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Particulate fouling of sensible heat exchangers Watkinson, Alan Paul 1968

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PARTICULATE FOULING OF SENSIBLE HEAT EXCHANGERS by ALAN PAUL WATKINSON B. Eng., McMaster U n i v e r s i t y , 1962 M.A.Sc, U n i v e r s i t y o f B r i t i s h Columbia, 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In the Department of CHEMICAL ENGINEERING  We accept t h i s t h e s i s as conforming r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA September,1968  t o the  In p r e s e n t i n g an a d v a n c e d the I  thesis  degree at  f u r t h e r agree  this  written  for  for extensive  may be g r a n t e d by  representatives. thesis  It  is  f i n a n c i a l gain  permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  2.<\  Columbia  shall  the requirements  Columbia,  I agree  r e f e r e n c e and copying  of  this  that copying  or  for  that  Study. thesis  t h e Head o f my D e p a r t m e n t  understood  Department  Date  British  it f r e e l y available for  that permission  s c h o l a r l y purposes  by h i s  in p a r t i a l f u l f i l m e n t of  the U n i v e r s i t y of  L i b r a r y s h a l l make  for  of  this  or  publication  n o t be a l l o w e d w i t h o u t my  i  ABSTRACT  F o u l i n g by a petroleum sand  gas o i l and a d i l u t e suspension o f  i n water was s t u d i e d as a f u n c t i o n of mass flow r a t e and  w a l l temperature.  The experiments  the l i q u i d through  a s i n g l e tube maintained  f l u x by e l e c t r i c a l h e a t i n g .  were c a r r i e d out by c i r c u l a t i n g  The change i n f o u l i n g r e s i s t a n c e  and pressure drop w i t h time was measured. of  the water and o f the o i l at low heat  t o t i c value.  At h i g h e r heat  i n c r e a s e d almost The  asymptotic  at constant heat  The f o u l i n g r e s i s t a n c e  f l u x e s grows to an asymp-  f l u x e s the o i l f o u l i n g r e s i s t a n c e  l i n e a r l y with time a f t e r an i n d u c t i o n p e r i o d .  f o u l i n g r e s i s t a n c e o f both the o i l and the water  decreased w i t h i n c r e a s i n g mass flow r a t e . w a l l temperature  the i n i t i a l  At constant c l e a n tube  f o u l i n g r a t e o f the o i l decreased  w i t h i n c r e a s i n g mass flow r a t e .  The i n i t i a l  f o u l i n g r a t e o f the  water i n c r e a s e d w i t h i n c r e a s i n g mass flow r a t e up t o a mass flow r a t e , mass flow r a t e .  critical  and then decreased w i t h f u r t h e r i n c r e a s e s i n At constant mass flow r a t e , the i n i t i a l  fouling  r a t e o f the o i l depended e x p o n e n t i a l l y on the c l e a n tube w a l l temperature.  An a c t i v a t i o n energy o f 29 Kcal/mole  was c a l c u -  l a t e d f o r the o i l f o u l i n g process by f i t t i n g  the i n i t i a l  r a t e data t o an A r r h e n i u s type o f e q u a t i o n .  The pressure  fouling drop  i n c r e a s e showed the same general trends w i t h mass flow r a t e and  tube w a l l temperature as d i d the f o u l i n g r e s i s t a n c e . F o u l i n g r e s i s t a n c e s f o r heated K r a f t cooking l i q u o r , c a l c u l a t e d from p u l p m i l l o p e r a t i n g data and from a s i n g l e f o u l i n g experiment,  appeared to f o l l o w s i m i l a r trends to those, followed  i n common by the gas o i l and the water. The experimental r e s u l t s of t h i s study were compared to the mathematical model o f Kern and Seaton. most f o u l i n g curves was  While the shape o f  i n agreement w i t h that p r e d i c t e d  by t h i s model, dependence of the i n i t i a l  generally  f o u l i n g rate and o f the  asymptotic f o u l i n g r e s i s t a n c e of the gas o i l on the mass flow r a t e were both i n disagreement w i t h the d e t a i l e d p r e d i c t i o n s of the model.  For low mass flow rates o f the water, however, even  "the d e t a i l e d p r e d i c t i o n s were borne out.  I t was,  moreover,  p o s s i b l e to remove part of the sand d e p o s i t by i n c r e a s i n g the v e l o c i t y o f the water,  i n accord w i t h the p o s t u l a t e d  removal  mechanism of Kern and Seaton, but the c o k e - l i k e d e p o s i t  from  the gas o i l could not be s i m i l a r l y removed by i n c r e a s i n g the o i l velocity. Mathematical models are developed i n which the d e p o s i t i o n term i s w r i t t e n  as the product of a m a t e r i a l  f l u x t o the w a l l  r e g i o n and a s t i c k i n g p r o b a b i l i t y , a f t e r Parkins,  and the removal  term depends on the shear s t r e s s , a f t e r Kern and Seaton, cases are c o n s i d e r e d where d e p o s i t i o n  Specific  i s c o n t r o l l e d by t r a n s f e r  to the s u r f a c e , both steps..  adhesion at the s u r f a c e ,  Where d e p o s i t i o n  and a combination o f  i s c o n t r o l l e d p a r t l y by t r a n s f e r  and p a r t l y by adhesion, the model p r e d i c t s mass flow r a t e and temperature  dependence o f the i n i t i a l  f o u l i n g r a t e i n agreement  w i t h the experimental r e s u l t s found f o r the o i l .  The observed  asymptotic f o u l i n g r e s i s t a n c e o f the o i l , however, depended l e s s s t r o n g l y on the r e c i p r o c a l o f the mass flow rate than i s p r e d i c t e d by the model.  Where t r a n s f e r alone c o n t r o l s the d e p o s i t i o n  process, the extended model reduces t o a form s i m i l a r t o that of Kern and Seaton.  iv  TABLE OF CONTENTS Page ABSTRACT  i  LIST OF TABLES  vi  LIST OF FIGURES  viii  ACKNOWLEDGEMENTS  x i :L  1.  INTRODUCTION.....  1  2.  PERTINENT PRIOR WORK  5  3.  SCOPE AND METHOD OF PRESENT WORK  4.  SELECTION OF WORKING FLUIDS.  18 „,  20  5,0 APPARATUS  23  6.  EXPERIMENTAL PROCEDURES  36  7.  RESULTS AND DISCUSSION  39  a) b) c) d) e)  39 46 48 60  f) g) h) i) j)  C a l c u l a t i o n Methods. I n i t i a l Experiments on Gas O i l F o u l i n g E f f e c t o f Mass Flow Rate on F o u l i n g o f O i l . . E f f e c t o f Wall Temperature on F o u l i n g o f O i l Combined E f f e c t s . o f Mass.Flow.Rate.and W a l l . Temperature L o c a l F o u l i n g Rates Nature o f Deposits i n Gas O i l F o u l i n g „ R e p r o d u c i b i l i t y o f Gas O i l Results and Somparison w i t h T a b u l a t e d . F o u l i n g F a c t o r s . . . Sand-Water Fouling................ Kraft Liquor Fouling  8.  EXTENSION OF EXISTING FOULING MODELS  9.  CONCLUSIONS  10,  RECOMMENDATION FOR FURTHER WORK..  62 68 69 75 76 89 95 124 12 7  11.  L I S T OF REFERENCES  12 9  12.  NOMENCLATURE  134  Appendix  1.  Calibration  o f Equipment.  a)  Thermocouple  b)  D i f f e r e n t i a l Pressure C e l l C a l i b r a t i o n  1-6  c)  O r i f i c e Plate Calibration  1-10  Appendix  2.  Calibration  1-1  C a l c u l a t i o n . o f . t h e . H e a t . T r a n s f e r Coefficient  a)  Determination  o f t h e Heat F l u x  b)  I n s i d e Tube W a l l  Temperature  c)  Determination.of  t h e Mean T e m p e r a t u r e  1-1  2-1 2-1 2-3  Difference  2-3  d)  Sample C a l c u l a t i o n  2-5  e)  D i m e n s i o n s o f T e s t S e c t i o n s I I and I I I  2-10  Appendix  3.  Experimental Data  3-1  vi LIST OF  TABLES  Table  Page  I,  P r o p e r t i e s of a T y p i c a l Gas  II.  Location  ill.  Comparison of C a l c u l a t e d  O i l Blend  of Thermocouples on Test S e c t i o n s  22 30  and Measured Water  Heat T r a n s f e r C o e f f i c i e n t s  47  IV.  F i t of Gas  55  V.  L i n e a r F i t of I n i t i a l F o u l i n g Rate Data  55  VI.  Gas  71  VII.  Approximate S i z e D i s t r i b u t i o n of P a r t i c u l a t e s in O i l Estimated Thermal C o n d u c t i v i t y of Gas O i l Deposits from Readings at End of Run  VIII.  O i l F o u l i n g Data to Equation 6  O i l Deposit  Weights  72 74  IX.  R e p r o d u c i b i l i t y of I n i t i a l F o u l i n g Rates  75  X.  F i t of Sand-Water F o u l i n g Data to Equation 6  86  XI.  Estimated Thermal C o n d u c t i v i t y of Sand Deposits  88  XII.  F o u l i n g Models f o r Thin Deposits  105  XIII.  F o u l i n g Models w'ithil.Bloc&age.'ffo& W Constant  106  XIV.  F o u l i n g Models w i t h Blockage f o r Constant Pressure Gradient  114  Quotient F o u l i n g Models w i t h Blockage f o r W Constant  119  XV.  Appendix Table  f o r W Constant  1  1-1  Resistance  Thermometer Data  l-II  Thermocouple C a l i b r a t i o n s - T e s t S e c t i o n I  1-3 1-4  V l l  1-5  l-III  Thermocouple C a l i b r a t i o n s - Test Section I I I  1-IV  C a l i b r a t i o n of O r i f i c e D i f f e r e n t i a l Pressure C e l l  1-8  1-V  C a l i b r a t i o n o f Tube D i f f e r e n t i a l P r e s sure C e l l  1-9  1-VI  C a l i b r a t i o n of O r i f i c e Plates  1-12  1-VII  F i t o f Regression Equations f o r Orifice Plates  1-13  O p e r a t i n g C o n d i t i o n s and C l e a n Tube C o e f f i c i e n t s f o r F o u l i n g Expeximents  3-4  I n s i d e W a l l Temperature P r o f i l e s and F o u l i n g Data  3-5  Comparison o f C l e a n Tube Heat T r a n s f e r C o e f f i c i e n t s w i t h Sieder-Tate Equation  3-10  3-IV  P r e s s u r e Drop and D e p o s i t T h i c k n e s s e s  3-11  3-V  Particulate Levels i n Fouling Experiments  3 -13  Appendix 3 Table  3-1 3-II 3-III  viii  LIST OF FIGURES  F i g u r e Number 0  Page  Computed F o u l i n g Curves f o r Kerris Example  2  12  1  Diagram of Heat T r a n s f e r Loop  24  2  Orifice  25  3  Diagram o f Test S e c t i o n I  27  4  Pressure Taps and E l e c t r i c a l Terminals  28  5  Photograph of Test S e c t i o n I I  31  6 7  O u t l e t M i x i n g Chamber Tube Wall Temperature P r o f i l e s and Terminal F l u i d Temperatures  33 43  Comparison of Measured Clean Heat T r a n s f e r C o e f f i c i e n t s and P r e d i c t i o n s of the S i e d e r Tate Equation f o r Gas O i l s  45  Heat T r a n s f e r C o e f f i c i e n t versus Time for. T « 295°F-Oil A  50  Heat T r a n s f e r C o e f f i c i e n t versus Time f o r T w « 295°F-Oil B  51  8  9  P l a t e s and Flanges  W c  10  c  11  Heat T r a n s f e r C o e f f i c i e n t versus Time f o r E . W 346°F-Oil B c w  12  F o u l i n g R e s i s t a n c e of O i l s versus Time f o r T « 2 9 5 ( S o l i d L i n e s are Least Squares F i t t o E q u a t i o n 6)  53  w  c  13  F o u l i n g Resistance and Pressure Drop Increase versus Time f o r T ,« 346°F-Oil "B 57 c V a r i a t i o n of Parameters of Equation 6 with Mass Flow Rate of O i l ( l o g - l o g ) 58 T>  w  14  54  ix  15  I n i t i a l F o u l i n g Rate of O i l versus Mass Flow Rate ( l o g - l o g )  16  F o u l i n g R e s i s t a n c e and Pressure Drop Increase versus Time f o r V a r y i n g Heat F l u x e s - O i l B  61  Log I n i t i a l F o u l i n g Rate versus R e c i p r o c a l of Average Clean Tube Wall Temperature-Oils A and B •  63  D e v i a t i o n s from I n i t i a l F o u l i n g Rate Correlation:;-  65  Thermal R e s i s t a n c e versus Time f o r V a r y i n g Mass Flow Rate at Constant Heat F l u x - O i l B  67  17  18  19  59  20  L o c a l I n i t i a l O i l F o u l i n g Rate versus R e c i p r o c a l of L o c a l Absolute Wall Temperature 70  21.  Heat T r a n s f e r C o e f f i c i e n t and Pressure Drop Versus Time f o r I n i t i a l Sand-Water F o u l i n g Experiments  78  Heat T r a n s f e r C o e f f i c i e n t versus Time f o r Sand-Water Experiments T « 1 7 5 ° F -  80  F o u l i n g R e s i s t a n c e and Deposit versus Time f o r Sand-Water  Thickness 81  F o u l i n g R e s i s t a n c e and Deposit versus time f o r Sand-Water  Thickness  22.  W  23  24  25  26  27  28  82  Parameters of Equation 6 versus Mass Flow Rate of Water ( l o g - l o g )  84  I n i t i a l F o u l i n g Rate of Water versus Mass Flow Rate (log-log)  85  F o u l i n g R e s i s t a n c e versus Time f o r M i l l K r a f t L i q u o r Heater  92  Heat T r a n s f e r C o e f f i c i e n t and F o u l i n g R e s i s t a n c e of K r a f t L i q u o r versus Time  94  X  29  Computed Curves f o r Constant Mass Flow Rate F o u l i n g w i t h Blockage  30  Computed Curves f o r Constant Mass Flow Rate F o u l i n g w i t h Blockage and Removal Rate Independent o f Thickness  108  110  31  Computed Curves f o r Constant Pressure Gradient F o u l i n g w i t h Blockage 113  32  Computed Curves f o r ^.Constant Mass Flow Rate F o u l i n g - Q u o t i e n t Model  117  Comparison of Experimental R e s u l t s w i t h Thin F i l m Quotient Model P r e d i c t i o n s  121  33  Appendix 1 Figure  1-1  C a l i b r a t i o n Curve f o r O r i f i c e D i f f e r e n t i a l Pressure C e l l  1-2  C a l i b r a t i o n Curve f o r Tube D i f f e r e n t i a l Pressure C e l l  1-16  Kinematic V i s c o s i t y and S p e c i f i c G r a v i t y of O i l A  1-17  1-3  1-7  Appendix 2 Figure  2-2  E s t i m a t i o n of Surface Temperature o f Insulation  2-11  2-2  Heat Loss Through I n s u l a t i o n  2-12  2-3  Thermal C o n d u c t i v i t y of Type 304 Stainless Steel  2-12  xi  ACKNOWLEDGMENTS  I*-.;wish t o t h a n k D r . N o r m a n this  investigation  was c o n d u c t e d ,  Epstein, for his  u n d e r whose  guidance  direction  throughout  this  study. •I' w o u l d their  assistance  apparatus. and of  Mr. A  and c o - o p e r a t i o n  . MacKenzie  used  donation  data,  work,  of Kraft  and t o t h e B r i t i s h  u s e o f some I  Chemical  am  of their  indebted  Engineering  Columbia,  Engineering  Berry  Department  Columbia. Canada  Ltd.  to the Electric  pulping  staff for  i n the construction ofthe  of the Electrical  a r e due t o S h e l l  i n this  and h i s  f o r t h e a s s i s t a n c e o f Mr. F.  the University o f B r i t i s h  oils  the  t o t h a n k M r . R. M u e l c h e n  I am g r a t e f u l  Thanks  for  like  liquor  Columbia  for donation  Steel  Company  a n d some p l a n t  Institute  o fthe  (Esco) L t d .  operating  o f Technology f o r  equipment.  to the National Department  Research  Council, the  of the University of British  a n d t o M r . a n d M r s . M.H.  McCurdy  for financial  support. I support  am a l s o  throughout  indebted this  t o my w i f e  work.  Elizabeth for her continual  1.  INTRODUCTION  The performance  o f heat exchangers  i n service condi-  t i o n s o f t e n does not l i v e up t o d e s i g n e x p e c t a t i o n s . o p e r a t i o n with many l i q u i d s o f i n d u s t r i a l importance  During a film  g r a d u a l l y b u i l d s up on the heat t r a n s f e r s u r f a c e due t o c r y s tallization,  p o l y m e r i z a t i o n , decomposition, sedimentation or  b i o l o g i c a l growth.  When the d e p o s i t e d f i l m changes the therm-  a l r e s i s t a n c e or the pressure drop measurably, r e f e r r e d t o as f o u l i n g .  the c o n d i t i o n i s  The u s u a l ' r e s u l t o f f o u l i n g i s a de-  crease i n the o v e r - a l l heat t r a n s f e r c o e f f i c i e n t . roughness  o r blockage e f f e c t s can produce  However,  an i n c r e a s e i n the  heat t r a n s f e r c o e f f i c i e n t under some circumstances, e s p e c i a l l y i f the f o u l i n g d e p o s i t has a h i g h thermal c o n d u c t i v i t y . i n g of heat exchangers  occurs i n many i n d u s t r i e s ,  r e f i n i n g , pulp and paper manufacturing, polymer  Foul-  including o i l  and f i b e r p r o -  d u c t i o n , sea water conversion, and i n c o n v e n t i o n a l and n u c l e a r power p l a n t s . The  causes o f f o u l i n g are numerous.  Rapid f o u l i n g o f  organic-polymer mixtures may be caused by h i g h temperatures promote p o l y m e r i z a t i o n , o r the formation o f t a r s , sludge.  coke, or  S c a l e s may be formed due t o an i n v e r s e temperature-  that  2  solubility relation.  The  presence of a s t i c k y o r g a n i c  film  may  a c c e l e r a t e the d e p o s i t i o n of p a r t i c u l a t e matter suspended i n the l i q u i d as a r e s u l t of c o r r o s i o n or other p r i o r h i s t o r y . may  s e t t l e out  slime may  i n regions of low v e l o c i t y i n heat exchangers or  grow at hot  spots  i n c o o l i n g water systems.  In most cases the f o u l i n g u n i t e v e n t u a l l y must be down and  Dirt  cleaned  out.  shut  For ease of c l e a n i n g the most s e v e r e l y  f o u l i n g streams are u s u a l l y c a r r i e d i n the tubes of s h e l l tube heat exchangers. ated may  be  drop across  The  amount of f o u l i n g t h a t can be  c o n t r o l l e d by the allowable  increase i n  and toler-  pressure  the exchanger as the tubes g r a d u a l l y p l u g up,  the a v a i l a b i l i t y of thermal d r i v i n g f o r c e to maintain f l u i d temperatures.  or by  outlet  I f a constant heat f l u x i s maintained  d u r i n g f o u l i n g of a tube, the o u t s i d e tube w a l l temperature must be  i n c r e a s e d with  time, and  the l i m i t i n g f o u l e d c o n d i t i o n may  be  governed by a maximum tube w a l l temperature above which c o r r o s i o n r a t e s become e x c e s s i v e to f a i l u r e .  F o u l i n g i s c o s t l y as exchangers must be  designed to provide cleaned. be may  or the m a t e r i a l becomes s u s c e p t i b l e  the e x t r a s u r f a c e , and  E x t r a f u e l or h i g h e r pressure  r e q u i r e d to maintain  then p e r i o d i c a l l y  condensing vapour  may  temperatures, or expensive s u r f a c t a n t s  be used to keep the f o u l i n g m a t e r i a l The  over-  dispersed.  s u r f a c e area of a heat exchanger may  be determined  3  from  the following equation:  A =  For  Q  process  from  R  fouling  correlations  +  h o  R^  the process  cases  or thermal  o f the order  +  f i  R  f  o  u  +  t  are usually  n  and f l u i d  o f the tube  fluids  the fouling  R  and R  resistances are usually  usually  some  R  exchangers  i s a property  w  ence w i t h are  +  h  heat  design  ysis.  (R .  Rw>  determined  mechanical  anal-  m a t e r i a l and geometry.  obtained  o r from  from  previous  experi-  tables  ( 1 ) , and  available  0 . 0 0 0 5 t o 0.01  r e s i s t a n c e may  The  (hr)(ft )(°F)/BTU. 2  be t h e c o n t r o l l i n g  In  resis-  tance . Kern methods for  and Seaton  forpredicting  Though  temperature  cases  published  quantities.  dependent is  are f a i r l y  that  flux  may  factors  Further,  and t h e time  be  tube  reliable,  material,  velocity,  influence fouling,  the fouling  methods  i n considerable  are represented  f o rwhich  although  as  i n many  independent  r e s i s t a n c e i s time  the fouling  resistance i s valid  not mentioned. Kinert  the  and h e a t fouling  1 q  out that  r e s i s t a n c e may  i t i s recognized  fluid  these  pointed  Rh^ and R J  estimating the fouling  error.  of  (2) h a v e  mechanics  ( 3 ) , i n 1949, c a l l e d and c h e m i s t r y  effect  of velocity,  change  of the heat  Knudsen  surface transfer  (4), i n a lecture  f o rbasic research  of fouling, temperature, coefficient  t o the Ninth  particularly and h e a t with  into as t o t h e  flux  time.  N a t i o n a l Heat  on t h e  Recently Transfer  4  Conference,  (AICHE-ASME 1967) d i s c u s s e d  ing resistances  as one o f t h e a r e a s  that  needs  that  improvements  troduce  "considerable  basic  i n assigning  i n process heat  and a p p l i e d  as b a s i c  parameters".  He  flow  o f heat exchangers,  f r e q u e n c y on t h e d e c r e a s e d locities.  I t was  "must i n temthe  the design  i n c l u d i n g the e f f e c t of  surface  suggested  out that  area  required  v e l o c i t y and t e m p e r a t u r e  dependence o f the f o u l i n g r e s i s t a n c e  and  cleaning  at higher  among t h e p u r p o s e s o f t h e p r e s e n t  study the e f f e c t s of f l u i d  He  as a f u n c t i o n o f t i m e , v e -  and t e m p e r a t u r e e n a b l e s one t o o p t i m i z e  operation  foul-  transfer  v e l o c i t y and  also pointed  b e h a v i o u r o f the f o u l i n g r e s i s t a n c e locity  study".  fouling resistances  f o u l i n g as a f u n c t i o n o f t i m e ,  perature  the p r e d i c t i o n of  ve-  work t o on t h e t i m e  f o r some f o u l i n g  fluids.  5  2.  PERTINENT PRIOR WORK  There have been a number o f attempts t o p r e d i c t  foul-  i n g r a t e s , the more s u c c e s s f u l o f which apply t o s c a l i n g , the formation verse  o f c r y s t a l s on a heat t r a n s f e r surface due t o an i n -  solubility-temperature relationship. McCabe and Robinson  s c a l i n g isothermal  fluid  (5) i n 1924 proposed that f o r a i n evaporation,  the amount of s c a l e  formed was p r o p o r t i o n a l t o the amount o f water evaporated up t o time t .  T h i s assumption i m p l i e s that a f i x e d p r o p o r t i o n o f  scale deposits  even though the s c a l e s u r f a c e  o f f as s c a l e b u i l d s up.  R  2  =  RJ  + a  A  x  Hasson  T h e i r equation  AT  has been w e l l v e r i f i e d  temperature drops  t  (£)  f o r s c a l i n g i n evaporators (5).  (6) considered  a s c a l i n g non-isothermal  liquid.  As the s c a l e accumulates, the temperature o f the s c a l e drops, d e c r e a s i n g  the r a t e o f s c a l e formation.  surface  The r e s u l t of  his analysis i s  R  2+n  =  R  A(T  2+n + ^  - .Ti.)  s t  n + 1  t  (WC )  ( 3 )  n  p  3-5 Hasson found that R-'-(It f o r three  t e s t s at low v e l o c i t i e s i n  s c a l i n g from hard water i n a double pipe heat exchanger w i t h steam i n the s h e l l .  At the h i g h e s t  v e l o c i t y (4.1 f t / s e c ) the  6  data d i d not f i t equation 3. Reitzer  (7) considered the r a t e of s c a l e  i n a t u b u l a r exchanger.  He  formation  assumed a l i n e a r i n v e r s e tempera-  t u r e s o l u b i l i t y r e l a t i o n and t h a t the r a t e of c r y s t a l growth was  p r o p o r t i o n a l t o the s u p e r s a t u r a t i o n r a i s e d t o the power n.  His d e r i v e d r e s u l t s f o r constant heat f l u x are  R = R  where K  r  + a  Q  n+1  K ( r  q  |  t  n  (4)  i s the o v e r - a l l c r y s t a l l i z a t i o n r a t e constant.  constant AT,  R  3  =  For  R e i t z e r obtained  R  n 1 +  +  ^  Ajr h  m t  ( 5 )  i  Thus, when r e a c t i o n at the s u r f a c e c o n t r o l s the s c a l i n g process, K  r  w i l l be r e l a t i v e l y independent  of v e l o c i t y ,  and h i g h v e l o c i t y  w i t h i n c r e a s i n g h^ should reduce the r a t e of s c a l e  formation.  When mass t r a n s f e r c o n t r o l s , v e l o c i t y should have l i t t l e as i t then i n f l u e n c e s h^ and K  r  similarly.  Miyauchi and M o r i -  yama (8) a r r i v e d at a s i m i l a r equation independently.  Palen  and Westwater (9) found t h a t f o r b o i l i n g C a S O ^ s o l u t i o n s f l a t p l a t e under c o n d i t i o n s of uniform heat r a t e depended on the square equation 4.  of the heat  effect  f l u x , the  flux, i . e .  on a  fouling  n = 2 in  S i m i l a r r e s u l t s have been obtained f o r d e p o s i t i o n  of i r o n oxide s c a l e s i n b o i l e r s .  Man'kina and co-workers  (10)  found the s c a l i n g r a t e t o be uniform w i t h time, and dependent on  7  the square o f t h e l o c a l h e a t  flux.  I t i s w e l l known t h a t i n many cases h i g h suppress t h e growth o f the f o u l i n g r e s i s t a n c e  velocities (11).  Smith (12)  measured t h e f o u l i n g r e s i s t a n c e o f exchangers o p e r a t i n g on w a t e r from t h e R i v e r Tees o v e r three-month p e r i o d s . range 2 t o 6 f t / s e c o n d ,  I n the v e l o c i t y  t h e amount o f d e p o s i t t h a t formed i n  t h r e e months was reduced as t h e v e l o c i t y was i n c r e a s e d . and Church  (13) have d e s c r i b e d  t h e use o f h i g h v e l o c i t i e s  30 f t / s e c ) i n h e a t exchangers i n f o u l i n g s e r v i c e . times have been i n c r e a s e d  Chantry (10 t o  Operating  from s i x days t o s i x months on some  u n i t s , due t o t h e combined e f f e c t s o f t h e s c o u r i n g a c t i o n o f t h e l i q u i d and t h e lower tube w a l l temperatures a s s o c i a t e d higher v e l o c i t i e s .  with  Kern and Seaton ( 2 ) , i n 1959, p r o v i d e d an  a n a l y s i s t h a t p r e d i c t e d t h e e f f e c t o f v e l o c i t y on t h e b u i l d u p of t h e f o u l i n g f i l m .  They observed t h a t f o r many d i f f e r e n t  f o u l i n g l i q u i d s the f o u l i n g r e s i s t a n c e appeared t o i n c r e a s e w i t h time t o an a s y m p t o t i c v a l u e .  The time dependence o f t h e  f o u l i n g r e s i s t a n c e was then approximated by R  f  =  Rf (1 - e " ) b t  (6)  A t h e o r e t i c a l model was d e v e l o p e d i n which t h e y a s sumed t h e n e t r a t e o f f o u l i n g f i l m f o r m a t i o n  i n a s i n g l e heat  exchanger tube c o u l d be w r i t t e n as t h e d i f f e r e n c e between a constant  ( w i t h time) d e p o s i t i o n r a t e and a v a r i a b l e removal r a t e .  8  The  deposition  tion  C  was  and t h e mass  pictured depth  rate  flow  as o c c u r i n g  change  and  and was  i n deposit  thickness  At showed  that  andTremains equation (putting deposit,  assumed  T  assumed  i s obtained  by  putting  is  the asymptotic  deposit  = x^ k  f  c  substituting  d  constant)„  Rf  R*  k  d  d .,  random  to the  shear  was  then w r i t t e n  The  as  where  with  x «  time,  surface  pipe  diameter  integration of  yields equation  i s the thermal  conductivity  The  fouling  dx/dt  asymptotic = 0  D,  i n equation  6 o f the  resistance  7 so that  i f x  thickness,  T  (  k  8  )  d  2  T = P_ g  2  at  of the deposit.  - KlCVW " K  was  (7)  a clean  where  d  o f weakness  x  e s s e n t i a l l y constant  Rf = x/k ,  concentra-  tendency  proportional  time  f o r thin deposits,  7 s t a r t i n g from  removal  thickness  with  2  The  as t h e d i r t  at planes  the instantaneous  d x _ K-j^C'W - K  They  to vary  r a t e , W.  i n chunks  i n the deposit,  stress T,  assumed  yb£  :(9)  2  c  and u  into  b  equation  R* assuming high  fchat  enough  =  8,  a  4  do)  W  pirn  2  i t i s seen  W"  'that  (11)  1  f i s independent  mass  flow  rate  o f Reynolds  i s used,  number.  an e x c h a n g e r  Thus could  i f a theoreti-  9 cally  operate  i n d e f i n i t e l y with  a small, tolerable  fouling  res i s t a n c e .  The  parameter b  b •-  (dRf/dt)  t  i s obtained  =  0  (dx/dt)x =0  =  k Combining equations  b = K T  12  f u£  a  2  2g If relative with  t  i n t e g r a b l e and  a series  of  of  constant  an  then T  i n equation  thickness is available  film  The  equation  7 will  the  asymptotic  asymptotic  film  7 i s not  thickness  pressure drop  Kern  pressure drop  explicit  tube w a l l . although  important  (14)  and  c o n s i d e r e d the  only can  as  The the  alternate  v a r i a b l e mass f l o w  d a t a were g i v e n this  role  im-  (14)  publication,  to support  vary  PVD0.8  attraction  a n a l y s i s was  s u r f a c e temperature i n many t y p e s  Nor was  o f the d i r t  restricted  of  t o the  w o u l d be  fouling.  case  rate.  i n e i t h e r o f the  t h e o r e t i c a l model.  given or p o s t u l a t e d f o r the  case,  to a considerable thickness  6  a later  the  (13)  2  wO-  a  In  tions  R*  case  integrals.  ( A  No  d  7 as  (12)  For t h i s  be w r i t t e n i n t e r m s o f t h e x*  up  diameter,  ( a t c o n s t a n t W).  mediately as  tube  k  W  6 and  c  the d e p o s i t b u i l d s t o the  equation  _ KiC'W  R*  d  9 and  KP  =  2  8,  from  publicaany  mechanism  particles  to  isothermal  expected  to play  10  Kern  (2,14) maintained  t h a t a c c o r d i n g t o h i s theory,  i n c r e a s i n g the v e l o c i t y o f a d i r t y l i q u i d  i n the tubes of a heat  exchanger would i n c r e a s e the o p e r a t i n g time due t o suppression of  fouling.  Equation 8 does i n d i c a t e t h a t i n c r e a s i n g the v e l o -  c i t y and hence W i n a tube decreases  the u l t i m a t e f o u l i n g r e -  •k  s i s t a n c e Rf.  D i f f e r e n t i a t i o n o f equation 6 y i e l d s ,  f o r time  zero, dR  f  =  dt  -* R b f  (15)  t=0  S u b s t i t u t i n g f o r Rf and b from equations 11 and 13 r e s p e c t i v e l y shows t h a t the i n i t i a l  f o u l i n g r a t e i n c r e a s e s w i t h mass flow  rate: dR  CC  f  dt  t  W  (16)  =0  Thus, i t i s c o n c e i v a b l e t h a t , i n r a i s i n g the d e s i g n l i q u i d v e l o c i t y , the h i g h e r i n i t i a l  f o u l i n g r a t e may more than o f f s e t the  lower u l t i m a t e r e s i s t a n c e , and lead t o a s h o r t e r o p e r a t i n g time. T h i s unexpected  f a c e t of the Kern-Seaton model has been pointed  out by the present authors t o Dr. Kern i n connection w i t h numerical  examples Kern c i t e s i n h i s two papers which are there  solved erroneously. which i s used  Kern confuses the mass flow r a t e per tube,  i n the d e r i v a t i o n o f h i s equations, w i t h the mass  flow per exchanger i n h i s numerical c a l c u l a t i o n s .  Thus, i n  Example 2 o f h i s most recent paper (14), Kern considered a s h e l l and tube heat exchanger w i t h two tube passes t h a t reached a  11  f o u l i n g r e s i s t a n c e o f 0.006(°F)(hr)(ft )/BTU i n e i g h t months 2  (Figure 0) .  By m o d i f y i n g the exchanger t o f o u r tube passes  f o r the same heat t r a n s f e r area and t o t a l mass flow r a t e , and a l l o w i n g f o u l i n g t o 90% o f the new asymptotic r e s i s t a n c e , he claimed t h a t the o p e r a t i n g time could be i n c r e a s e d t o twentytwo months.  T h i s o p e r a t i n g time was c a l c u l a t e d on the b a s i s  t h a t w i t h the change t o four tube passes the o p e r a t i n g v e l o c i t y would be doubled, w h i l e the t o t a l mass flow r a t e and hence the parameter b would  remain constant.  I t i s important t o note,  however, t h a t the W i n Kern'-'-'s d e r i v a t i o n i s the mass flow r a t e per tube r a t h e r than the mass flow r a t e per tube bundle. interpretation i s explicit  which u n d e r l i e s subsequent  i n the e x p r e s s i o n  =  r e l a t i o n s h i p s o f Kern.  the d i r e c t p r o p o r t i o n a l i t y between W and  This  W 7T (D-2x) ^ 4 In p a r t i c u l a r  is built  into  subsequent d e r i v a t i o n s i n such a way t h a t W must change when changes, whether or not the number o f f i x e d diameter tubes in p a r a l l e l , changes.  and hence the t o t a l mass flow r a t e per tube bundle,  Thus,  f o r example, the w a l l shear s t r e s s  T  i s taken  throughout as v a r y i n g w i t h W t o the same power as i t v a r i e s w i t h U-^, an assumption which does not allow W t o be i n t e r p r e t e d as the mass flow rate per exchanger when the number o f tubes i n p a r a l l e l changes.  F o r the new c o n d i t i o n o f four tube passes,  then, the parameter b w i l l quadruple when U, o r W doubles  2  12  0-OIOr  1  1—  TIME Figure  0.  Computed  Fouling  Curves  1—  r  months f o r Kern's  Example  2  13  (equation 13).  As a r e s u l t , the new  operating  decreases from e i g h t months t o f i v e months  time a c t u a l l y  (Figure 0), r a t h e r  than i n c r e a s i n g t o twenty-two months as c a l c u l a t e d by Kern. In many i n d u s t r i a l heat exchangers the f o u l i n g r e s i s tance grows almost l i n e a r l y w i t h time u n t i l c l e a n i n g out becomes necessary (15,23).  For such cases the i n i t i a l  fouling  r a t e i s o f primary importance as the asymptotic c o n d i t i o n i s never reached.  The i n i t i a l  r a t e p r e d i c t i o n of the Kern-Seaton  model i s that h i g h e r v e l o c i t i e s would increase The data o f Smith  i n i t i a l fouling.  (12) do not support t h i s p r e d i c t i o n .  Gardner  (15) s t a t e d t h a t i n c o n f i d e n t i a l data a v a i l a b l e t o him there i s evidence t h a t the " d e p o s i t i o n and removal" r a t e s do not always take the mathematical form suggested by the d i f f e r e n c e model of Kern and Seaton, and f u r t h e r that the asymptotic r e s i s t a n c e i s o f t e n not reached u n t i l the tube becomes b l o c k e d . In 1961  Parkins (16) proposed t h a t the r a t e of f i l m  formation due t o suspended  p a r t i c l e s was  product of the p a r t i c l e c o n c e n t r a t i o n ,  p r o p o r t i o n a l to the  the average v e l o c i t y of  p a r t i c l e s towards the surface Uj, and the p r o b a b i l i t y S j , that a p a r t i c l e c o n t a c t i n g the surface would become permanently attached: dx dT  =  7a.  C, U. S.  (17)  3  Parkins then c a l c u l a t e d the mass f l u x f o r the case of submi-  14  cron s i z e d p a r t i c l e s d i f f u s i n g by Brownian motion through laminar s u b l a y e r . was  of the  He  U  Q  assumed t h a t the s t i c k i n g p r o b a b i l i t y  form  exp(-EA T)  S = fo  where S  the v e l o c i t y was  (18)  B  b  i s a constant, not  s i n c e a p a r t i c l e would s t i c k only i f  l a r g e enough to produce mechanical  on the p a r t i c l e which would counteract h o l d i n g the p a r t i c l e to the w a l l . i n t e g r a t e equation  17,  In 1963,  Charlesworth  coolants  on the (17)  for nuclear  f o u l i n g f i l m s can be d e p o s i t e d occur simultaneously. i n the  coolant,  Further,  and  these two  by  One  attempt was  linkages  made to the  process.  i n a study of the f o u l i n g r e a c t o r s , pointed  out  that  by two mechanisms, which  may soluble  i n v o l v e s p a r t i c u l a t e matter.  types of f o u l i n g showed markedly d i f f e r e n t He  found t h a t i n o r g a n i c m a t e r i a l  a mass t r a n s f e r mechanism t h a t i n v o l v e d  of s o l u b l e matter to the hot formed, presumably due relation.  chemical  mechanism i n v o l v e s m a t e r i a l  the other  v e l o c i t y dependence. deposited  No  the  forces  or to develop equations d e s c r i b i n g  net e f f e c t of v e l o c i t y , say,  of o r g a n i c  the  Deposition  t o a power between 0.5  transport  surface where c r y s t a l l i n e  to an i n v e r s e  was  deposits  temperature-solubility  rates increased with increasing v e l o c i t y and  1.0.  Deposition  r a t e s depended  approximately e x p o n e n t i a l l y on the s u r f a c e temperature.  The  15  d e p o s i t i o n of predominantly i n o r g a n i c m a t e r i a l by mechanism was particulate fouling", an  termed "mass t r a n s f e r "  matter suspended i n the  i n l e t e f f e c t , and  decreased by  a f a c t o r of 1.9  Energy Commission  of the  promoted by  (18) on  of the  two  a certain  v e l o c i t y raised the  amount of d e p o s i t i o n  f o r three v e l o c i t i e s ,  i n 1964  to the  is diffusion controlled,  e x p l a i n e d the  For  and  follows.  an  thereby r e d u c i n g the  and  an  the  Fouling the  v e l o c i t y dependence For  p a r t i c l e s below  d e p o s i t i o n process will  by  adhesion of  the the  i n c r e a s e i n v e l o c i t y decreases  to i n c r e a s e d drag on the fouling rate.  particle,  N i j s i n g presented equations  f o r m a t e r i a l f l u x to the w a l l f o r s o l u t e the  to  p a r t i c l e s above a c e r t a i n s i z e ,  p a r t i c l e s to the w a l l , adhesion rate due  power 0.9.  increase i n v e l o c i t y  d e p o s i t i o n process i s p a r t l y c o n t r o l l e d  the  proportional  the  matter.  ( i n c l u d i n g molecules) the  enhance f o u l i n g .  increased  s u r f a c e temperature and  types of f o u l i n g as size  the  a f l a t p l a t e was  increasing  (19)  velocity,  when the v e l o c i t y was  showed that  c o n c e n t r a t i o n of p a r t i c u l a t e Nijsing  "particulate  Data from the United S t a t e s Atomic  f i l m formation rate  was  stream, termed  to  e x p o n e n t i a l s u r f a c e temperature dependence.  a f a c t o r of 2.3.  reciprocal  F o u l i n g due  showed d e c r e a s i n g r a t e s w i t h i n c r e a s i n g  Charlesworth's r e s u l t s showed that  by  fouling.  such a  molecules and  l i m i t i n g case of p a r t i c l e s of zero s i z e , based on  for a model  16  of an a l t e r n a t e l y growing and c o l l a p s i n g laminar  sublayer.  He a l s o considered some f a c t o r s that a f f e c t adhesion o f part i c l e s , but presented no equations d e s c r i b i n g the net b u i l d u p of a f o u l i n g f i l m w i t h time. In 1962, E p s t e i n mathematical s o l u t i o n s  and Evans  (20) obtained time dependent  f o r deposition  of radioactive  c l e s from a f l u i d stream as a s e r i e s o f f u n c t i o n s . ments o f the f u n c t i o n s and  include  partiThe argu-  a mass t r a n s f e r c o e f f i c i e n t ,  i n e r t i a l t r a n s f e r c o e f f i c i e n t ( d e s c r i b i n g t r a n s f e r due t o  i n e r t i a acquired core),  from v e l o c i t y f l u c t u a t i o n s i n the t u r b u l e n t  a s t i c k i n g c o e f f i c i e n t , an a b s o r p t i o n - d e s o r p t i o n coef4*  ficient  and a removal c o e f f i c i e n t .  a good d i s c u s s i o n  While t h e i r work presents  of p o s s i b l e processes o c c u r r i n g  in fouling,  t h e i r equations are o f l i m i t e d use i n p r e d i c t i n g f o u l i n g r a t e s , s i n c e the l a t t e r three c o e f f i c i e n t s cannot be  predicted.  Recently, Hasson, A v r i e l , Resnick, Rozenmann and Windreich  (21) have shown t h a t s c a l i n g o f s o l u t i o n s o f CaC03  i n water can be d e s c r i b e d and  r e a c t i o n a t , the w a l l .  by a model i n v o l v i n g d i f f u s i o n t o , In the Reynolds number range  13,000 t o 42,000 the i n i t i a l r a t e o f s c a l e growth i s d i f f u s i o n controlled.  T h e i r data were c o r r e l a t e d by the equation  dm dt  =  0.054  Refif®  (19)  17  These r e s u l t s s u b s t a n t i a t e the "mass t r a n s f e r "  fouling  results  of Charlesworth e£ a l (17), d e f i n i t e l y i n d i c a t i n g the i n c r e a s e in i n i t i a l  s c a l i n g rate w i t h i n c r e a s i n g  Matsuda, Akimoto and T a n i g u c h i r a t e o f Mg(0H)2 s c a l e  velocity.  (22) found that the  formation from a 8° Be'brine v a r i e d as  -2.2 Ub " second.  f o r three t e s t s at v e l o c i t i e s below two meters per  18  3.  SCOPE AND  While  METHOD OF  was  time  curves  t o suspended p a r t i c l e s ,  nent  PRESENT WORK  t h e r e are s c a t t e r e d d a t a a v a i l a b l e  resistance versus due  THE  process variables  i n which the  no  of v e l o c i t y  some l i q u i d s To  f o u l i n g was  found  fouling probably  s y s t e m a t i c study of the  c o u l d be  and  typical  study the  measure t h e  temperature  perti-  i n the l i t e r a t u r e .  f o u l i n g process  fouling  resistance,  to observe  as t o i t s d e g r e e  o f compactness,  evenness e t c .  I n most  f o u l i n g streams facilitate  f o u l i n g on  this  diameter  o f the tube  It  o f the  film  observed  of f o u l i n g fouling  in detail t o be  r e c o v e r y o f t h e d e p o s i t was  the nature  shell  and the  porosity,  tube h e a t tubes  exchangers  i f possible,  therefore decided to  flow r a t e s , in situ,  and  abandoned.  measured by  the  a l l but  the  of  o f the d e p o s i t  s u r f a c e roughness,  rendered  to  t h i c k n e s s and w e i g h t  several disadvantages.  reasonable  of  streams.  desirable  study tube  Because  i s of n e c e s s i t y small i n order to  t h i c k n e s s had  amount o f f o u l i n g was  the  r a t h e r t h a n on t h e o u t s i d e o f t h e  c h o i c e has  high v e l o c i t i e s with c o u l d n o t be  the  a r e pumped t h r o u g h  inside  although  important  directly  I t was  rate  i t w o u l d be  and  industrial  cleaning.  the  on t h e  of i n d u s t r i a l l y  t h e d e p o s i t , and  to  of  t h e o b j e c t o f t h e p r e s e n t work, t h e r e f o r e , t o s t u d y  effects  the  (23)  the  achieve  fouling deposit  direct  measurement  Quantitative impossible.  change o f t h e  heat  The  transfer resistance, pressure drop.  and a l s o i n d i r e c t l y by the change i n  A heat t r a n s f e r loop was designed and c o n s t r u c t e d  i n which f o u l i n g o f a s i n g l e heated tube could be and  f o r which p e r t i n e n t  variables  studied,  could be c o n t r o l l e d or mea-  sured . The fouling  s m a l l amount of a v a i l a b l e data on p a r t i c u l a t e (12,16,17) appeared t o c o n t r a d i c t Kern's model as t o  the e f f e c t o f v e l o c i t y on i n i t i a l  fouling rate.  There was a  need f o r more work on a theory t o p r e d i c t or e x p l a i n of the important v a r i a b l e s was  made t h e r e f o r e  i n particulate fouling.  the e f f e c t s An attempt  t o extend the models o f Parkins and Kern.  20  4.  SELECTION OF WORKING FLUIDS The problems  w e l l documented.  of f o u l i n g i n o i l r e f i n e r y equipment i s The American  on C o r r o s i o n r e p o r t e d i n 1963  Petroleum I n s t i t u t e  Subcommittee  (24) that, based on a survey  covering t h i r t y - s i x o i l r e f i n e r i e s ,  there was  g e n e r a l agree-  ment on the s e r i o u s n e s s of f o u l i n g from o p e r a t i o n a l and stand-points.  Feed preheat exchangers h a n d l i n g crude o i l , and  h y d r o d e s u l p h u r i z e r feed preheat exchangers other p i e c e s of equipment. temperatures  cost  above 300°F.  F o u l i n g was Nelson  heat t r a n s f e r c o e f f i c i e n t s  f o u l e d more than  most s e r i o u s at  (25) says that i n d e t e r m i n i n g  "the d i r t y i n g or f o u l i n g that  always  occurs i n petroleum equipment i s such an unknown f a c t o r t h a t . . . the  t r a n s f e r - r a t e f o r m u l a s . . . l o s e much of t h e i r  Crawford and M i l l e r  (26) s t a t e that  importance".  " i n c a t a l y t i c desulphurizer  u n i t s p a r t i c u l a r l y the problem of process s i d e f o u l i n g has become acute".  I t thus appeared that some study of a petroleum  o i l might be u s e f u l . of was  A sour heavy gas o i l was  i t s convenient range of p r o p e r t i e s . s e l e c t e d because  chosen  because  A s t r a i g h t run o i l  the severe o x i d a t i o n s u s c e p t i b i l i t y of  cracked products might  result  c h a r a c t e r i s t i c s as i t was s t r a i g h t run product was  i n r a p i d changes o f the o i l  recirculated„  The s t a b i l i t y o f the  chosen i n p r e f e r e n c e to the more r a p i d  f o u l i n g c h a r a c t e r i s t i c s of cracked stock (26) .  Properties  t y p i c a l o f the o i l s used i n t h i s s^udy are l i s t e d  i n Table I.  21  The major p a r t of t h i s study i s concerned w i t h gas o i l fouling.  Experiments were a l s o  pension o f f i n e sand p a r t i c l e s  conducted w i t h a d i l u t e susi n water.  Particles  of s i z e  12.8-17.3 microns were used i n c o n c e n t r a t i o n s of 2 t o 5 p a r t s per m i l l i o n .  I t was hoped that the r e s u l t s  of t h i s p o r t i o n of  the work might be a p p l i c a b l e t o some c o o l i n g water problems  fouling  caused by d i r t y water.  A single  experiment was done on K r a f t  liquor  fouling.  TABLE I .  PROPERTIES OF A TYPICAL GAS OIL BLEND  Kinematic v i s c o s i t y at  S p e c i f i c g r a v i t y at  •  210°F.  1.61 c e n t i s t o k e s  2 50°F.  1.24 c e n t i s t o k e s  300°F.  0.95 c e n t i s t o k e s  210°F.  0.797  2 50°F.  0.783  300°F.  0.765  Sulphur i n o i l  0.7%  Ash  0.006%  P r a n d t l Number at  220°F.  tt 20  I n i t i a l B o i l i n g Point  475°F.  10% d i s t i l l e d  537°F.  50% d i s t i l l e d  586°F.  80% d i s t i l l e d  610°F.  Sulphur i n p a r t i c u l a t e s  5.4%  Ash i n p a r t i c u l a t e s  4.6%  P a r t i c u l a t e s r e t a i n e d on 0.8 micron f i l t e r  K 15 p.p.m.  5.  APPARATUS  The  change i n heat t r a n s f e r c o e f f i c i e n t f o r a s i n g l e  heated tube was was  followed w i t h time.  The  l i q u i d to be  studied  c i r c u l a t e d around a c l o s e d heat t r a n s f e r loop at a measured  flow r a t e .  The  t e s t s e c t i o n was  r e s i s t a n c e heated by  passing  an a l t e r n a t i n g c u r r e n t d i r e c t l y through the tube w a l l . peratures  were measured on the outside  of the tube w a l l  around the loop w i t h thermocouples.  A f t e r passing  the tube o f a double pipe  f l u i d was  storage The  tank.  c o o l e r the  Temand  through  returned  A d e t a i l e d d e s c r i p t i o n of the equipment  to  the  follows.  apparatus f o r the study of f o u l i n g r a t e s i s shown  schematically  i n Figure  1.  Fluid  i s s t o r e d i n a 45  gallon  s t a i n l e s s s t e e l drum which i s equipped w i t h an e x t e r n a l steam c o i l and loop by  insulated.  The  liquid  i s pumped around the  a Siemen and Hinsch Type CAD  Model 3102  closed  stainless  s t e e l two-stage s e l f - p r i m i n g c e n t r i f u g a l pump d r i v e n by  a  3 HP motor.  one-  The  flow r a t e i s c o n t r o l l e d manually by a  h a l f inch Powell s t a i n l e s s s t e e l globe v a l v e w i t h T e f l o n packing, the excess f l u i d b e i n g spring-loaded  through a F a r r i s No.  bypass v a l v e to the storage  metered u s i n g two o r i f i c e plates  returned  tank.  1870  The  fluid is  c a l i b r a t e d s t a i n l e s s s t e e l sharp-edged  (fB~  flanges w i t h corner  0.301, fo = 0.602) supported by taps  (Figure 2).  The  orifice  metering equipment  Mixing  Chamber  Sewer  Cooler  ® ®  :r-<D  Pressure Gouge Thermocouple AC- Ammeter AC- Voltmeter  Flow Control Valve  0>= Orifice Plate  Differential Pressure Cell 220/IIOv IOKVA Transformer T-2 IIO/20v I7KVA Variable Transformer T-3 500/5a Current Transformer Figure  1.  Diagram  o f Heat  Transfer  Loop  |4- 0-8750754  ORIFICE  \  PLATE  H-0-75*1  FLANGE  Figure  2.  Orifice  Plates  and  Flanges  was  designed  and  installed  f o l l o w i n g recommended procedures  (27).  The  pressure  d i f f e r e n t i a l across the o r i f i c e p l a t e i s i n d i c a t e d  on a Honeywell d i f f e r e n t i a l pressure meter Model Y227X2-L2 which was pressure  p r e v i o u s l y c a l i b r a t e d (Appendix 1 ) .  The  pump d e l i v e r y  i s measured at the o r i f i c e with a 0-200 p s i Marsh  bourdon gauge. The 0.016  t e s t s e c t i o n was  c o n s t r u c t e d of 3/8  i n c h w a l l t h i c k n e s s Type 304  tubing  (Figure 3).  dynamic entrance  A 19-%  inch  l e n g t h was  inch O.D.  x  seamless s t a i n l e s s  steel  (51 i n s i d e diameters) hydro-  provided upstream of the heated  s e c t i o n t o s t a b i l i z e the incoming flow.  The heated p o r t i o n of  the tube was  provided wi'the  23 9/32  inches long and was  heavy brass e l e c t r i c a l t e r m i n a l bars wall  (Figure 4 ) .  two h a l v e s  s o l d e r e d t o the tube  (A t h r e e - t e r m i n a l t e s t s e c t i o n i n which the  of the a c t i v e length form p a r a l l e l  r e s i s t a n c e s was and Huber (28).  two  first built,  electrical  a f t e r the design of S i l b e r b u r g  T h i s model was  abandoned because the drop i n  w a l l temperature at the center t e r m i n a l a f f e c t e d the temperature  p r o f i l e on a s i z e a b l e p o r t i o n of the tube).  copper-constantan thermocouples the o u t s i d e of the tube with 3/8  (24 gauge) were s o l d e r e d to 1/2  inch of the  c o n t a c t i n g the tube w a l l to minimize conduction the thermocouple w i r e s .  Sixteen  thermocouple  losses  Thermocouple l o c a t i o n s are  along  along  specified  27  To 1 i FPT 8 2 Tube fitting x  Pressure taps  Electrical Cabl Size 000  Detail at Tube Wall  Tube type 304 stainless  I  Thermocouple  0-D  Split Teflon ring  Current Transformer  To$x£  MPT  Tube fitting  Figure  3.  Diagram  o f Test  Section  I  Solder  28  PRESSURE  TAPS  Stainless steel Dimensions - inches Two required  Drill a tap for 6-32 screwII II  i1: 1 1  II  1  41 J  Figure  4.  Pressure  8 16  Taps  and E l e c t r i c a l  TERMINAL BARS Brass Dimensions - inches Terminals Two required  2'9  in Table I I . resistance  The t h e r m o c o u p l e s were c a l i b r a t e d w i t h a p l a t i n u m  thermometer  p r i o r t o mounting  c a l i b r a t i o n data are given  i n Appendix  were s u p p o r t e d i n p o s i t i o n w i t h s p l i t  on t h e t u b e .  1.  The  Teflon  on t h e t e s t s e c t i o n was done w i t h a e u t e c t i c 600°F. m e l t i n g  temperature  is  a photograph  of  the water  failed. wise the  The with  are s i I y e r s o l d e r e d  section  are given active  i n Appendix  Te.fl.oiai r i n g s ,  portion  o f the t e s t  volt  to eliminate  electrical  AC 40 amp  test  t h e end section Other-  i n most o f  I I and a t h i r d  insulated  t o the diameter o f the  The t e s t s e c t i o n was  thick  mounted  s e d i m e n t a t i o n as a c a u s e o f f o u l i n g ,  power was  l i n e s which  Superior E l e c t r i c ,  test  e.  s e c t i o n was  t h e r e b y p r o m o t i n g e q u a l f o u l i n g around The  towards  5  and t h e n c o m p l e t e l y s u r r o u n d e d b y one i n c h  pipe i n s u l a t i o n .  vertically  Figure  oh t h i s t u b e .  section  2, p a r t  a s b e s t o s cement powder p a c k e d  Caposite  remelt.  i s s i m i l a r t o t h e one u s e d  The d i m e n s i o n s o f t e s t  A l l soldering  solder with a  f o u l i n g e x p e r i m e n t s , when t h e f i r s t  this test  section  thermocouples  rings.  o f a second t e s t s e c t i o n b u i l t  A l lparts  work.  and a 750°F.  The  supplied  radius.  from s i n g l e  phase  220  p a s s e d t h r o u g h a bank o f two  t y p e 1156D v a r i a c s ,  mounted on a common s h a f t .  the tube  wired i n p a r a l l e l  The o u t p u t from t h e v a r i a c s  and was  30 TABLE I I :  Thermocouple Number  THERMOCOUPLE LOCATIONSi ON TEST SECTIONS*  D i s t a n c e from Bottom Edge o f Lower E l e c t r i c a l Terminal (cm.) Test  Section I  Test S e c t i o n II  Test  Section III  1  0.0  0.0  59.4  2  0.95  0.9  1.1  3  4.85  5.0  4.55  4  8.55  8.2  8.25  5  12.75  12.3  12.5  6  17.35  16.7  16.4  7  22.05  21.4  20.8  8  26.45  25.4  2 5.5  9  31.05  29.8  29.6  10  35.65  34.3  34.7  11  40.05  38.7  39.7  12  •44.75  43.4  44.0  13  49.25  48.0  49.1  14  53.95  52.5  54.3  15  58.25  58.1  58.3  16  59.3  59.1  0.0  *  1  Test S e c t i o n I used f o r runs 7 t o 43 Test S e c t i o n I I used f o r fun 44 Test s e c t i o n I I I used f o r run 46  31  Figure  5.  Photograph of Test  Section  II  32  fed t o a 10 KVA former  s i n g l e phase 220/110 v o l t step down t r a n s -  (General E l e c t r i c Cat. 10M36) which fed a 17KVA Bartho-  lemew and Montgomery v a r i a b l e transformer 110/20 v o l t s . output  from t h i s transformer was  c a r r i e d i n heavy cables to  the t e r m i n a l bars of the t e s t s e c t i o n . to the t e s t s e c t i o n was 0-5  Amp  d u c t i o n w i t h a 500/5 Amp transformer, Model 4CT15. 1967  by Instrument  The  (1/2 t o 3/4  Instrument The  % accuracy)  ammeter was  0.5%  of f u l l  after re-  c a l i b r a t e d i n June  S e r v i c e L a b o r a t o r i e s , Vancouver.  (Range 0-15,  scale).  The  0-30  0-2%,  S e r v i c e Laboratory c u r r e n t  v o l t a g e drop across the t e s t s e c t i o n was portable voltmeter  current flowing  measured on a Weston Model 155  d u a l range ammeter  The  The  r e g i s t e r e d on a F u j i  v o l t s AC,  t e s t s e c t i o n was  Accuracy  insulated  -  electri-  c a l l y from the r e s t of the heat t r a n s f e r loop by a T e f l o n insert  (Figure 6).  Pressure drop measurements were made  across the t e s t s e c t i o n w i t h a c a l i b r a t e d  Minneapolis-Honeywell  d i f f e r e n t i a l pressure c e l l Model 227X2-C2.  Pressure  taps  (Figure 4) were provided a d i s t a n c e of 26-3/16 inches apart. The downstream pressure tap was of 6-1/2 stream  inches.  The  followed by an o u t l e t l e n g t h  t o t a l pressure was  measured at the down-  tap w i t h a Marsh 0-200 p s i "Bo,urdon gauge.  The  i n l e t and o u t l e t b u l k l i q u i d temperatures  measured by thermocouples i n mixing chambers. chamber was  a Jg" pipe "tee".  The  The  were inlet  o u t l e t chamber i s shown i n  33  DRILL  a  T W O  T A P  N P T  H O L E S  2  INCH  S C H E D U L E  S T A I N L E S S  4 0  S T E E L  PIPE  D R I L L S TA V  T A P  I T W O  H O L E S  WA  A R 6 0 N  E N D S  O F  S T E E L TO  I  P L A T E  W E  1  S T A I N L E S S T O  B E  W E L D E D  PIPE  O U T L E T  T E F L O N  Figure  6.  Outlet  Mixing  Chamber  M I X I N G  S H O R T  C H A M B E R  NIPPLE  F i g u r e 6.  A f t e r p a s s i n g through the o u t l e t mixing chamber,  the f l u i d was  cooled i n a double pipe c o o l e r .  flowed w i t h i n the c o o l e r tube, which was 3/8  inch O.D.  tubing.  The t e s t  a s i x foot s e c t i o n of  x 0.035 inch w a l l t h i c k n e s s s t a i n l e s s  The s h e l l was  fluid  steel  made o f one-half inch g a l v a n i z e d p i p e .  The c o o l i n g water was metered w i t h a Brooks rotameter - Type 12-1110.  The cooled f l u i d then returned t o the storage tank.  The loop was  c o n s t r u c t e d mainly of 1/2  inch Schedule  s t a i n l e s s s t e e l pipe, except f o r the h e a t i n g and sections  40  cooling  (described above) and the pump i n l e t p i p i n g which  was  of one-inch Schedule 40 s t a i n l e s s s t e e l p i p e . A l l temperatures were measured by means o f c a l i b r a t e d thermocouples  (Appendix 1) and a Leeds and Northrup P o r t a b l e  p r e c i s i o n Potentiometer (Model 8622, No. The r e f e r e n c e j u n c t i o n was  634358, Ch 1648B).  an ice-water s l u r r y .  A l l thermo-  couples i n c o n t a c t w i t h the t e s t f l u i d were Pyrptenax  iron-  constantan thermocouples w i t h i n s u l a t e d j u n c t i o n s and comp l e t e l y s t a i n l e s s s t e e l sheathed As i t was  (Model 122HT7/I-C).  necessary f o r the apparatus t o run unattended,  a h i g h temperature  alarm and power s h u t o f f system was provided  i n the event that the pump f a i l e d or the tube w a l l overheated. A Johnson E l e c t r i c Hot Water C o n t r o l remote mounting u n i t (Model 7T674) was  used w i t h the b u l b mounted i n the  insulation  of the t e s t s e c t i o n .  When the temperature exceeded the s  p o i n t the power t o the complete apparatus was buzzer alarm was  sounded.  cut o f f and  36  6.  EXPERIMENTAL  PROCEDURES  a)  Gas O i l F o u l i n g  The procedure follows.  f o r c a r r y i n g out a f o u l i n g run was as  (Refer t o F i g u r e 1 ) .  A f t e r the l i q u i d was  charged  to 'the storage tank the steam t o the tank c o i l was turned on, b r i n g i n g the o i l t o about 200°F. i n 6 t o 8 hours.  The pump  was s t a r t e d and the pressure drop across the o r i f i c e adjusted to and maintained at the d e s i r e d value by t u r n i n g the c o n t r o l valve.  The power t o the t e s t s e c t i o n was turned on tfcc? give  the d e s i r e d heat g e n e r a t i o n . the d e s i r e d temperature  Once the o i l i n the tank reached  ( t y p i c a l l y 1/2 t o 3/4 hour) the steam  was turned o f f and the c o o l i n g water turned on t o maintain the i n l e t o i l temperature  at the d e s i r e d v a l u e .  One-half t o 3/4  of an hour l a t e r the t e s t s e c t i o n would reach steady s t a t e and the run would commence.  Minor adjustments  o f o i l and water  flow r a t e s and of the power input were made t o m a i n t a i n constant flow and constant power d i s s i p a t i o n . Millivolt taken  readings on the twenty-four thermocouples  ( a f t e r b a l a n c i n g the potentiometer on an e x t e r n a l  standard c e l l ) as o f t e n as was necessary, depending fouling rate. hours.  were  on the  Readings were commonly taken every s i x t o e i g h t  Pressure drop, v o l t a g e drop, and c u r r e n t measurements  37  w e r e made  at  until  r u n was  to  the  sixteen Oil  ginning sured 53T  was that  using  been  operated  from  about  tank  near  continuously eight  The  The  hours  two  made  Two  on  calibrated the  measurements were  selected  D287-55  of  i n which  done  on  the  viscosity  Verteuil  using 1%  selected  and  ash  analyses  over  a  chemical laboratory. 300-400 h o u r s increased  of  usually  the by  (see  Appendix  o i l samples  to the  about  (29).  The  A.S.T.M.  Engler  distilla-  A.S.T.M.  I ) , were  longer  deter-  through  after  The  was  filtered  filters.  (Table  of  were measured  are  o i l samples  dis-  on  t h e A.S.T.M.  samples  diameter M i l l i p o r e  commercial  de  made  estimated according  pore  Sulphur  over  (29),  D445-  usually  o i l samples  t o method  were  by  calibration  according  m a t t e r was  mea-  Cannon-Fenske v i s c o m e t e r s  Kinematic viscosities on  be-  were  A.S.T.M. method,  v i s c o m e t e r c o n s t a n t s were w i t h i n  values).  method  the  Kinematic viscosities  previously  c h e c k was  the  of the  D86-56.  matic  a run.  from  gravity  micron  stable  lasted  Specific  tentative  local  Runs  1-3).  particulate  tions  equipment  temperature.  temperatures  Figure  mined  0.8  had  water.  of  of  followed  viscometer.  range  The  were withdrawn  inlet  Verteuil*s  each  time.  complete.  end  (A r o u g h  tilled  2,  the  the  50)  (30).  de  and  (2 9 ) ,  same  days.  samples  at  (size  the  o i l was runs. one  per  method  done by  a  fairly The  kine-  cent,  and  38  there was  v i r t u a l l y no change d e t e c t e d i n the s p e c i f i c  gravity.  At the end of each run the p i p i n g l e a d i n g t o and from the t e s t s e c t i o n was  removed, and the t e s t s e c t i o n was  cleaned w h i l e remaining i n p o s i t i o n . as f o l l o w s .  The tube was  C l e a n i n g was  soaked  then drawn through the tube a number of times.  of e t h e r .  accomplished  r i n s e d w i t h petroleum e t h e r .  of heavy pipe c l e a n e r a f f i x e d t o a wire was  sooty d e p o s i t was  d r a i n e d and  r i n s e d o f f the wad  A  wad  i n e t h e r and  The b l a c k ,  i n t o an erlenmeyer  Vigorous b r u s h i n g w i t h a long-handled t e s t  flask  tube  brush and s c r a p i n g w i t h a sharpened w e l d i n g rod, combined w i t h the above procedure, was The  s u f f i c i e n t to c l e a n out the tube.  i n s i d e of the t e s t s e c t i o n was  i n s p e c t e d v i s u a l l y by  s h i n i n g a l i g h t up from the entrance s e c t i o n . d e p o s i t as p o s s i b l e was  As much of the  recovered f o r a n a l y s i s , but i t was  not p o s s i b l e t o get q u a n t i t a t i v e recovery.  b)  Water F o u l i n g The o p e r a t i n g procedure was  above.  P a r t i c u l a t e matter was  s i m i l a r to that d e s c r i b e d  estimated as f o r the o i l .  v i s c o s i t y or d e n s i t y measurements were made. perties suspended  (31) were assumed v a l i d s o l i d s was  about  No  Pure water pro-  as the c o n c e n t r a t i o n of  f i v e p a r t s per m i l l i o n .  39  7.  RESULTS  a)  Calculation  An  AND  outline  Details The  DISCUSSION  Methods  o f t h e c a l c u l a t i o n methods  and sample c a l c u l a t i o n s fouling  R  f  resistance  1  =  is  presented, 2.  i s given by  1  (20)  h' m  c  t h e i n s t a n t a n e o u s rae.an h e a t  transfer  coefficient, h  m  given by h  The  =  m  w AT  (21)  q  m  c o e f f i c i e n t i s based T,  • _• T  / This  mean  uniform tube the  i n Appendix  a t any i n s t a n t  _  h_, m where  appear  i s herein  length,  flux  (22)  2  clTb T  w  -  ^  difference  condition  where  reduces T  w  to T  temperature  The  q  flux  w  = Q/A w a s  i n t h e tube  wall.  w  - T^ f o r t h e  - T^ i s c o n s t a n t w i t h  and t o t h e log-mean temperature  heat  difference  .  b  constant wall  dissipated  temperature  b,  temperature  heat  T  o n t h e mean  difference for  condition. determined  from  T h e p o w e r was  t h e power  calculated  from  40  the c u r r e n t f l o w i n g to the t e s t s e c t i o n and the v o l t a g e drop across the t e s t s e c t i o n , The power f a c t o r was  assuming a power f a c t o r of u n i t y .  measured at three d i f f e r e n t power l e v e l s  u s i n g a wattmeter, and the v o l t m e t e r and instrument e r r o r s unity*  (0.5%) the power f a c t o r was  The heat generated  Q = 3.413  i n the tube  e l e c t r i c a l t e r m i n a l bars, and  BTU hr  (23)  the i n s u l a t i o n and  the  along the tube w a l l .  at the tube ends are d i f f i c u l t  been ignored.  found equal to  i s t r a n s f e r r e d to the l i q u i d but there are  to conduction through  c a l attempts  Within the  i s then  x Voltage Drop x Current  Most of the heat l o s s e s due  ammeter.  to estimate  The l o s s e s  (although t h e o r e t i -  have been made f o r simpler geometry (32)), and have I t was  e v i d e n t from-measured  temperature  p r o f i l e s along the tube that these l o s s e s were q u i t e s m a l l . Losses by conduction through have been ignored.  the e l e c t r i c a l t e r m i n a l s a l s o  The heat l o s s through  estimated by measuring the temperatures i n the i n s u l a t i o n ,  and,  the i n s u l a t i o n  at two  r a d i a l distances  u s i n g the form of the heat  equation f o r c y l i n d e r s , e x t r a p o l a t i n g t o get the at the o u t s i d e of the i n s u l a t i o n *  conduction temperature  The heat l o s s due  n a t u r a l c o n v e c t i o n and r a d i a t i o n was  was  then c a l c u l a t e d  to (31),  (24)  41  where T3 i s the temperature and TQQ i s the temperature were very small, the heat  at the o u t s i d e of t h e i n s u l a t i o n ;  o f the a i r i n the room.  Losses  i n a l l cases amounting t o l e s s than 3% o f  generated.  The tube w a l l temperatures were measured on the o u t s i d e of the tube, and were c o r r e c t e d t o • g i v e the i n s i d e tube w a l l temperature by a p p l y i n g the s o l u t i o n of the steady s t a t e heat conduction equation f o r a long hollow c y l i n d e r w i t h uniform i n t e r n a l heat g e n e r a t i o n and an a d i a b a t i c outer w a l l (33):  T  o-  T  i .. =  Q  il/2 - r out 2 TT L K e t a l l r .vout 2  2  m  In o u t 1 r r. j r  (25)  2  1  T h i s c o r r e c t i o n was u s u a l l y about 3 or 4 °F.  1  J  For the o i l  experiments  the c o r r e c t i o n was a s m a l l f r a c t i o n of the mean  temperature  d i f f e r e n c e of 80 - 180°F»  The temperature  driving  f o r c e was c a l c u l a t e d by assuming a l i n e a r i n c r e a s e i n b u l k temperature w i t h l e n g t h o f the heated s e c t i o n ,  an  assumption  which i s e q u i v a l e n t t o assuming a uniform heat f l u x with distance.  The denominator  of the i n t e g r a l o f equation 22 was  evaluated at eleven thermocouple  p o s i t i o n s and. then f i t t e d t o  a q u a d r a t i c ^ e q u a t i o n i n d i s t a n c e by l e a s t squares.  The i n t e -  g r a l was then s o l v e d a n a l y t i c a l l y over the c e n t r a l p o r t i o n o f the tube, e x c l u d i n g the thermal entrance and e x i t r e g i o n s .  In  42  Figure  7  length  of  oil  the  inside  the  tube  experiment  at  the  for  which  t h e mean  low  temperature  indeed  least  indicates small.  wall  Appendix  3,  Table  is  time  This  fact  increasing with is  magnitude sistance  3-1,  of  f o r type  304  rise  resistivity  increases  fouling  on  AT  gas-  solid  of the  lines  tube  is calculated. side  of  the  The  heated  conduction losses  loss,  average  and-h^  m  heated  typical  The  section  either  heat  in a  flux.  the  longitudinal  tube  are  i s clean,  with  the  near  uniformity  from  thickness  of  resistance  clean  were  inside  listed  by  conditions  the  and  the w a l l  bulk  and  in  the  tube  conditions  coefficient  only this  about  This  and power  Thus  be  a  due  the  factor  of  the  low  re-  typical  over which  However, of  with  dissipated,  latter  i s 20°F.,  may  to  of e l e c t r i c a l  1-1/2%.  effect  flux  probably  because  (34).  tube  are  tubing,  length.  clean  temperature.  flux  thus  steel  temperature  of the heat  tube  stainless  along the  liquid  uniform heat  temperature  temperature  severe  the  along the  under  the  wall  along the  f o r a l l runs.  the  in wall  one  fouled  difference  temperatures,  electrical  a minor  the  parallel  temperature  became  generated,  Deviations  variations  i s shown  f i t over  tube  that  indicates  distance. to  the  z e r o when  essentially  tube  squares  Heat  tube  the  temperature  of  outside  At  as  temperature  a moderately high heat  represent  section  wall  the  under  greater  importance,  600 e  o400| o. £ 200h Run 27 Q/A=58,250 B T U / H R F T W-0-242 L B / S E C  C  1 20 LENGTH gure  7.  Tube  Wall  I  I  40 cm  Temperature P r o f i l e s Fluid Temperatures  60  and  Terminal  2  44  and may  result  i n a non-uniform heat  flux.  The c l e a n tube heat t r a n s f e r c o e f f i c i e n t s f o r the gas o i l were compared t o the v a l u e s p r e d i c t e d by the S i e d e r - T a t e equation (35),  h  calc  D  =  " 1 4  0.023  w' (26) Viscosities  f o r the o i l were measured over a range of tempera-  t u r e s and were e x t r a p o l a t e d i f necessary t o get the w a l l cosity  (Appendix 1, F i g u r e 1-3).  The heat c a p a c i t y was  viscal-  c u l a t e d from the heat balance  Q = W C_  A T  (27)  b  The thermal c o n d u c t i v i t y was  estimated from data f o r o i l s  Agreement of measured and p r e d i c t e d heat t r a n s f e r i s shown i n F i g u r e 8. 3-III.  Data are l i s t e d  Over the range  (36).  coefficients  i n Appendix  3, Table  182 t o 1010 BTU/(hr)(ft )(°F),  agree-  2  ment was w i t h i n 6% (standard d e v i a t i o n ) . The c l e a n tube heat t r a n s f e r c o e f f i c i e n t s f o r the water f o u l i n g experiments were compared w i t h the s i m p l i f i e d dimensional equation f o r water (35): , h  = m  calc  where D  1  120(1+0.013' T .' ) film  ug' b  8  ,  O  x (28) Q  ( ,)U.2 D  i s the i n s i d e tube diameter i n inches, T f i _  = %( w T  m  +  45  roooh 800 M  600h 400h 200h 200  400 h |c C0  Figure  8  Coefficients  Comparison and  600 800 BTU/hr ft °F  o f Measured  2  Clean  Heat  P r e d i c t i o n s o f the Sieder-Tate for  Gas  Oils  1000  Transfer Equation  46  and  i s the  and  measured  listed  III.  deviation  due  to  the  with  the  flow  measurement  of  i n feet  and  The  (4.0% standard  standard  partly  velocity  coefficients  i n Table  excellent a  bulk  4.4%.  The large and  conduction  second. balance  of  deviation),  o f AT^,  and  the heat  agreement  relatively  calculation  per  the  and  heat  deviations  heat  balance  percentage  losses  calculated  coefficients  the  possibly  The  deviation  due  v i a the  is  balances  error  also  are  show is  associated to  errors  in  electrical  terminals.  b)  Initial  The tube the  Experiments  most  with  important  a given  heat "flux  given  flow  effect held  of  flow  constant  and  inlet  rate,  the  series  experiments  done  i n random  with  time.  It  was  order  found  that  at  thought the  constant  wall  clean  wall  the  were flow  In  a  to  given  rate  rate.  were  done  adhesion  separate  of  were  i n the o i l to f i x  operating  temperatures  the  was  Experiments  changes  a  study  chemical in a  and  at  temperature  studied  convenient  flow  order  wall  possible  of  temperature  in possible  experiments  select  fouling  t o be  clean  effects  to minimize  and  tube  changes  Several i n i t i a l procedures  Fouling  affecting  average  temperature at  Oil  temperature).  to minimize  Wall  operating  were  governs  effects. of  Gas  factors  liquid  (which  rate  on  conditions.  400°F. w i t h  a  TABLE RUN  W lb/sec  0.1470  40  . 0.1722  38  III. WC  P  HEAT BALANCE  AT* b  BTU/hr  AND  CLEAN HEAT  Q  BALANCE BTU/hr  DEVIATION  HEAT  TRANSFER h  C O E F F I C I E N T S FOR  HEAT  h m  m  BTU/hrft °F 2  %  WATER  TRANSFER  calc  BTU/hrft °F 2  COEFFICIENT DEVIATION  %  5503  6326  -13.1  1343  1302  +3.2  6260  6928  -  1451  1466  -1.0  9.5  34  0.1920  7200  7532  -4.2  1604  1622  -1.1  39  0.2613  9030  9785  -7.6  2072  2061  +0.5  35  0.3866  12,100  12,539  -3.1  2559  2791  -8.3  42  0.3870  12,440  12,207  +2.0  2588  2804  -7.7  36  0.5457  15,600  16,633  -6.1  3427  3667  -6.5  37  0.3105  10,600  10,818  -2.0  2225  2368  -6.1  41  0.1722  12,020  12,718  -5.5  1516  1570  -3.4  *  AT-fr-:., a v e r a g e d  over  first  three  readings o f each  run  48  sample The  of fresh  experiment  excessive the a  oil,  had t o be  wall  third  that  temperatures.  experiment some  50°F.  yielded  a s t i l l  fouling  occurred  fouling  present  lower  when  i n the  From  even  about  these  increase supply made  under  tures  changed  half  b e made. rate,  because  of  repeated with  as g r e a t .  to give  The f o u l i n g  rate  For  a clean was  wall  then  such  Repeating this run  and e v e n t u a l l y conditions  fresh.  each  experiments  experiment  no  further  that  yielded  Particulates  o i l was  i t was  were  still  temperatures  of fresh  an  identical  temperature  a larger  limited,  concluded that f o r  should have  The c l e a n w a l l  before excessive  of fresh  about  and s e v e r e .  s i xhours  t h e r u n was  operating  i n order t o allow  wall  s h o u l d be  temperature  developed.  starting  Since the  o i l batches  o i l and r e - c i r c u l a t e d  oil,  were a s men-  "Experimental Procedures".  The E f f e c t  A  fouling  initial  up o f b l e n d s  tioned  could  t h e o i l was  o i l sample.  300°F.  was  was  lower.  under  i n about  rapid  oil.  reproducibility, starting  extremely  When  rate  the flux  a r u n o f 100 h o u r s  rapid  was  stopped  same o i l t h e f o u l i n g  temperature  c)  fouling  series o f about  o f Mass  Flow  Rate  at Constant Wall  o f e x p e r i m e n t s was done w i t h 295°F.  Four  r u n s w e r e made  Temperature  clean wall at clean  tempera-  tube  49  Reynolds numbers from 9800 t o 42,000 w i t h samples ft, and then two runs with samples were two samples  These  oils  from the same l o c a t i o n i n the r e f i n e r y but  were taken some nine months a p a r t . cients  of gas o i l B.  of gas o i l  The heat t r a n s f e r  coeffi-  (equation 21) are p l o t t e d a g a i n s t time i n F i g u r e s 9  and 10.  Temperature  p r o f i l e s , heat t r a n s f e r c o e f f i c i e n t s and  thermal r e s i s t a n c e s are t a b u l a t e d i n Appendix  3, Table 3 - I I .  The shape of the heat t r a n s f e r c o e f f i c i e n t - t i m e curves are s i m i l a r t o those r e p o r t e d f o r some i n d u s t r i a l heat (23), i n that h  m  i n i t i a l l y drops f a i r l y r a p i d l y from the c l e a n  value and then s l o w l y l e v e l s out. out of h  m  To check that the l e v e l l i n g  was not due t o exhaustion of the f o u l i n g m a t e r i a l i n  the c l o s e d system,  s e v e r a l runs were repeated a f t e r  out the tube without changing the gas o i l . in h  m  exchangers  was s t i l l  cleaning  The i n i t i a l  found t o occur (Figures 9, 10), but the r a t e  was l e s s r a p i d and the l e v e l l i n g out appeared sooner. agreement of the c l e a n c o e f f i c i e n t  gas o i l A.  The  f o r the main run and the  repeat run i n d i c a t e s t h a t the c l e a n i n g procedure was reproducible.  drop  quite  Gas o i l B f o u l e d t o a much l e s s e r extent than  The reason f o r t h i s was not apparent.  O i l B has  a s l i g h t l y lower k i n e m a t i c v i s c o s i t y than o i l A - 1.55 versus 1.62 c e n t i s t o k e s , at 210°F.  Particulate levels  Table 3-V) are about the same.  (Appendix 3,  W i t h i n the accuracy of the  50  T"  x -Sx  1020  ^  x  Re = 41,870  X  c  980  940 7 9 0 K  750  I _ Q *  Rec = 2 9 , 2 0 0  710 Re,H  460 ^ 4  2  >  K  ^  16,750  ^ * W-0-312 U  0  B  9  8  240  200  Re = 9,790 c  160  x  R e p e o t e d with s o m e oil ^ 3 Q > \  w-n.i7«  120 I  I  100  200 Time  Figure  9.  Heat  Transfer  T «  hours  Coefficient  295°F-Oil  300  A  versus  Time  for  Oil B T = 295°F 400 |- x Repeated with same oil Wc  R  ^ Ub 7-62 ft/sec u  i Z 5 J 5  8  c  380  O ^ C D Q )  360 Re * 8185 U W = 0151  260  c  s 4 7 3  b c  240  c2Q$£x5>  220  OOOCOCO OOOCPCOQ)  100  0 O  200 Time  ure  10.  Heat  Transfer  Coefficient  versus  Time  300  400  hours forT  W (  _« 295°F-0il  B  5-2  measurements, the sulphur and ash l e v e l s are a l s o the same.;The  f o u l i n g data f o r each o i l were t r e a t e d s e p a r a t e l y , t h a t  is,  as i f the two samples were two completely  different  liquids. A second  s e r i e s o f experiments  w i t h v a r y i n g mass flow  r a t e was done w i t h the heat f l u x adjusted t o give an average c l e a n tube w a l l temperature  o f about 346°F.  (Figure 11).  Much more severe f o u l i n g took p l a c e at the h i g h e r A b r i e f i n d u c t i o n p e r i o d at constant h v e r y r a p i d drop o f h  m  l e s s than f i f t y hours. to  was followed by a  t o about 60% o f the i n i t i a l value i n F o r these c o n d i t i o n s i t was necessary  terminate the experiments  before h  development o f e x c e s s i v e l y h i g h w a l l The  m  temperature.  l e v e l l e d out due t o  m  temperatures.  f o u l i n g r e s i s t a n c e s (equation 20) corresponding t o  the data o f F i g u r e s 9 and 10 are p l o t t e d a g a i n s t time i n F i g u r e 12.  The asymptotic behaviour o f Rf w i t h time as sug-  gested by Kern and Seaton  (2)  i s borne out. The s o l i d  i n F i g u r e 12 are the l e a s t square  f i t s o f Rf t o equation 6.  The v a l u e s o f the parameters are l i s t e d curve f i t appears  t o underestimate  lines  i n Table IV.  the asymptotic  While the  fouling re-  s i s t a n c e i n some cases, i t i s e v i d e n t that equation 6 i s f a i r l y good f i t o f the experimental d a t a .  53  f£>o  700  W  Ibm/sec  0-477 00  7 ^ = 3 4 6 <»F  100  J  0  15  Time Figure  11.  Heat  I  L  30  45  hours  Transfer Coefficient T . 346°F-Oil B w  versus  Time f o r  54  3v~"  ^  W* 0-178  lb /sec m  Time Figure  12.  —  T « w  Fouling Resistance °  295 F  /  (Solid  Lines  1  of Oils  are Least  Oil  A  hours versus Squares  Time f o r F i tt o Equation  6)  55  TABLE IV; Oil  FIT OF GAS OIL FOULING DATA TO EQUATION 6  w  Run  Re  lb/sec A  B  #  2  -i  b hr  10 R B 6  f  - 1  (BTU/ft  0.312  15,930  0.4.037  0.01128  4.553  15  0.543  29,200  0.1424  0.01855  2.64  19  0.778  41,870  0.0738  0.0280  2.125  22  0.151  8190  0.4125  0.0279  11.52  24  0.242  13,580  0.1256  0.0408  5.13  T  w c  «  295 F U  Run  LINEAR FIT OF INITIAL FOULING RATES  W  14 27 28 29 30 31 32 33  0. 1784 0- 2421 0. 2421 0. 4770 0. 1778 0. 2419 0. 2419 0. 2419  10  Re  lb/sec A B  3  17  TABLE V:  Oil  10 Rf (BTU/hrft °F)  #  6  Slope  Op  9, 790 14,320 14,120 27,880 10,620 14,970 14,580 14,480  298. 8 371. 4 348. 8 345. 4 346. 6 402. 7 348. 6 346. 8  8. 77 124. 5 70. 4 34. 7 •115. 9 310. 4 83. 0 :8i: 1  2  °I  As expected  from the heat t r a n s f e r c o e f f i c i e n t  the f o u l i n g r e s i s t a n c e s f o r the runs at T  «  w  plots,  346°F. do not  c l e v e l out t o an asymptotic value i n d u c t i o n time, Rf r i s e s almost l i n e s are l e a s t square curves. 13.  (Figure 13).  l i n e a r l y w i t h time.  Solid  f i t s of the l i n e a r p o r t i o n of these  The pressure drop i n c r e a s e s are a l s o shown i n F i g u r e  The pressure drop appears  to i n c r e a s e b e f o r e there i s a  measurable change i n thermal r e s i s t a n c e . effect.  A f t e r the  T h i s maybe aoroughness  A l s o the pressure drop i n c r e a s e appears  to l e v e l  w h i l e the thermal r e s i s t a n c e continues t o i n c r e a s e . p o s s i b l e due  t o a packing e f f e c t , or due  out  This i s  to a l e v e l l i n g o f f  of  the d e p o s i t i o n l o c a l l y .  R^  and b of equation 6 w i t h mass flow r a t e i s shown i n F i g u r e  14.  R  The v a r i a t i o n of the parameters  decreases w i t h mass flow r a t e , as suggested  t i v e l y by the theory of Kern and Seaton.  The  qualita-  slope of the  * l o g - l o g p l o t s of Rf vs W i s -2, however, as opposed t o the -1 p r e d i c t e d from equation 11. W,  The parameter b i n c r e a s e s w i t h  but t o the power 1 as opposed t o the power 2 suggested  equation 13.  by  T h i s fundamental d i f f e r e n c e between the data  and the theory i s most s t r o n g l y emphasized i n F i g u r e 15, i n which the i n i t i a l mass flow r a t e .  f o u l i n g r a t e i s shown t o decrease w i t h the Initial  the l i n e a r l e a s t squares  f o u l i n g r a t e s were c a l c u l a t e d f i t s of R  f  from  vs t curves where the  57  0  Figure  13.  15 Time Fouling Resistance v e r s u s Time f o r T  and w  30 hours Pressure 346°F-Oil  45 Drop B  Increase  58  i  i  01 W Figure  14  Variation Mass Flow  1  1  i  i  r  I—  0-2 0-5 lb /sec  10  m  of Parameters of Equation Rate o f O i l ( l o g - l o g )  6  with  59  jL  100  S*2  O A  o  Oil A Oil B Least squares fit  10 3 o Li.  T W c  1  1  01  0-2 W  Figure  15  Initial Fouling Mass Flow Rate  1  0-5 lb m /sec  295 «F  10  Rate of O i l versus (log-log)  60  asymptotic  resistance  Values  listed  gas  are  oils  A  and  asymptotic initial data  at  The  methods  (37)  predicts  up  a  W c  «  best to  does the  not  Wall  The  effect  of  clean  ing  the  inlet  The  average  295  to  and  the  bulk  clean  403°F. clean  resistances  The tube  and  in Figure of  describe  the  inlet  and  As  was  7.6  Fouling  for  the  and  B  initial  A  of  the three  at  T  W  c  «  statistical  difference 16).  model  This  f o u l i n g of  these  Fouling  temperature  already  im  a  the  series  mass  flow  was  rate  varied  feet  per  are  evident  maintain-  the  was  in Figure  range  212°F.  second.  plotted  much m o r e  ex-  constant.  over  temperature  buildof  fluxes, while  is profoundly  becomes  on  heat  increase  fouling resistance  temperature.  -1.33  (equation  on  liquid  v e l o c i t y was drop  the  slope  Seaton  studied  different  bulk  though  covered.  temperature  pressure 16.  the  tube w a l l  temperature wall  and  Temperature  at  is  for  The  for oils  curves  f o u l i n g r e s i s t a n c e was c a r r i e d out  even  c a l c u l a t e d by  Kern  13).  fouling rates  15),  plot  -1.02  was  such  conditions  of  growth  and  The  (Figure  different.  rate  slope  for  Effect  the  flow  initial  (Figure  quite  (  estimated  The  close  -1.07. +1  be  V.  346° F.  of  not  are  common  be  slope  under  periments  wall  very  The  of  time  T  therefore  oils  d)  are  f o u l i n g rate-mass  2 9 5 ° F.  gas  i n Table  resistances  points  model  B  could  Fouling  against 15,  affected  severe  as  the by the  61  003 002  1  Oil B W=0-242 l b  T  Q/A=58 250 T T_ = 371 °F  m  Q/A =69280 BTU/HR T = 4 0 3 °F Wc  •001  S  Q. <  20  .0/  15 Time  1  30 hours  F i g u r e 16 F o u l i n g R e s i s t a n c e and P r e s s u r e Drop I n c r e a s e v e r s u s Time f o r V a r y i n g Heat F l u x e s - O i l B  45  62  wall  temperature,  experiments is  RfVs of  from t  of  velocity  the  average  of  unit For  are  value  wall  15  °F.  fouling  and  rates  the  have  This than  material  the  Kcal/g-mole. formation.  also  organic reactor  of  from  c h e m i c a l bond (16)  for  rather  deposition  after  reaction  covered.  chemical  the  reciprocal  doubles  calculated  reported  coolants  that  increased  temperature.  Combined  Effects  o f Mass  Flow  A  problem  i n heat  exchanger  common for a  such  rate range  that  of  i n °Rankine,  i s a p p r o x i m a t e l y 29  of  the  f o r chemical  i n the  Parkins  i n most  portion  against  fouling  energy  i s suggestive of (17)  17  f o r these  temperature),  linear  (37)  over  important  17  the  (which  calculated  temperature  suggests  activation  slops i n F i g u r e  particulate  wall  initial  effect  The  Charlesworth  e)  The  about  processes  high  f i t of  Arrhenius equation  temperature  the w a l l .  rates,  i n Figure  tube  constants.  physical  with  plotted  flux  with wall  fouling  squares  clean  increase  strong  This  are  the heat  linearly  initial  least  average  form  every  the  alternately  almost  The  curve,  the  the  on  varies  increased.  cases  or  a  specified case  temperature.  an  heat  load  increased  I t was  useful,  and  Rate  and  design  inlet  to  Temperature  is to design  fluid  velocity w i l l therefore,  Wall  lower  temperature. the  correlate  surface the  a  63  5001  V  O\ \  % 100  £ 50 o or  £ x _ 10  x  \  O  A \  x  \ N  v  \  \  \  x  \  \ v  \ \  A W Ibm/sec \ V A O 0-242 Oil B A 0-1 78 Oil B L V 0-362 Oil A (100 % C» recirculated) 1-34 M8 _ 1-26 °R "'x I0 1000/ T 3  Wc  Figure  17. Log I n i t i a l F o u l i n g Rate versus R e c i p r o c a l of A v e r a g e C l e a n Tube W a l l T e m p e r a t u r e - O i l s A and B  64  initial  fouling rate  indicate fits  the  combined  w e r e made  Figures  15  data  to  and  an  The  dt  single T  equation  and  w c  equation  of  W.  the  that  Least form  would  square  suggested  by  equation,  0.1347 x 1 0 wTTO-T  dRf  a  e f f e c t s of  give  17.  into  e  1 6  -26030 .. T ^ c (°R)  (29)  t=o where fits The  time the  zero  data  wall  18.  For  the  the  constant  T  than  itself,  see  films  Q  increased  to  mass  of  initial  from  o i l studied  equation  strongly  the  strong  well  at  experiment  b c  of  =  7.6  felt  the  the  an  T  the  q  w  mass  W = 0.543 l b / s e c , h o l d i n g  W C  =  of  fouling W  reduction the  of  velocity  experiment  velocities.  were:  in  effects.  i n - v e l o c i t y would lower  effects  increasing  increasing  in  rates.  indicated  initial  through  period,  fouling  combined  temperature  ft/sec),  fouling,  are  e f f e c t of  illustrated  increases  deposited  (U  the  on  induction  29  the  d i r e c t e f f e c t of  was  the  hours  range  rate  i f moderate  four  any  flow  of  of  of  and  because  W=0.242 l b / s e c After  data  end  gives  the  conditions  150-fold  i s more  previously  the  then  gas  point  at  equation  through  This to  of  This  at  w  a  temperature  rate.  taken  over  deviations  Figure  is  remove The  designed fouling initial  = 402.7° F 69170 B T U / ( h r ) ( f t 2 ) , e  flow  rate  was  the  heat  flux  suddenly constant.  65  Calculated Initial Fouling Rate (BTU/hr ft°F)"/hr x IO 2  Fiqure  18  Deviations  from  Initial  Foulinq  f  Rate  6  Correlation  66  It  i s seen  the  i n Figure  fouling  rate  rate  to W =  caused  0.778  The  lb/sec, drop  in fouling  velocities  would  thermal  sistance  again with  rate.  increase  no  change  resistance  I t appears  resistance,  l/h ,  i s t h e sum  tion  of the l i q u i d  film  w h i c h was  m  film with  m  resistance.  previously  changes  the  t o give  flow  flow flux,  higher  of the fouling r e -  calculations  i n mass  and  further  that  Using  shown  resistance,  i n heat  probable  fouling.  dropped  i n mass  and a  further  equation,  in l / h  further  i n thermal  and t h e l i q u i d  drops  A  resistance  eliminate  Tate  the  the thermal  decreased.  a further  decrease  1.9 t h a t  Sieder-  good showed  rate  could  predicthat be  i completely liquid flow  film  rate  decrease by  the  f o r by the corresponding  resistance.  from  0.242  I n o t h e r words,  t o 0.778  i n the f o u l i n g  resistance  flow  the conditions rate  by  a factor  in  fouling  rate  with  calculated  from  equation  o f 39  t h e edge  place  increasing  d i d not result  due t o p o s s i b l e  of T  W ( c  of constant  a factor  by  at  lb/sec  decreases i n t h e mass i n any scouring  fluid.  Under mass  accounted  from  the i n i t i a l  t h e two  which  rate.  The e x p e c t e d  i n mass  mass  increasing  the f o u l i n g  flow  the estimated  a f t e r each  i s equivalent  load,  decreased  changes  29 u s i n g  of the deposit ,  o f 3.2  heat  flow  rate  the  rate reductions were  temperature rate  t o the temperature  change i n at the  67  Time Figure  19.  Thermal Resistance versus Flow Rate at Constant Heat  hours Time f o r V a r y i n g Flux-Oil B  Mass  68  edge  o f the deposit  condition the  was  6%  possibly  surface  due  on  occurs  stainless ture  with  of a heat  due  at a higher  rate  under  The  edge  The  than  comparable  of the reduction  discrepancy The  t o have  films  onto  velocity  a  strong  (11).  a previously  deposition  in  de-  surface.  i s known  onto  that,  calculated  of fouling  deposition  (The  t o the f o u l i n g  of the deposit  exchanger  rate.  dictates  reduction.  of buildup  that  tube,  time  time.)  the observed  the rate  steel  with  blockage  to the nature  not unexpected  film  f)  times  flux  flow  at the liquid-bounding  constant  material  influence is  of appreciable  remains  about  f o r the o r i g i n a l  heat  the temperature  deposit  is  of constant  absence  posit,  only  a  and  It  deposited clean tempera-  conditions.  Local  It  Fouling  i s evident  the  heated  length  was  observed  downstream  Ri  that end.  —  Rates  from  Figure  7 that  o f the tube. the deposits The  local  When  fouling cleaning  were h e a v i e s t  fouling  increases  out the tube i t at the upper  resistance  i s given  T Tz)-T ( ) w  b  with  or  by  (30)  z  Q/A Values  o f R^  f o r several  number  of fouling  values  experiments.  o f z were  calculated  The  fouling  local  for a  resistance  69  versus mean the  time  fouling slopes  induction the  same  runs  o f the l i n e a r  portions  of the local  line  The l o c a l  a s t h e mean values  fouling  dependence  that  the  tube  when  g)  Nature  from  those  calculated  usually  wall  rates  fall  f o r small  20 v s ' in  along the  f o r some  runs  values of z f o r  The agreement a n d mean  an  i n Figure  temperature  Points  between t h e  fouling  fouling with heated  by the axial  follow  from  temperature  rates  length  can  variation  of  of the Deposits  found  material.  several  primarily  rates,  f o r the  clean.  deposits  soot-like  tube  of the l o c a l  the increased  to those  are plotted  rates.  temperature.  adequately explained  The  (which  fouling  of z overlap  a t h i g h e r mean  indicates  clean  similar  fouling  p e r i o d ) o f R^vs t p l o t s ,  temperature  be  t o be  Initial  Rankine.  large  found  resistance.  reciprocal  degrees  at  c u r v e s were  i n t h e tube  Chemical  experiments  were  analysis  indicated  that  a soft,  powdery,  of a blended the deposits  black,  sample were  o r g a n i c and c o n t a i n e d 9.9% a s h and 5.5% sulphur*.  It  was  found  early  of  the o i l i n the heat  fouling  on a c l e a n  present  i n the o i l .  i n t h e work transfer  surface A  that  continuous  loop  resulted  even though  statistical  test  recirculation i n no  i particulates  further were  on t h e d i f f e r e n c e  still  70  1000  1  1  o  I  1  o o *>o  M  100  • o  A  £ r  10  o o o  —  q  BTU/hr ft 402-7 69,168 o 371-4 58,162 V 3488 49,523 A Solid points are meon fouling rates l 1 114  2  w  1-20 1-26 1-32 I000/T (z) •R"'x .0* wc  Figure  20,  _  L o c a l I n i t i a l O i l F o u l i n g Rate versus Reciprocal of Local Absolute Wall Temperature  between p a r t i c u l a t e c o n c e n t r a t i o n s at the b e g i n n i n g and end of  the runs  (Appendix  s i g n i f i c a n t decrease. of  the d e p o s i t weight  were unavoidable.  3, Table V) i n d i c a t e d a s t a t i s t i c a l l y F o r a few cases a reasonable estimate could be made, although some l o s s e s  Table VI gives these values f o r s e v e r a l o f  the more s e v e r e l y f o u l i n g runs.  TABLE V I .  Run  OIL DEPOSIT WEIGHTS  Rf at end o f run ( B T U / h r - f t °F)~ 2  25 28 30 31 32 33  The  average  1  Weight o f Deposit grams  0.0017 0.0022 0.0026 0.0032 0.0021 0.0017  0.32 0.13 0.16 0.42 0.23 0.44  o f these d e p o s i t weights  decrease o f about  i s consistent with a  3^ ppm o f p a r t i c u l a t e s d u r i n g a f o u l i n g run  i f a l l the d e p o s i t came from suspended p a r t i c l e s .  The observed  average decrease f o r these runs was 5^ ppm. A composite  sample o f p a r t i c u l a t e s from s e v e r a l  analysed 4.6% ash and 5.4% sulphur.  experiments  A n a l y s i s o f two o i l  samples i n d i c a t e d that i n each case there was a s l i g h t  drop  i n sulphur content upon f i l t e r i n g the samples through a 0.8 micron pore s i z e M i l l i p o r e  filter.  Since the sulphur content  72  of the  d e p o s i t and  and  are  oil  (Table I ) , one  is rich  the  particulates  a f a c t o r of 8 to 10 can  Presence of p a r t i c u l a t e s occur, however. sulphur i n the that may  lead  Canapary  (39)  to  guarantee that  process. f o u l i n g would  d i s c u s s e d the  role  of  of 2.5  analysed f o r s i z e d i s t r i b u t i o n of  follows.  The  l i t e r s each.  sample was One  divided  a l i q u o t was  coarse f r i t t e d g l a s s  nominal pore s i z e 4-5//,, 10-15/1,  An  fouling  fouling.  through f i n e , medium, and  then the  p a r t i c u l a t e matter which  i n the  has  and  40-60/1,  f i l t r a t e s were f i l t e r e d  into  filtered  f i l t e r s of  respectively,  through 0. 8/1 f i l t e r s .  approximate s i z e d i s t r i b u t i o n i s given i n Table V I I .  results  are  of course approximate due  f i l t e r pores to p l u g up  and  to the  tendency of  r e t a i n p a r t i c l e s s m a l l e r than  nominal pore s i z e .  TABLE V I I .  the  formation of h i g h m o l e c u l a r weight m a t e r i a l  p a r t i c u l a t e matter as  and  e s s e n t i a l l y equal,  sulphur content of  the  part  d i d not  A s i n g l e o i l sample was  four aliquots  times the  i n f e r that  i n sulphur i s t a k i n g  are  APPROXIMATE SIZE DISTRIBUTION OF  Approximate P a r t i c l e Size  Weight %  0.8/1  to 4-5/1  17  4-5/1  to 10-15/1  28  10-15/1 to 40-60/1 g r e a t e r than 40-60/1  51 4  PARTICLES  Particles  The the the  73  U n f o r t u n a t e l y no data could be obtained than 0.8 microns.  for particles  I t i s b e l i e v e d by some workers  smaller  (40) t h a t  p a r t i c l e s o f about 0.5 microns and s m a l l e r are r e s p o n s i b l e for  fouling. An attempt was made t o remove p a r t i c u l a t e s from the o i l  and measure d i r e c t l y the e f f e c t of p a r t i c u l a t e c o n c e n t r a t i o n omfouling.  O i l samples were f i l t e r e d  diatomaceous  earth f i l t e r ^ a i d  through a bed o f  ( H y f l o - S u p e r c e l s u p p l i e d by  Johns-Manvilie) backed by a f i l t e r paper. c u l a t e s i n the o i l dropped  Although the p a r t i -  from 39 m g / l i t e r t o 0.1 m g / l i t e r ,  a f t e r charging the o i l t o the tank and h e a t i n g t o 210°F.  i n order  to commence the f o u l i n g run,the p a r t i c u l a t e s had i n c r e a s e d again t o 19 m g / l i t e r .  F u r t h e r t e s t s i n d i c a t e d that the pre-  sence o f a i r was a i d i n g p a r t i c u l a t e formation b e i n g heated.  Crawford and M i l l e r  as the o i l was  (26) and Canapary (39)  have s t r e s s e d the importance o f e x c l u d i n g a i r from o i l s to minimize f o u l i n g due t o polymer  formation.  An attempt to  r a i s e the p a r t i c u l a t e c o n c e n t r a t i o n by b u b b l i n g  a i r i n t o the  tank as an o i l siample was b e i n g heated f a i l e d t o i n c r e a s e particulates  significantly.  I f the e f f e c t o f d e p o s i t roughness  i s ignored,  an e q u i v a l e n t  d e p o s i t t h i c k n e s s can be c a l c u l a t e d from the pressure  drop  74  increase.  The p r e s s u r e  dP  2f  dl  g  gradient i s  U^yo  32f  W  2  (31)  Assuming that 32fW  D  c  f does  />g  n o t change  c  TT  D  2  5  significantly  during  a run,  2  then from  P  _. c "  2 =  equation  inside has  y  a i s a constant  (31) a t t i m e  diameter.  thermal  listed  x  I  =  LdP/dlJ  27 28 30 31 32 33  a deposit  tube  thickness  I  x  (32)  x  from  i n Table  (mm)  equation  32  can be e s t i m a t e d  and m e a s u r i n g  R .  Some  f  THERMAL C O N D U C T I V I T Y OF O I L D E P O S I T S READINGS T A K E N A T END OF RUN x  by  values  VIII.  (ft)  FROM  Rf (BTU/(hr)  25  determined  i s the clean  c o n d u c t i v i t y o f the d e p o s i t  .TABLE V I I I .  Run  when  can be  formed,  calculating are  z e r o when D  A t any time,  D-2x  The  which  k<3 ( f t  2  ) (°F))-  1  B T U / h r ) ( f t ) (°F)  0.193 0.140 0.107 0.152  0.00063 0.00046 0.00035  0.0017  0.37  0.0028 0.0022  0.17  0.00050  0.185 0.103 0.362  0.00060 0.00033  0.0026 0.0032 0.0021  0.00104  0.0017  0.16 0.19 0.19 0.16 •  0.61  75  The  i n c r e a s e d pressure drop w i t h f o u l i n g i s d o u b t l e s s  partly  due  to roughness e f f e c t s .  will  then be overestimated.  The thermal  Most of the values are  c l o s e to the value o f 0.11 for  (31)  which a p p l i e s to more  (20-100 mesh) of petroleum  coke (31).  R e p r o d u c i b i l i t y of Gas O i l R e s u l t s and Comparison w i t h Tabulated F o u l i n g F a c t o r s  Initial experiments  f o u l i n g r a t e s were c a l c u l a t e d f o r the  of s e c t i o n  particulate level, there was for  reasonably  BTU/(hr)(ft)(°P) reported  powdered coke but lower than 0.55,  compact l a r g e r p a r t i c l e s  h)  conductivities  and  (g) where attempts were made t o change f o r the c o n t r o l experiment.  no trend of f o u l i n g r a t e w i t h p a r t i c u l a t e  these three experiments,  cates.  The  initial  mean value of 78.1 listed  i n Table  TABLE IX.  two  Since content  they were considered t o be  f o u l i n g r a t e s have a range of + 9% of the x 10~  6  ft -°F/BTU. 2  The  f o u l i n g r a t e s are  IX.  REPRODUCIBILITY OF INITIAL FOULING RATES  Run  I n i t i a l F o u l i n g Rate (ft )(°F)/BTU x 106 2  28 32 33  repli-  70.4 83.0 81.1  76  The range i s probably over-estimated because o f minor of the pretreatment o f the  effects  oil.  The f o u l i n g f a c t o r f o r heavy gas o i l recommended by the Tubular Exchanger Manufacturers A s s o c i a t i o n i s 0.003 /BTU  (1).  In the present work t h i s v a l u e was  i n a s i n g l e run.  (°F)(hr)(ft ) 2  never exceeded  There are i n d i c a t i o n s that under severe  operating conditions  (Figures 13 and 16), the f o u l i n g  tance would have exceeded 0.003 i n time.  resis-  As the heat  fluxes  i n the present work are h i g h e r than i s normal f o r s h e l l tube heat exchangers, the T.E.M.A. value appears  and  conservatively  sound when no o t h e r i n f o r m a t i o n i s a v a i l a b l e .  i)  Sand-Water F o u l i n g  A sample o f l o c a l beach sand was  s i e v e d through a 230  mesh screen (hole s i z e 57 microns), and the f r a c t i o n p a s s i n g the screen was  further c l a s s i f i e d  i n a Warman " C y c l o s i z e r "  at the B r i t i s h Columbia I n s t i t u t e o f Technology. o p e r a t i n g curves o f the C y c l o s i z e r ,  i t was  c a l c u l a t e d t h a t the  s m a l l e s t p a r t i c l e s i z e f r a c t i o n r e t a i n e d was microns  (Stokesian d i a m e t e r s ) .  i n tap water.  From the  12.8  to  17.3  This sand f r a c t i o n was  T h i r t y g a l l o n s o f 4 ppm  the tank o f the heat t r a n s f e r loop.  s l u r r y was  slurried  charged to  Particulate concentrations  were measured by f i l t e r i n g known volumes through 0.8  micron  77  pore s i z e M i l l i p o r e The  f i r s t two experiments were done w i t h average  w a l l temperatures 140°F.  filters.  I t was  of 175°F. and an i n l e t water temperature  found  (Figure 21), t h a t as the tube fouled,  heat t r a n s f e r c o e f f i c i e n t h pressure drop.  m  The pressure drop i n c r e a s e was  sand-water experiment.  The  The  or any other  increase i n h  increase i n h  m  due  I t was  m  was  and i n c r e a s e d  to the i n c r e a s e i n v e l o -  c i t y caused by blockage has been d i s c u s s e d i n the (41).  the  much g r e a t e r  probably due to a combination of s u r f a c e roughness area e f f e c t s .  of  a c t u a l l y i n c r e a s e d , as d i d the  than had been observed i n the o i l experiments subsequent  clean  literature  shown that i f h_ • D Nu  d  _  m  c K  > 2m'  (33)  d  J  m  1  where m  1  i s d e f i n e d by the r e l a t i o n Nu = a Re  amount of heat t r a n s f e r r e d w i l l  Pr , then the 11  increase with fouling.  the present case, D = 0.0286 f t and w i t h m' = 0.8,  the  For criti-  c a l d e p o s i t thermal c o n d u c t i v i t y above which f o u l i n g w i l l i n c r e a s e the amount of heat t r a n s f e r r e d i s k  For  dcrit a  - lw m<_ Z  5 6  ( 3 4 )  n  the range of heat t r a n s f e r c o e f f i c i e n t s covered k^w30  78  2900r-  !*" 27001  W =0-387 lb/sec Re = 5 6 , 6 6 5  A  csi  A  c  I  2500 m  '  _  I  1800  1700 1600  OO  W =0192 Re = 28,570 c  o  +  +-  1 AA-  16 W = 0-387 o c  A  12  CL <  A A  8  A O  I CL <  4 O  o zP  O  O  W=0I92  1  0 10  Time  °  20 hours  30  F i g u r e 21„ Heat T r a n s f e r C o e f f i c i e n t and P r e s s u r e Drop v e r s u s Time f o r I n i t i a l Sand-Water F o u l i n g E x p e r i m e n t s  BTU/(hr)(ft)(°F), deposits  a v a l u e more t y p i c a l of metals than s c a l e  ( k » l - 5 BTU/ (hr) (f t) (°F)). A c c o r d i n g t o t h i s d  analysis,  then, blockage alone i s u n l i k e l y t o cause an i n c r e a s e i n h w i t h time.  m  The d e p o s i t s f o r these two runs were found t o be  contaminated w i t h l a r g e chunks of c o k e - l i k e m a t e r i a l from the oil  f o u l i n g work, although c o n s i d e r a b l e e f f o r t had been made  to c l e a n out the loop.  I t i s c o n c e i v a b l e that t h i s  t i o n c o n t r i b u t e d t o an unusual i n c r e a s e o f s u r f a c e and/or s u r f a c e area. pressure drop  contaminaroughness  T h i s would a l s o e x p l a i n the i n o r d i n a t e  increase.  Fresh sand-water  s l u r r y was  then added to the tank,  and  a s e r i e s of experiments done to study the e f f e c t of the v e l o c i t y on f o u l i n g at constant T ^  and T . W c  a s m a l l q u a n t i t y o f make-up sand was P a r t i c u l a t e l e v e l s are l i s t e d these experiments h studied  m  (Figure 22).  A f t e r each  experiment  added to the tank.  i n Appendix  3, Table 3-V-  In  decreased w i t h time f o r a l l v e l o c i t i e s The  f o u l i n g r e s i s t a n c e s and d e p o s i t  t h i c k n e s s were c a l c u l a t e d as b e f o r e and are p l o t t e d versus time i n F i g u r e s 23 and 24.  As expected, f o u l i n g of the sand-  water system i s much l i g h t e r than f o r the gas o i l , s c a t t e r of the data i s g r e a t e r .  The  and the  f o u l i n g f a c t o r f o r un-  t r e a t e d muddy or s i l t y water recommended by T.E.M.A. (1) i s 0.003 (°F)(hr)(ft )/BTU f o r v e l o c i t i e s l e s s than three f e e t 2  80  3500f  T  — r O  3400  o  W = 0 - 5 4 6 lb/sec Re = 78,534  o  0  c  330C 2100s 2000  o o  OQ  W = 0-261 Re = 3 8 , 3 8 8  o  c  OO o  W = 0-172 Re = 24,961  °  LL  JZ  ° O Q  1300 ^ 0 O O  °  O  1200  2600 O O 2500  " O  - Q D  c  P o  .O  40 hours  Ti me  5>  W= 0-147 Re = 21,547  OO  20  rfJQ  2400  ° c  o  -  o  oo  1900 1500^ 1400  T  60  T  T  o o ° o o oo  W=0-3I Re = 45,809 r  c  0  O  oo  Q  2600 £  O  O °  O  W = 0-387 Re = 56,218 c  °o  O "OO  2400k  W =0-172 R e = = 26,430 26,430 Re  1500 t 1400  c  c  - " A M  1300  A  A A  A  A  A  A  A  A  A  40  22.  Heat  Transfer  A  A  T^«I75°F  A  A  A  A  120  hours  Coefficient  Experiments  A  80 Ti me  Figure  O  versus #  Time  f o r Sand-Water  81  60  W« 0-261 60 TIME Figure  23.  Fouling Resistance versus  Time  hours  and D e p o s i t  f o r Sand-Water  Thickness  82 '  1  1  Time Figure  24.  Fouling Resistance versus  Time  1  hours and D e p o s i t  f o r Sand-  Water  Thickness  83  per  second,  per  second.  work  and The  i s about The  0.002  maximum  0.00007  fouling  ness-time  for velocities fouling  greater  resistance of  the  fitted  by  least  parameters  of  the  values  of  are  listed  i n Table  the  feet  present  2  were  The  three  (°F)(hr)(ft )/BTU.  r e s i s t a n c e - t i m e curves  curves  than  X„  and  the  squares  fouling  The  influence of  and  the  deposit  to  thick-  equation  resistance  mass  flow  6,  curves  rate,  W,  •k  on  the  parameters  in  Figures  fouling in  25  and  model,  rates,  however,  at W  d e p o s i t s were  initial  the  parameter b  the  end  of  two  double  original  runs  the  increase  the  increased  suggested  by  plots  based  W  b  than  The  Kern on  versus  rapid  drop  The  then  of  that  W  on  drop  consistent trend  asymptotic  of  rate.  increased back  to  removed  of  At to the by  with  mechanism  Unlike  measurements these  flow  wall.  removal  W  and  deposits  plots  with  mass  tube  case.  shown  fouling  brought  the  fouling "resistance,  No  the  the  thermal  scattered.  higher  essentially  removal  pressure  is  the  Kern  temporarily  and  suggests  the  initial to  w e l l ' apply i n this  based  rate,  At  in  attached was  rate  show v a r i a t i o n s  d e p o s i t s were  stress  may  fouling  lb/sec.  velocity  in velocity. shear  0.3  velocity  initial  fouling  p r e d i c t i o n s of  loosely  the  condition.  the  the  is a  very  initial  The  less  there  The  badly  26.  conformity with  Seaton  and  , b  r e s i s t a n c e and  close  about  R  x*  the versus  were  computed  parameters  84  Figure  25  W  lb/sec  Parameters of Equation 6 versus Flow Rate o f Water ( l o g - l o g )  Mass  Fiqure  26  Initial Fouling Flow Rate  Rate o f Water (log-log)  versus  Mass  86  w i t h W was evident,  due,  i t i s thought, t o n e g l e c t of roughness  i n e s t i m a t i n g x.  TABLE X .  Run  FIT OF WATER FOULING DATA TO EQUATION 6  *  W lb/sec  Re  1 0 Rf (BTU/(hr)(ft* )(OP))" 4  1  b hr"  1 0 I n i t i a l Rate Rf b (BTU/(ft )(°F)) 6  1  2  40  0.147  21,550  0.668  0.054  3.62  38  0.172  24,960  0. 556  0.067  3.75  39  0.261  38, 390  0.334  0.165  5. 56  44  0.310  43,960  0.375  0.188  7.06  42  0.287  56,220  0.219  0.105  2.30  36  0.546  78,530  4i*  0.172  26,430  +  0. 58 0.498  0.181  9.01  = 196°F Kern and Seaton assume that the f i l m begins t o b u i l d up,  w i t h removal becoming important only a f t e r some m a t e r i a l has been d e p o s i t e d .  I t seems reasonable t o expect that f o r d i s -  c r e t e p a r t i c l e s as used i n the present work, a c r i t i c a l  velo-  c i t y would e x i s t above which the i n d i v i d u a l p a r t i c l e s would not be able t o s t i c k . t o the w a l l t o form any d e p o s i t . such c o n d i t i o n s ,  Under  i t would be expected that i n c r e a s i n g the  v e l o c i t y f u r t h e r would r e s u l t i n a lowering  o f the i n i t i a l  _1  87  fouling  rate.  One 196°F.  compared  times  about was  (Table  suggests  rate that  It tivities  estimated  continually  o f the water.  to rule from from  increase  time,  where  o f x used  were  also  deposits  to calculate  calculated. are l i s t e d  k  d  out. was  to level  Thermal  x  remained!  an A r r h e n i u s  of  o f the this  chemical  would  F o r such  out.  energy  formation. thermal  conduc-  i n some  cases  Values  increase  cases the  a t t h e time  conductivities  i n Table XI,  that  continues to  taken  —  about  the activation  thickness  value  than  23 a n d 24 t h a t  deposit  appeared  by  dependence  o u t chemical bond  Rf apparently has l e v e l l e d  first  temperature  Kcal/g-mole  assuming  however  after  resistance  o f 15.3  rather  8.  f o rthe other  The magnitude  physical  Figures  with  wall  increased  the temperature  perhaps  i s evident  rate  energy  are o f importance,  n o t low enough  common  two r e s u l t s ,  of equation described  attractions is  these  tube  i n part  the asymptotic resistance  An a c t i v a t i o n  fouling  was  fouling  X ) , whereas  from  further  at a higher clean  t o 170°F, , which  t h e same.  initial value  i s discussed  The i n i t i a l  calculated  type  point  r u n w a s made  experiments. 2^  This  that  *  o f k, = x*  f o r the water  the fouling  88  TABLE X I .  Run  THERMAL CONDUCTIVITY ESTIMATES FOR WATER DEPOSITS  10 Rf (BTU/hr f t O F ) 3  2  10 x ftxlO 3  - 1  10  3  k BTU/hr ft°F  Time o f k*j Run BTU/hr ft°F (Hours)  d  3  36  0.012  0.0855  7.1  29.8  37  0.038  0.189  5.0  23.5  38  0.055  0.198  3.6  24.0  4.7  39  0.042  0.136  3.2  30.8  5.3  40  0.056  0.170  3.0  40.8  2.5  41  0.050  0.400  8.0  131.3  9.3  42  0.022  0.14  6.4  72.0  44  0.035  0.097  3.6  The v a l u e s o f V, k  d  d  f o r CaS0  4  131.  2.5  i n Table XI are about i n the s ame range as  those reported f o r s c a l e s . k  10.3  P a r t r i d g e and White  (42) r e p o r t  o f 0.95 t o 2,1 BEy/(hr)(ft)(°F), w h i l e Hasson  (21) r e p o r t s a thermal c o n d u c t i v i t y o f 5 BTU/(hr)-(ft)(°F) f o r CaCO^ s c a l e .  The c o n t r i b u t i o n o f roughness t o the pressure  drop has been ignored i n c a l c u l a t i n g k table.  d  values i n the above  The d e p o s i t t h i c k n e s s c a l c u l a t e d from the  of smooth s u r f a c e s are then probably lower,  assumption  and the thermal  c o n d u c t i v i t i e s t h e r e f o r e somewhat h i g h e r than the true v a l u e s . I f the sand Stokejsian diameters  are used t o c a l c u l a t e a  89  r e l a t i v e roughness f o r the d e p o s i t ,  i t can be shown that at  l e a s t a 12 t o 40% i n c r e a s e i n pressure drop would be expected. The pressure drop i n c r e a s e s f o r these experiments were i n the range 3 t o 15% (Appendix 3, Table 3-IV).  I t seems l i k e l y ,  then, that the i n d i v i d u a l sand p a r t i c l e s were not d e p o s i t e d i n a form s i m i l a r t o sand g r a i n roughness.  j)  S c a l i n g o f K r a f t L i q u o r Heaters  Rapid f o u l i n g o f l i q u o r h e a t e r s on continuous K r a f t pulp digesfee>rs; causes a s e r i o u s maintenance  problem  (43).  In a  t y p i c a l o p e r a t i o n two l i q u o r h e a t e r s are used w i t h one o p e r a t i n g w h i l e the o t h e r i s b e i n g cleaned out.  Operating periods of  120 t o 180 hours are t y p i c a l o f some i n s t a l l a t i o n s .  The  cooking l i q u o r i s pumped through the tubes o f a s h e l l and tube heat exchanger.  Superheated steam i n the s h e l l heats the  l i q u o r some 2 5°F. from the i n l e t temperature o f 290°F,  The  l i q u o r i s under about 110 pounds per square inch pressure. When the tubes b e g i n t o f o u l the steam v a l v e i s opened f u r t h e r to m a i n t a i n a constant o u t l e t l i q u i d temperature. steam v a l v e i s f u l l y  "open and the o u t l e t temperature can no  longer be maintained, the flow o f l i q u i d spare exchanger.  When the  i s d i v e r t e d t o the  The d e p o s i t that forms i s predominantly  CaC03 (44,45), which i s thought t o be e i t h e r c a r r i e d over i n  90  suspension in  i n the l i q u o r  ESCO L t d . s u p p l i e d  the following  Coast  Superheated  yards  from  Kraft  mill:  the heater,  flow  rate,  heat  transfer  inlet  coefficient  side  steam  at the given  are  time the  temperature  plotted  heater  processing  or to originate  asymptotic  occurs  significantly  not clean  absence  fits  short  noted  at time  cooking  liquor  operated T^  =  zero.  This  27.  the  of the resistances  F o r the upper linearly  with  F o r the spare  well,  that  fact  that  although  shutdown  condition.  the  no doubt  heater  For  spareeheater explains  the  period. was  supplied  pressure.  172,3 ° F . T b  fouling  almost  period.  by the operator  c a r r i e d o u t on a sample  b y ESCO heater  as t h e e x p e r i m e n t a l  under high  c  increases  the data  of the i n d u s t r i a l  laboratory  i n Figure  100  The o v e r a l l  temperature The  a  liquor  assuming  o f the asymptotic  f o u l i n g experiment  conditions  used:  the saturation  induction  o f the induction  One Kraft  hour  equation  r u n i t was  calculated by  o f time  from  temperature  i n the s h e l l ,  s h e l l - s i d e pressure.  as a f u n c t i o n  a fifty  steam  data  l i q u o r temperatures.  was  was  operating  pressure  the fouling resistance  after  this  steam  and o u t l e t  shell  the  previous  t h e wood.  West  was  from  2  =  The  Ltd.  could  The  operating  n o t be matched i n  apparatus  could  following  conditions  152.5 +  of  lOF, W =  0.36  n o t be were  lb/sec,  91  Re  = 28900, qy, = 41,262 B T U / h r - f t , Ufe_ = 8.3 2  c  section  I I was u s e d  f o r the i n t i a l  when t h e pump a p p a r e n t l y became  attempt.  test  s e c t i o n was  I t was  Test  damaged  o v e r l o a d e d and t h e h i g h  t e m p e r a t u r e power c u t - o f f d i d n o t a c t i v a t e A third  ft/sec.  r a p i d l y enough.  c o n s t r u c t e d w h i c h was  identical to  t h e s e c o n d e x c e p t t h a t new t h e r m o c o u p l e s w i t h o u t s h e a t h i n g were u s e d . Dimensions  The T e f l o n of test  s u p p o r t s were t h e r e f o r e  section  Thermocouple-;, p o s i t i o n s  I I I are given  are l i s t e d  t h e r m o c o u p l e s were c a l i b r a t e d  unnecessary.  i n Appendix  In T a b l e I I .  The  over the temperature  t o 192.1°F. i n a w a t e r b a t h e q u i p p e d w i t h a C o l o r a T h e r m o s t a t b y means o f a t h e r m o m e t e r w h i c h 0.2°F.  Details  are given  o f pump o v e r l o a d , tion  and was  several resulted  i n Appendix  t h e e x p e r i m e n t was  s h u t down e a c h n i g h t .  1.  properties  mew  range  77.5  Ultra-  read t o the nearest Because  run under  o f the danger  constant atten-  The pufop o v e r l o a d e d  times d u r i n g the course o f the experiment, i n f u r t h e r temporary,  2,  s h u t downs.  The  which  following  o f t h e l i q u o r were d e t e r m i n e d i n a c c o r d a n c e w i t h  a c c e p t e d methods (51):  % S o l i d s = 14.8 />(150°F)=  1.079  2>(150°F). = 0.763CSg/ml  N a S = 24.8  The h e a t t r a n s f e r c o e f f i c i e n t  2  g/1  NaOH =5.0  g/1  Na 0 , N a C 0  3  2  and f o u l i n g r e s i s t a n c e  2  Na 0 2  = 8.1  are p l o t t e d  g/lNa 0 2  92  •008  1 At  1  time zero T = 535°F s t  P T .  s t  h  •006  U  b c  =90psig = 293°F = 3 - 8 ft/sec  Q  •004  u. e  CM  SPARE  R  •002  3  At  m •010  time T  s t  P  8 t  T U  -  f  =00099(1  HEATER  - e - ° '  0  0  9  ,  t  )  o H  zero  = 520°F  b i n  D e  Q>  = 8 2 psig »285<>F 8  UPPER  3 - 8 ft/sec  HEATER  O  008  a5?o o •006  •004  op  o  a9  •002P-  G LQ_ Ti  27.  Fouling  me  Resistance  Kraft  150  100  50  Figure  4  Liquor  hours  versus  Heater  Time  for Mill  93  versus  time  thought  t o be  periment is  much  tions  by  are  due  of  to  further  run  deposit to  its  partial  the  cold  solubility  scale.  the  nightly  content  the  data work  liquor  i n the  are on  as  s h o u l d be  liquor  fouling as  the  might  i f the  deposit  carbonate.  monitored  is  ex-  Fouling The  condi-  It is  induction  shutdown  calcium  the  p r e s e n t work.  continually  during  a  heaters.  i n a prolonged  Kraft  of  data  shutdown.  industrial  particularly  such  these  and  apparatus  solution,  of  interruptions  i n the  liquor  scatter  the  much m i l d e r  a l l these  wide  to  course  the  of  primarily  than  doing  better  The  severe  that  In  28,  pump o v e r l o a d s  less  possible  be  in Figure  period.  i t would  exposure result i s an The  throughout  in inverse-  CaCOg a  of  run.  94  2200 o  2 IOOD:  OJ  GO  o 2000 o °  ^°ooo°°° o °o o o  1900  O  Kraft liquor W =0-36 lb/sec Re = 28,900 T = 172-3 °F 2 q^=4l,262 BTU/hr ft U]SC= 83 ft/sec  1800 h  O  °  c  w c  L  o  CM  .o »-  O  4  o  oo°ooo o o c5>  CD  ^  2  rr  ODD  o o  La  1  l  20 TIME  Figure  28.  Heat  o  O  40 hours  T r a n s f e r C o e f f i c i e n t and F o u l i n g of Kraft Liquor versus Time  o  -A  60 Resistance  95  8,  EXTENSION  It  i s obvious  dependence  exceedingly  of the  data  deposit  so that  an a p p r e c i a b l e i s great  could  but  gives  i t does  mental  enough,  the  flow  systems,  (17) , t h a t  to build  up.  apparent  o f removal  on t h e t h i c k n e s s signficant  built  up.  that  and t h a t In this  p l a u s i b l e treatment  asymptotic  of only  I fthe  deposition no  deposit  respect  Parkins'  of the deposition,  t o asymptotic  the asymptotic  model  One  the rate  expect  suppressed  from  fouling i s  term becomes  has been  fouling  and  one s i m p l e  i s that  one m i g h t  indicates that  and t h a t  based  and a s y m p t o t i c  t o depend  not predict buildup  reached,  An  i s made  thickness  a more  evidence  mass  model  the removal  start  of the v e l o c i t y  of particulate fouling.  be completely  whatsoever would approach  rates  workers  o f the Kern-Seaton  deposit,  itself  fouling  forms  I t i s u n l i k e l y that  a l l types  the fouling  velocity  the d i f f e r e n t  of other  complex.  describe  after  MODELS  f o r t h e gas o i l and t h e w a t e r  experimental  weakness  from  FOULING  of the i n i t i a l  resistances  could  OF E X I S T I N G  values.  Experi-  conditions are  resistance  correlates  with  rate.  attempt  i s made h e r e  on c o n t r o l l i n g  make p r e d i c t i o n s  steps  about  to categorize  i n the fouling  the effects  types  of  process,  o f process  fouling  and t o  v a r i a b l e s on  96  fouling  rates.  Parkins  (16), is  flow  with  where  the  treatment  Nijsing  treatment rate  The  first  (19),  s t r e s s T,  with  equations  are  derived,  effects.  The  case  mass  rate  a)  It  is  time  of  they  are  of  made  are  for  pressure  (2).  thin do  Once  generalized  ideas  mass films,  not  the  to  increase  governing  include  gradient  of  The  constant  velocity  Deposits  f o u l i n g i s due  present  in  tion,  i , e , no  consideration  material.  case  blockage.  for Thin  ready  fouling  Seaton  the  and  blockage  variable  considered.  that  the  to  p a r t l y on  and  the  the  constant  Models  assumed  to  and due  i s then  Difference  Kern  Derivations  significantly  flow  and  restricted  time.  shear  i s based  liquid,  Three  either is  possible  constant)  to  in  given  (W  some m a t e r i a l  suspension  to  the  or  genesis-  processes  a l -  in of  important  soluthe  in  fouling  are (i)  transfer of the  (ii)  wall  adhesion  (iii)  removal  of of  weakness The bined  to  thickness. lated  a  part  of  of  from  the  material of  the  the  as  and  expression  Parkins, product  to  bulk  the of  the  film  deposit  Parkins,  general  Following  i n terms  the  i n the  approaches give  material  of  the  liquid  to  region  by  wall  flaking  suggested Kern  for  and  the  number  film at  by  planes  growth  of  term  of  Kern  Seaton  deposition  the  of  are  of is  com-  the  film  formu-  particles,  n,  97 and a  their  flux  velocities  J =  £  n  3  represents the w a l l ,  U. 3  the  normal  to  and  adhere  stances  a removal  of  Kern  and  is  then  surface,  a sticking  U,  which  probability,  represents which  3  probability  will  the  to  that  the  mechanism  Seaton  a particle,  surface. may  i s used.  Under  operate,  The  net  once  certain  and  rate  i n contact  the  of  film  with  circum-  removal  term  formation  dx =  a^  J  s  a T x  -  (35)  2  dt The  flux  mass  of material  transfer  to  the w a l l  coefficient,  is written  k-,.__,  and  the  i n terms  of  concentration  the difference:  O l f f J  Since  =  the  k  d i f f  fouling  ( C  b  " °w  )  material  (  i s assumed  matter,  or polymerized molecules,  large.  The  the  mass  Metzner-Friend equation  transfer =  1.2 i n the  limit  fine  Schmidt  (46)  6  particulate  number  i s used  )  to  Sc=  b  +  f  /  ,  2  — 11.8(Sc-l)  o f Sc » 1  Sc"  becomes  1  /  3  ^ (37a)  J~0~2  approximately  u -/f72 b  »  k d  i  f  f  TTa 11.8 S c 3  -j^  is  approximate  coefficient: U  k,.  which  the  t o be  3  (37b)  98  An by  e x p r e s s i o n f o r s t i c k i n g p r o b a b i l i t y , S,  assuming  that  a particle  physico-chemical wall  or film  adhesive  exceeds  at the instant  Assuming  that  on t h e  S  =  tion  So  Fadhesion  where  E.  The  drag  reaches  .  and t h e on t h e  the w a l l . to the drag  s  =  F  =  i t might  and w o u l d  adhesive  t o t h e number  force  (38)  I f the p a r t i c l e  o  e  i s the universal  Fdrag  forces  are proportional  i n the process  T ,  The  adhesion  Rg  hydrodynamic  the p a r t i c l e  bonding,  formed  temperature  proportional  F  the p a r t i c l e  drag  or physical  energy  i f the  particle,  o f bonds  surface  to the wall  between  forces  i s a constant.  Q  chemical number  that  the l a t t e r  F  w h e r e S;  force  adhere  the opposing  particle  force  will  i s developed  ~  E  /  R  g  p  I^L  C  expected depend  a particle  that  of the  on t h e by  an  activa-  i s assumed  formed:  s  (39)  gas c o n s t a n t  on t h e p a r t i c l e  A  T  because  characterized  on  o f bonds  be  would  be  force  adheres  and F  i s given by  Q  is a  constant.  (47)  (40)  D  \ where to  A  the  ir  i s the cross  flow.  sectional  area  o f the p a r t i c l e  normal  99  I f the t r a n s f e r o f m a t e r i a l to the s u r f a c e c o n t r o l s the d e p o s i t i o n process,  i . e . i f the s t i c k i n g p r o b a b i l i t y i s very  h i g h and independent o f v e l o c i t y ,  then the c o n c e n t r a t i o n of  p a r t i c l e s at the s u r f a c e i s very low. found by combining equations  dx dt  _ "  a i S Cb Ub ^/f/2 11.8 ' . 2/3 Sc  The f o u l i n g r a t e i s  35, 36 and 37b, taking'C_- = 0: w  -a  T x  2  (41)  In the absence o f a removal mechanism f o r the p a r t i a l l y deposited film, dx dt  the f o u l i n g rate i s simply  a i S Ch Ub ^172 11.8 g-^: 2/3  =  which i s a l s o the i n t i a l removal mechanism. with v e l o c i t y ,  R  f  =  dx dt  as i s expected  _  x k  f o u l i n g r a t e i n the presence  Thus the i n i t i a l  d e p o s i t i o n process. by s e t t i n g  (42)  f o u l i n g rate increases  f o r a mass t r a n s f e r  The asymptotic  controlled  f o u l i n g r e s i s t a n c e i s found  0 i n equation 41:  ai, S Ch Ub Vf/2 d  of a  a  2  11.8 @c 2/3  Cy, k  d  k  d  U  b  Jf  (43) This r e s u l t d i f f e r s on f, b e i n g % here  from the Kern-Seaton case only i n the power as opposed t o u n i t y i n the Kern-Seaton  derivation.,  Since f i s p r a c t i c a l l y constant f o r t u r b u l e n t  flow through  a given rough pipe, the d i f f e r e n c e i s only a  100  minor  one. If  very  fast  try  of  is  very  C  and  b  the  transfer  and  the  the  the  and  fouling material  deposition  adhesion  low  of  is  rate  process,  can  y  of  be  the  surface  c o n t r o l l e d by  i . e . the  independent  fouling rate  is  to  is  the  chemis-  sticking probability  velocity,  written  the  C  w  approaches  as  dx a dt  where  a,,  is  a  mechanism. respect of  the  e  -E/RgT  _  s  to  x  (44)  2  constant  The  T  a  5  which  initial  velocity,  adhesIon.  depends  upon  fouling rate  and  depends  Cj_ a n d  i s then  only  on  the  the  reaction  constant  with  reaction  kinetics  process:  dx a  This  dt  t=0  type  of  workers  city, film  but  who  river  depended  removal  fouling the  by  (C ) b  behaviour  (48),  surfaces  5  r e c i p r o c a l of  was  found  -  on  that  the is  /  R  g  T  s  (45)  the  by  rate  initially chloride also  predicted the  E  observed  w a t e r was  mechanism  resistance  e  shear  ion  M c A l l i s t e r and of  f o u l i n g of  not  equation  stress.  condenser  function  of  concentration.  operative,  from  a  the 44  co-  veloIf  a  asymptotic would  vary  with  101  x* R- '  =  f  e  the  surface  variables be  considered.  small  compared  velocity city  is  at  used thg  wall. given  the  to  the  by  the  of  Y  The  drag  Reynolds  U  probability  spheres of  force  The  (equation  viscous  particle, the  that D^,  38)  must  the and  are  sublayer.  i s the  which  to  important  diameter  calculation  the  U? o  wall.  is just  velocity  The  approach  velo-  touching  distribution  f (48)  i s assumed  i n which  the  to  depend  velocity  _  l  ,  ,n  (Re ) between drag  Then  —  n  ~  p  regime).  of  the  sublayer,  from  D„ P  =  number,  lies  the  material  f  b  distance  D  n  important,  i s r e w r i t t e n assuming  the  c  where  fouling  2  coefficient  ~  (46)  f  b  (47)  no  C j )  of  u  d  =  i s the  U  s  0  y Where  both  are  viscous  (47).  (Y)  40  drag  Y U  transfer  thickness  mid-point  g  k  sticking  fouling  i n the  In  are  Equation  causing  -E/R T —  T  d  where  adhesion  affecting  particles  the  situation  and  e  cc k  d  the  s  a  —  k_  In  ~E/RgT  zero  force  (Newton i s given  a  D  on  i s given  by  equation (49)  n (U f) x  b  regime) by  particle  6  2n , 2 p  the  and  unity  substituting  (Stokes  equations  48:  102  48  and  F  49  into  drag  =  ? 4  =  where  to  Assuming  Dp,  D  4  39  i n the  of  the  D  ( u  g  f  )  (50a)  n  D  which  f o r the F  i n c l u d e s the adhesive  the  Q  adhesive  (  effect  force  particle,  and  liquid  0  b  )  properties  force ds^mbdified of  5  particle  p  slightly  size.  i s proportional to  therefore replacing  the F  D  sur-  by  ag  gives  F  ^ . adhesion  Substituting  S  a  net  e -  q  rate  equations  dx  =  dt  of  52,  a  D  8  1  /  D  p  R  g  p  ^  and  D  51  into  equation  film  37b  _2-2n  5 1  )  38  yields  (52)  (Ugf)^-n  n  w  2/3  and  (  s  s  T  (Gb-C )  0  50b  fouling  36  S c  E  e"-E/R T  2  equations  a.  =  =  * The  *6 2n P  2  (u2f)2-n  2 n  term  the  i ? p j % _ l 6 y ^  2  constant  that  area  P-  P  D ~  7  Equation  include  face  a  a-j i s a  V.  and  40:  formation  into  e( u  E  2  /  R  •  equation  gT f ) 3  i s found  by  inserting  35:  -a T 2  s  x  /2-n (53)  For  slow  flow,  as w o u l d  usually  be  expected  within  the  viscous  103 1 sublayer,  n =  1  i.e. C  n  CC  . R  then  decrease  with  fouling  rate  g  s  e >  -E/RgT  s  (54)  CC  CC,  u  dt  w  y f  b  will  i n t h e manner  -E/R T  e  initial  P  e  velocity  dx  The  t=o for  f constant.  describing 29).  The  fouling  the i n i t i a l  *  x  *  = —  k  i s similar  rate data  velocity  cc  d  1  1 ;  u f 3  i . e . x<<D.  the shear  stress  differential  —  =  equations  a  - b  asymptotic  i s then  1  (55)  w  3  to this  are e s s e n t i a l l y  53,  cc —  3 / 2  F o r such  equation  f o r the o i l (equation  equation  cc— —-  u TfT  t o the  dependence o f the  the models c o n s i d e r e d  deposits  basic  fouling  corresponding  All  and  expression  r e s i s t a n c e , o b t a i n e d from  R  thin  This  point  cases  are r e s t r i c t e d  the bulk  independent  are a l l o f the  x  velocity  o f time.  The  form  (56)  dt where  a' a n d b '  are constants.  The  solution  of equation  56  is i  a x  2  =  =  i  —7 b  x  * T  (1 - e "  (1 - e  b  -b  t  )  i . r  )  (57)  104  The p a r t i c u l a r equations  f o r each proposed  controlling  mechanism o f d e p o s i t i o n are summarized i n Table XII, along with  * the p r e d i c t e d e x p r e s s i o n s f o r x , b and the i n i t i a l  fouling  rate. b)  D i f f e r e n c e models w i t h blockage e f f e c t s  (W constant)  Where the d e p o s i t s become t h i c k r e l a t i v e t o the tube diameter,  the v e l o c i t y and shear s t r e s s are no longer constant  for  a constant mass flow r a t e .  for  Ub andTTwhich take i n t o account the d e c r e a s i n g e f f e c t i v e  diameter  o f the tube  d e r i v e d equations.  U  b  =  F o l l o w i n g Kern,  expressions  are s u b s t i t u t e d i n t o the p r e v i o u s l y Substitute  _W_ yr,7T(D-2x)  (58)  2  and  . ,  T = PU f 2  2g  c  _  ..... 8f <3cpTT  i n t o equations 41, 44 and 53. listed  . . .. W^ (D-2x) 2  Z  (59)  4  The r e s u l t i n g equations are  i n Table X I I I i n terms o f the dimensionless d e p o s i t  t h i c k n e s s X=x/D..  The f o u l i n g r a t e i n the absence of any  removal mechanism can be determined the removal term. s e t t i n g X=0,  The i n i t i a l  as before by i g n o r i n g  f o u l i n g r a t e i s determined by  TABLE X I I .  Model  F O U L I N G MODELS  Differential  WITHOUT  B L O C K A G E FOR W =  Asymptotic Resistance Rf  Equation  Kern= K,C'W  Seoton Transfer Controlling Deposition  ,  - Kg T X  X  a,Sc U f  dx _ a , S c b L H ^ dt -  MS  Sc ' 2  «_K,C'W  b  " 2 Q  3  T  ~4~  X  f  b  2/3  II-8Q2SC%T  CONSTANT  Initial Fouling Rate R* b  Parameter b b  = K r  b  =a T  2  2  R«b  .  o * _ Q I s c ivfie b  L  118 Sc  \  Adhesion Controlling  ^-=a e5  E  /  R  « »  -a T  T  2  b = a T  X  2  Deposition  R  *  b  =  _9JL  e  -E/R T g  Transfer a Adhesion Controlling  dx _  q<fc -cje b  <" ' s<?W" (uff?*-" * /  B  /  rf _ oJc^-c^Je K  *  I^Sc^^T  </>=E/RCJTS  b =a T 2  sc k u vr 2/3  d  b  8  TABLE X I I I .  Differential  Model  Kern  F O U L I N G MODELS WITH B L O C K A G E F O R W=CONSTANT  Equation  Constants  i  Asymptotic  A p p r o x i mat e  Thickness  Asymptotic A, = K,C7D  -  j£ dt  Seaton  = A,W - A g W V ^ - T * " « (|-2X) 1  I  A =- *4 8K' f% A 2  4  2  +  2  3  A  X*«  24X*-32X%l6X*=^-3 8 +  Thickness  A +8 A.WD 2  3  .  Transfer Controlling Deposi t ion  dX - AW, _ 2± dt (1-2 X) 2  AoVI^X (I-2X)  =  '  4o,Scff/2 118 Sc />trD ,re  3  v* . *  I . 4 X -  +  4  A  2  as above  A W. 4~AT ' 2  AW + 4 ~AV  +  2  .. _ Qge ~ »  Adhesion  dX  Controlling Depos i t i o n Transfer & Adhesion Controlling Deposit i o n  dt  = A,  -  (I-2X)  £*+24X A  2  „  os above oJ[c -cjDeh  E / R  » » T  I  2  3  ,  +60X*-I60X"+240X*-I92X dX dt  AJ(I-2X)  2  W  A W  A W X 2  2  (I-2X)  2  4  A  2  as above  X*-  - 3 2 X + I6X = ^ r £ + 8 A,  X  4  3  .+ 12  to equations for thin deposits for 0 | a OJQ K| Kg  1  Refer  2  Approximation ignores terms In complete expression contributing less than 3-6% at 25% blockage  £  4  I AW — + 2  2  8  5  +60X*  ± X  + 6 0  x^M? A i  3  +  .2  107  When b l o c k a g e deposition  model  the  absence  for  thin  fouling  by  the  plotted  in Figure  values  results  of  the  parameters  and  the  totic  of  of  a  and  29  for a  vijittrally  Table  fixed  same  general  course  varies.  model, same  A  in  whereas  type  of  shape, For  as  the  lower  d e p o s i t t h i c k n e s s e s were  difficult have  Typical  and  2  are  solutions  value  of W.  but  the  deposition  are  behaviour  the  XIII  method.  parameters  asymptotes  rate  Kern-Seaton  numerical  cross-over effect,  final  of  Gauss  controlled  fouling  controlled  conditions.  so  point  transfer  the  predict  equations  the  the  transfer  produces the  eight  does  such  analytically,  different  and  than  under  the  different  models  differential  obtained  give  both  behaviour  solve  are  predicts  removal  films  The to  of  i s important,  results  , and  for  A l l equations the  influence  Kern-Seaton  model,  initial  rates  are W.  f o r the  of  model  increasing  for increasing  determined  been  W  higher Asymp-  different •k  models  by  setting  dX  0.,  Explicit  solutions  for X  were  dt not  possible.  where  the  However,  d e p o s i t s are  approximations not  too  thick.  w e r e made The  for  complete  cases expressions  * for is  X  and  at  least Other  approximations 75%  of  the  difference  valid  original models  f o r cases area  are  where listed  f o r constant W  can  the  flow  in Table be  area XIII.  considered.  108  TIME Figure  29.  Computed  Curves Fouling  (arbitrary)  f o r Constant with  Blockage  Mass  Flow  Rate  109  One  reasonable  depend  only  assumption  on  the  shear  deposit  thickness.  tion  removal  of  of  linear  asymptotic  dX  of  steps  _ fij_ W  ra  stress,  that  and  independent the  condition  controlling  be  Where b l o c k a g e  rate  growth  would  fouling  - A W  2  2  =  x  removal  deposition  of  important,  results  resistance. The  rate  independent  i s not  of  predicted.  i n the  be  the  in  process  the  the  assump-  predictions  There  equation  might  i s then  f o r the  no  different  is  constant  (60)  dt where the  m=-l,  0,  controlling  XIII,  except  or  +1.  When b l o c k a g e  differential  that  the  effects  equations  variable  X  does  are not  are  as  considered,  listed  appear  as  in a  Table  multiplier  2 in  A2W  the  removal  term,  which  A2W  becomes  Hl2X)4  2  X.  (1-2X)  and  some  Approximate predicted series  than  4  Numerical tion,  rather  solutions typical  values f o r each  (l-2X)  i  by  results  f o r the  obtained are  f o r the  plotted  asymptotic  model were  latter  in Figure  Kern-Seaton  o b t a i n e d by  Transfer  controlling  X  *  X*  situa30.  deposit thicknesses approximating  l-2ix;  Modified  depos i t i o n  were  »  w  1-A.2W Al 8  (l-A2_W)/4 A'  the  110  - A , = 250 W =0-5 W= I Kern-Seoton  =--W=0-5 —W= I Transfer Controlling Deposition 10  15  A, = 250 A^O W=0-5 W= I Adhesion Controlling Deposition T  W = 0-5 W= I /f,- 250 Transfer 8 Adhesion Controlling Deposition TIME Figure Fouling  30.  Computed  with Blockage  Curves  (arbitrary)  f o r C o n s t a n t Mass  and Removal  Rate  Flow  Independent  Rate of Thickness  Ill Adhesion c o n t r o l l i n g deposition  ,2. (1-A W^) /8  ^  2  X  »  I ^>  (61)  3 T r a n s f e r and Adhesion controlling deposition  *  (1-A W )/12 2  X  * A"' 1  These approximations X  are v a l i d only at low blockages, say  < 0.05.  c) Constant  pressure drop o p e r a t i o n  Many heat exchangers are operated drop, Kern  and the mass flow r a t e decreases  at constant pressure  as the d e p o s i t b u i l d s up.  (14) a p p l i e d these c o n d i t i o n s t o h i s d i f f e r e n c e model.  I n t r o d u c i n g equation 58 i n t o the Fanning e x p r e s s i o n f o r pressure g r a d i e n t i n the presence 2 f U  dP dl  yields  W  b  o f blockage.  P  =  (62) gn (D-2x)  =  IT / V  /Sep"  r  d  p  i (D-2x)  32f  D / /  (63)  LdlJ  S u b s t i t u t i n g t h i s l a t t e r e x p r e s s i o n f o r W i n t o the d i f f e r e n t i a l equations o f Table X I I I r e s u l t s i n the equations o f Table XIV (which are a l s o w r i t t e n i n terms o f the dimensionless t h i c k n e s s X), which are v a l i d  f o r constant pressure drop and v a r i a b l e  mass flow r a t e c o n d i t i o n s .  Kern has siolved the equation f o r  h i s model a n a l y t i c a l l y f o r X <  0.1 by approximating  the b i n o m i a l  expansion  of  (D-2x)  expressions  for X  also  on  two  depend terms,  expansion XIV  have  X  of X  at x  =  both  and with  and  increases  with  terms  are  constant with  case,  the  depositions-rate  moval  rate  in  the  used  d)  time.  appraoches  asymptotic  is valid  Quotient  Kern process. difference  or  (For t h i n time.)  of  from  Table  Gauss  31.  cases,  control,  XIV the  whereas the  no  Table  The  a maximum w i t h  time,  in-  that  for  deposition  f o r the  deposition  case term  film  conditions a l l deposition  Thus  as  This  X—0.5  situation  thickness equations  only  where  in Figure  increases rapidly  zero.  case  after  the' e i g h t r i p o i n t  control  adhesion  expressions  equations  shown  i s evident  X  These  controlling  through  transfer  Approximate  binomial expansions  are  goes  increasing  transfer  XIV.  differential  time  It  the  the  terms.  n u m e r i c a l l y by  versus  D/4.  of  The  two  i n Table  adhesion  f o r a l l models  decreases  where  f o r the  integrated  Kern-Seaton  term  listed  i s necessary.  term  creasing the  except  Plots  removal  are  its first  a truncation  been  method.  by  for relatively  whereas i s not  because  small  f o r the  the  latter  the  re-  ^reflected approximation  X,  models  tried Rather  a  second than  between  approach  to m o d e l l i n g the  express  the  net  fouling  deposition  and  removal  rate  terms,  a  fouling as  a  ratio  of  113  0 Figure  31.  1 TIME  2 (arbitrary)  Computed C u r v e s f o r C o n s t a n t Fouling with Blockage  Pressure  3 Gradient  TABLE XIV.  F O U L I N G MODELS WITH B L O C K A G E F O R CONSTANT P R E S S U R E  Model  Differential  GRADIENT  2  1  Equation  Approximation for X*  Constants A = K,C'Dt^ 3  Ke rn — ^=A aS(l-2X)  A c/>(I-2X)X  -  3  4  Seaton  A = K D/4 2  4  = dP/d 1  aS  Transfer Controlling Deposition  -ly  i  1/2  1/2  •2^ = AsaS ( I - 2 X )  -  A aMl-2X)X 4  Adhesion  A  , ab  4  as above  A';=A;/D  Controlling Deposition  A'  -A <£(I-2X)X  3  *_ 1 + * 4  Y  4  A ,aS as above 4  Transfer 8t  / l  A3  A^»2  A'" r A" •»  Adhesion Controlling  ^  3  A"  =  ^(i- r  1  Refer  to Toble XIII for  2  Based  on  (l-2X)'«  2 X ) X  2 X  A', ,  I- 2i X  A ,  V 3 2 f D^  A4.0S as obove  Aj" ( i= 3/2 for K-S 8 T+Ad ,  i= 1/2 for Tr control)  2  6  V  36  3A D 4  l / 2  ^z  115  deposition „ ,. Fouling  and removal  _ . Rate  Deposition — :—  =  - Removal  then  totic  stated  Xe was  that  behaviour  assumed _  b  t  that  used:  Terms ....  Terms  (64)  the deposition  that  had been  the d r i v i n g X and b  , where  assumed  was  E  . " : He  terms  terms  observed  force  i n many  f o rdeposition  are constants.  t o be the shear  must  impart  t h e asymp-  systems. was  The r e m o v a l  He  o f t h e form potential'J-  stress.  Thus  dRf  Xe~ T  =  dt  (65)  b t  Integrating, R  f  =  2g^  P  Assuming  R*  =  b  U  that  f  and  H  X  X  X  Z>b ^  U  the i n t i a l  dRf  ^ 2  b  f  the  (66)  )  of velocity,  (67) f  i s given  — L — \5  2  comment w a s made intial  t  1  *  rate  t=o  No  b  f  «  dt  _  i s independent  2g  r  ( l - e  f  b  by  cc  -U— U  2  ( 6 8 )  f  b  on t h e c o n t r a s t i n g  fouling rate  i n the quotient  v e l o c i t y dependence o f and d i f f e r e n c e  models,  116  nor  was  chosen  any  deposition  because as  the  fluid A  the  set  of  tended  terms  of  numerators  models  the  instead  the  of  be  solutions  film  the  differential  dX  _  dt  where £, square  £  D  '  W  a,  root  ft  .  Figure  32.  and  of  this lose  the  approach identity  are  developed  using  difference  the  models  arbitrary deposition  removal  listed  by  are  term easily  i n Table  equations  as  the  reduce  denominator.  solved  XV.  For  term  analytically. the  thin  to  3  m  and  X  m  (69)  are  dependence Solutions  Limitations  The  out  derived  Kern's  corresponding  and  e)  can  r e s u l t i n g differencial equations  case  form  abandoned  "cancel  previously  Equations  X CC  to  Kern  f o r the  entities".  quotient  ~Y e ""k^", a n d The  driving force.  variables  dynamic  deposition as  t h e o r e t i c a l r a t i o n a l e given  models  of  constants.. of for  the  This  deposit  cases with  proposed  considered  surface  temperature  with  surface  temperature  i s most  equation  thickness blockage  yields on  are  time  a i.e.  plotted  in  models  have  time  a l l assumed  i.e. a  important  constant for  the  a  constant heat cases  deposit  flux. where  The the  117  D  D  D Adhesion Controlling i Deposition  4  TIME Figure  32.  8  (arbitrary)  Computed C u r v e s f o r C o n s t a n t Mass F o u l i n g - Q u o t i e n t Model  Flow  Rate  118  reaction is  at  the  constant  with  time  surface i s important.  then  as  increases.  the  the The  I f the  wall  d e p o s i t surface temperature  deposit builds temperature  T  up  and  the  temperature  will  thermal  in equations  44  and  fouling  i s not  decrease  resistance 53  will  then  s no  l o n g e r be  and  the  mated  heat  load  does  I f the not  where  =  s  a  and  T | -a |t=o s  i s taken 53  probably  too  much,  T  too  thick  c o u l d be  g  be  rapidly  flux  case. The  approxi-  cases  been  ignored  more  (70)  constant.  Integration  difficult,  and  The  rate  of  with  time  than  the  corresponding  considered  are  of  highly  speculative.  include:  thickness, effect  size  fouling  nature  of  the  particles,  adhesive  consideration  rationalize  fouling  of  of  the  of  necessity  of  of  thermal  fouling  is largely  proposed  behaviour  will  constant  heat  simplified  and  and  fouling predict  operating information is  that  particles. It  models w i l l effects  available.  and  in  have with  distribution  unknown.  must  decrease  conductivity  o  when more  technique  course  s u r f a c e roughness,  shape  forces  equations  Complicating effects  variation  deposit of  fouling  of  a numerical  used.  models  some  x  t o be  becomes  more  that  change  film  by T  44  constant.  of  The i s hoped help trends  to  T A B L E XV.  Q U O T I E N T F O U L I N G MODELS  Seoton  B L O C K A G E FOR W  Differentia I Equation  Mode Kern -  WITH  dX dt  A, D A W  (I-2X)  4  Analytical 4 t  _ A W [ I " 4A, D L3(I-2X)  Transfer Controlled Deposition  dX dt  Adhesion Controlled Deposition  dX A'j D (I-2X) dt * A W 2 X  Transfer ft Adhesion Controlled Deposition  dX dt  A',D ( I - 2 X ) 2  A W  2  2  [-  2  2  4  >w r 2  4  4A  2  6  A, W  3  (I-2X) X  6  t*  I 2(I-2X)  3  - I  4A', D U - 2 X  A W  Solution  2  4  2  Al"D  CONSTANT  A  w  3  2  i L3(I-2X)  3  , _Ll 2  *  + ln(l-2X)  i " 2U-2X)  6j  ] _ L ]  2  6J  r 50-2X)  5  4(1-2X)  4  20.  120  f)  Interpretation of present of proposed models  rate  All  experiments  and  constant  deposit totic oil  and  data  heat  thicknesses  equation 0.0002  yield  percent  x/D  were  carried  flux  (Appendix  3,  f t f o r the values 100  lb  Since reached  The  i t was  for both  the  difference  not  apply  constant The fit  the  to  use  the  model w i t h  the  present  fouling  rate  present  data  proportional  t o W~ ,  be  on  The  dependent  2  W  and  as  because  proposed  f t . for  the  These  and  The  1.4%  models  i s then  justified.  c o n d i t i o n s were  this  often  i t appears of  model  thickness predicts  that does  a  films. Kern  initial  the  0.9%  independent  results,  the  asymp-  respectively.  experiments,  d e r i v e d by  as  the  0.00013  , was  film  water  removal  whereas  q u o t i e n t models  thin  for thin  q u o t i e n t model  by  flow  estimated  experiments.  asymptotic  o i l and  terms  mass  maximum  fitted IV)  in  J  the  that  constant  0.007  2  52  of  found  and  (D-2X) 1  -  2  were  fouling  0.0045  results  The  Table  water  of  at  time.  data  L respectively.  with  out  f o r which  were  blockage,  experimental  the  model by  the  does  fouling  not  r a t e s were  parameter b assumes b present  appear  was  to not  found  independent  author  to of  W.  a l l predict  j,  RfCC t  2  severe oil  and  for thin  deposits.  d e v i a t i o n s from water.  Some o f  the the  Figure  33  shows  square  root  time  experimental  that  there  are  dependence  for  data  c o u l d be  both  fitted  121  1-5  O X  I  1  A  A  A A^A a  1-0 " 0-5  1  A Oil-Run 15 W « 0 - 5 4 3 lb/ sec ~" T = 296 °F  -  Wc  A  e CM  Z  0-4  o ° o < * < p * °o o  "  b  o  3  Iffi  -  o  o Water-Run 44 W = 0-311 lb/sec T "70°F  o  W c  , °  1  5  , (TIME)  Figure  33  2  a  1  10  ±  1 15  (hours)  2  Comparison o f Experimental Results with Quotient Model P r e d i c t i o n s  Thin  Film  122  fairly  well with  For  thin  integration  this  films,  type  of equation,  the asymptotic  of a l l the difference  XII).  Correlation  of the i n i t i a l  showed  that  f i t was  tions  a good  by t h e form  equation  models  54.  over While  results  from  at constant  fouling  achieved  of equation  however.  rate data a wide this  W  (Table  of the o i l  range  fact  the  of condi-  does n o t  i imply  that  the assumptions  controlling support tion  d e p o s i t i o n model  t o the mathematical  o f t h e two Further  is  made  treatment  o f the importance  petroleum  streams  and  the use o f T e f l o n heat  and  promote The  W*", 2  for  flaking  asymptotic  r a t h e r than  W^  (equation  55)„  model  of fouling  adhesion  i t does as a  lend  combina-  processes.  evidence  from  plus  are enti.rely correct,  the successful application  fouling  i n the transfer  of surface  o f adhesion active  fouling  agents  (39,49) b y h i n d e r i n g  exchanger  in  to  reduce  sticking,  tubes  which  hinder  r e s i s t a n c e was  found  to vary  sticking  of deposits (50). fouling as  -  p r e d i c t e d by  The  form  the transfer  of the f o u l i n g  and  as  adhesion  resistance  equation  the o i l data i s  R  = Aw" ;|  f  (1 - e  _  B  W  t  )  (71)  2  where the  A'  and B a r e c o n s t a n t  governing  differential  with  respect  equation i s  t o mass  flow  rate.  If  123  dx  _  deposition  term  -  removal  (72a)  term  dt then dx  (72b)  BWx  dt A-^ =  whe r e W  1  rather  possible  to  Both of  the  initial  this  as  to  be  2  see  .  fouling,  value of  that  the  More work  removal  removal  could  the  t h e mass  flow rate,  asymptotic resistance  Above  the  transfer,  deposition  critical  important.  adhesion  the  model  varies on  as  other  and  of  Kern-Seaton is  applicable.  the  predictions  fouling  process  l e a d s one t o  transfer  process  and  process  is controlled  that  other processes  the  removal  very high,  indicate  follow  v a l u e o f W,  Consideration  become  done  experimental data  rate  and  be  term  term.  controlled  the d e p o s i t i o n  would  adhesion would  expect  cease  be  to  expected  important. If  the d e p o s i t i o n  surface, on  W  the  velocities  control  we  transfer  are  involving  that  of  model.  evidently as  as T o r  than  critical  or  and  d  the water  a  model  B k ,  forms  For up  A'  wall  temperature  the d e p o s i t i o n  s y s t e m was others. though  run  The the  at  s h o u l d have  rate.  A  a wall  temperature  initial  single  fouling  rate  asymptotic resistance  investigation  of  the  temperature  by  transfer  a relatively  experiment 26°F.  increased d i d not effect  with  the  h i g h e r than by  2%  change. may  minor  be  to effect  water the  times a l Further  warranted.  124  9.  CONCLUSIONS  Fouling gas  oil,  and b y  mentally fouling water, and  resistance builds  was  due  The  d e p o s i t s from  was  about  rate,  rate  rate.,  model  o f t h e mass  bonding  was  energy  data  irate  and h e a t  flow  tube  rate rate  wall  with  resistance squared.  equation  o i l :  had t o  powder  the  that  Kern-  initial  mass  varied  flow  as t h e  A t c o n s t a n t mass  o f the o i l depended  i n the f o u l i n g  asymp-  temperatures.  o f the  increasing  found  suggested  process.  the following  Over  flow  exponen-  i n the form  o f 29 K c a l / g m o l e  rates,  the  Kern  5.5% sulphur..  process,  temperature,  i n the l a t t e r  fouling  about  predictions  o f the f o u l i n g  by  the experiments  coke-like  The  and o f t h e  i n o i l fouling,  a black,  fouling  fluxes,  experi-  flux.  as s u g g e s t e d  and c o n t a i n e d  The v a l u e  f o r t h e gas  value  heavy  studied  of excessive wall  detailed  fouling  important  of initial  straight-run  has been  before  o f the o i l decreased  equation.  activation  the  t o t h e more  on t h e c l e a n  Arrhenius  range  t h e o i l were  the initial  tially  fluxes  not reached  and t h e a s y m p t o t i c  reciprocal  flow  t o development  difference  fouling  mixture,  asymptotic  90% combustible,  Contrary  a sour  o f t h e o i l a t low h e a t  At higher heat  terminated  by  o f mass  up t o an  condition  Seaton  tube  a sand-water  as a f u n c t i o n  Seaton.  totic be  of a heated  of the  f o r the  that  chemical  a 150-fold  equation  correlated  125  dRf  0.1347x10 1.0/  dt  -26,030  e  w  Tw  (°R)  c  t=o  Fouling tube.  of  Local  the  o i l increased with  fouling  rates  depended  on  distance the  along  local  the  clean  heated  tube  wall.temperature. The  asymptotic  decreased rates of  Kern-Seaton  rate.  fouling  the of  of  pressure  water  and  roughness, drop  estimated  values  the  drop  up  rate.  rate,  to  flow  a  sand  The  deposits  initial  f o l l o w i n g the  critical  rates  increase  time  as  value  resulted  data.  Thermal  fouling  predictions  of  the  i n lower  mass  initial  Seaton,  and  was  assumed  t o be  surface,  of  made  same  resistance for  both  Ignoring  were back  the  calculated  i n reasonable  effects  from  calculated  from  agreement  with  models  Kern  deposits.  to  the A  controlled partly  fouling  the  conductivities,  Parkins.  and  approximately  experiments.  were  for similar were  the  thicknesses  thicknesses,  reported  followed  did  o i l fouling  deposit  and  the  mass  with  Extensions  to  flow  model,  Higher  trends  pressure the  mass  flow  the  rates.  The type  resistance of  i n c r e a s i n g mass  increased with  the  flow  with  fouling  by  mathematical  model  partly  i n which by  adhesion  the  transfer of  of  material  of  deposition the to  material the  surface,  yielded  virtually the of  gas  an  identical  o i l .  transfer  Kern-Seaton  Models  expression  for  in  that  form  were  to  also  and  adhesion  initial  found  proposed  controlling deposition, model,  the  rate  experimentally  for  which  fouling  is  the  limiting  s i m i l a r to  controlling deposition.  for cases the  127  10.  RECOMMENDATIONS  Further  work  gathering  more  liquids.  Other  drop  FOR F U R T H E R WORK  on h e a t  data  o f the type  wall  data  are needed  The  work  o f Hasson  be extended  conditons  that  under  constant  ness  i s reached  been  cooking  controlled  CaC03.  therefore  open  reached  effort  type  be  c o u l d be  pressure  investigated.  on s e a w a t e r  models. scaling  t o see whether demonstrated thick-  also  might  scale  that  be s t u d i e d . forms  i s due t o  r a t e may t h e r e f o r e b e controlled  velocities  some  adhesion  as i n s e a w a t e r  of the scaling  I f asymptotic  It  rate i s  conditions  savings  could  i n maintenance  possible.  particulate  and m a g n i t u d e  particles  as c o n s t a n t  I t has n o t been  t h e CaC03  dependence  at reasonable  would  For  scaling  to question.  but f o r other  scale.  o r i t may b e d i f f u s i o n The v e l o c i t y  entail  c o n d i t i o n s an a s y m p t o t i c  The i n i t i a l  scaling.  be  flux  a compact  postulated that  particulate  here,  o p e r a t i n g times  are reached.  liquor  should  the mathematical  and co-workers  heat  with  also  to evaluate  to longer  asymptotic  has  presented  temperature  Reliable  Kraft  fouling  o p e r a t i n g c o n d i t i o n s such  and c o n s t a n t  could  exchanger  t o smooth  fouling  of forces and rough  i n general, involved surfaces  the question  i n adhesion i s open.  of the  of small The  effect  128  of  particle  size  some w o r k . approach  Effort  might  to fouling.  successful process  and c o n c e n t r a t i o n  i n some  that  be p u t i n t o  The d i f f e r e n c e  respects  has not been  Optimization  on f o u l i n g  of heat  i s based  directly exchanger  the effect  of velocity  attempted  using  o f the proposed  requires  improving  the mathematical  approach,  while  i t appears  on a h y p o t h e t i c a l  demonstrated  including  some  rates  design  to  exist.  for fouling  on t h e o p e r a t i n g  "removal"  time,  service, can be  expressions f o r the  fouling  rate„ The heat and  whole  question of shell  exchangers, geometry,  including  side  fouling  the influence  has had l i t t l e  exposure  of shell  o f process  i n t h e open  and  tube  variables  literature.  129  11.  1.  T.E.M.A.  Standards,  Manufacturers  Association,  and Seaton,  New  Tubular  York  Exchangers  (1959).  3.  Kinert,  4.  K n u d s e n , J , G.., L e c t u r e t o N i n t h N a t i o n a l H e a t T r a n s f e r C o n f e r e n c e , A.I.Ch.E.-A.S.M.E., S e a t t l e , A u g u s t 1967.  5.  McCabe,  C., T r a n s .  W,  R.  Edition,  Kern,  6.  Q.  Fourth  2.  478  D.  REFERENCES  A.S.M.E.  L, and Robinson,  E., B r i t . 7 1,  G,  Chem.  876  S.,  E n g . 4., 2 5 8  (1959)  (1949).  I n d . E n g . Chem. 1_6,  (1924),  Hasson,  D.,  Sonderdruck  aus Dechema-Monographien  Band  47(1962). 7.  Reitzer,  B. J . , I n d . E n g . Chem.  Proc.  D e s . a n d D e v e l . 3_,  345(1964). 8.  Miyauchi, Japan  9.  Palen, Sym.  .10,  T.  J : W.  and Westwater,  4,  60  11.  Clapper,  12.  Smith, Inst.  13.  14. 15.  Kern,  D,  Gardner,  Progr.  77(1966). M „ ...M. , B u l a v i t s k i i ,  I.. I . , T e p l o e n e r g e t i k a b y J.. J a c k s o n ,  R„ L . , T r a n s . 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NOMENCLATURE Typical  a  /  aj < Aj ,  .  constant  A  area  b  parameter  C  concentration  C  concentration of dirt  On  drag  coefficient  Cp  heat  capacity at constant  D  inside  diamter  D'  inside  diameter  D  particle  T'"..r.-1 :  f t of equation  6  units  L  2  hr"^ l b moles/ft  in liquid  lb/ft  3  3  dimensionless pressure  o f tube  BTU/(lb)(°F) f t  o f tube  in;.inches  diameter  inches feet  .tr ^  diffusion  e  base  E  activation  f  Fanning  F  force  g  c  h h  m  ft /sec 2  f o rnatural logarithm =  2,71828  energy  friction  dimensionless Kcal/g-mole  factor  dimensionless l b f  gravitational  constant  heat  coefficient  transfer  BTU/(hr)(ft )(°F.) 2  i n s t a n t a n e o u s mean h e a t transfer c o e f f i c i e n t f o r combined fouling resistance  J  coefficient  flux  and l i q u i d  of material  film  B T U / ( h r ) ( f t ) (°F) 2  lb/(hr)-(ft ) 2  135  k  thermal  kg  Boltzmann's  k^  thermal  k-diff k  m  a  s  conductivity  conductivity  reaction  r  K  liquid  constant  transfer  s  of  (  BTU/(lb of deposit  mole)(°R)  BTU/(hr)(ft)(°F) ft/sec  coefficient  rate  B T U / ( h r ) ( f t ) (>°F)  constant  constant  K  r  1  overall  crystallization  rate  constant  length  ft  LLI.  length  o f tube  m  mass  n  number  p,P  pressure  ft lb  l b / f t  2  f  q  heat  flux  BTU/(hr)(ft )  Q  heat  flow  BTU/hr  2  ft  r  radius  R  thermal  Rf  fouling  Rg  universal  gas  S  sticking  probability  t  time  hr  T  temperature  °F  U  velocity  ft/sec  TT u  ^  velocity surface bulk  resistance film  resistance  (BTU/(hr)(ft )(°F)) 2  =  R-R  Q  constant  o f p a r t i c l e s normal t o  velocity  (BTU/(hr)(ftl)(°F))  B\'.V/ '.'! ,.:) [ft  BTU/(lb  ft/sec ft/sec  ,  mole)!(j°R)  136  flow  lb/sec  W  mass  x  deposit  X  dimensionless = x/D  deposit  Y  distance  tube  z  length  Pr  ft  thickness  from  along  Dimensionless Nu  rate  Nusselt  Reynolds  Sc  Schmidt  ft  wall  ft  tube  Groups number  Prandtlnnumber  Re  thickness  number  h  C  U  D/k p / b  X  /  k  D/l/  number  Greek -Letters  O r*  ratio of inside orifice to inside pipe diameter  O"  Stefan-Boltzmann  €  emissivity  /\  difference  (^) p  power  factor  density  diameter  constant  dimensionless BTU/(hr)(ft )(°R) 2  4  a ime'ns!Lohle'ss).( 'R) r  dimensionless lb/ft  3  4  137  kinematic viscosity  T  shear  viscosity or  stress  ftVsec  micron  lb/(ft)(sec)  at  lb/(ft)  wall  (sec)  2  Subscripts  inlet 2  at  .outlet of  insulation  time  OR  orifice  out  outside  3  outside  b  bulk  P  particle  c  clean  s  surface  calc  calculated  St  steam  crit  critical  w  wall  CO  far  j  over  value  d  deposit  f  fouling  film  liquid  film  outside  film  film h  o  h^  inside  i  inside H  loss m  zero value  from  a l l particles  film  local lost mean  to  surrondoundings  value Superscripts  n *  power asymptotic  average value  source  value  1-1  APPENDIX 1:  a)  Thermocouple  All  CALIBRATION OF EQUIPMENT  Calibration  thermocouples were c a l i b r a t e d  i n an o i l bath equipped  w i t h an Instrument Co, L t d . thermoregulator (Model 7530) f o r temperatures above 200°F„  and i n a water bath equipped w i t h a  C o l u r a U l t r a thermostat f o r temperatures below The temperature  200°F.  i n the bath was measured w i t h a Platinum  r e s i s t a n c e thermometer (Leeds & Northrup No. Northrup Muel&er temperature b r i d g e No. the r e s i s t a n c e o f the thermometer. a Scalamp Galvanometer,  169314). A Leeds &  83429 was  used to measure  A u x i l i a r y equipment  an Eppley Standard C e l l No.  a Leeds & Northrup Mercury  included  737516 and  commutator.  The r e s i s t a n c e readings were c o r r e c t e d f o r r e s i s t a n c e of the l e a d w i r e s , and were converted to temperature v i a the C a l l e n d e r equation f o r the r e s i s t a n c e thermometer.  The constants  f o r t h i s r e s i s t a n c e thermometer were determined by the N a t i o n a l Research C o u n c i l of Canada i n October  T  (°C)  1  =  0.0038748  ["Jr [R !  T  ll "  J  1959:  +1.5  I"  T  jTT  "  x  |_10oJ [lOO (1-1)  T h i s equation was  s o l v e d by t r i a l  and e r r o r f o r the v a r i o u s  values of Rrp measured u s i n g the measured value o f the r e s i s t a n c e  1-2  at  the  the  ice point  resistance  readings  of  quadratic  In  =  1.  II  two  wall  thermocouples  equation of a + b ••  temperatures  the  "L'-CM •  :;vl  ''. -II  +  c x  of  the  calculated  near  the  (Table  II)  Thermocouples  17  inlet. outlet  are  19  water  temperatures  sheathed  measures  outlet  fouling 21  chamber.  fouling  indicates  by  °F.  the  values  The  least  and  Millivolts  values that to  liquid  to  a  2  and  from the  16  given  measured  mounted  measured  22  liquid  23  temperatures  temperature  the  i n the  on  inlet  the  24  at  the  measure  cooler.  tank.  the  tube  and  Thermo-  temperature  and  on  thermo-  Thermocouples  temperature  measure  along  values  individual  were 18  are  respectively.  Thermocouples  liquid  of  millivolt  squares  iron-constantan thermocouples.  the  Thermocouples mixing  fitted  range 1  24  and  the  b  Thermocouples  to  i n °G  gives  constants f o r the thermocouples  temperatures  cooling  1-1  form  Millivolts  x  were  used.  couple  20  the  Table  was  outlet  and  the  deviations  couple  19  and  T a b l e 1-1-1 t h e  with at  T  (2,5128 ohms).  heater in the  the inlet  Thermocouple  TABLE  Resistance (ohms)  2.593000  1-1:  RESISTANCE  Temperature °C.  THERMOMETER  DATA  Temperature °F.  8.15  46.66  2.65340  14.26  57.66  2.68210  17.17  62.91  2.72070  21.10/  69.98  2.80790  29.99  85.99  2,91470  40.91  105.65  3,05210  55.02  131.03  3,20795  71,09  159.96  3,37953  88.87  191.96  3.46700  97.97  208.35  3.63580  1.15.61  240.09  3.74035.  126.58  259.84  3.91578  145.07  293.13  4.11656  166.37  331.47  4.28806  184.67  364.41  4.35363  191.70  377.06  4.59115  217.28  423.10  4.74292  233.73  452.72  4,89970  250.82  483.48  1-4  TABLE  1-IIa.  THERMOCOUPLE  CALIBRATION  T E S T S E C T I O N I AND I I  Thermocouple Number  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  #  T'eale  43. 088 49. 3d6 42, 9l'5 41. 517 42 ,331 43, 565 43. 185 43. 078 47, 872 43, 102 43. 394 43, 080 41, 519 40. 961 42. 959 46, 292 34. 363 32. 227 38. 055 37. 106 35. 712 36, 611 36, 842 36. 982  *  a t 47°F.  ** ***  a t 131QF, a t 160°F.  T°F = a  Deviation  + b(millivolts)  41.501 40.405 41.557 41.854 41.636 41,317 41,404 41.361 40.377 41,365 41.359 41,497 41.906 42.062 41.423 40.272 44.191 46.560 32.939 33.258 33.248 33.203 33.109 33.101  +  -0.40063 -0.34253 -0.40932 -0.41836 -0.40749 -0.38472 -0,39123 -0.39282 -0.33106 -0.38766 -0,38945 -0.40308 -0,42814 -0.4367 -0,3979 -0.34193 -0.0000 -0.92456 -0.04098 -0.05664 -0.06034 -0.053612 -0.048376 -0.04755  c(millivolts)  2  -  T  #  °F me a s  192.0 ° F  483.  -0.3 -1.3 -0.2 -0.3 -0.4 -0.5 +0.1 +0.4 + 0,4 + 0.1 +0.2 +0.3 -0.3 -0.4 + 0.1 -1.0 + 0...4* :.o.6* 0.0** +0.3** 0. ** +0.1** +0.2** +0.2**  -0.4 -0.8 -0.6 -0.2 -0.4 -0.4 -0.5 -0.6 -0.5 -0.4 -0.4 -0.6 -0.6 -0.3 -0.5 -0.2 +0.6 ** -0.1 *** -0.5 -0.3 -0.4 -0.5 -0.6 -0.6  1-5  TABLE  1-IIb.  THERMOCOUPLE  Thermocouple number  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  +  a  31.838 29.192 32.679 32.651 32.502 30.713 31,939 32.255 32.255 31.901 32.311 31,580 31,178 31,577 32.130 32,788  Temperature °F =  CALIBRATION  FOR T E S T S E C T I O N I I I  b  46.642 48.473" 45.852 45.778 45.903 47,612 46,512 46.059 46,059 46.491 46.101 46.790 46.760 46.899 46.367 45.709  c .;  -1.0488 -1.3462 -0.89325 -0.84096 -0.87238 -1,0563 -1.0076 -0,85641 -0.85641 -0.99937 -0.94458 -1.0797 -0.76938 -1.1035 -0.9740 -0.86322  a + b(Millivolts)  +  Deviation Observed)  OF(Calcat  77.55°F  192.1°P  -0.07 *0„~23 :o?oo -0.'05 -0.02 0.00 -0.11 -0.09 -0.09 -0.07 0.01 -0.04 -0.02 0.00 -0.03 0.04  c(Millivolts)  0.09 -0.14 0.00 0.08 0.03 0.08 0.13 0.12 0.12 0.09 0.00 0.07 0.08 0.06 0.. 01 90?04  1-6  b)  Differential  i)  Orifice  The  instrument  5429001, tanks the  which  DP  was  used  s e t on  zero  manometer  given  i n Table  below  70 t h e p l o t  above  70  ii)  The  a Honeywell Model used  Test  instrument  With  0-20" w a t e r . reccpmmended  Pressure  was  range no  i n Section  with  calibrated  with  0- 1 0 0 "  water  curves  are plotted  with  The d a t a  1-1.  For used  are  readings while  Drop I n d i c a t o r  Model  227X2-C2  0-50" " w a t e r ,  with  No.  and t h e 0-150" w a t e r 1-2  range  and  range i s  column  Instruction  f o r t h e 0-20" w a t e r , manometer  B466  0-100" w a t e r ,  a water  195-F o f t h e H o n e y w e l l  i n Figure  wascdone  versus A P w a s  calibrated  a mercury  the  and t h e  s p r i n g i n , the instrument  the instrument,  and  used.  springs,  T h e m e t e r was  in  purpose  pressure  i n Figure  K678  i s empty  Calibration  a Honeywell  range  No.  levels  the l a b a i r supply.  Reading  was  liquid  the tank  differential  reversed.  Cell  292D11  For the present  and a r e p l o t t e d  used  three  0-150" w a t e r .  received  taps  o f DP  Section  1 0 0 % when  at zero  utilizing  l-III  to indicate  i s zero.  the inverse plot  7102002 w i t h  1- I V .  was  pressure  and low p r e s s u r e  a mercury  Calibration  Indicator  and t h e r e f o r e i n d i c a t e s  needle  dry  Cell  i s normally  differential  high  Pressure  span  as book  and  f o r t h e 0-50" w a t e r , springs.  and t h e d a t a  The  the  calibration  are l i s t e d  i n Table  1-7  100/DP Cell Reading  DP  Figure  1-1.  Cell Reading  Calibration Curves Pressure C e l l  forOrifice  Differential  1-8  TABLE  l-III.  Manometer (Inches  CALIBRATION  Reading Hg)  DP  OF  O R I F I C E D I F F E R E N T I A L PRESSURE  Cell  Manometer  Reading  (Inches  Reading Hg)  CELL  DP C e l l Reading .  13.15  84.0  11.01  81.0  1 5 . 92  86.7  12.45  83.0  20.08  90.1  14.46  85.1  25.06  94.5  19.0  89.8  27.12  96.1  1.48  19.5  3. 50  38.0  1.78  22.0  3.33  35.5  3.07  33.5  5. 78  57, 8  3. 90  41. 8  7.13  69.0  5.13  52. 5  8.05  74,3  5. 50  56.0  8.33  75,1  6„40  63.2  8. 89  76.5  7.26  69.5  9. 70  78,5  8, 32  75.2  7.68  72.0  TABLE  Range  Spring j None  Scale  Reading  0-50  +  OF  TUBE D I F F E R E N T I A L PRESSURE  inches H 0  TS cale..-.Read-.i'n g  A P inches  CALIBRATION  1-IV.  r  H 0  2  A P inches  2  0-100  inches  Scale  Reading  E^O  CELL  H 0 2  AP  0-150 Scale  inches H 0  inches H 0 2  Reading  AP inches  2  30.2  6. 06  40.8  "8". 14  57. 2 76.2  1 0 . 82  97,3 89.6  19.16 17,49  82,9 76.0  16.10 14. 71  70.0 59. 9 45-9  28.0 37.0  14.00 1 8 . 22  16.0 23.8  16.33  15. 5  23.37  23.11  26.4  40.39 66.87 89.57  38.07  34.0  3 3 . 58  44. 6  44.19  45. 5  45.28  44.19 48,94  .S.6..-2 63.54 .  58. 8 71.2  98,0 9.9  4 9 . 63  78.0 86.2  7 7 . 09 8 6 . 06  96.0  141.31 144.56  13.68 1 1 , 70  20,9 39„5  10.06  92. 86 95.04  87,0  131.59  76,0  114.65  9,06  61.1  1 9 . 85 31,41  94.0 ' 95.4  9 6 . 53  64. 5  96.46  38,7  7.-64  76.3  7 4 . 92  56.3 48. 5  -83-362  •"613)0 4. 904.02  3 1 . 95 4 0 , 79  81.57  30. 9 24. 9  62.0 78, 1  96.0 82.2  77. 5  39.16  67. 5  37.5  55.79  87.0  4 4 . 87 50.03 3 4 . 81 26.78 23.11  5 2 . 89  28.5 20. 9  42.5  99.0 68.0 53.0  60.5 53.3  62.13 5 9 . 28 41.33 31.00 26.10  15.0 9.4 5.9  20.0 15.0  96,0  3.09 2.11 1.54 1.12 0. 71  10.1 7.8 5.6 3.6  Range  74.0 87. 5 86,5  1 4 . 93  0-2O  inches  45.0 38.5 20.8 9.0 H 0 2  5.17  1 9 . 71 9. 93 4.08  41.8 30.8 27.0 20.0 10.1  74 63 ..36  35^  1 8 . 76 9. 65  82. 3 93.2  107.40 124.42  72.68  30.80 21.62 13.51 7.43  H 0 2  1-10  c)  Orifice  Two noting  to  collect  the time  orifice  the d i f f e r e n t i a l  discharge  w h e r e = S  Equation  ReOR C log-log  least  orifice  =  2  /  area 1-2  C was  2g  ( F i g u r e 2) w e r e  increments  across  pressure  diameter  / pipe  of RSQ  plot  squares  R  diameter  /  2g  c  V S ReQ^/c was  t h e gas o i l t o  A.P pS  1-3  made  and t h e d a t a  0 ft  =  0.301  Re O R  =  0.80564  (Re  0 R  For  ft  =  0.602  Re  =  0.925069  (Re  0  cients  1-V  fitted  by  yielding:  For  Table  orifice  opening  D2 l*.  =  2  The  1-2  of discharge  4W 7TD yU.C  on t h e  from  AP/O"  c  of water  measured,  read  cell.  (31)  i s g e n e r a l i z e d f o r use with  =  was  the o r i f i c e  calculated  calibrated  o f weight  The t e m p e r a t u r e  differential  coefficient  2  drum.  pressure  calibrated  W = C S  plates  f o r successive  i n a 45 g a l l o n  previously  A  Calibration  sharp-edged  by  and  Plate  gives  and T a b l e  Q R  the data  *  /C) • 0  R  for calculating  1-VI l i s t s  Q71R2  /C)  1-4  9  6  3  0  6  1-5  the discharge  coeffi-  the deviations of experimental  points  1-11  from the f i t t e d e q u a t i o n s . For 1-3  the o i l experiments R e / C i s c a l c u l a t e d from equation QR  knowing p  and p. at the temperature  of the o i l at the  and then ReQR i s c a l c u l t e d from equation 1-4 Re  or 1-5.  orifice,  W,  and  i n the t e s t s e c t i o n are then c a l c u l a t e d knowing the p h y s i c a l  properties  at the average temperature  Kinematic v i s c o s i t i e s temperature,  i n the t e s t  section.  and d e n s i t i e s were measured at the o r i f i e e  210°F.  Sample C a l c u l a t i o n  i)  Orifice Coefficient  For  the o r i f i c e w i t h  = 0.301  the f o l l o w i n g data were measured:  W = 0.1538 l b / s e c DP c e l l  reading  =60.  Water Temperature = 18.5°C. From F i g u r e 1-1, in. At  2  r e a d i n g o f 60 corresponds to A P =  6.0  Hg 18.5°C,  p. = 1.04  = 0.301, D  DP c e l l  0^  C = S  S  V  2  1-^g  4  (Reference  31)  = 0.9917915  = 1.91748 x 10~  4  ft  2  1-2  W ., ,. /2g &Pff~ 1-^4 r  2  p = 0.99853 g/ml  = 0.008285  = 0.187S.;in.  From equation  cp  ,Q-153;8 . ... .. . , . 1, 91748 x J-Q.y7x32.174x (6x7Q. 727) (-9983: -v/9917915 ~ 62.' J  =  TABLE  DP  Cell  Reading  (P1-P2) inches Hg  1-V.  CALIBRATION  Average Weight  30  °C  Re g/ml  0. 1 0 1 4  21. 4  0. 9 9 9 4  30  2. 68  50  4. 91  0, 1 0 1 9 0. 1 3 7 7  19. 0 19. 8  0. 9 9 8 4 0. 9 9 8 4 7  60  6. 0  75  8., 30  0. 1 5 3 8 0. 1 7 7 2  18, 5 17. 5  0. 9 9 8 5 3 0, 9987  0. 1 9 6 5 0. 2 2 9 3  18. 0  0, 9 9 8 6  85  10, 4 14. 2  17 , 0  90  1 9 . 55  0. 2 6 8 0  18. 0  95  19. 0 18. 0  25. 7  0. 3 0 8 8  .100 70  32. 9 7. 33  0. 3 4 5 1 0. 1 6 8 9  25  2. 13  0. 3 9 7 5  40  3. 77  0. 5 3 0 6  50 70  4. 90 :"6C 0 7. 33  80 80 85  10. 4 10. 4 1 4 . 25  90 95  1 9 . 55 25. 7 32. 9  60  100  PLATES  Rate  2 ,68  80  0.602  ORIFICE  Temp  lb/sec i>=0.301  OF  0. 605  12, 6 9 6  0. 6 0 8  12, 0 1 5  1. 033 1. 04  0. 6 0 8 0. 614  16, 1 8 9  1. 07  0. 585 0. 5 9 6  0. 9 9 8 8  1, 0 5 6 1. 083  IV, 960 19, 5 4 4 22, 5 9 9  0, 9 9 8 6  1. 0 5 6  0. 595 0. 594  25, 713 -30, 822  0. 9 9 8 4 3  1. 0 3 0 1. 0 5 6 0. 988  0. 5 9 0  36, 4 1 0  0. 588  39, 6 8 8  0. 6 1 0  20, 7 6 1  1. 0 5 5 9 1. 1 7 0 1. 083 1. 1 7 1  0. 623  22, 857  0. 625 0. 627 0. 6 2 6  27, 5 3 8 34, 012  20. 8 18. 0 14. 2  0. 9 9 8 6 0. 9992 *  0. 6 0 6 6 0. 6 7 0 9  17. 0  0. 9 9 8 8  14. 0  0. 7 3 5 3  17. 0  0. 9 9 9 3 0. 9 9 8 8  0. 8 7 5 0 0. 8 6 3 7  17. 0 13. 5 14. 8 16. 5 17. 2  1. 5 0 1 7  16. 5  cp 0. 97 1. 03  0. 9 9 8 6 0. 9 9 8 0 6  1. 0 0 0 1. 1 5 8 0 1. 3 3 8 9  OR  1. 083  0. 9 9 8 8 0. 9 9 9 3  1. 083  0. 621 0. 6 1 4  1. 185  0. 613  0. 9 9 9 1 0. 9 9 8 9 0. 9 9 8 8  1. 15 1. 095 1. 077  0. 9 9 8 9  1. 095  0. 6 0 6 0. 5 9 9 0. 6 0 4 0. 5 9 9  34, 7 9 0 41, 228 48, 5 0 0 44, 2 5 8 52, 802 64, 217 75, 4 8 9 83, 277  I  I—'  TABLE  A.  1-VI.  F I T OF R E G R E S S I O N EQUATIONS  Small O r i f i c e  RE/C  =  FOR  0.301  RE(OBS)  Re(CALC)*  %  Deviation  20983.  12696.  12771.  0.6  26637.  16189, 20761. 30822,  16103. 20434.  -0.5  34034. 51852. 61712.  36410. 39689.  36435,  0.1  39724,  22599.  22700.  0.1 0.4  25713.  25771, 17637,  67451. 37925,. 43214. 29251.  17960,  33437,  19545,  19772,  12015,  *  R E a l c by C  B.  30764,  20085. 12054,  -1.6 -0.2  0.2 -1.8 2.8 0.3  E q u a t i o n 1-4  Large O r i f i c e  =  0.602  RE/C  RE.(OBS)  RE(CALC)*  %  34736.  21700.  21838.„  0.6  51476. 65827.  32000, 40500.  31896. 40419.  -0.3 -0.2  74546. 77175.  45800.  45563. 47109.  -0.5  47100. 53300.  87531. 110506. 121181. 131451.  *  Re  c  a  53183. 66567.  67000. 72000.  72749. 78678.  78500,  ^  c  ORIFICES  by equation  1-5  Deviation  0.0 -0.2 -0.6 1.0 0.2  1-14  =  802.128 _ (1.71635xl06)*S  . 802128 1.31  0.6123  =  (Program  yields  .614)  Then,  Re  =  4 W  4(  =  7TD fjL  1538)  17,933  3 ,, 1 4 x ( . 1 8 7 5 / 1 2 ) x ( 1 . 0 4 x 6 .  2  7197xl0 7 _ 4  (Program where Re  0 R  1 cp =  /C  =  17933 0  These  6 7197 x  10  -  29,288  =  l b  4  m  /  yields  17,960)  ft-sec  (Program  yields  29,251)  6123  co-ordinates  give  one  point  f o r the c o r r e l a t i o n  (Table  1-VI).  ii)  Mass  Flow  Rate  and V e l o c i t y  0.301  D  reading  =90.  f o r O i l Flow  Data: P Run DP  =  2  =  0.1875  Viscosity  Calculate Re O R  _  and D e n s i t y  /2g  p-  ( A P =  c  equation  AP7^  1-^g  _  equation  ReOR  =  0 80564  R e p 7T D2H4  0.24209  i n . Hg.) /JL =  1.231  cp  p  0.795  g/ml  =  1-3  0,1875/12 1 231x6  4  / 6 4 . 3 4 8 x 1 9 . 6 x 7 0 . 7 2 7 x 6 2 . 4 3 x . 795  7197xlO  -  4  0.9917915  V  3 9 90 7  = From  19.6  measured at 210°F  from  R C Q R / C  D_2  C  =  (Figure 2).  27 cell  W -  inches  1-4, (39,907)° _. 2 3 , 8 5 2  lbn/sec  9  7  x  1  8  2  =0  80564  (29,606) =  3 1 4 1 6 x '1875/12 4  x  23,852  1.231  x  6 7197 x  10"  4  1-15  Average Tb  =  bulk  Tbin  +  temperature Tout  =  i n test  221.. ° F . p=  section  (Table  3-II, Appendix  0 - 7 9 1 g/ml ^ =  1.415  (Figure  1-3)  r  cs  2  U  b  = _W p  Re  = U^D  _ A  0.2421  _  7.63  ft/sec  (Appendix  3) =-- 1  0.. 7 9 1 x 6 2 . , 4 3 x 6 . 4 2 5 x l 0 =  ~V~  7. ...633?043,43 2:1,2  =  - 4  14,319  1.415x.03875 3600  These  data  are l i s t e d  i n Table  3-1  ?':• I..  3)  1-16  Scale Figure  1-2.  C a l i b r a t i o n Curves Cell ( 0 - 2 0 , 0-50, range) .  Reading f o r Tube D i f f e r e n t i a l Pressure 0-100 a n d 0-150 i n c h e s w a t e r  I-i /  Figure  1-3.  Kinematic of  Oil  A.  Viscosity  and  Specific  Gravity  2-1  APPENDIX  a)  2:  CALCULATION  Determination  The  power  Power  o f the heat  dissipated  = Volts  x Amps  where  <J) i s t h e p o w e r  leads  the voltage.  the  accuracy  was  purely resistive  is  then  Q  A  portion  and  lost  This  =  where  t  The  =  2  loss  T  R  L  alternating  watts  the angle  at three  (2-la)  by which  power  the current  levels  instruments 1) .  current i s  showed  (0.5%)  The h e a t  the  that  within  circuit  generated  i n the  tube  by  3.413  x Volts  will  i s given  x Amps  be  insulation  a plot  film  BTU/hr  conducted  (2-lb)  through  by n a t u r a l  the  insulation  convection  and  radiation.  [^] ]}  (">  by  {^(Ta-T^)  the temperature  outside  COEFFICIENT  flux  cos(|j)  (cOsC|) =  i s the temperature  extrapolating The  x  to the surroundings  outside  suring  Tests  THE HEAT TRANSFER  an  factor,  of the heat  heat  Qloss  by  o f the measuring  given  total  OF  +€CT  [[13_] -  i n °R,  4  and R  temperature a t two  radii  4  i s the radius  T^ was  determined  i n the pipe  o f l o g ( r / R ) v s T t o r/R =  coefficient  for natural  2  2  in by  feet.  mea-  insulation, 1  (Figure  c o n v e c t i o n was  and  2-1). calculated  2-2  by  (31)  h  where  Q  =  Dp  0.5  <T =  asbestos  j °-  - Top  3  i s the outside  Inserting for  |~ T  0.1713,  pipe  R =  2 5  (2-3)  diameter  0.12 5 F t ,  ( r e f e r e n c e 31,  i n inches L = .1.932  p. 484)  into  (Dp = 3 . 0 ) . f t . and  equation  2-2,  € =  0.93  one  ob-  tains  Q  loss  =  12-135  |  (0.0475) ^ - T ^  J  '  1  2  5  *  ] -[ 00 ]  0.019995^3  4  t  (2-4) Heat  losses  at four  temperature  measured  insulation equation  Qloss  heat  for  which  and  =  °-  that  Qliq  AT  =  w  6  2  = Qua A  5  T  w  passes  m  "  1  5  plotted  situated  the heat  t  o  t  a  plane  tube  ( F i g u r e 2 - 2 ) , and  an  l  5  i n the p o r t i o n of the  i s then  _ Q  l  o  s  s  )  (2-6)  is  T  the  loss:  '  B  wall  at which  2  to the l i q u i d  ( Q  versus  < ~ )  6  i s calculated  flux  were  i n t h e same h o r i z o n t a l  to estimate  49.1 58.95  the heat  q  levels  thermocouples were  fitted  The  power  < -7)  U  2  (hr)(ft ) 2  tube  4  jj  2-3  where  inside  area  corrected  by  factor  equation  2-7.  b)  the  Inside  The outside  the  Tube W a l l  inside values  wall using  for  a  long hollow  and  an  adiabatic  of  the  tube,  0.1742  49.1/58.95  f t  in order  2  , must  to  also  yield  A  be  for  Temperature  temperature the  solution  cylinder outer  was  with  surface  of  calculated the  uniform  heat  from  the  measured  conduction  equation  internal  (equation  2-14d  heat  of  generation  reference  ln (2-8) for  r  i  n  =  0.1715  representing Stainless  k  The  =  -  T-  in  by  the  +  u  =  =  t  0.1875  linear  QLIOUID  of  +  the  appropriateAT  m  equation  the  x  tube  (34)  (Figure  wall  0.0033884  0.00455  Mean  1.945  BTU h r ft°F  T  across  8.45  i n . , L ,=  conductivity data  0.00455  drop  Determination  The  Q  thermal  8.45  temperature  T,o u t  c)  the  steel  wall  in,, r  type  2-3)  (2-9)  then  becomes.  (2-10)  T  Temperature  i s given  of  f t . , and  by  Difference  304  33):  2-4  AT, m (22) dTb  The  integral  location, suming  a  linear T  squares  and  and  solved  correcting  fitting  3  was  14  to  then  evaluating  f o r the  increase  - T^  w  by  at each  w  across  the  i n T-^ w i t h h e a t e d  a quadratic  integrating  (Figure  drop  T  thermocouple  tube w a l l ,  length,  and  equation in length  analytically  by  between  by by  least  thermocouples  7).  Thus  x  .dTb. T  w  Tbout  -  T  E  b  C  2  T bi'-n "i n / X-/ i  n  dX  n ax^  +  +i  bx  (2-11) where For  b  a, 2  <  b,  and  c  are  the  least  square  f i t coefficients  4ae, *2  Integral  =  _2  t n a  ./lac  -  b  ^  2ax </4ac  2  +b -  I b  2  (2-12)  J  X  For  b•  >  4ac, x  Integral  =  1 yb -4ac 2  In  2 ax  + b  -  2ax  +  4-,/b^-4ac  b  A/b -4ac  as-  2  2  X  n  (2-13)  d)  Sample  The  Calculation  computer  calculations  program  that  i s appended.  The  run  27.  i)  Calculation  Voltmeter Ammeter the  500/5  2.675 From  Q =  reading  =  amp  267.5  equation  3.413  x  o f Heat  =  =  amps.  current  used  sample  routinely  f o r these  calculation  i s done f o r  Flux  reading 2.675  was  11.2  volts Correcting  transformer,  t h e ammeter  actual  current  =  reading f o r 500/5  x  amps. 2-1,  11,2 x  the heat  267.5 =  generated i s  10,225.4  BTU  (2-15)  hr The 3  average w a l l a n d 14,  temperature  excluding  i s calculated  thermocouple  12 w h i c h  between gave  thermocouples  consistently  low  values, T  A  V  =  (354,4 + +  =  385.7 +  374,2  The  heat  and  14  3678  +  369,6 +  380.1 +  365,5 +  381.3 +  °F,  lost  373.2 +  377,6  385.9)/ll. (2-16)  through  i s given  375,2 +  the i n s u l a t i o n between thermocouples  by equation  2-5.-  3  Heat  loss  =  0.625  (274.2)  -  156  =  233.9  -  156  =  77.9  BTU hr  (2-17) The  heat  Heat  to  transferred liquid  =  to  the  49,1  liquid  (10225.4  -  i s then 77.9)  =  8451.9  BTU  58.95  hr (2-18)  The  heat =  flux  ii)  .  Calculation  sample  Appendix  reading  the  8.15  42,915 +  millivolts  =  42.915 +  338.69  =  354.42  The  thermal  equation  ^wall  The  =  ^'  Drop  Through  millivolts,.  -  x  41.557  2  Tube  f o r thermocouple  equation f o r thermocouple  ^ = out  (2-19)  hr f t  i s done =  BTU  ~  of Temperature  calculation  1  58,254  =  (49.1)/(|8.95)  Potentiometer  T  becomes  8451.9 0.1742  The  then  From  Wall  3. Table  I-IIa,  3 is  - 0.40932  (millivolts)  2  27.19  °F.  (2-20)  conductivity  of  the  tube w a l l  is calculated  from  2-9.  4  5  +  ° -  temperature  0  0  4  5  drop  5  (354.4) =  across  the  10.06  BTU hr  tube w a l l  (2-21) ft°F i s then  found  from  equation 2-10  T  out  " in T  =  as,  Q l  1 Q U I X 0.0033884 _ 8451.9 (0.0033884) _ 2.87 10.06 10.06  °F.  D  (2-22)  T  = 354.4 - 2.9 = 351.5  i n  °F.  (2-23)  C a l c u l a t i o n s are repeated f o r each of the e l e v e n  iii)  C a l c u l a t i o n of  A.T  thermocouples,  m  The equation f o r the b u l k l i q u i d  temperature  is,,assuming a  l i n e a r i n c r e a s e w i t h heated l e n g t h ,  T  = ^outlet binlet 58.95  x  T  = 231.9 - 210.7 58.95  +  T inlet  x  +  210.7  = 0.359627 x + 210.7  where x i s the heated  (2;-24b)  l e n g t h of the tube i n c e n t i m e t e r s .  of Tb o u t l e t and T^ i n l e t are taken from Table 3-1, A  T  x  _  4  >  8  5  c  m  _ 1 . 7 4 4 + 210.7  w  The measured l o c a l (T  w  The  (2-24a)  temperature  Appendix 3.  = 212.44 °F.  d i f f e r e n c e i s then,  - Tt,) measured = 351.-56 = 212.44 = 139.12 °F. l e a s t square  f i t of T  w  Values  - T^ w i t h length i s found to be  2-8 (T  - Tb) c a l c u l a t e d = -0.010389 x  w  2  + 0.76306 x + 140.15 (2-25)  At x = 4.85, the c a l c u l a t e d l o c a l temperature d i f f e r e n c e i s (T  - T ) c a l c u l a t e d = -0.24437 + 3.7008 + 140.15 = 143.61°F.  w  b  The  i n t e g r a l i n equation 2-11 i s then,  Integral  t  =  .x  2  dx ax2+bx+c  J xi  53. 95 _C dx -0.010389 x2 + 0.76306 x + 140.15 J 4.85 (2-26)  The  discriminant,  b - 4 a c = 0.76306 2  Since the d i s c r i m i n a n t given by equation 2-13. ^/b - 4ac = 2.53106. 2  2  - 4(140.15)(-0.010389) = 6.40633  i s g r e a t e r than zero, the i n t e g r a l i s The square root of the d i s c r i m i n a n t i s At x = 53.95, Numerator = -2.88896,  Denominator: = 2.17314. The  upper l i m i t o f equation 2-13 i s then,  Upper l i m i t =  1 l n 1-2.888961 2.53106 I 2.173141  =  0.39509 l n (1.3239) = 0.112383  At x = 4.85, Numerator = -1.86876, Denominator = 3.19334 The  lower l i m i t o f equation 2-13 i s then,  Lower l i m i t = 1 2.53106 The  total  ln  -1.86876 | 3.19334  _ 0.39509 l n (0.585205)=-0.211689  i n t e g r a l i s the upper l i m i t minus the lower l i m i t ,  T o t a l I n t e g r a l = 0,112383 - (-0.211689) = 0.32407. The  computer program y i e l d e d a value of 0.32416.  The b u l k  2-9  l i q u i d temperatures  at the upper and lower l i m i t s are found  from equation 2-24b.  (x = 53,95) = 0,359627 T  b  (53,95) + 210.7 = 230.10 °F.  (x = 4.85) = 212.44 °F., c a l c u l a t e d  The mean temperature  difference  above.  i s then found by s u b s t i t u t i n g  the necessary values i n t o equation 22,  AT  The  m  -  230.10 - 212.44  = 17.66 = 151.53°F. 0.359627 (0.32407)  computer program y i e l d s A.T = 151.47°F. m  An  independent  check o f the i n t e g r a t i o n was made by determining the area under a plot of T  1 versus T^ by counting the squares. w"Tb  This g r a p h i -  c a l method y i e l d e d  AT  m  = 152.5°F„  The mean heat t r a n s f e r c o e f f i c i e n t i s then c a l c u l a t e d by equation 21,  58,254 151.53  _  384,4  BTU/hr-ft  2  These data appear i n Appendix 3, Table  - °F,  3-III,  2-10  e)  Test  Runs  Sections  44  a n d 4 6 w e r e made w i t h  respectively, thermocouple on  I I and I I I  which  had s l i g h t l y  positions  the integral  were  (Table  also  Section  Test  Section I I I  The  II).,  of test  areas  The u p p e r  I I and I I I and  different  and l o w e r  Limit  Upper  Limit  5.0  58.1  4.55  58.3  sections  I I and I I I a r e g i v e n  below  r  -Hg KDimension  (cm)  Test  Section II  a  66.4  Test  Section III  67.1  b  59.1  59.4  c  46, 9  46.2  d  5,7  5.7  e  2.0  ,2.3  f  2,1  2.2  3.2  3.2  0.1740  0.1750  Inside  area ( f t  2  )  limits  different.  II  dimensions  sections  different  Lower Test  test  2-11  Figure  2-1.  Estimation  of Surface  Temperature  of  Insulation  2-12  Figure  2-3  Thermal  Conductivity of  Stainless  Steel  Type  304  2  COMPUTER  PROGRAM C  I I  1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 40 41 42 43 44 45 46 47 50 51 52 53 54 55 56 57 60 61 62  223 10 149 111  3 7  444 555  1  -13  TO C A L C U L A T E H E A T T R A N S F E R C O E F F I C I E N T S  CORRECTED P R O F I L E S AND C O E F F I C I E N T S DIMENSION Z ( 2 0 0 ) , T ( 2 0 0 ) , T C O N ( 2 0 0 > , C O R ( 2 0 0 ) , T C ( 2 0 0 ) DIMENSION X ( 2 0 0 ) , Y ( 2 0 0 ) , Y F ( 2 0 0 ) , T B ( 2 0 0 ) R E A D ( 5 f 2 2 3 ) ( X ( I ) ,1 = 1 , 11) F0RMAK8F10.5) READ(5,10)N,M,NI FORMAT(315) READ(5tlll)RUN»FNP FORMAT(2F10.5) NP=FNP DO 4 8 4 L = 1 , N P READ(5,7)TIME,VOLTS,AMPS,DPT F0RMATKF10.5) ATEST=0.1742*49.1/58.95 I F I R U N . L T . 1 3 . 8 ) GO TO 4 4 4 AMP=AMPS*100. GO TO 5 5 5 AMP=AMPS*240. CONTINUE Q=3.413*V0LTS*AMP QDIS=49.1/58.95*Q READ(5,1)(Z(I),1=1,24) F0RMAK8F10.5) T( 1 ) = 4 3 . 0 8 8 + Z { 1 ) * ( 4 1 . 5 0 1 - . 4 0 0 6 3 * Z ( 1 ) ) T(2)=49.386+Z(2)*(40.405-.342 53*Z(2)) T(3)=42.915+Z(3)*(41.557-.40932*Z(3)) T(4)=41.517+Z(4)*(41.854-.41836*Z(4)) T(5)=42.331+Z(5)*(41.636-.40749*Z(5)) T(6)=43.565+Z(6) *(41.317-.3857?*Z(6)) T(7)=43.185+Z(7)*(41.404-.3912 2*Z(7)) T(8)=43.078+Z(8)*(41.361-.39282*Z(8)) T(9)=47.872+Z(9)*(40.37 7-.33106*Z(9)) T(10)=43.102+Z(10)*(41.365-.38766*Z(10)) T(ll)=43.394 +Z(11)*(41.359-.38^45*Z(11) ) T(12)=43.080+Z(12)*(41.497-.40308*Z(12)) T(13)=41.519+Z(13)*(41.906-.42814*Z(13)) T(14)=40.961+Z(14)*(42.062-0.4367*Z(14)) T(15)=42.959+Z(15)*(41.423-.3979*Z(15)) T(16)=46.292 +Z(16)*(40.272-.34193*Z(16) ) T(12)=T(13) T(13)=T(14) T(14)=T(15) T(15)=T(16) T(17)=34.363+44.191*Z(17) T(18)=32.22 7+Z(18)*(46.560-.92456*Z(18)) T(19)=38.055+Z(19)*(32.939-.04098*Z(19)) T'(20)=37. 1 0 6 + Z ( 2 0 ) * ( 3 3 . 2 5 8 - . 0 5 6 6 4 4 * Z ( 2 0 ) ) T(21)=35.712+Z(21)*(33.248-.06C34*Z(21)) T(22)=36.611+Z(22)*(33.203-.053612*Z(22)) T(23)=36.842+Z(23)*(33.109-.048376*Z(23)) T(24)=36.982+Z(24)*(33.101-.04755*Z(24))  —•  2-14  63 64 65 66 67 70 71 72 73 74 75 76 77 ICO 101 102 103 104 105 106 107 110 111 112 113 114 115 116 117 120 121 122 123 124 125 126 127 130 131 132 133 134 135 136 137 140 141 142 143 144 145 146  C  456  C  157  751  " ,  47  C O R R E C T I O N FOR LOSS THRU I N S U L A T I O N ST=0. DO 456 1 = 3 , 1 3 ST=ST+T<I) CONTINUE TAV=ST/11. QL0SS=0.625*TAV-156. QF=QDIS-(QL0SS*49.1/58.95) QW=QF/ATEST TC(1)=T(1) C O R R E C T I O N FOR DROP THROUGH TU EE WALL DO 157 1 = 2 , 1 5 TCON(I)=8.45+0.00455*T(I) COR(I)=QDIS*0.0411755/(2.*3.14 16*1.940*TCON(I)) T C U )=T( I ) - C O R ( I ) CONTINUE DO 751 1 = 1 , 1 1 TB( I ) = ( T ( 2 2 ) - T ( 1 9 ) ) / 5 8 . 9 5 * X ( I ) + T ( 1 9 ) K=2+I Y(I) = TC(K)-TB( I ) CONTINUE SY=0. SX1=0. SX2=0. SX1Y=0. SX2Y=0. SX1X2=0. SSX1=0. SSX2=0. DO 47 1 = 1 , N SY=SY+Y(I) SX1=SX1+X(I) SSXI=SSX1+X(I)*X(I) SSX2=SSX2+X(I)**4 SX1X2 = SX1X2 + X{I )**3 SX1Y=SX1Y+X(I)*Y(I) SX2Y=SX2Y+X(I)*X{I)*Y{I) CONTINUE FN=N SX2=SSX1 B=SSXl-((SX1**2)/FN) C=SX1X2-SX1*SX2/FN D=SX1Y-SX1*SY/FN F=SSX2-((SX2**2)/FN) G=SX2Y-SX2*SY/FN B2=(D*C-G*B)/(C*C-F*B) B 1=(D-B2#C)/B B0={SY-B1*SX1-B2*SX2)/FN AA=B2 BB=B1 CC=BO VV1=2.*AA*53.95+BB VV2=2.*AA*4.85+BB DISC=BB**2-4.*AA*CC  2-15  f  147 150 151 152 153 154 155 156 157 160 161 162 163 164 165 166 167 170 171 172 173  373  374  IF ( D I S C . G T . 0 . 0 ) GO TO 373 RMDIS=SQRT(-1.*DISC) AREA1=2./RMDIS*(ATAN(VV1/RMDIS) ) AREA2 = 2 . / R M D I S # ( A T A N ( V V 2 / R M D I S )) GO TO 3 7 4 CONTINUE RDIS=SQRT(DISC) . ' . . VV3=ABS( { V V 1 - R D I S ) / {.VVl+RDIS ) ) VV4=ABS{(VV2-RDIS)/(VV2+RDIS)) AREA1=1./RDIS*AL0G!VV3) AREA2=1./RDIS*ALOG(VV4) AREA=AREA1-AREA2 DTM=58.95/AREA*(TB(11)-TB(1))/{T(22)-T(19)) H=QW/DTM R=1000./H WRITE(6,727) ( T C ( I ) , 1 = 1 1 5 ) , T ( 1 9 ) , T I 2 2 ) , H , R , T I M E FORMAT(IX,17F6.1,1X,F8.ItlX F8 .3,IX,F6.1) CONTINUE GO TO 149 STOP END 1  727 484 234 $ENTRY  t  3-1  APPENDIX  Table  3-1  calculated heat  values of Reynolds  coefficient,  set  thermal  3-II l i s t s  coefficients  and  resistance  terminal  13  not  used  i n the thesis  for  funs  6 and  runs  34  test  on b l e n d s t o 44  liquor.  lower  electrical  on  Run  43 w a s  due  ( i t i s thought)  next  I I was  run. A  Test  legend  tube  heat  wall  transfer  temperature. f o r each  run, along with  the heat  transfer  the sand  21 w a s  runs  22  17.  discarded  because  which  runs  33  through  on  o i l B,  4 6 was  section  shutdown f o l l o w e d i t was  used  f o r r u n 46.  below. temperature,  °F  3-1  done  damaged  and  on  at the shutdown.  was  destroyed,  by burnout.  then  of Tables  rates  14  of trouble  the test  on  were  fouling  Runs  Run  done  l e d t o o v e r h e a t i n g and  done when  I I I was  these  though  system.  f o r r u n 44,  liquid  from  water  t o pump  section  experiments  for initial  i n Figure  o f o i l A,  partially  used  Results except  appear  f o r the headings  TB=average b u l k  initial  velocity,  profiles  proper,  terminal  Run  section  only  average  rates,  r u n and  temperature  sections.  7, w h i c h  Kraft  and  are the p r e l i m i n a r y  two  and  flow  f o r each  resistances.  5 through  done  mass  flux  and  wall  f o r each  the  20 w e r e  heat  DATA  conditions  number,  losses,  the inside  o f measurements  Runs  EXPERIMENTAL  contains the operating  generation, heat  Table  3:  during  Test the  3-II i s given  3-2  VISK = "kinematic v i s c o s i t y at TB, c e n t i s t o k e s RHO = s p e c i f i c g r a v i t y at TB RE = Reynolds number W = mass flow rate, lb/second UBULK = b u l k v e l o c i t y ,  ft/second  Q = heat generated, BTU/hr QLOSS = heat l o s t through i n s u l a t i o n , BTU/hr QW = heat f l u x t o l i q u i d ,  BTU/hr-ft  2  TWOUT = o u t s i d e average w a l l temperature, °F TWIN = i n s i d e average w a l l temperature, °F DTM = A.T  m  HC = c l e a n tube-heat t r a n s f e r c o e f f i c i e n t ,  BTU/hr-ft  2  °F  ^  1000 RO = 1000/HC TWC = clean tube i n s i d e average w a l l temperature, °F DTMC =  T  m c  TIN = l i q u i d  i n l e t temperature, °F  HM = mean heat t r a n s f e r c o e f f i c i e n t ,  BTU/hr-ft  °F  1000 R = 1000/HM TIME = time from s t a r t o f run, hours  Table 3-III i s a comparison  of the c l e a n tube o i l heat  t r a n s f e r c o e f f i c i e n t s w i t h values p r e d i c t e d by the S i e d e r - T a t e equation.  3-3  Table  3-IV  experiments, 32. the  Data  contains  and t h e d e p o s i t  from  a few  differential  Table  3-IV,  deposit  liquids.  DELP  thickness  Table  the pressure  3-V  runs  pressure =  drop  thicknesses  are missing cell  pressure  were  drop  data  f o r the  estimated  because  from  range  equation  springs f o r  not y e t a v a i l a b l e .  i n inches  fouling  o f water,  In  and X  =  in millimeters.  contains  the data  on  particulate  levels  o f the  TABLE  3-1.  RUN "5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Oil B 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. Wftter 34. 35. 36. 37. 38. 39. 40. 41 . 42. 44. Kraft 46.  Oi 1 A  Liquor  OPERATING  VI SCK  2 2.0. 5 1.49  2 21.3 218.0 218.0 219.0 217.0 220.0 219.3 216.0 215.8 215.3 214.4 216.0 215.6 214.5 215.3 216.4 216.0 216.3 222.0 217.0 221.0 219.0 21 7.0 218.0 223.5 220-2 219.2 146.0 144. 5 142. 2 144.7 143. 1 144.7 144.3 149.1 143.5 144. 7 155.2  1.49 • 1.50 1.50 1.50. 1. 50 1.54 1.50 1.52 1. 52 1 .55 1.57 1.55 1.58 1. 55 1 .58 1 .49 1.49 1 .49 1.41 1.46 1.42 1.44 1.43 1.40 1.36 1.39 1 .40 0.45 0.46 0.47 0.46 0.46 . 0.46 0,46 0.44 0.46 0.46 0.76  RHO 0. 794 0. 794 0.793 0. 793 0.793 0.793 0. 794 0. 794 0. 794 0.794 0. 795 0.796 0. 796 0.795 0 . 794 0.795 0. 79 5 0.795 0.793 0.793 0.794 0. 791 0.79 1 0.79? 0. 792 0.789 0. 790 0.790 0.962 0.982 C.983 0.98? 0. 982 0.98? 0.98 2 0. 980 0.98? Q.9S2 1.080  CONDITIONS  W 0.3621 0.3621 0.3621 0.3621 0.1781 0.5413 0.0922 0.17R4 0.1781 0.1784 0.54^2 0.5421 0.3123 0.31?4 0.77P4 0.77^1 0. 1503 0.1503 0.?4?4 0.24'5 0.2424 0.24 21 0.2421 0.4770 0.17 78 0.2419 0.2419 0.24 19 0.1920 0.3866 . 0.54 7 0.3105 0.1722 0.2613 0 . 1 4 70 0 . 1722 0.3870 0.3105 0.35S8 c  AND C L E A N  UBULK  RE  20263. 11.37 11.37 20263. 20153. 11.38 20153. I 1 . 38 9914. 5.60 30125. 17.02 4993. ?.90 5.60 9951.1 5.59 9768.1 9787. 5.60 17.04 29200. 28699. 16.97 16746. 9.77 9.80 16468. 41874. 24.44 41061. 24.43 4.72 8185. 7841. 4.71 13575. 7.62 7.62 14356. 13845. 7.61 14322. 7.63 14122. 7.63 27883. 15.02 10617. 5.60 7.64 " 14968. 14581. 7.63 14481. 7.63 28570. 4.87 56665. 9.82 78534. 13.84 7.88 45809. 24961. 4.37 38388. 6.64 21547." 3.73 26430. 4.38 56218. 9.82 7.88 45809. 28909. 8.31  TUBE  0 15543. 15260. 12324. 12 324. 5942. 16112. 4176. 6877. 4216. 4180. " 10578." 10587. 6948. 6948. 1392 2. 13922. 3744.' 3744. 5541. 12048. 7654. 10225. 8703. 15364. 6681. 12166. 8763. 8746. 7532. 12539. 16633. 10818. 6928. 9785. 6326, 12718. 12207. lOTSS. 6500.  HEAT  QLOSS  TRANSFER  ow  89. 88711. 89. 87093. 70391. 61. 63. 70382. 60 . "'33764. 63. 92132. .23611. 63. 71. 39070. 31. 24025. 31. 23815. 29. 60557. 28. 60615. 3 9709. 31. 30. 39713. 30. 79751 .. 29. 7^758. 31. 21314. 31. 21312. 31636. 30. 94. 68624. 43655. 49. 78. 58252. 64. 49596. 87838. 63. 3 799 7. 62. 48. 69281. 63. 49940. 62. 49848. 43236. 0. 71979. 0. . 95484. 0. 0. 62102. 39773. 0. 56170. 0. 0. 36313. 0. 73010. 70072. 0. 0. 61657. 0. 41262.  COEFFICIENTS  TWOUT TWINS 393. 391. 348. 350. "346. 350. 350. 362. 300.. 300. ?96. 294. 299-. 298. 297. 295. 299. 299. 298. 400. 329. 374. 351. 350. 348. 406. 351. 349. 176. 173. 174. 175. 172. 174. 173. 200. 174. 1.70. 175.  388.2 387.2 344.5 347.0 343.9 345.5 348.7 360.5 298.5 298.8 29P.6 291.4 29^.3 296.4 293.5 291.4 297.6 29?.2 296.6 396.6 32* .6 37!.4 348.8 34 5.4 346.6 402.7 348.6 34f .8 173.7 169.6 169.3 17?.2 17C.0 171.4 171.5 196.3 170.2 166.0 172.3  DTK 168.5 166 .9 124.8 131.0 127.0 127.0 129.3 142 .6 85.9 32.5 78. 1 77.1 81.9 81.2 78 .9 76. 1 82 .2 8 3.0 -81 .2 176 .4 I'lO .7 151.5 131 . 1 129 .6 129. 1 131.0 1 29 . 7 128 .9 26 .9 28 . 1 27.9 27 .9 27.4 27.. 1 27 .0 48 .2 27. 1 23.5 19.4  HC  1000RO  526. 6 522. n 563. 9 537. 3 265. 8 725. 7 182. 6 273. 5 2 79. 7 288. 8 775. 8 7S6. 1 485. 0 439. 0 1010. 3 1048. 3 259. 3 256. 8 389. 5 389. u 394. 2 384. 6 378. 3 677. 8 294. 2 382. 8 385. I 386. 8 1604. 4 2 5 59. 1 3426. 6 2224. 8 1451. 3 2071. 5 1343. 0 1516. 2 2588. 1 2626. 212 8 . 6  1.8991 1.9159 1.7733 1.8612 3.7623 1 .37 8 0 5.4763 .3.6562 3.5747 3 . 4 6 24 1 . ?G90 1.2721 2.0617 2 . 04 5 1 0.9898 0.9539 3. 8564 3.8937 2.5672 2.5707 2.5369 2.6002 2.6435 1.47 54 3.39 8 8  2.6124 2.5970 2.58 55 0.62 3 3 0.3908 0.2918 0.4495 0.6890 0.48 27 0.7446 0.6595 0.38 64 0.38 07 0.4700  3-5 TABLE  3 - I I . I N S I D E WALL T E M P E R A T U R E S RUN 5.  M 0.362  RE 20263.  OW 88711.  AND F O U L I N G  TWC .388.2  DATA  OTMC 168.5  TOUT T(l) TI21 T(3) TI4) T<5> TI6) TI7) TIB) T (91 TI10) T(U) TI12J T1131 THAI TU5I TIN 1 208.7 232.3 235.7 3 75.3 396.1 364.2 3 7 3 . 6 384.7 3840 3'9"l';5 460. 6 392. 8.391.1 3*9.4551.6 74.0 397.1 384.9 373.3 384.8 384, C 391,8 399, 9 391,8 391.6 399.5 363.0 7 210.6 234.6 206.0 315.6 3 7 398.8 3B5.4 373.0 85.3 3840 393.2 404. 0 393.2 395.4404.0 384.0 4_210.8 234.9 208.0 316.7 373. 381.9 415.0 401.9 369.7 3 1 210.2 232.4 " 0 426 5 417, 0 425.6433.2 401.7 207.3 324.9 4 99.5 401. 50 413. 6.0 442.2 430.7 422.0 32 8 209.9231.9 207.3 335.5 40 2 463 2 456. 1 467.5474.8 424.1 6.5 4367 446. 7 209.9231.9 206.1 338.5 13.4 450. 440.0 433.4 4 456, 7 475 1 467.9 488. 429, 4 3 * . B 445 4 8 0 . 4 1 209.3231.3 342.3 423.2 459.6 450.2445.0 444.2 456B 467 8 487.8 48) 0 495.5504.7 438.3 Tor 452.8 450.8 465 .6 4 74.T 497, 0 491, 2 507.Z516.4 442.4 1 209.9231.5 205.7 345.0 429.7 466.5 456. 1 4 7 210.2 231.'3 61.0 457.0 473 0 482.3 505. 1 499 6 515.5 525.8 445.9 206.5 347.3 435.3 471.5 462.8 47 5 492, 0 515. 539. 1 4 4 6 . 6 4 209.1 230.3 0 . 1 4 6 4 . 8 4 8 3 5 511, 4 528.1 3 4 9 . 5 4 4 3 . 4 4 8 0 . 4 4 7 1 . 6 205.0 4 206.9 229.7 205.4 352,3 448.3 486.1 476.1 475.2 469.5 489. 0 497. 1 521.4 517. 8 535.6547.8 449.9 266.5  HM 526.6 533.2 528.9 468.5 394.6 376.6 354.9 343. 7 334. 0_ 322.6 315.4  10100.89R9 0.0 .6 1.676 0 !•>_  2.134, 3.1 2.534 4.6 2.655 512 2.8lB 5T7 2.910 6.2 2.99*_ 6.8 " 3^100 "" " 7.3" 3.171 7.9 -  TWC 367.2 DTMC 166.9 TH) 206.9 207.7 208.0 208.3 207.7 205.7 206.8 206.5  TI2) T<3) T(41 T!5) T16) TIT) Tl a 1 T(9) T110) T(ll) T(t2) T(13> TI14) T115) TIN TOUT HM 1000 R 9.3 382.4 245.7 210.0 232.5 522.0 1.916 314.5 369.4 394.8 382.0 372.4 385.1 383.1 392.3 397.7 393.439390.1 3 9 9 . 7 383.1 2 4 6 . 6 210.5 2 3 3 . 0 521.5 _1.917_ 314.8370.3 396.2 383.7 373.2 386. 1 384.C 392.6 398.1 393.2 389.8 2 383.1 247.1 210.3 232.9 ~'526.6~ 1.921 30 90 1.4 315.7371.3 396.5 383.1 373.5 385.9 383.1 393.2 397.9 392.9 4 520.2 1.923 392.4384.3 245.8 210.4 233.1 316,8371.0 396.2 383.3 372.2 386.1 383.6 394.0 398.7 392.7401.5 4.3994.3 587.4 244.5 209.6 232.3 516.5 1.936 317.1369.9 395.2 363.3 372.0 385.8 383.4 394.9 399.3 393.4 20 4. 12 7 . 84 30.0 403.8 241.8 208.2 229.8477.8 2.693 321.4374.1 398.2 384.1 378.2' 391.9 392.3 405.2 414.8 409 4 5 7 . 7 417.7 241.9 210.5 231.6 4 3 5 .2 2.298 329.2387.8 412.1 406.1 397.4 406.9 411.2 423.5 437.2 443433..36 487. 1 432.9 239.8_207.9 228.7_ _3B5.7 2.593 333.B405.7 431.1 426.2 419.4 <.25.3 434.7 445.6 461.2 45 48 7. 26 .Q TWC  344.2  Till T12) T(3I T(4) TI5) T(6) T(7J T18) TI9) T(10> T(ll) ril2I TI13I TI14) TU5) TIN ! 2211.8 8.9 206.1 289.' 289.3 3 331.4 350.0 3 48.99 343 347.1,8 3351. 54. 0fl\922226. 1 34 42 1. .9 0 341.7 : .0 352.1 7 3345, 3 1 . 0 5^ 9 345 .3 353.' 340.5 243.2 208.9 225.4 559.4 1.788 206. 287.' 330.9 346.1 338.7 330.0341.0 5 345, 350. 63 344. 352. 347.6 347 ,7 355-' 344.8 243.2 210.5 227.7 557. B 1.793 206. 290. 332.7 350.8 341.0 332.4 343.5 0 347, 205, 7 290.1 331.6 352.2 341.0 333.0 344.9 C 350. 353. 6 349. 8 347 ,0 356.1 347.4 244. 1 209.1 226.2 547.4 1.827 207. 1 ,290.'3 1 3514 352. 3 348.7 349 .1 358.! 351.2 242.8 210.8 227.B 555.8 ' 11..7 99 2.0 350.7 340.2 331.5 343.1 207. 1 291.! 33 7 355 355. 4 351. 3 354 .7 365.' 357. 242.8 210.3 227. D 538.: 858 33.3 351. 342.4 333.9346.3 1.907 ~T 5 T 5 292. 334.5 355.2 343.7 3 3 3 . 2 349.8 4 361 7 359. 7 357. 1 361, 3 375 9 365.1 243.2 2 1 0 . f i 2 2 7 . 5 5 2 4 . 3 364, 1 371, 8 387. 6 374.7242.6 209.5 226.1 494.5 2.022 205. 7 292,9 337.3360.5 349.0 338.1 356.1 8 366 6 367.28 364. 5 373, 9 375.7 243 209.2 226.6 492.9 2.029 205, 8 29?,2 338.1 359.9 349.2 337.5355.1 0 366 6 369. 365. 5 374 89 390, 59.5 348.5 335.7354.2 392. 6 375.3242.8 210.8 22B.3 499,4 2.003 206, 9 291.5 337.63 1 366 6 369, 48 365, 60.5 349.0 336.4355.6 392 375.7 243.2 209.5 226.1 491.9 2.033 206. 9 290.9 336.63 9 368, 6 366 8 375, 2 367. 3 6 0 . 8 3 5 5 . 4 397 37B.4 243.2 209.7 226.2 467.2 2.052 206, 1 290.9 337.4 350.0 336.63*5" 370 3 371 63TT 353.0 3 5 373, 374. 5 37T 9I 379. 385. 4 0 3 . ; 376.5 243.2 2 t 0 . 2 2 2 7 . 0 478.3 2.091 -2 T T 1 290 ,5 339.3 3368.8 39.4 363. 1 206. 5 293 ,3 341.9 356.9 342.4 7 3 790 381.0 379 6 397. 416.' 389.4 243.2 2 0 9 . 5 2 2 5 . 9 456.5 2.191 206. 9 295 ,8 344.83 7 2 . 0 359.6 345.6366. 1 2 382, 3 386.4 365. 0 404.. 423.! 393.1 235-1 210.3 2 2 7 . 1 ' 447.3 2.236 205, 7 294 ,7 345.33 7 3 . 0 •360.2 346.0366.3 6.7 234.7 2 0 9 . 7 2 2 6 . 6 440.9 2.268 9 384, 1 387.7 337, 0 410. 430.1 39 207. 2 294 ,7 343.1 3 7 2 . 6 360.2 346.0366.8 98.3 33.6 2 0 9 . 7 226..5 436.0 2.283 7 385, 1 369.0 389. 6 414. 435.' 3 205. 9 294 ,7 345.43 7 4 . 4 361.5 347.9 367.3 399.4 2 1 421. 233.3 2 0 9 . 5 2 2 5 . 9 429.0 2.331 3 386, 3 391, 7 393. 444.' 208. 298. 3 346.8377.1 364.1 35019 371.6 0 392.4 399.1 403.6 436.3 460.1 406.02 33.6 209.5 226.1 413.8 2.416 208. 04 298 66.9 354.4372.8 3 396, 1 405.2 416.0 455, 3 488.4 418.6 233.6 210.2 226-8 401.0 2.494 48.533 86 03 .. 50 3 206. 9-298.73 3 3 7 1 . 8 3 6 6 . 9 3 5 5 . 4 0 416.7 9 464. 2 497. 2 33.3 209.9 226.2 394.6 2.534 3 5 0 . 3 f 396, 409.2 421. 4 477. 2 513. 206, 300 5 352.73 6 6 . 7 372.0 360.7178.7 8 403.8 417. 232.6 210.3 226.T 380.2 2.630 7 432. 207, 299. 4 349.9384 366.9 357.9373.8 7 400, 415. 7 433 6 481 0 517.2 423.1 232.2 210.0 225.7 383.6 2.607 2.649 1 403, 1 422. 5 443.2 496. 537, 2 429.4231.B 210.3 226.2 377. 206. 1 298, 351.0 384.5 369.6 359.6374.6 431.7 231.0 209.3 225.0 366.2 .2.716 207, 5 300. 8 354.1 385.2 369.4 360.9376.5 5 406. 4 426. 7 452.7 508. 550. 95 422.1 39.8231.4 210.5 225-_B_ _ 356-B _2iB03_ 206, 7 299.4 353.1 390.5 373.8 366.6378.5 0 412, 8 <>3a. 5 466.2 528.5 573, 50 44 4 7 . 5 2 3 1 . 8 206, 3 301. 7 357.6393.6 378.6 370.6380.6 210.5 226.8 346.7 2.884 1 418. 4 446. 9 476.5 543.7 592, HUN 8.  W 0.362  KE 20153.  OH 70382.  TWC 347.0  TIME 0.0 10 1. .3 8 2 24.5 26.6 28.9 30.3 33.4 36.3 43.8 52.5 55.6 59.3 66.1 69.9 73.5 75.9 79.7 83. 6  DTMC 131.0  fill T<2) T(3) T(4) TI5) T16) TI7I U8) T(9) TUOJ Till) 7(12) T ( 131 TI 14) T(15) TIN TOUT HM 1000 R 0 284. . 326.0347.1 338.7 328.0 341.0 340. 1353.6 356.1 355.0 347. 8 383.6 346. 4 230, 7 208,4 224.8 537.3 1.861 207. 1 288. 330.7 350.8 34?. 7 332.4 345.6 344.7 359.6 362.0 361.3 354, 1 391.3 352, 4 233.3 211, 0 226.3 528.0 1.894 325.6 348.9 341.7 329.4 342.6 342.? 355.5 358.8 357.1 346. 4 388. 1 350.3 232. 0 209. l_225.7 533.2 1.675 206. 3 284. 3 9.2 349.3 341.8 330.0 344. 1 342.3 356.6 360.0358.4 349. 2 390, 0 352.3 232. 9 210, 1 227.3 533.2 1.876 206. 9 286. 32 1.3 351.6 343.4 332.2 345.9 344.9 59.7 363.1 361.6 354, 0 394.7 356. 6 234.0 210.9 227.5 523.8 1.909 208. 0 269.1 33 29.2 349.6 342.4 330.9 344.3 342.6 3 62.2 24.9 1.905 207. 1 286. 33 5B.7 3 352. 2 394.9 357. 3 232. 7 209.9 226.4 5 0.4 352.0 344.7 332.4 347.3 344.23 368.9 361.6 511.9 68.9 355. 3 403. B" 366.2 233. 3 210. .953 ~2OT: 76 287. 3 3 0.7 351.7 344. 7 332.2 347.2 344.fi 365.5 73.2 3 508.8 1 367.3 3 372.5 357. 0-407. 369 .1 80 1 211, .965 2 B 7 . i 3 3 1 . 3 352. I 3 4 5 . 2 3 3 2 . 3 3 7 3 . 0 3 4 6 . 8 3 4 5 . 0 505.5 1 207. 7 286. 332.7 353.3 347.0 332.4 346.7 345.4 367.0 375.9 372.5 356. 3 407. 369 5 233 3 210. 1.976 4 9 6 . 4 206. 1 2B7.< 3 7 5 . 7 357, 4 233 2 210. 3 6 9 . 0 2 . 15 5 411. 3 7 2 53.5 347.3 333.2 350.2 346.2371.5 376.8 378.3 356, 4 412. 372 1 232 5 210. 94.0 .0 206. 3 267. .331.8 3 024 54.2 348. 1 333.6 352.2 347.2 373.2 379.6 363.4 358. 4 417. 375 6 232 9 210, 2 227.7 4 490.0 2 207. 6 287. 331.6 3 2.041 3 5 4 . ? H e . 4 3 3 4 . 5 3 9 3 . 3 3 5 3 . 3 3 4 6 . 9 4 8 0 . 9 2 2 2 7 . 0 207. 7 286. 331.3 356.5 351.0 336.4 355.4 350.6 375.9 368.6 386.5 354. 9 420,.5 37B, 9 232 .9 209. .079 473.4 2 32.7 357.1 351.2 335. 3 354.7 350.3 360.6 390.5 393.7 364. 8 430.2 386, 4 234 ,2 211, 0 226.5 •467. 207. 5 287. 3 2.112 32.3 359.4 352.0 335.7 355.1 351.0 382.4 390.5 396.4 363, 0 429,.8 384, 9 232 .9 209, 2 226.7 465.5 207. 3 266. 3 .139. 2 2 33.8 359.1 351.5 336.6 356.3 352.7 382.1 393.1 396.6 360, 9 429,.5 384, 9 233 ,0 209, 7 227.4 460.9 206. I 267. 3 2 .150 205. 7 286.' 334.1 399.5 .363.2 431. 8 385.5 233 .0 209, 6 226.4 384.0 2.170 1 227.6 7 226.2 3 225.9 TWC 343.9 DTMC. 127.0.„ 2 226.0 "To?;  8 tir;o~  0.0  1.9 7.4 20.B  23.6 37.7  44.9  !  TIU TI2) T < 3 > TI41 TI5) TI6) TI7) T(8) T(9) TUO) Till) TU2] TI13) T(l'4) T (15) TI TN DUT HM 1000 R TIME 205.4 8 318.8 337.! 338. 7 331.! ,1 .341.9 350. 352. 352. .6 354. 362.6 330.7 0 209.5 227.0 265.8 3.762 3 340.4 349. 350.1 351. 2 353.1 362.0 330. 2_ 0 210..5 227.3 270. 2_ 3.700 205.8 6 318.2 336.: 336. 7 3 30.] 67.1 3.744 6.1 334. ,3 209. 4 341. 5 349. 351. : 351. .4 354.' 362.0 329.2 205.4 B 318.04 334.' "2 261.9 3.819 337.: 337. 51 330.1 67.8 333.3 ,6 206.29 222255-.7 , 1 359., 3 4 .5 205.7 9 316.4'33 5 343.6 351. 352.1 353. 259.1 3.860 13 8.' 337, 6 3332.' 370.1 332.9 .1 207..9 31.E 7 342. * 350. 352. ! 354. 6.7 204.2 9 317,2 334. 356. 55 361. 335.9 ,4 2 1 6 .,6 222274. 4.4 260.1 3.644 1 7 340. 3 6 7 . 1 0 3 7 3 . 9 7 320. 2 333.^ 2 3 4 5 . 6 352..7 3 5 3 . ' 19.4 266.5 354. 2 6 0 . 2 7 338. 3 3 3 . 6 , 1 209. 1 338. 9 366.: , 3 226.1 4 344. 6 3 3 3 . J 3 350. , 6 351.' 3 . 8 4 4 ' 5 318. 2 3 7 2 . 3 2 3 . 6 205.4 8_ 1 366.:3 373:9332. 52.1 356. 338. 5 332.< .7 344. 7 350.,,57 3 5 227.3_ -22*517..33- -3.827_ 26.1 206.2 8 319...49 337, 338.86 339. 333.2 56 210. 2.1 357. , 7 372. 209. 319.,3 339, 7 335.( 1 345.7 351.,3 3355 2 3 7 6 . 5 , 9 2 2 6 . 8 3 . 6 8 7 2 9 . 6 205.8 65 320. 334.9 ,6 209,.6 226.8 253. B 3.909 . 9.6 0 340, 5 335.' 4 346. 6 352. 3. 357. ,6 373, 5 378.73 205.0 6 340.0 340. 1 334.' .6 346. 3 352.,6 354.16 357. 8 379.4 34.6 ,5 209.,6 226.6 254.'9 3.922 2 33.2 205.7 91 3 320. 360..14 373, 2>.l"- 31.5 3.976 3 2 2 . 6 341.6 342. 6 3 3 7 . ! 4 346.6 354.0 355.6i 359, 380. 1 363.6338.5 210.,,22 2 6.5 566.5 0 340. 3 37.7 66 211. 227.4 2 S 353. 3 321. 6 3 3 6 . < 9 379. 8 347.5 355.6 354.6 372. 1 340. 3 383.334 3.931 38.7 2 5 4 i 4 205.9 3 . 1 , 9 ^ 2 2 6 . 7 7 337. 4 340.1 343.6 343.! 6 355. .3 413.3 414.0 345.5" > 209.,1 225.6 " _238.3 ' 4.193 >5.2. 206.1 95 322. 321.0 342.6 349. 1 349.3 5 365.0 365.0" 363.1 365.9 432,6~429,9 354.6 .2 209. 224.6 .465 204.8 1 381.2 376.6 377.6 409.0 458.2 454.9357.2 4 210.0 226.8 207.8 4 322.0 345,6 355.7 361.1 .812 206.5 66 321. 99.6 4 5 347.2 359.2 366.t .59 391. 4 385.2 386.8 423..6 472.0 465.1 360.0 5 210.2 227.3 1 i.oit 205.8 399. 1 9 3 . 5 . . 5 434. , 4 4 7 3 . 2 3 320, , 7 347, 2 362. . 0 3 7 2 . 1 , 3 390. . 3 3 9 5 . , 1 210. . 4 2 2 7 . 6 .8 462. 5 478.7361.6 206.9 5.167 .0 403..9 395.. 189.3 .5 348. 4 363.,8 374.' .1 489, 05.7370.5 .1 210.,5 227.1 320.,,58 355. 263 205.4 26 321, ,9 431, 8 425,,7343401. 66.7 . .2 394.: 7, 274 443. ,4 225.8 1 462,.0 526,.,43 5516.6 .999 206.5 372.5 ..30 209, .2 449,,6 444,,5 458, 159.0 5 356. 91 379. 210. . 2 2 2 6 . 7 504, 384.,7 404.' . 4 548, 6 .290 63.1 320,.,93 357. 3 7 3 . 6 206.5 .48 319, • 6 453. 155.a 0 5 2 4 . 5 . 4 465, . 5 2 2 5 . 7 , 1 '512, 5 4 0 7 . 1 557. 5 209. 6 . 4 9 2 386. 2 448. . 206.1 .7 320,.3 356, 5 389. 153.6 ' .51 9 4476. 7 1,4 , 526 '226^7 "1 09 85.6 7 4 5 8 . 3 453,, 67.9 533.3 376.6 232.6 ,.15216, 7.S 264.2 35B, 390. F8T T413T i 4402 fl 226.7 51.3 "6 ,3 525 .17 5 6.609 969 .9 456...9 0 5 5 6 9 . 9 5 3 7 . 9 3 7 5 . 9 2 3 2 . 6 210. 8 462, . 6 204.6 9 321,,.85 360. 483. • 2 _ 2 2 _ 6 . 7 .765 394. 7 419 409 4 469,, * 464, 2 534 9 579.2 544.5 377.8 232.6.,27102 ,26.7 _147.B 6 205.7 9 321, .833 96.1 541 5 584.7 548.7 377.1 233.2 210. 46.4 6 Ml 3 473. 1 468..5 488,,.40 551 0 321, 360, 395. 20S, 227.7 1 6.996' 101.9 399. 79 421 142.9 427 416 8 461,,7 475,..26 4496, 1 322. 364, 4 395.0 556.9 379.4 232.6 .•12211,2 205, 9 9 , 2 3 . 8 7 . 089 1041 400. . 2 552 141. 363, • ' 6 477. 321 1 429 418 0 484, 2 597.2 557.2 379.5 232.0 . 620?.2 2 V . 1 . 205. 5 427.4 418.B 485,4 477,.8 560, 141.6 7.661 104.6 7 599.8 539.0 380.5 233.1 211, 206.1 265.7 322.1 364.7 400, 1  3  RUN 10. W 0.541 RE 30125. OH 92132. TWC 3*5.5 DTMC 127.0 Til) T12) Tl 3) TC) T(5) T(6) T(7) TI8 » T(9) Tt 10) T C11 T >( 12) T(13) Tl 14)Tl 15) TIN TOUT HM 1000 R TIME 206.4 296.0 330.6 354.A 340.5 325.8 344.3 340.4 352.4 351.0 346.6 351.2 363.5 338.4 233.2 210.8 227.2 725.6 1.378 0.0 206.2 295.6 330.2 353.3 340.3 325.9 343.5 340.1 352.6 350.1 346.5 351.7 363.2 339.1 23?. 121Q.5 226.5 724.3 1.361 0.9 207.3 295.1 330. 1354.0 340.2 325.1 343.5 340. ?353.2 349.1 346.5 351. 1363.0 338.6 232.2 2L0. 7226.3 725.0 1.379 2.4 209.2 295.8 329.8 354.0 340.7 325.4 342.3 341.0 354.2 349.8 346.0 351.1 362.7 337.5 231.7 210.7 226.1 723.8 1.382 7.1 207.3 295.4 328.4 354.4 340.2 325.0 343.7 341.7 355.4 350.4 346.9 351.5 362.8 338.6 232.0 210.1 225.7 718.6 1.392 9.9 208.5 294.7 329.7 353.6 339.6 325.6 343.3 341.f 355.3 349.7 346.0 350.8 3&32 . 337.6 232.1 210.3 725.3 719.6 1.390 17.7 206.5 294.0 328.6 353.1 .338.8 324.7 343.3 340.'8 355.4 349.3 346.2 350.2 362.5 337.2 231.4 208.6 224.3 714.5 1.400 20.9 207.2 295.3 330.6 353.7 339.7 325.8 344.5 343.0 357.4 350.9 348.2 351.8 364.3 339.3 231.9 209.8 225.1 711.3 1.406 23.9 207.6 293.B 328. 7 352. 3 330.6 325.1 343.1 341.3 355.4 549. 1 346.3 549.5 362.8 338.0 236.2 209.5 224.8 718.7 VTW[ 36.4 207.3 294.3 329.2 353.1 338.5 325.1 343.2 341.? 355.9 349.7 346.4 350.4 362.9 338.1 230.7 209.6 224.8 716.7 1.395 29.9 207. 3 293.B 329.1 352.4 33B.B 324.7 343.3 342.1 356.3 349.6 346.3 351.0 362.8 338.0 231.7 210.7 226.5 724.5 1.380 33.9 208.0 294.4 329.4 353. 1 330.8 324.9 342.7 341.8 356.4—349.0 345.9 350.2 362.5 337.7 231.7 210.5 226.0 723.7 1.3B2 41.2 209.4 295.5 329.6 353.5 339.2 325.4 343.5 342.2 356.7 350.0 347.1 351.1 363.4 339.1 231.8 210.3 225.7 718.4 1.392 45.2 206.5 294.7 329.9 353.3 338.7 325.6 343.8 342.'- 356.8 350. 1 347.5 351.6 363.7 339.4 232.5 210.0 225.3 715.4 1.39B 49.2 207.6 294.8 330.3 353.9 330. 7 325.0 343.5 343.4 357.9 351.0 347. <) 351.8 364.1 '339."62"32.2 2t0.3 225.7 715.3 1 .398 5275"" 207.6 294.0 328.8 353.2 340.5 325.2 343.1 343.3 358.1 350.3 347.6 351.3 364.1 338.3 231.9 711.1 226.6 720.9 1.387 57.5 20B.0 295.6 330.6 353.2 340.0 324.4 344.9 343.7 358.? 351.0 348.7 351.3 363.7 338;9' 230.8 209.4 224.5 708.2 1.412 64.9 207.7 295.1 330.2 353.7 339.7 325.2 344.3 343.1 358.1 351.0 348.3 352.0 364.2 339.4 231.4 209.B 225.1 711.0 1.407 69.1 208.6 294.9 330.6 353.9 339.5 325.4 344.4 343.3 357.4 350.2 347.9 351.1 363.5 339.8 231.3 209.7 224.8 708.9 1.411 73.1 V±* - ?! Z ?7.6 33B. 1 324.1 342.8 341.1 357. 1 349.6 347. 3 350.5 362.5 338.0 230.7 208.6 223.B 708.6. 1.411 77.3 205.7 293.3 329.7 353.0 339.0 323.6 343.8 343.1 356.3 349.6 346.4 350.1 363.5 339.4 229.9 208.8 224.2 709.5 '• I'.Vto Bl.9 205.9 293.1 329.fl 353.0 339.7 324.5 343.4 343.? 357.4 .349.8 347.0 350.8 364.0 339.5 230.5 209.4 224.9 710.6 1.407 B9.1 206.7 293.9 329.7 354.4 339.6 325.1 343.8 343.4 358.8 350.8 347.8 351.5 364.4 339.5 230.7 209.0 225.0 706.5 1.412 93.6 207.6 293.9 329.8 353.3 330.4 324.1 343.1 342.5 357.5 349.7 347.3 350.4 363.2 339.2 230.9 209.7 224.9 713.0 02 208.0 294.7 330.5 354.6 340.0 325.8 344.8 343.6 358.2 349.6 348.7 352.5 365.0 340.4 231.7 210.2 225.4 709.2 1..44 10 103. £UO.U * T t . ( J . J J i J t . O 3 1 V . <J 9£ 1 • O 3*t*».d J t j . O Jff.O 371.3 3*t-VJ . £31*1 £ 1 M . I d d 3 . *t I VI t £ 1 • <t 1 U 208.0 294.7 329.9 353.2 338.5 324.5 343.5 342.9 357.6 350.1 347.7 351.2 363.7 339.5 231.2 2p9.9 225.3 712.8 1.403 106. 206.7 294.2 330.2 354.0 339.4 325.3 344.5 343.3 358.7 350.3 348.7 351.9 365.2 340.9 236.9 209.9 22S.2 708.2 f".4'12 TTTTv 207.7 294.3 330.3 353.1'338.6 324.1 343.5 342.9 358.5 349.7 348.1 351.2 364.2 340.2 230.7 209.4 224.7 709.2 1.410 116.9 208.0 294.3 330.3 353.8 339.8 325.0 344.5 343.6 359.7 351.9 350.1 352.9 366.0 341.5 232.5 210.7 225.9 711.4 1.406 120.4 -  ml  9,  3  "RUN TT.  V) 0.092  RE. 4993.  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T(12) T113) T(14> T1 15) TIN TOUT H M 1000 R TIME 205.7 276.0 334.3 357.5 357.7 351.4 361.5 362.3 369.8 366,2 365.6 365.4 374.3 351.2 331.7 209.6 228.9 273.5 3.656 0.0 205.8 277.9 336.5 357.8 357.2 550.9 361.2 362.3 369.6 366.8 365.6 366.6 376.7 356.1 266.4 209.4 228.8 272.5 3.669 1.3 206.3 278.4 337.8 358.9 358.6 352.B 362.2 362.1 369.4 367.3 364.9 367.fl 377.8 356.3 267.8 210.6 230.B 274.4 3.644 3.9 207.3 279.5 337.B 359.0 35T.6 351.7 360.8 362.3 405.1 367.0 368.0 360.9 378.B 358.8 268.8 209.B 230.6 265.B 3.762 7.7 206.0 279.8 342.6 363.0 361.1 358.0 363.3 367.g 379.8 378.0 380.3 387.5 411.4 367.8 265.9 210.3 230.1 255.3 3.917 U.7 276.1 1st I? 395:i 412.1 427> 40!*.8 452.6 462.7 492.1 4I3U 519.8 541.9 407.1 2S5,V 265.9 22H.2 TCTTl 57977 TBTTT 207.3 277.5 350.7 410.1 431.8 452.5 420.3 478.fi 484.9 515.4 514.4 525.8 554.fl 416.9 258.4 210.3 229.4 155.3 6.440 19.9 205.4 275.3 358.4 418.3 441.8 463.5 427.8 491.4 493.0 513.3 527.5 533.2 570.7 422.2 259.1 209.0 228.1 148.0 6.758 21.0 204.2 276.3 364.4.430.7 453.0 477,8 437.0 510.4 501.2 524.I 536.9 550.0 589.3 428.7 259.1 208.4 227.5 139.9 7.150 22.0 206.3 276,8 366.1 435.3457.1 482.8 440,6 513.3 503.7 525.1 537.9 554.3 595.6 430,2 259.1 209.6 228.9 138.8 7.205 22.5  3-7  RUN  Til)  Tl?)  13.  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T W C 297.3  0TKC 81.9  T i n — r m — T m — f r o — r r n — m n — r m — m n — T I M T t IO> T i m TI 121 T J U J r n o TI 15)  v  mr  TUTT?  1000 «  HM  TTM?  206.8 262.2 289.7 ?97.R 292,8 269.6 297.1 294,P 299.6 304.5 301.0 300.9 302.8 309.1 261.3 210.0 222.1 485.0 2.062 0.0 208.3 262.5 290.3 258.6 293.6 290.0 206.9 295.* 300.4 305.3 301.8 301.3 303.5 310.0 261.7 210.6 222.9 485.7 2.069 1.0 206.9 261.8 289.4 298.?. 294,1 209.6 207.0 295.f 299.6 304.6 299.9 301.4 303.8 310.7 261.6 210.7 222.2 485.8 2.059 4^0 207.1 261.8 289.0 29R.1 293.4 288.4 ?96.0 294.? 298.3 304.3 299.7 300.0 302.5 308.0 260.2 209.6 221.6 487.2 2.053 7.0 2UU.0 263.1 ^90.1 294./ 290.2 2-W.7. 2^.6 301.5 305.9 301.8 301.3 303.5 312.6 264.9 210.2 221.6 479.5 2.086 1576" 209.2 264.5 291.6 299.9 ?<5.3 290.7 297.4 296.2 302.2 306.0 301.8 301.3 303.0 313.8 264.9 210.1 221.6 476.6 2.09B 19.0 208 .6 264 . 7 292.3 3C0.4 ?oh.7 201.3 298.1 296. *l 303.9 307.4 302. 7 302.2 303.2 315-3 264.0 209.7 221.4 469.8 2. 129 24.3 207.7 262.9 293.2 301.0 2^7.0 200.9 298.7 297.^ 304.0 308.6 302.8 302.3 303.5 316.1 263.1 209.8 221.7 468.3 2.135 29.8 2C8.0 264 .4 29*.5 302.1 79H.1 290.9 2°R.9.208.? 306.2 310.8 303.5 303.0 303.0 319.1 265.1 209.7 2 2 1 . 6 462.9 2. 160 39.0 208.8 264.0 295.2 3C&.1 299.4 29V.2 301.1 300.2 3C7.7 311.3 303.6 3D4.5 303.4 320.7 267.1 210.9 222.5 461.6 2.165 42.1 ZCB:0"~2'5Vn~795V2 3Ci.? 7 ^ " , / 7m.2 13013 . 300. * i 09 .'9 "TIT. 5~37fc". 1 30571~30~372~ 322 - 2 269.6 ZIO.b Z7.2.1 4 b b . 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S _2_9b. 0 _3Q6,8_i9_7 , 4 3 14 ,8_ 3 70 . 4 31 1.4 311.5 307.3 327.2 265.6 209.2 220.7 422.6 2.366 116.8 208. 1 267.5 300.4 309.0 305 .'0 297. 2 307. 2 307 .8 316.8 321.5 313.5 311.4 307.5 330.3 269.6 210.4 221.9 423.8 2.360 122.8 208.4 267.6 300.3 309.5 305.7 298.5 308.3 303.9 317.8 322.3 314.3 312.7 308.3 332.3 272.2 211.2 222.7 427.2 2.368 132.1 2C6.5 265,5 798.8 310.7 30^.8 297.4 308.4 308.5 317.4 321.7 313.7 313.1 306.5 330.7 263.2 210.6 222.3 421.4 2.373 138.3 207.7 267.6 300.3 30O.9 305.7 298.7 308.1 308.7 317.6 322.0 313.8 312.6 308.1 329.3 266.4 210.1 221.7' 417.9 2.393 144.7 208.6 266.4 301 .6 309.-1 3C6.0 293.4 306.2 308.T 317.7 322.4 314.7 313.0 308.2 330.3 268.2 210.5 221.3 417.6 2. 393 156.2 267. 3 267. 1 3G1 . 3 309.9 3C0.ti 298.6 308.6 309.5 3 17.3 322.4 313.6 313.3 308.6 331 .5 269.3 210.9 222.2 419.3 2.335 162.7 208.e 269.1 302.0 311.3 306.4 290.0 309.0 309.0 318.0 323.2 314.7 314.0 309.2 330.0 264.4 210.fi 222.1 416.3 2.402 170.3 207.7 267.6 30C.8 310.7 306.5 298./. 307.4 309.' 317.9 322.4 314.5 313.3 306.2 331.2 266.9 210.1 221.2 415.5 2.406 180.6 2C7.7 267.6 3C1 . 4 310.6 305.9 790.6 308.0 309.? 316.6 323. 5 314.4 31 3. 5 308.9 .332.2 26B.~9 210.2 222.2 417.8 2.394 186.6 208.4 268.7 301.5 310.0 305.° 29B.8 308.3 309.? 317.6 323.5 315.0 314.0 309.1 333.3 271.1 210.8 222.3 417.8 2.394 193.8 208.9 26H.9 302.1 311.1 306.1 299.6 308.3 309.8 3IB.4 324.1 315.4 314.2 308.8 333.3 270.9 210.9 222.3 416.4 .2.401 205.1 268.9 269.1 301.9 311.7 306.1 290.3 308.7 309.1 316.8 324.2 315.4 314.0 308.1 332.6 267.1 210.4 221.7 413.9 2,416 219.8 208.9 269, 8 307 . 3 3.1 1 .7 306,P 299.,6 308.3 310.1 318.7 324.7 315.6 314. 1 308.8 332.3 268.5 210.8 222.3 415.2 2.408 229.7 208 .0 260. H 302 .8 31 1 .3 307, 1 299.5 308.6 310.7 318.4 324.4 315.4 314.4 306.9 333.3 271.4 210.7 222.4 414.7 2.412 236.7 208.0 269. 1 3C2.1 311.6 3C.2 3C0.4 308.3 310.4 310.4 324.2 315.6 314.4 308.8 332.8 269.6 210.4 22l\7 412. B 2.423 242.8 208.4 269,1 307.4 311.7 307,7 3C0.4 303.6 310.5 318.6 324.4 315.8 314.6 308.8 332.3 267.8 210.6 222.2 413.7 2.417 252.6 20B.4 768.4 301.3 317.1 307.3 208.2 308.7 310.7 318.4 323.9 315.7 314.1 303.4 332.3 267.8 209.7 221.1 410.7 2.435 7.56.8 206. 4 269.b 302.6 312.6 307,2 2?9.? 309.6 311.? 3 19. 5 324 .3 3 l6.2 314.6 369.0 332.5 268.2 210. 2 221.6 4T677 2.438 266.6 . 2C8.0 266.8 302.3 312.4 307.7 3C0.4 308.6 311.4 318.4 374.9 315.8 314.9 309.1 3*3.6 269.0 210.0 221.1 408.B 2.446 27t>.6 2C7.3 268.4 302.1 312.2 307.0 3C0.3 309.4 311.4 318.4 324.7 316.6 314.8 30B.4 3 3 5 . 3 271.4 210.6 222.8 414.3 2.414 284.1 208.0 270.0 302.9 312.8 307.4 3C0.9 309.2 311.9 319.0 325.4 317.0 315.6 309.5 335.7 271.1 210.8 222.3 410.7 2.435 291.1 206.5 270.5 303.9 313.1 307.7 301.0 308.6 311.? 318.6 325.4 316.6 314.8 308.9 335.9 274.3 209.9 221.2 407.5 2.454 300.£ | 208.2 270.3 304.2 312.0 307.5 301.5 309.3 311.7 318.2 326.5 316.3 315.1' 309.5 335.6 275.1 210.5 221.B 409.1 2.444 308.7 208.6 270.4 361.5 312.7 3o7.7 306.5 368.7 311 .8 318.3 325.5 316.9 315.3 510.6 334.4 2/1.1 210. 3 221 .U 47J9T3 27T4~1—3T470" 208.1 270.0 303.3 313.0 307.4 3C0.5 308.2 312.0 318.1 325.3 316.9 314.9 309.7 333.5 268.5 210.3 221.8 409.8 2.440 324.5 ,  ,  -  1  HUN IB.  W 0.312  RE 16468.  QW 39713.  T W C 296.4  DTWC 81.2  Till Tl?) TI3> T(4) T(5) T<6) T{7) TIB) T(9) TIIO) Till) T112) T(13> Tl14) TI IS) TIN TOUT 207. 8 261 .? 288.0 296. f, 297 . 6 2PR.3 296.1 204.7 299.4 303.0 300,3 300. 1 301 .0 311 .4 262.7 209.9 221.6 207.6 261 .4 288.4 296.b 293.3 289. 0 797. 1 295. 1 299.5 304. 5 30 1 . 2 301 .2 303. 5 312.8 265. 1 21 1 . 1 223. 1 207.6261 .4 289.4 799.7 2^4.ii 290.3 297.8 235. 7 299.3 364.3 301.6 3 6 2 . 2 304. 1 315.2 267.4 209.5 2 2 o . 9 209.0 262. 7 2 O 0 . 4 239.7 2^5.8 240.6 298.9 291.0 300.5 306.0 302.5 303.3 306.2 316.2 269.3 211.3 22?.8 208.9 263.6 20Q. 1 290. fj 29<-.0 2-.0.7 297.9 296. 301 . 2 305.7 302. 1 302.7 305.6 316.5 269.4 210.8 222.6 2C9.3 262.9 289.0 29d.0 294.7 2 0 0 . 0 298.4 296.r 301.7 304.9 303.0 303.0 305.2 317.2 269.2 210.2 221.8 206.4 2ft?.7 ?89.3 290.3 294.6 290.1 708.1 297. * 302.3 306.5 303.5 302.9 305.3 317.7 ?66.3 210.0 221.6 207.8 2bi.fi. 208. 5 300. 2 295.6 ?89.fl 297.3 297.0 301.9 305.9 303.2 302.9 305.6 316.2 264.5 210.2 221.9 208.0 262.3 289.2 299.7 2*5. 2 290.0 297.8 296. 6 301 . 5 365.9 3 0 3 . 2 3 0 3 . 1 305.6 319.3 266.3 2 6 9 . 2 2 2 1 . 2 208.8 263.0 ? ; o . l 300.3 295.6 290.6 298.3 297.r 301.7 306.3 303.8 303.6 305.3 320.0 268.0 209.7 221.4 c  RUN 19.  W 0.770  RE 41874.  OW 79751.  THC 293.5  H M 1000 R TIME 489.0 2.045 0.0 490.9 2.037 0.6 476.4 2.099 276" 480.6 2.081 4 . 0 490.3 2.082 6.0 476,5 7.099 11.0 473.3 2.113 23.0 475.2 2.104 29.0 47077 77174 3T7o" 470.3 2.126 45.8  DTMl 78.9  Til) T12) T13) T(4) T(5) T16) T(71 TIB) T(9) T(101 TIU) T(12) T (13) Tll4> TI15) TIN T PUT H M 1000 ft TI ME 209.1 273.6 287.7 301.0 289.2 282.0 292.7 268.1 295.7 302.7 296.1 294.9 297.4 300.0 234.6 211.9 221.5 1036.1 0.965 0.0 208.8 273.3 28B.3 301.9 28B.6 2-81.6 ?92.6 288.9 295.2 302.9 296.2 296.3 298.6 300.3 234.4 209.9 219.3 1004.4 0.996 0.5 208.8 273.6 289.I 301.o 28B.9 281.6 292. 1 289. 1 295.3 303.2 296.6 296.7 299.8 301.2 235.7 209.9 219.4 1002, 5 0.997 1.3 209.2 273.5,0 9 288.9 301.5 289.1 2-81.6 292.6 289.1 294.5 303.4 295.3 296.5 300.2 301.9 236.4 209.9 219.5 1004.6 0.995 3.3 IZ g - 289. 3 282.5 292.7 289.6 296.3 304.0 296.5 297.3 300.9 303.2 237.2 210.3 220.1 1001.6 0.998 6.5 208.8 274.4 289.9 302.9 289.9 282.6 293.9 290.7 296.5 304.7 296.5 29B.0 301.2 364.6 '237.0 210.0 71978 991.2 1.009 T T T T 208.0 274.3 290.6 304.6 291.6 283.1 295.1 291.« 299.6 305.3 298.3 298.4 301.5 305.3 236.2 209.6 219.1 969.6 1.031 21.8 209.5 275.7 292.1 305.4 29?.8 284.2 296,1 291,? 300.2 305.B 298.5 298.9 301.2 307.4 738.3 210.0 219.7 968.5 1.033 26.9 209.9 276.3 292.4 306.6 292.8 284.7 295.8 291.5 300.3 306.2 299.4 299.2 302.3 306.9 237.2 210.1 219.2 962.0 1.039 31.9 208.4 273.7 292.5 306.5 292.5 284.3 295.9 291.5 300.3 305.7 298.7 299.9 302.6 308.4 233.2 210.0 219.B 966.5 1.035 36.4 209.7 275.8 292.8 307.0 292.9 2-65.5 296.4 292.1 301.1 307.5 299.2 300.1 303.1 309.1 236.7 209.8 ?19.4 954.4 1.048 46.6 209.1 274.7 291.7 307.1 3 0 3 . 5 284,2 296.5 291.3 299.8 307.0 298.7 300.2 307.9 309.6 239.8 209.3 219.1 955.3 1.047 53;1 209.3 276.0 293.0 307.1 294.4 285.6 296.5 292.5 301.0 307.6 300.4 300.7 303.7 310.3 240.6 210.0 220.0 953.4 1.049 59.6 209.6 276.0 293,6 307.1 294.2 265.9 ?9?.2 292.7 301.8 308.1 300.8 301.1 303,8 311.6 243.B 210.3 219.7 949.9 1.053 69.6 209.1 275.5 293.0 307.3 295.0 285.2 297.7 292.8 301.8 307.6 300.1 300.5 304.0 309.8 236.7 210.5 219.9 953.4 1.049 75.9 210.0 276.7 294.4 308.0 295.0 287.1 297.9-293.5 302.3 308.6 301.5 302.0 304.7 311.6 239.6 210.5 220.1 944.2 1.059 83.4 210.1 276.6 293.6 307.5 294.8 286.8 298.0 293.3 302.4 308.6 301.2 301.8 304.7 311.3 239.4 210.6 270.0 945.9 1.Q57 93.9 209.6 275.5 292. 5 307,8 295.4 286.0 297.8 292. * 301.7 307.9 300.5 300.9 303.9 3l LVo 239.8 209;7"Tl"97l 9"42"8 .' 1.061 99~79~ 209.0 276.1 293.2 307.5 295.0 286.0 297.2 293.1 301.9 308.6 301.0 301.0 304.3 311.8 241.6 209.8 219.4 942.3 1.061 137.1 209.5 277.3 293.9 307.5 295.'3 286.2 297.2 293. 1 302.4 308.3 301,2 301 .4 304.3 311.3 240.2 210. 1 219.7 944.3 1.059 117.9 209.7 276.2 293.6 308.2 2^5.3 2B6.0 298.1 293.0 302.1 307.7 301.9 301.4 303.5 311.4 240.2 210.6 Z20.3 949.9 1.053 123.9 209.9 276.9 293.9 308.? 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 B  (  :  3-10  DTMC  76.1  Q H 79758: Til).  712)  T131  TIM  206.4 272.0 285.9 297.7 209.4 273.3 287.3 298.2 2 0 8 . 6 2 T 1 . 5 161.6 2 9 8 . 6 209.6 272.5 287.0 299.9 209.1 272.9 287.1 299.4 209.6 273.3 286.9 300.0 2 0 9 . 5 .273.6 2 8 8 . 2 3 0 0 . 0 208.8 272.9 286.9 299.8 209.8 274.T 266.6 306.6 209.9 274.2 287.7 300. 7  T l 51  TT 6)  286.3 280.5 285.9 280.6 2 4 6 . 3 2-S6.7 286.6 260.9 286.5 261.2 287.3 281.4 286.2 281.7 287.7 282.1 "2T8T4~~58"276~ 3 282.3  TI7). 291.4291.2 291.2 292.1 292.4 293.3 293.0 2931.2 293.5 297.9  T(8> 287. 288. 567. 288. 288, 289, 289, 289. 269. 289.  TI9)  HID]  Till)  TI1Z) T113) TI14)  TI15)  TIN  4 293. 1 293. 4 293. 4 294.0 C 2 9 3 .8 0 295. 0 1 295.4 1 295. 2 5 295. 2 5 296. 0  300. 9 301. 0 300. V 3 0 1 .4 301.5 3 0 1 .4 302. 303. 303. 303.  294.0 294.0 294.1 294.9 295.5 295.0 296.6 296.1 296.5  292.7 293.5 293.6 294.7 294.5 295.3 295.3 295.6 295.1 295.2  299.0 299.1 300.1 300.1 300.5 301.1 301.5 302.0 3o2.4  234.3 234.3 231.9 234. 1 234.3 236.1 234.6 235.9 238.3  302.6  238.3  210.8 210.5 209.5 209.6 209.9 209.9 209.9 210.2 210.3 210.2  TWC  Tit).  TI21  TI3I  T14)  206.' 208., "ToX 206. 210. 211. 211. 210. 210.7 210.3 211.2 210.7 211.1  258.0 259.9 260.! 260.6 262.9 262.4 264.1 262.0  283.1 264.8 285.1 264.4 268.3 288.6 290.7 291.0 240.7 290.7 292.5 291.9 292.5 292.9 293.2 292.5 292.1 293.1 292.9 292.1 293.6 295.6 295.0 295.4 292.9 295.2 295.8 294.7 293.9 297.2 295.4 297.2 296.5 296.8 296.5 297.9 297.9 •299.1  294.5 295.6 296.4 295.7 297.5 298.3 P99.1 300.2 E99.9 299.9 300.8 300.1 300.3 301.7 301.2 299.6 300.6 299.9 300.5 301.9  ill  241.6 262.0 264.7 264.2 264.9 264.9 265.3 262.8 264.8 266.0 266..7 C6B.6  211.1 209.9 211.2 211.1 211.1 211.2 21S.4 271.9 I l » . 9 274.4 214.1 274.0 214.9 274.8 2 1 4 . 9 2175.1 216.4 B76.S 2 1 6 . 0 S76.'6 213.8 272.9 214.1 273.7 217.2 277.9 214.1 275.9 216.6 279.1 115.7 278.8 115.3 277.3 216.5 280.2 217.9 263.4 220.2 286.4  302.3 302.8 302.1 302.1 301.7 303.5 303.5 303.5 302.8 303.6 702.4 303.2 302.8 303.4 303.2 305.2 304.4 304.6  TI5)  TI6I  TI7]  TIB)  TI9)  295.2 292.2 298.2 298.2 301.2 2 9 6 . 2 2 9 2 . 9 2 9 9 . 4 299.3 3 0 2 . 5 296.2 293.3 299.6 2 9 6 . 6 3 0 1 . 4 296.6 292.4 296.1 298.2 301.0 297.9 295.5 301.3 299.7 303.1 296.3 295.8 301.4 300.6 303.2 2 9 9 . 4 2 9 7 . 0 3 0 2 . 4 301.9 304.6 300.5 297.4 303.0 302.6 305.2 300.8 E H . 7 303.0 303. ! 305.0 300.5 296.4 303.8 303.7 305.3 301.6 299.2 304.1 304. ? 306.1 301.2 299.1 304.1 303.7 305.7 301.2 299.1 304.1 304.4 3 0 5 . 7 301.2 304.4 305.7 301.4 299.1 304.1 299.8 304.1 304.0 305.7 300.5 2 9 9 . 1 3 0 3 . 0 303.7 305.3 301.6 301.4 298.7 304.3 304.4 306.2 301.2 299.1 304.1 303.7 305.7 302.3 299.1 303.8 304.0 306.1 302.5 299.4 304.1 304.0 307.1 306.0 299.8 307.8 304. C 306.8 302.7 300.7 305.6 305. 1 307.1 302.5 299.8 304.1 304.6 306.4 302.3 301.1 304.7 305. 1 306.4 303.1 700.2 304.3 304.7 306.4 304.1 299.8 304.8 3 0 4 . 7 306.6 303.6 301.1 305.6 305.1 306.4 303.6 301.3 305.2 304.7 307.1 304.3 301.3 305.6 304.7 306.8 308.2 302.4 306.3 306.5 308.6 304.8 300.2 305.2 304.7 306.4 304.1 301.6 305.6 305.5 307.6 304.6 302;0 305.9 305.8 307.9 304.1 702.0 306.3 305.8 307.5 305.0 302.0 305.9 305.8 307.1 304.5 703.2 306.5 307.2 308.9 304.5 7 0 2 . 4 3 0 6 . 3 3 0 5 . 8 306 302.4 305.9 366.5 306.9  TI10) T i l l ) 303.6 304.T 304.0 303.9 306.5 307.6 307.7 308.8 308.7 309.3 309.9 309.4 310.6 310.1 310.4 310.1 310.3 309.9 310.6 310.8 310.4 311.0 311.2 311.3 310.4  304.1 303.9 303.2 302.7 304.4 305.2 306.9 306.6 30T.4 307.5 308.3 307.7 308.8 309.2 309.2 30B.4 308.9 306.4 309.2 308.8  J l 1).  TI2J  T l 31  TC4)  TI5)  T16)  TI7)  294.5 294.5 J95..9 2 9 S . 4 299.1 298.0  295. L 297.7 294.2 299.4 296.6 301.3  218.7 215-5  299.7 299.0 299.5 29B.7  295.B 296.2  260.6 264.9  290.4 290.9  T(8)  T<9)  298.1 301.2 298.6 302.0 29B.9 302.2  301.2 300.6 301.2 300.4  303.5 303.2  297.6  DTMC  TC12) TI13I  T1141 T l 1 5 ) 308.9 309.6 309.8 312.7 314.6 317.1 318.2 321.3 321.7 322.0 324.2 323.8 323.1 323.1 324.5 324.9 323.1 323.4 324.2 323.4 323.4 324.2 323.8 323.4 322.7 324.5 324.5 325.9 326.3 326.8 325.9 326.6 326.3 327.7 328.1 327.7 327.0 326.3  263.8 263.5 264.0 268.7 270.5 273.8 272.9 277.8 276.6 277.4 279.9 277.1 273.4 273.1 277.4 2.80.0 273.8 273.8 274.5 274.2 272.4 272.7 274.3 274.7 274.2 274.9 275.3 276.0 276.1 279.8 273.8 275.6 277.1 276.9 277.4 276.7 275.6. 275.6  DTMC  83.0  302.5 303.5 303.5 303.5 306.1 306.8 308.1 306.5 309.0 309.0 310.1 310.1 310.8  310.B T n r t r 311.5  310.1 311.5 310.4 311.1 311.1 309.2 311.4 310.8 309.5 312.1 312.6 309.2 312.6 311.9 309.2 313.2 312.9 309.5 312.5 312.2 310.6 3 0 9 . 5 312.1 312.9 3 1 1 . 3 309 . 5 3 1 2 . 5 3 1 2 . 6 311.2 309.2 312.5 316.3 310.8 309.2 312.5 313.6 312.2 310.6 314. > 313.5 3 1 0 . 8 309.2 312.1 312.2 311.9 310.2 313.5 313.5 311.5 309.5 313.2 312.9 312.6 311.3 313.5 314.3 311.5 310.2 313.4 313.8 313.0 311.3 314.8 314.4 312.6 311.3 313.5 314.5 312.3 3 1 1 . 7 3 1 4 . 3 314.6 310.7 311.4 311.4 311.6 311.4  298.2  220.5 219.9 219.1 218.9 219.5 220.0 219.4 220.1 220.0 219.2  10,48.3 1037.0 1024.5 1015.5 1020.5 1018.3 1007.2 1012.9 1010.0 1003.9  222.8 223.2 222.5 222.6 222.3 222.3 223.1 222.9 222.9 220.9 222.0 222.8 223.1 222.2 222.4 221.4 222.5 221.6 221.6 222.8 222.7 223.6 222.7 222.6 221.3 222.4 222.5 221.6 220.7 222.8 220.2 223.5 221.8 222.9 222.2 223.8 223.2 222.3  259.3 257.3 256.2 257.5 249.1 247.8 246.4 243.3 242. : 237.4 238.4 241.1 240.3 238.3 238.1 236.4 239.4 237.4 236.6 239.0  0.954 0.964 0.976 0.985 0.980 0 . 962. 0.993 0.9B7 0.990 D.996  0.0 0.0 1.5 3.5 5.5 11.3 21.8 30.5 45.4 51.0  82.2.,  300.9 301,9 363.4 303.1 306.3 306.7 308.3 309.4 309.6 309.2 310.5 310.8 311.4 31L.4  TWC  215.3 272.6 286.7 216.0 274.2 287.1 218.3 2 75.7 268.6  295.0 297.3 297.9 297.9 298.1 297.4 298.2 299.4 299.0 298.6  TIN 210. 0 210. 3 210. 0 209.9 209. 5 209. 8 210. 2 209. 6 209.9 2D8. 2 209.6 210. 2 210. 3 209.9 209. 209 210 209 209 210 209. 9 211. 2 210. 3 210, 2 209. 1 209, 209. 9 208, 6 208. 1 210. 8 206, 5 210, 209, 2 210. 2 209. 8 211. 1 210, 2 209, 6  T-l 101 T i l l )  T 112 1 T l 131  T l 14)  TI15I  TIN  304.4 304.4 306.5  303.0 302.1 306.3  302.7 •302.9 303.1 303.0 305.6 305.9  310.2 311.5 314.7  271.6 272.4 274.5  210-1 209.9 210.2  306.8 307.6  305.2 305.6  306.7 306.0  3 0 6 . 1 313..4 2 7 5 . 6 305.7 312.7 274.2  HM  TOUT  3.856 0.0 • 3.8B6 0.6 3.903 1.6 3.684 i.3 4.015 7.3 4.036 11.8 4.058 22.8 4.110 29.5 4.121 35.8 4.213 48.5 4.194 54.5 4.148 60.3 4.161 71.0 4.196 78.0 4.206 B4.3 4.230 95.0 4.177 1 01.5 4.212 4.223 . 109.5 121.3 4.1B4 128.3 4.199 146.3 4.192 156.3 4.212 170.5 4.233 182.3 4.266 192.0 4.241 206.5 4.259 216.3 229.0 4.307 243.3 4.326 254.5 4.281 2b8.3 4.320 4.246 280.0 4.311 293.3 4.268 302.5 4.294 315.0 4.285 326.3 4.297 339.3 4.336 343.5  236.1 238.5 237.4 236.2 234.4 235.8 234.8 232.2 231.1 233.6 231-5 235. 5 232.0 233.2 232.9 233.4 232.7 230.6  HM  222.2 222.9 223.4  256.6 256.4 251.2  2 1 0 . 4 223.4 209.1 221.8  250.1 2.45.8  '  1000 8  TIME  3.894 3.900 3.961  0.0 0.5 3.3 6.3 11.0 22.0  3.999 4.069  3-11  R U N T(ll  24.  TI21  205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 205.0 253.0 241.3-335.B  289.3 288.3 268.3 288.3 268.3 288.3 28B.3 288.3 288.3 288.3 2B8.3 288.3 288.3 288.3 288.3 288.3 295.6  RUN  -  Ill) 206.5 205.'. 2C5.4 206. 1 205.0 208.9  25.  j m  296.1 296.1 296.1 296.1 296.1 296.1 296.1 296.1 296.1 296.1 296.1 296. 1 296.1 296.1 296.1 296.1 299.B  .  305.2 301.5 30*. 1 30*.9 304,9 328 .5  293.0 294.2 295.2 294.2 294.5 294.5 296.3 296.3 295.6 296.0 296.7 296.3 297.1 296.3 297.4 297.5 296.3  T<4)  371.5 37?.* 174.3 3 75.5 3 76.0 *5*.6  392.3 392.7 397.3 193, 7 1S3.3 *7*.7  26.  T ( 6 ) T(7I 2B9.0 296.4 290.8 297.6 291.7 298.5 2 9 1 . 3 29B.2 2 9 1 - 0 298.2 291.0 297.5 292.4 299.3 292.1 2 9 9 . 6 292.1 2 9 9 . 6 292.4 299.3 293.1 2 9 9 . 6 293"."l ' 3 0 0 . 0 293.5 299.6 292.8 299.6 293.5 300.4 292.8 2 9 9 . 3 29?.1 298.9 „ „  C.2'.2  T I6)  391.0 390. 7 391. 3 393.1 39?.0 495.8  3B6.7 3?6.3 367.2 307.7 3E7.7 *70.5  TI4)  2 9 6 . 1 298.5 295.= 2 9 9 . 7 296.1 300.7 296.1 300.2 2 9 6 . 6 300.2 296.6 300.3 297.301.6 298.6 101.6 298.4 301.2 29B.4 301.2 299.9 301.7 299.5 361.6 299.5 301.6 2 9 8 . 4 301.2 299.2 302.3 298.1 302.1 297.7 301.?  TI7) 197.2  397.9 198.9 399.6 398..1 469.1  OW  T(6)  T{7)  302.9 304.0 304.7 304.7 304.5 304.9 306.0 306.3 305.6 306.3 306.7 307,0 306.7 305.2 306.7 306.7 305.2 —  Mill  T ( 1 2 ) T1131  300.2 301.7 301.6 301.8 301.4 301.4 303.2 304.4 303.2 302.9 304.3 304.3 303.6 303.2 305.0 304.0 303.2  300.9 301.9 303.1 302.9 302.6 302.6 303.3 304.4 303.7 303.7 305.5 305.5 304.7 304.0 304.7 304.4 303.7  &86?*.  TIB)  T |9)  194.9 396.7 395.'> 317.1 397.3 *8*.6  *01 .3 4C? . * 402.4 '.04. 1 *03 . 1 *9* .9  R E 11E45.  T15)  TWC 2 9 6 . 6  TIB! t ! 9 l TltOI  1 14156.  ri51  W 0.242  T ( ? l TI31  Q W 31601.  RE 13575.  T15I  W  H I )  R U N HI!  W 0.242  T O ! TI41  TWC  3 0 1 . * 307.6 302.3 308.6 303.4 311.1 3Q3.4 3 0 9 . 7 302.7 310.0 3 0 3 . 6 310.4 3 0 4 . 3 310.4 304.8 3 1 1 . 3 304.5 311.2 3 0 4 . 5 312.2 304.B 312.2 305.2 3 1 2 . 6 304.8 317.2 3 0 4 . 7 311.1 305.7 113.5 305.6 312.7 304.5 311.8 ~  396.6  TUSI  T I N  TOUT  H M  260.9 262.9 264.2 262.4 261.7 262.4 263.1 264.6 262.4 263.1 263.5 264.2 262.4 262.0 264.6 263.5 259.5  201.1 210.2 210.9 209.9 206.8 208.6 210.5 210.6 208.2 209.2 210-2 210.5 210.3 208.4 210.0 2o<).4 208.3 - -  222.2 222.1 223.1 222.5 221.2 220.8 222.8 223.2 221.2 221.5 222.9 222.9 222.8 221.1 222.7 221.9 221.4 "  389.5 385.7 386.3 393.5 378.6 376.9 380.5 379.9 371.9 372.9 376.5 376. 7 377.0 371.4 374.3 373.3 370.6 =  Tl 12)  r i 131  II 14)  1115)  TIN  * 12.0 *12.' *12.7 413.7 MO.* 5*4 .5  403.6 404 . 4 403,8 405.4 40*. 1 523.2  407.3 407. E 407.6 *09.6 4QB.6 5 71.0  407 . 1 407.? 407.i 415.S 417.8 424.5  799. 1 797. 7 ?98.0 305.2 798. 1 308.*  209. ? 2L'E.9 2.'8. 7 21C.5 2 C.<i. 2 3l2.1  404.6 *05.8 *05.3 407. 3 *06.0 514. 7  T<9) TI 10)  TWC 3 2 6 . 6 Till)  T112)  UT^C  Till]  TUMI 23'.6 734. 5 734.'. 235, •) 735.4 736.6  g&q.a  su.fe  271 .5 271 . 1 271 .8 271 270.0 271 .4 27?.0 271.* 270. 7 270.3  315.5  .3  203.8 205.7 270.7 205.4 270.7 205. 1 270.3 206. 1 271.6 2C6. 1 273. 1  2C*.6 203.8 2C5.0 2C5.7 204.6 "'^Ub.O 7C 5 . 6 205.1 205.1 CVJJ.J 205.1  270.7 270.3 271.1 277.7 272.2 27?.4 2- 77 .- 7 273.0 73 t2p j .. 3j 273.3  lll'l „ 272.  314.4  315 315 316 316 317  5 5  292.8 ?92.8 297.5 293.7 296. 1 31 2.5 316.1 316.1 316.7 31B.7 320.1 370.1 323.0 324,8  326 326  ? 375  9 7  326 126  I 0 6  R 5 5  •-• 126.9 126.5 326.9 527.7 327.5 326.1 327.tS - - 319.1 326.1 3 1UB..T9 j328.4 JI £c. 3 1 9 . 6 327.9 316. 6 116.6 117.1 317.3 117.7 117. 7 JIB.4  319.3  T(2)  325.* 325.9 125.4 325.* 175.4 3?5.* 325.)  114.4  204.6  RUN  325.3  315.5  SLU.J 315.2 115,'5 316.3 117.7 112.1  275.0  375.?  31 3.7 31 5.9 315.5 114.8 314 .B 314 3  2.05.0 2C2.7 27?.? ? C 2 . 7 271 . S 203.4 2 7 2 . 7 7C3.8 776.0 2C5.0 275.J5  _^ 204.6 2C5.4 205.4 204.6 206. 1 207. 3 207.3 206.1 205.0 205.4 2C5.0 207.3 234.2 205.0  32T,e  3?4.7  77C.0 114.4  27.  K l )  353. 7 352.6 352.6 355.2 356.8 394.9 468.6 413,1 *17.0 426.2 438.'. 446.9 455.1 463.0  .n 125.8 375. 1 325.6 326.8 J77.7  J  £  J  324.5 120.3 126.2 nt.} 332.0  375.2 325.6 375. 125.6 125.^ 326. 1 l?5.fc 325.6  378.8 120.6 179.6 379.9 111.0 3*P.?  125 126 326 176 326  130.? 330.2  329.4 378. 7  131.0 331.0 331.0  3 - — 3 1-0.- •e 3 110. 4' 3 35,9  2  3??.* 122.4  1 127.3 13 ?2 1 .  7  — 326. 7 3 26.7 177.2 327.4 328.1 327.4 178'.* - - - 128.o 1 j £2n8,.-9i  I-i ••>  329.2  TI\  *  7 3 3 5 35 6 6  J E  3?9.2 324.6 3 2 7 . 7 324.2 3 7 8 . * 125.0 3 3 0 . 6 326.2 330.^2 3 ? 6 . 1  T(5)  32S.6  0 7 3 7  34C 139  3*C  0  140 141  4  117.7 337.* 337.4 337.4  117.7 336.6 338-6 336.0 318.4  338.  362.8 362.7 362.3 363.* 362. 7 393.7 468.6 414.5 421.8 431.9 444.B 454.7 465.6 476.1  340.3  llfi.9  341.0 341 .0 1 340.7  an.4  1 269.0  TOOT  3*7  3*5  348 349 3*8  1 3 6 5 8  276.8 2 76. 1 286.*  208.9  208.0  344.5 3*3.7 343. 1 34313 343.6 143.6 345.2 347.7 347.8 149.3  369;7 ini i I 398.1 3 33 31 1 .. 9 9 311.7 332.3 334.0 335.8 336.7 337.3  3 0 5 . 7 710.2 au->,f * IU. { .151.0 ? 0 9 . ? 2 ? ?H.6 2268 . 1o ' 200 5 2?5 5 ?oe ? ?24 3 208 4 226 6 208 ? 227 6 209 5 227 6 210 5 228 O 210 2  1  T(7I  373.3 373.0 372.7 374.6 376. 1 408.6' 4 08.6 422.0 4?7.0 *31.7 447.4 453.? 462.1 471.fl 480.8  T(8)  371.C 371.C 371 . r 372.4 373.(S 411 41 1 .. *427.9 433.3 441.7 452.* 46*.1 475.5 486.e 498.*  9  f  QW 5B252.  TI91 T ( t 0 1  378.2 378.5 378. 2 37B.9 3B2.7 *19. 1 434.6 440.4 446.9 457.7 464.2 475.3 481 .5 491.9  365.5 385.3 385.3 385.6 387.? 4*0.2 45B.8 466.4 475.8 488.1 501.1 514.7 528.6 542.5  t  TWC 3 7 1 . *  Till)  TI121  378.4 '380.3 3 8 0 . 6 380. 1 379.9 380.5 3 7 9 . 9 380.8 381.1 3 8 0 . 8 384.1 3B2.4 435. 3 431.9 454.1 4 5 1 . 7 459.9 458.0 469.0 467.9 480.7 480.4 * 9 2 . 2 496.2 5 0 5 . 8 505.8 513.0 517.2 525.5 530.0  T1131 383.0 392.7 383.5 384.0 385.1 385.3 384.1 443.8 466.4 473.8 484.9 49B.7 517.5 529.1 541 .4 556.5  HM  0.0 1.0 2.0 5.0 7.8 14.3  1000 R  TIME  2.529 1 9 5 . 0 2.532 VFJ7%  337.0 31-5.0 19 / . 19 I. 1  u  226.7 i.i.b. t ,, 226.0^ ? ? 7 . 7 >,>* ;  9  ??3 6 223 9 ??3 5 ??4 B276 2 9 225  TI14) T115) 2*41. 1 242.2 240.6 239.4 241.4 240.7 237.6 236. 1 236.1 236.) 234.2 232.4 ?34.7 235.1 234.4 235.5 235.5  0.5 TTT  rrsn  2.58* 4.0 2.598 5.5 582 6.5 7. 582 15.3 7. 580 18.5 5TTT" 2.594 2 4 . 5 2.594 30.3 2.596 3 9 . 5 2.61? 48.5 2.617 64. 8  '39^.6  385.4 165.1 382.8  •Mil. 1  179.5 377.1 " 377.7 373.2 381.6 375.4 TTTTS 375.1 -i-,7 7 -t .-> 3 2 373.5 3fJ.5  171.2 378.7 371.6 366.5 368.? 36.3.8 363.0 165.8 363.3  2.62B 2.633 '2.599  73.3 7B.5-  2.635 2.603  652 2.647 2.644 2.620 7.66* 2T5TI ?.666 2.687 2.677 2.694 2.691 2. 728 2.716 2.749 2.755 2 . 734 2 . 753'  UTMC 1 5 1 . 5  363.8 364.8 365.9 365.2 366. 1 364.8 365.5 392.3 392.1 402.2 403.5 406.9 414.0 421.6 423.6 42A.I 431.7  0.0  0.3  4 2.  387.6  TgTTl  38*.7 379.5 38*.2  725.* 27 7.5  2.517  395.5  390.5 379.8  , , . , j. , 2 0 8 . * 224.9 20G.1 224.7 2H6.8 2 ? 4 . 9 ? 1 0 . 2 226.7 709.? ? ?? ?55..55 207.224.1 7 1 0 . ? 276. 1 ir\n ic n 2 0 9 . 7-, 275.8  3a1i i2. .i*: 3 343.4 * 2 . 6 i*tc 3 4 2 .. 3J j 1• 9 y ., 5a ^ j . i 3 31^.0 3 3 2 . 9 319.1 3 * 7 . 1 3 * 3 . 0 347.1 ^ ' ' 3 4 2 . 5 342. 3 3*1 .9 ,„.^H^.H ,H*.W 3 4 2 . 9 341 .9 333.9 317.2 3 4 1 . 7 3 * 1 . 1 3 4 3 . 0 341 . 6 113.<* 13 1.9 3 * 0 . 7 3 * 2 . 8 3 4 2 . 6 342 1 3 3 * . 3 - 3 3 2 . F 3 * 1 . 7 , 4 * . 6 3 4 4 . 0 .14* 1 3 3 6 . 5 334.1 3 * 2 , ° 3 4 6 . 0 345. e 345 . 6 316.4 3 3 * . ! 3 4 3 . 5 3 4 6 . 1 3 * 6 . 0 146 3 337.1 3 1 * . 7 3 * 3 . 2 3 * 6 . * 3 4 7 . 0 3*7 . 6 4  P  2 5 7  ?65. 3 275.6  ... . . 294.6 781.7 283.1 281.0 785.7 299.3 295. 7 ioi 2 9 2 . 8a  J  225. 72*. 226.  210.e 20*5.2 210.8  354. 1 351.6 352.0 352.0 3 5 1 ..6 6 359.3 360.7 u i /. 361.4  J  TIME  7 . 571 2.563 2. 587 2. 585 7.601 *.2l?  394.2  200.9 225.3  709.9 2 2 5 . 3 271 .2 2 0 9 . 5 ' 2 4 . 9 2 7 0 . 5 ?rr».5 275. 7 7 7 5 . 2 7J-J.9 776.2 2 7 6 . 5 210.Z ??6.7 773^6 ?0>*.2 ?25\ 7 271 . 9 709.8 2?b.I 2 7 7 . 7 2 0 9 . 9 226,1 2 7 5 . 9 ? u v . B 226.0 2 7 9 . 9 209.6 ? ? 4 , 6 ?0O. i 225.0  340-7 340.0 3*0.3 340.e 3 * 1 ..7 7 3*1 341 . C 342.4 i *n 3 3 . 5c  HE 1*322.  7(6)  v . i . i  . 337.0 337.0 337.0 118.4 339.1 3 39. 1 330.4 339.5 s t n r> 140.2  324.3.i 3j 3j 1i,. 0a .-tct. 324.8 333.4 1 7 .j-'  ^-'^ ll, ."'< .  367. 3 366.* 367. 1 368.4 36S.8 402. 7 416.2 421.9 426.8 436.9 446.7 457.0 465. 8 475.0  9  334 313  333.8 334.6 136.4  3*3.9  1 3*.5  130.6 310.4  337.7  IE.2  3 335. 7 31*.9'337.8 .119. 339.6 3 3 5 . 5 135.2 337. 1 319.7 HP.6 315.9 336.3 337.fi 3 1 9 . 7 133.6 116.1 135.') 3 3 9 . 1 3 4 2 . 5 1 1 9 . 7 .317.5 336.1 318.6 1*"-. 9 336.6 3 3 6 . 5 339.6 3 4 1 . 6 33-7.5 336.3 337.0 340. 1 147.9 3 3 9 . 7 335.9 3 3 6 . 5 139.1 3 4 3 . ? 340.0 117.3 3 3 7 . * 3 3 8 . 7 3*4.6 319.7 116.6 3 3 6 . 6 3 3 7 . 5 346.4 K.C 337. 7 357.4 3 4 0 . 0 347 9  . 36 371.5 330.2 3*1 . 0 338. 7 373.2 310.2 330.4 3 3 5 , 2 140.0 1 3 7 . 7 322.8 3 1 0 . 6 330.4 3 3 5 . 7 1 4 0 . 5 3 3 7 . 7 323.2 1 1 1 . 6 330.P 1 3 5 . 9 341.1 339.1 324.1 317.0 3 3 0 . 6 1 3 8 . 0 1*1 1 * 1. .33 340.1 340 . 1 3 2 31 ^ n z T O T J ' U T H ~i IB ."4 " 3 4? . 5 340. 1 1 -? * -. 7 3 3 3 . 1 3 33. 1 3 38. 7• 343.4 341 -2 37";.ft TAI n 325-6 117.7 312.7 3 3 2 . 1 l3* 3n 8 . 4t 3 * 2 . 8a 141.2  W 0.2*2  365.2 367.3 365.9 367.7 367.3 398.2 411.7 416.4 421.8 431.9 4*1.* 4*9.2 45e.? *67.2  .9  0 ?  3 ? 6 . " 311.1  T<4)  329.3 1 3 2 . 0 120. 1 3 ,1 .7 379.5 331.7 3?.). 7 ,33.4 1?B.7 l j t . , 0 33 3 .T~3 3 4 . ? 130.2 329.2 131.0 3?<>.7 3 1 4 . 5 3 1 C ? 3?^.C 3)*.5 179.5 3 2 S . C 3 33 .3 33B. 7 3 1 4 •J  370.7 3 7 1 . f. 321 3?'.I 371.0 370.7 320.7 3'?..4 325.2 327.1 325.4 -21.4 J25 • 6 •.JI.  1000 *  110.7  TI14) T115)  269.0 312.3 323 . 3 323.1 1 2 C . 7 126.5 37.5.8 3 2 9 . 0 335. 1 331 .6 331 .3 333.2 3*0.8 279. 7 2 0 9 . 6 225. 1 769.4 313.5 3 7 * . 0 323.5 319.2 3?6.7 3 2 5 . 3 2 9 . ? 335.2 312.4 337.0 334.5 319.0 271.0 ?09.9 275.3 205.1 270.7 114.6 324.4 323.0 321.2 328.5 327.* 331.9 317.5 314.3 313.5 335.0 3*1.2 273.4 210.2 277.1 20*.8 206. 5 206.5 206.5 ?05.7 204.6 2C5.4 2C5.4 207.7 205.0  T I HE  2.567 0.0 2.593 0.8 2.589 l.a 2.608 4.0 2.641 7.3 2.654 12.3 2.628 23.0 2.63? 29.0 2.6B9 37.7 2.682 47.7 g.b56 51.7 2.654 59.7 ?.652 70.7 2.692 91.1 2.672 94.1 2 . 6 7 9 101.1 2.699 106.1 ^-TTS 106.T  369.0 367.2 3P5. 5 3E6.8 334. 5 2 37.*  204.2 2C3.e  :JO4.6  1000 R  DTMC. 1 76.4  T 1 10 ) T i l l )  QW 43655.  TI81  DTMC B 1 . 2 T t 14)  90.8 102.3  115.0  '  t i  161.8 17*.5 185.8 1'99". 3 " 213.3 223.5 236.8 248.8 257.0 270. 5 276.5 2B<!. 0 293.8 307.8  j  f[N 2 10.7 211 . 6 210.5 210.0 210. 1 20".9 ?09.9 210.5 £\0.t 211.8 210.8 208.5 210.5 208.6 208.0 308.6 210.2  TOUT 231.9 233.3 737. 3 231.6 231.7 231.6 231 .5 23 2.3 Z3Z.J 233.2 232.0 230.3 231.9 229.8 228.4 210. 1 231.3  HM 384.6 384.7 3B0.8 379.3 379.6 376.7 373.3 • 295.3 273.B 264.9 253.b 736.0 222.6 209.4 20276^ 195.4  1000 R  TIME  2.600 0.0 2.599 1.0 2.626 4.0' 2.636 5.5 2.634 6.8 2 . 6 5 4 ., 10.I 2.679 13.3 3.386 21 . 6 3.653 23.4 3.775 24.7 1.^*0 dt..u 4.237 27.5 4.493 29.5 *- ?5 31.7 479T7 33.8 5.117 36.1 7  3-12  RUN  Till 2C5.1 204.7 205.7 204.4 204.4 2C5.0 2C5.0 .205.4 2 06.9 itJO.^ 204.2 205.4 204.7 „ .6 204 2 2 s0 n6 * .. ? 206 3 206 1 2C4 6 204 6 202 7 205 0 t  v  u  T<2)  26.  T(31  W  1412>.  0.242  T(5)  TI4)  T(6)  T(7)  2M.1 281.0 382.0 281.0 281.1 281.1 281.3 285.0 2 87.0 £Of.U  333.7 342.9 144,0 3 3 3 . 7 3 4 4 . 3 345.1 334.5"345.0 346.3 332.7 344.3 345.5 333.4 344.3 345.8 334.1 344.8 3 4 5 . 5 3 3 4 . 1 345.4 3 4 5 . 7 3 4 1 . 0 349.8 3 5 9 . 9 3 4 5 . 0 3"5T:?"365".fl 3*t?.<J  340.2 340.6 342. 1" 341.0 341.0 341.0 340.6 351.2 357.2 331. *  346.9 349.9 3~5T.2 350.1 349.8 349.9 349.9 366.6 371 .! 3(1.1  285.0 2B5.7 287.2 *2 8 7, ..5 , 2 89.7 ?flo_7 291.0 290.4 289.0 2B9.7 290.B 291.9  345.9 346.B 351.1 354.8 3 0 * t5;0n. n 360.4 366.6 368.9 374.6 377.3 381. 1  358.6 363.2 369.0 376.3 3 0 . 3•x i o8n 385.i 4C0.3 404.4 417.9 473.9 427.9  173.8 376.9 3B2.4 3 8 6 . 9, 3 n o9n0.. 3 * 395.1 404.6 406.3 416.5 419.2 422.9  a  351.5 357.4 361.2 3 6 5 . 7. 368.8 ^mn.fl 371.6 3 77.B 381.7 389.5 311 . 9 397.7  366.7 370.7 375.1 3 9.1 .. 7. 366.3 390.6 401 . 1 404.2 416.3 4L9. 7 424; 7  J  U  T181  QW 4 9 5 9 6 .  TI91  346.4 348.7 346.B 348.8 348.= 34B.5 34B. 1 364.0 370. 5  351.6 353.5 354.6 353.6 352.9 353.9 353.6 374.1 3 80.5 JOU.J 3 7 4 . 2 384.2> 37B.4 3 8 8 . 2• 3 8 4 . ( 394.1 3 9 1 . 4 ,3 9 9 . 6 3 7 4 C4.5 39 06 * .. ? 4f:4.5 401.6 409.a 418. 1 423.0 422.4 424.0 436.4 434.7 439. * 4 3 8 . 7 444.7 443.1  TWC  Till  T(2)  T'131  296.0 297.2 296.4 2o8.5 2«-9.6 303.0 304.7 3C6.5 ~~" '  337.1 338.5 337.9 340.3 341.4 348.0 350.2 358.2 "  RUN  Til) 203.8 202.7 2C3.8 2C3.4 203.5 21:5.4 2C5.9 205.7 205.7 205.7 2C5.4 205.7 2C5.4 204.6 2C3.B 203^8  T131  271.4 270.3 273.0 271.0 271.4 2M.4 217.2 278.7 281.6 282.0 284.0 2Bb.9 268.4 2B7.7 285.9 287.0  327.9 327.2 328.8 376.7 326.3 IZg,C 332.2 337.B 346.3 350.8 357.5 364.4 371.C 372.7 376.5 381.9  RUN  Illl  3C.  T(2)  T(2)  31.  T13)  TI4)  . T15J  T<6)  T(7)  344.4 345.6 345.6 346.7 348.1 351.7 352.7 359.8  340.1 341.3 340.1 340.8 344.0 352i4 355.3 359.4 '  313.8 334.2 333.5 333.2 335.2 341.2 342.7 346.0  344.4 345.4 344.4 344.5 349.3 359.1 362.6 368.5 "  W  C.176  TI41  T|51  337.5 336.6 339.4 330.7 3)7.1 338.7 33E.9 342.1 349.5 355.4 360.8 36b.6 373.5 376.3 380.1 387.3  343.0 342.9 344.3 343.1 343.3 343.5 345.4 351.7 360.4 368.8 375.3 3S5.0 393.2 396.2 403.0 41 1 . 1  W  C.242  T<41  T15)  2 0 5 , 7 * 3 1 1 . 3 37B.0 3 9 ) . 6 400.8 2 0 4 . 6 3 1 2 . 0 360.4 393.5 4 0 3 . 0 2 0 5 . 7 31 1.5 383.7 355-3 4 0 5 . 9 1 3 1 2 . 7 385.6 306.4 4 1 0 . 6 2 0 3 . 8 3 1 4 - 9 3 8 3 . 3 4 C 2 . 5 4 19. 7  207.3  260.7 298.7  RUN  T(  11  205.4 205.4 2 . .C w5 . *. 2 204.6 207.3 202.7 2C5.1 205.11 203.4 203.1 204.4 204.4  32.  319.5  W  T<2)  T l 3)  Tl 4)  270.7 279.7 2 0 2 . 5^ «.„«.. 2B4.0 287.8 289.6 295.0 2 79 Q4 Z. 31 296.1 298.3 3CO.0 300.8  33 3 .7 331.9 3 j j3i2.. 3 j 334.4 337.6 350.2 363.8 3 iT/s 7 0 . 6i .380.7 389.9 4CC.5 402.8  341. 3 340.4 340.B 339.4 340.1 349.9 359.1 3 ifcfc 65.0 n 374.7 381.2 366.8 392.9  RUN  33.  330.2  HE 10617.  T<6)  1(51  W  0.242  Till  T(2)  T(3>  TI4)  T t 51  204.6 205.0 204.8 203.B 202.7 205.4 2C5.'6 2C5.4 205.1 2C6.3  279.5 280.2 280.6 282.6 281.7 289.6 29l.fl 290.7 294.0 296.5  332.I 332.6 333.7 330.5 328.4 363.5 381.4 385.1 3S5.0 399.4  341.7 341.7 340.8 334.1 328.7 345.0 355.9 356.6 362.2 366.4  TI71  340.1 347.2 338.7 345.7 340,8 3 4 6 . 4 3 3 9 . 1 347.9 330.7 346.5 339.3 346.5 341.9 351.4 340.6 361.5 361.9 374.9 371.3 3B3.0 370.2302.9 3 9 0 . 3 403.2 4C0.5 414.3 4C6.3 417.0 412.7 4 2 3 . 7 423.4 4 3 2 . 0  TI8)  TI7)  TO)  393.5 396.2 397.6 402.4 413.5  406.0 399.3 413.5 404.7 419.2 407.4 424.5 411.B 431 .5 4 2 2 . f  341.0  3SS.8  HE  HI?)  T ( 1 3 ) " T ( 1 4 1 T115)  360.2 360.8 361.1 359.7 361.1 361.1 362.0 386.6 3 96• . 5:> 3-JO 4 03 3 .. 8 8 40 4 0 9 . 9-  355.3 356.5 356.5 356.0 356.0 357.1 356.7 380.7 3j8q 9 i ..6O 396.1 396.1  156.0 356.9 357.4 356.7 356.4 358.5 356. 1 390.6 4t0u 0 u ..7l 4 08 8 .. 4 4 40  401.5 40B.3 41B.0 424.1 424.i 426.9 445.6 448.6 459.7 464.5 471.7  416.1 424.1 435.0 4 44 41 1 .. 2 2 449.4 463.9 468. 1 478.0 483.4 491.9  357.9 359.3 359.7 359.0 358.6 360.7 361 . 4 415.9 41C1.-» 29.9 4 44 41 1 .. 3 3 4 51.8 1.8 4 66.2 6.2 ,4. 7 88. 6 .6 4B7.2 407.? 497.8 516.3 518.5 525.5 532.8 543.9  418.5 428.7 4 43 36 6 .. 4 4 445.3 468.2 477.7 484.9 487.8 494.5  T<6)  T(7)  TI8) 346.4 345.0 344.4 349.5 354.1 369.4 386.6 3 i9m7 . 5e 412.0 420.0 430.8 435.4  RE 14481.  T(6)  T I 7)  342.3 338.9 346.6 341.3 339.6 346.6 3 4 0 . 9 339.2 3 4 8 . 0 334.0 325.0 333.5 332.4 3 2 5 . 0 3 3 2 . 8 3 5 9 . 6 349.1 367.2 3 7 6 . 5 3 6 3 . 8 383.1 3 7 9 . 3 3 6 7 . 6 386.2 369.2 3 7 6 . 3 3 9 5 . 3 394.3 381.8 400.5  TI8) 346.4 345.0 346.4 331.2 332.( 373.9 391.7 397.5 406.3 414.0  T110)  Till)  356.5 358.2 357.9 359.3 361.7 375.1 379.5 391.8 " "  350.0 351.8 350.3 35077 354.9 365.7 370.2 378.5 """ "  T110)  TwC  Till)  3 5 6 . 5 353.4 354.7 350.6 357.0 353.3 357.2 353.8 3 5 4 . 7 352.4 356.5^352.0 361.7 358.0 373.4 371.2 391.8 390.8 403.7 402.7 417.9 417.9 430.3 429.3 445.5 443.5 453.4 4 4 7 . 8 -.60.b 4 5 4 . 7 472.6 464.B  TI10)  TI131  340.5 342.2 34?T4 339.8 340.5 347.6 340.5 359.4 365.0 367.0 369. 1 375.7 378.8 382.6 38?.9 389.7 3<)0.4 395.2 397.6 400.6  43.5 209.6 43.5 210.5 4 3 . 5 211.1 43.5 208.7 43.5 208.6 4 3 . 5 210.1 43.5 209.3 43.5,210.6 4 3 . 5 211.2 43.5 209.5 43.5 209.7 43.5 209.7 43.5 209.9 43.5 211.3 43.5 210.2 43.5 210.2 43. 5 ? o o . e 43.5 210.P 43.6 208.9 43.6 2 09.9  129.6  T ( 1 -41  1(151  TIN  227.5 229.0 229.4 230. 5 230.1 729.4 229.8 727.6 "  208.5 209.2 209.1 ? 107?" 210.6 210.8 711.2 203,9 "  0TMC  T f 13 > TI14)  353.3 352.0 354.0 354.8 352.4 3S3.4 361.8 377.0 398.8 412.3 425.1 43B. 1 452.5 458.5 467.6 47B.8  3 5 5 . 0 ,333.6 2 3 4 . 9 2 0 9 . 6 354.6 334.0 234.2 203.6 3 5 6 . 9 335.7 2 3 4 . 7 208.2 356.4 3 3 4 . 7 2 3 6 . 4 2 1 0 . 3 3 5 5 . 0 3 3 3 . 3 236.4 2 0 9 . 5 3 5 7 . i 3 3 4 . 7 2 3 7 . 1 21 1.2 374.1 3 3 7 . 9 2 3 3 . 4 2 1 1 . 3 3 9 5 . 3 344.2 2 3 1 . 6 2 0 9 . 5 421.1 355.1 2 3 1 . 6 2 1 1 . 8 444.1 362.4 231.2 2 0 9 . 3 4 6 1 . 0 368.3 2 3 2 . 0 2 0 9 . 8 4 7 6 . 0 3 7 4 . 9 2 3 2 . 0 21 1.0 496.1 3 8 1 . 7 2 3 2 . 3 2 1 0 . 0 504,8 3 8 1 . 0 2 3 2 . 7 210.2 5 1 3 . 2 3 8 3 . 8 2 3 2 . 7 209.2 5 2 1 . 7 306.8 2 3 2 . 0 2 0 8 . 5  402.7  T i m  T1131  DTKC  U14)  T1151  OW 4 0 0 4 0 .  TIO) 354.6 351-5 352.7 360.0 365.4 382.7 401.7 4 A11 3 1 . 3i 429.3 437.7 443.2 449.0  T (10)  346.3 34B.3 349.7 332.8 337:0 375.8 391.3 395.8 407.4 412.B  7 472.5  TWC  TI10)  354.3 352.9 3 57 7..B 8 369.9 376.4 400.3 426.2 4 I.J,*> 4 2 . 8a 469.3 480.1 486.2 493.0  TWC  5 4 2 . 9 374.7  34B.6  T< 1 U T(12)  360.1 3 5 3 . 6 158.9 352.5 362.9 355.0 370.0 363.5 376.4 370.6 393.2 389.6 416.0-413.0 430.4 A I A I. . 4 /. 2 6 . 7T 448.2 4 4 7 . 6 460.2 459.7 463.5 464.3 4 6 8 . 5 470.1  QW 4 9 8 4 8 .  T(9)  432.  359.2 3 5 2 . 9 3 5 2 . 5 3 6 0 . 6 352.2 353.4 360.4 3 5 3 . 6 3 5 4 . 3 34S.9 340.9 343.8 3 4 8 . 5 3 4 6 . 9 350. 1 4 0 1 . 4 39B.B 4 0 9 . 0 421.0 417.7 428.7 4 2 9 . 7 424.1 4 3 5 . 9 444.6 435.4 450.0 452.2 439.7 457. 1  178.3 377.B 37772 372.8 372.7 375.2 373.0 320.8 30671S 796.0 267.7 273.8 768.6 260.0 751.1 234. 7 230.4 219.0 71 1.6 207.2  TOUT 224.5 226.1 226.4 227.4 227.9 227.3 228.0 225.B  HM  1000 R 2.643 2.647 2.651 2.682 2.683 2.665 2.681 3.117 37260 3.379 3.476 3.587 3.723 3.846 3 982 4.260 4 340 4 .565 4 727 4 826  37.8 40.0 41.7 43, 7 45. 7 48.2  1000 R  TIME  677.7 676.0 677.7 &B3.4 669.6 614.2 592.3 551.9 515.6  1.476 1.477 1.475 T776T 1.493 1.628 1.688  25,0 27.0 29.0 31.0  0.0 0.5 2.0 TTS 7.0 12.0 13.0  1  -  TIN  TOUT 228.2 227.4 226.7 229.2 227.9 229.2 229.4 227.4 229.7 227.1 227.5 229.4 220.6 228.2 227.4 226.6  HM 294.2 295.1 290.1 295.8 295.2 ?9T72 287.4 261.3 239.4 220.3 208.0  3.399 0.0 3.388 0.3 . 3.447 1.3 3.381 2,9 3.387 5.4 3736"4" 77V 3.480 11.2 3.819 14.5 4.177 18.5 4.538 21.2 4.807 23.3 STToTJ 25.3 5.375 27.3 5.562 29.3 5.770 31.6 5.972 34.6  YWTX  1B6.1 179.B 173,3 167. 5  216.  '1*4  _ _ 21)0.1 2 3 4 . 5  1 211.2  DTMC 129.  IQUT  219.6  • 415,9  2.294  15.7  1000 R  TIME  7  TI131  T( 14)  T( 151  TIN  TOUT  HM  355.1 354.5 371.4 371 .4 388.9 399.4 427.5 459.5 4 i. 8 •1 1 . 5c 509.5 523.0 530.0 537.1  337.6 336.2 335.5 342.9 348.5 359.0 375.3 383.2 lai i 394.5 400.6 402.0 405.3  234.7 234.3 2 31.4 231 229.1 231.0 227.3 230.3 2 n3 0 A . 6i 22B.4 229.9 23\.\ 200.4  210.7 210.2 210.1 t.u.. 2J9.4 211.3 208.2 208.8 2 ^0\r\ 9 . 2-* 207,0 208.0 209.5 208.7  229.6 228.8 2 2o 8.3 228.0 229.6 226.1 226.5 2 tt-r 2 7 . 2i 225.2 226.1 227.0 226.9  385. 1 3B6.2 377.7 3 6 0. . 0 352.6 307.0 275.1 258.2 i e n -i 2 36.7 225.4 214,6 213.8  2.597 2.589 2.647 2 ..7. 7 < . ,B 2.836 3.257 3.635 i 3.873 o -»-i 4.225 4.436 4.654 4.677  HM  1000 R  TIME  2.565 2.603 2.6p5 2.391 2.472 3.266 3.605 3.741 3.973 4.065  070~ 1.3 3.8 • U.O 15.2 21.0 24.3 27.3 30.5 34.-3  346.8  T | U | TI12)  228.1 ??9.3 229.B 227.3 227.4 22B.9 226.2 279.4 229.9 278.0 22B.0 22S.2 228.7 229.2 226.4 229.3 228.4 228.7 227.0 227.9  HM  181.0  TH5)  4 1 0 . 5 4 1 2 . 7 410.4 410.1 4 1 6 . 6 394.2 2 4 5 . 4 7 0 , 6 422.1 4 2 0 . 8 4 1 9 . 3 4 2 7 . 6 3 9 0 . 9 244. 427." ' " ' '" " " 434. _ 4 4 5 . 2 4 5 6 . 5 461 .7 471 . 6 5 0 4 . 0 4 1 9 . 5 2 4 0 . 0  433.4  TOUT  129.1  TU2)  TWC  Till)  146.6  ;  TIN  DTKC  349.1 3 5 4 . 3 341.1 351.2 3 5 7 . 9 343.2 351.4 3 5 8 . 5 3 4 5 . 3 '351.7 "3"5"8.6 344.2 354.2 3 6 1 . 6 349.1 3 7 0 . 5 395.2 363.1 377.1 4 0 4 . 7 36B.0 3 9 1 . 7 4 3 7 . 9 377.3 " ' "  OW 69281.  TI01  345.4  T(12)  Ow 37097,  T(9)  3 6 2 . 5 382.8  14501.  3 4 0 . 3 34,9.7 3 3 8 . 5 349.4 3 38.9 349.6 338.1 341.1 357.7 3 4 7 . 0 355.4 360.B 3 7 0 . 3 3 7 6 . 9 386.2 3 io*. B 6 . 6*. 395.8 lac a 390,i 4 0 8 . 3 400.1 417.1 4 1 7 . 4 426.2 422.4 430.8  TI9)  347.0 351.0 345.2 349.6 346.6 351.7 3 4 6 . 3 350.6 345.0 3 4 9 . 6 346.3 3b0.b 348.4 3 5 1 . 0 3 5 7 . 1 3 58.3 374.6 372.6 385.E 382.6 397.C 3 4 3 . 3 409.2 404.2 421.3 415.7 427.? 419.8 435.f 427.9 444. 1 438.2  * E 14968.  T16)  C'. 242  345.1 344.6 3 , -4. 4 . 4 347.4 351.1 362.6 377.2 3 i8 a -a 3 . 77 395.3 4C3.6 413.6 416.8  T(8!  341.4 3 4 6 . ? 342,^ 348.9 341.0 34B.2 341.4.34T.9 344.2 352.4 351.2 365.B 355.1 3 6 9 . 4 361.0 376.4  DTMC 131.1  Till)  TWC  205.8 205.8 205.6 206.9 2C6.3 207.3 207.7 2C5.4 '  348.6  T(10)  DTMC  t  c  t  t  J  J  U  U  V  u  0.0 2.3 57T~ 8.8 10.9  128.9  TI13)  TIM)  T 1.15»  353.9 356.9 356.2 369.0 384.0 479.9 502.4 507.4 518.4 523.9  335.9 232.8 337.6 233.6 336.9 234.7 323.8 230.6 328. 1 227.3 3 5 5 . 5 229.1 364.2-228.4 365.3 229.2 369.4 2 2 8 . 0 372.2 2 2 9 . 9  TIN  TOUT  209.9228.4 209.1 2 2 7 . 8 209.5 228.4 211.0 229.5 207.4 226.6 210.9 2 2 9 . * 2 1 0 . 8 229.1 210.6 228.9' 210,1 2 2 8 . 0 21 1 .2 2 2 9 . 1  386.8 384.2 3B3.9 418.3 404.5306.2 277.4 267.3 251.7 246.0  3-13  Tt'll T<2) TI3I T(4) J15) T(6) T I 7 J T18) T(9) T I 10 ) Till) T (12 ) TI13) T114) TOU 115) T 141.2 164.3 168.2 168.9 165.2 166.0 168.6 169.9 173 175.0 176.8 180.7 198.0 178.8 153.3 151.1 141.0 165.6 168.2 168.8 166.3 166.4 168.2 170.2 173 .7 174.6176.8 179.8 201.5 179.0 154.4 1 5 1 . 8 _1*0-P_ 165.2 167.1 168.2 165.2 '164.9 166.6 168.3 171.0 174,3176.8 179.7 202.3 178.5 152.9 I 39.9150.4 140.4 165.2 168.6 166-5 165.2 164.9 166.7 168.1 171 175.4 175.7 179.5 202.9 176.9 152.1 140.4 150.6 139.6 165.9 168.4 168.0 165.1 164.4 166.6 167.5 171.0 173.8175.2 179.4 204.9 178.6 152. 7139.4 149.6 141.2 167.5 166.9 169.3 164.0 164.5 166. 7167. r, 1 76 0 173.5174.9 180.1 203.4 176.9 154. 1141.0 150.9 137.2 165.2 167.5 166.5 162.4 162.9 163.q 165.6 169.1 171.9173.3 179.1 205.0 1 7.7 152. 5140.1 150.2 141.2 166.4 166.6 167.7 163.6 162.5 164.4 164.8 166.7 171.7172.8 179.8 205.0 17 6.7 152.9 140.8 150.6 140.8 164.1 166.0 165.7 162.4 160.9 163.5 164.0 168.3 170.3171.6 177.5 203.8 17 73.8 150.2 139.1 149.1 136. 8162.5 164. 3164.2 160.1 159.0 160.8 161.7 164.9 169.2169.5 175.2 201.1 17 3 4 149.1 136.5 146.5 140.6 165.6 167.5 167.7 162.4 162.1 163.5 164.6 167.9 171.2173.0 177.9 202.9 175. .9 152.5.140.5 150.2  HM 1000 R TIME 1614.2 0.620 0.0 1655.0 0.604 0.8 1625.2 0.615 1.6 1627.6 0.614 3.1 1637.5 0.611 5,8 1692.0 0.591 8.5 1775.4 0.563 12.5 1798.8 0.556 15.0 1794.0 D.557 18.3 1757.7 0.569 22.5 1828.9 0.547 27.5  TWC 169.6 DTMC 28.1 Hi)  TTT)  138.0 162.2 140.8 164.5 138.8 164.5 138.0 164.8 138.0 165.1 139.6 167.5 139.6 168.0 141.6 171.4 136.4 166.3 141.6 173.4 139.J 171.4  3 8 3 3 7 5 7 3 7 8 8  TTT) TTT) T T m f m TW) T(9) t i i o i Till) Tim t m i TU4iTINt i i sTTOUT 170.7164.8 164.5 169.6 167.6 172.7 173.5 173.4 171.1 172.4 173.4 147.9 137.5 146.3 173.2168. 1166.6 171.8 170. 1 1 75.8176.6 176.1 175.1 175.5 176.2 150.2 40.2 148.9 173.2 167.6 166.1 170.3 169.7 176-0 176.6 175.5 174.1 172^8 174.0 148. 71 39.4 148.2 171.6164.4 164.1 169.4 167. 7172.9 175.0 173.4 172. 72.3 173.0 146.3 1 138.0 146. 171.7164.1 163.8 68.0 166. I171.1 172.9 170.5 169.1 1 170.5 1 70.0 146.4 l3fl.l 146.4 174.0165.2 165. 11 70. 1167.2 172.5 175.3 172.2 171.4 172.8 172.2 147.9 139.6 148.5 173.7165.7 165.5 1 168.4 166. 7173. 1174.7 171.9 170.0 172.' 171.2 147.9 139.1 148.0 175.0166.8 167.3 1 69.8 168.4 174.3 175.9 174.2 171.6 174.0 174.6 149.5 142.5 151.2 170.1 164.0 162.9 166.3 163.3 169.8 171.2 170.2 167.1 171.0 170. 145.6•137.4 146.2 165.4 167.5 166. 1172.3 1 73.6173.9 169.9 173.6 173.5 147.6 139.7 148.0 171,9 166. 11 6 4 . 5 171.3164.5 166.8 1 6 5 . 5 1 7 1 . 2 1 7 3 . 2 171 . 1 170.2 172.2 1 7 2 . 0 146.8 1 3 9 . 9 H A . 3  tTT)  HM  2568.8 2540.0 2558.7 2618.8 26ft2. 2739.7 2699.9 2892.9 2834.3 2706.4  2A9O.T"  1000 R T I MET 0.389 0.394 0.391 0.382 0.373 0.365 0.370 0.346 0. 353 0. 369 0.346  TWC 169.3 DTMC 27.9 HI) TI2) TI3) T(4) T151 T(6) T(7) T(9) T(10) Till) Tl12) TI13) T114) T115) TIN TDUT136.6 164.0 165.2 173.5 164.8 164.0 169.3 166.3 172.6 173.8 172.3 170.6 169.6 172.6 146.6 13B.1 145.3 3436.3 0.291 138.4 164.0 165.5 173.4 164.8 163.9 169.3 166.7 172.7 174.7 173.0 170.9 170.0 172.7 145.9 138.2 146. 1- 3450.3 0.290 139.2 164.8 166.5 174.7 165.6 164.8 169.7 167.3 173.2 175.9 174.3 171.7 171.7 174.0 146.7 139.1 147.1 3448.3 0.290 138.4 163.9 165.0 1 7 3 . 5 U 4 . 7 162.4 168.5 166.0 172.4 174.0 72.5 171.7 170.7 172.5 144.9 13d.1 146.1 3504." 1 0.285 138.7 164.6 166.2 174.4 165.3 163.6 169.3 166.7 172.8 174.4 1 173.0 171.7 171.5 173.9 146. 3138.5 146.0 3433.3 0.291 138.2 164.8 165.6 173.9 164.5 163.3 166.6 166.7 172.1 173.8 1 2-3 171.7 171.1 173.1 145.9 137.6 145.3 3393.7 0.295 140.0 165.5 167.2 174,7 165.8 163.9 169.8 167.6 173.5 175.3 17 74.2 172.9 173. 1173.9 146.3 139.2 146.7 3383.7 0.296 14.6 138.8 165.5 166.0 175.4 165.2 164.6 169.8 1 175.4 173.3 173.0 173.1 174.5 146. 3138.6 146.2 3376.4 0.296 2 6 7 . 3 1 7 3 . 6 138.0 165.2 166.7 174.7 165.7 163.7 169.8 166.6 172.5 175.2 172.7 171.3 172.3 173.9 146. 3137.8 145.3 3 3Q6-2 0. 302 0.8 TWC 172.2 DTMC 27.9 "Till  TT21  139.2 163.4 140.6 165.3 141.1 167.0 141.0 166.9 134.6 165.8 139.0 166.2 137.2 165.8 137.2 165.0 138.0 165.6  TTTT  TPD  TT51  167.0 172.2 168.5 167.4 173.7 169.5 167.6 174.3 169.7 168.0 175.3 170.3 166.1 173.6 148.1 165.9 174.2 169.3 165.3 173.2 168.5 163.7 171.5 166.5 165.3 173.0 166.1  TTT" T T7T r T F J fl") T I I O I T ' 1 1 1 T ( 1 2 , 166.6 171.5 170.1 176.1 176.4176.6 175.0 167.4 172.7 170.5 176.9 177.7 176.9 174.7 168.1 173.5 171.2 176.8 177.7 176.8 176.2 168.2 173.1 171.4 176-9 178.7 177.4 176.6 166.6 172.3 1 7 6 . * 176.5 178.3 177.4 176.2 167.1 172.7 172.1 175.9 178-3 177.0 175.2 166.3 170.8 170. 174.7 177.2 175.9 173.8 165.5 170.3 169.] 173.3 175.0 174.7 173.8 165.8 170.7 169.: 173.5 175.8 175.5 173.4  T I B ) T(141TtT51  rnur  TTW  174.1 176.3 151.1 139.9 149.5 175.6 176.3 1 50.8139.2 1<>B.6 176.8 176.7 151.5 140.4 149.5 177.1.176.6 151.5 140.1 148.6 176.2 176.2 151.5 13B.7 U 8 . 2 175.7 173.6 150.0 138.9 148.2 174.1 173.9 149.? 136.1 147.3 172.5 170.9 146. 5137.5 146.5 173.7 173 149.? 137.8 147,2  HM 2234.3 2)00.8 2140.4 2074.2 2073.3 2062.5 2100.3 2141.9 2132. 1  1000 R 1 I ME 0.448 0.0 0.476 3.B . 0.467 10.3 0.482 13.0 0.482 19.0 0.485 23.5 0.476 30.3 0.467 36.5 . 0.469 36.5  TWC 170.0 DTMC 27.4 TOUTT115) T Till) T(2) TO) T14) T15) T161 T17) T I 8 ) T(9) T 110 ) Till) T112) T 113 ) T (14) H | MN 138.4 162.7 166.5 170.4 166.9 164.3 169.0 168.7 173.7 173.3 173.1 172.6171.7 174.4 150.1 138.0 147.9 1461.5 136.4 162.7 166. 1170.6 167.3 165.4 169.6 169.1 173.7 173.7 173.5 173.0 172.9 175.2 150.: 138.7 149^3 1496.0 140.4 164.6 167.2 172.2 169.3 166.6 171.5 169.I 175.0 174.6 174.8 173.9 174.5 175,2 152. 139.8 149.6 1463.7 136.4 163.9 166.5 172.2 168.5 166.2 170.0 170.1 174.7174.6 175,5 174.0 174.1 175.5 152. 139.3 149.4 1458.3 139.6 165, 165.3 171.8 168.5 166.2 170.2 170.1 174.3 1 74.5174.7 175.0 175.4 177.3 152. 139.1 149.1' 1443.9 138.4 164. 164.9 171.0 167.7 166.2 170.3 169.6 173.9 174.8 173.9 175.0 175.3 175.9 151. 138.5 148.4 1418.1 140.8 166.5 165.7 172.2 169.5 167.5 171.5 172.1 176.5 176.4 176.6 175.8 177.2 176.7 157. 140.1 150.2 1424.0 140.4 167.3 166.5 172.4 170.9 168.2 171.7 171.8 176.9 177.4 177.0 175.7 176.0 177.1 15?. 139.9 149.7 13B3.6 137.6 165.0 163.7 169.8 168.5 166.2 169.9 169.7 174.3 176.0 174.7 174.2 174.5 175.5 151. 137.5 147.6 1381.8 139.6 166.2 164.9 170.6 169.3 167.0 171.1 170.9 175.0 1 76.4175.1 175.0 175.4 175.9 151. 139.3 146.6 1412.5  1000 R 0.684 0.668 0.683 0.686 Q.693 0.705 0.702 0.723 0.724 0.708  6. 10. 61 15.8 20. 1 24.1 2t>. 1 33.6  TWC 171.4 DTMC 27.1 TUUT tusj U N 176.6 152.2 140,0 149.3 175.3 150.3 138.1 148.1 174.7 150.3 137.5 147.3 174.7 150.3 137.9 147.3 147.9 177.4 150. 176.2 150.7 1381 147.9 175.9 150.7 1376 147.4 .9 147.6 175.2 149.9 137 175.2 149, 6 1390 148.5 175.1 149.3 1376 146.6 175.5 149.9 1377 147.1 0 136 1 139 TWC 171.5 OTMC 27.0  • HM 2081.5 2082.9 2043.0 2048.1 1970.8 1959.4 1963.5 1985.1 1981.5 1912.4 1926.1 1934.8 1961.5  0.460 0,480 0.489 0.468 0.507 0.510 0.509 0.504 0.505 0.523 0.519 0.517 0.510  T(3) Tt4) T15) T16) T(7( T(8) T19) TUO) Till) TI 12 ) T I 13 ) T ( 14) T 115 ) TIN 165.3 166.5 167.5 166.5 17Q.9 171.0 175.3 175.9 1 32 58 3. .1 13 176.4 165.9 TS9TT 16?.0 172.6 5 176. 166.2 171.2 o 175. 174.4 174.5 174.5 173.5 176.1 153.7 138.7 149.0 1325. 165. 168.1 1 3 1 2 .7 . 1 7 5 . 6 1 7 5 . 4 1 7 6 . 5 1 5 3 . 7 1 3 9 . 3 1 5 0 . 0 68.9 166.8 172.1 7 176.2 176.4 175.1 165.8 1 166.8 165.2 169.7 7 174,4 175.0 174.1 174.0 172.7 175.3 151.7 137.7 147.9 1301.0 1 7 6 . 8 1 7 6 . 6 1 7 8 . 1 1 5 3 . 3 1 3 9 . 2 1 4 9 . 6 1 6 9 . 6 1 6 6 . 8 0 1 7 6 . 0 1 7 6 . 6 1 7 5 . 6 1 2 8 1 .7 1 7 1 . 8 164.8 169.4 _ 166.6172.2 9 175.6 177.0 176.9 174.8 175.5 177.0 152.5 136.2146.9 1257.2 170.2 ,0 167.0 171.5 0 176.2 177.0 176.0 175.3 175.8 178.4 152.9 138.5 149.0 1259.7 134.6 iti.b 167.6 1 1 7 7 . 1 1 7 5 . 8 1 7 7 . 7 1 5 3 . 3 177.2 175.8 171.5 7 176.9 138.6 149.2 1257.S 62.5 167.5 70.2 .7 167..2 139.4 1 6_173.0 1 177.5_177.7 178.2 176.3 175.5 177.0 153.3 139.4 149.8 1253.3 63.7 168.0 170.4 ,53 116687. 139.4.1 2 172.9 6 177.1 177.4 177.4 174.8 175.5 178.0 152.5 138.7 149.2 1236.8 163.9 168.1 170.8  00 .. 77 35 92 0.755 0.762 0.769 0.780 0.795 0.794 0.795 0.796 0.809  Tin  fm  TTT)  tTv)  tTsT  TTT)  fm  Tie)  Ti9)  tuo)  t u d  t< 12>  nm  72.6 1 7 2 . 8 140.4 163.8 166.8 171.3 168. 166.8 171.1 169.( 174.9 175.3 175.2 1 71.1 1 7 1 . 8 136.0 161.5 165.0 169.4 165.9 165.1 169.1 167.S 173,8 174.0 173.8 1 174.0 173.0 171.4 171.2 136.0 160.7 164.0 169.8 166.3 164.6 169.2 166.2 173.7 1 4.0 173.5 171.6 1 7 1 . 6 138.1 160.7164.2 169.2 165.9 164.6 169.2 169.2 173.7 7 75.4 174.i 174.1 1 7 4 . 4 136.8 161.5 165.8 176.6 167.6 165.6,TTOTS" 170.0 174.5 1 175.9 174.2 173.7 1 7 3 . 8 139.6 163.6 166.6 172.0 167.9 165.7 170.6 170.0 174.9 1 7 5 2 174.4 172.6 173.1 136.4 163.4 166.5 170.7 167.3 165.3 170.8 166.8 174.5 174.0 174.8 172.2 1 7 2 . 9 137.6 163.4 165.6 171.0 166.9 165.0 169.7 168.'' 173.9175. 175.2 174.2 172.B 136.4 163.0 166.6 171.2 166.9 165.8 172.0 170.0 175.4 175.6 3 174.6 173.0 1 7 4 . 0 138.0 164.0 166.4 171.3 167.3 165.7 171.2 169.2 174.9 175.9 T t T T o " 173.6 1 7 3 . 7 138.3 164.1 166.6 171.3 167.6 166.1 171.2 169.2 174.5 139.0 164.5 167.2 171.6 167.4 165.7 171,0 169.2 175.3 139.5 165.2 167.8 173.1 168.4 166.9 171.8 170.4 175.6  " T i l l "  tu4)  -  T m  136.8 159.8 139.4 16l.i 137.6 159. 138 160.5 138 139 159.6 138  i  10.0 17.0 21.0 25-5 30.8  34.0 40.8 4T.0  3-  RUN 41. Til)  Tl 2)  TI3I  139.6 139.3 138.0 137.6 136.4  174.2 174.7 175.1 176.3 175.9  139.4 139.8 139.8 140.6 139.2 139.8 138.4 1.38.8 139.0 136.4  W 0.172 T(4)  RE 26430.  OH 73010.  T(5>  TI6)  TI7)  TI81  1B6.1 186.2 185.4 186.4 169.1  194.1 188.9 194.2 169.1 193.4' 1B9.3 194.9 190.1 196.1 190.B  187.7 188.1 188.3 189.2 192.3  195.5 195.6 195.7 197.2 199.5  194.7 194.4 195.? 196.1 198.C  183.1 189.9 182.4 1B9.9 182.0 189.9 183.9.191.1 183.5 190.3 183.2 191.1 193.9 196.7 184.3 190.3 183.5 191.1 171.6 187.2  196."/ 191.2 196.4 191.8 196.1 192.0 197.6 192.0 196.5 191.6 197.4 193.7 198.6""[VS" 1 196.5 192.0 '196.9 192.8 193.8 1B9.7  lsl.2 191.2 191.2 191.5 190.8 191.9 191.6 191.6 191.9 186.4  197.6 196.9 198.0 196.9 197.8 197.3 198.3 197.3 197.2 196.5 198.7 197.8 19871" 197.7 198.3 196." 19B.7 197.7 194.5 193.8  201.3 201.8 202.2 203.1 204.2  204.7 205.5 205.8 207.3 210.2  T(2I T131 163.8 165.3 163.4 165.3 162.9 165.4 163.4 166.0 163.9 166.2 163.9 166.4 163. 2 166,4 164.9 167.2 164.9 166.4 163.4 166.0 164.6 166.4 163.8 166.0 164.9 1 6 5 . 8 164.4 165.6 165.5 166.4 165.4 166.4 165.5 166.2 159.2 158.2 159.3 159.0 163.0 165.3  T14] 171.4 171.7 172.0 171.4 171.6 172.5 172.3 172.3 171.9 171.0 172.7 171.8 172.1 171.8 17219 172.5 172.5 164.1 164.0 171.6  T(5) 165.8  TI6) 164.6 164.2 164.9 164.6 165.1 165.6  T(7) 169.5 170.0 169.9 169.5 170.7 171.0  165.7 166.2 166.5 166. 1 167. 1 167.9 165.4 171.8 167. 3 165.6 171.1 166.9 165.4 170.3 166. 1 164.6 170.3 166.5 164.6 170.7 166. 1 164.6 169.9 166.5 165.0 170.3 166. 1 164.6 170.3 166.3 165.6 171. 1 165.5 164.6 170.7 165.3 164.4 170.9 157.9 1 56. B160.9 15B.3 157.3 161.2 165.7 163.8 170.2  136.2  138.0 136.4 136.0 137.6 138.0 137.6 136.0 137.6 137.6 136.8 138.0 136.& 138.0 138.0  T12) 156.2 156.4 156.0 156.0 157.8  T(31 T14) 15B.6 160.3 159.5 160.6 ISP.8 159.5 15B.0 159.8 160.7 160.7 161.7 159.6 161 . 1 160. 1 161.3 157.5 159.6 160.9 158.2 161.1 161.4 158.2 160.9 161.9 157.6 160.3 161. 1 157.8 161. 1 161'.7 159.2 161.7 162.2 157.4 160.0 160. 157.fl 160.4 161.9 157.6 160.3 161.5 156.7 161.9 158.0 161.4 158.3 162.2 159.3 161.1 162.7 158.2 160.8 167.3 158.2 160. 7 162.5 158.2 161.7 157.4 161.9 158.2 160.4  161.7  TI5) TI6) 161.7 161.6 162.6 162.6 162.0 161.7 162.0 161.9 162.9 163.3 163.3 163. (. 163.6 163.(1 163. 1 162.0 162.6 162.B 163.7 163.6 164.3 162.B 163.4 162.9 164.3 163.2 164.3 163.6 163.0 163.6 163.9 164.2 163.1 163.4 164.5 1 6 4 . 6 163.9 163 164.7 163 164.3 163 164.3 163 164.3 163... 164. fi 163.6 164.4 163.B  203.0 203.6 204.1 205.4 206.8  201.9 201.6 200.0 200.7 203.8  TWC  TIB) T19) TI101 173. 2. 174.6 174. 0 174.7 173. B 175.0 173. 5 175.1 174. 2 175.6 173. 8 175.9 1 7 3 . 6 175.9 174. 6 175.9 174. 2 175.9 173. 4 175.2 174. 3 175.9 173. 4 175.6 173- B 177-3 173. 2 176.3 173. 6 177.3 173. 2 176.3 169.f 173. 0 175.9 159.1 163. 8 165.4 159.5 163. 8 165.2 16B.4 172. 7 174.8 16"B'.1 16B.1 168.1 169.2 169.2 169.1 169.4 169.2 168.9 168.5 169.2 169.1 169.h 168.9 169.8 169.7  RE 45809. Till 135.9 136.4 135.8 135.4 136.8 137.6 136.4 136.8 136.4 138.0 137.6  DTMC 48.2  201.5 201.5 199.9 201.4 202.8  205.4 204.5 203.4 204.6 205.B  163.2 163.6 163.6 163.6 163.2  202.6"20871"205."5~202.3 262.3 205.0 161.7 202.6 207.4 205.1 202.7 202.8 205.0 162.1 202.5 207.3 205.3 203.7 203.8 205.3 162.2 202.9 207.3.205.3 204.4 204.0 206.9 162.4 202.5 206.9 205.3 203.5 201.9 205.3 161.3 203.3 206.3 206.4 203.3 203.4 207.6 163.1 203.7 207.3 206.6 202.7 203.0 205.3 161.7 202.9 206.6 205.9 202.7 202.5 205.7 161.7 203.1 207.3 205.7 203.7 202.6 705.3 161.7 199.9 205.0 204.1 202-7 202.3 203.8 163.6  RE 56216. Til) 139.8 139.0 139.8 140.4 140.2 140.4 140.0 140.8 139.6 13B.B 139.2 139.7 140.0 140.0 140.9 140.1 139.2 138.8 139.2 139.1  TWC 196.3  TI9) T 1 10) T(ll) TU2) Tl 131 TI14) T(15)  170.2  Till) TI12) 173.5 173.1 173.6 173.0 174.0 173.0 174.6 173.5 174.6 173.8 174.6 173.2 174.8 1'74.4 174.8 173.6 174.2 173.8 173.5 173.1 174.3 173.1 173.9 173.0 174. 1 173.2 174.3 173.3 175.7 173.B 175.0 173.6 174.6 173.6 164. 1 162.0 163.9 162.B 172-7 171.5  TI13) 172.8 172.1 172.5 172.3 172.5 173.5 173.3 172.7 171.7 172.1 173.3 172.5 173.3 172.6 173.3 172.9 172.9 161.8 162.2 171.5  TWC 166.0  T(7) TI81 T|9) TUP) 164.3 165.2 169.5 178.1 164.9 165.7 169.5 179. 4 164.9 166.0 168.6 178.8 164.4 166.0 168.0 179.4 165.5 166.3 169.6 179.4 165.7 166. 169.7 179.3 165.0 165.9 169.7 179.9 i65.o :165.3 169.9 179.3 165.6 :165.t 170.3 1B0.4 1H0.B 166.7 167. ? 170.3 180.6 166.0 166.T 170.7 165.3 166.0 169.9 179.7 166.2 166.7 170.5 1B0.1 166.9 167. ' 171.1 181.6 165.6 165.*- 170.3 179.9 166.8 167.1 171.4 101.0 165.4 165.* 170.7 181.0 167.1. 166.9 171.5 166.4 166.3 170.8 166.9 167. ? 171.6 166.8 167.7 171.5 166.9 167.5 171.1 166.6 167.3 171.1 166.4 167.1 171.1 166.B 167.3 171.4 166.*) 166.'' 171.1 :  f.  Till) T<12) 170.8 172. 5 170.9 171.4 170.1 172.0 170.2 172.6 170.8 172.8 171.6 172.8 171.0 172.2 170.8 173.4 171.6 173.9 172.6 1 73.5 171.9 173. 171.2 1 73.7 172.4 174.6 172.9 173. 1 171.4 174. 1 172.6 172.6 171.6 174.2 173.2 173.7 172.0 174. 1 172.6 174.3 172.1 174. 1 172.4 174.4 172.2 174.1 172.8 174.6 173.4 172.8 TWC  TI131 161.8 162.2 161.7 161.3 163.2 163.6 163.2 163.2 163.2 164.2 164.7 163.6 164.0 165.2 163.8 164.9 164.1 165.0 164.4 165.4 165.0 164.4 164.6 164.B 164.6 164.0  172.3  TIN  139.4 139.3 137.8 139.2 139.2  TOUT  156.7 158.7 157.3 158.6 158.7  138.9 158.1 138.6 157.9 138.5 157.9 137.9 157.3 137.6 156-9 139.2 158.6 138.B 158-1 137.8 157.3 138.7 157.3 139.B 158.8  •  HM  1000 R  1519.9 0.65B 1509.0 0.663 1470.2 0.680 1477.1 . 0.677 • 1428.2 0.700  1436.8 1425.8 1423.8 1398.9 1412.9 1430.4 1415.1 1407.9 1400.2 1529.2  TI HE 0.0 0.7 3.0 5.0  o76"9"5 84.3 0.701 91.5 0.702 97.B 0.715 102.5 0.708 107.8 0.699 115.0 07707—13075 0.710 125.5 0.714 131.3 0.654 131.5  -  DTMC 27.1 TI14) 175.1 175.1 175.1 175.2 175.9 176.0 175.5 175.1 175.1 174.5 174.7 173.6 175.2 173.9 175.2 174.3 174.3 163.0 163.4 173.9 DTM:  T(15) TIN 149.5 139.4 150.3 138.9 150.3 139.0 149. 5 138.9 149.2 138.8 150.3 139.2 149.5 139.6 149.5 136-8 149.2 13B.5 149.2 137.B 149.5 138.9 149.5 137.7 149.2 138.6 148.4 138.3 149.5 139.3 150.3 138.3 149.5 138.1 144.5 138.3 144.2 139.0 149.5 13B.9  TOUT 147.6 148.2 147.6 147.2 147.3 147.7 148.4 147.6 146.9 146.2 147.5 146.0 146.8 146.4 147.8 146.6 146.5 143.6 144.1 147.5  HM  1000 R  2598.1 2594.9 2554.2 2516.9 2487.3 2501.1 2530.4 2466.9 2464.0 2448.2 2496.4  0.385 0.392 0.397 0.402 .400 6.395 0.405 0. 406 0.408 0.401 0.413 0.409 0.409 0.403 0.411 0.411 0.793 0.288 0.3B4  24ie.9  2443.4 2447.3 2462.5 2433.1 2433.7 3416.2 3475.6 2601.4  15.8 19.8 24.1 27.5 32.4 39.4 45.4 56.4  102.1 102.4 102.5 102.6  23.5  T JUT TI14) TI15) TIN 143.6 13E.1 147.9 2626.5 143.6 138.8 148.6 2643.7 2663.9 167.5 142.8 13B.1 148.2 167.6 143.2 1 17.3 147.2 2596.9 16B.7 1 43. B 136.4 147.7 2526.4 143.9 138.1 146.6 2434.5 143.9 137.9 147.3 2485.1 143.2 1)6.9 H6.3 2417.3 141.2 137.7 146.6 2411.2 1 44. 5 139.4 144. 1 2556. •) 144.0 13B.7 14B.3 2497.3 143.2 l3?.3 U 7 . 1 2436.2 2478.7 143. 2 139.6 14B.3 2418.? 144.3 138.6 US.2 2425.1 144. I 137.3 146.B 2441.4 144.4 138.8 148.? 2435.7 143.6 137.5 147.3 23B8.1 170.1 143.6 13B.7 147.7 2417.1 170.0 144. 3 133.0 147.5 242B.6 170. I 143.7 138.7 143.) 2416.2 170.2 144.D 139.9 147.9 2441.8 169.7 144.5 138.7 148.2 2396.7 143.6 169.3 13B.1 147.5 "TTTBTT"" 169.7 144.4 139.5 147.3 169.3 143.6 130.0 147.7 241B.0 170. 1 143.6 138. 3 1 47. 7 2402.2  0.378 0.375 3. 3B5 0.396 0.411 0.402  5.0 7.3  9.D  0.403 0.413 0.412 0.410  -  •TH:  TIME  0.365  0.414 0.412 0.414 0.410 0.417  -57417—111.5  0.413 0.416  123.3 131.0  19.4  "TTTI  TTD TTO TT51 TTTi TI6) ' TI7) ITB7 T|9) TtlO) Till) H12J TU31 TI14) IMS) TT3 TUOT152.5 156.8 2128.6 0.470 171.9 165-5 176.0 176. 1 177. 1 174.0 149.6 156.6 171.3 170.4 169.1 172. : 153.2 157.9 2103.6 0.475 173. ' 167.3. 177.2 176.8 177.3 175.0 151.0 157.6 171.9 171.2 170.3 17 3.1 153.8 158.6 2024.4 0.494 174.8 167.7 178.5 178.4 179.2 175.6 181 .6 152.7 158. B 172.2 172.5 171.2 174.; 153.2 158.4 2078.8 0.4B1 171.1 174. C 167.5 170.7 178.0 178.7 174.3 181.4 150. B 158.1 172.5 171.6 170.3 "2TT9T3 "D'.472"' 1 7 1 . 1 173.A 167.1 178.4 177.6" 178.7 173.6 180.5 151.0 153-3 1 5 8 . 8 151.6 1 5 7 . 1 172.5 170.fl 2132.2 0.469 149.8 157.1 171.9 170.0 171.1 173.1 169-5 172. 8 166.3 178.8 177.2 178.3 173.8 181.7 149.8 153.6 15B.4 1978.1 0.506 149.8 157.1 172.7 171.7 171.3 T737i 169.9 174.0 166.1 17B.4 177.6 178.7 174.6 181.9 149.8 152.7 157.4 19B6.1 0.504 151.8 158.8 172.9 172.0 170.7 173. ' 170.1 172.9 167.3 178.1 177.4 177.9 174.1 181.5 15! .B 152.2 157.2 2003.5 0.499 177.6 178.3 174.5 1 52.2 181.9 173.3 172.0 171.1 169.9 173.2 152.5 157.7 152.2 159.1 174. ' 167.9 178.4 1932.2 0.518 169.5 174.1 169.5 172. B 166.3 177.7 177.2 177.1 173.B 180.8 150.2 151.7 155.7 150.2 157.9 171.7 C7T77 150.9 158.7 172/9 " 173.1 169.9 17 3.2''T&7.I 177.5 177. B 1 77.9 TT4TTT 181 .b 150.9 152.5 15 7. 7 :"TTJTtJTB 0. 496 16.1 2015.4 151.4 158.7 174.3 1 73.1 169.5 173.2 167.5 178.0 178.0 176.3 175.0 IB1.9 151.4 152.8 158.1 0.496 17.6 2015-7 150.2 158.9 172.3 L71.6 170.7 173.1 169.5 173. 7 166.9 177.6 177. B 178.5 174.6 1B2.7 150.2 152.5 157.8 0.510 1961.5 19.4 150.2 158.1 173.3 1'72.4 171.1 173. ' 169.5 173.B 166.9 177.6 177.6 178. B 175.1 182.3 150.2 151.9 157.2 0.492 175.4 151.4 182.7 20.7 2031-1 151.4 157.9 172.5" 171.6 170.7 1 7.3. ( 169.9 174 17B.B 179.1 152.8 159.7 160.1 170.2 0.516 21.6 1937.3 152.7 15B.3 172.1 171.6 171.5 174. ( 171.1 175 167.9 179.6 180.4 181.6 177.7 1B2.7 152.7 153.2 158.7 176.9 162.5"fSlTB-lW.l 159.5 ' 202BT6 lt>l .6 T5T7T" 173.5 172.6 17179"T747J 172.1 L 7 5 - 1 167.7 "17976™ ISO.2 180.8 074()3 2T78 150.4 L57.5 172.3 171.6 171.1 1 74.( 171.1 174.2 179.8 179.5 175.9 182.9 150.4 152.2 157.4 1889.9 .529 22.5 180.0 180.6 176. 1 183.9 151.6 153.5 159.1 1975.8 0-506 23.5 172.0 171.7 174.1 172.0 175.4 151. B 158.7 173.3 176.1 183.9 173.3 171.7 179.2 179.9 151.B 157.9 1975.4 0.506 26.7 171. 1 174.' 152.8 158.3 172.3 174. 3 151.8 175.7 182.7 172.9 171.1 17B.4 179.9 151.0 158.7 0.510 2B.7 1 70.5 1 73.1 172.0 173.6 1961.2 152.2 157.7 151.0 182.5 151.2 152.3 0.517 29.5 172.4 170.9 174. ( 170.7 174.6 167.4 178.9 17B.2 179.6 175.7 1934.0 157.3 151.2 156.5 172.9 175.7 182.9 1 72.3 1 70.5 197678" ""0.'5D"f" 30.4 151';'2""15877 172.9 171.5 170.5 1737' 170.6 173.1 1 6 7 . 0 1 7 8 - 4 176.4 179.4 175.3 182.5 151.2 T"52".l 157.6 0.504 33.4 1985.9 151.4 158.7 173.5 177.4 171. 5 174.1 170.3 1 74.5 168.1 178.5 178.2 179,5 175.3 1B3.3 151.4 152.8 158.1 0.495 34.4 2019.9 149.8 157.9 172.1 172.2 170.9 173.' 170.3 174.6 167.7 178.9 179.4 178.7 174.1 1B2.1 149.6 152.6 158.4 0.504 35.B 1984.9 150.2 157.5 173.1 171.6 170.7 1 73.; 170.9 173.8 167.3 177.9 178.6 178.1 174.6 183.3 150.2 151.9 157.4 0.489 38.8 152.2 159.1 172.7 171.6 171.6 173.' 170.1 174.7 167.5 178.9 179.2 179.7 174.7 182.5 152.2 153.1 15B.7 2044.7 178.0 178.7 157.9 0.498 40.9 170. 7 171.8 ISO.2 150.2 152-2 157.8 2008.1 173. : 170.7 173.8 167.7 178.3 182." 7"T 172.4 T7TTT 151.0 157.9 173.3 5T7TJ174". V T67."517B.3 178. B 17B.7 175.3 158". 4"" -2 03X73 D7T9T 42.2 1 172.9 171.5 T7TT 180.3 176.1 183.1 150.2 152.8 ISO. 2 158.7 174. 1 75.2 179.2 1653.5 0.540 151.9 157.1 • 171.5 167.8 178.7 175. i 175.7 172.2 170.7 174. : 170.7 174.6 167.6 178.3 17B.4 179.5 175.9 162.3 151.4 151.3 157.3 151.4 156.3 173.7 1890.8 0.529 182.7 151.4 1 172.4 151.4 157.9 174. 1895.9 0.527 152-3 157.3 167.8 178.5 179.2 160.3 174.1 171.1 175.2 179.9 175.7 182.5 151.4 157.9 173.7 172.2 1923.5 0.520 49.4 174.1 171.3 175.2 167.6 178.7 178.8 179.1 174.8 182.7 151.4 152.3 157.5 150.6 157.9 173.3 172.3 150.6 1681-9 0.531 152-5 156.6 50.0 174.1 170.7 1 74.5 167.5 178.8 178.8 179.3 182.7 151.4 178.4 ~ T T o T T " T747 "77077" 183.1 T5T T5775—TTT77- "195673 D.511 52.5 151.0 171.1 I 73. 169.9 : 151.0 151.3 155.9 1862.6 0.537 177.B 178.7 1  -  -  -  -  1  3s-15  TABLE  3-III:  COMPARISON WITH T H E  RE  I !  PR  5203. 8209. 9914. 9766. 9594. 10622. 14119. 14472. 14577. 13580. 14319. 14351. 14918. 13841. 16738. 20146. 27892. 30131. 29193. 28342. 41871.  t  '  =  Reynolds  PR  =  Prandtl  VISR  = 'fJL/  CP = h e a t  =  2 .27 1 .82 2 .16 1 .68 1 .71 2 .03 2 .07 2 .17 2 .17 1 .71 2 .49 2 .79 2 .99 1 .90 1 .71 2 .31 2 .07 2 .16 1 .71 1 . 75 1 .71  /A  NU  HC AL  193. 266. 3 19. 306. 303. 3 25. 407. 416. 415. 3 88. 4 26. 432. 439. 398. 4 70. 570. 7 12. 765. 718. 725. 9 50.  183. 259. 266. 280. 289. 294. 378. 387. 385. 390." 385. 389. 383. 394. 485. 564. 678. 726. 776. 786. 1010.  = Nusselt  HR  NU  1.06 1.02 1.20 1.10 1.05 1.10 1 .08 1.08 1.08 1.00 1.1L 1.11 1.15 1.01 0.97 1.01 1.05 1.05 0.93 0.92 0.94  number  w  capacity,  0.023 HCAL/H  0 .656 0 .598 0 .672 0 .677 0 .663 0 .660 0 .635 0 .600 0 .585 0 .633 0 .665 0 .659 0 .573 0 .635 0 .650 0 .639 0 .667 0 .643 0 .612 0 .653 0 .595  Re  BTU/lb  °F  transfer °'  8  p  0 r  -  coefficient, 3  3  3  (U/LL) ° ' >  ~ nv  COEFFICIENTS  EQUATION  number  D HR  TUBE HEAT TRANSFER  H  CP  number  H = measured heat HCAL =  CLEAN  SIEDER-TATE  VISR  25. 7 24. 4 25. 0 25. 5 25. 5 23. 0 22. 6 ' 22. 4 21. 8 23. 4 23. 3 23. 1 21. 5 23. 0 25. 0 25. 3 23. 7 23. 9 23. 5 25. 7 22. 9  RE  OF  1 4  BTU/hr-ft  2  °F  6 7 . 65 9 5 . 71 9 8 . 18 1 0 3 . 24 1 0 6 . 58 1 0 8 . 65 139. 7 5 1 4 2 . 90 1 4 2 . 32 143. 7 6 1 4 2 . 18 1 4 3 . 85 1 4 1 . 63 1 4 5 . 53 1 7 8 . 99 2 0 8 . 25 2 5 0 . 23 2 6 7 . 92 2 8 6 . 25 2 9 0 . 00 3 7 2 . 68  ! !  i  ;  3-16 TABLE  9. 10 8.90 8.9U 9.25 a.90 9 . 10 9.00 B.90 • 9 . Ill 9.CO 9.CO 9.00 9.00 9. IQ 9.00 9.00 9.00 9.00 9.00 9.10 9.10 9.20 9.20 9. 10 9.30 9.25 9.2? 9.25 9.20  0.! 1.2 3.3 7.7 . 16.0 19.5 24.1 26.3 29.4 31.5 41.2 44.3 *e.a 53. 2 57. 5 65.1 69.fi 74.0 60.8 89.6 lOl, I 10). 1 113.8 119,6 123.1 127.3 1?S.6 137.6 143.-) 1*7.1 152.5 16L.G 145. 1 169. 5 LT5.2 185.4 189. 6 194.4 200. 0 209.0 213.5 216.7 219.0 224.3 233.1 238.5 243.5 248, 257.a 262.4 261.9 271.S 2B0.7 2B5.1 290.4 295.6 304.7 301.0 314,7 311,7 32fl.3 3)3.6 336. 3 3*4.6 352.B 356.4 362.4 368.4 374.2 377.4 382.6 38B.fi  9.25 9.*5 9.55  9.55 9.60 9.60 9.65 9.90 9.90 10. IS 10. 10 10. 10 LO. 10 10. 10 10.35 10..)5 10.50 10.50 10.35 10.7fi 10. "Cl 10.65 10.65 10.70 10.70 10.75 10.95 u.co 11.15 11.00 11.10 ll.lO 11.10 11.05 11.15 11.20 11.30 11.25 11.20 11.20 11.35 11.70  3-IV.  P R E S S U R E DROP AND D E P O S I T  RUN TIME  15. RUN TIME DELP X 1.5 69.00 a.cooo 3.7 68.70 o.cooo 6.2 69.00 o.oooo IS. 4 69.00 19.3 69.CO o.cooo 23.4 69.00 o.cooo 25.9 69.00 O.COOO 31.4 69.00 o.aooo 39.9 69.00 o.ccao 0.0000 44, 7 69.00 *9.6 69.00 o.oaoa 5).* 69.CO o.ccco 63.8 69. 00 o.cooo 6B.6 69.00 o.aooo 73,8 69.00 o.cooo 74.0 64.00 O.COOO 0.0000 SB.8 69.00 92.5 69.CO a.coco 9B.3 69.00 o.cooo 103.B 69.00 o.aooo 112.4 69.00 o.aooo 69. CO fl.CCCfl 111.8 122.2 69.00 'O.COOO 132.7 69.00 O.cono 140.3 69.00 o.cooo 14B.7 69.CO o.coco 137.2 69.00 o.cooo 1*4.1 69.00 0.0000 170.2 69.CO o.cooo 181,* 69.00 o.caoo 187.9 69.00 o.oooo 18).* 69.00 20 5.4 69.15 O.COOO 312.4 64.14 0.0014 0.CO19 219.2 69.15 0.0019 229.1 69.30. 0.0018 237.1 69, 38 0.0048 2*2.1 69.15 0.0019 2S2.3 69,15 . . 0.0019 69. 15 0.0019 165.2 176.5 69,15 0.0019 287,0 69.30 O.OOJB SOO.T 69.45 0.0057  7.0  15.0 14.0 2*. 3 29.8  42.1 39.0 43.0 **.!  49.0 59.8 6B.5 75. 8 8*.5 ' 90.S 97.8 108.4 112.8 116.8 122.B 139.1 138.3 1*4. 7 156.2 162.7 170.3 1H6.6 186.6 193.8 219. B 205.0 229.7 .  RUN TIME 0.7 1.4 3.8 9.0 17.3 21.* 33.*  DELP X 69.00 69.CO 69.00 69.00 69.00 69.00 69.00  0.0000 o.caoo o.coco 0.0000  o.ccoo o.cooo 0.oonn  236.r  2*2.8 252.6 258.B 266.6 276.6 28*. 1 291.1 300. e 308.7 324.5 314.0  DELP 21.85 21.85 23.85 21.85 24.00  X  24.00 24.00  24,15 24. 15 23.70 21.85 23.70 21.85 21.85 21.85  24.00 24.00 23.85 24. 00 21.85 24.CO  23, 70 23.70 2 1 . 70 2 1 . 70  24.00  23.85 2.1. it 5 ii. 115 2 1.05 23.85 2 (.85 23. 85 23.B5 24.CO 21.B5  24.00 24.CO 21.85  24. 00 24.CCO 2*. O 24.CO 23.85 24.CO  24.00  18. RUN TIME OELP X 0.6 2.0 23.0$ 23.40 6.0 21.25 23.25 23.25 21.55 36.0 23.55 46.0 23.55  4.0  24.00  11.0  23.0 29.0  RUN 22. TIME HELP X 0.5 b.OO 1.0 6.CO 3.3 7.3 6 . 10 11.8 b. 10 22.8 6. 10 S4.5 6. 1ft 35.8 6 . 10 46,5 6.10 54.5 60.3 71.0 Tfi.O 6.10 6. 84.3 6.10 95.0 6.10 10L.5 109.5 121.3 128.3 6 . ID 146.3 6.10 156.3 6 . 10 170.5 6.10 187. 3 6. 10 192.0 204.•> 6. 6. Ill 216.J 6. 10 229.0 6.10 243.3 254. 5 6. 10 263.3 6.10 6.10 243.3 6. 10 102.5 6. 10 315,0 6.10 326.1 6.10 339.3 6.10 3*3.5 6.10  6.00  6.10  6.10  10  6. 10 6.10 6.10  60 .606  16.  17.  1.0 4.0  0.03B2 ' a.coon O.COQO 0.0135 D'.OOQO 0.0193 0.0097 0.OOQO 0.0193 0.0097 0.0097 0.C097 0.0097 0.0193 6.C097 0.0097 0.0097 O.C097 0.0097 0,0191 0.0191 0.0288 0.02BB 0.0302 D.0387 0.0135 0.03i5 0.0315 0.02B8 O.0302 0.0135 0.0520 0.0610 0.0610 0.0655 0.0655' 0.0700 0.0918 0.0918 0.1 111 0.1009 0.1089 0. 1089 0.1089 • 0.1596 0.1296 0.1416 0.1418 0.1296 0.15 76 0.1576 0.1537 0.1537 0.1576 1>. 1576 0. 1616 ti. 1770 o.ieo8 0.1921 0.1808 0.1SB4 0.1884 0. IB84 0.1046 0. 1921 0.1958 0.203Z 0.1995 0.195R 0.1958 0.2069 D.195B  0334  0134 0334 •0 00314 0 3 0oifla 0180 0388 0 0442 0 0442 0 02 79 0 0334 0 0 (1314 0 0334 0 0114 0 03B8 0 0 0388 0388 0 0388 00314 0 0134 0 0 0279  TIME  10.4  13.3 Sl. 6 23.4 24.7  26.0  0 0 0 0 0 0 00134  RUN 3.7 6.8 25.0 23.0 27.0 29.0 33.5  11.0  35.5 37.8 40.0 41.7 43.7 45.7 48.2  12.5  t  0144 0.0144 0.0144 0144 0.0144 0 0144 0.0144 0.0144 0 0144 0144  0  . ,  0144 1 . 0 0144 1 0 00144 0 0144  200.0  1  . 1 j;  RUN 23. ' TIME DELP X . 0.5 6.10 3.3 6.10 . 6.3 . 6.10 11.0 6,10 22.0 6.10 BUN 24. TINE DELP X O.B 14.55 1.8 14.45 4.0 14.45 7.3 i*.*i 12.3 14.4! 13.0 14.60 29.5 14.45 37.7 14,50 47.7 14.45 il.7 14.50 54.7 14.45 70.7 14.S5 81.1 14.50 94.1 lit.50 101.1 14.50 166.1 14.6J 106.1 14.60 113.1 14.60 124.1 14.80 137.4 14,90 1*8.4 15.10 114.4 14.40 171.4 14.90 IS*.9 14.90 196.9 15.00 209.4 14.90 220.4 14.80 132.4 14.40 145.* 15.05 156.7 15.00 15.10 m.« 240.0 14.95 303.5 15.00  17.0  0.0144 0144 U.U144 0.0144 0.0144 0144  0 00144 0.0144 0 0.0144 0.0144 0.0144 0.01*4  0  0.0144 0144  1  0  11.2 2 1 .2 25.3 23.3  OELP 7.70 7.80 7.90 8.25 8.45 • 8.80 8.85  31  2 .4 3.6  32.  DELP 14. CO 14.50 15.30 15.70 15.70 16.40  RUN 41. TIME DEL P o.t 5.95 3.0 5.95 5.0 6.CO 6.8 6.00 10.5 6.10 13.3 6.05 20.5 6.15 25.3 6.25 30. B 36.3 6.45 43.5 48.3 6.45 53.0 6.50 60.3 6. 50 67.3 6.60 73. B 6.70 84.3 6.BO 91.5 6.80 97.8 4.80 102.5 6.80 107.8 6.60 115.0 6.75 . 120.B 6.75 125.5 6.80 .1S1.1 6.80  0.1119 0.1524  0.1524  0.1524 0 . 1432  0.0510 0.1268 0.0B11  0.  14B6 6.1652 0.I486 »  OELP  ' X  14.20  5.8 2.3 B.8 10.9 17.4  15.Oo 15.40 15.60 16.40  23.4 2 0.9 26.9  16. 00 14.00 16. 00 16. 00 16.CO 16, 00  29.4 32.4 33.4  0.0445 0.0445 0.04*5  0 . 0.1197  9.20  1.1 1.9  RUN 40 TIME DELP 1.2 4.75 3.0 4.85 6.8 10.6 4.45 16. B 4.95 20.8 4.9B 25.8 4.98 31.3 4.99 34.0 4,99 40.8 45.0 5.00 51. B 5.Q0  0.0221 0.0597 0.0B03 1149  9.00 9. 20 9 . 10  31.6 29.6  0.C091 0.0091 0.0226 0.0226 0.0358 0.0511 0.0445 0.0445  O.COOO  9.^0  27.3  RUN 33. TIME OELP 1.3 14.20 16.90 15.3 17. 70 19.60 24.3 27.3 30.5 20.70 34.3 20.70  11.0 21.0  0  ,0  36.  1  20.20  o.caoo 0.0475 0.07Q1 0.0812 0.1238 1028 0.102B 0.1028  0.  RLJN TIME 1.1  0.1028 0.1028  0.1028  *2.  2.1 4.8 6.8  OELP 22.10 21.20 22.30 22.33  22.50 22.60 22.4! 22.65 22.75 22.75 23.CO 23.00  20.70  HUM 14. TIME OELP 0.8 13.BO  1.8  3.1  5.8 8.S  1 2.5 18.1 19.0 22.5 27.5  13.00 14. 20 [5.20 13.00 17.00 16. 0 0 17.30 18.10  18.50  33. RUN TIME OELP 31.30 t' 4.3 Si.10 T.B JS. so 3  11.B  13.3 18.3 22. B 23.6 30.8 32.8  36.00  37.70 39,90  42,00  43.40 46.60 * 7 .CO,  9.0  0 .0000 0.1491 0.1879 0.2721 0.2967 0.3165 0.3165 0.3165  15.8 19. B  24.1 Z7.5 <  32.4 39.* 45.4  0,1443'' 0.2013 0.1902  OELP  16,00  0,2437 0.3073 0.2913  0.0111 0.0275 O.0T2O 0.1Z5T 0.1646 0.2119 0.2542 o.'ALo 0.3366 0.3455  23.00 23.15 23.60 21.30 23.75 23.40  63.7 . 71.9 79.9 87.7 93.9  O.0692 0.1201  0.3440 0.3615  0.C019 0.0000  0.0057 0094 0131 0 0149 0.0187 0 0206 0.0261 0.0279 0 0  X  0162 0423 0500 0 0525 0 0576 a 0651 0 0B71 0 0920 0 0 0  1  1  C069 C097 02 74 0 0341 0 0472 0517 0 0602 0 0666 0 0666 0 0 0  RUN 19 TIME OELP 0.8 12.70 1.8 12.80 3.0 12.95 7.8 13.00 10.0' 12.90 17.0 11.05 21.0 11.15 25.5 13,25 30.8 13. 10 34.0 11.40 40.8 13.35  1  1 0 0060 COOO 0 0000 COOO o.cooo 0.C090 o.aooo • 0 0030 0 caoo 0 OOifl 1 0.0000 0.C060 0.00)0 0.0030 0 0030 1 0.0120 ! 0 C090 0.0209 0 0208 I 0.0267 0 0382 0247 0.0267 0 0267 0 0324 0.0267 0 0208 0.0267 0 0153 0 0124 0.0382 0.0296 ' 0 0324  ft  10.00  4.2  0000 0 0000 0. 0 0 0 0 0 coco COOO  0  10.00 10.00 10.oa  2.9  1  0 . 0.1078  0.107B 1022  10.10  14.5 18.5  RUN TINE  0.1078  10,00  31.0 33.0  RUN Tint  1  0.0909 0.0852 0.065" 0.0852  9.90  5.4 2.9 7.4  | 1  0.0064 0.0064 0.006* 0.0794 0.067.3 0.0857 0.0966  DELP 9.60 g.iti  'X  RUN 38 TIME DELP O.B 6.30 2.B 6. 32 6. 1 6.45 10.4 4.50 15.8 6.60 20. 1 6.65 24.1 6.70 28.1 6. 75 33.6 6.75  O.COOO  9.75 9.75  24.3 21.3 <f/.U 29.0  I1 1  DElP 11.50 13.60 11.60 13.60 14.BO 14. 14.90 15.10 14.90 15.CO  0.0096 29  RUN TIME  1  0.1168 0.1394  14.90 14,90 15. )J0 15.30 15.20 15.30 13.45  T.O 2 .0 1 2 .0 13.0  0 COOO caoo o.cooo 0144  10 0  6.10  RUN TIME  C056 0 ccao 0 0ccao 0 0000 00112 0112 ! on? •0  0 0 0144 0.0144 0144 0 0 ti  15.95 1 5,95 16.CO  2.3  0 0114 03BB  0276 0272  16.00 28  . RUN 37. ' TIKE DELP 3.8 16.30 10.3 16.80 13.0 16.95 14.0 17,00 23.5 17.10 30.3 17.25 36.5 17.70 38.5 17.BO  0.0114 0.COOO 0.1168 0.1394 0. 1473 0.1420 0.1446 0.1194 0.1368  16. 10  YIHE  0314 00188 0 0388 0334 0 0388 00386 0 03BB 03BB 0 0134 0 0188 0 0181 0 0  8.3 11.5 14.4 20. B 26.3 29.8 37.1  0.0158 0.0017  16. 00 16. 15  46. 10 46.00 46.30 46.50 46.70 46.40 47.00 47.10 47.40 47.50  5.0  X  1 5.9? 16.05  27.5 29.5 31.7 33.B 36.3  02 ?9 0279 0279 03BB 0114 0314 0 0414 0334 0134  1.3 2.5  27 DELP 11.85 13.65 13.60 14. 10  OELP  TIME  •.0111 0.0192 0.O243 0.0261 0.192B  13.40 13.40 15.10  14.3  0  X  DELP 13.20  1 ..0 5.0 2 0 7.8  RUN TINE 4.0 6.8  THICKNESS  —II. « .. 1ft.00 16.00 _ 16.25 16.19 9.0 ' 16.20 u.o 14.15 '"16.0 16.19 23.3  •?:!-  _*7..l. 29.5 S2.fi 36.0 42.0 30.0 . 93.3 60. S 67.3 72.3 65.5 93.5 100.5 113.5 120.5 111.0  16.25 16.40 16.90 45 16.40 16.49 _ 16.40 16.40 16.33  —M. —  16.43 16.49 16.90 16.90 16.90  0 0 0 0 0 0. 0 0  X.  0014 0082 0183 0217 0150 0250 0316 0382 041* 04T9 0*47  0.C092 0.0271 0.0367 0449 044 9 0.050? 0.0507 0 . 0519 0.0519 0 . 0519 0. 0516 0 . 053(S 0. 0.  0.0O73 0 . 0073 0146 0.0146 0290 0218 0360 0.0499 0 . 0S6B 0.0770 0 . 0703  0. 0.  a.  0.  0.0B34 0.0S36 0966 1094 1220 1220 0. 1220 0.1220 0 . 1220 0 . 1159 0 . 1158 0 . 1220 6. 1170 0. 0. 0. 0.  X '  C040 0.C079 0.  • 0.one  0.0137 0234 0.0195 0. O Z S J 0253 0291 0 . 029L 0.0386 0. 0386 0.  0 0..  0.0386 0.0442 0.0608 0.0371 0.0662 0.040S  0.0027  o.caoo— 0.C027 O.COZT 0.016Z  00 .10a  0.0133 0.Oioa 0.0108  0.010a  0.0162 0.0242 0.0295 0.S245— . 0.0242 ' . 0.0268 ' _ .0.0242 0.0242 0.02H O.OSil 0.0260  „O.0IM_ 0.0293 0.0299 0.0295 ,  1  3-1:7  TABLE Oil  3-V:  P A R T I C U L A T E CONCENTRATIONS  Fouling Run  Particulate Beginning  Water  14  22. 6  Concentration  o f Run  (mg/liter) End  o f Run 24.0  15  15. 8  6.5  17  13.4  18.4  19  25. 5  28.6  25 27  25. 8  14.8 24.1  28  37.6 21.8  21.5  29  22.2  20.7  30 32  18. 8  18. 5 17.7  22.7  Fouling Run  Particulate Concentration  34  3.47  35 36 37  3.1 8.7  38  3.0 2.6  39  2.1  40 41  5.1 4.3  42  4.4  44  4.0  (mg/liter)  

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