38)  reported  that  the  has very  presence  of  briefly +2 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 less than 0.5% M g (39)  fouling resistance and resulted i n a deposit containing content.  ++  has reported  However, i n h i s further study,  that as the M g / C a ++  ++  increases,  Watkinson  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 i n the l a t t e r . The presence of any impurity i n a solution may also a l t e r the p r e 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 p r 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 i n 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 r a t i o i n the scale i s an influencing parameter i n  the magnitude of the fouling resistance.  I t has been observed that when t h i s  ratio i s about 3.0, the fouling factor i s high while i t decreases as the ratio becomes unity or l e s s . The presence of dissolved oxygen and chloride ion might also a f f e c t 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 i n the tube and i n 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 t r a n s f e r under the steady state condition in the absence of radiation, which i s negligible, would be (46): q =  = (q ) = q c  0  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:  - V,-  t,  \  %  '  0  | T  V ° ' 0  • w TS^ 2k  ,-„-y  V  T  0  ° '  ' W  , 2  ( 2  ( 2  -  7 1  ~  -  '  7 2 1  7 3 )  - 44 where:  h*  = the average unit thermal conductance for convection  k  = the average unit thermal conductance for conduction  c  w  D,i-> o = the inside and outside tube diameters T« , T = the temperatures of the inner and outer streams n  T  s  i  Q  , T = the inside and outside surface temperatures o s  Aj, A  = the inner and outer surface areas  0  A -A. the logarithmic mean area = ^ 0  757 1  substituting equations 2-71 to 2-73 i n equation 2-70 yields:  1 • ^ c / ^ n - V  =  A  o c B  0  ( T  s -V 0  "  2k  w D7D7  ( T  s"  T  < 2  which can also be expressed by:  T. - T i n  i  i _ Ah oc  0  D-D.  + Q  ,  _°_L _ l „. T A.h 2k A i c. +  w  (2-75)  7 4  '  - 45 -  The denominator of the above equation represents the overall resistance of the exchanger.  The overall unit thermal resistance, -jj, of the exchanger  based on the outside area i s given by: 1  , 1  =  ^  +  (D -D.)A  A  o i o  o_  +  \  2k  w*  (2  .  76)  Vi  thus,  « •oV 1n- o> U  T  ">  (2  T  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, dA , Q  more properly be represented by:  d  < = o o in- o U  d A  ( T  T  )  =  U  o o d A  A T  (2  "  78)  dividing both sides of the equation 2-78 by daT would y i e l d : dq — = dAT  U dA AT 0  0  dAT  (2-79)  and can  - 46 -  Now considering the heat balance equations i n the absence o f phase change: dq = W. c in P  1 n  where W and c respectively. T.  dT. = W C dT in o p o  (2-80)  Q  are the mass flow and the s p e c i f i c heat o f the f l u i d ,  p  The above relationships represent that q i s l i n e a r both i n  and T ; 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 Q  can be given over the length o f the exchanger, L, by:  &r UT) a  - uT)  " >  q  x = L  ,2 x = 0  81  substituting equation 2-81 i n equation 2-79 y i e l d s : U dA AT 7-Ti  9  (AT)  -7-n  =- 7i4-  - (AT)  L  (2-82)  2  0  dAT  For a constant overall unit thermal conductance, U , the integration o f the o  above-mentioned equation along the path o f the exchanger y i e l d s : q = U A AT 0  where  0  (2-83)  m  A T ^ i s the  logarithmic mean temperature difference,  LMTD,  given by:  - 47 The above-mentioned procedure can be c a r r i e d out to f i n d the overall unit thermal conductance based on the inner surface area: q=U.A.AT  (2-85)  m  Equation 2-76 represents the overall unit thermal resistance o f a clean tube.  To calculate the o v e 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: , (1 ) ^ d where  . (D "D.)A = 1 + + \ w 0  2k  1  0  A  A °  A  ry  D  + f + f ° R  R  °  (2-86) ^  i s the fouling f a c t o r and the subscript d i s denoted to the fouled  o r d i r t y exchanger.  Using the same analogy as i n equation 2-70, the  performance o f a heat exchanger can be defined by (47):  q  =  * r ° A  A T f  = 0  * rA ^  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 f l u x ,  are equally important.  - 48 Equation 2-76 implies that the overall unit heat flow conductance of an exchanger depends on:  the geometry; the flow velocity; the s p e c i f i c heat;  the thermal conductivity of both the surface material and the stream; and the viscosity.  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, i n turn, the fouling  process are also affected by these f a c t o r s . Table 2-2 shows how factor i s related to temperature  and velocity (1).  fouling  It increases with  increasing the temperature and decreasing the velocity. 2.9  Heat Transfer From Extended Surfaces To increase the rate of heat t r a n s f e r per unit volume o f the  exchanger, extended surfaces as f i n s attached to the heat t r a n s f e r wall have a wide industrial application. They compensate f o r the poor rate of heat flow i n the f l u i d with lower heat t r a n s f e r c o e f f i c i e n t by exposing more surface to i t . q = q + q t  p  Therefore, the total rate of heat flow would be:  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 ) i s defined (47, 48) by: f  - 49 -  Table 2-2. EFFECT OF TEMPERATURE AND VELOCITY ON FOULING FACTOR (47) FOULING  FACTORS*  Temperature of heating medium  Up to 240°F  24O-4O0°Ft  Temperature of water  125"F or less  Over 125°F  Water velocity. fi sec  Water velocity. /Usee  Water  Sea water Brackish water Cooling tower and artificial spray pond: Treated make-up Untreated City or^well water (such as Great Lakes) Great Lakes River water: Minimum Mississippi Delaware, Schuylkill East River and New York Bay Chicago sanitary canal Muddy or silty Hard (over IS grains/gal) Engine jacket Distilled Treated boiler fcedwater Boiler blowdown  Over  3/'  Over  0.0005 0.001  0.001 0.003  0.001 0.002  0.001 0.003 0.001 0.001  0.001 0.003 0.001 0.001  0.002 0.005 0.002 0.002  6.002 0.004 0.002 0.002  0.002 0.003 0.003 0.003 0.008 0.003 0.003 0.001 0.0005 0.001 0.002  0.001 0.002 0.002 0.002 0.006 0.002 0.003 0.001 0.0005 0.0005 0.002  0.003 0.004 0.004 0.004 0.010 0.004 0.005 0.001 0.0005 0.001 0.002  0.002 0.003 0.003 0.003 0.008 0.003 0.005 0.001 0.0005 0.001 0.002  3/'  and less  3/'  0.0005 0.002  and less  3/'  • 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 -  n  actual heat transferred by f i n f ~ heat which would have been transferred i f entire f i n were at the base temperature  q  (2-89)  where  • yf YV (  (2-90)  T s = prime surface temperature or the temperature at the base of the fin = 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 yields:  (2-91)  assuming that fi, i s invariant over the total surface would simplify the equation 2-91 t o : n  t \ =Vf (  A  )  (2-92)  - 51 where n A i s the e f f e c t i v e area ( A t  t  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  by conduction into  = by conduction out  element x  of element x+dx  rate of heat flow +  by convection from surface between x and (x+dx)  with regard to Figure 2-4. % - Vdx  +  The above-mentioned  equation becomes:  2y »t)dx(T-T )  (2-93)  b  or f o r uniform  • fin k  fa dx  b t  £  =  - f1n -S *a5  2Tr(b+t) C  2  k . bt f  n  k  b t  (T-TJ b  ( T  d x )  +  2Fi (b t)dx(T-T ) c  +  b  (2-94)  (2-95)  - 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 , between surface c  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 = "k - A ^r= f  fl  n  f  k . A m(T -T )tanh(ml) fl  n  f  s  where A = f i n cross section = bt r  b  (2-96)  - 54 P = perimeter = 2(b+t)  . - (V fiA'0.5  (2-97)  /k  F i n e f f i c i e n c y can be estimated by substituting equations 2-90 equation  and 2-96 i n  2-89:  Knowing that (ml) grows more rapidly than Tanh (ml) with increasing (ml), i t can be seen that nf and therefore nt Ti . c  are  r e c i p r o c a l l y related to  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 r e s u l t s i n the o v e r a l l unit thermal resistance of a d i r t y exchanger as follows:  .  .  ° d 'tA O  V o-°1» D  2  0  v  \  \s 1  \  X  •  \  When the outer surface i s finned, p a r t i c u l a r consideration should be given to the f o u l i n g resistance o f the inside o f the tube. When the inside fouling resistance, R , i s very large, there would be no use i n adding external f i n s i f  and increasing the outer surface which would, i n turn, increase the total fouling resistance. 2.10 Comparison Between an Enhanced and a P l a i n Heat Transfer Surface In a tubular heat exchanger,  f i n s can be attached e i t h e r to the  inside o r to the outside surface area o f the tube.  There are d i f f e r e n t f i n  designs  two major  which  are generally  longitudinal and r a d i a l .  classified  into  categories:  Both the existence and the design o f 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 o f the dynamics o f the f l u i d . In a turbulent annular flow, the presence o f f i n s would result i n the formation o f eddies and subsequent disturbance o f the laminar sublayer as was shown by Knudsen and Katz (49). These investigators showed that the number o f eddies and therefore the degree o f turbulence increases with increasing the f i n height, 1, to the f i n spacing, Sf, r a t i o .  The study o f  - 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 rise to the notion that the fouling f a c t o r s 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. Knudsen and Roy  (30) studied the CaC0  3  However,  scaling and reported the same  fouling 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).  Plain,  inner f i n and s p i r a l l y indented heat exchanger tubes were tested. experimental  results  showed  substantial advantage  in  The  heat t r a n s f e r  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 i n 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 o f 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 t r a n s f e r surface, i t i s important to know the e f f e c t of fouling on the total efficiency o f the surface, r\..  Epstein and Sandhu (54) presented two mathematical  models  - 57 to p r e d i c t the e f f e c t of uniform fouling on the total e f f i c i e n c y o f extended heat t r a n s f e r 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 i n p a r a l l e l with the f i n . Dirty fin efficiency,  was expressed i n terms of parameter m^ f o r a d i r t y  Ti j, f(  surface i n the same manner shown i n equation 2-98 f o r a clean surface. The models suggested that i n 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 i n 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 o f 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 i n 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 t r a n s f e r due to the insulating e f f e c t o f the d i r t and a lower e f f e c t i v e convective heat t r a n s f e r c o e f f i c i e n t .  However, heat t r a n s f e r  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. e f f i c i e n c y o f the clean enhanced n  t^ td' n  w a s  c n o s e n  an extended  a s  a  m e a s u r e  surface.  0<Aj;/A <l),  this  t  The ratio o f the total  surface to that o f the d i r t y one,  to see the actual e f f e c t o f fouling on  Holding a l l the other parameters  ratio  constant ( f o r  increases with increasing ml f o r the p a r a l l e l  model while i t goes through a minimum o f ml-2 f o r the series model. In both cases  at A /A =0, f  t  n /n j t  t (  i s constant  and has a higher  value  than  those with A^./A >0. Therefore, both mathematical models show that t  an increase i n thermal resistance caused by a uniform fouling deposit on an enhanced  heat t r a n s f e r 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 factor,  n /n |, t  t c  o f an exchanger  i s enhanced  according  to t h e 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 s u r f a c e 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 /n t  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 ratio  a t lower  values  o f A^/A^,  e f f i c i e n c y ) and lower values o f h/h . d  conservative results.  higher  values  o f ml  , n /n t  t d  (lower f i n  The s e r i e s model g i v e s r i s e t o more  I t p r o v i d e s a higher value f o r  n /n t  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 .  t c  |  ratio  than  - 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 v i a 1-1/2 i n . copper pipes. The flowrate o f 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 o f a 1.15 meter long glass tube with an inside diameter o f 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 helical heat exchanger. Cooling water i s supplied v i a the building mains and controlled 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).  by a  Dr F He  Drain Filter Heat exchanger  HHE SHC VTS  Helical heat exchanger Steam heated coil Valve for sampling  Figure 3-1. FLOW DIAGRAM OF APPARATUS  P Pressure gauge R Regulator Tc Thermocouple  - 61 Recirculating water which exits the finned helical 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 filter.  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 i a a 1-1/2  i n . copper pipe to the pump o r to the drain v i a a valve.  samples are taken using t h i s o u t l e t . heating  coil  temperature.  to  heat  the  test  Water  The tank i s equipped with a steam  fluid  up  to  the  initial  operating  I t 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 e i 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 o f 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:  first,  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 i n case o f the p l a i n tubes and the finned tube, the length of the tube i n 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  direct measure and comparison o f 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  O.D. (mm)  I.D. (mm)  S.S.  19.1  2  Cop  3 4  Tube No.  Material  1  Properties of Fins Width (mm)  Net Free Area x 1 0 (m ) 4  2  No.  Length (m)  15.9  -  -  -  0.01 791  7.9128  19.1  15.3  -  -  -  0.01791  7.9128  M.S.  19.1  13.3  -  -  -  0.01 791  7.9128  M.S.  19.1  14.7  12  1.2  0.5  0.00869  6.9528  S.S. = stainless steel Cop = copper M.S. = mild steel  Height (mm)  De (m)  6  -  3.5  Temperature  67  -  Measurements  H a r d w a t e r and steam t e m p e r a t u r e s a r e measured u s i n g i r o n - c o n s t a n t a n thermocouples.  The t e m p e r a t u r e o f t h e h o t s t r e a m i s measured  at the  inlet  and o u t l e t o f the tube.  O t h e r t h e r m o c o u p l e s t o measure  the temperature o f the  t e s t f l u i d a r e 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 t h e 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 h e a t e x c h a n g e r .  The  thermocouples  are connected  to  a switch, which  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 ) . measures  i s in  turn  The d a t a l o g g e r  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  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 b a t h ( F i g u r e 3 - 6 ) .  by  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.  e  Switch  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 Artificially Ca(N0 ) 3  2  water.  . 4H 0 2  or  hardened CaCl  2  .  water 2H 0 2  was  and  prepared  NaHC0  3  to  by  210  adding  liters  of  To avoid corrosion on mild steel by c h l o r i d e ion, calcium nitrate was  used as a source o f calcium. Nitrogen gas was introduced into the water to remove the dissolved oxygen i n 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 f u r t h e r introduction o f 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 o f 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 o f the water i n the exchanger was nevertheless kept as constant as possible. A f t e r being assured, by taking several temperature readings, that the steady state condition was reached, C a C l . 2H 0 o r C a ( N 0 ) 2  was added.  2  Two o r three minutes l a t e r , NaHC0 was added. 3  3  2  . 4H" 0 2  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 size. Several water samples were taken during each run, approximately 8-12 hours apart, and more chemicals constant.  were added to keep the water quality  It should be mentioned that the addition o f chemicals was done  during the run with higher concentration o f 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 o f suspended solids.  However, f o r runs at lower concentration o f 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 n e g l i g i b l e . 4.2 Solution Preparation For the low concentration early runs, 97.35 gr o f C a C l • 2H 0 2  and 64.58 gr o f NaHCO^ were used to provide an a r t i f i c i a l l y with the i n i t i a l concentration o f 0.126 g o f C a In  later  runs,  Ca(N0 ) . 4H 0 was 3  2  2  used  + +  2  hardened water  and 0.084 g/1 of Na . +  as a source  of calcium to  reduce corrosion arising from the chloride i o n . Since the deposit obtained using the above-mentioned concentrations of chemicals was muddy, the amount o f substances was increased by a f a c t o r of 2.2 (0.00694 m o l e / l i t e r of C a  + +  and 0.00805 m o l e / l i t e r o f Na ) i n  order to get a harder and better constructed scale.  +  In e i t h e r case, the  chemicals were separately dissolved i n the water before addition to the supply tank.  - 72 4.3 pH Measurements pH i s measured using an Orion Research Digital 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 0 2  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 indicator 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 Na S203 and 3 drops of the mixed indicator are added 2  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. calculated using the following formula:  Total A l k a l i n i t y = ' B  where  x  N y  *  5 0 0 0 0  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)  Total a l k a l i n i t y i s then  - 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 i n the t i t r a t i o n . sharpness  of the end point and the tendency  of CaC0  3  Both the  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 interfering 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 i n 100 ml of 95 percent ethyl-alcohol i s used as an i n h i b i t o r . M disodium  ethylenediamine  A solution of 0.01  tetraacetate dihydrate (EDTA) i s used  as a  titrant. 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 i n d i c a t o r are added to 25 ml of sample which i s already diluted to 50 ml. sample until  0.01 M solution of EDTA i s added to the reddish  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 i n 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 o f the t i t r a n t (ml) B " = mg o f CaC0 equivalent to 1 ml of EDTA 3  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 o f total dissolved s o l i d s (TDS). If solutions of x mole/liter of NaHC0 and y 3  m o l 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 NaHC0  xHC0 + xNa  3  yCa(N0 ) — 3  xHCD  yCa + 2yN0 +  2  |C0 + y C a  3  £ C0 + £ CD + £ H 0  3  3  +  3  2  + ;  3  — C a C 0  2yN0 + xNa -—3  2  + (y-|) C a  3  +  xNaN0 + (2y-x) NQ 3  (2y-x) NO" + (y-£) C a - -*-  3  (y~£) Ca(N0 )  +  r  3  2  Therefore, summation of the above chemical reactions y i e l d s :  xNaHC0 + yCa(N0 ) 3  3  »- | CaC0 + x NaN0 + (y-£)Ca(N0 ) + £ C0 + | H 0 3  3  3  2  2  2  - 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 ) + £ CaC0 3  2  3  TDS (mole/liter) = \ CaC0 + x NaN0 + (y-£) Ca ( N 0 ) 3  3  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 y +  +  5  C a - T.A. = 10 (y-|) +  5  TDS = 10 (x+y) 5  Also, TDS can be evaluated i n terms of total weight of solids per volume (mg/l):  TDS = (10 |) + (85000x) + (164) ( 5  Ca 1Q  "  T,A  -  )  TDS = T.A. + 1.7 T.A. + 1.64 ( C a - T.A.) = 1.06 T.A. + 1.64 C a +  +  - 76 Procedure For a Scaling Run (1) Install one of the clean test sections i n 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 i n  millivolts. (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 o f 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 o f the runs). (11) Turn the steam  on the exchanger  at 115.15 kPa absolute  pressure (used f o r almost a l l o f 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 o f 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  CaCl  required) solution.  2  .  2H 0 2  or  Ca(N0 ) 3  2  . 4H 0 2  (as  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 o f the wooden l i d o f 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 f o r the rest o f 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  alkalinity  and  hardness  measurements a f t e r f i l t r a t i o n o f 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 i n total 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 o f chemicals, addition o f 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 i n both  total  a l k a l i n i t y and  - 79 hardness should be exactly the same (see determination o f TDS). Considering the above assumption, the addition process i s c a r r i e d out according to the following relationships:  2 1 0  weight o f C a ( N 0 J  9  . 4rU0  added gr =  *  M  . 4H 0 £-= =-  Ca(N0J  9  ?  10 4 2 0  weight o f NaHCO^ added gas (gr) =  1  1  M  NaHC0 P  3  HT  where: Z = the change i n a l k a l i n i t y o r 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 o f make up chemicals and re-evaluate water quality. (22) Calculate the heat flux, the overall 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 o f 70 hrs, where there i s not a big change i n the fouling resistance f o r 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 line 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. tube's deposit f o r hardness.  Examine the  Measure the thickness of the  deposit at several places throughout the length of the tube. Scrape o r 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 o f 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. from the exchanger  I n i t i a l l y , after removing the tube  and scraping o f f the heavier deposit, the tube  was  replaced i n 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 i n the rest o f the equipment. Since the s o l u b i l i t y o f CaCO^ i n 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 Firstly,  i t was  not satisfactory f o r two  not possible to clean the tubes well.  procedure enhanced the corrosion of mild steel tubes. to clean the tubes by hand.  reasons.  Secondly, the  One alternative was  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 cloth.  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 inhibited hydrochloric acid.  Pickling 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 o f 5 cm. procedure was completed using an emery c l o t h .  The cleaning  However, a mixture o f oakite  solution was pumped around the system to clean the rest o f 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  Tests were f i r s t done on the stainless steel and copper tubes with ++ + concentration o f Ca = 0.126 g/1 and Na = 0.084 g/1, using  initial CaCl  2  Low Concentration Runs  .  2H 0 2  respectively.  and  NaHC0  3  as  sources  of  calcium  and  These are termed "low concentration runs".  carbonate,  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 calculation of heat flow, q, and overall heat t r a n s f e r 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 calculation of q and U. As time passed and the tube scaled, the overall  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 i n the total resistance of the exchanger with respect to time.  The e f f e c t o f 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 overall  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 f o u l i n g process was by a drop both i n total a l k a l i n i t y and the hardness.  accompanied  The reductions i n the  magnitude o f these parameters f o r the subsequent water samples were not high enough to require the addition o f more chemicals.  A f t e r 70 hrs., the  changes i n the magnitude o f 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 i n the hot f i l m adjacent to the interface.  The s l i g h t reduction i n the suspended  solids content i n the  l a t t e r part of the run indicates the possible existence o f a small extent o f p a r t i c u l a t e fouling.  X  E a. a.  cn; a)  a25 7.7 5  Q-  18.3 4  "a—r  RUN 5  3_  TI  g-  a H  300 j 280  o  260  o  1  3^  E  10 O U  -a  + + o 240  u  I75P cn E  155  o  135  10 O O  o  I 15 2.6 j CVJ  E  24 2.2  o 3  2.0  10  ao  1  20  30  40 Time  (hrs)  Figure 5-1, RUN 5 TYPICAL OUTPUT  50  60  70  - 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 i n Table 5-1.  Since heat flow increases with annular mass flow rate, both the heat flow rate and the overall heat transfer c o e f f i c i e n t of a clean tube increased with  increasing  velocity,  as i s shown i n the table.  Comparing  the  non-corroding tubes under approximately identical operating conditions, the stainless 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.  T h i s 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 evident through the experimental results.  also  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) i n which  there was  no change either i n the magnitudes o f water  quality  parameters or i n the overall 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. off.  The deposits could not be cracked  Hence, they were taken out p a r t l y by scraping o f f with a spatula,  resulting i n a rusty coloured powdery residue. The remainder was removed by chemical cleaning. 5.1.2  High Concentration Runs  Tests were carried 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  S t a i n l e s s Steel  Copper  v (m/s)  T.A. Run  U (kW/m *)  Ca++*  q  Run  a v e  (kW)  Start  0.299  0.503  1A 1 3A  7.9  188  10.4  182  168 148 175  3  0.695  2A  Start  305  310  175  11.5  158  182  2  T.A. Ca** * ** A  End  302  125  = total alkalinity » hardness Units In mg CaC0 /l Values determined by e x t r a p o l a t i o n • runs l a s t e d 48 hours 3  T.A.*  2  pH End  Start  285  7.84  270  7.86  302  7.89  302  7.93  280  7.92  247  7.95  1.37  1.68  2.03  Ca*+*  q  U  pH  ( k W / o A )  a v e  (kW)  End  I Drop  1.16  1 5.3  6A  1.16  15.3  6  1.68  0.0  5A  1.68  0.0  5  1.83  9.9  4A  1.73  14.8  Start  11.5  177  14.1  176  End 129 105 140  Start  298  298  115  18.0  170  151  294  End  Start  250  7.61  228  7.60  260  8.11  235  8.11  274  8.03  2.25  2.56  3.29  End  % Drop  1.74  22.7  1.69  24.9  2.17  15.2  2.09  18.4  2.73  17.0  2.55** 22.5**  00  - 87 o f chemicals.  The p l o t s 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 e s p e c i a l l y 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 o v e r a l l  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 total  a l k a l i n i t y and the hardness throughout the run.  A typical example f o r 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 f a c t o r responsible f o r t h i s behaviour e s p e c i a l l y i n the case of the p l a i n tube. liquid  i n the  Therefore, nitrogen gas was tank  and  CafNC^^  . 4^0  introduced to blanket the 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 i n 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 o f 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 f a c t o r of 2.2 to  get  a more pronounced  r e s u l t since  the  main objective was  the  determination of the f o u l i n g resistance and i t s v a r i a t i o n with the time. These runs are designated "high concentration runs". amount of scale deposited,  With the increase i n  the changes i n 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  8.3 X  TT  •  7.9  RUN  Q.  16  e CL  3 tn  to  •  7.0  •  3.C  E 3 ^ 300 o 2 + +  •  •  •  280  •  •  •  u 260  ID  ^1 7 0  •  O  •  <^I50 o  •  •  I 30 1.8 E  1.6U  => 1.4  0  CD  ccP, 10  20  1  30  40  50  Time (hrs)  Figure 5-2. RUN 16 TYPICAL OUTPUT  60  70  - 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 o f the suspended solids 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 typical  output  f o r a high concentration run i s shown i n  Figure 5-3. At 0.299 m/s annular velocity, as the tube fouled, the overall heat  transfer coefficient  o f the p l a i n  mild  steel  tube  decreased  approximately from 1.45 kW/mK to 1.25 kW/mK (13.8%) after 70 hours. 2  2  Figure 5-3 also represents a rapid decrease i n the magnitudes o f 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 o f 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" to 5.50 x 10~ m /s), were used to investigate 4  4  3  the e f f e c t o f velocity on the fouling process o f the mild steel tubes. The copper tube was also tested under high concentration o f chemicals at three d i f f e r e n t annular water flow rates i n the above-mentioned  region. Table 5-2  summarizes the results o f the high concentration runs.  The data i n the  table indicate an increase i n the overall heat t r a n s f e r c o e f f i c i e n t with the velocity f o r e i t h e r tube. Under identical operating conditions, the rate of heat transfer and the clean and the d i r t y heat t r a n s f e r 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 o f  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 o f the copper and the finned mild steel  10  20  30  40 Time  50  (hrs)  Figure 5-3. RUN 24 TYPICAL OUTPUT  60  70  Table 5-2. SUIMARV QF RESULTS FOR RUNS AT HIGH CONCENTRATION OF CHEMICALS Vol. R ate iFlo. 10 (•/«l  Finned HI Id steel  Plain Mild steel  Capper  s  "o  3  Run  q  UU)  T.A.* ave  Ca"* ave  PH aw  Run  Start End  I Drop  27  9.8  371  661  7.64  1.61  1.54  4.3  30  10.1  365  650  7.S4  1.69  1.45  14.2  32.00  28  11.3  347  633  7.60  2.00  1.78  11.0  39.83  26  12.7  361  648  7.S8  2.24  2.02  9.8  47.50  31  13.85 340  626  7.64  2.32  2.10  55.00  32  15.45 318  603  7.68  2.70  2.15  23.67  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 o2 Finned annular cross sectional area - 69.528 < IO" •? -5  6  o. T.A.' UN) ave  U„ tkU/aA)  ave  pH ave  Start End I Drop  24  8.4  415  697  7.78  1.45  1.25 13.8  29  9.1  351  639  778  1.58  1.32 16.5  23  11.2  3S8  644  7.68  1.84  1.43 22.3  33  9.4  353  640  7.93  1.63  1.48  9.5  25  10.9  356  651  7.45  1.90  1.63 14.2  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 10.9 2.15 14.0 1.85 15.1  9.2  Run  i IkUl  T.A.* am  Ca"* ave  PH ave  Ho Start End I Drop  38  9.9  361  659  7.69  1.70  1.48 12.9  37  12.5  346  642  7.81  2.28  1.80 21.1  36  13.4  320  619  7.79  2.4  1.80 25.0  - 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 o f the l a t t e r . The overall heat transfer c o e f f i c i e n t o f 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 o r after fouling.  The experimentally determined  ratio o f the clean overall  heat transfer o f the finned tube to that o f 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 o f the same wall  thickness, one would expect the value o f t h i s ratio 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 total surface e f f i c i e n c y o f the surface are 33% and 53%, respectively.  Therefore,  would be i n a close agreement with the experimental (1.25).  the expected  result  value o f t h i s ratio  The value o f 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 o f 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 o f the scale decreased  with distance from the base o f the f i n s .  Both the  yellow shiny deposits formed on the copper tube and the gray ones on the p l a i n mild steel tube were hard and b r i t t l e , and could be cracked o f f easily.  However, the deposits on the finned mild steel tube had to be  scraped  o f f with  a spatula, providing  photographs of the three disassembled  a l i g h t grayish powder.  The  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  -  Figure 5 - 6 .  95  -  PHOTOGRAPH OF DISASSEMBLED FOULED FINNED MILD STEEL TUBE  - 96 5.2  E f f e c t o f 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 positive e f f e c t of  Reynolds number on the value o f the overall heat transfer c o e f f i c i e n t i s evident from the graphs. heat  transfer  coefficient  In e i t h e r clean o r d i r t y conditions, the overall 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, i n the value o f 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  -  1—i—I—r  i—r  'o  CVJ  E  C V  o 3  1  H  "I  r  1  1  1  r  4 A 5A  E  6A  o  3A V  o  O  2A  V  IA V  T3 C  a> o  I  II  -\  I  Copper  h  O  S.S.  V  CVJ  E  r  2  o in  o  8  12  16  20 R  e  f i l m  X  l  °  -3  24  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 ' (m /s)  5  Run  3  23.67  39.83  55.00  1A  3A 3 2A 2  (m/s)  Re  R e b  0.299  6271  0.503  10554  0.695  14573  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  fllra  T.A. ave  CA+** ave  TDS ave (mg/l)  pH ave  11136  181  298  681  7.84  11194  173  290  659  7.86  18576  177  304  686  7.89  18599  177  304  686  7.93  24984  173  294  666  7.92  25261  161.4  283  635  7.95  U (kW/ra K) 2  ave CO  23.0  27.3  27.0  Rf  0  ave CO  ave CO  106.09  95.43  106.80  96.14  103.95  89.91  104.12  90.08  102.18  86.66  103.66  88.14  (kU)  (ra K/kU) 2  Start  7.9  1.37  10.4  1.68  11.5  2.03  End  I Drop  1.16  15.3  0.140  1.16  15.3  0.140  1.68  0.0  0.000  1.68  0.0  0.000  1.83  9.9  0.052  1.73  14.8  0.085  Table 5-4. SUMMARY OF THE RESULTS FOR THE COPPER TUBE AT LOW CONCENTRATIONS OF CHENICALS  Vol. Flow Rate x l O " (m /s)  Run  (m/s)  5  R«b  Re  f11m  T.A.* ave  CA * ave ++  3  23.67  39.83  55.00  6A  0.299  6 5A  0.503  5 4A  0.695  4  T.A. = t o t a l a l k a l i n i t y C a * = hardness TDS = t o t a l dissolved s o l i d s * Units i n mg CaC0 /l +  3  6829  11494  15870  12921  154  275  TDS ave (mg/l)  pH ave  641  7.61  Tb  Ts ave  CC)  12987  141  262  579  7.60  21170  162  281  633  8.11  21397  150  269  600  8.11  29506  169  294  661  8.03  31.0  30.6  31.8  ave  ave  CC)  CO  109.81  109.01  110.60  109.80  106.42  105.43  107.83  106.84  106.80  105.54  U (kW)  (kW/m K) 2  0  Rf (m K/kU) 2  Start  11.5  2.25  14.1  2.56  18.0  3.29  End  % Drop  1.74  22.7  0.130  1.69  24.9  0.147  2.17  15.2  0.070  2.09  18.4  0.088  2.73  17.0  0.062  2.55  22.5  0.088  - 100 5.2.2  Copper and Plain Mild Steel Tubes  The copper tube was tested under high concentrations of chemicals and three different  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 overall  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 positive 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. percentage drop i n U at higher v e l o c i t i e s .  The result was a higher An increase i n 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 o f 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 velocity.  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  -  i — i — i — i — i — i — i — i — r  2.5  steel  O  Mild  •  Copper  21  O  2.0  CM  E  37 •  P=l29kPo T»25°C  20 °  2?  o  361  P=l29kPa  T  T« 3 0 ° C  C V  3  o  23 3  J  29  o  24  ^—I—hH—i—i  1.0  i  i  3.0  E \  21  2.5  37 •  -St:  CO  o  ID  O  2.0 38 •  1.5, 24  I 16  O  20 O  33  29  €>  I  1  I  20 R  Figure 5-8.  22  25 23 o O  J  36  e  I  I  24  f i . m *  1  0  '  I  28  I  32  3  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" (u. /s)  5  Run  (ra/s)  3  Re  0  Refiim  T.A.* ave  CA++* ave  TDS ave (mg/1)  pH ave  ave  Ts ave  ave  CO  CO  CC)  (kW/m K) 2  q (kU)  Rf (ra K/kW) 2  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 i n mg CaC0 /l +  3  Table 5-6. SUMMARY OF RESULTS FOR THE PLAIN MILD STEEL TUBE Vol. Flow Rate x l O " (m /s)  5  Run  3  (m/s)  Re  R e b  filra  T.A.* ave  CA * ave ++  TDS ave (mg/l)  PH ave  Tb ave  ave  CC)  CC)  q  Tw ave  CO  (kW)  "o (kW/ra K) 2  Rf (m K/kU) 2  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  10767  21312  358  644  1436  7.68  27.92  119.77  109.02  11.2  1.84  1.43  22.3  0.156  10831  19394  353  640  1424  7.93  28.21  103.99  94.97  9.4  1.63  1.48  9.2  0.062  39.83  23 33  0.503  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  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 + +  o co  - 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 i n 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, i n  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 ave  ) of the hot stream (Table 5-6). ave  Amongst these, Run 21 yielded the highest heat flow rate as the result of the  greater magnitude of the temperature driving force.  initial  value o f the steam temperature (Run 21) was  Increasing the  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 results of the tests done on the finned mild steel Table 5-7.  tube  under  five  different  velocities  are given i n  Figure 5-9 and both Tables 5-6 and 5-7 show the positive 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 o f the clean c o e f f i c i e n t due to the greater heat transfer area in 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 o f 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 .  V o l . Flow Rate x l O  Run  Ret, (a/s)  - 5  Refllm  T.A.* ave  SUMMARY OF RESULTS FOR THE FINNED MILD STEEL TUBE  CA*** ave  (• /S) 3  27  TDS ave (ng/1)  pH  ave  T  b  ave  Ts  ave  Tw  q ave  CO  CC)  CC)  (kU)  "o  (kU/aK) 2  Start  End  30  X Drop  (lA/kU)  3844  6917  371  661  1477  7.64  31.88  108.73  101.87  9.80  1.61  1.54  4.3  0.028  3735  6849  365  650  1453  7.54  30.57  111.73  104.66  10.10  1.69  1.45  14.2  0.098  0.340  23.67  Rf  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 l k a l i n i t y Ca** ' hardness TDS = t o t a l dissolved s o l i d s * Units in ag CaC0 /1 3  - 106 -  l — i — i — r — i — i — i — i — i — i — i — r ,. 31 A  26 A  32 A  21 O  P«l29kPa T»25°C  8  20  A  8°  2  27  A A  33  30  2  24 O  4—1  1  23  O  r—I  25 O  9  C  9  H  22 O  1 1—I 1 O  Plain  A  Finned  r—r  32 A 21 O  31 A  26 A  23 O 0)  28 30  A  .5h J  ?  27  8  24  O  I  I » 12 Re  Figure 5-9.  22  T»30°C  o  20  25  A  I  P = l29kPa  Q O  I 16 f j l m  °  "  33  I  I 20  xio"  I  I 24  I  I 28  3  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. to f l a t t e n out (Figure 5-9).  R e  f-fi ^  ten(  m  *ed  No specific relationship was found between the  percentage of the drop i n the overall c o e f f i c i e n t and Reynolds number i n either case. Due to the e r r a t i c behaviour of the fouling curve, Run 27 repeated on the finned tube. first  (Run 27)  was  Considering the experimental errors, both the  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 fouling process took place, the overall  c o e f f i c i e n t o f the exchanger was  heat t r a n s f e r  reduced due to a r i s e i n the overall  resistance of the heat t r a n s f e r unit as a result of the occurrence o f 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 o f 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 linear, 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 i n the cooling water flow rate. As a consequence of the reduction i n the usage of the main supply water at night, the cooling water flow  rate increased resulting  temperature. driving  i n a lower  inlet  This situation increased the magnitude  force, the rate o f  heat flow and  recirculating of the  the overall  water  temperature  heat t r a n s f e r  c o e f f i c i e n t , resulting i n a lower value o f 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) o r "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 o f 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 o f fouling resistance than a non-porous tenacious scale f o r  - 109 -  0.21  0.16  0.12  RUN 2 11.5 kW Q 0.695 m/s V 25261 Re I 6 1.4 mg/l T.A. C V '283 mg/l PH 7.9 5 • •  cvj  e  0.0 8  0.04  -0.04'  20  30 Time  Figure 5-10.  40 (hrs)  50  RUN 2 FOULING RESISTANCE VERSUS TIME  60  70  - 110 -  0.2  0.16  1 —  0.12 -  *  CM  RUN Q V Re T.A. pH  1  i  1  i  4A 18.0 kW 0.69 5 m/s 29506 169 mg/1 2 9 4 mg/1 8.0 3  —  0.0 8 •  E  or  1  0.0 4  0.0  -0.04  1  10  i  20  i  30 Time  Figure 5-11.  1  40  1  50  1 60  (hrs)  RUN 4A FOULING RESISTANCE VERSUS TIME  70  - Ill  -  Figure 5-12. RUN 20 FOULING RESISTANCE VERSUS TIME  - 112 -  RUN Q V Re T.A. CcT* pH  0  10  26 l2.7kW 0.5 7 3 m / s 10904 361 m g / l 6 4 8 mg/l 7.5 8  20  30 Time  40  50  60  (hrs)  Figure 5-13. RUN 26 FOULING RESISTANCE VERSUS TIME  - 113 -  RUN Q  0  10  36  !3.4kW  20  30 Time  40  50  (hrs)  Figure 5-14. RUN 36 FOULING RESISTANCE VERSUS TIME  60  -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 Time  40  50  (hrs)  Figure 5-17. RUM 23 FOULING RESISTANCE VERSUS TIME  60  - 117 -  0.2  1 RUN  0.1 6 h-  Q V  Re T.A.  Ca * +  0.1 2  pH  27 9.8 kW 0.340 m/s 69 1 7 371 m g / l 66 I m g / l 7.6 4  0.0 8  0.0 4 W  °  r?  a  «Po «bP B  0.0  pBa  £  •  a  _p  D  •  an  •  CD  •  • • -0.04  10  20  30 Time  Figure 5-18.  1  40  50  60  (hrs)  RUN 27 FOULING RESISTANCE VERSUS TIME  70  - 118 -  0.2 RUN Q  0.16  „  0.12  °E  0.0 8  l3£5kW 0.683 m/s I 3579 3 4 0 mg/1 6 2 6 mg/1 7.6 4  V  Re T.A. Ca* pH  +  " f t  0.04  •  • 0.0  •  D  •o  U  • •  CO  • • •  _ —I  • SP • • • • • • •  -  • •  • •  tm  0.04 20  1  30 Time  Figure 5-19.  1  40  50  60  ( hrs)  RUN 31 FOULING RESISTANCE VERSUS TIME  70  - 119 -  0.2.  T RUN  0.16  Q  V Re T.A.  0.1 2  Ca * +  PH  38 9.9 kW 0.299 m/s 12938 361 mg/ I 659 mg/1 7.69 ml •  0.0 8  riP  D  •  8  0.04  0.0  -0.041  10  20  l  30  1 40  50  60  Time (hrs) Figure 5-20.  RUN 38 FOULING RESISTANCE VERSUS TIME  70  - 120 a s p e c i f i c mass o f 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 o f the scale and the absence or negligible e f f e c t o f removal as the result of the low annular velocity value during the i n i t i a l part of the run, followed by enhancement o f 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 o f both non-corroding tubes decreased with increasing Reynolds number (see Tables 5-3 and 5-4). At low velocity i n e i t h e r case, the majority o f the fouling process occurred during the early part o f the experiment while at higher annular  flow  velocities,  throughout the run.  the  fouling  resistance  increased gradually  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 -  0.16  f~6  1  O  I  i—I—I—r  T"  l—r  0.12 h CM  5  E  4'  2  ^01  0.08 h -  \ 0.15  I  1 I  IA  h  V.  6A  1  O  Copper  V  S.S.  I  1 h  w  0.11 h OJ  5A  0.07  2A 0.03  J 8  J  L 12  16  I  I  20  J 24  I  L 28  -3  Re„, XIO film 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 s t a i n l e s s steel tube at flow velocity of 0.503 m/s which resulted i n zero f o u l i n g 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 t e s t s done under high concentration of chemicals on both the copper and the p l a i n mild steel tubes are given i n Tables 5-5 and 5-6.  The comparison between these two sets of  data was c a r r i e d out (Figure 5-22) to see the e f f e c t of the surface material on the f o u l i n g 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 f o u l i n g factor was followed by a decrease at Reynolds numbers approximately  above 18000.  This might have  been due to the reduction i n 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 f o u l i n g 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 r e s u l t of either  high pressure or both high temperature and pressure (Runs 21 and 22) i s also  0.1 8 1  T — i — i — T O  Mild  steel  •  Copper  0.14  37 •  38 •  E  cr  I  12  I  I  16  I  022  21  33 O  J  T-30°C. P=l29kP0  25 O  0.0 6  0.041 8  23  29 O  24 O 0.10  i—r  P = l29kPa O T = 25°C  I  20  Re... film  I  I  24 -3 XlO  I  _  20  I  28  Figure 5-22. EFFECT OF REYNOLDS NUMBER ON FOULING RESISTANCE FOR COPPER AND PLAIN MILD STEEL TUBES  L  32  co  -  124  -  evident from the f i g u r e . In general, even though the non-corroding  copper  tube showed lower f o u l i n g 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  P l a i n 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 v e l o c i t y and the Reynolds number based on the equivalent diameter i n Figure 5-23. Except f o r Run 32, the f o u l i n g resistance decreased with increases i n the Reynolds number i n the v e l o c i t y 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 numbers  e f f e c t of v e l o c i t y on  above  16000 could  r e c i r c u l a t i n g water flow rate.  not  be  the fouling resistance at Reynolds investigated due  to  the  limited  In general, i t can be considered that the  enhanced tube provided more favorable f o u l i n g resistances than the p l a i n one at the corresponding v e l o c i t y values.  I t should also be mentioned that since  the f o u l i n g resistance of the finned tube i s evaluated based on the prime area, the weight of the deposit per total 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 -  O.I4[  l  i  i  i  i  i  FJii—i—i—i—r  29  a  i  ° f "  °  *  2  O 28  a06r-  A  33 C  22  2 5  OP=l29kPa  21  26  2 0  A  3I  1 1 1 1 1 1 1 1 1 1  0.0 2|  0.2  0.3  0.4  0.5  0.6  A Finned  0.12|-  0.081-  ° °  C  8 A A  |  f-  0.7  29 O 32 A  25 O 33  26  A  3  O  °  28  =  23  24  30 A  T  V ( m /s )  O Plain  0.16  32^  5  C  T  22  P-l29kPa 21 ' ° C ° O 2  5  O.  2  0  0.04  J  6  1  I  10  I  I  14  I R e  Fiqure 5-23.  I  18  I  film '0" x  I  22  I  I 26  I  30  3  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 f o u l i n g 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 o f 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 v e l o c i t y and temperature were used to c a l c u l a t e the predicted fouling rate based on the ionic d i f f u s i o n model o f Hasson (Appendix I I I ) . The average concentrations o f the carbon species and calcium ion f o r each run were determined.  The f o u l i n g rates were calculated using both Hasson's  low and high pH equations.  Since the bicarbonate ion concentration was  higher than the carbonate one, the f o u l i n g 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. calculations are summarized i n Table 5-8.  The r e s u l t s o f model  Table 5-8. SUMMARY OF MODEL CALCULATIONS  Run  pH  HCO3 x l O * 2  a v e  CO3 x 10 * 4  C0 x 10 * 4  2  Ca x lO * +  2  Calculated** Scaling Rate x l O 6  1A 1 3A 3 2A 2  7.84 7.86 7.89 7.93 7.92 7.95  0.1748 0.1668 0.1703 0.1696 0.1661 0.1540  0.2687 0.2689 0.2944 0.3218 0.3032 0.3029  0.4237 0.3860 0.3672 0.3337 0.3347 0.2895  0.2977 0.2897 0.3037 0.3037 0.2937 0.2827  0.0914 0.0844 0.1353 0.1359 0.1586 0.1403  6A 6 5A 5 4A  7.61 7.60 8.11 8.11 8.03  0.1504 0.1377 0.1510 0.1396 0.1593  0.1422 0.1273 0.4488 0.4158 0.3961  0.6256 0.5868 0.1983 0.1835 0.2513  0.2748 0.2618 0.2807 0.2688 0.2937  0.0853 0.0715 0.1415 0.1242 0.2075  24 29 23 33 25 20 21 22  7.78 7.78 7.68 7.93 7.45 7.74 7.72 7.63  0.4017 0.3397 0.3485 0.3375 0.3505 0.3406 0.3502 0.3397  0.6056 0.5144 0.4240 0.7123 0.2457 0.4781 0.4480 0.3683  1.1068 0.9352 1.2149 0.6565 2.0562 1.0212 1.1040 1.3261  0.6964 0.6384 0.6434 0.6394 0.6504 0.6994 0.6404 0.6384  0.4747 0.4815 0.6327 0.5480 0.6388 0.7281 0.7048 0.7807  30 27 28 26 31 32  7.54 7.64 7.60 7.58 7.64 7.68  0.3579 0.3621 0.3394 0.3536 0.3318 0.3096  0.3145 0.4007 0.3393 0.3352 0.3654 0.3745  1.7205 1.3800 1.4154 1.5412 1.2634 1.0763  0.6494 0.6604 0.6324 0.6474 0.6254 0.6025  0.5233 0.5321 0.5938 0.7316 0.8181 0.8464  38 37 36  7.69 7.81 7.79  0.3511 0.3334 0.3086  0.4413 0.5541 0.4915  1.1983 0.8679 0.8457  0.6584 0.6414 0.6184  0.4289 0.6416 0.7797  * **  Units i n mole/1. Unit i n m K/kJ. 2  - 128 5.6  E f f e c t of Reynolds Number on the Measured Fouling Rate 5.6.1 The  Copper and S t a i n l e s s Steel Tubes experimental  measurements o f the fouling  rate under  concentration of chemicals on the two non-corroding tubes accompanied type of f i t t e d curves are given i n Table 5-9.  low  by the  As i s shown i n 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 e i t h e r 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 velocity leading to a very high i n i t i a l fouling 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 fouling.  Therefore, the growth i n the deposit thickness and the reduction  i n the adherence f a c t o r would result 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 i n both a more gradual increase in the  Table 5-9. COMPARISON OF MEASURED FOULING RATES ON COPPER AND STAINLESS STEEL Copper  V  (m/s)  Run*  R e  film  Stainless Steel dR 6 de" (m K/kJ) x  i n 10  Fit  Run  R e  Fit  film (m K/kJ) 2  2  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 Lin Asymp * Low  = runs lasted 48 hours =1inear = asymptotic 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 velocity 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 i n a reduction of the net fouling rate with further increases i n 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 i n 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 e i t h e r experimental errors o r 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 result.  T—i—i—i—i—i—i—i—i—i—i—i • 38  •  r  Copper  O  Plain M.S.  36^ 29 O 2  3  33 O  °  37 C L  2  5  2  •  I  8  I I  12  I  I  16 R  I  *fi.m  I  20  -3  X  ,  I  |  20 o  O  22 O  P'l29kPaT«30°C  P*I29 kPa T«25°C  I  24  I  °  FIGURE 5-24. EFFECT OF REYNOLDS NUMBER ON MEASURED FOULING RATE FOR COPPER AND PLAIN MILD STEEL TUBES  I  28  I  32  - 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 e f 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 e n t i r e 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 i n the cooling water flow rate and hence the behaviour of the fouling resistance curve (see Section 5.3).  sawtooth  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 i n 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 effect 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)  Reynolds numbers about 7000 (V=0.340 m/s)  f o r the p l a i n tube, while at f o r the finned (Figure 5-25).  This might be due to the fact 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 30  24 O  1  1  29 O  A  23 O  22 O  25 O  20  28A 26 A  ,, 3 1  1  0.2  1  1  0.3  0.4  1  1  0.5 V(m/s)  0.6  32 A  O  A  021 P=l29kPa T = 25°C  -  1  0.7  Finned  A  Plain  O  29  _  30 A  O 32 A  24  O  28 A  —  26  A  1  1  10  33 O  31 A  1  14  2 2~ P=l29kPaO T» 30°C O °*0 21  1  1  18  Ref„ XI0" m  5-25.  25 O  22  26  3  EFFECT OF BOTH VELOCITY AND REYNOLDS NUMBER ON MEASURED FOULING RATE FOR PLAIN AND FINNED MILD STEEL TUBES  -  30  - 134 o f 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 velocity 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 velocity  was  expected since the model was based on both the d i f f u s i o n c o n t r o l l e d 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 c a l c u l a t i o n s resulted i n a lower magnitude of fouling rate f o r the copper tube than the stainless steel one  under  approximately  identical  operating conditions at Reynolds numbers below 22000. The fact that the plot of the predicted fouling rate versus Reynolds number f o r the stainless steel tube had a reduction i n i t s slope at higher annular flow velocity 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 i n experimental fouling resistance with velocity (Figure 5-21) was in contradiction with the model's p r e d i c t i o n (Figure 5-26).  - 135 -  T — r  " i — i — i — i — i — i — r ~  0.14  "I—r -—V2  0.10  o'e 0.06  ^—I—I—I—I—I—I O V  0.20  V  1 1 1 1  4AOI  Copper  SS  2A 0.16  5A £  0.12  IA <^6A  0j08r-  J  I  I  10  I  I  14  I  I  I  18  22  26  r3  R e X 10 f  5-26. EFFECT OF REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR COPPER AND STAINLESS STEEL TUBES  30  -  T a b l e 5-10.  136 -  COMPARISON OF PREDICTED FOULING RATES ON COPPER AND STAINLESS STEEL  Copper v (m/s)  Run"'  Stainless Steel Run  Re f i l m  R e  film  (nTK/kJ)  (nTK/kJ)  0.299  6A 6  12921 12987  0.0893 0.0757  1A 1  11136 11194  0.0956 0.0886  0.503  5A 5  21170 21397  0.1497 0.1323  3A 3  18576 18599  0.1416 0.1424  0.695  4A  29506  0.2180  2A 2  24984 25261  0.1666 0.1484  Note:  A = r u n s 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 i n the fouling rate with the velocity was also held to be generally i n e f f e c t f o r these tubes.  The s l i g h t inconsistency occurred  during Run 24, on the p l a i 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 i n 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 i n good  agreement with Hasson s model i n the case of the copper tube. 1  However, the  reverse relationship i n 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 i n Figure  5-28, the predicted fouling rate also  increased with increasing velocity i n 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 i n d i c a t i v e of the f a c t that the plain tube behaved more favourably than the enhanced one i n the velocity region  — i  n  1  1  O Mild steel • Copper 23 rA 3 t-O 33 25 € 3  24 °  10  29 38 •  1 *u 0 ° P"l29kPa T *25°C  22  r-  361  *g P-l29kPa T-30°C  °  14  18 R e  f„m  -3 X  ,  22  26  °  FIGURE 5-27. EFFECT OF REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR COPPER AND PLAIN MILD STEEL TUBES  30  - 139 -  3.  0.8  26  A  23  0.6  27 24 O  0.4  CM  J  28  30  _J_  0.2  0.4  0)  25 O  _L 0.5  0.6  V (m/s) A  Ct>  0.91  31  or  A  26  T3  0.5 h  3 0  0.7  22  23  3  18 Re film  25 O  33 €  29 O  24 O  I4  FIGURE 5-28.  8  20  A  A  0  A  28 27  r  32  A  0.7 h  022 . P=l29kPa 8 T=30 C_ 21 n  Plain Finned  O  0  ^  2  A| _  29 O  _l_  0.3  ?  3 2  A  x io  22  °  %°P=l29kPo T = 25°C  26  - 3  EFFECT OF BOTH VELOCITY AND REYNOLDS NUMBER ON PREDICTED FOULING RATE FOR PLAIN AND FINNED MILD STEEL TUBES  30  - 140 investigated. diameter,  and  This i s due to the e f f e c t s of the f i n s on the hydraulic hence  the  Reynolds  number.  This  trend  was  also  in  contradiction with the results based on the f i t t e d value of f o u l i n g 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 ratio 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 ratio f o r low concentration runs with respect to Reynolds number (Tables 5-11  and 5-12)  was not f e a s i b l e due to the wide range o f  variation i n 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 f o u l i n g rate, p a r t i c u l a r l y at low values of the annular v e l o c i t y . This i s also the case f o r s t a i n l e s s 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 f o u l i n g rates f o r these high concentration runs. the two  mild steel tubes,  the consistency  In the case o f  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  10  St*  Run*  6  (m K/kJ) 2  V  R e  (m/s)  film  Predicted  Measured  ( d R / d 6 )  ( d R / d e )  meas pred  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 hours, * Low concentration runs. Table 5-•12.  COMPARISON OF PREDICTED AND MEASURED FOULING RATES ON STAINLESS STEEL dR 10 di (m K/kJ) 6  x  Run*  2  V  (m/s)  R e  film  Predicted  Measured  meas (dK/de)  ( d R / d e )  pred  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  de (m/s)  R e  (m K/kJ) 2  film  Predicted  Measured  meas (dR/de)  ( d R / d e )  pred  38 37 36  Cop Cop Cop  0.299 0.503 0.695  12938 22488 32072  0.4288 0.6423 0.7826  3.3839* 0.3369 0.6442  7.8897 0.6055 0.8262  24 29 33 25 20 21 22  P.M.S. P.M.S. P.M.S. P.M.S. P.M.S. P.M.S. P.M.S.  0.299 0.404 0.503 0.600 0.695 0.695 0.695  11952 16253 19394 23078 26624 25770 29030  0.4723 0.4818 0.5483 0.6389 0.7286 0.7047 0.7814  0.3552 0.4711 0.3453 0.3196 0.2541 0.2156 0.3369  0.7483 0.9784 0.6301 0.5003 0.3490 0.3050 0.4315  30 28 26 31 32  F.M.S. F.M.S. F.M.S. F.M.S. F.M.S.  0.340 0.460 0.573 0.683 0.791  6849 8973 10904 13579 15882  0.5230 0.5943 0.7314 0.8194 0.8497  0.4173 0.2415 0.1455 0.1000** 0.3920  0.7974 0.4067 0.1989 0.1222 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 o f removal process at high velocity values.  The copper  tube provided good agreement between the predicted and experimental value of the fouling rate at annular flow velocity o f 0.695 m/s.  No other s p e c i f i c  relationship was found between velocity and the magnitude o f t h i s ratio using the copper tube.  In general, f o r either the copper tube o r the mild steel  ones, the e f f e c t o f Reynolds number on the magnitude of t h i s ratio followed the same trend as d i d the value o f the corresponding measured fouling rate (see Figures 5-24 and 5-25).  38D • O A  Copper Plain M.S. Finned M.S  29 O  30 A  24  []  O  33 O  32 A  28 A 26 A  6  36_  10  37 •  ,25  20 2l 0 0  P=l29kPa T=25°C  31 A  14  18 Re,.,  film  22 XlO"  26  3  Fiaure 5-29. COMPARISON OF MEASURED SCALING RATE WITH RATE PREDICTED BY THE IONIC DIFFUSION MODEL  22 O  P*l29kPa T»30°C  30  -  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 o r after 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 o f 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 linear i n time except f o r the low velocity (0.299 m/s) runs which showed an asymptotic behaviour.  The magnitude o f the fouling resistance,  f o r e i t h e r tube, decreased with increasing velocity, unlike the values o f heat flow rate, clean and d i r t y overall 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 o f 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 t r a n s f e r 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 velocity.  However, f o r 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 o f fouling resistance  f o r the copper tube than the p l a i n mild steel one at low velocity 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  e i t h e r 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 e i t h e r tube, the model over-predicted the experimental  rates of fouling except f o r Run 38.  increased with the velocity  resulting  The  predicted rates  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.  Totally, i t can be said that the copper tube had  always a better performance, regarding the d i r t y heat t r a n s f e r 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  parameters with the velocity was evident.  these  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 f o u l i n g resistance f o r the finned tube generally  with increasing v e l o c i t y .  decreased  However, in the case of the p l a i n tube,  fouling resistance reached i t s maximum at Reynolds number of 18000 as was mentioned e a r l i e r .  the  approximately  The enhanced tube always gave rise 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. model over-predicted the experimental  For both tubes, the  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 f o u l i n g 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  steel tube under these  on  the mild  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 f o u l i n g 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 i n 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 e i t h e r 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 fouling resistance was  also reasonable  deposits formed on the enhanced tube. both clean and  dirty  considering the structure of the In conclusion, the greater values of  heat transfer c o e f f i c i e n t s along with the  lower  magnitudes of f o u l i n g 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 p r e d i c t the magnitude of the f o u l i n g 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  9^,  9Q»  Description * • • » <*9  deposition constgnts  A  surface grea  A  logarithmic mean area  A  eff  e f f e c t i v e area  A  f  surface area o f the f i n s  V  A  Prime  prime o r unfinned area  o  nominal (bare-tube) outside area  t A'  total surface area  Asymp  asymptotic  A  A  volume o f the t i t r a n t (EDTA)  bj, b , bg  removal constants  b  length o f the f i n  b'  degree o f supersaturation  B'  volume o f the t i t r a n t (HC1)  B"  mg o f CaCOg equivalent to 1 ml o f EDTA  2  C  b  C  P  C  s  bulk concentration specific heat concentration o f saturated  l i q u i d at  the surface C  T  total carbon species concentration  150 Description diameter diffusivity equivalent diameter diameter of the shell diameter o f 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 o f 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 o f CaCO^ rate  coefficient  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 o f l i q u i d average unit thermal conductance o f wall  151  -  Description  constant  for  the  Reitzer  gross  deposition rate first  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 s o l u b i l i t y 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  pn  (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 i n 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  Description  Pr  Prandtl number, Cpn/k  Nu  Nusselt number, hD/k  Re  Reynolds number, PVD/n  Sc  Schmidt number, u/PD  Greek Letters  Description d i s t r i b u t i o n f r a c t i o n of carbon species  6  a function  2  dependent on wall,  scale  surface and bulk temperatures difference between values  A  m  logarithmic mean temperature difference (LMTD)  n  f  fin efficiency  fd  dirty 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  td  total d i r t y surface e f f i c i e n c y  n  n  ¥  constant = 3.14  e  time  e  c  time constant  e  D  delay time viscosity  u  density of the l i q u i d  p  p  f  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  Edition, New York, 1968. 2) Thackery, P.A., In:  "The Cost of Fouling i n Heat Exchanger Plant".  Proceedings of the Conference "Fouling - Science or Artu",  Surrey, Guildford, England, March 27-28, 1979. 3) Hasson, D., Sherman, H. and Biton, M., Carbonate Scaling Rates".  "Prediction of Calcium  Proceedings 6th International Symposium  on Fresh Water from the Sea, Vol. 2, p. 193, 1978. 4) Epstein, N.,  "Fouling i n 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., Surface". 1960.  "Scale Deposition on a Heated  Advances in Chemistry Series, Vol. 27, p. 105, April  - 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  Engineering and Process Development, September  and  Engineering  Vol. 43, No.  Chemistry  9, p.  2144,  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 i n Tubular Heat Exchangers". Industrial and Engineering Chemistry Process Design and Development, Vol. 3, No. 4, p. 345, October  16)  Bransom, S.H.,  1964.  "Factor in Design  of Continuous  Crystal!isers".  B r i t i s h Chemical Engineering, Vol. 5, No. 12, p. 838, 17)  1960.  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  Vol. 7, No. 1, February 18)  and  Engineering  Chemistry  1968.  Taborek, J . , Aoki, T., Ritter, R.B. and Palen, J.W., Major Unresolved  Problem  "Fouling: the  in Heat Transfer Transfer".  Engineering Progress, Vol. 68, No. 2, February 19)  Fundamentals,  Taborek, J . , Aoki, T., R i t t e r , R.B. Methods f o r Fouling Behavior".  1972.  and Palen, J.W.,  Chemical  Chemical  Engineering  "Predictive 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 Calcite 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,  Carbonate  Crystallization  P. and Marais,  Kinetics".  G.V.R.,  Water Research,  "Calcium V o l . 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,  Exchangers". 26)  of Heat  Chemical Engineering, p. 96, January 26, 1970.  Fanaritis, J.P. and Bevevino, J.W., "Designing Shell and Tube Heat Exchangers".  27)  P.E. and Slusser, R.P., "Design  Chemical Engineering, p. 62, July 5, 1976.  Cleaver, J.W., Yates, B., "Mechanism of Detachment of Colloidal Particles from a F l a t Substrate i n a Turbulent Flow".  Journal of  C o l l o i d and Interface Science, Vol. 44, p. 464, September 1973.  - 160 28)  Cleaver, J.W. and Yates, B., "The E f f e c t of Re-Entrainment on Particle  Deposition".  Chemical  Engineering  Science,  V o l . 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 i n Fouling of Heat Exchangers i n Cooling Water Service". The Canadian Journal of Chemical Engineering, V o l . 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)  " P r i n c i p l e s of Industrial Water Treatment", Third E d i t i o n , 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, V o l .  28, p. 1500, 1936. 33) Langelier, W.F., "Chemical E q u i l i b r i a i n Water Treatment".  Journal  of the American Water Work Association, V o l . 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  Controlling Scale Formation in B o i l e r s " .  Methods  of  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  Distributions  in the Simultaneous Precipitations of CaCOg and  MgtOH)^".  Stevens, J.D.,  "Additivity  of Crystal  Size  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 i n the Presence of Heat Transfer.  In:  Symposium "Corrosion i n 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 Edition, 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., Annuli". October  50)  "Heat Transfer and Pressure Drop in  Chemical Engineering Progress, Vol. 46, No. 10, p. 490, 1950.  Knudsen, J.G. and McCluer, H.K., at Moderate Temperatures".  "Hard Water Scaling of Finned Tubes  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., Money".  "Under Fouling Conditions Finned Tubes Can  Save  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  Vol. 52, p. 558, October 54)  Journal of Chemical  Engineering,  1974.  Epstein, N. and Sandhu, K., "Effect of Uniform Fouling Deposit on Total Efficiency of Extended Heat Transfer Surfaces".  In:  International Heat Transfer Conference, Vol. 4, p. 397, Ontario, August 1978.  Sixth  Toronto,  - 164 55) "Standard Methods of Chemical Analysis", Sixth Edition, V o l . 2, p. 2399.  Welcher,  F.J. (Editor).  D.  Van  Nostrand  Company  Incorporated, Princeton, N.J., 1963. 56) "Standard Methods f o r the Examination of Water and Wastewater", Twelfth Edition, APHA, AWWA, WPCF, 1965. 57) "CRC Handbook of Chemistry and Physics", 57th Edition, Weast, R.C. (Editor), CRC Press Incorporated, Cleveland, Ohio, 1976-1977.  - 165 -  Appendix I.  CALIBRATION OF THERMOCOUPLES AND ROTAMETERS Table 1.1 Calibration Table* f o r Thermocouples (57) (Eltctron&tin Force io Absolute Millivolt*. Tnoprrttum in Dtfreca C (lot. 1943). Rtlntne* Junctiooi tt 0* C.) T T T •PI ° 1 ' i T T -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 3 6 -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 --13. 4 3 -3.47 3 S3 -3 66 -3.60 -3 6 3 -3 69 -3.74 -3 9 1 — 50-2.19 -2.94 -3 03 -2 07 -3 12 -3 16 3 21 -3 23 -3 30 -2 -2 -SO-2.43 -3 48 -2.32 -2 67 62 -2.66 -3.71 75 80 -2.M -40-IK -2.01 -2.06 -3.10 -2 15 -2 20 -3.34 -2 29 - 2 34 -2.33 -1 8 -30-1 48 -1.33 -1 58 -1.63 -1 67 -1.72 -1.77 -1 2 -1 87 -1.91 -1 20-l.OO -1 4 -1 09 — 1.14 -0 19 -1.24 -1.29 -0 34 -1 39 -1.43 -0 055 -10 -00.00 JO -0 60 -0.65 -0 7 0 -0.75 -0,60 -0 85 -0 90 -0.85 <-)0 -0.03 -0 10 -0.15 20 -0 25 -0.30 35 -0 40 -0.45 .10 0.15 0 20 0 25 0 SO 0 35 940 0.45 (+)0 0.00 0 05 0 10 0 SO 0 58 0.61 0.66 0 7 08 1 0 . 7 6 0 6 1 6 0 91 0.97 JO 1 02 1.07 111 1.17 11 22 1.28 1 33 11 38 1I 43 2.00 1.48 JO 1 34 21.1519 1 64 2.22 1.69 2 74 1 80 1 85 2 90 2 95 40 2.03 2.16 27 2 32 2.37 2 42 01 48 2 53 2 M 2 S3 2 M 2.69 2.74 80 2 63 2.90 96 3 3.06 eo 3.11 3 17 3 .33 1.27 333 1 38 3 43 349 3 54 3.60 7 0 3 6 3 3 . 7 0 3 . 7 6 J 8 1 3 8 f 3 . 9 2 3 . 9 7 4 0 2 4 0 8 4.13 so 4 19 4 .24 4.39 4.35 440 4 46 4.61 456 462 4.67 90 4.73 4 71 4 63 4.89 5494 5.00 6 06 5 10 5 16 5.21 100 3.37 1.32 6.38 5.43 43 5.54 5.59 665 670 3.76 110 3.81 1 (8 6 93 5.97 603 6 OS 6.14 619 625 6.30 1» 3 36 9 41 6.47 6.53 658 6.63 6.68 674 679 6.83 110 i n 8.98 7.01 7.07 712 7.18 7.13 729 731 7.40 140 ;.4S 7.31 7.66 7.62 767 7.73 7.76 7 M 739 7.85 150 3.00 3 OS 1.13 8.17 313 8.36 3.34 1 39 843 8.SO too 8.to a 31 3.67 8.72 376 3 84 8.(9 I 93 900 9.08 1 70 9.11 9 17 9 22 9 28 933 9.39 9.44 950 95 6 9.61 in 9.87 9.73 9.78 9.83 969 9.95 10.00 1006 1011 10.17 ISO 10. r 10 28 i10o n34 10.39 1000 45 10.50 10.56 1061 1067 10 72 100 10.78 10.M 10.93 11 11.03 11.13 1117 1123 11.28 >I0 11 34 11.39 11.45 11.80 1156 11 81 11.67 1171 11 73 11.81 B0 11 89 II 95 13.00 12.06 1313 12 17 11.23 13 38 1234 12.39 230 12.43 13.60 13 M 13 «3 1367 12 73 12.73 12.84 1289 12.95 140 13 01 13 03 11.13 13.17 1323 13 28 13 34 13 40 1300 48 13 51 UO 13 56 13 32 13.67 13 73 1378 13.64 13.39 13.95 14 14.06 M0 14 13 14 17 14 S3 14 28 1434 14 89 14 45 14.50 14M 14 61 no 1 4.87 14.73 •4 78 14 83 1480 14.94 13.00 13.06 1611 15.17 no 13 11 18.33 15.33 1 8.39 1544 15.50 13.15 15.6) IS 66 15.72 no 15.77 13.33 15 38 15.94 1600 16 OS 16.11 16.16 1622 16.27 300 It 33 16 38 16.44 16 49 1635 16 60 16 66 16 71 1677 16 82 110 1983 It 43 16.99 17 04 1710 17.15 17.31 17.26 1731 17.37 130 17.43 17.48 17 54 17.60 1765 17 71 17.76 17.62 1787 17.93 130 17.93 18 04 18 09 18 15 1620 18 26 18 33 18.37 1843 18 48 140 18.34 18.69 18 15 18.70 1676 18.81 16.87 1892 1898 19.03 360 19 00 19.14 19.30 19.36 1931 19.37 19.13 19 49 19S3 19.39 9.34 19.70 19.73 19.81 1966 19.93 19 97 20 03 2008 20.14 no 1 370 20.20 10.23 10.31 20.36 3042 30.47 30.63 30.58 20 64 20.69 330 20 75 30.80 30 66 20.91 3097 31.02 31.03 3113 2211 19 21.24 3 30 21.30 11.35 31.41 21.48 3162 31.57 31.63 31.68 22 74 21.79 too 2 1.33 11.90 81.94 22.02 1107 13.13 33.18 22.24 29 32 35 410 22 40 12 41 22.51 22 57 22 62 22 68 31.73 22 79 22 84 22.90 43 «3 23.01 33.03 83 12 2317 33.23 33.38 23.34 21 2339 23 45 4 30 0 323.3 0 11.M 23.31 23.67 S372 23.71 13 13 23.39 94 24.00 4402 24.03 34.11 11.17 24 22 3421 24 S3 14 39 3444 2430 24.55 430 34.31 34 M 14.72 24.77 3431 24.18 34.94 S3 00 2305 2S.11 480 23.18 33.21 13.27 25.33 25IS 25 44 33.49 23 55 3560 23 66 470 25.72 33.77 35 83 25.88 2594 25.99 26.05 26 10 2616 26.22 430 23.27 36.31 16.38 38.44 2849 26.53 26.61 26.68 2672 26 77 400 28.83 26.19 36 94 27.00 2705 27.11 27.17 27.22 2728 27.33 100 27.39 37.46 77.50 27.56 2761 27.67 27.73 27.78 2784 27.90 310 27.93 18 01 28 07 28.12 28IB 28.23 28.29 38 33 2S 40 28 49 130 29 33 38.67 38 63 26-69 2874 28 80 28.86 28 91 2897 29 o: 130 29.08 29.14 19.20 29.23 2931' 29.37 29.42 29 48 295 4 29 59 340 39 33 29 71 39 33 29 82 39•8 29.94 19 99 30.OS S O11 30 16 30.22 30 ta 10.34 30.39 3043 30.51 30.67 30.63 ao 43 30 71 MO Bami on UM laurui^u) Ttapcrtlun 8c*k of IMS. -in  * Used i n Runs 1 to 8.  - 166 -  T a b l e 1.2.  CONSTANTS CORRESPONDING TO THE CALIBRATION EQUATION* FOR THERMOCOUPLES  C CC)  b CC/mv)  a (°C?/mv)  Range CC?  Tank o u t  -1.67865  21.65324  -0.71004  25-50  9-38  Exch i n  0.25190 0.37845  19.79763 19.10536  -0.29185 0.0  25-50 20-40  9-21 22-38  Exch o u t  2.40695 0.20770 0.15810 0.34057  17.71571 19.34461 19.27142 19.12506  0.24891 0.0 0.0 0.0  25-50 20-40 20-40 20-40  9-21 22 23-26 27-38  Steam i n  9.60230 0.65260  15.75524 18.80879  0.18182 0.0  100-130 90-130  9-21 22-38  Steam o u t  9.97206 0.39281  15.60082 18.85247  0.18964 0.0  100-130 90-130  9-21 22-38  Location o f The T h e r m o c o u p l e  * T = a v + bv + c ( T i n °C, v i n m i l l v o l t s ) . Exch = exchanger. 2  Run  - 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 o f Heat Flow Rate The  rate o f heat flow  (q) to the r e c i r c u l a t i n g water was  calculated by: q = W c AT c  p  where m, c  p  (H-l)  c  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 A T was calculated using the c a l i b r a t i o n table  the cold stream (water).  £  or c a l i b r a t i o n equations shown i n Appendix I. W was determined using the c  volumetric flow rate (V) as follows: W = V c  (11-2)  P  Physical properties (Cp and p) of water were evaluated at the bulk temperature (T^) using: (kg/m ) = -0.3269 f + 1005.4  (II-3)  c  (II-4)  3  P  where  5  p  (k /kg°C) = -0.00108 T + 4.1818 5  i s i n degrees centigrade.  - 170 II.2  Determination o f Heat Transfer Area The outside nominal area o f the tubes were used as a reference  area i n 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  TrD L  (11-5)  Q  where D i s the outside diameter (19.1 mm) and L i s the length (1.33 m) o f Q  the tubes i n contact with the water. 11.3  Determination o f Logarithmic Mean Temperature Difference Following the evaluation o f the i n l e t and o u t l e t temperatures of  both streams v i a e i 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 =  ^ ln  ^  (II-6)  <V c.i n V c out> T  ) / (  T  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^) o f that stream, which were s l i g h t l y different due to the experimental errors, was used i n the determination o f 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:  (II-7)  A (LVD)  o~  O  11.5  Determination of the Fouling Resistance  The  change  i n the magnitude of the overall  heat  transfer  coefficient over the length of the run was due to the fouling resistance (R ) which was calculated through: f  R = f TT I T d c 1  (II-8)  1  R  where U  c  and  are the clean  and the dirty  overall  heat transfer  coefficients evaluated,  respectively, at the start and end of a run. I t  should  the fouling resistance of the finned  be noted  calculated  that  based on the nominal  area (bare-tube) outside  tube was  diameter (see  Appendix II.2).  To relate the mass and thickness of the deposit on the finned tube to that of the p l a i n tube, the effective area ( into consideration.  A e f f  ) should be taken  The relationship between the fouling resistance based  - 172 on the prime area (R ) and the one based on the e f f e c t i v e area (R ) can l 2 be expressed by: f  f  T  T  R  f r  =J^-  2  %  T  R  (II-9)  f  l  The unit thermal resistance (R^), the mass per unit surface area (m^) and the thickness of the deposit (x^), are i n t e r - r e l a t e d as: =p k R  m = f  f  f  (11-10)  f  Therefore, the total mass of the deposit on the finned tube would be  \  f ^f \ r i m e  = p  k  { I I  x  -  U )  or m  t„  =  p  f f f„ eff k  R  A  ( I I  "  1 2 )  Thus, the mass o f the deposit per unit prime area (m ) and per unit total f  T  l  area (m ) would be 2 T  f  m^ = p^k^R^  (11-13)  f f f eff = j± 2 t f f eff p  k  R  A  9  m  T  m  R  2  mT~ r  (11-14)  A  l  A  2  R A. l c  f  t  (11-15)  - 173 Considering equation 11-10 and substituting  equation 11-9 into  equation  11-15 would y i e l d : 2 m /nu = x* /x* = A;;„/A A. 2 1 2 1  (11-16)  f  A  can be evaluated using the f i n e f f i c i e n c y ( n ) through:  e f f  f  0.5 m = (i. A ) K  n f  A  =  eff  (11-17)  fin f A  tanMrrnjL a  V t  -(  ( I I  V  A  f  where, 1, P, A and k^.  )  +  V f  (II  .  -  1 8 )  19)  are the height, the perimeter, the surface area  f  and the conductive heat transfer c o e f f i c i e n t o f the f i n . The convective heat transfer c o e f f i c i e n t h was approximately 2.8 kW and evaluated by: c  K° n no? n 0.8 0.333 - c . 0.023 Re . P r l D  N u  fl  lm  f 1 1 m  K  A sample c a l c u l a t i o n i s given i n Section 11-11.  / T T on\ (11-20)  -  11.6  174  -  Determination o f the Wall Temperature The average wall temperature throughout a run was evaluated using  the radial rate o f heat flow equations f o r concentric cylinders i n the steady  state  condition.  Wall  temperatures  were  required  f o r model  calculations only.  q = irD.Lh.(T  2irLk  -T  i i s,..,. ave w.i ave  ) = _ _ "  ) = *D L h ( T I nl Do /v.) i (T iw. o-T w o o wo -T. oave ) ave ave ave (11-21)  where T i s the temperature and subscripts s, w^ and w  Q  the steam, inside and outside tube wall, respectively. inside wall and the steam temperatures  are denoted to Assuming that the  are equal, the following equations  can be written:  * w " In (D /D.) 2  q  Lk  Q  w_  = T ave  11.7  (T  (11-22)  ave w_ ave  q ln(D /D.) 2^LlT w Q  ave  (II- 23)  Determination of the Equivalent Diameter The equivalent diameter  (D ) was required f o r the subsequent g  determination of the Reynolds number.  The magnitude o f t h i s parameter  (D ) should be evaluated by d i f f e r e n t means considering the geometry of the tubes. g  -  175 -  In the case of p l a i n tubes, the following equation was applied: D = D e  where D  s  i  - D o  (11-24)  t  and D. are, respectively, the inside diameter of the shell and i o the outside diameter of the tube. s  z  The equivalent diameter of the enhanced tube was calculated using: n U  _A  e "  4  Net Free Area (NFA) Total Wetted Perimeter (TWP)  ,  T T9 C  x  UWb)  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 - D ) - 12 t l ^ i o  (11-26)  TWP - TJ (D + D. ) + 12(2) 1 i o  (11-27)  2  s  2  z  and s  z  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. and the f i l m (T^) temperatures using the following equation: Re = vD /n = VD /Sn P  e  P  ave  )  (11-28)  e  where p, v, V and u are, respectively, the density, the velocity, 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 o f density, and: u (kg/m.s) = -0.1731 x 10" T  + 1.3177 x 10*  4  where T.  3  (11-29)  ave  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: (kg/m ) = 1181.32 - 0.593 T  (11-30)  3  P  f  n(kg/m.s.) = 0.1/[2.148 ((T -281.435) + f  (8078.4+(T -281.435) ) )-120.] 2  0,5  f  (11-31)  - 177  -  where T i s i n degrees kelvin and evaluated by: f  (11-32)  )/2 + T w ave o ave 11.9  Determination o f Water Quality Parameters Total  alkalinity  (T.A.) was  evaluated  using  the following  expression: T.A. = B x N 1  [X  5000  ( n  _  3 3 )  where B', N and v' are the volume o f the t i t r a n t (HC1), normality o f 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  where A' and v  1  (11-34)  1000  are volumes o f the t i t r a n t (EDTA) and of the sample,  respectively; B'' i s the weight (mg) of CaC0 equivalent to 1 ml of EDTA. 3  The magnitude of total dissolved solids (TDS) was required f o r model calculations and as explained i n Section 4.6, can be approximated by:  TDS = 1.06 T.A. + 1.64 Ca  (11-35)  +  The values of total 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 i n equation 11-23 f o r evaluation of average total dissolved s o l i d s . 11.10  Numerical Example Using Run 26 Run  26 corresponds to the test on the finned  rotameter setting o f 50 (V = 39.83 x 10~  5  m /s). 3  tube having  Using the c a l i b r a t i o n  equations (Table 1.2), the temperature readings f o r the start o f the run are: T T  c  in  c  out  Ts  = 25.18°C = 32.80°C = 100.07°C  - 179 -  T.D  = 28.99°C  Applying equations 11-3 and 11-4: P c  = 995.969 kg/m  b  p  c  3  = 4.1787 kJ/kg°C  Using equations 11-1 and 11-2: q = (39.83 x 10" ) (995.969) (4.1787) (32.80-25.18) = 12.68 kW 5  Substituting the temperature values i n equation II-6 y i e l d s : LMTD = 32.80 - 25.18 , 100.07-25.18 100.07-32.80  =  7 0 > 9 7  °  c  ln  Applying equation II-5: A = Tr(0.0191) (1.33) = 0.0796 m  2  Q  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  dirty  overall  heat  transfer  c o e f f i c i e n t would  be  evaluated  using  the  temperature r e a d i n g s f o r the end o f the run f o l l o w e d by the above p r o c e d u r e :  ( 3 9 . 8 3 x 1 0 ~ ) (995.44) (4.1785) ( 3 4 . 3 5 - 2 6 . 8 4 ) i (0.07976) ( 3 4 . 3 5 - 2 6 . 8 4 ) "I (107.78-26.861 107.78-34.35  II V  5  a  _  9 2  n  '  ^,,J-  9 0  V  2  k  W  /  m  K  l n  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 a c c o r d i n g t o e q u a t i o n 11-8  R  = — — - — — = 0.049 m K/kW 2.02 2.24 2  f T  The average steam temperature and the heat f l o w r a t e t h r o u g h o u t a run were,  r e s p e c t i v e l y , 1 0 4 . 8 4 ° C and 16.7 kW.  Thus, a c c o r d i n g to  11-23  T  _ °ave"  Having  T  i  .  12.7 1 n ( 1 9 . 1 / 1 5 . 9 ) _ , o ~ 2w(44.99)(l.33) " ' Q (  M  9  = 29.70°C  ave  f  =  P  b  = 995.74 k g / m  n  b  = 0.0008051 kg/m.s  P  u  5  9  5  \  2  9  -  yields:  T  9  '  n  7  = 62.32°C  0  3  = 982.081 k g / m  f  f  3  = 0.0004484 kg/m.s  Q  5  9  5  f C  equation  - 181 Using equations 11-25, 11-26 and 11-27 y i e l d s : n - 4 TT(0.037 - Q.Q191 )/4 - 12(0.006)(0.0005) e W0.037 + 0.0191) + 12 (2) (0.006) 2  2  4  Therefore,  the Reynolds  numbers  can  be  n nno  ,  Q  m  u.UU»°9 m  calculated  knowing  S = NFA = 69.528 x 10 m and using equation 11-28: _5  2  Re = (995-74) (0.0239) (0.0869) (69.528 x 10" ) (0.0008035) b  =  6 1 7 Q  5  Re = (982.081) (0.0239) (0.0869) (69.528 x 10" ) (0.0004484) f  s  1 Q 6 5 2  5  50 ml o f the water sample taken at the start of the run was t i t r a t e d with 19.1 ml o f 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 o f the sample was t i t r a t e d with 0.01 M EDTA (1 mg CaC0 per 1 ml of EDTA). 3  was used until the occurrence o f the indicator 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  16.8 ml o f the t i t r a n t  colour change.  Equation  - 182 Having the average a l k a l i n i t y and hardness values o f 361 and 648, respectively, the magnitude o f the average total 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 F i n 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 = m  n  _ f ~  r(2.8 X 1Q ) (2) (1.2) -,' _ 3  L  (44.99) (1.2) (0.0005)  0 5  "  J  4 q a 4 9 8  '  ,  q 9 4  tanh [(498.94) (0.006)] _ oo (498.94) (0.006) n  U , J J  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 o f the finned tube would be evaluated through equation 11-19 having A = 2 (12) (1.2) (0.006) = 0.1728 m  2  f  and  A = 0.0796 - 12 (1.2) (0.0005) + 0.1728 = 0.2452 m t  2  - 183 -  A  e f f  = (0.2452 - 0.1728) + 0.1728 ( 0 . 3 3 ) = 0.1294 m  and  i t = 0.2452 P- = 0 ' 53 1294  t  u  b  J  Therefore, using equation 11-16:  2  - 184 Appendix I I I . 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 o v e r a l l  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 f o u l i n g resistance data to a l i n e a r (Figure III.2), an asymptotic polynomial  (Figure 111.4) function.  (Figure III.3) or a fourth degree  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) T I M E ( I ) . R 1 ( I ) . R 2 ( I ) . R 3 ( I ) . R 4 ( 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.  3 1 2 12 11 10  4 5 6 7 8 30  PROGRAM TO LINEARLY FIT FOULING RESISTANCES  DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) . Y F ( 2 0 0 ) , W T ( 2 0 0 ) . E 1 ( 6 ) . E 2 ( 6 ) . P(6) COMMON M R E A D ( 5 , 1 ) N.M.NI FORMAT(315) READ(5.2) EPS F0RMAT(F1O.5) FORMAT(6F10.5) FORMAT(F10.1,F10.4) READ ( 5 . 1 2 ) ( P ( I ).1=1.M) DO 10 1=1.N R E A D ( 5 , 1 1 ) X(I ) . Y(I) EXTERNAL AUX CALL LOF(X,Y,YF,WT.E1.E2.P,0.0.N.M.NI,ND,EPS,AUX) IF ( N D . N E . 1 ) STOP WRITE (6,4) F O R M A T ( ' ESTIMATES OF ROOT MEAN SOUARE TOTAL ERROR IN THE PARAMETERS WRITE ( 6 , 5 ) ( E 2 ( I ) , 1 = 1 . M ) FORMAT ( 1 X . 8 G 1 5 . 5 ) WRITE (6,6) F O R M A T ( ' VALUES OF X VALUES OF Y F I T T E D VALUES OF Y ' ) DO 7 1 = 1 , N WRITE ( 6 . 5 ) X ( I ) . Y ( I ) . Y F ( I ) WRITE ( 6 . 8 ) P(1),P(2) F O R M A T ! / , ' a= ' . G 1 2 . 5 . ' b= ' . G 1 2 . 5 ) 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 ) . W T ( 2 0 0 ) . E 1 ( 5 ) , E 2 ( 5 ) , P ( 5 ) COMMON M 3 READ(5,1 ) N.M.NI 1 F0RMAT(3I5) R E A D ( 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 LOF(X,Y,YF.WT,E1,E2,P,0.0,N.M.NI,ND,EPS,AUX) IF ( N D . N E . 1 ) GO TO 3 WRITE ( 6 , 4 ) 4 F O R M A T ( ' ESTIMATES OF ROOT MEAN SOUARE TOTAL ERROR IN THE 1 PARAMETERS ') WRITE ( 6 , 5 ) ( E 2 ( I ) ,1=1.M) 5 FORMAT ( 1 X . 8 G 1 5 . 5 ) WRITE ( 6 . 6 ) 6 FORMAT'( ' VALUES OF X VALUES OF Y F I T T E D 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= '.G12.5.'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 ( 2 0 0 ) . Y ( 2 0 0 ) , Y F ( 2 0 0 ) , W T ( 2 0 0 ) , E 1 ( S ) . E 2 ( 6 ) . P ( 6 ) COMMON M 3 R E A D ( 5 , 1 ) N.M.NI 1 FORMAT(315) R E A D ( 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 R E A D ( 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 ( 1 X . 8 G 1 5 . 5 ) WRITE ( 6 , 6 ) 6 FORMAT(' VALUES OF X VALUES OF Y F I T T E D 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 A U X ( 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.  3 2 4 1  5  INTEGER N DIMENSION X(200).Y(200),Z(200).XX(200) READ ( 5 . 3 ) A . B . C . D . E FORMAT ( 5 E 1 2 . 9 ) READ ( 5 , 2 ) N , R U N , Q RE.TA.CA.PH FORMAT (I5.F5.0.F5.1.F6.3.F7 0.2F5.0.F5.2) READ ( 5 . 4 ) M,K,W FORMAT ( 2 I 5 . F 5 . 0 ) READ ( 5 , 1) ( X ( I ) , Y ( I ) , I = 1,N) FORMAT ( F 1 0 . 1 . F 1 0 . 4 ) (M**2.K/kW)'.14,6..90.0,-0.04.0.04) CALL AXIS ( 2 . , 2 . . ' R f CALL PLOT ( 2 . , 2 . , 3 ) CALL PLOT ( 2 . , 1 9 . 3 ) C A L L PLOT ( 2 . , 2 . . 2 ) T=3 . DO 5 1 = 1 . 7 .2) C A L L PLOT ( T C A L L PLOT ( T 9,2) C A L L PLOT (T .3) T = T+1 CONTINUE CALL PLOT ( 2 . , 2 . , 3 ) XS = 0 . CALL NUMBER ( 1 . 975 1 . 7 5 , 0 . 1 , X S . O . - 1)  xs=xs+eoo.  30  40  50  20  90  PROGRAM TO PLOT THE FOULING RESISTANCE DATA AND THE BEST FIT  CALL NUMBER ( 2 . 8 7 5 , 1 . 7 5 1 . X S . O . - 1) R=3.825 DO 3 0 1 = 1 . 6 XS=XS+600. C A L L NUMBER ( R , 1 . 7 5 , 0 . 1 . X S . 0 . - 1 ) R = R+1 CONTINUE CALL PSYM ( 4 . 9 5 1 . 5 5 , 0 . 1 5 , ' T I M E ( m i n ) ' , + 0 . 10) CALL PLOT ( 2 . , 8 . 3 ) F=3 . DO 4 0 1 = 1 , 7 C A L L PLOT ( F . 8 . . 2 ) CALL PLOT ( F , 7 9 , 2 ) CALL PLOT ( F , 8 .3) F = F+1 CONTINUE P =7 . DO 5 0 1=1 .6 C A L L PLOT ( 9 . , P , 2 ) CALL PLOT ( 8 . 9 . P . 2 ) C A L L PLOT ( 9 . , P , 3 ) P = P- 1 . CONTINUE DO 2 0 I = 1 . N X(I)=2.+X(I)/600. Y ( I ) « 2 . +(Y(I)+.04)/0.04 C A L L SYMBOL ( X ( I ) , Y ( I ) , O . 0 8 . 0 , 0 . •1 ) CONTINUE XX(1)=0.0 IF ( C . E O . O . ) GO TO 6 0 IF ( D . E O . O . ) GO TO 7 0 DO 9 0 J » 1 ,K Z(J)«A+XX(J)*(B+XX(J)*(C+XX(,J)*(D+XX(J)»(E)))) XX(J+1)«XX(J)+30. CONTINUE  - 190 -  Figure I I I - 5 .  91 70  80  81 60  10  11 100  15 8  120  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 CONTINUE GO TO 100 CONTINUE DO 8 0 J=1 ,K Z(J)=A+B*(1-EXP(-C*XX(J) ) ) XX(J+1)=XX(J)+30. CONTINUE DO 81 J = 1 , K XX(J)=2.+XX(J)/GOO. Z(J)=2.+(Z(J)+0.04)/0.04 CONTINUE GO TO 100 CONTINUE DO 10 J = 1 , K Z(J)=A+B*XX(J) XX(J+1)=XX(J)+30. CONTINUE DO 11 J = 1 , K XX(J)=2.+XX(J)/600. Z( J ) = 2. + ( Z ( J ) + 0 . 0 4 ) / 0 . 0 4 CONTINUE CONTINUE C A L L PLOT ( X X ( M ) , Z ( M ) . 3 ) DO 15 J=M,K C A L L PLOT (XX(J),Z(J),2) CONTINUE WRITE ( 6 , 8 ) X ( N ) . Z ( M ) , Y ( N ) . A , B FORMAT (/,'X='.G12.5.'Z=',G12.5.'Y=',F9.5,'A=',G12.5,'B=',G12.5) C A L L SYMBOL ( 3 . 0 . 7 . 4 . 0 . 1. ' R U N ' . 0 . . 3 ) C A L L SYMBOL ( 3 . 0 , 7 . 2 5 . 0 1. ' 0 ' . 0 . .1 ) C A L L SYMBOL ( 3 . 0 . 7 . 1 , 0 . 1, ' V , 0 . . 1 ) CALL SYMBOL ( 3 . 0 . 6 . 9 5 , 0 1 . ' R e ' . 0 . . 2 ) C A L L SYMBOL ( 3 . 0 , 6 . 8 , 0 . 1, ' T . A . ' , 0 . , 4 ) CALL SYMBOL ( 3 . , 6 . 6 5 . 0 . 1, ' C a ' . 0 . , 2 ) C A L L SYMBOL ( 3 . 1 7 , 6 . 6 9 . 0 . 1 0 . ' + + ' , 0 . , 2 ) C A L L 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 ) C A L L NUMBER ( 3 . 6 . 7 . 1 , 0 . 1, V , 0 . , 3 ) CALL NUMBER ( 3 . 6 , 6 . 9 5 , 0 1 . R E . 0 . , - 1 ) C A L L NUMBER ( 3 . 6 . 6 . 8 . 0 . 1, T A , 0 . , - 1 ) C A L L NUMBER ( 3 . 6 , 6 . 6 5 , 0 1 , C A . O . , - 1 ) C A L L NUMBER ( 3 . 6 . 6 . 5 . 0 . 1. P H . O . . 2 ) C A L L PSYM (4 . 1 5 , 7 . 2 5 , 0 . 1. ' k W ' . + 0 . . 2 ) C A L L PSYM (4 . 1 5 , 7 . 1 , 0 . 1 ' m / s ' , + 0 . , 3 ) C A L L PSYM (4 . 1 5 , 6 . 8 . 0 . 1 ' m g / 1 ' , + 0 . , 4 ) C A L L PSYM (4 . 1 5 . 6 . 6 5 , 0 . 1, ' m g / 1 ' . + 0 . , 4 ) I F ( W . E Q . O . ) GO TO 120 C A L L PSYM (3.7,7.4.0.1.'A'.+0.,1) C A L L PLOTND STOP END  - 191 -  Figure  111-6.  PROGRAM TO DETERMINE THE RATES PREDICTED BY THE HASSON"S IONIC DIFFUSION MODEL  /COMPILE I M P L I C I T REAL ( A - Z ) INTEGER RUN C INPUT UNITS OF T A , T D S 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 . E O . 0 ) GO TO 3 TEMP=.5*(TW+TB) PRINT,'RUN=',RUN C FIND L I Q U I D DENSITY AND V I S C O S I T Y AS A FUNCTION OF TEMP C L I Q U I D DENSITY=P LIQUID VISCOSITY=U P=(1181.32-0.593*TEMP)/1000. U=1./(2.148*((TEMP-281.435)+(8078.4+(TEMP-281.435)**2)**.5)-120.0) C FIND REYNOLDS NUMBER ( R E ) AND SCHMIDT NUMBER ( S C ) RE=V*D*P/U SC=U/(P*1.E-05) PRINT,'P=',P,'U=',U,'RE=',RE,'SC=',SC C C A L C U L A T E MASS TRANSFER C O E F F I C I E N T KD K D = 0 . 0 2 3 * R E * * ( - 0 . 1 7 ) * S C * * ( - 0 . 6 6 6 ) *V C C A L C U L A T E KR- REACTION RATE CONSTANT KR=EXP(38.74-20700./(1.987*TEMP)) C CHANGE UNITS OF KR TO KR1 ( C M / S ) / ( G C A C 0 3 / C M * * 3 ) TO ( C M / S ) / ( G M O L E C A / L ) ) KR1=KR*2.497239*40.08/1000. KR1=100.*KR1 C DETERMINE IONIC STRENGTH OF THE SOLUTION I = (1 . E - 0 3 ) * T D S / 4 0 . C DETERMINE FI FI=(I**.5)/(1+I**.5)-.3*I C CHANGE UNITS OF T A , T D S , A N D CA (AS PPM OF C A C 0 3 ) TO MOLES/L TA = T A / ( 1 0 0 0 . * 1 0 0 . 0 8 9 3 5 ) CA = C A / ( 1 0 0 0 . * 1 0 0 . 0 8 9 3 5 ) P R I N T , '1 = ' , 1 , ' T A = ' , T A , ' T D S = ' ,TDS C FIND FM AND F D , ALSO K1 AND K2 AND HENCE K11 AND K21 FM=10.**(-0.51*FI) FD=10.**(-2.04*FI) 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 * A L O G 1 0 ( T E M P ) - 0 . 0 1 0 3 7 * T E M P + 2 2 . 8 0 1 ) ) 1/H)/FM PRINT,'FM=',FM,'FD=',FD K1 = 1 0 . * * ( - 1 7 0 5 2 / T E M P - 2 1 5 . 2 1 * A L 0 G 1 0 ( T E M P ) + 0 . 1 2 6 7 5 * T E M P + 5 4 5 . 5 6 ) K2=10.**(-2902.39/TEMP-0.02379*TEMP+6.498) PRINT,'K1=',K1,'K2=',K2,'TEMP=',TEMP K11=K1/FM**2 K21=K2/FD**2 P R I N T , 'K1 1 = ' ,K1 1 , 'K21 = ' ,K21 C NOW USE THE VALUES OF T A , H , O H , K 1 1 , K 2 1 TO DETERMINE (HC03).(COS).(C02) HC03=(TA+H-0H)/((2.*K21/H)+1.) C03=(TA+H-0H)/(2.+H/K21) C02 = ( H * ( T A + H - 0 H ) )/(K11 + 2 . * K 1 1 * K 2 1 / H ) PRINT,'PH=',PH,'H=',H PRINT.'(HC03)='.HC03,'(C03)=',C03,'(C02)=',C02 PRINT,'(OH)=',OH,'K11=',K11,'K21=',K21 C NOW WE C A L C U L A T E W USING CA++ CONC. KSPU=10.**(-0.01183*(TEMP-273)-8.03) KSP=KSPU/(FD*FD) PRINT,'CA++=',CA.'KD=',KD,'KR=',KR,'KSP1=',KSP 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 = K 2 1 * K R 1 * H C 0 3 * * 2 / ( K 1 1 *KD*CA ) - K S P * C 0 2 * K R 1 / ( C A * * 2 * K D ) 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 PRINT,'VV=',VV,'WLPH=',WLPH.'WHPH=',W.'IN G/(CM**2-S)' P R I N T , ' W LPH A P P = ' , W P WRITE(6.12) 12 F O R M A T ( / / ) 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  I RUN Q  0.1 6  V  Re T.A. Ca + *  PH  0.1 2  2A I 1.5 kW 0.695 m/s 24984 I 73mg/l 2 9 4 mg/l 7.9 2  0.0 8  • • as  0.04  •  a?  00  -0.04  •  1  10  20  1  30 Time  Figure IV-2.  1  40  50  (hrs)  RUN 2A FOULING RESISTANCE VERSUS TIME  60  70  -  195 -  0.2 RUN Q V Re T.A. Ca* pH  0.16  0.1 2  +  3A 10.4 kW 0.503 m/s 18576 177 m g / l 3 0 4 mg/l 7.8 9  0.08  0.0 4 • ft  n  O.Ofr•  -0.04  1  an  -a—  ft  • L  CD  10  20  30  40 Time  50  60  (hrs)  Figure IV-3. RUN 3A FOULING RESISTANCE VERSUS TIME  70  - 196 -  0.2, RUN  Q V  0.16  Re T.A.  Ca" 0.1 2  0.0  pH  I 0.4 kW 0.503 m/s I 8 599 I 77mg/l 3 0 4 mg/l 7.93  8  0.04  0.0  8=  -0.04  20  30 Time  Figure IV-4.  40  50  (hrs)  RUN 3 FOULING RESISTANCE VERSUS TIME  60  70  - 197  0.21  T Run Q  0.16  V  Re T.A. Ca" PH  0.12  0.0  8  0.0  4  -  5A  14.1 kW 0.50 3 m/s 2 1170 I 62 mg / I 281 mg/1 8.1 I  00  -  0.04  1  10  20  30  40 Time  Figure IV-5.  50  (hrs)  RUN 5A FOULING RESISTANCE VERSUS TIME  60  70  - 198 -  RUN  Q  0.1 6  V  Re T.A. Co~ PH  0.1 2  0  14.1 kW 0.503 m/s 21 397 I 50mg/l 269 mg/l 8.1 I  10  20  30 Time  Figure I V - 6 .  40  50  (hrs)  RUN 5 FOULING RESISTANCE VERSUS TIME  60  -  199  -  Figure IV-7. RUN 6A FOULING RESISTANCE VERSUS TIME  - 200  -  Figure IV-8. RUN 21 FOULING RESISTANCE VERSUS TIME  - 201 -  0.21 22 I 2.0 kW 0.695 m/s 29030 3 4 8 mg/l 6 3 9 mg/l 7.6 3  RUN 0.16  0.1 2  Q V  Re T.A. Co** PH  •  0.08 i f •  cp  •  0.04  rSj •  -0.04'  10  DU eg  •  HD  20  30 Time  40  50  (hrs)  Figure IV-9. RUM 22 FOULING RESISTANCE VERSUS TIME  60  70  - 202 -  0.21  0.16  5  O.I2|  RUN Q V Re T.A. Ca pH  + +  24 8.4 kW 0.2 99 m/s 1 1 952 4 1 5 mg/1 6 97 mg/1 7.7 8  0.08  •1  •  • ••  —I  60  70  0.04  -0.04  10  20  30 Time  40  50  (hrs)  Figure IV-10. RUN 24 FOULING RESISTANCE VERSUS TIME  - 203 -  0.2 RUN O.I 6  Q V Re T.A.  Co"  pH  O.I 2  25 1 0.9 kW 0 . 6 0 0 m/s 2 3078 3 56 mg / I 6 5 1 mg/l 7.4 5  o W  E  or  0.0 8  0.04  -0.04  1  10  20  30 Time  40  50  60  (hrs)  Figure IV-11. RUN 25 FOULING RESISTANCE VERSUS TIME  70  - 204 -  0.2i  RUN 0.16  5  0.1 2r—  Q  V  Re T.A.  Co** pH  28 I 1.3 kW 0.460 m/s 8973 3 4 7 mg /I 6 3 3 mg/1 7.6 0  CM  0.0 8 r-  0.04  0.0  0.04  10  20  1  30  1  40  50  60  Time (hrs)  Figure IV-12.  RUN 28 FOULING RESISTANCE VERSUS TIME  70  - 205 -  O.I 6 r -  O.l 2 h-  CVJ  E  0.0 8  r —  *#-  or  0.04  -0.04  Figure IV-13.  RUN 29 FOULING RESISTANCE VERSUS TIME  - 206 -  0.1 6  RUN  30  V Re J-  0.3 4 0 m/s 6849 36 5 mg/| 6 5 0 mg/| 7.5 4  A  C  a  +  PH  ; + +  Time  (hrs)  Figure IV-14. RUN 30 FOULING RESISTANCE VERSUS TIME  - 207 -  40 Time  50 (hrs)  Figure IV-15. RUN 32 FOULING RESISTANCE VERSUS TIME  70  - 208 -  0.2 RUN O.I 6  ^  O.I 2  Q  V  Re T.A. Ca PH  + +  33 9.4 kW 0.503 m/s I 9394 3 5 3 mg/ I 6 4 0 mg/1 7.9 3  CM  E  0.0 8  0.04  - 0.0 4 0  20  30 Time  40  50  60  (hrs )  Figure IV-16. RUN 33 FOULING RESISTANCE VERSUS TIME  70  -  -  6h  O.I  0.1 2  <?  209  H  0.08  or 0.0  4  0.0 Q>-  -0.04  30 Time  40 (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