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The impact of computer networking developments on computer based information systems, user organizations… Stevenson, David Lyle 1975

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PULP HILL EFFLUENT TREATMENT USING COMPUTER SIMULATION TECHNIQUES by NICHOLAS C. SONNTAG (B.A.Sc, U.B.C, 1970)  A Thesis submitted i n P a r t i a l F u l f i l l m e n t of the Requirements f o r the Degree of Masters of Science i n Business Administration i n the Faculty of Commerce and Business Administration  We accept t h i s t h e s i s as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA AUGUST, 1975  i  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t of the requirements f o r  an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia I a g r e e  that  the l i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree that p e r m i s s i o n f o r extensive  copying of t h i s  thesis  f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my d e p a r t m e n t , or h i s r e p r e s e n t a t i v e s .  I t i s understood that copying or p u b l i c a t i o n  of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my written  permission.  Department o f Commerce and B u s i n e s s The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, B.C. August, 1975  Administration  ii  ABSTRACT In t h i s study  a v a l i d a t e d model of the suspended s o l i d s and  oxygen demand e f f l u e n t s of a k r a f t pulp m i l l was s t o c h a s t i c chemical  The  effluent  s p i l l s and  normal p r o c e s s  lagoon waste treatment model.  d e r i v e d from the l i t e r a t u r e , system c o n f i g u r a t i o n s and  c a p i t a l and  to i n f l u e n t  concentration,  A l e a s t c o s t system c o n f i g u r a t i o n was level. were  I t was  The  superimposing  discharge.  Utilizing  operating  aerobic  cost r e l a t i o n s h i p  costs for various  s i z e s were determined.  Numerous experiments were run to e v a l u a t e sensitivity  d e v e l o p e d by  generated i s input i n t o a v a l i d a t e d c l a r i f i e r  stabilization  biochemical  the waste t r e a t m e n t  temperature and  hydraulic load.  determined f o r any  i m p l i c a t i o n s of a s p i l l b a s i n and  increased  system's  desired spill  effluent  frequency  evaluated.  concluded  t h a t the models c o u l d be a v a l u a b l e p l a n n i n g  p u l p m i l l management.  tool  to  TABLE OF CONTENTS  ± i i r  Page INTRODUCTION  1  CHAPTER I - THESIS DEFINED AND LITERATURE REVIEW. 1.1  THE PULP MILL MODEL  1.2  THE WASTE TREATMENT MODEL  1.3.  WASTEWATER TREATMENT PLANT COSTS  '.  CHAPTER II - SYSTEMS IDENTIFICATION 2.1  2.2  THE PULP MILL: WASTEWATER  3.2  . . . . i  4 7 10  . . . . .  . . .  FUNDAMENTAL PROCESSES AND RESULTING  12 12  Biochemical Oxygen Demand (BOD)  17  2.1.2  Suspended S o l i d s (SS)  18  THE WASTE TREATMENT PLANT  19  2.2.1 2.2.2  19 22  Introduction The C l a r i f i e r  . . . . . . . .  - SYSTEMS ANALYSIS  . . . .  27  THE PULP MILL.  27  3.1.1 3.1.2 3.1.3 3.1.4  28 29 39 42  S p i l l Data S p i l l Data Analysis . . . Production and Water Usage. . . Regular E f f l u e n t . . . . . . .  WASTE TREATMENT. 3.2.1 3.2.2 3.2.3 3.2.4  3.3  4  2.1.1  CHAPTER III 3.1  .  . . . '  The C l a r i f i e r . . The Lagoon. . Waste Treatment G e n e r a l i z a t i o n Discussion.  CAPITAL AND OPERATING COSTS OF WASTE TREATMENT  43 45 55 59 63 63  CHAPTER IV - MODEL DEVELOPMENT  74  4.1  74  PULP MILL MODEL DESCRIPTION. 4.1.1  Generating Chemical S p i l l s .  .'•  78  TABLE OF CONTENTS (Cont'd) 'Page  4.1.2 4.1.3 4.1.4 4.2  Production and Water. Bringing i t a l l Together. .' V a l i d a t i o n of Pulp M i l l Model  84 88 91  WASTE TREATMENT MODEL 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5  97  The General Structure The Model Subroutine TREAT. . . . . . . . . . . . . . . . . . . The COST Subroutine . Waste Treatment Model V a l i d a t i o n  CHAPTER V - MODEL EXPERIMENTS . . 5.1  116  DESIGN VERSUS COST 5.1.1 5.1.2 5.1.3  97 99 104 105 105  . . . . . . . . .  The Lagoon Cost Curves S e n s i t i v i t y Tests on Lagoon Cost Curves . . . . . . The C l a r i f i e r Cost Curves  116 121 134  5.2  SHOCK LOAD EXPERIMENTS  5.3  SUGGESTED DATA COLLECTION SCHEMES AND MODEL IMPROVEMENTS .  145  5.3.-1  The Pulp M i l l Model  145  5.3.2  The Waste Water Treatment Model  146  CONCLUSIONS  . . . . .  116  140  .  148  BIBLIOGRAPHY  151  i  LIST OF TABLES Table No.  Page  2.1  Typical BOD and SS Levels f o r K r a f t M i l l Sewers.  . .  19  3.1  Major and Minor S p i l l Locations i n Pulp M i l l Model .  30  3.2  Goodness of F i t Results f o r S p i l l Amounts (units of 1000 lb) .  32  3.3  Goodness of F i t Results f o r Time Between Unrelated S p i l l s (units of hours). . . . . . . . . . . . . . .  32  3.4  Related S p i l l Count f o r 3 Major Areas. . . . . . .  34  3.5  Goodness of F i t Results f o r Time Between Related  .  S p i l l s (units of hours). . . . . . . . . . . . . . .  35  3.6  Related S p i l l Count f o r Each S i t e  36  3.7  Related S p i l l Decision Matrix f o r Recovery Area (#1)  37  3.8  Related S p i l l Decision M a t r i x f o r Recaust Area (#2).  37  3.9 3.10  BOD, TS and SS of M i l l Liquor Samples. . . . . . . . . Pounds Na S0 Equivalent to Gallons of Liquor Conversion Factors . . . . . . . . . . . . . . . . .  38  3.11  Two Empirical D i s t r i b u t i o n s f o r D a i l y Water Usage Determined by Level of Production. . . . . . . . . .  40  3.12  Empirical D i s t r i b u t i o n f o r D a i l y Production i n A i r Dry Tons  40  3.13 "3.14 4.1 4.2 4.3  5.1  2  4  BOD, TS and SS Means and Standard Deviations f o r the Six M i l l Areas  .  39  44  Proportions of Total Hydraulic Flow from the Six M i l l Areas . . . . . . . . . . . . . .  44  A Sequence of S p i l l s Generated by the Pulp M i l l Model f o r the Recovery Area.  85  P r o d u c t i o n , Water Flow and Fiber Loss Data Generated by the Pulp M i l l Model . . . . .  89  Summary of k-s Tests f o r Simulation Generated and Real Data E f f l u e n t f o r D i f f e r e n t Steady State Time Interval and Temperature Combinations. . '.. . . . . .  112  Lagoon Capital Cost and Operating Costs f o r Combination 3 and Combination 4 Systems Standard M i l l E f f l u e n t . . . . . . . . . . .  117  . . . .  LIST OF TABLES (Cont'd) Table No.. 5.2A  5.2B  5.3A  5.3B  5.4A  5.4B 5.5  5.6  5.7  5.8  5.9  Page Lagoon Capital Cost and Operating Costs f o r Combination 3 and 4 Systems - Standard Influent Load, Temp = 30°C  123  Lagoon Capital Cost and Operating Costs f o r Combination 3 and 4 Systems - Standard Influent Load, Temp = 40°C  124  Lagoon Capital and Operating Costs f o r Combination 3 and Combination 4 System - Standard Hydraulic Load X . 9 .  "126  Lagoon C a p i t a l and Operating Costs f o r Combination 3 and; Combination 4 Systems - Standard Hydraulic Load X 1.1  127  Lagoon Capital Cost and Operating Cost f o r Combination 3 and 4 Systems - Standard Influent Load X .9  129  Lagoon C a p i t a l and Operating Costs f o r Combination 4 Systems - Standard Influent X 1.1. . . .. . . . .  130  Lagoon C a p i t a l and Operating Cost f o r Combination 3 and Combination 4 Systems - Increased S p i l l Frequency i n Recovery Area of M i l l . . . .  135  C l a r i f i e r Capital and Operating Cost f o r the Combination 1 and 2 Systems with D i f f e r e n t C l a r i f i e r Detention Time •  137  S e n s i t i v i t y Experiments on C l a r i f i e r Model f o r Hydraulic Loads ±10% of Standard and E f f l u e n t Loads ±10% of Standard  139  BOD lbs/Ton E f f l u e n t from a Combination 2 System for Various Factor Shock Loads over Various Time Intervals. .  141  Table Showing Lagoon Maximum Concentrations and Recovery Times as a Consequence of Various Shock Loads  143  vii  LIST OF FIGURES Figure Number  Page  2.1  Schematic Outline of Bleached K r a f t M i l l Operation .  13  2.2  C i r c u l a r C l a r i f i e r With Center Feed. . . .  20  3.1  Cumulative D i s t r i b u t i o n s f o r Pulp M i l l D a i l y Water Usage  41  3.2  D i s t r i b u t i o n of Terminal S e t t l i n g V e l o c i t i e s  for  Pulp M i l l Wastes  .  3.3  Dispersion Curve f o r Center Feed C l a r i f i e r . . . . .  3.4  Properties of Age D i s t r i b u t i o n i n Tank and of Outflows f o r Various Flows  . .  3.5  Schematic of Generalized Model  3.6  C a p i t a l Cost VS. Flowrate at Various % Removal of BOD: Aerated Lagoon Annual Operating Cost VS. % Removal of BOD: Aerated Lagoon . . . . . . . . . . . . . . C a p i t a l Cost VS. C l a r i f i e r Area: Primary & Secondary C l a r i f i e r . . . . . . . . . Annual Operating Cost VS. Flow: Primary & Secondary C l a r i f i e r . . . .  3.7 3.8 3.9 4.1  47 49  50 60 65 67 69 71  Diagram of Waterborne E f f l u e n t Streams Included i n Model I n d i c a t i n g S p i l l and Regular E f f l u e n t Locations. .  75  4.2  Flow Diagram of Pulp M i l l Model  76  4.3  Flow Chart of Subroutine S p i l l  4.4  BOD V a l i d a t i o n f o r Pulp M i l l Model. Real E f f l u e n t and Simulation Generated E f f l u e n t with I d e n t i c a l Input  96  SS V a l i d a t i o n f o r Pulp M i l l Model. Real E f f l u e n t and Simulation Generated E f f l u e n t with I d e n t i c a l Input  96  4.5  ; . . . . . . . . . . . . . .  86  viii  LIST OF FIGURES (Cont'd) Figure Number 4.6  -  •  Page  Four Wastewater Treatment Plant Configurations P o s s i b l e i n Waste Treatment Model.  100  4.7  Flow Chart of Waste Treatment Model. . . . . . . . .  102  4.8  Lagoon V a l i d a t i o n Showing Real Data and Simulation Generated E f f l u e n t (using same i n f l u e n t ) f o r Steady State Operation Time, t = 1 hr and t = 24 hr . . . . .  107  P l o t Showing Regions of A c c e p t a b i l i t y as Determined by K-S Goodness of F i t Test f o r Simulation Generated E f f l u e n t and Real Data E f f l u e n t Using D i f f e r e n t Steady State Time Interval and Temperature Combinations  Ill  Lagoon C a p i t a l Operating Cost Curves f o r Combination 3 and Combination 4 Systems. Numbers Beside Data Points Indicate Lagoon Area i n Acres . .  118  Lagoon Capital and Operating Cost Curves f o r Combination 3 System with Standard Influent Load and Lagoon Operating at 30°C and 40°C. Numbers Beside Data Points Indicate Lagoon Area in Acres f o r Indicated Temperature  125  Lagoon C a p i t a l and Operating Cost Curves f o r Combination 3 System with Standard Hydraulic Load M u l t i p l i e d by 1.1 and . 9 . Numbers Beside Data Points Indicate Lagoon Area i n Acres . . .  128  4.9  5.1  5.2  5.3  5.4  5.5  5.6  5.7  Lagoon C a p i t a l and Operating Cost Curves f o r Combination 3 System with Standard Influent Load M u l t i p l i e d by 1.1 and . 9 . Numbers Beside Data Points Indicate Lagoon Area i n Acres . . . . . . .  .  131  Lagoon C a p i t a l and Operating Cost Curves f o r Combination 3 System with Increased S p i l l Frequency i n Recovery Area of M i l l . Numbers Beside Data Points Indicate Lagoon Area i n Acres . . .  136  C l a r i f i e r Capital Cost Curves f o r Combination 1 and Combination 2 Systesm. Numbers Beside Data Points Indicate Theoretical Detention Time . . .  138  Lagoon Response Curves f o r Shock Interval of 24 Hours  142  ix LIST  OF APPENDICES  Appendix Number I II  Page Semi-Markov A n a l y s i s o f Related S p i l l s D e r i v a t i o n o f Conversion F a c t o r s t o Convert Na2S04 E q u i v a l e n t S p i l l s t o G a l l o n s o f Chemical  III IV  A-l  .  A-2  A L i s t i n g o f the Pulp M i l l Model  A-3  A L i s t i n g o f the Wastewater Treatment Model . . .  A-4  X  ACKNOWLEDGEMENTS I would l i k e to thank Dr.  D.H.  Uyeno at the U n i v e r s i t y of B r i t i s h  f o r h i s i n v a l u a b l e guidance and thesis.  A s p e c i a l thanks to Dr.  of B r i t i s h Columbia. T. Howard of B.C. me  I am  encouragement i n the development of  indebted  Research f o r t h e i r p a t i e n c e  to R o l f and  of the k r a f t p u l p i n g  Serenius  Council.  author i s g r a t e f u l f o r the a s s i s t a n c e and staff.  m i l l samples and  Mrs.  from the B r i t i s h Columbia Research  S p e c i a l thanks to Mrs. V.  Coates and  her  Dr.  process.  s u p p o r t e d by a F e l l o w s h i p  the C o u n c i l ' s  and  encouragement i n g u i d i n g  T h i s work was The  this  J : Stephenson, a l s o a t the U n i v e r s i t y  a l s o very  through the c o m p l e x i t i e s  Columbia  D.  library  back-up g i v e n  Dove f o r a n a l y z i n g  by  the  staff for a l l their  assistance.  I would a l s o l i k e and  to thank the f o l l o w i n g p e r s o n n e l  for their  co-operation:  1)  Mr.  N.  E c k s t e i n , M a c M i l l a n B l o e d e l , Harmac  2)  ,Mr.  Horwood, M a c M i l l a n B l o e d e l , Head O f f i c e , Vancouver  3)  Mr.  D.  Hill,  4)  Mr.  M.  Hague and Mr.  B.C.  Forest Products,  Crofton  Zagar, Weyerhaeuser, Kamloops.  assistance  1'  INTRODUCTION P u l p and paper i s a major i n d u s t r y i n B r i t i s h Columbia. were 22 pulp m i l l s process.  i n t h e p r o v i n c e , 18 o f which use the k r a f t p u l p i n g  T h e i r t o t a l p r o d u c t i o n f o r 1972 was 1,853,000 tons of wood  a c c o u n t i n g f o r 37% o f the p r o v i n c e s f o r e s t e x p o r t s .  (Stephenson  pulp  In 1969 t h e f o r e s t  i n d u s t r y employed 17,500 people and had m a n u f a c t u r i n g dollars  In 1973 t h e r e  s a l e s o f 1.7  billion  and Nemetz, 1974).  B r i t i s h Columbia e x p o r t s i t s f o r e s t p r o d u c t s  to over 40 c o u n t r i e s o f which  Japan, the U n i t e d S t a t e s and Great B r i t a i n a r e t h e b i g g e s t a c c o u n t i n g f o r 43% of t h e e x p o r t s .  customers,  The p u l p and paper market has about  the same number o f customers w i t h the U n i t e d S t a t e s b e i n g t h e l a r g e s t . m a j o r i t y of the e x p o r t s i s newsprint i s p r i m a r i l y bleached  The  by  79.8%) w h i l e t h e remainder  pulp.  pulp and .paper p r o c e s s g e n e r a t e s  pollution.  (approx.  a c o n s i d e r a b l e amount o f a i r and water  The s e v e r i t y o f t h e problem was emphasized i n a r e c e n t  the Swedish Environment P r o t e c t i o n Board.  as BOD  ( b i o c h e m i c a l oxygen demand), from  domestic  (Lekander,  s i m i l a r s i n c e both  1972).  pollution,  and i n d u s t r i a l  waste i n Sweden, and 80% o f the f o r e s t i n d u s t r y c o n t r i b u t i o n was pulp m i l l s  study  They s t a t e t h a t as of 1972  t h e f o r e s t i n d u s t r y was r e s p o n s i b l e f o r more than 80% o f t h e t o t a l expressed  A  from  The p r o p o r t i o n s f o r Canada a r e p r o b a b l y  very  c o u n t r i e s have a s i m i l a r dependence on the f o r e s t i n d u s t r y .  2  B e f o r e 1950 the i n d u s t r y f e l t absorbed by the environment ment.  As a r e s u l t  t h a t t h e p u l p i n g e f f l u e n t s would be e a s i l y  and l i t t l e  thought was g i v e n to. waste  treat-  tons o f t o x i c c h e m i c a l s and wood f i b e r were r e l e a s e d  i n t o the n a t u r a l water systems each day.  However i n the f i f t i e s  and s i x t i e s  pulp m i l l o p e r a t i o n c o s t s r o s e and i t became e c o n o m i c a l l y advantageous to develop more e f f i c i e n t ways of r e c y c l i n g t h e p r o c e s s c h e m i c a l s and t h e lost  fibers.  D u r i n g t h i s same p e r i o d t h e l a k e s and r i v e r s became i n c r e a s i n g l y more r e s p e c t e d as r e s o u r c e s t o be p r o t e c t e d and m a i n t a i n e d .  As a consequence  of t h i s combined economic and e n v i r o n m e n t a l push the p u l p i n g i n d u s t r y has become i n c r e a s i n g l y more concerned w i t h m i l l wastes and t h e i r  subsequent  treatment.  Over t h e past decade hundreds o f t e c h n i c a l and economic s t u d i e s have been c a r r i e d out pn treatment o f p u l p m i l l wastes. C o u n c i l o f Paper B.C. R e s e a r c h ,  I n d u s t r y f o r A i r and Stream  Groups such as the N a t i o n a l Improvement I n c . (NCASI),  t h e Canadian Department of t h e Environment,  and t h e U.S.  E n v i r o n m e n t a l P r o t e c t i o n Agency have a l l b e e n . a c t i v e i n t h i s a r e a . d e s p i t e a l l t h e new i n f o r m a t i o n b e i n g g e n e r a t e d by t h e s e groups, management c o n s i d e r i n g waste treatment a l t e r n a t i v e s can s t i l l  However,  mill  n o t be s u r e  how t h e i r p a r t i c u l a r m i l l s i t u a t i o n w i l l be handled by any g i v e n waste treatment  system.  There  i s great v a r i a b i l i t y  i n mill effluent  between m i l l s and w i t h i n a s i n g l e m i l l from day to day. the t o t a l c h e m i c a l and f i b e r  quality  both  Over one t h i r d o f  l o s s e s a r e due t o a c c i d e n t a l s p i l l s  (Lekander,  3  1972).  S p i l l s a r e u s u a l l y due to f a u l t y equipment,  the human f a c t o r  It  (negligence,  incorrect  c o n t r o l or  etc.).  i s t h e s e a c c i d e n t a l surges of t o x i c c h e m i c a l s and wood f i b e r  r e p r e s e n t a t h r e a t t o the s t a b i l i t y system.  of o p e r a t i o n of a waste  They a r e a l s o h a r d to d e s i g n a g a i n s t .  treatment  A waste t r e a t m e n t system  which can handle such o p e r a t i o n a l t r a n s i e n t s e f f i c i e n t l y may the s i z e of a system needed  which  be many times  f o r normal o p e r a t i n g c o n d i t i o n s and  exponen-  t i a l l y more e x p e n s i v e .  M i l l management t h e r e f o r e f a c e s a d i f f i c u l t  t r a d e o f f problem, namely  reli-  a b i l i t y o f the system i n meeting r e q u i r e d d i s c h a r g e l e v e l s v e r s u s c o s t s of the waste  treatment p l a n t .  Management o b v i o u s l y would  like  to m i n i m i z e c o s t s  but a l s o wants t o be s u r e t h a t the investment i s e f f e c t i v e i n meeting i t s original  purpose.  The problem i s to study the systems b e h a v i o u r i n r e s p o n s e to t y p i c a l and determine subsequent c o s t s and e f f i c i e n c i e s of o p e r a t i o n .  There a r e  t e c h n i q u e s which f a c i l i t a t e b r i n g i n g t h e r e a l w o r l d s i t u a t i o n i n t o laboratory.  These permit the d e c i s i o n maker to experiment w i t h  inputs  the  different  p o l i c i e s and i n v e s t i g a t e t h e i r e f f e c t over time w i t h o u t w o r r y i n g about d e s i g n failures. modelling.  The t e c h n i q u e s r e f e r r e d to a r e computer  s i m u l a t i o n and m a t h e m a t i c a l  They have been a p p l i e d to many i n d u s t r i a l p r o c e s s e s w i t h v a r y i n g  amounts of s u c c e s s .  T h e i r development  and use can g r e a t l y  i n c r e a s e the  u n d e r s t a n d i n g o f t h e problem and p r o v i d e i n v a l u a b l e i n f o r m a t i o n on of proposed  solutions.  feasibility  4  CHAPTER I THESIS DEFINED AND LITERATURE REVIEW T h i s study had 1.  two  Develop two  objectives: computer s i m u l a t i o n models.  The  first  e f f l u e n t s generated by a k r a f t pulp m i l l and  of  a second of the e f f l u e n t s  subsequent m o d i f i c a t i o n i n a waste treatment p l a n t . f u n c t i o n on a one  hour time step  the waterborne  to g i v e r e a s o n a b l e  Both models representation  of the systems dynamic b e h a v i o u r . 2.  Use  published  c o s t r e l a t i o n s h i p s to study c o s t v a r i a b i l i t y  treatment as a f u n c t i o n of d i f f e r e n t and  the l i t e r a t u r e ,  s e c t i o n s the h i s t o r y of the above, as r e f l e c t e d  i s reviewed and  1.1  THE PULP MILL MODEL  Past  computer s i m u l a t i o n  concerned w i t h  i t ' s i m p l i c a t i o n s on  s t u d i e s i n the p u l p i n g  c o n t r o l and  example, S u l l i v a n and  process  and  (1965) p r e s e n t e d  c o n t r o l schemes i n response to p r o c e s s  transients.  Tehrar  i n d u s t r y and  He  discussed  nature.  a technique for evaluation  m o d i f i c a t i o n s and  system  approach t o s i m u l t i o n i n  s i m u l a t i o n and  then developed a model of the wet  discussed.  engineering  f o u r d r i n i e r dynamics p e r m i t t i n g  (1967) gave a more g e n e r a l  in  i n d u s t r y have, been p r i m a r i l y ~  of d i f f e r e n t  paper i n d u s t r y .  t h i s study are  problems of a c h e m i c a l  Schoeffler  simulating stock preparation  pulp and  efficiencies  inputs.  In the f o l l o w i n g t h r e e  For  system d e s i g n s ,  of waste  end  i t s p o t e n t i a l to  the the  of a paper machine to  5  study b a s i s weight  changes and t h e i r  control.  a d i g i t a l s i m u l a t i o n o f paper making systems. steady s t a t e models Smith  B.W.  was  p u l p i n g p r o c e s s and no attempts (1960) the k r a f t  pulping process i s modelled  a t the complete  A  (1972) to e v a l u a t e  t o model the  mill  kraft  ( p u l p i n g and  cooking k i n e t i c s a r e measured, the  bleaching)  kraft  and a n o n - l i n e a r t e c h n i q u e f o r o p t i m i z i n g  p l a n t o p e r a t i o n c o s t s i s developed. independent  connecting pipes.  System b a l a n c e e q u a t i o n s w i t h s i x  c o n t r o l v a r i a b l e s can be m o d i f i e d i n order t o maximize the  objective function.  B o y l e and T o b i a s  (1972), developed  r e p o r t e d l y c o r r e c t i n g some of the d e f i c i e n c i e s  a new  model  i n C a r r o l l ' s model.  None of the above models d e a l w i t h waterborne e f f l u e n t s g e n e r a t e d pulp m i l l operation.  in a  However t h e r e have been numerous d a t a s t u d i e s made i n  the p a s t few y e a r s which t r y t o e s t a b l i s h the main s o u r c e s of m i l l and p o s s i b l e o p e r a t i o n a l c o r r e l a t i o n s . over 1000  as  possibilities.  The p u b l i s h e d l i t e r a t u r e r e v e a l s v e r y few attempts  In C a r r o l l  and  simulated process concentration f l u c t u a t i o n s  taken by H e n r i c k s o n and Meinander  various process design  (1969) d e v e l o p e d  U s i n g both dynamic  a consequence o f f l o w surges i n s t o r a g e tanks and s i m i l a r approach  Smith  effluent  Howard and Walden (1971) a n a l y z e d  samples c o l l e c t e d over a AO-day p e r i o d from major p r o c e s s  of seven B.C.  k r a f t pulp m i l l s .  were determined  Means and v a r i a n c e s f o r B0D  a l t h o u g h no r e l i a b l e c o r r e l a t i o n was  found.  5  and  streams  toxicity  6  In a l a t e r  study, Walden, Howard and  t e c h n i q u e s t o c o r r e l a t e B O D 5 and interesting  in-plant  Sheriff  (1971) used m u l t i p l e r e g r e s s i o n  t o x i c i t y with m i l l o p e r a t i n g data.  Some  c o r r e l a t i o n s were o b t a i n e d , however, c o r r e l a t i o n s f o r  combined m i l l o u t f a l l s were poor.  The  Swedish Steam U s e r s A s s o c i a t i o n (1974) made one  t o l o o k a t dynamic a s p e c t s of p u l p m i l l l o s s e s .  of the f i r s t  They l o o k e d a t a p u l p  o p e r a t i o n on d i f f e r e n t  time s c a l e s w i t h i n t e r v a l s r a n g i n g from  1 hour.  s t a t e v a r i a b l e was  T h e i r primary  c o n c e n t r a t i o n i n the e f f l u e n t s . d i s c h a r g e s i n the m i l l , discharges  salts  accidental  t h a t i n many sewers t h e r e were temporary  ( s p i l l s ) of l e s s than one  A more e x t e n s i v e study, Gove (1974),  hour d u r a t i o n over 50%  of the  time.  d e s c r i b e d a c o n t r o l s t r a t e g y and  a n a l o g s i m u l a t i o n r e s u l t s of the impact treatment  mill  .25 h r s to  the v a r i a t i o n of sodium  U s i n g t h i s as a measure of  they found  attempts  some  of above normal l o a d i n g s on a waste  plant.  F o r t h i s study a " b l a c k b o x " a p p r o a c h was e f f l u e n t model.  Regular  s t o c h a s t i c a l l y , based  used  to develop  the p u l p  p r o c e s s l o s s e s f o r v a r i o u s m i l l a r e a s were  on e m p i r i c a l d a t a .  sequence of s p i l l s generated  generated  Superimposed upon t h i s was  from a d e r i v e d d i s t r i b t u i o n .  The  "black  approach e l i m i n a t e s the need f o r a d e t a i l e d model of the p r o c e s s .  mill  a box"  I t does  however s a c r i f i c e the d e t a i l and p r e c i s i o n of a more e x a c t model.  The " b l a c k box" d e s c r i p t i o n i s a g e n e r a l term a p p l i e d t o an i n p u t - o u t p u t device. The b l a c k box r e p r e s e n t s a f u n c t i o n a l t r a n s f o r m which g i v e s the e f f e c t of i n p u t changes on o u t p u t . The c o n t e n t s of the b l a c k box a r e not of i n t e r e s t as l o n g as the t r a n s i t i o n i s a c h i e v e d i n a way t h a t r e f l e c t s a c t u a l system b e h a v i o u r .  7  T h i s approach i s supported by a statement i n t h e Swedish Association  (1974) r e p o r t which  "The  Steam U s e r s  states:  t o t a l d i s c h a r g e from a p u l p or paper m i l l  i n t o normal p r o c e s s d i s c h a r g e s , dependent p r o c e s s and the equipment  can be  divided  on the d e s i g n of t h e  b e i n g used, and temporary  or a c c i d e n t a l  d i s c h a r g e s caused by d i s t u r b a n c e s t o the p r o c e s s " .  1.2  THE WASTE TREATMENT MODEL  With the growing concern f o r the environment  i n the l a s t  10 y e a r s ,  waste  treatment models have become an i n c r e a s i n g l y more p o p u l a r t o o l f o r d e s i g n and management of wastewater  treatment systems.  They o r i g i n a l l y were d i r e c t e d  towards domestic sewage but i n r e c e n t y e a r s many i n d u s t r i a l l y  oriented  models have been d e v e l o p e d .  Montgomery  (1964) developed a model of a sewage treatment system which a l l o w e d  e f f l u e n t s t o r a g e and low-flow augmentation ment p l a n t was i n f l u e n t was  i n the r e c e i v i n g  stream.  The  treat-  r e p r e s e n t e d as an e f f i c i e n c y o f o p e r a t i o n r e l a t i o n s h i p , and i t s  an e m p i r i c a l time t r a c e which the model sampled  every two h o u r s .  The  i n t e r a c t i o n s w i t h i n the model were t r e a t e d as a system of queues and  service  facilities.  implications  The model determined the d i s s o l v e d oxygen  on the r e c e i v i n g stream f o r d i f f e r e n t  R.  Smith  concentration  r i v e r flow l e v e l s .  (1969) developed a model f o r d e s i g n and e v a l u a t i o n of waste  water  treatment systems u s i n g e m p i r i c a l l y d e r i v e d r e l a t i o n s h i p s f o r o p e r a t i o n a l  8  e f f i c i e n c y and c o s t s . component  The model p e r m i t t e d s p e c i f i c a t i o n o f v a r i o u s  combinations and modelled  t h e i r steady s t a t e o p e r a t i o n .  all  t h e i n p u t s and o u t p u t s assumed  for  t h e dynamic i m p l i c a t i o n s of the system.  However  c o n t i n u e d steady s t a t e and gave no f e e l S i m i l a r approaches  treatment d e s i g n have been developed by E i l e r s and R. Smith  t o waste  (1973), R.  Smith  (1968) and C h a i n b e l t I n c . (1972).  In  r e c e n t y e a r s v a r i o u s models have been developed f o r s p e c i f i c  of  waste treatment systems.  the  Many of these models have t r i e d  dynamic b e h a v i o u r o f the component  Takamatsu and N a i t o (1967)'developed  components  to represent  as a consequence of l o a d  variations.  a number of m a t h e m a t i c a l models of  h y d r a u l i c f l o w i n a s e d i m e n t a t i o n b a s i n e n a b l i n g them t o s i m u l a t e e f f i c i e n c y v a r i a t i o n as a f u n c t i o n o f t u r b u l e n c e and changing h y d r a u l i c  loads.  Naito,  Takamatsu and Fan (1969) developed a m a t h e m a t i c a l model o f t h e a c t i v a t e d s l u d g e p r o c e s s t o f a c i l i t a t e o p t i m i z i n g the system's c a p i t a l c o s t . (1969,  1971) developed r e s i d e n c e time d i s t r i b u t i o n s of s e t t l i n g b a s i n s and  used them i n a s i m u l a t i o n of mean performance plant.  Silveston  Some r e a s o n a b l e f i t s  (1974) a f i r s t  of a m u n i c i p a l waste treatment  t o r e a l d a t a were found.  o r d e r c h e m i c a l r e a c t i o n was assumed  I n Sakata and S i l v e s t o n  to r e p r e s e n t s e t t l i n g of  a n o n - f l o c c u l a t i n g s u s p e n s i o n and an e x p o n e n t i a l r e l a t i o n s h i p f o r s e t t l i n g v e l o c i t y was d e r i v e d and v e r i f i e d .  In  Beak-Environment Canada  (1973) v a r i o u s m a t h e m a t i c a l models o f r e s i d e n c e  time d i s t r i b u t i o n s f o r a e r a t e d lagoons were d e r i v e d and v e r i f i e d  against  9  three o p e r a t i o n a l lagoons.  Other o p e r a t i o n a l c h a r a c t e r i s t i c s of t h e lagoon  o p e r a t i o n a r e a l s o d i s c u s s e d and a c o n s i d e r a b l e amount of summary d a t a i s presented. to  changes i n i n p u t over time.  Bodenheimer for  However, the r e p o r t does not t r y t o model the systems r e s p o n s e  (1967) i s a summary paper of t h e treatment systems a v a i l a b l e  pulp m i l l wastes d i s c u s s i n g many p r i m a r y and secondary systems and  costs.  A more d e t a i l e d  their  d i s c u s s i o n o f the d e s i g n and o p e r a t i o n of secondary  waste treatment systems i s c o n t a i n e d i n a r e p o r t p u b l i s h e d by t h e C i t y of A u s t i n , Texas summarized  (1971).  The p r i n c i p l e s o f secondary waste t r e a t m e n t a r e  and t h e d e s i g n of f o u r major b i o l o g i c a l t r e a t m e n t systems  ( a c t i v a t e d sludge, aerated lagoon, t r i c k l i n g f i l t e r s ponds) a r e d i s c u s s e d i n c o n s i d e r a b l e  and waste  stabilization  detail.  The need f o r dynamic models of wastewater treatment p r o c e s s e s was emphasized i n Andrews (1974).  On page 263, he  recently  states:  "....dynamic models and c o n t r o l systems do o f f e r many p o t e n t i a l b e n e f i t s , however  i t s h o u l d be emphasized t h a t  the development of  dynamic models f o r wastewater treatment p r o c e s s e s and the use of .  t h e s e models f o r the improvement difficult  of c o n t r o l s t r a t e g i e s i s a  t a s k and i s p r e s e n t l y i n i t s i n f a n c y " .  Some b e n e f i t s o f dynamic models c i t e d by Andrews a r e : 1.  Performance - one can study range of p l a n t e f f i c i e n c y r a t h e r than j u s t a v e r a g e .  levels  10  2.  The development and e v a l u a t i o n o f b e t t e r c o n t r o l  3.  One can study s t a r t - u p b e h a v i o u r and e v a l u a t e a l t e r n a t e up  4.  start-  procedures.  One can e v a l u a t e t h e p r o c e s s s t a b i l i t y t o system  and study i t s response  transients.  For t h i s study a f i r s t  o r d e r model of a wastewater treatment  to a number o f B.C. p u l p m i l l s , was developed. assumptions  systems.  C e r t a i n steady  system.,  common  state  were made i n t h e model which p r e v e n t i t from b e i n g dynamic i n  the t r u e sense of t h e word. The model o p e r a t e d on t h e same time s c a l e as the pulp m i l l model and gave response  1.3  a r e a s o n a b l e r e p r e s e n t a t i o n o f t h e system's  to t h e p u l p m i l l e f f l u e n t over  time.  WASTEWATER TREATMENT PLANT COSTS  Numerous papers and manuals a r e a v a i l a b l e f o r e v a l u a t i n g t h e c o s t s of a wastewater treatment  plant.  Some even complement t h e c o s t i n g a s p e c t s w i t h  a steady s t a t e a p p r o x i m a t i o n  of t h e systems performance  t o experiment  component arrangements.  with d i f f e r e n t  (1973), R. Smith w i t h domestic  (1968), Logan e t a l (1962)].  and a l l o w t h e user  [ E i l e r s and R.  Smith  They a r e p r i m a r i l y f o r use  sewage a p p l i c a t i o n s .  A comprehensive r e p o r t on wastewater treatment p r e p a r e d by t h e U.S. Department of t h e I n t e r i o r  systems f o r p u l p m i l l s was (1967).  of a n a t i o n a l study o f o p e r a t i o n a l p u l p m i l l s w i t h ranges  I t g i v e s the r e s u l t s o f treatment  11  costs experienced  i n the i n d u s t r y f o r d i f f e r e n t  treatment  processes  versus  m i l l p r o d u c t i o n and age.  Reports  p u b l i s h e d by NCASI have a l s o d e a l t w i t h the c o s t s of p u l p  treatment  facilities  papers  by Haynes  Bower  (1971).  F o r the purposes were used. facilitate  mill  [Edde (1968), Gehm and Gove (1968)] as have o t h e r  (1968), White (1968), E c k e n f e l d e r and Barnard  of t h i s study  the r e l a t i o n s h i p s p l o t t e d  (1971) and  i n Bower  (1971)  They r e p r e s e n t a summary of much of t h e p u b l i s h e d d a t a and the d e t e r m i n a t i o n of c o s t as a f u n c t i o n of f l o w and  efficiency.  Bower's a e r a t e d lagoon c o s t c u r v e s were the o n l y ones t h a t c o u l d be i n the published  literature.  found  12  CHAPTER II SYSTEMS IDENTIFICATION  2.1  THE PULP MILL:  FUNDAMENTAL PROCESSES AND RESULTING WASTEWATER  P u l p i n g i s t h e p r o c e s s by which wood i s reduced  t o a f i b r o u s mass.  In  o t h e r words i t i s the means of r u p t u r i n g t h e bonds between t h e f i b e r s of wood T h i s t a s k can be accomplished t h i s study  First  t h e r m a l l y , or c h e m i c a l l y .  In  a m i l l u s i n g the p r i m a r i l y c h e m i c a l p r o c e s s known as t h e k r a f t  p r o c e s s i s modelled. be found  mechanically,  A flow chart of a bleached  k r a f t m i l l o p e r a t i o n can  i n F i g u r e 2.1.  i n t r o d u c e d by C. S. Dahl i n 1879, the k r a f t p r o c e s s  s e p a r a t e s the  c e l l u l o s e f i b e r s from t h e l i g n i n m a t e r i a l s by u s i n g a d i g e s t i o n m i x t u r e c o n s i s t i n g o f c a u s t i c soda and sodium s u l p h i d e , t o g e t h e r known as w h i t e  liquo  The wood, w h i c h a t t h i s p o i n t i s i n t h e form o f s m a l l c h i p s , i s cooked i n a pressure v e s s e l (the d i g e s t e r ) with white l i q u o r f o r approximately t h r e e hours.  two t o  The l i g n i n i s d i s s o l v e d forming a b l a c k , t o x i c substance  as b l a c k l i q u o r .  Black l i q u o r contains approximately  50 p e r c e n t of t h e  o r i g i n a l wood weight i n the form o f wood e x t r a c t i v e s and s o l u b i l i z e d The  black liquor  unbleached  pulp  i s then s e p a r a t e d  known'  lignin.  from the c e l l u l o s e f i b e r by washing the  (brownstock) i n a number of c o u n t e r  c u r r e n t wash s t a g e s .  The b l a c k l i q u o r e x t r a c t e d from t h e p u l p d u r i n g the i n i t i a l washing i s r e t u r n e d to t h e c h e m i c a l r e c o v e r y system.  Overflow  stages  from t h e l a s t washer  i s d i s c h a r g e d as t h e main p r o c e s s  sewer from t h e p u l p i n g s e c t i o n of t h e m i l l ,  (unbleached  i . e . UWW).  w h i t e water o v e r f l o w ,  The combined b l a c k l i q u o r s a r e  13 FIGURE 2.1 SCHEMATIC OUTLINE OF BLEACHED KRAFT MILL OPERATION WOOD  V  CHIP PREPARATION  >-DIGESTER -  PULP WASHING  A  WEAK B L A C K LIQUOR  TO B L E A C H PLANT  W erj 11  0  A  CWJ  , > X  «rr» c-=,  RECOVERY FURMACE n U G R E E N I) LIQUOR I  RECAUSTICIZING  FILTRATION  cr=2»  t.T^~3> <anr=*  mv*  U V/ VV V OVERFLOW  «--r>  _  V  CAUSTIC EXTRACTION  II 1st v/ CHLORINATION  c&J  V  WHITE LIQUOR  e^i  CONDENSATE  B L A C K LIQUOR OXIDATION fl SALTCAKE n ADDITION „  V  CHLORINATION  MULTIPLE EFFECT EVAPORATORS  i!  V  IL» S E C O N D A R Y CHLORINATION 0  l L ™ ^ = > SECONDARY EXTRACTION  WASHING, D R Y I N G , BALING  *t:  MARKET  BLEACHED PULP  1 st i! CAUSTIC v"; E X T R A C T I O N V  14  concentrated i n m u l t i p l e e f f e c t  evaporators  t o produce s t r o n g b l a c k  liquor  which i s burned i n a r e c o v e r y f u r n a c e to r e t r i e v e p u l p i n g c h e m i c a l s . smelt from green  the r e c o v e r y f u r n a c e i s r e d i s s o l v e d to g i v e " g r e e n  liquor  liquor".  The  i s r e c a u s t i c i z e d , a d j u s t e d to s t r e n g t h and "white  l i q u o r " i s reused  p r o p o r t i o n s of added b l a c k l i q u o r .  liquor".  called  The  "white  i n the d i g e s t e r t o g e t h e r w i t h  Approximately  The  95% of the p u l p i n g  a r e r e c y c l e d and most o f the s o l u b l e o r g a n i c m a t e r i a l e x t r a c t e d from  variable chemicals the wood  d u r i n g d i g e s t i o n i s burned i n the c h e m i c a l r e c o v e r y f u r n a c e .  The volume of e f f l u e n t from n o r m a l l y between 8,000 and w i t h a pH of 7 to 10. seven B. C. b l e a c h e d  the p u l p i n g s e c t i o n of a k r a f t m i l l 12,000 gal/ADT (ADT  kraft mills  t h a t the unbleached effluent  white bleached washed p u l p and  pulp.  of  w h i t e water e f f l u e n t  k r a f t pulp l i m i t  most m i l l s f u r t h e r p r o c e s s the unbleached  was  i t s market fibers  The b l e a c h i n g p r o c e s s i n v o l v e s c h l o r i n a t i o n of  e x t r a c t i o n of the c h l o r i n a t i o n p r o d u c t s  e x t r a c t i o n stage.  production)  streams.  The dark c o l o r and c o a r s e n a t u r e of unbleached Consequently,  = a i r d r y ton of p u l p  is  Howard and Walden (1971) r e p o r t e d from a s u r v e y  the most t o x i c of the d i f f e r e n t  usage.  (UWW)  i n an  to  the  alkaline  Because of the d e t r i m e n t a l e f f e c t c o n t i n u e d exposure of  the f i b e r s t o c h l o r i n e has on the r e s u l t a n t p u l p ' s s t r e n g t h , b l e a c h i n g i s c a r r i e d out as a m u l t i s t a g e p r o c e s s .  B a s i c a l l y the system i n v o l v e s c h l o r i n a t i o n ,  a t about 20°C, of the r e s i d u a l l i g n i n m a t e r i a l s r e m a i n i n g a f t e r d i g e s t i o n brownstock washing by c o n t a c t i n g the pulp a t a c o n s i s t e n c y o f 3 - 3.5% one h a l f  to one hour w i t h c h l o r i n e .  T h i s i s f o l l o w e d by washing and  and  for  then  by  15 caustic extraction  ( i n NaOH) of the p u l p a t a c o n s i s t e n c y of 10 - 12  for  one hour a t a temperature  The  a l k a l i n e e x t r a c t e d pulp i s s u b s e q u e n t l y  with further  of a p p r o x i m a t e l y  Finally  10 p e r c e n t o f the unbleached p l a n t w i t h the  first  washed w i t h water and t r e a t e d  the pulp i s d r i e d and b a l e d .  f u r t h e r l o s s e s of o r g a n i c m a t e r i a l from  The  60°C.  c h l o r i n e , h y p o c h l o r i t e and/or c h l o r i n e d i o x i d e s t a g e s  i n t e r v e n i n g washing.  stock.  percent  with  Bleaching  the pulp which amounts to 5  causes to  These l o s s e s a r e d i s c h a r g e d from  the  effluent.  c h l o r i n a t i o n e f f l u e n t n o r m a l l y has a volume of 15,000 - 25,000  gal/ADT p u l p w i t h a pH of 2 t o 3.  The  first  caustic extraction  effluent  has a f l o w volume of between 5,000 - 8,000 gal/ADT p u l p w i t h a pH of 9 to 11.  Both these sewers r e p r e s e n t a v e r y h i g h p e r c e n t a g e  p o l l u t i o n load.  Although liquid  of the m i l l s  .  the p r o c e s s streams mentioned above do not account  f o r the  total  l o s s e s i n a k r a f t p u l p m i l l they do r e p r e s e n t the main s o u r c e s of  pollution.  Superimposed upon these streams a r e l o s s e s from f a u l t y  p r o c e s s c o n t r o l f a i l u r e s and a c c i d e n t a l s p i l l s of  outfalls.  First  the a l k a l i n e  the a l k a l i n e b l e a c h i n g e f f l u e n t ,  equipment,  chemical.  E f f l u e n t s from a b l e a c h e d k r a f t p u l p m i l l a r e u s u a l l y d i s c h a r g e d two  total  through  (or g e n e r a l p u l p i n g ) o u t f a l l which i n c l u d e s the unbleached  Whitewater and  residuals  from  16  the p u l p i n g and r e c o v e r y a r e a s .  Second the a c i d o u t f a l l c o n t a i n i n g the  c h l o r i n a t i o n s t a g e b l e a c h p l a n t sewers. produced treatment  when these sewers a r e combined. facilities  or are combined and  The  L a r g e q u a n t i t i e s of foam can Consequently,  in mills  be  without  the o u t f a l l s a r e e i t h e r a c o n s i d e r a b l e d i s t a n c e a p a r t f e d through  a foam tank b e f o r e f i n a l d i s c h a r g e .  r e c o v e r y p r o c e s s mentioned e a r l i e r , w h i c h r e c e i v e s the b l a c k l i q u o r  the d i g e s t o r and  the brown s t o c k washers,has the p o t e n t i a l of b e i n g  o f t e n i s one  of the main p o l l u t e r s i n the k r a f t p u l p m i l l .  l i q u o r s used  i n the k r a f t p r o c e s s a r e extremely  contributions.  Although  A l l the  t o x i c and have h i g h  from  and chemical pollution  the r e c o v e r y p r o c e s s i n theory i s a n e a r l y c l o s e d  system the c a u s t i c n a t u r e of the l i q u o r s and frequent process s p i l l s .  The b a s i c c y c l i c  other f a c t o r s  precipitate  s t a g e s i n v o l v e d i n the r e c o v e r y  system a r e : 1.  S e p a r a t i o n of the spent  2.  E v a p o r a t i o n o f the l i q u o r t o a c o n c e n t r a t i o n of 50 - 60  liquor  ( b l a c k l i q u o r ) from  the p u l p . percent  solids. 3.  Combustion of the c o n c e n t r a t e d l i q u o r f o r s e p a r a t i n g the l i g n i n and  i n a s u i t a b l y designed  o t h e r o r g a n i c compounds from  furnace  the  sodium s a l t s by b u r n i n g , f o r r e d u c t i o n of the s u l p h u r - c o n t a i n i n g s a l t s m o s t l y Na2S04 ( s a l t the heat produced 4.  Withdrawal from and  cake) to sodium s u l p h i d e and  to generate  for u t i l i z i n g  steam.  the f u r n a c e of the sodium s a l t s  t h e i r s o l u t i o n i n water g i v i n g green  liquor.  i n molten c o n d i t i o n  17  5.  Treatment to  ( c a u s t i c i z i n g ) of the green  c o n v e r t the sodium carbonate  liquor with calcium  i n the smelt  w h i l e a t the same time c a l c i u m h y d r o x i d e  t o sodium  hydroxide  hydroxide  i s converted to calcium  c a r b o n a t e , which i s a p r e c i p i t a t e , a c c o r d i n g to the f o l l o w i n g reaction: Ca(OH) 6.  + Na C0 2  • CaC0 + + 2NaOH  3  3  Withdrawal of the c a u s t i c i z e d and for  The  2  use  i n another  c a l c i u m carbonate  clarified  separated i n step 5 i s u s u a l l y converted  i s c o n v e r t e d by the water to c a l c i u m h y d r o x i d e  The  two most w i d e l y used measures of pulp m i l l oxygen., demand and  to CaO  then i s s l a k e d , w i t h the green  and  they w i l l be used  (white  liquor)  cycle.  a k i l n t o g e t h e r w i t h make up l i m e and  chemical  solution  suspended s o l i d s .  e x t e n s i v e l y throughout  and  reused  effluent  liquor 5.  i n step  q u a l i t y are b i o -  These a r e now  the remainder  in  of the  defined since study.  1.  Biochemical  Oxygen Demand (BOD)  BOD  i s a q u a n t i t a t i v e t e s t , u s u a l l y done on a 5-day b a s i s , which  indicates  the r a t e a t which oxygen i s used by o r g a n i c wastes i n the e f f l u e n t .  Oxygen  i s used by b a c t e r i a t o degrade o r g a n i c c o n s t i t u e n t s to carbon d i o x i d e , water and o t h e r n o n - o r g a n i c s . to  F o r pulp m i l l s the BOD  level i s proportional  the amount of d i s s o l v e d wood c o n s t i t u e n t s i n the water.  18  BOD  has  s e r i o u s i m p l i c a t i o n s to the n a t u r a l a q u a t i c  stream s i n c e i t too depends on water.  I f a high  oxygen w i l l be  BOD  and of  2.  the  stream, most of  the  the b a c t e r i a i n d e g r a d i n g the o r g a n i c  a r e s u l t the n a t u r a l a q u a t i c a n a t u r a l system can  i n the  l i f e w i l l not  t o l e r a t e depends on  i t s r a t e of f l o w .  receiving  the d i s s o l v e d oxygen c o n c e n t r a t i o n  e f f l u e n t enters  used by  life  survive.  The  in  the  dissolved wastes.  As  amount of BOD  that  the volume of the r e c e i v i n g water  I t s u n i t o f measurement i s mg/1  o r pound of BOD/ADT  pulp.  Suspended S o l i d s  (SS)  T h i s r e f e r s to a l l m a t e r i a l which can be also often called  total  filtered  hour) and  on i g n i t i o n at 5 7 5 ° C ) .  suspended s o l i d s are  The  removed because b e i n g  oxygen demand  (although  of a l i q u i d .  suspended s o l i d s s i n c e i t i n c l u d e s  ( s o l i d s which s e t t l e i n one  They must be  out  not  a high  volatile  organic BOD).  As  settleable solids  suspended s o l i d s  (lost  composed m o s t l y of  they r e p r e s e n t  It i s  fiber.  a very high  a consequence they can  total  greatly  d e c r e a s e the e f f i c i e n c y of b i o l o g i c a l waste treatment systems i f a l l o w e d b u i l d up.  I f dumped d i r e c t l y  a major t h r e a t to the a q u a t i c a p p e a l of the a r e a . of  The  i n t o the r e c e i v i n g stream SS life  and  s e t t l e and  a l s o g r e a t l y a f f e c t the  I t s u s u a l u n i t of measurement i s mg/1  to  become  aesthetic  or pound of SS/ADT  pulp.  t y p i c a l BOD  and  summarized i n T a b l e  SS l e v e l s e x p e r i e n c e d a t the main k r a f t m i l l sewers 2.1.  are  19  TABLE 2.1  TYPICAL BOD AND SS LEVELS FOR KRAFT MILL SEWERS  Sewer P u l p i n g (U.W.W.) 1st  Chlorination  1st C a u s t i c E x t r a c t i o n  BOD  SS  12 - 30 lb/ADT  10 - 15 lb/ADT  ^25 lb/ADT  1-  2  lb/ADT  ^20 lb/ADT  2-  4  lb/ADT  The b r i e f d e s c r i p t i o n g i v e n here does not r e f e l c t a p u l p m i l l s BOD and SS l e v e l s .  a l l the f a c t o r s  affecting  The wood s p e c i e s used v a r i e s between  mills  and has w i d e l y v a r y i n g c h a r a c t e r i s t i c s , i h terms of i t s c o n t e n t of e x t r a c t a b l e m a t e r i a l s , b o t h s e a s o n a l l y and due t o t h e t r e e s l o c a t i o n when h a r v e s t e d . procedures varies.  a r e a l s o v a r i e d to s u i t product r e q u i r e m e n t s .  A combination  2.2 2.2.1  M i l l design also  of these f a c t o r s , a l l o f which a r e d e s i g n e d t o  produce a p r o d u c t o f r i g i d variable  Mill  s p e c i f i c a t i o n s , r e s u l t s i n e f f l u e n t with highly  characteristics.  THE WASTE TREATMENT PLANT Introduction  In t h i s study two p r o c e s s e s a r e m o d e l l e d ,  a primary s e d i m e n t a t i o n  (or c l a r i f i e r ) and a 5-day a e r o b i c s t a b i l i z a t i o n  lagoon.  tank  The two q u a n t i t a t i v e  measures of e f f l u e n t l o a d i n g and system e f f i c i e n c i e s a r e BOD and SS.  The  clarifier  removes  removes p r i m a r i l y SS w h i l e t h e a e r o b i c s t a b i l i z a t i o n lagoon  p r i m a r i l y BOD.  S i n c e t h e SS l o a d i n g can g r e a t l y a f f e c t  c l a r i f i e r precedes  the lagoon.  lagoon o p e r a t i o n the  20  FIGURE  2.2  CIRCULAR CLARIFIER WITH CENTER FEED  21  The c l a r i f i e r  and a e r o b i c s t a b i l i z a t i o n  proven r e l i a b i l i t y and e f f i c i e n c y . and  improvement of the environment  with respect  to BOD  the i n c r e a s e d use of e f f l u e n t  f o r r e l i a b l e , c o n t i n u o u s performance,  high rate  earlier,  i n d u s t r y and occur a t a s u f f i c i e n t of d e s i r e d d i s c h a r g e l e v e l s . absorb sudden shocks.  The  and  s p i l l s a r e a major f a c t o r frequency to r e s u l t  Therefore a r e l i a b l e  The system must a l s o be equipped  limits there  i n the p u l p i n g  i n costly  system  their  protection  systems,  As mentioned  both SS and  With the c u r r e n t emphasis on  of  and SS i n the d i s c h a r g e to p u b l i c water  has developed a need processes.  lagoon were chosen because  violations  i s one which  can  t o e f f i c i e n t l y remove  BOD.  clarifier,  and e f f e c t i v e  p o s s i b l y f o l l o w e d by a s e t t l i n g pond, i s the most e f f i c i e n t way  of removing  suspended  solids.  f o r both m u n i c i p a l and i n d u s t r i a l waste.  I t has found wide a c c e p t a n c e  On the average c l a r i f i e r s  pulping i n d u s t r y are of centre feed, c i r c u l a r  type w i t h an i d e a l  i n the  retention  time of 3 hours and a depth of no more than 15 f t .  The a e r o b i c s t a b i l i z a t i o n because little  of i t s r e l i a b i l i t y or no r e f l e c t i o n  lagoon,which  and c a p a c i t y t o absorb s h o r t term s p i l l s  i n output.  As a consequence  wide a c c e p t a n c e i n the p u l p i n g i n d u s t r y (1967)].  p r i m a r i l y removes BOD,was chosen  [see Rand  of t h i s  (1972) and  i t has  with found  Bodenheimer  I t s main d i s a d v a n t a g e i s the l a n d a r e a needed to p r o v i d e an  d e t e n t i o n time  (4 to 10 d a y s ) .  study, w i t h an average water  A m i l l of the t y p e b e i n g m o d e l l e d  f l o w of 65 MUSGD, r e q u i r e s a 15'  adequate  in this  deep lagoon  22  of about 75 a c r e s s u r f a c e a r e a t o p r o v i d e t h e needed r e t e n t i o n  time.  Maintenance can a l s o be a problem s i n c e b i o l o g i c a l o x i d a t i o n g e n e r a t e s suspended s o l i d s . secondary at  Often t h i s  clarifier  7.0 ± 2.0  i s s o l v e d by f o l l o w i n g t h e lagoon w i t h a  or a s e t t l i n g pond.  G e n e r a l l y i n p u t pH s h o u l d be kept  i n order t o ensure b a c t e r i a l  should n o t drop  survival.  A l s o water  too low so as t o s i g n i f i c a n t l y slow the b i o l o g i c a l  D e s p i t e t h e s e c o m p l i c a t i o n s however, w i t h s u f f i c i e n t p r o c e s s a e r a t e d lagoons  2.2.2  control,  The C l a r i f i e r  clarifier  i s t o remove suspended s o l i d s  (SS).  Basically  o p e r a t i o n i n v o l v e s d e t a i n i n g wastewater i n a l a r g e b a s i n f o r a  sufficient  l e n g t h o f time  Settled  so t h a t t h e SS can s e t t l e  t o the bottom of the  s l u d g e i s c o n t i n u o u s l y removed u s i n g a motor d r i v e n  r e v o l v i n g rake mechanism t o c o l l e c t and c o n c e n t r a t e t h e s l u d g e 2.2).  reaction.  f u n c t i o n e f f i c i e n t l y i n many a r e a s of B.C.  The purpose of a c l a r i f i e r  basin.  temperature  The c l a r i f i e r  d e s i g n common t o p u l p m i l l s  (see F i g u r e  i s the c i r c u l a r  type i n  which t h e waste f l o w e n t e r s i n the c e n t r e and l e a v e s v i a an o v e r f l o w r u n n i n g around t h e c i r c u m f e r e n c e o f t h e tank near study t h e e f f i c i e n c y  water.  of a c l a r i f i e r  In t h i s  o f SS removal was assumed t o be a f u n c t i o n of t h e  d e t e n t i o n time and the s e t t l i n g c h a r a c t e r i s t i c s  Design  the upper r i m .  weir  i s based  on f i b e r  o f the waste b e i n g t r e a t e d .  slowly s e t t l i n g  To be removed, t h e f i b e r must s e t t l e f a s t e r  the water i n the c l a r i f i e r .  through  quiescent  than t h e r i s e r a t e of  L a r g e f i b e r s may s e t t l e a t speeds o f 10 t o  23  15 f e e t p e r hour. About  As they become s m a l l e r t h e i r s e t t l i n g r a t e d e c r e a s e s .  92% of t h e p a r t i c l e s w i l l  (Bodenheimer,  1967).  The c a p i t a l c o s t of a c l a r i f i e r area  s e t t l e f a s t e r than 3 1/2 f t p e r hour  (Bower,1971).  volume ^ flow rate  i n general i s proportional to i t s surface  To ensure an adequate  d e t e n t i o n time  ( D e t e n t i o n time =  volume must be kept c o n s t a n t ( f o r an assumed steady s t a t e  f l o w r a t e ) i m p l y i n g an i n v e r s e r e l a t i o n s h i p between depth and c o s t f o r any g i v e n volume.  I n Chapter I I I , an e x p o n e n t i a l a p p r o x i m a t i o n f o r t h e  s e t t l i n g r a t e i s developed.  For pulp m i l l wastes  a nominal d e t e n t i o n time i s from 3 to 4 hours and  depth i s 12 to 15 f t . F o r a 3 hour d e t e n t i o n time and a 15 f t deep tank w i t h an average f l o w o f 35 M.U.S.G.^^ day, t h e volume r e q u i r e d would be,  35 Vol =  J  J  x  1 0  • 24  6 MUSG day x 3 h r s = 4.4 x 1 0 US g a l 6  ^ day  w i t h a depth o f 15 f t , t h e diameter would be,  D = 2x \J 4.4 x 1 0  2.2.3  6  g a l x .134  x j^rjr x -y-  £ 224 f t  The Aerated Lagoon  The p r i m a r y purpose o f the lagoon i s t o remove s o l u b l e BOD u s i n g treatment.  ^M.U.S.G.  B a s i c a l l y t h e p r o c e s s p r o v i d e s an environment  =  m i l l i o n U.S. g a l l o n s  biological  i n t h e lagoon  24  which p e r m i t s b a c t e r i a to use and  energy.  In the a e r o b i c  the o r g a n i c m a t e r i a l as a s u b s t r a t e  s t a b i l i z a t i o n l a g o o n d i s s o l v e d oxygen a s s i m -  i l a t e d by m i c r o - o r g a n i s m s i s s u p p l i e d by m e c h a n i c a l a e r a t o r s . b i o l o g i c a l reactions following  taking place  2  + NH  + P  3  d e g r a d a t i o n of c e l l m a t e r i a l (C H NO ) 5  7  2  1 0  P + 0  +C0  2  2  i s the BOD  5  of  the  -» New  cells  then o c c u r s as  + H0 2  Both r e a c t i o n s r e q u i r e oxygen and required  i n the lagoon are  The  summarized  in  the  equations:  org m a t e r i a l + 0 The  f o r growth  + NH  the  3  +  (C H N0 ') 1 o 5  7  p  2  +  c o  2  +  H  2°  follows:  Polysaccharides  5-day r a t e at' which oxygen i s  w a s t e .  In the C i t y of A u s t i n , Texas (1971), the b i o l o g i c a l k i n e t i c s a c t i v e i n a lagoon were d e s c r i b e d . the a e r o b i c K,  can be  They s t a t e t h a t i f oxygen and  s t a b i l i z a t i o n l a g o o n are h i g h ,  assumed c o n s t a n t .  For a s u f f i c i e n t l y a e r a t e d  the a e r a t o r m i x i n g i s s u f f i c i e n t  o b t a i n a r e a s o n a b l e BOD  efficiency,  SS  i n the  the a e r a t o r s (and  The  deeper the lagoon the  to f u n c t i o n e f f i c i e n t l y .  t h e r e f o r e volume) the  surface area  For the remainder of t h i s study BOD w i l l be understood.  that  lagoon i n s u s p e n s i o n .  the minimum recommended  r e t e n t i o n time f o r a l a g o o n i s 5 days, (Bodenheimer, 1967). from 6 f t to 15 f t i n depth.  in  lagoon t h i s i s a  I t i s a l s o assumed  to keep a l l the  reduction  concentration  the b i o l o g i c a l r e a c t i o n r a t e ,  r e a s o n a b l e assumption f o r p u l p m i l l e f f l u e n t .  To  BOD  Lagoons  stronger  However, f o r a g i v e n  must  detention  a v a i l a b l e w i l l d i c t a t e the  w i l l be w r i t t e n  for B O D 5 .  vary be time  depth.  The  five  days  25  The  SS generated by the o x i d a t i o n i n t h e a e r o b i c s t a b i l i z a t i o n  lagoon i s  an i n s o l u b l e m a t e r i a l which i t s e l f has a 5-day BOD e q u i v a l e n t . m i l l wastes, at  Bower (1971), c l a i m s t h a t t h i s b i o l o g i c a l s l u d g e i s produced  a r a t e o f .15 l b f o r each pound of BOD removed and t h a t  approximately  on BOD removal have been documented f o r many b i o -  l o g i c a l waste treatment p r o c e s s e s i n l a b o r a t o r y s t u d i e s .  for in  r a t e g e n e r a l l y o c c u r s around  the b a c t e r i a  (Beak-Environment  c o l d e r c l i m a t e s t h e temperature  system's treatment e f f i c i e n c y . effects i n f u l l temperature  i t contributes  .1 l b of BOD per pound of s l u d g e g e n e r a t e d .  E f f e c t s of temperature  removal  For pulp  The maximum  37°C which i s the optimum  Canada, 1973).  temperature  In most systems o p e r a t i n g  becomes a major f a c t o r a f f e c t i n g the  L i t t l e has been p u b l i s h e d on  temperature  s c a l e a e r o b i c s t a b i l i z a t i o n lagoons however the l i q u i d  w i t h i n an a e r o b i c s t a b i l i z a t i o n  l a g o o n w i l l depend upon the  r a t e a t which heat i s l o s t and t h e e x t e n t of m i x i n g which e x i s t s . Environment to  Beak-  Canada (1973) found lagoons w i t h a l a r g e l e n g t h - w i d t h r a t i o  have a r o u g h l y l i n e a r  temperature  T h e r e f o r e t h e mean l a g o o n temperature between lagoon i n f l u e n t and e f f l u e n t  d e c r e a s e through t h e 5-day l a g o o n . can be taken as the a r i t h m e t i c mean temperature.  N u t r i e n t s such as n i t r o g e n and phosphorus o f t e n must be added t o a l a g o o n to  m a i n t a i n the b a c t e r i a l i f e  cycle.  The dosage r e q u i r e d  i s governed by  the c o n c e n t r a t i o n o f t h e s e c h e m i c a l s a l r e a d y p r e s e n t and by t h e BOD s t r e n g t h o f t h e wastewater. assumed a v a i l a b l e .  I n t h i s study a l l n e c e s s a r y n u t r i e n t s a r e  26  Another  important  factor  i n the o p e r a t i o n of a lagoon i s i n f l u e n t  The pH s h o u l d i d e a l l y . b e between.6 and 8 f o r optimum BOD m i l l wastes (Beak-Environment Canada 1973).  pH.  r e d u c t i o n of pulp  To a c c o m p l i s h  t h i s some m i l l s  combine the a c i d and a l k a l i o u t f a l l s b e f o r e e n t e r i n g the l a g o o n . i s not s u f f i c i e n t , p o s s i b l y due may  be added as needed.  a r e s u l t of s p i l l s  The  to a b l e a c h p l a n t shut down, c h e m i c a l s  i n f l u e n t pH  of  these t r a n s i e n t s .  hours r e s u l t i n g  i n a s u b s t a n t i a l pH  days.  I n Gove (1974),  be p o s s i b l e to d i v e r t s p i l l s r a t e which can be handled  i s a major s p i l l )  the lagoon  i n a system  over a number  f a i l u r e f o r a number b a s i n s be c o n s t r u c t e d  w i t h c o n d u c t i v i t y probes.  to the b a s i n and  I t would  r e l e a s e them l a t e r  e f f i c i e n t l y by the lagoon.  a r e c o n s i d e r e d i n t h i s study i t was  can  shock to the system.can d e s t r o y  i t i s recommended t h a t s p i l l  and m i l l o u t f a l l s be monitored  as  i s of major p r o p o r t i o n s  However a c o n t i n u e d s p i l l  the b a c t e r i a i n the lagoon and r e s u l t of  can e x p e r i e n c e sudden s h i f t s  i n the m i l l but u n l e s s the s p i l l  (100,000 g a l l o n s of weak b l a c k l i q u o r u s u a l l y absorb  If this  Although  then  at a  spills  not p o s s i b l e to model the e f f l u e n t  pH.  27  CHAPTER I I I SYSTEMS ANALYSIS 3.1  THE PULP MILL  The pulp m i l l model generates a t y p i c a l water borne effluent time trace by sampling each hour empirical BOD and SS d i s t r i b u t i o n s f o r each of the main sewers within the m i l l and multiplying the r e s u l t s by hourly hydrauli c flows.  Superimposed upon this normal effluent stream i s a sequence of  model generated  spills.  To establish the above d i s t r i b u t i o n s a considerable amount of data were required.  Most of the data were supplied by one B. C. pulp m i l l .  The data  made a v a i l a b l e are the following: 1.  Six months of conductivity charts at the m i l l ' s main o u t f a l l s with notes i n d i c a t i n g s p i l l locations (not complete).  2.  Typical d a i l y m i l l flow values f o r main m i l l sewers.  3.  Some BOD and SS sampling r e s u l t s f o r the same sewers as #2.  4.  Twelve months of m i l l d a i l y operating summaries, s i x months of of which overlap with / / l .  5.  BOD and SS readings taken at main o u t f a l l s as required by P o l l u t i o n Control Branch f o r same four months as ill.  Also, m i l l supplied samples of the following were analyzed at B. C. Research. 1.  Weak black liquor  2.  Strong black l i q u o r  3.  White l i q u o r  28  4.  Green liquor  5.  Acid sewer  6.  A l k a l i sewer  7.  Recovery sewer  8.  Flyash sewer  9.  Recausticizing sewer  10.  Machine room sewer  Additional data were also supplied by Dr. T. Howard (personal, communication) from previous work at the m i l l .  3.1.1  SPILL DATA  A s p i l l i s an accidental discharge of chemicals frequently caused by human error, f a u l t y control or equipment f a i l u r e .  S p i l l s present a very r e a l prob-  lem to m i l l management since they are next to impossible  to predict and r e -  present a f i n a n c i a l loss as well as a p o l l u t i o n problem.  To incorporate s p i l l s i n the model, s i x months of continuous conductivity charts f o r the main sewer o u t f a l l were analyzed.  Each day m i l l personnel  c o l l e c t e d the charts, wrote comments as to s p i l l locations and  summarized,'  the past 24 hours t o t a l chemical losses expressed as Na^SO^ per ton of production equivalent  , tons of f i b e r l o s t , and water usage f o r that  day.  It i s common practice i n the pulp m i l l s to measure chemical losses i n terms of i t s N a 2 S 0 ^ equivalent. The conductivity reading i s proportional to the Na , S 0 4 and S concentrations and since sodium and sulphur are necessary constituents i n the white l i q u o r (NaOH and N a 2 S ) they must be r e placed. Usually N a 2 S 0 4 - ( s a l t cake) i s added i n the recovery cycle to replace l o s t sodium and sulphur, thus the term "Na2S04 equivalent". +  =  =  29  By establishing a  Na S04 2  operating day the N a ^ O ^  loss per ton of production base l e v e l for a clean equivalent  for each s p i l l was  determined as the  area  under each of the s p i l l peaks on the conductivity chart expressed as a f r a c t i o n of the t o t a l area of a l l s p i l l s for each day.  These f r a c t i o n s are the prop-  o r t i o n of the above base l e v e l loss that each i n d i v i d u a l s p i l l represents. multiplying each f r a c t i o n by the t o t a l above normal Na SOi 2  4  equivalent for each s p i l l was  This was  2  +  loss for that day,  the  estimated.  done for a t o t a l of 178 days.  About 70% of the chart indicated  s p i l l s were i d e n t i f i e d as to l o c a t i o n , although the most s p i l l s could be determined.  Na SOi  By  Na^SO^  equivalent  of  Approximately three weeks of m i l l opera-  t i o n which were not monitored with the conductivity probe were removed from the data.  M i l l start-ups which represent a considerable amount of chemical loss were not incorporated  i n the data base since the conductivity charts did not  supply enough information.  Their possible implications on the waste t r e a t -  ment system w i l l be considered 1.  later.  Two  items to note are that:  Although a s p i l l on the conductivity chart may i t s e f f e c t is. recorded which i t was  l a s t over an hour,  as only being f e l t during the hour i n  initiated.  Very few s p i l l s were over an hour i n  length. 2.  The extra hydraulic load created by the s p i l l was  assumed n e g l i g i b l e  since even a large s p i l l of say 100,000 gallons represents 3% of the hourly m i l l  3.1.2  less than  flow.  SPILL DATA ANALYSIS  S p i l l locations were broken down into three major locations with 12 (The 12 sublocations belong to one of the three major l o c a t i o n s ) .  sublocations.  30  T a b l e 3.1 summarizes these.  TABLE 3.1  MAJOR AND MINOR SPILL LOCATIONS  IN PULP MILL MODEL  MAJOR AREA RECAUST-//2  RECOVERY-//1 Sub Loc 'n  Name &/or L i q u o r  1  Wood Prep'n  Precipitators -strong black l i q .  6  White  liquor  2  Knots-W.B.L.  Condensates -strong black l i q .  7  White  liquor  11  Kamyr  8  Slaker-Green liquor  13  B.S.  14  Kamyr Condensates  4  liquor  Spills-W.B.L. Washers-W.B.L.  r e c o v e r y , r e c a u s t and p u l p i n g l o c a t i o n s r e p r e s e n t n e a r l y 100% o f t h e s p i l l s  recorded all  Name &/or L i q u o r  Green l i q u o r  Weak b l a c k  The  Sub Sub Name &/or L i q u o r Loc n Loc 'n 5  3  12  PULP ING-// 3  i n the d a t a .  spills  The r e c o v e r y a r e a a l o n e accounts  f o r n e a r l y 71% of  recorded.  Goodness o f f i t t e s t s were r u n f o r t h e s p i l l a m o u n t s ^ ^ a n d t h e time between successive s p i l l  (2) sequences f o r each o f t h e t h r e e major a r e a s .  ^^Note: The s p i l l amounts d a t a were expressed Na2S0^ e q u i v a l e n t . The time d a t a i s i n h o u r s .  The computer  i n u n i t s o f 1000 l b s o f  (2) What i s meant by a " s p i l l sequence" w i l l become c l e a r i n t h e next few pages. The time d i f f e r e n c e s a n a l y z e d here were t h e time ( i n h o u r s ) between the l a s t s p i l l o f a sequence and t h e next s p i l l i n t h e a r e a which has t h e p o t e n t i a l o f i n i t i a t i n g a new sequence. .  31  program used was one developed  a t UBC w h i c h uses t h e Kolmogorov-Smirnov  (K-S) and t h e C h i - s q u a r e goodness o f f i t t e s t s f o r f i t t i n g seven t h e o r e t i c a l d i s t r i b u t i o n s  (Kota and M o r l e y , 1973).  1.  Normal d i s t r i b u t i o n  2.  Poisson d i s t r i b u t i o n  3.  Binomial d i s t r i b u t i o n  4.  Negative Binomial d i s t r i b u t i o n  5.  Gamma d i s t r i b u t i o n  6.  Log normal d i s t r i b u t i o n  7.  Exponential d i s t r i b u t i o n  The K-S t e s t was used s i n c e i t i s l e s s s e n s i t i v e e r a l l y a c c e p t e d as a more p o w e r f u l t e s t  These i n c l u d e :  t o sample s i z e and i s gen-  ( S i e g e l , 1956).  The t e s t  t h e g r e a t e s t d i s t a n c e between t h e d a t a and t h e t h e o r e t i c a l t r i b u t i o n s and compares i t t o a t a b l e nificance  level.  given data to  determines  cumulative  dis-  of c r i t i c a l . v a l u e s f o r a g i v e n s i g -  I f t h e d i s t a n c e i s l e s s t h a n t h e c r i t i c a l l e v e l , then t h e  n u l l hypothesis i s accepted,  ( i . e . , we cannot r e j e c t  the d i s t r i b u t i o n s a r e t h e same).  the hypothesis that  F o r a more complete d i s c u s s i o n o f t h e  K-S t e s t see Fishmann (1973) o r S i e g e l  (1956).  The r e s u l t s o f t h e t e s t s  a r e found i n T a b l e 3.2 f o r t h e s p i l l amounts, and T a b l e 3.3 f o r t h e i n t e r arrival  times.  The K-^S r o u t i n e e s t i m a t e s t h e d i s t r i b u t i o n p a r a m e t e r s from t h e sample d a t a . If  t h e s e parameters a r e ones o f s c a l e o r l o c a t i o n , however, t h e K-S  i c a l v a l u e s become d i s t r i b u t i o n dependent (Fishmann, 1973) .  crit-  Lilliefors  (1969)  g i v e s a t a b l e o f K-S c r i t i c a l v a l u e s f o r t h e e x p o n e n t i a l d i s t r i b u t i o n w i t h a sample e s t i m a t e d mean.  Comparing t h e s e v a l u e s t o a s t a n d a r d K-S t a b l e , i t  TABLE 3.2 GOODNESS OF FIT RESULTS FOR SPILL AMOUNTS (units of 1000 lb)  Area  X  R  D  Log Normal  Negative Binomial  Gamma  # of Observations  KS (.05)  P  K  D  KS (.05)  M  S  D  KS (.05)  K-S Adjusted  100  .414  .024  .074  .136  .109  .364  .087  .136  -  -•  -  -  .107  #2 Recaust  30  .515  .045  .064  .245  .189  .444  .072  .245  3.76  2.91  .081  .245  .196  #3 Pulping  19  1.191  .065  .124  .301  .313  .078  .301  5.47  2.85  .214  .301  .246  #1 Recovery  1.55  TABLE 3.3 GOODNESS OF FIT RESULTS FOR TIME BETWEEN UNRELATED SPILLS (units of hours)  Area  R  X  D  Log Normal  Negative Binomial  Gamma D i s t r i b u t i o n  # of Observations  KS (.05)  P  K  D  KS (.05)  M  S  D  KS (.05)  K-S Adjusted  //I Recovery  55  .511  .0024  .089  .183  .1117  .459  .092  .183  10.66  2.75  .034  .183  .144  #2 Recaust  23  .807  .002  .104  .276  .091  .823  .110  .276  12.4  3.16  .103  .276  .223  #3 Pulping  13  1.101  .001  .183  .361  .086  .197  .361  13.8  2.9  .170  .361  .297  Note:  1.25  See Table 3.5 f o r d e f i n i t i o n s of parameters CO  to  33  is seen that the 0.05 significance level c r i t i c a l values for L i l l i e f o r s ' table are about the same as the c r i t i c a l values for a standard table .20 significance level.  This implies that the probability of a type I error  (rejecting a true null hypothesis) is decreased when using the standard K-S tables but the probability of a type .II error (accepting a false null hypothesis) i s increased.  In the context of this study, a type II error  is more serious. A suitably adjusted K-S c r i t i c a l values table could not be found for the gamma, log-normal or negative binomial distributions, therefore, the K-S standard c r i t i c a l values were also determined for ^ = .2. These are found i n the column labeled "K-S Adjusted". .Assuming that L i l l iefors' result of the similarity of the values for « = . 2 and  11  = .05 dis-  cussed earlier can be generalized to other distributions the results of the tests are not affected and the null hypothesis s t i l l cannot be rejected at both the .05 and .20 significance levels.  Often i n the s p i l l data, a sequence of up to six s p i l l s with only a few hours between each occured in the same sub location implying a possible recurring failure.  To handle this situation i t was assumed that any sequence  of spills occurring in the same sub area, with ten hours or less between each successive s p i l l , were "related" permitting creation of a "related s p i l l distribution". sub location.  Table 3.4 summarizes the number of related spills for each The goodness of f i t routine results can be found in Table 3.5.  Since not a l l s p i l l s are part of a related sequence i t was necessary to establish a related s p i l l decision strategy. Each s p i l l , i f not imbedded in an already initiated sequence, i s a potential initiator of a related sequence.  TABLE 3.4  INTERVAL TIME  RELATED SPILL COUNT FOR 3 MAJOR AREAS  AREA RECOVERY  RECAUST  PULPING  1 hrs  28  5  0  2  "  11  1  0  3  "  7  1  0  4  "  3  3  0  5  "  5  3  0  6  "  2  0  0  7  "  2  0  0  8  "  1  2  0  9  "  1  1  0  10  "  2  0  0  XA15LE J . }  UUUUIMlibtJ  Uf  M X KCbUL/ib  tUK l i n t  Gamma Area  # of Observations R  BtiWttlN  Negative  K£,L.A1CX) 5riJ-,l_,a  V.U1NJ.XJ  Binomial  ur  nuuno;  Log Normal K-S Adjusted  X  D  KS (.05)  P  D  K  KS (.05)  M  S  D  #1 R e c o v e r y  67  1.24  .447  .191  .166  .287  .722  .041  .166  1.62  1.77  .268  #2 R e c a u s t  16  2.04  .528  .220  .328  .392  1.86  .136  .328  2.45  1.92  .211  KS (.05) .166  .123 .267  N 3 RELAT ED SPII LS  #3 P u l p i n g  NOTE (FROM KITA AND MORLEY (1977)  1.  2,  Gamma D i s t r i b u t i o n f  x  00 - <  where  k =  R  "  1  e  e f(R) K  R =  X =  _ 2 x  o=2  1 = x o 2  -  x/B  for x > 0 f o r x <. 0  3.  Negative Binomial D i s t r P ( x ) = (K+x-1)! x!(K-l)!  q p X  k  where k = # of successes success i n 1 t r i a l P = prob m = average # o f s u c c e s s b e f o r e k success ,2 k = .2 SD "- nT  Log Normal M  =  ili  l o  gio i x  n S =.| (log X -M) 1  1 0  i  i  n-1  t n  2  m 2 SD SD = s t a n d a r d dev'n o f # o f f a i l u r e s before K success. t n  CO  36  Using empirical data i t was possible to e s t a b l i s h a decision matrix of p r o b a b l i l i t i e s that a related s p i l l w i l l occur.  An i n t e r e s t i n g way of  thinking of i t i s as a semi-Markov p r o c e s s . A  f i n i t e Markov chain  can be structured by defining a state as a s p i l l s time l o c a t i o n i n a r e lated sequence, ( i . e . , the f i r s t s p i l l i n the sequence puts the system i n sta 1, a second s p i l l i n a sequence puts the system i n state 2, e t c . ) .  Table  3.6 i s a summary of related s p i l l sequences f o r each of the three major areas.  For each state i , the count.represents the number of s p i l l s  occurred as the i - t h s p i l l i n a related sequence. covery area, state 3 has a count of 14.  that  For example, i n the r e -  This means that of t h e 5 2 i n i t i a l -  i z i n g s p i l l s , (the count of state 1), 14 of them resulted i n sequences of related s p i l l s at least 3 s p i l l s long.  As indicated i n Tables 3.5 and 3.6,  the pulping area did not have any " r e l a t e d " s p i l l s .  TABLE 3.6  RELATED SPILL COUNT FOR EACH STATE Major Area  State  Recovery-#l  Recaust-#2  1  52  24  2  30  7  3  14  4 .  4  10  3  5  4  2  6  2  0  7  1  0  ^ A semi-Markov process i s a stochastic process which makes t r a n s i t i o n s from state to state i n accordance with a Markov chain but i n which the time spent i n each state before a t r a n s i t i o n occurs i s random.  37  Using the data of Table 3.6, i t i s now possible to construct the r e l a t e d s p i l l decision matrices.  For the recovery area, the following matrix r e -  sults:  TABLE 3.7  RELATED SPILL DECISION MATRIX FOR RECOVERY AREA (#1)  State  1  2  3  4  5  6  7  1  .423  .576  0  0  0  0  0  2  .533  0  0  0  0  0  3  .285  0  0  0  0  0  4  .6  0  0  0  .4  0  0  5  .5  0  0  0  .0  .5  0  6  .5  0  0  0  0  0  .5  0  0  0  0  0  0  7  1.  .467  .714  S i m i l a r l y f o r the recaust area, the following matrix  TABLE 3.8  results:  RELATED SPILL DECISION MATRIX FOR RECAUST AREA (#2)  State  1  2  3  4  5  1  .708  .292  0  0  0  2  .428  0  .571  0  0  3  .25  0  0  .75  0  4  .33  0  0  0  .67  0  0  0  0  5  1.  Notice, given the sequence i s i n state i , only two jumps are p o s s i b l e , to state i + 1, or back to state 1.  This provides s u f f i c i e n t structure f o r  38  the semi-Markov process.  The r e s u l t s summarized i n Table 3.5 provide a time  d i s t r i b u t i o n between related states  ( i . e . , state i to state i + 1) while  the r e s u l t s summarized i n Table 3.3 provide a time d i s t r i b u t i o n between the end of a related sequence and the beginning of a new p o t e n t i a l sequence ( i . e . , state i to state 1).  Using these r e s u l t s i t i s possible  to determine  lim-  i t i n g p r o b a b i l i t i e s of being i n any state, mean f i r s t passage times and limiting transition probabilities.  An analysis of t h i s sort can be found  i n Appendix I.  To translate a s p i l l amount i n terms of i t s Na SO^ equivalent into an equi2  valent BOD and SS load, l i q u o r samples from the m i l l were analyzed and are summarized i n Table 3.9  TABLE 3.9  BOD, TS AND SS OF MILL LIQUOR SAMPLES  Liquor Weak Black Liquor Strong Black Liquor  BOD  m  g  / l  TS  m  g  / l  ss  m  g  36,700  176,148  272  131,250  624,127  800  White Liquor  0  Green Liquor  0  unreliable it  /i  300 2021  The Na SO, equivalent to volume of liquor conversion factors were deter2 4 mined from the l i t e r a t u r e and the calculations can be found i n Appendix II.  A summary of the r e s u l t s are:  39  TABLE 3.10  POUNDS Na S0 2  EQUIVALENT TO GALLONS OF LIQUOR CONVERSION FACTORS  4  US gal of l i q u o r / l b of Weak black liquor  1.063  Strong black l i q u o r  .270  Green l i q u o r  .325  White l i q u o r  .325  To convert a Na^SO^ equivalent to a BOD loading: , , me BOD lbs BOD = (lbs Na S0 Equiv.) X ( / 2  X 10"  3.1.3  Na^O^  6  4  ^mg X 2.2 ^kg  I i t r  o f l i q u o r  >  , „ ,gal's of l i q u o r v X (« ) l b  p f  X 3.785- lBift ir e-  PRODUCTION AND WATER USAGE  Daily production i n a i r dry tons and water usage i n U. S. gallons per day were transcribed from monthly operating sheets and used to e s t a b l i s h empiri c a l distributions.  It was  o r i g i n a l l y hoped that there would be a reasonably good c o r r e l a t i o n  between water usage and production; however, t h i s proved not to be the case. The highest c o r r e l a t i o n for various combinations of complete runs was .26.  The data did indicate, however, that days with lower production tend-  ed to use l e s s water. ship.  about  This also f i t s the i n t u i t i v e f e e l of t h e i r r e l a t i o n -  Consequently, two empirical d i s t r i b u t i o n s for water usage were de-  veloped, one f o r production greater than 1,000 one for l e s s .  a i r dry tons per day  The two d i s t r i b u t i o n s are given i n Table 3.11  u l a t i v e d i s t r i b u t i o n s are plotted i n Figure  3.1.  and  and t h e i r cum-  AO  TABLE 3.11 TWO EMPIRICAL DISTRIBUTIONS FOR DAILY WATER USAGE • DETERMINED BY LEVEL OF PRODUCTION  Production >1000 Tons  Production ^1000 Tons MUSGD  Count  Cumulative Prob.  MUSGD  Count  Cumulative Prob.  51  11  .31A  57  2  .023  53  1  .3A3  59  1  .035  55  1  .371  61  1  .0A7  57  1  .4  63  3  .081  59  A  .51A  65  7  .163  61  3  .6  67  11  .291  63  2  .657  69  28  .616  65  3  .7A3  71  2A  .895  67  A  .857  73  9  69  1  .886  71  3  .971  73  1  1.0  1.0 Total=86  Total=35  TABLE 3.12 EMPIRICAL DISTRIBUTION FOR DAILY PRODUCTION IN AIR DRY TONS  Production ADT  Count  Cumulative Prob. .0819  0 -  500  12  500 -  600  5  .090  600 -  700  9  .114  700 -  800  4  .147  800 -  900  10  .180  900 - 1,000  16  .286  1,100  10  .367  1,100 - 1,200  32  .573  1,200 - 1,300  50  .893  1,300 - 1,400  24  1.000  1,000  -  »  " P r o d ' n <1000 tons ,Prod'n >1000 tons  FIGURE 3.1 CUMULATIVE  DISTRIBUTIONS FOR PULP MILL DAILY WATER USAGE  42  An empirical d i s t r i b u t i o n for production was i s summarized i n Table  s i m i l a r l y established and  3.12.  Since the empirical d i s t r i b u t i o n s f o r water and production give a d a i l y figure and the intent i s to run the model on an hourly b a s i s , i t i s assumed that the production and water per hour w i l l be constant for any given day. T>  In other words, /i  ,  Day production  Production/hr = — i r r ^ ,  H,OFWhr 2  n  24 hrs/day = ; ° 24 hrs day f l  W  3.1.4 REGULAR EFFLUENT If i t were possible to prevent a l l major s p i l l s , the pulping process, by the very nature of i t s operation, would s t i l l generate e f f l u e n t .  Activities  such as debarking, dreg and mud washings, brown stock washers, screening and bleaching a l l r e s u l t i n l i q u i d r e s i d u a l s .  This "regular" effluent  grouped according to o r i g i n into s i x areas or streams.  was  These s i x areas  and t h e i r r e s u l t i n g effluent streams represent, i n several cases, quite a large portion of the m i l l ' s operation. standard one  (see Bower, 1971).  However, the breakdown i s a f a i r l y  The s i x streams and what they include are:  1.  Acid stream - the bleaching area  2.  A l k a l i n e (general) stream - brown stock washers, digestors, blow tanks, screen rooms  3.  Recovery - recovery b o i l e r s , p r e c i p i t a t o r s , black l i q u o r storage, evaporators, Na^SO^ storage.  4.  Flyash c l a r i f i e r  43  5.  Recaust stream - lime k i l n s , white liquor and green l i q u o r c l a r i f i e r s , washers and storage  6.  Machine room - pulp drying and stacking.  To represent these streams the e f f l u e n t s were assumed to be normally d i s tributed.  This i s a f a i r l y standard assumption i n the industry (Howard &  Walden, 1971).  The means and standard deviations were determined from a  combination of m i l l data and from Howard and Walden (1971).  The r e s u l t s  are summarized i n Table 3.13.  By sampling from these d i s t r i b u t i o n s each hour i t i s possible to generate hourly "regular" BOD and SS concentrations for each of the streams.  Multi-  plying these concentrations by the water flow i n the stream the actual BOD and SS loads f o r that hour can be determined.  The water flow f o r each  stream i s a proportion of the hourly m i l l flow as'summarized i n Table  3.2  3.14.  WASTE TREATMENT  Most models of waste treatment systems consider only steady state operation. Therefore, given a constant hydraulic load and concentration, i t i s p o s s i ble to determine the average performance of a system. approach used i n engineering design.  This i s the common  However, i n recent years more i n t e r -  est has been shown i n the dynamic response of a waste treatment system to hydraulic surges and changes i n input concentrations.  One concern i s that a hydraulic surge e f f e c t s the effluent detention time. Detention time i s an important parameter since the amounts of BOD and SS  44  TABLE 3.13  BOD, TS AND SS MEANS AND STANDARD DEVIATIONS FOR THE SIX MILL AREAS  BOD mg/l AREA MEAN  ST. DEV.  SS mg/l  TS mg/l MEAN  ST. DEV.  MEAN  ST. DEV.  79  22  800  100  26  3  ALKALINE "  157  55  1500  200  155  55  RECOVERY "  86  36  900  150  33  17  FLYASH CLAR.  10  2  200  40  48  5  RECAUST STREAM  12  3  220  40  118  41  9  .2  58  15  26  5  ACID STREAM  MACH. ROOM  TABLE 3.14  PROPORTIONS OF, TOTAL HYDRAULIC FLOW FROM THE SIX MILL AREAS  AREA  FLOW GAL/MIN  PROPORTION OF TOTAL  ACID STREAM  22,400  .477  ALKALINE "  18,750  .400  RECOVERY "  2,900  .063  FLYASH CLAR.  900  .019  RECAUST STREAM  700  .014  1,250  .027  MACH. ROOM " TOTAL  46,900  1.00  45  reduction are a function of the length of time a given u n i t of polluted water i s i n residence.  The waste treatment model i n this study enables a  pulp m i l l manager to study some of the dynamic e f f e c t s of pulp m i l l operation on the c l a r i f i e r - l a g o o n treatment f a c i l i t y .  3.2.1  THE CLARIFIER  The c l a r i f i e r model treats the c l a r i f i e r as a f i r s t order chemical reactor where the degree of s e t t l i n g i s d i r e c t l y proportional to the concentration of suspended s o l i d s i n the c l a r i f i e r at any time t .  This r e s u l t s i n an  exponential r e l a t i o n s h i p f o r the weight f r a c t i o n of SS removed i n the basin by time t .  Sakata and Silveston (1974) developed a f i r s t order reaction  assumption f o r s e t t l i n g .  For the f i r s t order reaction assumption, they  state: X(t)  = 1 - exp (-kt)  eqn 3.1  where X(t) = weight f r a c t i o n of SS removed i n the basin by time t k = apparent sediments removal c o e f f i c i e n t (rate of reaction) -1 sec t = time (sec) h If we l e t t = — where h = depth of c l a r i f i e r i n cm v  Til v  D  = threshold s e t t l i n g v e l o c i t y cm/sec  ~  Threshold v e l o c i t y v  Q  i s a lower bound on the s e t t l i n g v e l o c i t y .  Any  p a r t i c l e s with s e t t l i n g v e l o c i t y v £ v w i l l s e t t l e i n the time = ~. I f h ^ we l e t vo= detention time, then v i s the minimum v e l o c i t y any p a r t i c l e Q  Q  s t a r t i n g at a distance h from the bottom of the c l a r i f i e r must have to ensure s e t t l i n g .  46  we get X(t) = 1 - exp  -hk (——) v  Note:  v  D  =  o  | 3  where  Q = f l u i d flow rate into c l a r i f i e r i n cm /sec  2 A = surface area of c l a r i f i e r  cm  Sakata and Silveston then showed that a d i f f e r e n t i a l weight d i s t r i b u t i o n of the s e t t l i n g v e l o c i t y v could be expressed as: p(v) = exp (-^) + ^ exp  (~)  eqn.  3.2  where a = hk p(v) = d i f f e r e n t i a l weight d i s t r i b u t i o n of v  This implies f o r any suspended matter, i f the s e t t l i n g v e l o c i t y curve i s f i t t e d by equation 3.2,  the f r a c t i o n a l removal can be expressed as a f i r s t  order exponential equation, namely equation  3.1.  In Silveston (1969) a graph of the s e t t l i n g v e l o c i t y f o r pulp m i l l wastes i n a 6 f t column i s presented.  (This i s reproduced as Figure 3.2).  By  f i t t i n g equation 3.2 to this graph the parameter "a" f o r pulp m i l l wastes was estimated ( i . e . , equation 3.2 was  evaluated at 3 points on the graph cni  i t e r a t i v e l y , u n t i l a reasonable f i t was  found).  A value of a =  .104  f i t the p l o t quite w e l l .  Therefore, f o r any given depth of c l a r i f i e r i t  was possible to determine  the  parameter k f o r pulp m i l l wastes.  Namely:  .6  % Suspended S o l i d s w i t h S e t t l i n g V e l o c i t y E q u a l o r L e s s than V(D)  FIGURE  3.2  DISTRIBUTION OF TERMINAL SETTLING VELOCITIES FOR PULP MILL WASTES  48  .104 a sec V = — = —; h h cm C m  ,J  .104, h  UH  -1  - —:—sec  In Figure 3.3 i s seen a copy of a t y p i c a l residence time plot f o r a centerfeed c l a r i f i e r  (Chainbelt Inc. 1972).  The output has a quick response to  the change i n inflow concentration. To mathematically model t h i s kind of behaviour a technique popular i n the f i e l d of chemical r e a c t i o n engineering was  used.  B a s i c a l l y , the problem i s to model the c l a r i f i e r ' s mixing behaviour so as to adequately represent i t s response to changes i n i n f l u e n t concentration. Levenspiel (1972), i n h i s book, "Chemical Reaction Engineering", goes into considerable depth on this problem.  Tank mixing models are bounded by  two extremes, the backmix (completely mixed) flow model and the plug flow model.  The backmix model assumes any incoming reactant i s mixed immediately  upon entering, the tank, implying that the tank has a uniform concentration at any time t .  The plug flow model assumes no mixing and the plug moves  i n the d i r e c t i o n of flow as a separate element.  The plots i n Figure 3.4  should help i n understanding these concepts.  By l i n k i n g a number of tanks i n series i t i s possible to approximate a p a r t i a l l y mixed system.  The greater the degree of mixing the less the  number of tanks i n series (Note: i s equivalent to plug flow).  an i n f i n i t e number of tanks i n s e r i e s  The mathematical modelling technique i n -  volves solving a system of d i f f e r e n t i a l equations representing the mass balance of two completely mixed tanks i n s e r i e s , where the t o t a l volume of the tanks equals the c l a r i f i e r volume.  FIGURE 3.3 DISPERSION CURVE FOR CENTER FEED CLARIFIER  TIME - MINUTES  51  T h e r e f o r e , take t h e f o l l o w i n g  Q(t) C  IN  -  Q(t) C,<t)  9Stl  I  ( t )  system  c^t)  t  V  /  'A v„  1  2  where Q ( t ) = h y d r a u l i c f l o w a t time t . Ci(t)  = c o n c e n t r a t i o n of SS i n tank i a t time t  Vi (Note:  = volume o f tank i .  V^ and V^ a r e assumed t o be e q u a l and V^ + clarifier.  A l s o t h e volume o f l i q u i d  retained  = volume o f i n each  tank  remains c o n s t a n t independent o f Q ( t ) ) . First  p e r f o r m a mass b a l a n c e on tank 1 a t time t over a time span o f  At  (a)  Change i n mass from time t t o time t + A = M(t +.A t) - M ( t ) t  - Q(t)C  (t)At - Q(t)C (t)At - V C ( t ) k A t 1  i n f l o w mass of SS k  c  o u t f l o w mass of SS  1  .104  c  mass of SS which i n time At  = sediments removal c o e f f i c i e n t = first  1  order " r e a c t i o n " r a t e  -1, (sec )  settles  52  (b)  Now d i v i d i n g by At we get M(t+At)-M(t) At  =  Q(t) C ( t ) - V C ( t ) k  Q(t) C ( t )  L  1  1  r  Mas s U s i n g 77-^ = concentration Volume 0  (c)  we c a n express  (b) as AC, ( t )  TT  =  1  V D e f i n i n g QTJTS, dividing  V  ~At  l  - Q  ( t )  C  IN  " *M  ( t )  C  l  (  t  )  "  V  l l C  (  t  )  k  c  d e t e n t i o n time = T ( t )  =  (c) by V^and t a k i n g t h e l i m i t as At +  0  We get  dc (t)  c (t).  1  c (t)  IN  1  - k.C, ( t ) T(t) c 1  T(t) rearranging dC (t) 1  4F-  1 + k T(t)  iV  c +  °IN T(t)  ( t )  T(t)  eqn. 3.3  E q u a t i o n 3.3 i s a l i n e a r d i f f e r e n t i a l e q u a t i o n of t h e g e n e r a l form,  &  + P ( x ) y = Q(x)  which has a s o l u t i o n  Y = e ^  P  (  x  )  d  x  r (x)e^  ( x ) d x  Q  dx + Ce ^ < P  x ) d x  (Wilcox and C u r t i s  (1966))  A p p l y i n g t h i s t o e q u a t i o n 3.3 we get  C (t) = e 1  l+kr.T(t) T(t)  d  m<m) dt T(t)  t  rt C  IN T(t)  ( t )  e  whereJT^ = i n t e g r a t i o n c o n s t a n t f o r end c o n d i t i o n s .  l+k T(t) •T(t) r  dt + 0 e. eqn.  3.4  d  53  Feeding the c l a r i f i e r i s the pulp m i l l model which has a constant hydraulic flow over a 24-hour period and a constant effluent concentration C\(t) each hour.  Making these assumptions i n equation 3.4  ution.  greatly s i m p l i f i e s the s o l -  Since the pulp m i l l model cycles on an hourly b a s i s , l i t t l e r e s o l -  ution should be l o s t as a consequence.  Therefore assuming T(t) = T Q(t) = Q  =  "  "  — r  —  "  II  n C  = constant for each 24-hour period  c  IN  U ;  II  " IN~ C  is(t) =  T  " II  II  1  and solving eqn. 3.4, we  c  "  11  C l N  1+k T c c  get  -(1+k T )£1 - e c c 1 c  + CA0)e~ c c T (1+k  T  )  1  c  eqn.  3.5  where C.^ = inflow concentration of SS f o r any given hour (mg/l) T  c  C^(0)  = detention time (for each tank) for current 24-hour period (sec „ Vol of tank i.e., T = = concentration of SS i n tank 1 at t = 0 (mg/l)  For the two-tank s i t u a t i o n , a d i f f e r e n t i a l equation s i m i l a r to equation  3.3  was derived, only i n this case the feed concentration from tank 1 to tank 2 i s changing with time as described by equation 3.5. The assumption that 0,T and the feed concentration  into tank 1 are constant i s retained.  54  The d i f f e r e n t i a l equation f o r the outflow concentration of tank 2 was then  dC  2< > fc  d  . C (t) •  t  c  l \c 1+  2  \  T  T  C  is(t>  eqn. 3.6  ,  Applying the general s o l u t i o n indicated e a r l i e r (t) = e " J < K c > £  f\(t).  T  '2S  J substituting  C  1-e  2S  " (1+k T )' c c'  -(1+k  +  c  c +Le 2 °  V  T  T )±c c 1 c  J\  c  I -=  e q u a t i o n 3.5 f o r C^Ct)  IN  ( t )  J ( l k T ) ^  c  and s o l v i n g  +e  c c  t  T  c  c (0) 2  + C ; L  C  IN  (0)f-^L-c  c  eqn. 3.7  Looking at equation 3.7 notice that: at t = 0, we get C_(t) = C (0) as expected. t - Cl+k T ) — — 9  e  c c T 2  C  2 C  ( t ) =  ln  Now as t increases the term  decreases implying that the second term i n 3.7 has less  e f f e c t on C ( t ) as t increases.  As t approaches i n f i n i t y , 3.7 becomes  _ J L (1+k T ) c c  2  implying that with a constant input concentration and no changes i n T, the. output concentration C ( t ) approaches a constant and the system has there2  fore a l i m i t i n g e f f i c i e n c y .  For an instantaneous  shock load  = 0 and C^(0)  ( t )  mass of shock load v o l . of tank 1  c  55  and C (0) = 0, we get the t h e o r e t i c a l response curve of the c l a r i f i e r model. 2  C (t) s 2  C  l  (0)f c  e - ^ c V f  which has a shape s i m i l a r to that of Figure 3.3.  3.2.2  THE LAGOON  In Chapter I I , the b i o l o g i c a l oxidation process occurring i n an aerated lagoon was described.  The removal rate  for oxidation i s treated here as a con-  stant, implying that the amount of BOD removal at any time t i s d i r e c t l y prop o r t i o n a l to BOD concentration at time t .  To model the temperature depend-  ence of K^, an empirical r e l a t i o n expressing  as a function of temperature  was used (Beak - Environment Canada (1973)).  The function i s :  T-20 K j * - .256 (1.032)  Where T = temperature, °C K_ * ='lagoon removal rate, day ^ J-i  (Since the model i s run on an hourly basis the resultant K^* must be divided by 24).  In Beak-Environment  Canada (1973) and i n C i t y of Austin, Texas (1971), the  tanks i n series model was found to give reasonable representation of a lagoon's response time curve.  As f a r as BOD reduction was concerned however, they only  looked at the long term steady state operation and did not t r y to model lagoon performance v a r i a t i o n s as a function of changing hydraulic loads and input concentrations.  In other words, f o r steady state, they claimed:  56  l a g o o n removal r a t e  =  BOD  cone,  out  BOD  cone,  in  (1+K^)  (hr  -1. )  where:  3  = d e t e n t i o n time of each of the tanks  f o r t h r e e e q u a l volume tanks i n s e r i e s .  F o r the purposes  of t h i s s t u d y , a t h r e e - t a n k s - i n - s e r i e s model of the  b e h a v i o u r over time was  lagoon's  developed.  S c h e m a t i c a l l y the model i s : Q CINBUD  c  B l  CR2(t)  (t)  p£B3<t>  Q  Note:  =  V  2  =  V  3'  V  l  +  V  2  +  V  3  =  vo  -'-  ume  o f  l g a  o  o  n  Q = h y d r a u l i c f l o w , assumed c o n s t a n t f o r each 24-hour p e r i o d CINBOD  = c o n c e n t r a t i o n of i n f l u e n t c o n s t a n t f o r any g i v e n hour  BOD (  /l)  S e t t i n g up mass b a l a n c e r e l a t i o n s h i p f o r each t a n k , r e l a t i o n s h i p s t o eqns. 3.3  and 3.6,  except w i t h d i f f e r e n t c o n s t a n t s , r e s u l t .  r e s u l t s of s e c t i o n 3.2.1, i t was  identical U s i n g the  o n l y n e c e s s a r y t o c a r r y the s o l u t i o n one more  s t e p and s o l v e f o r the output from tank 3 i n terms o f the s o l u t i o n a l r e a d y developed  (1/sec)  i n the c l a r i f i e r model f o r tank 2 (eqn.  3.7).  57  A p p l y i n g a mass b a l a n c e t o tank 3 r e s u l t s i n t h e f o l l o w i n g  linear  differential  eqn.  +  C  B 3  c  =  (t)  B ?  (t)  TL  U s i n g t h e g e n e r a l s o l u t i o n and s u b s t i t u t i n g the n e c e s s a r y parameter  c  B3  r  CINBOD  (t)  -at  • + e  L  T  (with  changes)  -at  1-e  e q u a t i o n 3.7 f o r C g 2 ( t )  ICRI B  1  (0)_t2  2T~2+C (0)t„+  L  B 2  C  R 3  (0)-  CINBOD t 2a T  CINBOD t  Eqn. 3.8 where a = (1 + K T ) L  L  (subscript L indicates  lagoon parameters)  C- (0) = Bl  c o n c e n t r a t i o n of BOD (mg/l) i n tank 1 a t t = 0  Cg (0)  c o n c e n t r a t i o n o f BOD (mg/l)  =  2  C  B3  < 0  c o n c e n t r a t i o n o f BOD (mg/l) i n tank 3 a t t = 0  > =  BOD removal r a t e c o n s t a n t (hr *)  =  d e t e n t i o n time f o r each tank f o r any g i v e n 24 hour Volume o f tank g a l  = =  TTZ  •  n  —  R  which  1 a  3  =  period  . (hrs)  gal/hr inflow time i n hours  For steady s t a t e o p e r a t i o n as t approaches C (t) CTEOTJ  i n tank 2 a t t = 0  1 (1 + K ^ )  infinity  e q u a t i o n 3.8 r e d u c e s t o  3  i s i n complete agreement w i t h Beak-Environment  Canada  (1973) r e p o r t .  58  To model the suspended  s o l i d s g e n e r a t e d as a b y p r o d u c t  o x i d a t i o n p r o c e s s an a p p r o x i m a t i o n developed was used. and  I f t h e complete  of the b i o l o g i c a l  i n C i t y of A u s t i n , Texas (1971)  lagoon i s t r e a t e d as a c o m p l e t e l y mixed b a s i n  the s l u d g e age i s assumed e q u a l t o the d e t e n t i o n time;  a*(Sp  =  +  X ) n  1 + b *t  .  where X = effluent X  0  = influent  SS c o n c e n t r a t i o n mg/l SS c o n c e n t r a t i o n mg/l  a  =  l b s of SS generated per l b of BOD  removed  b  =  r a t e of endogenous r e s p i r a t i o n of a c t i v e s o l i d s  V a l u e s f o r the c o n s t a n t s were o b t a i n e d from two s e p a r a t e a = .15 l b SS/lb BOD b = .2 d a y "  removed  Bower  papers  (1971)  Kormanik (1972)  1  T h i s r e l a t i o n has no d i r e c t  ( l b / l b - day)  time dependence and d i f f e r s w i t h the BOD  model i n i t s m i x i n g s t r u c t u r e and t h e r e f o r e was used o n l y as an SS on a d a i l y  indicator  basis.  The SS g e n e r a t e d a l s o c o n t r i b u t e s BOD generated  lagoon  .1 pounds of BOD  to the l a g o o n .  i s c r e a t e d (Bower, 1971).  F o r each pound of SS T h i s was i n c o r p o r a t e d  i n a change o f the r e a c t i o n r a t e c o n s t a n t as f o l l o w s The s l u d g e g e n e r a t i o n r a t e = k * L  generated^ j ,in'each tank over time At /  =  .15K^  'amount of s l u d g e  = k^* x volume x c o n c e n t r a t i o n ( t ) x At  59  R e w r i t i n g the mass b a l a n c e e q u a t i o n f o r tank i AM(t) = Q C ( t ) A t I N  - QC.  (t) - K V L  ±  C  ±  ( t ) A t + .1 k * V L  ±  C  ±  (t)At  giving AM(t) At and d i v i d i n g  through by V i (K^ - . l k * ) C  ±  (t)  T where - .Ik*  =  .985  T h e r e f o r e , w i t h the appropi'iate change i n K , e q u a t i o n 3.9  3.2.3  Waste Treatment  is still  valid.  Generalization  In most m i l l s , as w i t h the one m o d e l l e d  i n t h i s study, the a c i d and  (or g e n e r a l ) e f f l u e n t sewers were kept s e p a r a t e and were not l i n k e d j u s t b e f o r e the waste treatment  plant.  When f i n a l l y  linked  mixed i n a c o n t r o l l e d manner so as to ensure a n e u t r a l i n t o the l a g o o n . clarifier in  the BOD  clarifier  until  they were  (pH - 7 ± 2)  In some cases o n l y the g e n e r a l sewer was  alkaline  influent  f e d to the  and the two sewers were mixed j u s t , b e f o r e the lagoon. T h i s  resulted  i n the g e n e r a l sewer f e e d to the lagoon b e i n g b u f f e r e d by the as a r e s u l t o f i t ' s 2 or 3 hour d e t e n t i o n t i m e .  a chemical s p i l l  i n the a l k a l i n e sewer w i l l have i t s impact  b u f f e r e d and somewhat d i s p e r s e d by the  clarifier.  I n o t h e r words on the lagoon  60  To f a c i l i t a t e v a r i o u s combinations g e n e r a l i z e d model was FIGURE 3.5  developed.  of i n f l u e n t  i n t o the l a g o o n a more  S c h e m a t i c a l l y t h i s model l o o k s  SCHEMATIC OF  Z  Q2  like  GENERALIZED MODEL  CBOD(t)  Ql CINB«  i  t  i  t  Ql  Vcl clarifier  lag oon v  The two main changes were f i r s t made a f u n c t i o n of time and between the c l a r i f i e r and  To s o l v e f o r C_  U-J  V  Z, 02)  developed the BOD  0  (t)  the lagoon i n f l u e n t BOD  second  the m i l l h y d r a u l i c l o a d was  lagoon f e e d s ( i e . , Q l and  split  Q2).  i n terms of the knowns ( i e . , Q l , V„. , V „ , V , , V , CNIB LI LZ LI LZ T  f i v e d i f f e r e n t i a l e q u a t i o n s one  i n the c l a r i f i e r  through the c l a r i f i e r  s e c t i o n s , remembering i n the  [ i t i s assumed t h a t 10% o f the BOD  s e t t l e s out  s t a r t i n g w i t h the f i r s t  two  i s . o n l y m i x i n g and not t a k i n g p a r t  "reaction",  T  f o r each of the tanks were  i n the same manner as i n the l a s t  order s e t t l i n g  c o n c e n t r a t i o n was  that  first  travelling  ( p r i v a t e communication - T. Howard)] then  tank i n the sequence,  the e q u a t i o n s a r e s o l v e d  s u c c e s s i v e l y , the s o l u t i o n f o r each tank i n t u r n b e i n g s u b s t i t u t e d the d i f f e r e n t i a l e q u a t i o n f o r the next  tank.  The f i n a l s o l u t i o n f o r C j g C t ) i n terms of the known parameters, i s  into  61 " fCINB*Ql + Z*Q2]  1-e  T  L  t  -tvt  -a_t • +e  T  L  _ - 2*TT^)^ J  e ^ f l  Eqn. where  F + G  J = C o(0) + vu, T R  B 3  CBINCL*Q1 a *Q  L =  Z  Ql  _  H  a° ~ Q 2  2  CBINCL Q l a Q  H = C  B 2  Ql - —  (0)  Q  (T )  1  1  2  g  J  A + B  3  2  L  Ql Q (T )'  (1  — +  —o  L  D =  QT  _  C B I N C L  CBINCL c  c  A =  C B I N C L  T 3  T 3 -  _  T  ClliO) _  B =  CT*(0)  C?*(0)  -Ql  C,*(0)  B  +  and a = (1 + k T ) c  CT*(0)  "TTF  _ CBINCL _ CBINCL  3  TB  Z  +  G \. Gt  Lt +  "If  + C  B1<°>  3.10  62  Q  = t o t a l f l o w i n t o lagoon  Ql = flow i n t o c l a r i f i e r Q2  = Q-Ql  (1/sec)  (1/sec)  = f l o w which bypasses  CBINCL = c o n c e n t r a t i o n of BOD Z T  = c o n c e n t r a t i o n of BOD c  clarifier  into c l a r i f i e r  i n Q2  (mg/l)  (mg/l)  = d e t e n t i o n time f o r each tank i n c l a r i f i e r  model  = d e t e n t i o n time f o r each tank i n lagoon model C_. *(0) = i n i t i a l  c o n c e n t r a t i o n of BOD  (mg/l), i = 1, (0) = i n i t i a l  (sees)  (hrs)  i n tank i of c l a r i f i e r  at t = 0  2  c o n c e n t r a t i o n of BOD  i n tank j of l a g o o n  at t = 0;  (mg/l)  j = 1,2,3,  I f i t i s assumed t h a t the c l a r i f i e r  i s completely  implying C  ±  *(0) = 0,  Q = Q2  (ie.  i = Ql =  1,2 0)  a = 1 1  3 =  T  L  CBINCL  =0  Z = t o t a l BOD T  c  c o n c e n t r a t i o n from m i l l  = 0  then e q u a t i o n  3.10  reduces to e q u a t i o n  3.8.  bypassed by a l l the  sewers,  63  3.2.4  Discussion  In the l a s t  three  s e c t i o n s a m a t h e m a t i c a l model was  and  aerobic  s t a b i l i z a t i o n l a g o o n waste treatment system.  the  system to which t h i s study was  d i r e c t e d should  hour r e s o l u t i o n the model o p e r a t e s under. f i n a l model i s not  dynamic i n the  constant  are  changed a c c o r d i n g l y  and  changes i n c o n c e n t r a t i o n a l t h o u g h not  3.3 Two  I t should  i n the  stressed The  that  At  the end  each hour, and should  i n h y d r a u l i c load reflect  parameters the  final  The  f o r one  the  runs  of the hour the  s t a t e f o r the next hour.  one  model i n f a c t  Each hour the v a r i o u s  the model i s run a g a i n  smooth t r a n s i t i o n s ,  reflected be  clarifier  dynamics of  the c l o c k s t a r t i n g at t = 0,  hour.  of each tank becomes i t ' s i n i t i a l are  state.  set and  model i n steady s t a t e f o r one  be  The  t r u e sense of the word.  f u n c t i o n s ' i n a k i n d of q u a s i - s t e a d y assumed to be  developed f o r a  state  parameters  hour.  The  each 24  hours,  o v e r a l l system b e h a v i o u r .  CAPITAL AND OPERATING COSTS OF WASTE TREATMENT of the major f a c t o r s i n any  t h a t d e c i s i o n and are no  management d e c i s i o n a r e  the f u t u r e c o s t s i t may  exception.  The  two  To  engineering  c o s t a s t r u c t u r e as feasibility  However i n u s i n g are not  Waste treatment  processes modelled here, a c l a r i f i e r  s t a b i l i z a t i o n lagoon,represent a very money.  create.  the c a p i t a l c o s t  and  an  aerobic  study would almost s u r e l y have to be  What i s more c r u c i a l i s to get  and  intensive  completed  t h i s model as a management a i d , f i g u r e s o f t h i s  essential.  systems  l a r g e investment i n space, time  l a r g e as a l a g o o n a c c u r a t e l y  of  first.  accuracy  a f e e l of the magnitude  of c o s t changes as a r e s u l t of changes i n the b a s i c d e s i g n  of the  system.  64  In F i g u r e s 3.6,  3.7,  3.8  and  3.9  can  be  seen graphs of  operating costs for a center feed c l a r i f i e r lagoon  (Bower, 1971).  cost r e l a t i o n s a)  U s i n g the  f o r use  i n the model.  Lagoon C a p i t a l In F i g u r e 3.6 efficiency the  different  the  cost r e l a t i o n s h i p  for a l l efficiency  To  determine B,  In 8.1  The  = A*(FLOW)  levels.  t a k e the 5  f o r f l o w = 1.  CC  8  a log-log  plots plot,  form:  mgd  curves  p a r a l l e l , the  The  40%  following  the  lagoon  5  log-log  l i n e a r and  (The  developed,  a f u n c t i o n of  A intercepts  B c o e f f i c i e n t w i l l be however w i l l be  identical  different.  curve  x 10  k =  2.092 + 11.51 - (1.131 + 4.61 - 0  .708  A intercepts  be  l i n e a r on  w i l l have the  x 10 - In 3.1 l n 100 - l n 1.0  =  to develop e x p l i c i t  S i n c e each of  e f f i c i e n c i e s are  B = s l o p e of  are  These w i l l now  f l o w i n MUSG/day.  for  plots  and  aerobic s t a b i l i z a t i o n  i t i s possible  lagoon c a p i t a l c o s t s a r e  where A = c o s t i n t e r c e p t  S i n c e the  an  capital  Costs  and  CC  plots  and  the  v a l u e f o r Flow = 1 mgd) efficiency  .40  are  intercept  $3.  x  10  .5  6 x  10  .6  9 x  10  .7  12 x  10  .8  18.8  4  4  h  x  4  10  9.21)  FIGURE 3.6  65  CAPITAL COST VS. FLOVJRATE AT VARIOUS $ REMOVAL. OF BOD : AERATED LAGOON CURVE NEW H  Flow, mgd ( At any removal below 1*0$ , use the ko£ l i n e )  66  intercept  efficiency .85  23.0  x  10'  .9  29.0  x  10  .95  37.0  x  10  For e f f i c i e n c i e s below .4, the i n t e r c e p t lagoon e f f i c i e n c i e s between any i s determined  by l i n e a r  between .8 and GA  .85,  f o r the .4 curve i s used.  2 c o n s e c u t i v e data p o i n t s the A  interpolation.  4  intercept  For example i f the e f f i c i e n c y  then the A i n t e r c e p t  = l o g (18.8 x 1 0 )  For  i s calculated  as  + [(EFF - .8)/(.85 - . 8 ) ] * [ l o g  (EFF) i s  follows: (23 x 1 0 ) 4  - l o g (18.8  then A = EXP(GA) The  c a p i t a l c o s t of the l a g o o n i s then e v a l u a t e d as CC  L  = A*(FLOW)'  Note:  7 0 8  EFF = l a g o o n e f f i c i e n c y ,  determined  a t the c o m p l e t i o n of  the  experiment gpp  _ t o t a l BOD  into  lagoon - t o t a l BOD out of t o t a l BOD i n t o lagoon  lagoon  where t o t a l s a r e taken f o r the complete experiment.  b)  Lagoon O p e r a t i n g F i g u r e 3.7  Costs  i s a semi-log p l o t  of lagoon o p e r a t i n g c o s t s (per(MUSG/day)  flow) v e r s u s lagoon e f f i c i e n c y . o p e r a t i n g c o s t s are a l i n e a r  For any  given  f u n c t i o n of lagoon  efficiency flow.  Namely O p e r a t i n g C o s t s = OC = C*FL0W where C = c o n s t a n t dependent efficiency.  on  xlO  68  The c o n s t a n t s C were determined c a p i t a l costs.  The d a t a p o i n t s taken from F i g u r e 3.7 a r e :  efficiency C  If  f o r t h e same e f f i c i e n c y l e v e l s used f o r  .4  .5  .6  .7  .8  1480  2400  4100  7600  14700  .9  .85 21500  .95  33000 53000  l a g o o n e f f i c i e n c y f a l l s between any 2 c o n s e c u t i v e d a t a p o i n t s C i s  determined between  using linear  interpolation.  F o r example, f o r an e f f i c i e n c y  .8 and .85  GC = l o g (14700) + [(EFF-.80)/(.85-.8)]*£log (21500) - l o g (14700) ] then  N  C = EXP(GC)  The o p e r a t i n g c o s t s a r e then OC = C*FL0W d o l l a r s .  c)  Clarifier  Capital  Costs  F i g u r e 3.8 i s a l o g - l o g p l o t o f c l a r i f i e r clarifier  surface area.  form: C a p i t a l Costs = C C  The r e l a t i o n s h i p w i l l .  c L  c a p i t a l costs versus  = D*(AREA)  .  have the f o l l o w i n g '  E  2 where  D = Cost i n t e r c e p t a t A r e a E = slope of l o g - l o g  =1. f t  curve  To e v a l u a t e D i t i s n e c e s s a r y t o e x t r a p o l a t e t h e c u r v e beyond t h a t shown on the p l o t , g i v i n g D = $29.5  69 FIGURE 3.8 CAPITAL COST VS. CL4.RIFIER AREA : PRIMARY & SECONDARY CLARIFIER CURVE C 6  1——: r~  K •;.. 1 '..1....! .|  1  i —- t ' 1  -:. j. r  -  ...... 1 :4 . i : 1 • n - ! i. 1 ~4  -:.!••-!- j - i - i - •t • n't-  ri  Sf  ;  •  -  ' ' " '  I • i  . .  ...i  ::  rrrt-  ... | ...  -1 —  .1!  ri -t"1  i  .iJi.T.  j. -, - t..  :.U.  : T . i ::-\- : . : ' P_  1  '1 4 -::\:  1  -rp  1  .. ;.:.. 1::': T T '/••\ : -ppi :.:.; .\iurL : — • t —i ;.i r : rrr i....iff:ru --! L.:: : 1 ±1  j::  i — ( •"!" ::: ••[ . < :: | : -'TP 4 _: L -! : !" '• 1' ; -r:-;T rr - j :-4 \ ri E - ! R•—1 - u It S t t ; t- -i P. f'-' J i T J T . ' . : ..:T -1•- ;I ' : t . ' ! 1 r \-• j~ "4 ... 1.-.• i.-. | • f -• '.TA: .riq:::.- T€1 ~-:\: -r- T.LTI .r.l — T E E irSfTP. ~ r.Lii"i_ ~:;.;;;| 1_ ' i .....j•. L fcr r •+ P i •: .! t-—r-j HZ: LE'iTr. "r: SE S I —-|-r7-4 r-j-t Pr ~" '\'.", 4: L :i•" « - = i_ 1. " — _~Xz r--T-~ l_j j-r-r r T H p~" 1.. - - 7 -4 1'— • • ; • j •i f( .'_ hi_ ! —• .. i-— r1_-4L-4TLTJ 44-j4 4-4-PpTE; T'" __i j j —ft 1 -P-L. _L.L_ : i ± -r!-:r'-4 1—1—1—j—|— 1 11 -'rr L i M 1;:j:' TT 4 1—• i T~\T' i h i: t ! ' ' . . _-l 1 —-t — ... .. / ; PT i i i 1 r EE "1 — 4 1—!-4 _ 11 -tih i • .i -.-i-r ' 1 I-. ——(t1..i i -7— -1 - i 4-t- 1 i ' 1 rr -Pi-1" r -r— -4-rH -1——i : : 1 i • l-i'!~~r~ 4-H — !-Hr t : ± T i iT -4 ilil ' i i"iTTT TTT; i •4 4 - r. 4.-1 — 1 4-7'F-ir4 7i:l 7 ^ "f•I444-f:L ~ i t-—• l" •T-r-rr- " . -1-T P S — !±i- I....'.... —H—-rptU. r t" f-r-PV-it i l -j-T H T "7 772 f " -rlt' :( —. -il-_-_i-4_i-C-'LL. -!-1 rripp— •'! r —— L- -h- ; 1 r~T~ l_ -H-hr -ERPT^ -l -rr-r |l!T -Pi4 r rr' :c: i -r7-r-f '.lip • '. [• !r • T I.-r.rr7i_L7 iz~c: 3 . • •• • 1ri4 L. 774•H!-^ 4::.-7.7: 7': : 77-77 - i r h i • t •[ jf-t • '• j- — _.7 ir. 1 t"" -.tr rEtTir _77 ; :: i _ rv PP hPlJ- 1 4• P •;-:r:-: ~J 1 — -i i i PfTTpT * t 4 t T TrP -•1 7T u ± T=1 i4- : t -^-r-t--4-j-r ~i S [ 4 74E ±T£T 4-r-rrri •j4 , 1 i :a I T1 |-r; r •I !St • ;l -1- L —1 !4-t-H I-HT! •1 4 i -rrt — J r 1 -r*"VE T r r f rH-r T i ; i r i T T i'T L - - »;—— -rrf : -1 ; f ': ; T i ;' P T A }";~; fT 1 '1 Iff:: IVl" i 1 i 1T!: i •1 i i 1 i !Ttrrr T1r i !! i t-r- 1:1' --T f H : r t-7•r-77-rt -H a — tvT Tr"r~~ -h-r P-rr-f • ••" 1 l i t - : 1- . -l • '1._. _ t_. • i • • • •. 1 L: |..-L " K'TT 1 l 1; ! • hr • \ •••••• I "f 11 • 1 ! j hr . LJL:.L•t~- i - ! • i' • : 1 :1: . 1r •Krr ! i , • I,1 i rr -H-H jliii : / •' i rT -- 1; rzifp; P Htfl 14 it" iiiifr L , . ^ — T 17:7;:. — ip.EP TTTT —-^-1—— -i•t——7- -|— -r *t-Vr— pi™;-r;- r - r - i — 1 . +±tz • .J -IL -: ~r:—r —11 ' -i-r-r-H-rr4 Eii'itrl'irr ± 1 Jr. }± ':'. iZ'SI" d t -1 - -t'rH _|X rprrrp iiti P rprl -P>r F-t-F4zE -i 11-, : : !- f -44- f f ± t i 4'rfP -47 +rr4 7:::.: T : T T ^ I : U " : ~ :f77 /P.. [• H: PPTT .r.:T~ f. i-7 777;7_-"".*.:.-. 7 •|: i: L 177-."/ PTTT .!;LT.T • p-r..v .TTEIPPT 1D ..1 •_ . \-rrr l--r-i-t-T-r-f -1-1 ^_^^_.._^_ l-; : p: p: .~-_p:4 ri;.: :|T.i._L. ' I - ; ;—r .i—. r t : IT T" i~T~ - • — -r . -L — -i — —-—'—. -7- • 'V— r r .j —|—; r - i T. -1. 1 t ; : 'V . !,.:.4-- f— - —.i— - -—r-r~ i...: (—7- -7.p: fj t, i i " * ~"7 :i" _ rtf=Li±. T-T p.,,..4L f-7 1 -jip "M.. t . j I t:... i • ' I 1, . j • P • i.i P ... _ j1 •PP; !1. i 1 i :L .Lj_U.... -p p : ; ..Li r:r . i:.' iPT.: " rr j ~ | •!- I T T i .ii. ."!'.i ; " " " 1 •" 1 1" i n 3 i ..i..T. i 1' 'i ' i 3 JJ 3 4 5 6 s 2 9 10 6 7 o 4 i 3  }  :  :|  7-'  '  1  :  !  1  / •  :  •7;"  :  :  :  1  I  1.  \  -?  :  1  1  - i  :  r  1 ; !  1  H  :  1  1  i  ;  :  7-.;{  .  -  :  _  / :  -s. •ttE  ±  I  1  m  ffi  HE  ; :  j  1  ;  t  t  T  1  JS  r  r  ;  ;  —  1  !  :  -  1  -  :  10, 000  1,000  C l a r i f i e r Area, f t  r  1Q0 1  70  To e v a l u a t e E  E = sl o p e = In (2 x 1 0 )  - In (2 x 1 0 ) (1.5 x 1 0 ) - I n ( 1 0 ) 5  In  J  H  A^6  z  .92  =  therefore clarifier  c a p i t a l costs = C C  Knowing the depth o f the c l a r i f i e r  2,-92 = 29.5*(Area i n f t ) 2  c L  d a i l y f l o w and t h e o r e t i c a l  detention  time, the s u r f a c e a r e a can be determined.  Daily  ft  flow.  - -^d  24 S u r f a c e Area =  d)  Clarifier  x  detention  time ( h r s )  ^ day depth ( f t )  Operating  Costs  F i g u r e 3.9 shows a l o g - l o g clarifier  3  d a i l y flow.  plot of c l a r i f i e r  operating  Due t o i t s l i n e a r n a t u r e  costs  versus  i n t h e a r e a of  i n t e r e s t i n t h e model (10 MUSGD/day t o 100 MUSGD/day) the p l o t was linearized operating 0C  c L  (dashed l i n e ) .  The m a t h e m a t i c a l form f o r t h e c l a r i f i e r  costs i s  = F*(FL0W)  G  where F = cost intercept  f o r f l o w = 1. mgd  G = slope of log-log  plot  FIGURE 3.9 ANNUAL OPERATING COST' VS. FLOW : PRIMARY & SECONDARY CLARIFIER  Flow, ingd  71  72  The constants were evaluated as F = $3600 i n (3.2 x IP* ) - i n (3.6 x 10 ) i n (20)- i n (1) 4  =  S  °  l  p  e  =  2  = .726 Therefore ti  726 c l a r i f i e r operating costs = 3600* (FLOW) '  d o l l a r s where  FLOW i s i n MUSG/day. A l l the cost relationships are i n 1970 d o l l a r s .  To determine the  operating costs the following r e l a t i o n was used by Bower;  Total Annual Operating Costs = 1.25 (Capital Cost) + operation and maintenance costs based on 350 days operation per year.  The elements Bower included i n the costs are: 1.  Clarifier a.  C a p i t a l Costs - concrete structure, sludge pumps, rakes  b.  Operating Costs - power, administration, maintenance, sludge removal.  2.  Aerated Lagoons a.  C a p i t a l Costs - f l o a t i n g aerators, PVC l i n i n g , power supply (the land was assumed to be already available)  b. ' Operating Costs - power, operating labour, maintenance, nutrients, administration.  73  The  f o l l o w i n g assumptions  were made by Bower i n the development o f the c o s t  data: 1.  A l l facilities  2.  Primary c l a r i f i e r Clarifier  o p e r a t e f o r 350 days per i s of the c i r c u l a r  year.  type w i t h c e n t e r upflow  diameter depends on f l o w r a t e , s e t t l i n g v e l o c i t y o f  suspended matter  and d e t e n t i o n time.  3.  Clarifier  4.  Chemical  5.  The a e r a t e d l a g o o n i s assumed to be water  6.  A e r a t o r s a r e o f the f l o a t i n g to  7.  The  s l u d g e i s assumed t o have 5%  solids.  a d d i t i v e s were assumed not r e q u i r e d i n the  clarifier.  tight.  t y p e and have s u f f i c i e n t horse power  maintain a l l s o l i d s i n suspension. lagoon f e e d i s assumed t o be n e u t r a l i z e d .  be accomplished  by combining  the g e n e r a l and  T h i s can acidic  in for  c o s t s o f the m i x i n g the model.  s t a t i o n and  However,  used.  t h e s e c h e m i c a l s a r e not i n c l u d e d  Bower does i n d i c a t e however t h a t the c a p i t a l c o s t s  the h o l d i n g tanks and  c h e m i c a l f e e d e r s a r e around  o p e r a t i n g c o s t i s n o m i n a l l y around 8.  usually  sewers.  o f t e n c h e m i c a l a d d i t i v e s such as ammonia or l i m e must be The  feed.  Sludge d i s p o s a l i s not i n c l u d e d .  $10,000.  $65/ton o f ammonia r e q u i r e d .  The  74  CHAPTER IV MODEL DEVELOPMENT 4.1 The  PULP MILL MODEL DESCRIPTION model d e s c r i b e d  herein  i s concerned w i t h the waterborne e f f l u e n t  c h a r a c t e r i s t i c s of a k r a f t p u l p m i l l . sampling from e m p i r i c a l l y d e r i v e d  I t i s p r i m a r i l y a s t o c h a s t i c model  d i s t r i b u t i o n s each hour.  program i s w r i t t e n i n FORTRAN (a l i s t i n g The  model was  not  d e s i g n e d to be  can be  The  computer  found i n Appendix I I I ) .  used as a p u l p m i l l d e s i g n  aid.  It's  purpose i s to g e n e r a t e a t y p i c a l p u l p m i l l e f f l u e n t time t r a c e to used as  i n p u t i n t o the waste treatment model.  the d i s t r i b t u i o n parameters i n the model and  be  I t i s p o s s i b l e to change thereby create  a better  or  worse than normal time t r a c e .  F i g u r e 4.1  provides  i n the model.  a general  Notice  f l o w c h a r t of the p u l p m i l l  t h a t each of the  e f f l u e n t c o n t r i b u t i o n while only The  streams combine and  three  as v i s u a l i z e d  s i x e f f l u e n t streams have a streams have a s p i l l  e x i t from the m i l l m o d e l l e d as  regular  contribution.  indicated.  These  t h r e e e f f l u e n t o u t f a l l s from the m i l l a r e m a i n t a i n e d i n the model a l t e r n a t e combinations of them a r e a v a i l a b l e as treatment  and  i n f l u e n t to the waste  plant.  F i g u r e 4.2  i s an o v e r a l l schematic of  generation  sequence and  pages the model w i l l be r e s u l t s of c h a p t e r  III.  the model's s t r u c t u r e g i v i n g  the model d e c i s i o n p o i n t s . discussed  In the  the  following  i n d e t a i l w i t h a d i s c u s s i o n of  the  75 ICAL SOURCE OF EFFLUENT S = SPILLS R = REGULAR  MILL OUTFALLS  CHIPS  FLYASH CLARIFIER  Sewer #4  RECAUST  S.R Sewer #5  I  I RECOVERY FURNACE  DIGESTORS  I  S,R Sewer #3  EVAPORATION  SCREEN ROOM  S,R  Sewer #2  BLEACH PLANT  MACHINE ROOM  Sewer #1  Sewer #6  1 = ACID  R  OUTFALL  2 = ALKALINE  (GENERAL)  OUTFALL  3 = MACH. ROOM OUTFALL  PRODUCTION  FIGURE 4.1 DIAGRAM OF WATERBORNE EFFLUENT STREAMS INCLUDED IN MODEL INDICATING SPILL AND REGULAR EFFLUENT LOCATIONS  FIGURE 4.2  FLOW DIAGRAM OF PULP MILL MODEL  76  Set ITime, # of Hours Model i s to Run  Generate a Sequence of S p i l l s for Each of the 3 Major Areas up to ITime  Generate a Sequence of Daily Productions and Water Usage up to ITime - Write into L.U. #1  Day = 1 Hour = 1  Read Time of F i r s t S p i l l s for Each of 3 Major Areas  Read Prod'n/hr and Water/hr For Current Day  Generate Regular Effluent Level for the Six Streams For Current Hour .  No  Is There a S p i l l This Hour? Yes  (go to next page)  Which Area?  Add S p i l l For  to Regular E f f l u e n t Indicated Area  Read Time and Amount For Next S p i l l i n A r e a Which J u s t Had S p i l l  W r i t e BOD Cone. - 3 O u t f a l l s CSS Cone. - 3 O u t f a l l s f o r C u r r e n t Hour  No  _  I s Hour = 24? Yes W r i t e Days - BOD/ton SS/ton - Prod'n - T o t a l Water  Has experiment r u n f o r ITime hours?  I  Yes  Stop  System L o g i c a l  Unit  78  4.1.1  GENERATING CHEMICAL SPILLS  In chapter  I I I the s p i l l  a summarized form.  Using  data  acquired  t h e r e s u l t s shown t h e r e ,  g e n e r a t e b o t h r e l a t e d and u n r e l a t e d  Looking a t T a b l e s binomial  was  spills  i t was p o s s i b l e t o  i n t h e model.  3.2 and 3.3 t h e n u l l h y p o t h e s i s  f o r t h e gamma,  negative  and log-normal d i s t r i b u t i o n s cannot be r e j e c t e d f o r both the s p i l l  amounts and times between u n r e l a t e d statistic  from a B.C. m i l l was p r e s e n t e d i n  f o r both t h e s p i l l  spills.  The Kolmogorov-Smirnov D  amounts and t h e times between u n r e l a t e d  t h e s m a l l e s t o r second s m a l l e s t f o r t h e gamma d i s t r i b u t i o n .  spills  Consequently  i t was used i n the model t o g e n e r a t e those random v a r i a b l e s . The d i s t r i b u t i o n parameters were s u p p l i e d by the goodness o f f i t program. spill  The  (Note f o r t h e  amounts the v a r i a t e s u n i t s a r e i n terms o f 1000 l b s of Na2S0t ). t  gamma d i s t r i b u t i o n has t h e f o l l o w i n g d e n s i t y x  a-1  oo  e  function:  ^ x > 0, a and 3 a r e c o n s t a n t s .  where T (cx) = gamma f u n c t i o n and  a = shape parameter 6 = a s c a l e parameter  (the mean r a t e )  Note when a = 1, f ( x ) becomes t h e d e n s i t y f u n c t i o n f o r t h e e x p o n e n t i a l decay d i s t r i b u t i o n .  As a i n c r e a s e s beyond 1, t h e d i s t r i b u t i o n  approaches  the normal d i s t r i b u t i o n more q u i c k l y as t h e number of sample p o i n t s  increases.  79  B y c a l c u l a t i n g t h e sample mean, x, and sample v a r i a n c e S , t h e parameters 2  a and 3 can be e s t i m a t e d E(x)  =  var(x)  since  a3 a3  =  2  T h e r e f o r e s o l v i n g f o r a and 3 A  = £ 2  Phillips  &  = ~  t  r e f  -  Phillips  and B e i g h t l e r (1972)]  and B e i g h t l e r (1972) p r e s e n t e d  a new a l g o r i t h m f o r g e n e r a t i n g  gamma v a r i a t e s w i t h i n t e g e r o r n o n - i n t e g e r technique".  I t appeared  parameters,  called  "Phillips  t o have more s t a t i s t i c a l r e l i a b i l i t y f o r gamma  d i s t r i b u t i o n s w i t h ct<l and e q u a l r e l i a b i l i t y f o r a > l when compared t o other techniques  Phillips  f o r g e n e r a t i n g gamma v a r i a t e s .  t e c h n i q u e employs a n u m e r i c a l a p p r o x i m a t i o n  v a r i a t e over v a l i d  ranges  o f a and B.  r e l a t i o n s h i p s f o r d i f f e r e n t ranges  Using  t h e gamma  stepwise r e g r e s s i o n , f u n c t i o n a l  of a were determined.  g e n e r a t i o n o f gamma v a r i a t e s f o r 0 < a < °°. computational  t o generate  These permit  The method has a g r e a t  advantage over o t h e r methods i n t h a t i t r e q u i r e s t h e gener-  a t i o n of o n l y one random v a r i a b l e each time t h e a l g o r i t h m i s used. for  any g i v e n a and 3 parameter s e t , t h e f u n c t i o n a l r e l a t i o n s h i p s need  o n l y be determined for  Also  once and t h e r e s u l t s then s t o r e d f o r any f u t u r e c a l l s  t h e same parameter s e t .  T h i s a l g o r i t h m was programmed f o r the model and can be found listing  i n Appendix I I I as s u b r o u t i n e GAMMA.  i n t h e program  80  As l i s t e d i n the appendix i t i s only v a l i d f o r 0 £ a £ 2.  If a higher  range i s needed, the required functional expressions can be found i n P h i l l i p s and Beightler (1972).  For times between related s p i l l s table 3.5  indicates these were best  f i t t e d by the negative binomial d i s t r i b u t i o n .  The negative binomial  d i s t r i b u t i o n i s based on the number of .independent B e r n o u l l i t r i a l s (K + x) which occur before a given number of successes K are observed (It i s x that has the negative binomial d i s t r i b u t i o n ) .  The p r o b a b i l i t y mass function i s :  Therefore the p r o b a b i l i t y that x f a i l u r e s are encountered  p r i o r to the K  success i s : , p(x) N  =  ,k + x-lx k,>x ( ) p (1-p) x  =  (k + x-1)! (x!)(k-l)!  where p = p r o b a b i l i t y , of;success i n one  P  k,.. " ( 1  P )  .x  trial  k = number of successes x = number of f a i l u r e s  Using the moments method the goodness of f i t routine discussed i n Chapter III determined  the d i s t r i b u t i o n parameters l i s t e d  i n Table  3.5.  81  Note, when K = 1, t h e n e g a t i v e b i n o m i a l reduces  to t h e g e o m e t r i c  distribution.  In the model s i t u a t i o n K was n o t an i n t e g e r and t h e r e f o r e t h e concept of the k*"* s u c c e s s becomes somewhat m e a n i n g l e s s . 1  However by making use of  a r e l a t i o n s h i p between t h e n e g a t i v e b i n o m i a l , P o i s s o n and gamma d i s t r i b u t i o n s a n e g a t i v e b i n o m i a l d i s t r i b u t e d x was generated follows.  f o r a non-integer  K as  '  Suppose X i s from a P o i s s o n d i s t r i b u t i o n w i t h parameter Y, where Y i s a random v a r i a b l e generated  from a gamma d i s t r i b u t i o n w i t h parameters a = K  and  3 = 1-p , where K and p a r e as p r e v i o u s l y d e f i n e d , then X i s a n e g a t i v e P binomially distributed variate.  In o t h e r words f(X=x/Y) = e ~ Y Y  X  x = 0,1,  and f  , ,  ,K K-1 -Xy  where A 1-P then  f(X=x) =JfQ(=x/Y)  f (y)dy y  o  = T(x+K) . A K. 1 r(x+l)r(K) ^ 1 + A  x  ;  = T(x+K) r(x+l)r(K)  K P  U  x p  ;  which i s the d e n s i t y f u n c t i o n f o r t h e b i n o m i a l d i s t r i b u t i o n . [ F i s h m a n (1973)]  subroutine  NEGBIN  then l o o k s  like:  P X = -= 1-p  GENERATE Y = GAMMA (a=K,(3=X ) _1  S= I  A=  1  e"  Y  X = 0  i  U  Generate random x+1 " number  YES DONE!  83  Note p and k are given parameters to the routine.  The l i s t i n g f o r  subroutine NEGBIN can be found i n appendix I I I .  The two d i s t r i b u t i o n s , gamma and negative binomial, were used i n subroutine SPILL to generate three t y p i c a l m i l l chemical s p i l l time traces, one f o r each the 3 major areas. by the main program. for  In that one c a l l i t generates the s p i l l sequences  the number of hours previously defined i n the main program.  In determining for  The subroutine SPILL i s only c a l l e d once  the s p i l l time traces, the following procedure i s followed  each of the major areas 1.  (recovery, recaust, pulping) i n turn.  Determine time i n t e r v a l (in hours) and amount (in //Na2S0i equiv.) 1  of next unrelated s p i l l using Gamma d i s t . 2.  Determine s p i l l s sublocation within current major area  3.  Convert s p i l l amount into gallons of s p i l l f o r chemical  typical  of sublocation determined i n 2. 4.  Convert gallons of s p i l l into BOD, TS and SS equivalents (kgs)  5.  Record location, time i n t e r v a l , amount ( i n gals) and BOD, TS and SS equivalents of s p i l l .  6.  I f current clock time i s equal to specified number of hours f o r current experiment go to 10, otherwise  7.  Determine i f current s p i l l i s to be followed by a related If No, then return to 1.  8.  continue spill.  If YES, continue.  Determine time i n t e r v a l (subroutine NEGBIN) and amount (subroutine GAMMA) of related s p i l l .  84  9. 10.  Return  to 3  Repeat 1 to 9 f o r next major a r e a , r e t u r n i n g c l o c k to 0.  A copy o f a model generated found  i n T a b l e 4.1.  spill  In F i g u r e 4.3  showing more e x p l i c i t y how  sequence f o r the r e c o v e r y a r e a can i s a f l o w c h a r t of s u b r o u t i n e  the v a r i o u s d i s t r i b u t i o n s and  be  SPILL  d e c i s i o n matices  are used i n the model.  4.1.2  PRODUCTION AND WATER  P r o d u c t i o n s e r v e s two  f u n c t i o n s i n the model.  d e c i d e which water d i s t r i b u t i o n t o use and the pounds of e f f l u e n t per ton of  The  First  as a p o i n t e r to  second as a f a c t o r  to determine  production.  p r o d u c t i o n d a t a d e s c r i b e d i n Chapter  empirical d i s t r i b u t i o n f o r production.  HI The  w a  s  used to e s t a b l i s h  cumulative  read i n t o the model as 11 d a t a p o i n t s (see T a b l e 3.12).  an  distribution i s To determine a  day^s p r o d u c t i o n , a u n i f o r m l y d i s t r i b u t e d random v a r i a b l e i s g e n e r a t e d l o c a t e d i n an i n t e r v a l of the c u m u l a t i v e is  then determined  by i n t e r p o l a t i o n .  distribution.  The  T h i s i s accomplished  production i n subroutine  PRODN which r e t u r n s the d a i l y and h o u r l y p r o d u c t i o n i n a i r dry  In the model the two  cumulative  d i s t r i b u t i o n corresponding  tons.  d i s t r i b u t i o n s f o r the water usage a r e  read i n as e m p i r i c a l d a t a p o i n t s (see T a b l e 3.11).  The  to p r o d u c t i o n i s determined  c o r r e c t water and  and  a uniformly  85 TABLE ib it ion 12 12 12 4 4 3 3 4 4 4 3 -•  4 4  J  -3 3 2 3 4 3 3 3 3 3 ^ 3 4 4 4 4 4 •t 4 •t 3 :> 3' 3 4 + -+ 4 + 4 4 4 4  4.1  A SEQUENCE OF SPILLS GENERATED BY THE PULP MILL MODEL FOR THE RECOVERY AREA  Time (hr) Interval 17 2 1  il  2 ol5 8 1 1 3 2 95 5 25 1 ~34 108 7 1 5 1 ••I <i 4 183 110 2 _iO l.»J4 5 1 2 15 142 2 5 5 21 4 161 ^34 ?  9.5 1 14J 12 2 3 3 93 5 3 32 7 54 39 3  Gal of Liquor 242.6849 23704.7578 95.3940 7 6 7.6257 3241.493J 4856.2422 2230lo93 7 5 196t.2071 63 2 3 „ 2 9 3 0 46o«7 375 46 5 2 . 9 3 36 9 o 2 3 j. 0 2 2 7.6367 842.4756 19 7 1 . 1 5 4 i 9 7 0 7 . 7 695 2261, J . o914 6695,9023 6 86.54 6 1 6210.2333 402 5 102 lOO-t.5 8 6 7 3733.5679 8 1 2 2 o 2 352 3;.io05.3 4 3 3 6842ob3o7 1 1 9 9 . 9 7 80 44 4 3. 3J 08 164S io 0 2 3 4 2926.1909 44 5 2 . 56 6 4 120l6ol060 7635.3555 4 2 7.0323 2 3 43 32 37 1 3 . 6 3 9 9 9 75.9705 7 5 5 5 . 1 367 186 3 5 . 16 J 2 44 9 5. 1 2 8 9 a 1 2. 36 99 2045 3 . 2 2 2 7 2062.6860 1513.t2io 106.2967 9 J . 4 520 6 51.23u0 3793.2J6 5 12821.8 59t 0  3 4 3.3 6 79 1280.6885 1 5 3 3 . 75 32  BOD Equiv in KGS J.20. o ! 4 4 11781.2617 4 7 . +1 O b 381.5098 1611.0244 60 0 . 4 4 6 7 3 J 3 3 o-jt 3 0 "'976.2 5 5 0 3 142. 6 7 6 2 231o9686 6 3 2.79cib io 2 5 5 5 113.1355 418. 7 1 J 2 979.6633 1 32j . 250 3 3 J 7 3 . 6 934 91Uot 423 9 . 3 . 3 7 03 844 5 920 54/4.9375 13o«59o6 1 8 5 5. 5 8 3 0 i 104.63J4 t 162. 3 2 4 2 93Oo 6 3 2 3 1 6 3 . 1 9 IJ 6 J4. 96 83 2 2 4 3 o 3667 3 9 7 . V 6 17 2 212.9253 3 972o0 352 3 7 9 4 . 7 7 15 212. 658J 12o6433 1348.1638 4 o 5 o 0 5 II 3 75 4 . 9 0 2 6 2534.3813 6x1.3374 110 . 4 3 23 2 781.63 7 7 1 J 2 5 o 1 5 48 752.1704 52. 8 3 0 4 4 4 . 9 5 46 323.6oll i 885.2234 o 3 7 2 . 4 6 09 169.1628 636.5u20 762.2/37 e  TS Equiv in KGS 5 73.2217 55990.6484 2 25 . 3 2 0 7 1313.132 3 7 6 5 6 . 4 180 3 234.2 573 148 5 3 . - < 8 9 8 46 39.668a 14 9 3 5 . 6 1 7 2 11J2.4341 3 J 98 . t 5 3o 6 1484 337«o78^ i 93v.92 75 4 6 55 o 8 6 3 3 t +bj . 3 7 1 1 15 0 3 2 o 0 5 b 6 4 459.46 88 4 37 . 2 3 9 5 4 1 36 . 0 1 5 6 0  26 S l i d w1 6 6 6 o .9 2 1 4 3 319.6875 5 4 09.4414 2u383.1563 4 5 5 7 . 2 5 94 799 . 1 853 2 962 . 5 6 8 1 1J 9 3 o . 3 4 7 7 1 9 4 8 . 8 -r3 J H) 5 1 6 . 9 6 0 9 28332.1914 18034.71J9 I 0 i 0 . 6 6u4 63 . 0 7 3 1 8783 .425o 2 3 05.2427 17 3+5.234^ 12411 . 0 1 5 6 2993.7559 5 4 1 . 0 382 13621.8438 48 72.0625 3574.702-+ 2 51.07 76 213 . 6 4 7 6 1536 .2053 8959.5547 3U 2 8 5 . 2 3 4 4 303.9493 3)24.9866 3622.718b  SS Equiv in KGS 0 . 7 23 1 71. 1143 0.286 2 2. 3C2 9 9. 7245 4.8 56 2 22.3C1 9 5 . 892 9 "" 16.9699 1.400 2 4 . 6 52 9 0.009 2 0 . 6 82 9 2 . 5 27 4 5.9135 9 . 7 27 8 22.600 7 6 . 695 9 0 . 6 86 5 6.210 2 4 0 . 2 56 9 1. JC4 4 11 .200 7 8.122 3 30.605 3 6.8429 1. 2 0 3 0 4.448 3 1 6 . 4 99 0 2. 926 2 13.3577 36.0485 2 2 . 9 06 1 1.2 63 6 0.076 3 11.1559 2.9279 2 2 . 665 4 1 8 . 6 35 1 4. 495 1 O . 8124 20.453 2 6.188 1 4. 540 3 0.3189 0.2714 1.9537 1 1 . 3 79 6 38.4656 1.021 1 3. 842 1 4.6C13  FIGURE 4.3  FLOW CHART .OF SUBROUTINE  SPILL  86 RELATED SPILL SEQUENCE  Clock = 0 KK = 1  Generate a U n i f o r m R.Vv(RN2)  E s t a b l i s h Parameters f o r S p i l l Q u a n t i t y Gamma V a r i a t e s  V  NSP(KK) = 0?  NO  Determine PRQB. o f T r a n s i t i o n NSP(KK) ->• NSP(KK) + 1 = RPROB(KK)  KES Yes E s t a b l i s h Parameters f o r Unrelated S p i l l I n t e r a r r i v a l Time Gamma V a r i a t e  Set NSP(KK) = 0  C a l l Gamma (Time) (Generates Time Between L a s t S p i l l and Next S p i l l ) Unrelated  C a l l Gamma (Amt.) (Generates t h e ^ £ 8 0 ^ E q u i v a l e n t f o r t h e Amount' of S p i l l i n Thousands o f l b )  Is RN2 > RPROB(KK)? No  E s t a b l i s h Parameters For R e l a t e d S p i l l I n t e r a r r i v a l Time (Negative B i n o m i a l V a r i a t e )  t C a l l NEGBIN (Time) (Generates Time Between L a s t S p i l l and Next R e l a t e d S p i l l )  C a l l Gamma (Amt.)  Convert # Na S0 Into Gallons of Chemical Equiv. f o r the Current Sublocation 2  C l o c k = C l o c k + Time  [t  87  Generate a Uniform R.V. - RN1  I Determine RNl's Interval Loc'n i n the Sublocation Cumulative D i s t r . f o r Major Area KK (This Determines S p i l l s Sublocation)  t Convert lb of Saltcake of S p i l l into Gal's of Chemical T y p i c a l of Sublocation Just Determined  Convert Gals of Chem. into I t s BOD and SS Equivalent kg's.  NSP(KK) + NSP(KK) + 1  Record S p i l l Data According to Major Area  No  Clock > I Time?  I Yes  KK+1 No  KK = 3? Yes  Return to Main  88  d i s t r i b u t e d random number i s l o c a t e d w i t h i n a d i s t r i b u t i o n i n t e r v a l . water usage i s then determined  The  by i n t e r p o l a t i o n between t h e i n t e r v a l end  points.  In s u b r o u t i n e WATER, t h e d a i l y and h o u r l y ^ ^ y . ) a  w a  ter  usage l e v e l s a r e determined.  A l s o t h e h o u r l y f l o w s f o r t h e s i x m i l l streams a r e c a l c u l a t e d - u s i n g t h e proportions presented  The  r e s u l t s of c a l l i n g  i n T a b l e 3.14.  t h e two s u b r o u t i n e s PRODN and WATER f o r each  s i m u l a t e d day a r e r e c o r d e d f o r t h e number o f days s p e c i f i e d . of t h e experiment. r  ,# of hours of experiment ( • :— c  as computed by the model i s i n T a b l e 4.2. for  at the s t a r t  , . . ^ . ,^ 1- 1 ) . A copy of t h i s d a t a A  A complete r e c o r d o f t h i s  data  t h e s p e c i f i e d number of days i s c r e a t e d by the model b e f o r e the a c t u a l  experiment  i s run.  4.1.3  BRINGING IT ALL TOGETHER  Having  c r e a t e d t h e s p i l l p r o d u c t i o n and water usage d a t a f o r t h e s p e c i f i e d  number o f days the model uses t h i s i n f o r m a t i o n , combined w i t h h o u r l y d a t a generated  by s u b r o u t i n e REGUL, t o g e n e r a t e  the m i l l e f f l u e n t  time  trace.  S u b r o u t i n e REGUL i s c a l l e d by t h e main program each hour of s i m u l a t e d It creates a regular effluent losses not c l a s s i f i e d  stream  as s p i l l s  t o account  time.  f o r c h e m i c a l and f i b e r  s i n c e by t h e v e r y n a t u r e o f t h e p u l p i n g  p r o c e s s , a c e r t a i n amount of e f f l u e n t  i s generated  no m a t t e r  how adequate  Fiber Losses  Production Day  6 7 3 9  1) 11. l 3  14 15 IS 17 13 19 2)  21 22 23 24 25 2.1  2f 23 29 3J J1 32 33 34 33 36 j>7 33 39  Ton/Hr  ;  5 J . 32 37o9i 15.40 56. 74 47.80 54. 92 41.31 18.63 46. 78 21oii 4 9.2 ) 43.41 43.39 52.06 46.53 51.99 38.67 53. 08 50.61 54. 38 41.33 49. 23 53.72 46.34 49.54 36.42 54.Oi 44.00 52.46 5 2.49 4 3.6 5 5 6.17 51.01 4 7.96 4 3.04 48.09 21.84 57.46 4 3.49  2  3  Area 1  0. 08 0.03 0.04 0. 03 0.08 0. U3 0. 04 0 o 34 0. od u .08 0.03 0. 03 0. J8 0.04 0. 04 0 . 08 0. 21 0.04 0. 0.8. 0. 13 j . 03 0. 21 0. 04 0.08 0. 34 O . J8 0.25 0. 03 0.03 0. J't 0o 04 0. )8 0.03 u o j3 0.03 O . 13 Jo 34 J. Oo J . 03  0. 04 0. 04 0.04 0. 04  1 .34 1.18 1.32  1 0. 2 9' ' 0. 83 0.67 0. 5 4 0. 33 0. 54 0. 17 .0.25 0.21 0.33 0. 54 0.54 ^0.33_ ~0. 17 0. 1 7 0.1 7 0. 3 8 0. 46 0. 50 0. 1 1 0.29 0. 46 0. 50 0.63 0. 33 0.5 4 0. 50 0. 50 0. 29 j . 17 0. 5 4 54 0. 5 J 0a 3 3 3.53 0. 5 J 3.17 0. 6 7  Water Flows (xlO  (Tons/Hr)  :  0.04 0. 04 0. 04 0.04 0.04 0. 04 0. 04 0 . 04 0. 04 0.04 0 .04 0. J4 J . J4 •J.JJ^_ 0. 04 0.04 0. 04 "0o 04 0.04 0. 04 0. 04 0 . 04 0o 04 Oo 21 0 . J4 Oo 04 03 J4 04 0 ,04 •J. 04 j4 0 . 34 0.21  lo 41 1.44 1.03 1. 32 1 .41 1.03 1.39 i . 45 1_.33 1 . 23 1. 37 1 .41. 1. 03 1. 35 1 .33 1.37 lo 36 1 .30 1.33 1. 44  J-_?A _  Area 2 1. 10 0.97 1.09 1.15 1. 16 1.18 0.85 C. 84 1.16 0. 85 1.14 1.19 1.0 9_  T.ol  1.48 .1 .26 1.14 1 . 38 1. 34  0.17 0.1 5 G.17 0.18 0.1 3 0.19 0.13 0.13 0.18 0.13 0.18 0.19 0.17  6716  1. 13 1.16 0. 85 1. 11 1.10  0.1 8 0.18  1.13  0.1 3 0.18 0.17 0.17 0.19 0.18 0.1 5 0.17 0.19 0.1 7 0.18 u.l 9 0.17 0.18 0.1 iL 0.19 0.16 0.1 5 0.18 0.17  1.12 1.0 7 loll 1.18  6  I . 18 .1.33 lo44 1, 29 1.39 1. 45 29 39  Area 3  0.9 7 1.09 1.18 I. 06 1.14 1.19 1.06 1.14 1.15 1.21 1.04 0.9 3 .1.13 1.10  0.1 7  o-LL  6  Gal/Hr)  Area 4 0.05 0.05 0.C5 0.06 . 0 o 06 0.06 0.04 0.04 0. 06 0.04 0.06 0 .06 0.-35 0.05 0.06 0.06 0.04 0.05 0.05 0 .06 0.05 0.05 0.05 0.06 _0_.05_ 0.05 0.06 0.05 0.06 0 .06 0.05 0.06 0.06 0. 06 0.05 0o 05 0.06 0.05  Area 5 0.04 0.04 0.04 0.04 0.04 0.04 0.03 0.0 3 0.04 0.03 0. 04 0.05 0.04 0.04 0.04 0.04 0.03 0.0 4 0.04 0.04 0.04 0. 04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.04 0. 04 0.04 0.05 0.04 0.04 0.04 0.04  Area 6 0.07 0.07 0.07 0.08 0.08 0.08 0.06 0.06 0. 08 0.06 0.08 0.08 J3.J37. 0.07 0.08 0.08 0.06 0.08 * .0.07 0.08 0.08 0.07 0.08 0.08 0.08 0.07 0.07 0.08 0.07 0.08 0.08 0.07 0.08 0.08 0.08 0.07 0.06 . 0.08 ° 0.07 M  90  the  process control.  To account for t h i s the regular effluent flows for  the  s i x major effluent streams were s t a t i s t i c a l l y modelled by assuming  a normal d i s t r i b u t i o n with empirically determined means and standard deviations f o r each of the streams. section 3.1.4).  (These parameters can be found i n  Sampling s t o c h a s t i c a l l y each hour from these normal  d i s t r i b u t i o n s a reasonable representation of the m i l l ' s regular effluent concentration i s generated.  To determine actual effluent loads the sub-  routine m u l t i p l i e s each of the s i x stream variates by t h e i r corresponding water flows f o r that hour and returns the BOD and SS l e v e l s i n pounds for each of the streams (see Figure 4.1). the  To get a true m i l l representation,  s p i l l s and regular effluent are superimposed.  The following steps are executed each simulated hour by the main program to generate the m i l l ' s f i n a l e f f l u e n t . (see also Figure  4.2)  0)  T = 0  1)  Read day number, hourly production and hourly water flow f o r six streams for current day  2)  Determine water flows (MUSG/hr) for 3 main o u t f a l l s for current day (see Figure 4.1)  3)  Generate this hours regular effluent l e v e l s ( CLOCK = CLOCK  lbs/hr)  +1  T = T +1 4)  Is there a s p i l l t h i s hour i n any of the 3 major areas? If No go to 7 If YES continue  91  5)  Add  BOD  and  effluent  SS  l e v e l s of s p i l l  to the c o r r e s p o n d i n g  regular  stream  6)  Read time and  amount of next s p i l l  7)  Record t h i s hours e f f l u e n t a c t i v i t y  i n a r e a which j u s t had to be  totalled  on a  spill  daily  basis 8)  Add  BOD  and  outfalls, 9)  SS f o r the streams, which make up  the  entration units and  Record BOD  11)  I f CLOCK = s p e c i f i e d number of hours f o r c u r r e n t  SS f o r each main  otherwise  continue  12)  I f T = 24  (has  13)  Go to 3  14)  Record BOD  and  c u r r e n t day  Go  to  outfall  ended) go  experiment  to 14,otherwise  SS as l b s / t o n a l o n g w i t h  water usage f o r c u r r e n t  16)  i n t o conc-  mg/1  10)  T = 0  mill  together  Convert l b s / h r of e f f l u e n t f o r the t h r e e o u t f a l l s  15)  three  production,  stop  continue  and  total  day  1.  4.1.4 VALIDATION OF PULP MILL MODEL The  v a l i d a t i o n of a s i m u l a t i o n model i s d e f i n i t i e l y  p h i l o s o p h i c a l l y represents cannot a b s o l u t e l y be  the a c i d t e s t  solved.  This  a "pandora's box".  f o r any model but  i s a consequence of the  in reality l a c k of a  I  92  technique or groups of techniques  which can e s t a b l i s h beyond  doubt that the model i s a true representation of r e a l i t y .  reasonable  There i s also  the problem of r e a l i t y i t s e l f since once data i s gathered and i n t e r pretated we have taken the " r e a l i t y " out of i t s natural environment and imposed our own conceptual i n t e r p r e t a t i o n .  However i n approaching t h i s seemingly impossible task the o r i g i n a l purpose of the model must be kept i n mind. of a system can give a reasonable  Often a major s i m p l i f i c a t i o n  representation of the system's behaviour  on the same scale as the model's structure.  For example to model a truck  carrying produce from warehouse A to warehouse B, we don't require information on engine behaviour or axle molecular  structure, as long as  this information i s not needed to f u l f i l l the model's purpose.  For example  a broken axle can usually be modelled as a stochastic event quite accurately rather than modelling  the molecular  behaviour r e s u l t i n g i n an axle f r a c t u r e .  This example i s rather extreme but the major point i s a l l too often forgotten. you need!  You can't get more than you put i n and don't put i n more than y  Before v a l i d a t i n g the o v e r a l l simulation tests were made on the various d i s t r i b u t i o n s used i n the model to check that they were functioning as designed.  Goodness of f i t tests were run for the gamma d i s t r i b u t i o n to insure that the routine used was indeed generating gamma variates with the given  93  parameters. Na2S0i  +  S u b r o u t i n e GAMMA was  amounts and  the same parameters are  used  t o g e n e r a t e 250 v a r i a t e s  for s p i l l  compared t o t h e t h e o r e t i c a l gamma d i s t r i b u t i o n w i t h as those used  to g e n e r a t e the v a r i a t e s .  The  results  summarized below;  Area  R  stat.  Recovery  .414  .024  .086  .039  Recaust  .515  .045  .086  .028  .064  .086  .034  Pulping  1.19  For  a l l t h r e e a r e a s the D s t a t i s t i c  are  the same.  S i m i l a r l y 250  D  kS(.05)  A  <kS(.05) i m p l y i n g t h a t  the  distributions  time i n t e r v a l s between u n r e l a t e d s p i l l s were g e n e r a t e d f o r  the t h r e e a r e a s u s i n g s u b r o u t i n e GAMMA and were r u n . These r e s u l t s a r e l i s t e d  Area  R  goodness o f f i t comparison  below:  A  kS(.05)  D  stat.  Recovery  .511  .0019  .086  .080  Recaust  .807  .0017  .086  .061  Pulping  1.101  .001  .086  .073  A g a i n the d i s t r i b t u i o n s a r e the same a t the .05 s i g n i f i c a n c e s u b r o u t i n e GAMMA t h e r e f o r e i s c r e a t i n g  the expected v a r i a t e s  level.  The  adequately.  94  N e x t , s u b r o u t i n e s PROD and WATER were checked. the  I t would be e x p e c t e d t h a t  r e a l d a t a and t h e d a t a c r e a t e d ' by t h e model would c o r r e s p o n d f o r  p r o d u c t i o n and water s i n c e t h e d i s t r i b u t i o n s used were e m p i r i c a l l y based. However a Kolmogorov - Smirnov two sample goodness o f f i t t e s t was done for  b o t h p r o d u c t i o n and w a t e r i n o r d e r t o r e i n f o r c e c o n f i d e n c e i n t h e model  technique.  The r e s u l t s a r e summarized  Distribution  below:  kS(.05)  D(N,M)  Production  .1923  .051  Water  .1923  .073  N = 100 M = 100  To t e s t t h e complete model u s i n g t h e t e c h n i q u e o f h i s t o r i c a l  verification^  r a t h e r t h a n g e n e r a t e a s p i l l sequence and d a i l y - o p e r a t i n g l e v e l s o f p r o d u c t i o n and w a t e r f l o w s , r e a l m i l l d a t a was used as i n p u t .  The e f f l u e n t  I  data a v a i l a b l e f o r the r e a l w o r l d s i t u a t i o n r e p r e s e n t e d averages over a p e r i o d o f days.  By f o r c i n g t h e model t o average over t h e same t i m e span  as t h e r e a l d a t a , a c o m p a r i s o n o f t h e r e s u l t s was p o s s i b l e .  The i n p u t s t o the model were: 1.  E m p i r i c a l s p i l l sequences f o r t h e t h r e e major a r e a , c o n v e r t e d to  c h e m i c a l and BOD and SS e q u i v a l e n t s i n t h e same manner as  described  earlier.  H i s t o r i c a l v a l i d a t i o n i n v o l v e s comparing t h e model and t h e r e a l w o r l d f o r t h e same i n p u t s .  95  2.  D a i l y water usage f o r the s i x m i l l  streams and  the c o r r e s p o n d i n g  p r o d u c t i o n , a l l taken from m i l l o p e r a t i n g summaries, f o r the same time span as the  spills.  The r e g u l a r e f f l u e n t g e n e r a t i o n was d a t a f o r t h i s time span was  For  each s i m u l a t e d day  averaged data.  untouched  s i n c e no c o r r e s p o n d i n g r e a l  available.  the l b s / t o n of BOD  and  SS were determined  and  over a c e r t a i n number of days to c o r r e s p o n d to the " r e a l  world"  In the m i l l s i t u a t i o n the samples a n a l y z e d r e p r e s e n t e d m i x t u r e s of  samples taken over 4 t o 7 days. F i g u r e 4.4  and 4.5.  and  SS a r e p l o t t e d i n  These p l o t s i n d i c a t e a r e a s o n a b l e congruence  between model and m i l l d a t a . r e a l and s i m u l a t e d r e s u l t s . coincide.  The r e s u l t s f o r BOD  of b e h a v i o u r  Both p l o t s have numerous i n t e r s e c t i o n s of the A l s o the n o t i c a b l e or " u n u s u a l " peaks g e n e r a l l y  There i s some disagreement  i n magnitude f o r the f i r s t  h i g h peak  (data p o i n t a t time 4 ) ; however, l o o k i n g a t the r e a l d a t a , t h i s time includes a m i l l  s t a r t up f o r which a c o n s i d e r a b l e amount of the s p i l l  c o u l d not be d e c i p h e r e d from the c o n d u c t i v i t y c h a r t s .  A l s o the model  not d e s i g n e d w i t h the a b i l i t y  up e f f l u e n t  Kolmogorov-Smirnov two and BOD  to g e n e r a t e a m i l l s t a r t  interval data  time  sample goodness o f f i t t e s t s were run f o r b o t h  f o r these r u n s .  The r e s u l t s a r e summarized below:  D(N,M)  kS(.05)  SS  .327  .414  BOD  .207  .414  N = 22,  was  M = 22  SS  trace.  REAL SIMULATION  8  to  IZ  IH-  1$  18  ZQ  2Z  TIME SS VALIDATION FOR PULPMILL MODEL. REAL EFFLUENT AND SIMULATION GENERATED EFFLUENT WITH IDENTICAL  I N P U T  97  The  final vefification  t e s t f o r the p u l p m i l l model c o n s i s t e d o f a  K-S  goodness of f i t between r e a l w o r l d and model e f f l u e n t d a t a u s i n g model generated s p i l l and SS, days.  sequences.  The model was  run f o r 100 days and the  expressed as pounds per t o n , were averaged The goodness o f f i t r e s u l t s a r e as  D(N,M)  T h e r e f o r e we  f o r every 5 out o f 7  follows:  KS(.05)  SS  .471  .482  BOD  .124  .482  cannot r e j e c t  BOD  N = 17, M =  the h y p o t h e s i s t h a t the two  15  distributions  are  different.  4.2 4.2.1  WASTE TREATMENT MODEL The General S t r u c t u r e  In Chapter  III  the waste treatment model's m a t h e m a t i c a l  d i s c u s s e d and g e n e r a l i z e d s o l u t i o n s f o r BOD effluent  development  was  e f f l u e n t from the l a g o o n and  from the c l a r i f i e r were d e r i v e d (see eqns 3.7  e q u a t i o n s were programmed i n FORTRAN and a l i s t i n g  and 3.10).  SS  These  can be found i n Appendix I V .  A l t h o u g h the model was  d e s i g n e d t o use the p u l p model's output as i n p u t , i t i s  c o m p l e t e l y independent  o f the p u l p m i l l model s t r u c t u r e and  model the systems b e h a v i o u r f o r any g i v e n i n f l u e n t . c e r t a i n system parameters  The  can be used  program  (such as the lagoon a r e a , depth, and  depth) as i n p u t b e f o r e an experiment  can be r u n .  appendix w i t h t y p i c a l v a l u e s and u n i t s i n d i c a t e d .  requires  clarifier  These a r e l i s t e d The model was  f u n c t i o n as an a i d t o m i l l management i n d e s i g n i n g a  to  i n the  designed to  clarifier-lagoon  98  treatment system. easily.  The  C o n s e q u e n t l y , e s s e n t i a l d e s i g n parameters can be  program a l s o determines c a p i t a l c o s t s and  c o s t s f o r both c l a r i f i e r and  lagoon  i n each  yearly  changed  operating  run.  A v a r i a t i o n of the program was. w r i t t e n which p e r m i t t e d  artificially  hourly  to 24 h o u r s ) .  loads  to the system f o r any  g i v e n time span (up  increased The  i n c r e a s e d l o a d i s a m u l t i p l i c a t i v e f a c t o r times the o r i g i n a l  load  considered  example,  as the normal o p e r a t i n g  influent  pulp m i l l model c r e a t e s a t y p i c a l BOD basis.  SS  effluent  T h i s i s then g i v e n to the treatment model as  from the program, the user time span and user  and  time t r a c e .  can  For  being the  time s e r i e s on an influent.  On  hourly  prompting  specify a multiplying factor, i t s active  the h o u r , t o s t a r t  the i n c r e a s e d l o a d .  For example i f the  g i v e s a f a c t o r of 10 f o r a time span of 5 hours s t a r t i n g a t hour  the program w i l l m u l t i p l y the BOD  and  SS  the hours from 100  through to 105  and  use  hours of s i m u l a t e d  operation.  influent these  concentrations  as i n f l u e n t  by  data f o r  100  10 f o r those  I t then r e t u r n s to the o r i g i n a l time t r a c e  f o r the remainder of the run.  T h i s p r o c e d u r e g i v e s the user  versatility  t h e systems r e s p o n s e to v a r i o u s degrees of  to experiment w i t h  shock l o a d i n g .  It also provides  systems r e c o v e r y published  i n 1974  The model p e r m i t s 4 different  times.  considerable  some i n t e r e s t i n g i n f o r m a t i o n on  T h i s f e a t u r e was  prompted by a  NCASI  the  study  (Gove, 1974).  the user  influent  to combine the  three m i l l o u t f a l l  combinations to the treatment model.  streams i n t o  T h i s was  duced as a consequence of the d i f f e r e n t arrangements e x i s t i n g at  intro-  various  99  mills.  Some m i l l s combine t h e g e n e r a l and a c i d o u t f a l l s between t h e c l a r i f i e r  and t h e l a g o o n , o t h e r s o n l y feed t h e g e n e r a l and machine room streams the  treatment system and c o m p l e t e l y bypass the system w i t h t h e a c i d  The c o m b i n a t i o n d e s i r e d IV are  listing  into  stream.  i s s p e c i f i e d a t t h e b e g i n n i n g of a r u n (see appendix;  and v a r i a b l e d e f i n i t i o n ) .  shown i n F i g u r e 4.6.  Schematics o f t h e 4 p o s s i b l e combinations  The d i f f e r e n t  combinations r e s u l t  in' v a r i o u s  h y d r a u l i c l o a d i n g s t o t h e system and t h e r e f o r e p r o v i d e an o p p o r t u n i t y t o experiment w i t h a l t e r n a t e f a c i l i t i e s  4.2.2  and o b s e r v e t h e i r e f f l u e n t  The Model  The waste' treatment model i s a m a t h e m a t i c a l model e v a l u a t i n g developed i n Chapter 3, f o r t = 1 hour.  T h i s assumes t h a t  o p e r a t e s i n a steady s t a t e over each hour. concentration are constant). of  outcomes.  the e q u a t i o n s  t h e system  (The h y d r a u l i c l o a d and i n f l u e n t  A t the end o f t h e hour, t h e f i n a l  each tank i n t h e s e r i e s model i s made t h e i n i t i a l  concentration  concentration f o r  the  next hour.  are  determined, system parameters such as d e t e n t i o n time a r e a l t e r e d ( i f  the  hour b e g i n s a new day) as r e q u i r e d and t h e system i s r u n a g a i n f o r  a n o t h e r hour. At  The next hour's h y d r a u l i c l o a d and i n f l u e n t  concentration  The p r o c e s s i s r e p e a t e d f o r t h e s p e c i f i e d number of h o u r s .  t h e end o f each hour t h e model r e c o r d s t h e f o l l o w i n g : 1.  Influent  SS c o n c e n t r a t i o n i n t o c l a r i f i e r  2.  SS c o n c e n t r a t i o n o f stream which bypasses c l a r i f i e r  3.  SS c o n c e n t r a t i o n o f c l a r i f i e r  4.  BOD c o n c e n t r a t i o n i n t o c l a r i f i e r  5.  BOD c o n c e n t r a t i o n of stream which bypasses c l a r i f i e r  6.  BOD c o n c e n t r a t i o n of lagoon e f f l u e n t  effluent  (mg/1) (mg/1)  (mg/1)  (mg/1)  (mg/1).  (mg/1)  ACID  "ACID  GENERAL  GENERAL  ROOM  LAGOON  ROOM COMBINATION 1  ACID  COMBINATION 2  ACID  GENERAL  ROOM  COMBINATION 3 FIGURE 4.6  ROOM  LAGOON  COMBINATION 4  FOUR WASTEWATER TREATMENT PLANT CONFIGURATIONS POSSIBLE IN WASTE TREATMENT MODEL  o o  101  At the end of each 24 hour p e r i o d the model r e c o r d s the t o t a l amounts of SS and per  BOD  which e n t e r e d and  t o n of m i l l p r o d u c t i o n .  left  the treatment  system expressed  A l s o lagoon generated  SS  as pounds  i s g i v e n as the  mg/1  average f o r the day as w e l l as l b s / t o n .  The model i s composed of t h r e e p a r t s , the MAIN program, s u b r o u t i n e TREAT and  s u b r o u t i n e COST.  S u b r o u t i n e TREAT i s c a l l e d  every  MAIN w h i l e s u b r o u t i n e COST i s c a l l e d once a t the end f l o w c h a r t of the model can be  in running  found  i n Figure  the model, the user has  control  s i m u l a t e d hour by  of the run.  A  general  4.7.  over c e r t a i n d e s i g n  parameters.  : include:  To  a.  Steady s t a t e time  interval for c l a r i f i e r  b.  The  c.  Clarifier  d e t e n t i o n time  d.  Estimated  average d a i l y f l o w i n t o  e.  Clarifier  depth ( f t )  f.  Treatment system l a y o u t (1 to  8-  B i o l o g i c a l r e a c t i o n r a t e i n lagoon  h.  Lagoon water temperature  i.  Lagoon s u r f a c e a r e a  3•  Lagoon depth ( f t ) .  r a t e of s e t t l i n g as a f i r s t o r d e r  ( i n sees) and  linear reaction  lagoon (m  ( i n hour  sec  )  (hours) c l a r i f i e r (MUSGD)  4) (hr  ^)  °C  (acres)  c a l c u l a t e the p r e c i s e mass of e f f l u e n t which i s d i s c h a r g e d over a  i n t e r v a l TI the f o l l o w i n g e x p r e s s i o n must be  evaluated;  time  FIGURE 4.7  FLOW CHART OF WASTE TREATMENT MODEL 102  T=0 DD=0  Reads I n f l u e n t BOD SS C o n c e n t r a t i o n s F o r 3 Input Streams - U n i t #9  Set D e s i g n Parameters  t Determine Cone, of System Inputs As R e s u l t o f System Layout  C r i t i c a l Constants etc. Calculated  Is T J < T ^ T J + Step? Yes  Program Requests I n f o , on A r t i f i c i a l Loads, T J , Step, Factor Cycle  M u l t i p l y System Input Cone, by F a c t o r F o r Step I n t e r v a l  Reads Water Flow f o r 3 O u t f a l l s and Days Prod'n ( U n i t #8)  C a l l Treatment Which Returns E f f l u e n t Cone's.  I s T=24? Yes DD=0  Determines Water Flows f o r D e s i r e d Treatment Layout  C a l c u l a t e I n f l u e n t and Effluent Statistics for 24 Hour P e r i o d s and Run Averages  J  t  C a l c u l a t e s 24 h r Parameters f o r C l a r i f i e r and Lagoon-Detention Time, Flows, e t c .  C a l c u l a t e SS Generated i n Lagoon on D a i l y B a s i s Yes  No  IS DD=24?  i s T=Run Time?  T=T+1 DD=D0+1  Yes Calculate Efficiencies and C a l l C o s t  End  No  103  TI  Maes o f p o l l u t a n t p a s t any p o i n t  Q*C(t)dt  o v e r t h e i n t e r v a l o f time 0 t o T I  i f we assume Q i s c o n s t a n t  TI Q \ C(t)dt  f o r t h e time 0 t o T I , where  C ( t ) = t h e d i s t r i b u t i o n o f p o l l u t a n t c o n c e n t r a t i o n over Q  = h y d r a u l i c f l o w a t p o i n t of i n t e r e s t  Due t o t h e c l a r i f i e r ' s changes i n e f f l u e n t  i n equivalent  units  s h o r t d e t e n t i o n time i t may e x p e r i e n c e  large  c o n c e n t r a t i o n over t h e p e r i o d o f one hour.  t h i s e x p r e s s i o n was e v a l u a t e d C(t) equal  time  t o equations  f o r t h e c l a r i f i e r SS e f f l u e n t .  Consequently, By s e t t i n g  3.7 we g e t .TI 1-e  Mass o f SS(kgs) =  -IN  -at + e  -at Tc  t \L _ IN(t.) C  C (o)  + C  2  ^ T  Q  -aTI T |. 1+e c  -aTI T ' + C (0)Tc 2  a  1-e  4C|0)T^ a"  = 1 + k * T  TI = 3600  For  the lagoon  C  c  -aTI Tc -C-£0)TI e  2  u  Eqn.  4.1  c  sees.  i t was assumed the 5 day d e t e n t i o n time would b u f f e r system  surges r e s u l t i n g i n v e r y hour.  c  -aTI T e - l  Where Q i n i n l i t r e s / s e c a  1  T (l+k Tc)J  0)  s m a l l BOD e f f l u e n t  The h o u r l y mass o f BOD e f f l u e n t  concentration  changes w i t h i n one  i s t h e r e f o r e the product  of BOD  c o n c e n t r a t i o n a t time t = 1 h r times h y d r a u l i c f l o w f o r t h a t hour.  104  At  the s t a r t of a model experiment the tank volumes f o r the c l a r i f i e r  are  determined.  The model determines a new  parameter e v e r y 24 h o u r s .  T  £  =  The l i n e a r  REST  model-  one tank d e t e n t i o n time  This i s :  =  clarifier  tank's d e t e n t i o n  time  =  Volume o f tank 1 (or tank 2) i n l i t r e s f l o w i n t o tank i n l i t r e s / s e c  =  r e s i d e n c e time i n s e e s .  "reaction r a t e " s e t t l i n g constant i s .104 clarifier  CK  depth i n cm  (  s  e  e  c h a  Pter III)  S i m i l a r l y f o r t h e l a g o o n t h e model d e t e r m i n e s the d e t e n t i o n times f o r each of  the t h r e e e q u a l volume t a n k s . T^  =  TT  =  lagoon tanks d e t e n t i o n  time  Volume o f a tank i n l i t r e s f l o w i n t o tank i n l i t r e s / h = and then the BOD  time i n hours  removal r a t e c o n s t a n t KK a c c o r d i n g to the  KK =[(1.256) * ( 1 . 0 3 2 ) ]  relation  T E M P / 2 4  d i s c u s s e d i n Chapter I I I .  4.2.3  Subroutine TREAT  S u b r o u t i n e TREAT r e a d s the c l a r i f i e r  and lagoon i n f l u e n t c o n c e n t r a t i o n s  each hour and e v a l u a t e s t h e system's e f f l u e n t c o n c e n t r a t i o n s .  The  final  105  c o n c e n t r a t i o n s f o r each tank a r e made t h e i n i t i a l  concentrations f o r the  next hour. The p r e s e n t s t r u c t u r e o f t h e s u b r o u t i n e uses the g e n e r a l i z e d model developed in  i n s e c t i o n 3.2.3 f o r the l a g o o n and the model developed  s e c t i o n 3.2.1 f o r t h e c l a r i f i e r .  Although  the p r i m a r y purpose  removed as SS.  o f the c l a r i f i e r  To accommodate t h i s ,  which passes through t h e c l a r i f i e r  i s t o remove SS; some BOD i s  t h e model assumes t h a t 10% o f the BOD  s e t t l e s o u t and i s not, passed on t o t h e  lagoon.  4.2.4  The COST Subroutine-  U s i n g t h e r e l a t i o n s h i p s developed  i n s e c t i o n 3.3 t h e s u b r o u t i n e COST e v a l u a t e s  the f o u r c o s t r e l a t i o n s h i p s a t t h e end of t h e s i m u l a t i o n experiment. are  r e c o r d e d and comprise  the f i n a l  statements  These  i n t h e output of t h e waste  treatment model.  4.2.5  Waste Treatment Model V a l i d a t i o n  A v a l i d a t i o n o f t h e complete lack of a v a i l a b l e data.  waste treatment model was n o t p o s s i b l e due t o  The d a t a which was used f o r h i s t o r i c a l  validation  was s u p p l i e d by Weyerhaeuser, Kamloops f o r t h e i r o p e r a t i o n a l a e r o b i c stabilization  lagoon.  The two months of d a t a o b t a i n e d c o n s i s t e d o f d a i l y  BOD c o n c e n t r a t i o n , e x p r e s s e d i n mg/1, a t t h e e n t r a n c e t o t h e s e d i m e n t a t i o n ponds and t h e e x i t o f t h e l a g o o n , and t h e d a i l y h y d r a u l i c l o a d t o t h e l a g o o n i n MUSGD.  The s e d i m e n t a t i o n ponds a r e the f i n a l  stage i n SS removal  e n t e r i n g t h e l a g o o n and have a d e t e n t i o n time o f a few h o u r s .  before  The i n f l u e n t  c o n c e n t r a t i o n t o the l a g o o n was assumed t o be e q u a l t o t h e s e d i m e n t a t i o n  106  ponds i n f l u e n t .  Using  t h i s data  i t was p o s s i b l e t o v a l i d a t e t h a lagoon  s e c t i o n of t h e model.  R e f e r r i n g t o F i g u r e 3.5, by making Ql = 0 Q2 = lagoon h y d r a u l i c l o a d (1) Z  = influent  the lagoon equation  BOD c o n c e n t r a t i o n  (mg/1)  f o r m u l a t i o n , as expressed  3.10.  Lagoon area  i n equation  3.8, can be o b t a i n e d  i s 74 a c r e s and i t ' s depth i s 15 f t .  temperature was a p p r o x i m a t e l y  from  Input  40°C and t h e e f f l u e n t 30°C, t h e r e f o r e t h e  average temperature o f 35°C was used.  S i n c e t h e d a t a was on a d a i l y b a s i s t h e model c o u l d be r u n e i t h e r on an h o u r l y b a s i s ( t = 1 hour) u s i n g t h e same i n p u t c o n c e n t r a t i o n f o r each o f t h e 24 hours,  o r on a d a i l y b a s i s , u s i n g each i n p u t c o n c e n t r a t i o n and  h y d r a u l i c f l o w o n l y once and r u n n i n g  t h e model f o r t = 24 hours.  In F i g u r e 4.8 a r e p l o t s o f a) r e c o r d e d b)  e f f l u e n t d a t a f o r the a c t u a l  t h e s i m u l a t i o n r u n on an h o u r l y b a s i s  lagoon,  ( t h e p o i n t p l o t t e d i s the concen-  t r a t i o n a t hour 24 o f each day) and c ) the s i m u l a t i o n r u n on a d a i l y b a s i s . S i x t y data p o i n t s a r e p l o t t e d . at i n i t i a l  As seen from the f i g u r e the model,  c o n c e n t r a t i o n s o f zero i n a l l t h r e e t a n k s ,  8 days t o r e a c h r e a s o n a b l e  operating l e v e l s .  p l o t s appear t o g i v e a r e s o n a b l e  took  starting  approximately  Both the t = 1 and t = 24  f i t to the data.  The model f o l l o w i n g  O  if-  3  IZ.  lb  20  2<+  2B  3Z  3<>  Vo  <f<f  </g  56  60  fctf-  Day FIGURE 4.8 LAGOON VALIDATION SHOWING REAL DATA EFFLUENT AND SIMULATION GENERATED EFFLUENT (USING SAME INFLUENT) FOR STEADY STATE OPERATION TIME, t = 1 hr and t = 24 h r  108  the sudden drop i n c o n c e n t r a t i o n f o r days 50  to 56 comes as a consequence  of s i x low f l o w and  zero p u l p p r o d u c t i o n days a t the m i l l .  day  MUSG/day (normal  53 f e l l  to 16.2  There a r e c e r t a i n i m p l i c a t i o n s t = 1 hour.  As  seen i n eqn.  i s approximately  The  Iterating  the model each  hour, o n l y a v e r y s m a l l p o r t i o n of the e x p o n e n t i a l decay curve A t y p i c a l negative exponential plot  where f = e  -ct  and  c =  l o o k s as f o l l o w s :  constant  t = t ime  For the lagoon model a t y p i c a l v a l u e of C would  c = "  T  =  1+k  L  T,TT,  T  =  L  .025  =  =  1+. 0169*40. .  +  40-  .0169  .0419  Therefore f o r  i u  t = 1 hour  P -.0419*1 =f = e  .96  while for  . .  t = 24 hour 0  ,  f = e  state for  t h e r e a r e a c o n s i d e r a b l e number of  e x p o n e n t i a l terms w i t h time i n t h e i r exponent.  used.  on  60 MUSG/day).  i n u s i n g the model i n a steady  3.8,  flows  -.0419*24 =  .37  be:  i s actually  109  Looking  at equation  n i f i c a n t while fact  3.8  f o r t = 1 hour the f i r s t  concentrations  experience  concentration  l a r g e r than  (t) value the  c o n c e n t r a t i o n due  could  influent  In the  actually  i s high.  to a sudden  increase  c o n c e n t r a t i o n a c t u a l l y d i d occur when the model was  using a r t i f i c i a l still  the C  a drop from i t s p r e v i o u s v a l u e a l t h o u g h  the i n f l u e n t  and  i s considerably  of the t h r e e . t a n k s ,  ( T h i s p r e d i c t e d drop i n the e f f l u e n t in  insig-  the second term i s v e r y much the dominating element.  i f the i n f l u e n t BOD  initial  term becomes q u i t e  shock l o a d s .  reflected  intuitive result  The model r e c o v e r e d  the time d e l a y e d  run  w i t h i n 3 hours however  r e s p o n s e of the system). . T h i s  comes from the steady  counter  s t a t e assumptions made i n the model  development.  For  t = 24 hours the f i r s t  term becomes a much more s i g n i f i c a n t  the impact of the second term i s reduced by infinity,  the output  c o n c e n t r a t i o n approaches a lower  , . \~i / \ limC (t)y  Using  about 60%.  co  t y p i c a l values,  •  As  limit.  CINBOD cr 5  the time u n t i l  C_. (t) = . 99*CINBOD 0  or - 3 —  be -  t -  40 3-49  while  t approaches  B3  would  term  x  / r 4.6  - 123^|}ours - 5 days (ie.  .99  = 1-e  • - TT  In.01  = - a -  t  J. La  or the f u l l lagoon  detention  would not g i v e a v e r y  time.  or t  = —  TT  *  (-In.01)  (X  T h i s i s an u n r e a l i s t i c extreme  dynamic r e p r e s e n t a t i o n of the l a g o o n s  and  operation.  110  K-S goodness  of f i t t e s t s were done f o r both t h e t = 1 hour and t = 24 hour  e f f l u e n t data a g a i n s t the a c t u a l data.  The r e s u l t s a r e seen below:  Time  D(N,M)  t = 1  .334  .268  .321  t = 24  .251  .268  .321  KS(.05)  KS(.Ol)  N = it of r e a l world o b s e r v a t i o n s = 49 M = // of s i m u l a t e d o b s e r v a t i o n s  = 53  The n u l l h y p o t h e s i s t h a t t h e t = 24 r u n and t h e r e a l d a t a a r e e q u i v a l e n t a t t h e .05 s i g n i f i c a n c e l e v e l cannot be r e j e c t e d . hour r u n t h e n u l l h y p o t h e s i s i s r e j e c t e d .  However, f o r t h e t = 1  This implies that  time i n t e r v a l between t = 1 and t = 24 which r e p r e s e n t s acceptibility  f o r u s i n g t h e steady s t a t e assumption  experiments were r u n u s i n g t h e same l a g o o n i n f l u e n t i n t e r v a l s and temperatures and K-S goodness results.  there i s a  a threshold of  i n t h e model. Some for various  time  of f i t t e s t s performed on t h e  These a r e summarized i n T a b l e 4.3  A p l o t o f time i n t e r v a l v e r s u s temperature c a n be found i n F i g u r e 4.9. There i s a t h r e s h o l d boundary which  between a c c e p t a b i l i t y and non a c c e p t a b i l i t y  i s a f u n c t i o n o f the time i n t e r v a l and temperature.  Beak-Environment  Canada (1973) s t a t e t h a t t h e r e a c t i o n r a t e r e a c h e s a maximum a t about and f a l l s o f f f o r h i g h e r temperatures. i n F i g u r e 4.9.  37°C  The i m p l i c a t i o n s of t h i s a r e seen  The d o t t e d l i n e r e p r e s e n t s a s y m m e t r i c a l drop i n t h e  Ill  Ol 3 5  :  36  :  3?  3 8  3*?  • • 4 o  Lagoon Temperature °C  FIGURE  4.9  PLOT SHOWING REGIONS OF ACCEPTABILITY AS DETERMINED BY K-S GOODNESS OF FIT TEST FOR SIMULATION GENERATED EFFLUENT AND REAL DATA EFFLUENT USING DIFFERENT STEADY STATE TIME INTERVAL AND TEMPERATURE COMBINATIONS  112  TABLE 4.3 SUMMARY OF k-s TESTS FOR SIMULATION GENERATED AND REAL DATA EFFLUENT FOR DIFFERENT STEADY STATE TIME INTERVAL AND TEMPERATURE COMBINATIONS.  Temp °C  Time Interval  D(N,M)  KS(.05)  Accepted  36  12  .280  .261  No  37 37 37 37  1 4 8 12  .335 .335 .298 .244  .261 .261 .261 .261  No No No Yes  38 38 38  1 4 8  .335 .317 .244  .261 .261 .261  No No Yes  39  4  .244  .261  Yes  40  1  .245  .261  Yes  35 35 35 35  1 8 12 24  .334 .314 .316 .251  .261 .261 . .261 .261  No No No Yes  r e a c t i o n r a t e w i t h i n c r e a s i n g temperature  beyond  37°C.  The minimum time i n t e r v a l which i s a c c e p t e d by the K-S t e s t w i t h a lagoon o p e r a t i n g temperature  i s t = 12 hours  o f 37°C.  D e s p i t e the r e j e c t i o n o f the n u l l h y p o t h e s i s f o r t = 1 hour, i t was d e c i d e d t o proceed 1.  as o r i g i n a l l y  The K-S t e s t  intended.  The reasons  f o r doing so a r e :  i s n o t an a b s o l u t e t e s t and the p l o t s i n F i g u r e 4.8  i n d i c a t e t h a t the t = 1 hour model g i v e s a r e a s o n a b l e a t i o n of r e a l i t y .  represent-  113  The  intent  o f the model i s t o t r y and o b s e r v e  a s p e c t s of the treatment if  system's b e h a v i o u r .  the model were i t e r a t e d every 12 or 24  The  t = 1 f i t i s bad p r i m a r i l y  low p o i n t s i n the day = 24  as i t i s now  drop  T h i s would be l o s t  hours.  because i t f a i l s  t o day =? 52  region.  g r a d i e n t along the lagoon were accounted t = 1 p l o t may  the more dynamic  to f i t r e a l d a t a I f the  temperature  f o r i n the model, the  s u f f i c i e n t l y to f i t the r e a l d a t a .  structured  The  can not i n c o r p o r a t e a temperature  model  gradient  relationship. Some BOD  will  s e t t l e out i n the s e d i m e n t a t i o n ponds i n the " r e a l  w o r l d " s i t u a t i o n w h i l e the model does n o t take t h i s i n t o This w i l l  account.  r e s u l t i n the model e f f l u e n t b e i n g somewhat h i g h e r i n  concentration.  F o r the c l a r i f i e r model v a l i d a t i o n d a t a was a c q u i r e d were SS r e a d i n g s on composite  not a v a i l a b l e .  The o n l y d a t a  samples of 5 days of o p e r a t i o n .  In  o r d e r t o perform a r e a s o n a b l e v a l i d a t i o n , data would be needed on an h o u r l y b a s i s due  to the c l a r i f i e r s  s h o r t d e t e n t i o n time.  The  c l a r i f i e r model does  not s u f f e r from the e x p o n e n t i a l cut o f f e x p e r i e n c e d w i t h the lagoon model for  the t = 1 s t e a d y s t a t e a p p r o x i m a t i o n .  _  1 +  C  k T T c  c  c  1  +  =  =  2 2 4753.5  .104 15.*12*2.54 4753.5 =  4.52 x  *  4753.5  10~  4  For the c l a r i f i e r  the c o n s t a n t  114  T h e r e f o r e f o r t = 1 hour = 3600 sees -4.52 f = e = e  - 1  *  x 10 =  6 3  x 3.6 x 1 0  - 4  3  .1959  R e f e r r i n g t o eqn. 3.7, the i m p l i c a t i o n s of t h e second term on C2(t) a r e g r e a t l y reduced by t h e e x p o n e n t i a l f a c t o r . clarifier  i s t y p i c a l l y r u n n i n g a t about  determined by t h e model s t r u c t u r e .  „ max  ,  eff  =  1 -  =  1 -  C (t) ?  Jl_ (3.2)'  - 7 ^ 2  T h e r e f o r e the c l a r i f i e r This w i l l  clarifier  _  ,  -  1 -  =  90%  i -f clarxfxer  ee- • efficiency  Where S S T J ^ J  =  =  1  SST  ^ = out  (  1  +  k  c  T  c  )  2  SST  I  o n r  N  s o l i d s which e n t e r e d c l a r i f i e r  over  experiment  t o t a l suspended v  s o l i d s which l e f t  clarifier  over  experiment  In a s i m u l a t e d 15 day experiment, t h e c l a r i f i e r as 77%.  In  i s determined f o r a completed r u n as f o l l o w s ;  t o t a l suspended  complete  .8 x 90% = 72% e f f i c i e n c y .  of the change i n d e t e n t i o n time.  SSTlN - S S T - — —  complete  t h a t the  .8 of the maximum e f f i c i e n c y as  i s o p e r a t i n g a t approx.  efficiency  this implies  The maximum e f f i c i e n c y p o s s i b l e i s  v a r y each day as a r e s u l t  the model,  In f a c t  e f f i c i e n c y was determined  T h i s i s a t y p i c a l v a l u e f o r SS% removed f o r c l a r i f i e r s  d e t e n t i o n times between 2.5 t o 3.0 hours  (Bower, 1971).  with  The d a t a g i v e n  115  by Bower, a c q u i r e d from NCASI Tech. B u l l e t i n #190,  Detention 2.5  different  hrs  88  A.O  90  5.0  92  6.0  96  d e s i g n d e t e n t i o n times.  clarifier  SS  model some experiment runs were run f o r The  time  results  can be  % removal of  3  77  4  83  5  87  6  90  seen below.  SS  model appears to g i v e a somewhat c o n s e r v a t i v e r e d u c t i o n i n SS  when compared to the NCASI d a t a . maximum e f f i c i e n c i e s c o r r e s p o n d i n g The model developed clarifier  below:  75  3.5  Detention  The  % removal of  time  To p a r t i a l l y v a l i d a t e the c l a r i f i e r  i s reproduced  here  iterates  model a t maximum steady  However the NCASI d a t a r e p r e s e n t s t o l o n g term steady  s t a t e d e s i g n models.  every hour so i t does not o p e r a t e state  efficiency.  ideal  the  116  CHAPTER V MODEL EXPERIMENTS 5.1  DESIGN VERSUS COST  A s e r i e s of s e n s i t i v i t y experiments were run f o r each of the f o u r wastewater treatment p l a n t combinations changing c l a r i f i e r area s e q u e n t i a l l y .  d e t e n t i o n time and  The same i n p u t s , c o n s i s t i n g of 65 days of p u l p m i l l  model e f f l u e n t , were used f o r each of the experiments. each experiment  At the end of  the mean and v a r i a n c e of the l b BOD/ton and l b SS/ton f o r  lagoon and c l a r i f i e r  i n f l u e n t and e f f l u e n t were determined.  goodness of f i t t e s t s were performed comparing for  daily effluent  each of the experiments to a s t a n d a r d d a i l y time s e r i e s .  chosen was  lagoon  f o r a system w i t h a 3 hour c l a r i f i e r  15' deep l a g o o n o p e r a t i n g a t 35°C.  Also  K-S  time  series  The s t a n d a r d  d e t e n t i o n time and a 75 a c r e -  T h i s s t a n d a r d i s m a i n t a i n e d throughout  t h i s chapter.  5.1.1  The Lagoon Cost Curves  The f i r s t to  3 combinations (see F i g u r e 4.6)  p r o v i d e almost i d e n t i c a l  influent  the l a g o o n , t h e r e f o r e o n l y the r e s u l t s f o r combinations 3 and 4 w i l l  be  discussed.  Keeping a l l o t h e r f a c t o r s i d e n t i c a l t o the s t a n d a r d , experiments were r u n for  l a g o o n a r e a s r a n g i n g from 20 a c r e s t o 125 a c r e s .  mean and v a r i a n c e of i n p u t and output, and the K-S generated f o r each of the experiments.  The c o s t s ,  efficiency,  t e s t r e s u l t s were  These a r e summarized i n T a b l e  The c o s t s v e r s u s mean l b BOD/ton a r e p l o t t e d  i n F i g u r e 5.1.  5.1.  The shaded  areas  117  TABLE 5.1  LAGOON CAPITAL COST AND OPERATING COSTS FOR  COMBINATION 3 AND COMBINATION  Lag Area  Lag CC  Lag OC  4 SYSTEMS - STANDARD MILL EFFLUENT  Lag Eff.  Lag Flow  In BOD ///ton  Lag Out  Out BOD ///ton  Mean  Var.  Mean  Var.  D(N,M)  KS (.05)  20  744,219  115,296  .44  65.4  58.13  373.9  32.7  140.8  .985  .238  30  1,479,917  217,089  .56  65.4  58.13  373.9  25.3  69.7  .907  .238  40  2,010,489  367,299  .65  65.4  58.13  373.9  20.1 ,  37.2  .89  .238  50  2,512,848  560,595  .72  65.4  58.13  373,9  16.1  22.1  .553  .238  60  3,159,961  785,020  .77  65.4  58.13  373.9  13.2  14.3  .538  .238  70  3,756,611  1,027,242  .81  65.4  58.13  373.9  10.9  9.7  .154  .238  75  4,013,043  1,163,444  .83  65.4  58.13  373.9  9.96  8.2  0  .238  80  4,255,601  1,299,584  .84  65.4  58.13  373.9  9.1  6.9  .092  .238  100  5,196,448  1,882,834  .88  65.4  58.13  373.9  6.6  3.7  .35  !•  125  6,144,990  2,590,252  .92  65.4  58.13  373.9  4.6  1.9  .415  II  20  1,222,529  177,598  .64  33.9  58.13  373.9  33.7  106.9  .985  .238  30  1,898,220  381,195  .76  33.9  58.13  373.9  29.2  .7.3  .985  40  2,586,116  633,013  .83  33.9  58.13  373.9  26.5  59.3  .938  Tf I?  50  3,164,647  921,895  .88  33.9  58.13  373.9  24.8  52.5  .938  II  60  3,655,048  1,207,746  .91  33.9  58.13  373.9  23.6  48.6  .938  70  4,053,501  1,476,957  .93  33.9  58.13  373.9  22.8  46.2  .938  II 11  80  4,364,435  1,705,257  .94  33.9  58.13  373.9  22.3  44.6  .938  II  Temp.=35° Standard Influent  °  0  2.  4-  6  8  IO  IZ  1+  ((*  18  ZO  7.Z  2-f ^ t 2.S 3o  32. 3f 3fe 38 f o  System Mean BOD lb/ton FIGURE 5.1 LAGOON CAPITAL OPERATING COST CURVES FOR COMBINATION 3 AND COMBINATION 4 SYSTEMS. NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES  119  in Figure 5.1 represent one standard deviation regions about the e f f l u e n t means for c a p i t a l cost curves.  The numbers beside each data point indicate  lagoon acreage.  The effluent mean lb BOD/ton was chosen as the x-axis as a consequence of the 1971 report on " P o l l u t i o n Control Objectives for the Forest Products Industry" (Department of Lands, et a l , 1971).  The objective BOD  effluent  l e v e l s for the chemical pulping process were given as Level A = 15 lb/ton Level B = 60 lb/ton Level C = 80 lb/ton for marine discharge.  The l e v e l A applies to new m i l l s and i s the l e v e l they  must meet immediately.  I t i s to t h i s l e v e l that the r e s u l t s of this chapter  w i l l be directed  (Note the effluent mean lb BOD/ton includes a l l the o u t f a l l s .  Therefore for the combination 4 system i t includes the acid wastes which bypass the system).  Figure 5.1 i s a plot of change i n c a p i t a l and operating costs of an aerated lagoon with a change i n mean effluent l e v e l .  One of the most s t r i k i n g r e s u l t s  i s the cost dominance of combination 3 over combination 4 f o r any effluent mean.  Given an effluent l e v e l which management wants to meet i t i s always  less costly to construct a combination 3 system, ( i . e . feed a l l the m i l l o u t f a l l s through the lagoon) than a combination 4 system (bypass the lagoon with the acid e f f l u e n t ) .  In other words, given a lagoon area, the effluent  q u a l i t y possible i s always better with a combination 3 system and at less  120  c a p i t a l and operating cost.  The reason f o r t h i s i s that i t i s not necessary  to operate a combination 3 lagoon at such a high e f f i c i e n c y i n order to obtain the same quality effluent as with a combination 4 system.  Operating  a lagoon at high e f f i c i e n c i e s i s one of the major cost factors since i t requires more aerators and power.  In fact with a combination 4 system  one  i s paying very highly for the p r i v i l e g e of dumping acid wastes, since i t i s the acid effluent  that i s putting a lower bound on the lb/ton l e v e l which a  combination 4 system can a t t a i n .  For the given m i l l , the combination 4  system would not be able to a t t a i n l e v e l A at any cost.  Another way  to look at the plot i s , given a c e r t a i n amount of c a p i t a l which  management i s w i l l i n g to invest i n an aerated lagoon, a higher q u a l i t y effluent w i l l always r e s u l t with a combination 3 system. system requires a n e u t r a l i z a t i o n  A combination 3  mixing basin ahead of the lagoon.  However  such a basin w i l l cost approximately $10,000.00, a small investment r e l a t i v e to lagoon c a p i t a l costs.  To meet the l e v e l A requirements with a combination 3 system, the c a p i t a l investment w i l l be approximately 2.7 x 10  5  costs would be about $600,000.00 per year.  d o l l a r s and expected operating At an operating temperature of  35°C the lagoon s i z e needed i s approximately 55 acres - 15' deep.  Since  t h i s i s mean performance, i t implies that the m i l l w i l l often have days with operation above and below t h i s l e v e l .  If t h i s i s of concern i t may  advisable to work along the p + a curve. investment of approximately 3.5 x 10  6  be  This would require a c a p i t a l  d o l l a r s with operating costs at about  121  1 x 10  d o l l a r s per year.  6  At an operating temperature of 35°C this would  mean a lagoon s i z e of approximately 65 acres - 15' deep.  Although management may be w i l l i n g to invest i n the larger lagoon, land a v a i l a b i l i t y could w e l l be a l i m i t i n g factor preventing construction of the more r e l i a b l e system.  As indicated e a r l i e r these r e s u l t s are based on a 65 day experiment of the m i l l and lagoon models.  A f u l l year experiment was also run f o r the standard  system and the r e s u l t s were s i m i l a r . reduced  The lagoon e f f i c i e n c y was  slightly  (approximately 1%) and the lagoon c a p i t a l costs dropped to about  3.9 x 10  d o l l a r s . (From Table 5.1 the 65 day run resulted i n lagoon CC =  6  4.01 x 10  6  dollars).  S ince the r e s u l t s are almost i d e n t i c a l , i t was decided  to proceed with the 65 day operation.  5.1.2  S e n s i t i v i t y Tests on Lagoon Cost Curves  To test the s e n s i t i v i t y of the curves i n Figure 5.1 experiments were run with each of the following changes.  (Note:  the v a r i a b l e indicated was altered.  The other variables were l e f t as they  were i n generating Figure 5.1). a.  Temperature Two experiments were run 1.  temperature = 30°C  2.  temperature = 40°C  For each of the following only  122  b.  H y d r a u l i c Load Two experiments were r u n .  c.  .1.  i n c r e a s e d by 10%  2.  d e c r e a s e d by 10%  Effluent  H o u r l y f l o w s f o r a l l 3 o u t f a l l s were  Load  Two experiments were r u n .  The h o u r l y SS and BOD c o n c e n t r a t i o n from  the 3 o u t f a l l s were 1.  i n c r e a s e d by 10%  2.  d e c r e a s e d by 10%  For a l l s i x experiments d a i l y i n f l u e n t and e f f l u e n t l o a d s f o r the waste treatment system,  expressed as l b / t o n , were compared t o the e s t a b l i s h e d  s t a n d a r d system u s i n g t h e K-S goodness of f i t r o u t i n e .  R e s u l t s o f these  experiments a r e summarized i n T a b l e s 5.2 A and 5.2 B and F i g u r e 5.2 f o r temperature  , T a b l e s 5.3 A and 5.3 B and F i g u r e 5.3 f o r h y d r a u l i c l o a d , and  T a b l e s 5.4 A and 5.4 B and F i g u r e 5.4 f o r e f f l u e n t  load.  L o o k i n g a t F i g u r e 5.2 t h e c o s t c u r v e s generated f o r t h e changes i n l a g o o n o p e r a t i n g temperatures a r e i d e n t i c a l t o t h o s e i n F i g u r e 5.1.  The mean l b  BOD/ton i s i n essence a measure of t h e lagoon's e f f i c i e n c y and t h e e f f i c i e n c y f o r any g i v e n l a g o o n volume i s a f u n c t i o n o f h y d r a u l i c f l o w and temperature. T h e r e f o r e , s i n c e t h e f l o w i s n o t a l t e r e d i n the temperature r u n s , t h e model i s e s s e n t i a l l y working i t s way up a v e r t i c a l f l o w l i n e on F i g u r e 4.8. matter what t h e temperature of the l a g o o n model, i t w i l l  still  No  f o l l o w t h e same  f l o w l i n e and t h e r e f o r e g e n e r a t e the same c o s t v e r s u s e f f i c i e n c y c u r v e .  The  TABLE 5.2A LAGOON CAPITAL COST AND OPERATING COSTS FOR COMBINATION 3 AND 4 SYSTEMS - STANDARD INFLUENT LOAD,TEMP = 30°C  Comb  3  Lag Area  20 30  4  Lag CC  582,576 1,221,460  Lag OC  97,195 168,478  Lag Eff  .39  Lag Flow  65.4  1,755,114  274,445  .60  50  2,143,343  421,343  .67  60  2,618,152  595,452  .73  Out BOD ///ton  Mean  Var  Mean  Var  58.1  373.9  35.2  166.7  •" "•  .51  40  In BOD ///ton  "  "  II  it it ti  70  3,173,116  789,827  .77  II  80  3,693,615  995,000  .80  II  100  4,543,221  1,468,835  .86  125  5,504,752  2,094,492  20  1,057,085  133,395  .59  30  1,567,784  287,804  40  2,230,943  50  ti II  .896 33.9  58.1  Lag Out D(N,M) 1.0  28.1  86.0  .969  22.7  47.1  .908  18.7  29.3  .831  15.6  19.8  .554  13.1  14.1  .538  11.1  10.4  .215  8.2  5.98  .307  5.9  3.2  .369  117  37.3.9  35.5  .72  ii  30.8  79.2  .985  483,299  .80  IT  27.8  63.6  .985  2,757,697  714,697  .85  Tl  25.9  55.5  .938  60  3,250,358  968,576  .88  II  24.5  50.8  .938  70  3,664,426  1,213,780  .91  II  23.6  47.9  .938  80  4,011,143  1,447,091  .93  II  22.9  45.9  .938  D In Lag  D In CL  D Out CL  KS(.05) .238  •"  0  0  0  II  II-  it  .984  » II  „  TABLE 5.2B LAGOON CAPITAL COST AND OPERATING COSTS FOR COMBINATION 3 AND A SYSTEMS - STANDARD INFLUENT LOAD,TEMP = 4Q°C  Comb  3  4  Lag Area  Lag CC  20  1,019,959  30  1,779,258  Lag OC 143,642 282,608  In BOD ///ton  Out BOD ///ton  Mean  Var  Mean  Var  D(N,M)  58.1  373.9  30.0  117.7  .985  .61  IT  II  II  22.6  56.1  II  II  17.4 •  Lag Eff  Lag Flow  .48  65,4  40  2,296,200  488,449  .70  II  50  3,044,594  743,269  .76  II  II  II  II  ti  Lag Out KS(.05) .239  D In Lag  D In CL  D Out CI  0  0  0  .908  it  II  it  II  28.7  .646  it  II  II  it  13.7  16.2  .554  II  II  II  it  10.9  9.9  .169  II  II  it  tt  60  3,747,094  1,022,340  .81  II  70  4,323,528  1,338,975  .83  II  IP  II  8.9  6.5  .154  it  II  it  tt  II  II  7.36  4.4  .323  ii  II  tt  tt  80  4,886,945  1,680,806  .87  II  100  5,844,085  2,349,295  .91  II  it  it  5.2  2.2  .415  II  ii  ti  II  125  6,737,215  3,097,800  .94  II  ii  it  3.5  1.1  .415  II  n  II  ti  20  1,397,832  236,747  .69  II  II  31.9  97.3  .985  II  tt  it  tt  II  II  27.7  67.5  .985  II  II  tt  it  II  it  it  it  tt  .938  II  it  it  tt  33.9  30  2,268,214  495,210  .80  it  40  2,969,456  819,554  .86  ii  it  II  25.3  55.7  50  3,571,540  1,154,664  .90  •t  II  II  23.8  49.9  60  4,047,108  1,472,429  .93  n  II  II  22.8  46.8  II  it  tt  II  ti  70  4,403,577  1,735,125  .95  II  II  II  22.2  44.8  II  II  tt  ti  ti  ° 0  2  U-  fe  8  to  f+ Ho 18 2 0 2 2 . Z(+ System Mean BOD lb/ton  IZ  2 6  2<S  3 0  32.  3^-  3 6  FIGURE 5.2 LAGOON CAPITAL AND OPERATING COST CURVES FOR COMBINATION 3 SYSTEM WITH STANDARD INFLUENT LOAD AND LAGOON OPERATING AT 30°C AND 40°C. NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES FOR INDICATED TEMPERATURE  3 8  4 0  .TABLE 5 . 3 A LAGOON CAPITAL AND OPERATING COSTS FOR COMBINATION 3 AND COMBINATION 4 SYSTEM - STANDARD HYDRAULIC LOAD X . 9  •  Comb  Lag Area  Lag CC  Lag OC  Lag Eff  Lag Flow  In BOD ///Ton Mean  Var  Mean 9.96  3  75  4,013,043  1,163,444  .83  65.4  58.1  374.0  3  20  657,839  111,015  .41  71.9  60.2  397.7  30  1,401,728  203,324  .53  40  1,974,161  336,183  .62  50  2,406,035  513,921  .69  60  3,005,475  726,484  .74  70  3,623,340  956,175  .78  75  4,012,049  1,126,397  .81  80  4,169,655  1,211,281  .82  100  5,117,131  1,777,065  .87  125  6,142,215  2,496,760  .91  1,200,074  162,439  .61  !  20-  4  ; )  30  1,801,808  351,732  .73  40  2,527,544  587,199  .81  50  3,106,911  865,218  .86  60  3,635,840  1,156,976  .89  70  4,077,201  1,441,087  .92  75  4,335,058  1,623,623  .93  80  4,435,267  1,697,411  .93  100  4,844,983  1,990,699  .96  it  II  ti  ti  II  II  ti  II  it  it  ti  ti  i'  II  it  ti  ii  n  it  ti  ti  ii-  tt  ti  ti  n  it  37.3  Out BOD ///Ton  60.2  397.7  II  ti  ti  it  ii  ii  it  it  it  ti  it  it  it  ii  it  tt  ti  it  it  it  ii  it  tt  tt  36.5  Var 8.15 182.7  Lag Out D(N,M)  KS(0.5)  0  0  .985  .239  28.9  96.6  .969  23,2  52.8  .908  18.9  31.6  .815  15.6  20.5  .554  13.1  14.0  .538  11.5  13.1  .338  11.1  10.0  .200  8.1  5.5  .308  5.7  2.88  .385  D Lag In  .200  ti  ii  it  ti  it  II  ti  ti  II  it  II  it  it •  ft  II •  ti  it  ti  36.9  132.3  .984  32.2  90.8  .984  »  29.3  73.6  .984  »  27.5  64.8  .984  »  26.2  59.8  .938  25.3  56.7  .938  24,8  53.1  .938  24,7  54.6  .938  »  23.8  52.2  .938  "  -. 2 3 9 ' '  D CL In  .246  &  Out  .215  TABLE 5.3B LAGOON CAPITAL AND OPERATING COSTS FOR COMBINATION 3 AND COMBINATION 4 SYSTEMS - STANDARD HYDRAULIC LOAD X  Comb  Lag Area  Lag CC  Lag OC  Lag Eff  Lag Flow  In BOD #/Ton  Out BOD #/Ton  Mean  Variance  Mean 9.96  3  75  4,013,043  1,163,444  .83  65.4  58.1  373.  3  20  858,525  120,765  .47  58.8  56.1  350,  3  30  1,572,301  233,563  3  40  2,047,783  3  50  3 3  Variance 9.96  D(N,M) 0  28.8  103.9  .969  .59  21.9  48.3  .908  403,529  .68  16.9  25.3  .600  2,669,224  615,209  .75  13.5  14.9  .538  60  3,316,581  846,445  .80  10.8  9.6  .138  70  3,851,704  1,115,489  .83  8.9  6.5  .185  75  4,191,905  1,307,630  .85  7.7  6.2  .338  3  80  4,349,930  1,400,199  .86  7.4  4.5  .338  3  100  5,239,442  1,976,666  .90  5.21  2.39  .415  3  125  6,092,680  2,650,693  .93  3.6  1.2 .  .415  4  20  1,246,026  195,298  .67  30  1,997,521  412,605  .79  40  2,639,093  680,808  50  3,200,079  60 70  30.5  84.0  .989  26.1  57.3  .938  .85  23.6  46.8  .938  972,175  .89  22.0  41.5  .938  3,649,124  1,252,717  .92  21,0  38.6  .938  3,992,827  1,492,375  .94  20.4  36.9  .892  30.5  ii  56.1 n  350.9  Lag In •  Lag Out  CL Out  KS(0.5) Stand  0 .239  ti it  .154  .16+  Temp. = 35° Factor X Hydraulic Load  J2S  Cost Cost  u o Q  io  O  O  2.  4-  6  8  /o.  "71  7£  71" 71  20  System Mean BOD lb/ton  2Z  2JT~2G  2-8  30  3Z  3fc  36  3§  %  .  FIGURE 5.3 LAGOON CAPITAL AND OPERATING COST CURVES FOR COMBINATION 3 SYSTEM WITH STANDARD HYDRAULIC LOAD MULTIPLIED BY 1.1 AND NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES.  LAGOON CAPITAL COST AND OPERATING COST FOR COMBINATION 3 AND 4 SYSTEMS - STANDARD INFLUENT LOAD X . 9  Comb  Lag Area  3  20  4  Lag CC  744,249  Lag OC  115,300  Lag Eff  .44  Lag Flow  65.4  In  BOD ///Ton  Out BOD ///Ton  Lag Out  D In  D(M,M) KS(.05: Lag  Mean  Var  Mean  Var  63.9  452.4  35.9  170.4  "  tt  27.9  84.3  .954  II II  .985  .239  30  1,479,950  217,095  .56  40  2,010,533  367,296  .65  ti  22.0  45.0  .908  50  2,512,910  5,60,616  .72  it  17.7  26.7  .708  it  60  3,160,015  785,040  .77  it  it  14.5  17.3  .554  ii  70  3,756,705  1,027,290  .81  »  tt  11.9  11.8  .431  it  75  4,107,108  1,215,400  .83  it  10.5  11.2  .169  tt  80  4,255,723  1,299,654  .84  10.0  8.3  100  5,196,483.  1,882,857  .88  tt ti  7.2  4.5  .338  ti ti  125  6,145,002  2,590,265  .92  it  5.04  2.3  .415  it  20  1,222,553  177,606  .64  30'  1,898,313  .381,223  40  2,586,126  50  0.0  tt  37.1  129.3  .985  tt  .76  tt  32.1  88.3  .985  tt  633,017  .83  29.1  71.8  .985  3,164,641  921,892  .88  ti it  27.2  63.5  .969  ti it  60  3,655,051  1,207,748  .91  tt  25.9  58.8  .938  it  70  4,053,494  1,476,951  .93  ti  25.1  55.9  .938  tt  75  4,281,726  1,642,975  .94  ti  24.6  52,5  .938  it  80  4,364,427  1,705,253  .94  it  24.5  54.0  .938  ti  33.9  "  .246  D In CL .277  D Out CL .215  tt  tt  to vO  LAGOON CAPITAL AND OPERATING COSTS FOR COMBINATION 3 AND COMBINATION 4-SYSTEMS STANDARD INFLUENT X 1 . 1  Comb  3  4  In BOD ///Ton  Lag Eff  Lag  1,163,444  .83  65.4  744,086  115,282  .44  ti  30  1,479,887  217,083  .56  it  it  40  2,010,499  367,302  .65  II  50  2,512,810  560,583  .72  60  3,159,880  784,990  70  3,756,650  75  Lag Area  Lag CC  75  4,013,043  20  Lag OC  Flow  Out BOD ///Ton  Mean  Var  Mean  Var  58.1  373.9  9.96  8.15  Lag Out D(N,M) 0  KS(.05)  D In Lag  D Out CL '  D In CL Standard  .239  29.4  114.1  .984  it  .277  II  22.8  56.5  .907  it  tt  II  tt  II  it  18.0  30.1  .738  II  tt  tt  it  II  it  ti  14.5  17.9  .554  II  ti  II  tt  .77  tt  II  ti  11.9  11.5  .385  n  ti  ti  n  1,027,186  .81  it  ti  it  9.8  7.9  .015  II  ti  II  tt  4,106,861  1,215,264  .83  it  it  it  8.6  7.5  .200  II  it  it  80  4,255,414  1,299,478  .84  it  it  II  8.2  5.6  .292  II  it  it  tt  100  5,196,448  1,882,835  .88  it  II  ti  5.9  3.0.  .385  it  ti  ti  tt  125  6,144,984  2,590,247  .92  it  II  it  4.1  1.5  .415  it  ti  II  II  20  1,222,499  177,589  .64  it  ti  30.4  86.6  .984  30  1,898,068  381,151  .76  it  it  II  26.3  59.1  .954  it  ti  II  it  40  2,586,104  633,007  .83  it  II  it  23.8  48.1  .938  ii  II  it  ti  50  3,164,620  921,881  .88  ti  ti  it  22.3  42.5  .938  II  ti  ti  ti  60  3,655,045  1,207,744  .91  it  ti  II  21.3  39.4  .938  II  it  it  II  70  4,053,494  1,476,951  .93  II  ti  ti  20.5  37.4  .923  II  ti  ti  tt  75  4,281,730  1,642,976  .94  II  II  n  20.2  35.2  .877  IT  tt  ti  ti  80  4,364,419  1,705,246  .95  tt  II  it  20.0  36.2  .877  II  it  II  II  33.9  52.32 302.9  .239  .239  .277  .308  .308  .169  .153  O I  O  i  2  <r  6  :  8  'O  12.  If-  /fe  /8.  20  :  22-  :  Of-  2&  :  28  3°  32.  3<£  36  38  4 0  System Mean BOD l b / t o n FIGURE 5.4 LAGOON CAPITAL AND OPERATING COST CURVES FOR COMBINATION 3 SYSTEM WITH STANDARD INFLUENT LOAD MULTIPLIED BY 1.1 AND NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES.  .9.  i *  132  expected difference however i s that the e f f i c i e n c y of any given s i z e lagoon has gone up for higher temperatures and down f o r lower.  The data points  on Figure 5.2 are l a b e l l e d according to lagoon temperature and s i z e .  Notice  also that the c a p i t a l costs of any given sized lagoon increase with temperature.  With an increased reaction rate more oxygen i s required i n order to  maintain f i r s t , the b i o l o g i c a l a c t i v i t y and, second, the assumption  that  the reaction rate i s constant, therefore more aerators and/or more power are needed, r e s u l t i n g i n increased c a p i t a l cost.  From these r e s u l t s , we would therefore a n t i c i p a t e the change i n flow and effluent load to enclose the curve i n Figure 5.1. and 5.4 we see that this i s the case.  Looking at Figures 5.3  The higher load and higher flow curves  are both above the standard curve and s i m i l a r l y the lower load and  lower  flow curves are below.  Note also from Tables 5.3 A and 5.3 B the lb BOD/ton inflow into the lagoon i s not changed s i g n i f i c a n t l y (at .05 s i g n i f i c a n c e l e v e l ) , according to the K-S  test, f o r the 10% change i n flows (.200  <.239).  S i m i l a r l y the output  from the 80 acre lagoon i s not s i g n i f i c a n t l y d i f f e r e n t from the 75 acre standard for the 10% increased flow, while for the 10% decreased flow both the 60 and 70 acre lagoon effluents are accepted by the K-S  test.  Looking  at Tables 5.4 A and 5.4 B the lagoon i n f l u e n t into the lagoon d i f f e r s s i g n i f i c a n t l y for both factor loading experiments.  The e f f l u e n t i s s i g n i f i c a n t l y  i d e n t i c a l for a 70 acre lagoon with a .9 factor loading and f o r an 80 acre lagoon with a 1.1 factor loading.  133  R e f e r r i n g t o T a b l e s 5.3 A and 5.4 A, d e s p i t e t h e lower mean and v a r i a n c e for to  the i n f l u e n t  i n T a b l e 5.3 A (and n o t i c e a b l y i t s s i g n i f i c a n t  the standard i n f l u e n t ) ,  similarity  lagoon e f f i c i e n c i e s f o r any g i v e n a r e a a r e l e s s  i n T a b l e 5.3 A than i n 5.4 A as a r e a l s o t h e means and v a r i a n c e s o f l a g o o n effluent.  T h i s i m p l i e s t h e l a g o o n model i s more s e n s i t i v e to change i n  f l o w than changes i n i n f l u e n t c o n c e n t r a t i o n . decreased  The c a u s e . i s p r o b a b l y the  r e s i d e n c e time w i t h i n c r e a s e d f l o w r e s u l t i n g  i n a lower  operation  efficiency.  To t e s t t h e i m p l i c a t i o n s o f s p i l l  frequency  on the waste treatment  c u r v e s , an experiment  was r u n u s i n g a p u l p m i l l  frequency d r a s t i c a l l y  increased.  maintained  except  effluent  trace with  cost spill  A l l c h a r a c t e r i s t i c s o f t h e m i l l were  f o r t h e "time between u n r e l a t e d s p i l l s "  distribution for  the r e c o v e r y a r e a .  For the s t a n d a r d m i l l  t r a c e the time between u n r e l a t e d s p i l l s  ( i n the r e c o v e r y  area) had a mean of 207.45 hours and a s t a n d a r d d e v i a t i o n of 290.13 h o u r s . To i n c r e a s e s p i l l to  100 hours.  be changed.  frequency  To a c c o m p l i s h  t h e mean and s t a n d a r d d e v i a t i o n were b o t h this  t h e gamma d i s t r i b u t i o n parameters had t o  From K i t a and M o r l e y  A - -  2  (1973),  -  100 (100)  2  the parameters a r e r e l a t e d as  = .01  and  8=  changed  (a)  2  = 1.0  134  These changes were i n t r o d u c e d i n t o t h e p u l p m i l l model, a new e f f l u e n t s e r i e s was g e n e r a t e d and was g i v e n a s i n f l u e n t t o t h e w a s t e t r e a t m e n t The d a i l y i n f l u e n t and e f f l u e n t l e v e l s , e x p r e s s e d to the standard  time model.  as l b BOD/ton, were compared  system t r e a t i n g t h e s t a n d a r d m i l l e f f l u e n t t r a c e , u s i n g  the K-S goodness o f f i t t e s t .  The r e s u l t s a r e summarized i n T a b l e 5.5 and  F i g u r e 5.5.  Comparing T a b l e s had  5.1 and 5.5 we c a n s e e t h a t t h e i n c r e a s e d number o f s p i l l s  l i t t l e e f f e c t on l a g o o n e f f i c i e n c y and c o s t s f o r a g i v e n l a g o o n a r e a ,  although  i t d i d i n c r e a s e t h e mean and v a r i a n c e o f t h e l b BOD/ton o f t h e  lagoon e f f l u e n t .  As a consequence, t h e s i z e o f l a g o o n n e c e s s a r y  a below 15 l b BOD/ton e f f l u e n t average i n c r e a s e s s i g n i f i c a n t l y . e a s i l y seen i n F i g u r e 5.5.  to maintain T h i s i s more  F o r t h e i n c r e a s e d s p i l l s e x p e r i m e n t a 70 a c r e  l a g o o n i s r e q u i r e d a t a c a p i t a l c o s t o f 3.75 m i l l i o n d o l l a r s , w h i l e f o r t h e s t a n d a r d m i l l a 55 a c r e l a g o o n i s s u f f i c i e n t a t a c o s t o f 2.7 m i l l i o n d o l l a r s , a s a v i n g o f up t o a m i l l i o n d o l l a r s .  5.1.3  The C l a r i f i e r Cost Curves  T a b l e 5.6 i s a summary o f e x p e r i m e n t s r u n f o r d i f f e r e n t c l a r i f i e r times f o r system c o m b i n a t i o n s 1 and 2.  detention  The c o s t c u r v e s a r e p l o t t e d i n  F i g u r e 5.6.  The  c l a r i f i e r doesn't have t h e c l e a r dominance p r o p e r t y t h a t was o b s e r v e d  f o r t h e lagoOn model.  The c a p i t a l c o s t c u r v e s  SS/ton w i t h a c a p i t a l c o s t o f a p p r o x i m a t e l y  i n t e r s e c t a t a mean o f 11.6 l b  750,000 d o l l a r s .  For e f f l u e n t  TABLE 5.5 LAGOON CAPITAL AND OPERATING COST FOR COMBINATION 3 AND COMBINATION 4 SYSTEMS - INCREASED SPILL FREQUENCY IN RECOVERY  ~omb  3  4  Lag Area  Lag CC  Lag OC  Lag Eff  Lag Flow  66  AREA  OF  In BOD ///Ton  MILL  Out BOD ///Ton  Lag Out  Mean  Var  Mean  Var  D(M,M)  76.0  542.1  43.7  189.2  .923  KS(.05) .239  20  734,982  114,920  .43  30  1,472,846  215,871  .56  34.1  109.7  .908  40  2,008,340  364,419  .65  27.2  76.4  .831  »  50  2,499,467  555,974  .72  21.9  57.3  .554  »  60  3,145,531  779,420  .77  18.0  32.9  .354  70  3,747,071  1,018,655  .81  . 14.9  16.4  .123  80  4,248,220  1,290,683  .84  12.5  13.7  .231  100  5,189,286  1,871,823  .88  9.1  8.4  .477  125  6,145,750  2,580,405  .92  "  "  6.3  4.1  .569  20  1,222,285  176,539  .64  »  »  44.5  146.3  .923  30  1,891,877  379,161  .76  38.4  97.9  .923  40  2,583,722  629,646  .83  34.8  79.2  50  3,162,426  917,664  .88  32.4  66.9  .892 :  »  60  3,656,087  1,203,548  .91  30.8  57.2  .861  »  70  4,059,416  1,475,186  .93  29.7  56.1  .862  »  80  4,375,071  1,706,449  .94  28.96  55.7  .862  "  "  » »  Ui  0  2  ^  6  ' /o  /2  /</ ' <6  /8  2D  Z2  Z¥-  26  28  50  3 2 . 3<r-  36  System Mean BOD lb/ton FIGURE 5.5 LAGOON CAPITAL AND OPERATING COST CURVES FOR COMBINATION 3 SYSTEM WITH INCREASED SPILL FREQUENCY IN RECOVERY AREA OF MILL. NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES.  38  to  42  TABLE 5.6 CLARIFIER CAPITAL AND OPERATING  COST FOR THE COMBINATION  WITH DIFFERENT CLARIFIER DETENTION  Comb  Det. Time Hrs  Clar. CC  Clar. OC  Clar. Eff.  In SS ///Ton Mean  Var  3  3  584,190  47,566  .82  42.6  187.7  1  2  711,020  74,555  .69  42.6  187.7  2  4  1,345,351  5  1,651,934  6  1,953,617  7  2,251,286  2  402,300  74,555  Tl II  11 47,566  4  761,199  II  5  934,663  II  6  1,105,355  7  1,273,776  it ti  1 AND 2 SYSTEMS  TIME  Out  CL Out  SS ///Ton  Mean  Var  D(M,M)  9.96  8.2  0  KS(.05) 0  12.7  13.0  .092  II  6.1  2.9  .938  II  II  II  4.7  3.1  .923  II  .91  ii  if  3.7  2.7  .938  II  .93  it  II  3.0  2.6  .938  it  .70  42.6  187.7  17.1  24.9  .538  .238  ii ii ii it  ti  11.5  11.7  .262  10.3  9.5  .523  9.5  8.2  .723  8.9  7.3  .830  .85 .89  .86 .90 .92 .94  II  II II  ii  .238  II  it II II  O  /  2  •3  • £  S  6 ? 8 9 to Effluent Mean SS lb/ton  II  /Z.  IS  rf  15  FIGURE 5.6 CLARIFIER CAPITAL COST CURVES FOR COMBINATION 1 AND COMBINATION 2 SYSTEMS. NUMBERS BESIDE DATA POINTS INDICATE THEORETICAL DETENTION TIME.  Z6,  If  18  TABLE 5.7 SENSITIVITY EXPERIMENTS ON CLARIFIER MODEL FOR HYDRAULIC LOADS ±10% OF STANDARD AND EFFLUENT LOADS ±10% OF STANDARD  Experiment  Clar. Det. Time  Input  Clar.  Mean  Var  Mean  Output Clar  KS Tests  Var  D In  D Out  KS(.05)  .9* Hydraulic  3  39.04  157.6  12.1  12.9  .231  .169  .239  1.1* Hydraulic  3  46.2  220.5  14.9  19.1  .246  .215  .239  .9* Standard Influent Load  3  38.3  152.1  12.1  12.7  .307  .169  .239  1.1* Standard Influent Load  3  46.9  227.2  14.8  19.0  .215  .215  .239  3  42.6  187.7  13.4  15.7  Standard  140  l e v e l s greater than or equal to 11.6 l b SS/ton the combination 2 cost curves dominate since both i t s c a p i t a l and operating costs are l e a s t .  Some experiments were run with the c l a r i f i e r model for ±10% changes i n the hydraulic load and the effluent load f o r a 3 hour detention time c l a r i f i e r i n a combination 3 system. the  K-S goodness of f i t tests were performed against  e a r l i e r described standard.  The r e s u l t s are summarized i n Table 5.7.  In a l l cases the n u l l hypothesis cannot be rejected for c l a r i f i e r output although i t can for a l l inputs except the .9x hydraulic load experiment.  5.2  SHOCK LOAD EXPERIMENTS.  Various Experiments were run with the previously defined standard system for shock loads of various i n t e n s i t i e s and over various time periods. summarized i n Table 5.8.  These are  A l l the experiments were monitored f o r 11 days  a f t e r the shock was i n i t i a t e d and the d a i l y l e v e l s represent l b BOD/ton. A l l the experiments peak on day s i x as a consequence of the exponential form of the lagoon model. altered by s p i l l s  Remember i t was assumed that the hydraulic flow i s not  (and therefore shock loads).  To i l l u s t r a t e the lagoons response to a shock load, Figure 5.7 i s a plot of the  change i n BOD concentration with time as a consequence of various size  shocks over a 24 hour period.  The time u n t i l the lagoon reaches i t s normal  operational e f f l u e n t concentration (approximately • 20 mg/l) i s about 3 days less for the 10 x normal than the 100 x normal shock load.  The 100 x normal  curve r e s u l t s i n an effluent concentration 30 x normal f o r a period of 40 hours  TABLE 5.8 lbs/TON EFFLUENT FROM A COMBINATION 2 SYSTEM FOR VARIOUS FACTOR SHOCK LOADS OVER VARIOUS TIME INTERVALS  Day  Factor  5  10- HOUR  24 HOUR  48 HOUR 10  100  5  10  50  100  10  100  5 HOUR 5  1 HOUR  100  100  1  15.4  15.4  15.4  15.4  15.4  15.4  15.4  15.4  15.4  15.4  15.4  15.4  2  7.4  7.6  11.4  7.4  7.6  9.3  11.5  7.9  15.1  10.7  14.3  10.7  3  17.7  26.3  180.4  17.6  26  93.3  177.3  19.6  106.8  41.8  73.2  34.6  4  28.4  50.1  442.1  22.5  36.9  152.4  296.8  22  133.2  47.6  85.0  37.6  5  31.2  57  523.3  21.2  34.5  141.6  275.5  19.7  112  40.2  70.5  31.6  6  61.1  110.6  1002.7  39.6  62.2  243.2  469.5  36.3  184.4  68.5  116.5  54.6  7 '  28.2  48.9  420.1  18.6  27.2  95.9  181.8  17.1  71.2  28.7  46  23.6  37  59.6  466.1  26  34.8  105.5  193.7  24.3  78.3  35.8  53  30.6  9  17.6  25.8  173  13.5  16.6  41.1  71.8  12.9  31.3  16.8  22.6  15.0  10  18.4  24  123.6  15.6  17.6  33.6  53.6  15.2  27.0  17.6  21.4  16.5  11  15.4  18.1  67.6  14  14.9  22.6  32.3  13.8  19.4  14.9  16.7  14.4  12  11  12.2  32.9  10.4  10.8  14.0  17.9  10.3  12.6  10.8  11.5  10.6  . 8  142  Shock Interval  O  2.0  <fO  60  g o  /oo  /2.0  fao  /fco /60 200 Z2x>  2Ho  Time - Hours FIGURE 5.7 LAGOON RESPONSE CURVES FOR SHOCK INTERVAL OF 24 HOURS  2&a  143  TABLE 5.9 TABLE SHOWING LAGOON MAXIMUM CONCENTRATIONS AND RECOVERY TIMES AS A CONSEQUENCE OF VARIOUS SHOCK LOADS  Size of F a c t o r  Time Interval  Time t o Max  Max Cone.  Time From Max t o Normal  100  1  54 h r s  81 mg/1  100  5  53 h r s  185 mg/1  270  "  50  ti  ti  105  250  "  100  10  43  "  54  "  10  11  "  300 mg/1 50  "  244 h r s  300 h r s 176  "  700 mg/1  306  "  100  24  50  II  ti  350 mg/1  294  10  II  it  90 mg/1  230  100 10  44 h r s  48  29 h r s  II  29  1230 mg/1 140 mg/1  Normal Cone 21 mg/1  " ».  "  " 11  "  337 h r s 264  "  "  144  which a c c o r d i n g to the r e s u l t s i n Gove (1974) w i l l fish k i l l .  (Note a s p i l l  r e p r e s e n t s e v e r a l hundred  almost s u r e l y r e s u l t  of t h i s s i z e i s somewhat u n l i k e l y s i n c e i t would thousand g a l l o n s o f weak b l a c k l i q u o r ) .  Some o t h e r response c u r v e s a r e summarized i n T a b l e 5.9. on the environment  in a  Their  implications  however, are not i n t e r p r e t e d h e r e .  To t e s t whether the a c t i o n of c o l l e c t i n g a s p i l l  in a spill  b a s i n and  then  r e l e a s i n g i t over time makes a c o n s i d e r a b l e d i f f e r e n c e on a lagoon's p e r f o r mance, two for  experiments were r u n .  The f i r s t w i t h a f a c t o r of 10 x  normal  10 hours and the second w i t h a f a c t o r of 2 x normal f o r 70 h o u r s .  10 x normal  spill  f o r 10 hours r e p r e s e n t s , a s p i l l  equivalent  (The  to a p p r o x i m a t e l y  100,000 g a l l o n s of weak b l a c k l i q u o r ,  the 2 x normal f o r 70 hours r e p r e s e n t s  a p p r o x i m a t e l y the same BOD  The r e s u l t s a r e p r e s e n t e d below.  loading).  Normal Cone. (mg/l)  Max. Cone. Reached (mg/l)  Time of Max.  Time Max. to Normal  lb/ton Max. Out  lb/ton Max. I n  10 x 10 h r  20  40.9  33 h r  178 hr  32.7  102.1  2 x 70 hr  20  23.0  33 hr  170 hr  21.0  106.3  Experiment  Both experiments reached maximum c o n c e n t r a t i o n a t the same time and took the same l e n g t h of time to r e c o v e r .  However, the 2 x 70 experiment r e s u l t e d i n  c o n s i d e r a b l y lower e f f l u e n t c o n c e n t r a t i o n s over the same time span. i m p l i e s t h a t i f adequate s p i l l m o n i t o r i n g i s m a i n t a i n e d e n a b l i n g a  This spill  145  to be diverted to a c o l l e c t i o n basin, releasing i t at controlled l e v e l s over time w i l l greatly decrease the s p i l l ' s impact on the treatment system and the receiving  5.3  stream.  SUGGESTED DATA COLLECTION SCHEMES AND MODEL IMPROVEMENTS  5.3.1.  The Pulp M i l l Model  One d e f i n i t e improvement for the pulp m i l l model i s a better data base.  The  following i s a l i s t of the i d e a l data base that would f a c i l i t a t e the development of a better pulp m i l l model. 1.  Hourly samples from the s i x major m i l l sewers indicated i n Chapter III,  determination of t h e i r BOD  and SS loadings, and pH  Also a  record of the hourly flow past each of the monitored points. Continue f o r one week of operation. 2.  For a period of 2 to 4 months d a i l y samples at the same locations determining t h e i r BOD  3.  Complement #1 and ill  and SS  loadings, pH and d a i l y flows.  with conductivity charts f o r each of the s i x  sewers with complete i d e n t i f i c a t i o n of s p i l l locations and the chemical s p i l l e d . 4.  Possibly make a more extensive study of the related s p i l l developed i n Chapter I I I .  concept  Such things as r e p e t i t i v e equipment  f a i l u r e s can often be modelled very w e l l with simple stochastic models. 5.  Maintain a record of m i l l production etc., such that implications of a production stoppage can be correlated with the data gathered i n 1, 2 and 3.  146  6.  M o n i t o r c h l o r i n e and h y p o c h l o r i t e s p i l l s a d e q u a t e l y s i n c e t h e y r e p r e s e n t a s e v e r shock t o secondary w a s t e t r e a t m e n t  7.  systems.  F o r the same p e r i o d s as #1 and #2,hourly and/or d a i l y samples from the main m i l l o u t f a l l s d e t e r m i n i n g t h e i r BOD temperature  and SS l o a d i n g s , pH,  and f l o w .  A n o t h e r p o s s i b l e improvement i s an i n c r e a s e i n the number of major a r e a s c o n s i d e r e d by the model.  However, i g n o r i n g the i n c r e a s e d d a t a  t h i s would e n t a i l , i t may  a l s o d e s t r o y the v a l i d i t y o f t h e s t o c h a s t i c  " b l a c k box" approach used.  To m a i n t a i n t h e model's v a l i d i t y ,  requirements  development  of more e x a c t t r a n s f o r m f u n c t i o n s to g e n e r a t e the r e g u l a r e f f l u e n t would p r o b a b l y be n e c e s s a r y .  T h i s t h e n g e t s back t o the problems o f m o d e l l i n g  the k r a f t and b l e a c h i n g p r o c e s s d e t a i l s . more d e f i n i t i v e model but may t o t h e purposes  5.3.2.  The  Such an approach  should give a  not i n c r e a s e t h e a p p l i c a b i l i t y of the model  a t hand.  Waste Water Treatment Model  Data was not as c r u c i a l to development o f t h e w a s t e t r e a t m e n t model s i n c e i t was  a m a t h e m a t i c a l model of t h e p r o c e s s .  needed f o r model v a l i d a t i o n . 1.  However a b e t t e r d a t a base i s  The i d e a l d a t a base here would be the f o l l o w i n g .  H o u r l y a n a l y s i s o f i n f l u e n t and e f f l u e n t f o r b o t h t h e c l a r i f i e r l a g o o n , r e c o r d i n g BOD  and SS l o a d i n g s , pH, t e m p e r a t u r e  F o r the c l a r i f i e r one week o f d a t a s h o u l d s u f f i c e . at  l e a s t two weeks i s recommended.  and  and f l o w .  For the lagoon  A l s o the c l a r i f i e r s h o u l d have  samples t a k e n every 10 o r 15 m i n u t e s over one o r two days t o get a  147  b e t t e r p i c t u r e o f i t s dynamic b e h a v i o u r . 2.  T h i s s h o u l d be complemented w i t h continuous the i n f l u e n t  One  and e f f l u e n t  c o n d u c t i v i t y c h a r t s of  f o r both c l a r i f i e r  and  lagoon.  improvement of the waste treatment model would be the i n c l u s i o n of  models and  c o s t c u r v e s f o r o t h e r p r o c e s s o f t e n used  ( i . e . , A c t i v a t e d sludge, t r i c k l i n g a user t o experiment  to t r e a t p u l p m i l l wastes,  f i l t e r s , e t c . ) By making i t p o s s i b l e f o r  w i t h v a r i o u s p r o c e s s combinations,  other r e l i a b l e  w i t h i n a m i l l s budget and/or space l i m i t a t i o n s c o u l d be e x p l o r e d .  These  models c o u l d be o f a steady s t a t e n a t u r e , i t e r a t i n g on a r e a s o n a b l e time s c a l e . to  systems,  dynamic  Of course the v a l i d i t y o f the steady s t a t e approach would have  be e x p l o r e d .  Another  improvement would be the development and v a l i d a t i o n o f a b e t t e r  clarifier  model.  at Waterloo s e t t l i n g may  I t . appears  University  from a r e c e n t communication w i t h Dr.  t h a t the l i n e a r r e a c t i o n assumption  be an o v e r s i m p l i c a t i o n of the p r o c e s s .  d e v e l o p i n g another approach  for  Silveston,  clarifier  Silveston i s currently  t o m o d e l l i n g the dynamic o p e r a t i o n of a  clarifier.  148  CONCLUSIONS  The purposes 1.  '  o f t h i s study as s t a t e d a t the b e g i n n i n g of Chapter I I were t o :  Develop  two  s i m u l a t i o n models, one  of the wastewater from a k r a f t  p u l p m i l l and another of a t y p i c a l waste m o d i f i c a t i o n system to 2.  the p u l p i n g i n d u s t r y .  Study  the c o s t v a r i a b i l i t y o f waste treatment  different  It  is felt  common  system  as a f u n c t i o n of  designs.  t h a t t h e s e purposes were s a t i s f i e d .  The  first  four  chapters  d e s c r i b e the development, s t r u c t u r e and v a l i d a t i o n f o r the two models i n #1. Chapter V d e s c r i b e s a sequence o f experiments  run w i t h the models to  determine  the waste treatment systems s e n s i t i v i t y both i n terms of c o s t and q u a l i t y of effluent, f u l f i l l i n g  purpose  #2.  The models developed a r e not p e r f e c t by many means and o f t e n r e p r e s e n t simplifications  of the p r o c e s s e s i n v o l v e d .  number o f u s e f u l f u n c t i o n s . 1.  A " b l a c k box"  These are now  approach was  A first  attempt was  summarized:  s u c c e s s f u l l y used  a p p r o x i m a t i o n of the water borne 2.  They have however s e r v e d a  to p r o v i d e a r e a s o n a b l y dynamic  e f f l u e n t s from the p u l p i n g p r o c e s s .  made to a n a l y z e c h e m i c a l s p i l l data and t r y and  i n c o r p o r a t e the e f f l u e n t  i m p l i c a t i o n s o f the s p i l l s  i n a model o f  the m i l l ' s e f f l u e n t p r o d u c t i o n . 3.  A r e a s o n a b l y w e l l v a l i d a t e d model o f a l a g o o n was found to be more s e n s i t i v e t o changes i n f l o w than  developed influent  and  149  concentration.  Also i t was  shown that operation of a s p i l l basin  can greatly reduce the impact of a s p i l l on an aerated 4.  lagoon.  The frequency of s p i l l s , which although observed to have l i t t l e e f f e c t on the e f f i c i e n c y of a lagoons performance, greatly affected the mean lbs BOD/ton of the e f f l u e n t .  The cost implications of  t h i s were found to be quite s u b s t a n t i a l . Also the size of required to meet the P o l l u t i o n Control Boards Level A was  lagoon also  greatly affected. 5.  A c l e a r cost dominance r e l a t i o n s h i p was  found for three of the  four waste treatment system configurations experimented with. attempting  to s a t i s f y any effluent BOD  less expensive,  q u a l i t y l e v e l i t was  When  always  given any size lagoon over 25 acres, to operate  the  lagoon less e f f i c i e n t l y and feed a l l the m i l l o u t f a l l s through the lagoon rather than bypass the lagoon with the acid sewer. 6.  The l e v e l A standard for c l a r i f i e r operation was  demonstrated to  be s a t i s f i e d with less cost, by feeding only the general machine room o u t f a l l s to the  These are the major r e s u l t s .  and  clarifier.  Many more observations and conclusions can be  drawn from the experiments run.  Also the experiments described i n Chapter V  do not exhaust the p o s s i b i l i t i e s a v a i l a b l e with the models as they now  stand.  For example shock load experiments for d i f f e r e n t s i z e lagoons could be  tried.  Shock load cycles could be experimented with to see i f there are any natural frequencies at which the system reaches a s t a b i l i t y threshhold.  More  experiments could be run for d i f f e r e n t s p i l l d i s t r i b u t i o n s to determine the  150  m a r g i n a l c o s t s o f r e d u c i n g t h e mean l e v e l s , e t c .  I t would appear i n c o n c l u s i o n t h a t the t e c h n i q u e s  employed  i n this  be o f c o n s i d e r a b l e use t o p u l p m i l l management i n making a waste system investment designs  decision.  could  treatment  The t r a d e o f f s become much c l e a r e r and a l t e r n a t e  can be examined w i t h o u t  the " r e a l world"  i m p e r f e c t i o n s o f t h e models s h o u l d be kept f u t u r e development.  study  Through c o n t i n u e d  consequences.  i n mind b u t o n l y as i n d i c a t o r s f o r  experimentation  v a l i d i t y of a model and t h e r e f o r e i t s u s e f u l n e s s grows. t h i s study has p r o v i d e d another  The  step i n that  direction.  and development, t h e I t i s hoped t h a t  BIBLIOGRAPHY  152  1.  Andrews, J.F. (1974) "Dynamic Models and' c o n t r o l S t r a t e g i e s f o r Wastewater Treatment P r o c e s s e s . " Water R e s e a r c h , V o l 8, 1974 pp. 261-289  2.  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(1973) "A G e n e r a l P e r s p e c t i v e C o n c e r n i n g t h e Cost of P o l l u t i o n Abatement a t Any S p e c i f i e d L e v e l " TAPPI, V o l . 56 #3 March 1973 pp. 126-130  24.  Howard, T.E. and Walden, C C . (1971) " E f f l u e n t C h a r a c t e r i s t i c s of Bleached K r a f t P u l p M i l l s " Pulp and Paper Magazine o f Canada V o l . 72, #1 T3-T9, J a n . 1971  25.  K i t a , S., and M o r l e y , R. (1973) - UBC- FREQ Goodness of F i t T e s t s Computing C e n t e r , U n i v e r s i t y o f B.C. (1973)  154  26.  Kormanik, R.A., (1972) "Design of Two WPCF'Vol. 44, #3, March 1972.  Stage A e r a t e d  27.  Lekander, K.E. (1972) " E n v i r o n m e n t a l Care a t Pulp M i l l s , R e s u l t s and Expectations" Svensk P a p p e r s t i d n i n g #1 15 J a n u a r y 1972 pp. 5-14  28.  L e v e n s p i e l , 0. (1972) "Chemical R e a c t i o n E n g i n e e r i n g John W i l e y & Sons I n c . , N.Y., 1972  29.  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Employing B i o l o g i c a l O x i d a t i o n " NCASI S p e c i a l R e p o r t .  34.  Mishna, P.N., et a l . " B i o l o g i c a l Wastewater Treatment System D e s i g n - P a r t s I and I I " The Canadian J o u r n a l of Chemical E n g i n e e r i n g , V o l . 51, December 1973, pp. 694-708.  35.  Montgomery, M.M., and Lynn, W.R. (1964) " A n a l y s i s of Sewage Treatment Systems by S i m u l a t i o n " J o u r n a l of the S a n i t a r y E n g i n e e r i n g D i v . , P r o c . of the American S o c i e t y of C i v i l E n g i n e e r s , SA1, F e b r u a r y 1964, pp. 73-97.  36.  N a i t o , M., e t a l . (1969) " O p t i m i z a t i o n of the A c t i v a t e d Sludge P r o c e s s Optimum Volume R a t i o of A e r a t i o n and S e d i m e n t a t i o n V e s s e l s . " Water R e s e a r c h V o l . 3 pp. 433-443.  37.  Naylor., T.H. et a l . , (1966) "Computer S i m u l a t i o n T e c h n i q u e s " W i l e y & Sons, N.Y., 1966.  38.  John  P h i l l i p s , D.T. and B e i g h t l e r , C.S. (1972) " P r o c e d u r e s f o r G e n e r a t i n g Gamma Vanates w i t h Non-Integer Parameter S e t s " J o u r n a l of S t a t i s t i c a l Computation and S i m u l a t i o n V o l . 1, #3 J u l y 1972.  155  39.  R a i f f a , H. and Blaydon - u n p u b l i s h e d m a n u s c r i p t Markov C h a i n s "  "An  I n t r o d u c t i o n to  AO.  Rand, G.H., (1972) "Elements of S e l e c t i o n f o r Secondary Waste Treatment Systems" TAP PI,- V o l . 55, #8 Aug 1972 pp. 1192-1194  41.  Romans, H., (1970) " P r o c e s s M o d e l l i n g and A n a l y s i s i n the Wood P u l p i n g I n d u s t r y : Wood P u l p i n g , P u l p B l e a c h i n g and Stock P r e p a r a t i o n " U n i v e r s i t y of Idaho Ph.D. 1969  42.  Ross, S.M., " A p p l i e d P r o b a b i l i t y Models w i t h O p t i m i z a t i o n A p p l i c a t i o n s " Holden Day, San F r a n c i s c o , 1970  43.  Sakata, N., and S i l v e s t o n , P.L., (1974) " T e c h n i c a l Note - E x p o n e n t i a l A p p r o x i m a t i o n f o r S e t t l i n g Rate" Water R e s e a r c h V o l . 8 pp. 491-492, 1974  44.  S e r v i z i , J.A. and Gordon, R.W. (1973) " D e t o x i f t e a t i o n of K r a f t P u l p M i l l E f f l u e n t by an A e r a t e d Lagoon" Pulp and Paper Magazine of Canada, V o l . 74 #9, Sept. 1973 pp. T295-T302.  45.  S i e g e l , A. (1956) "Non P a r a m e t r i c S t a t i s t i c s f o r the B e h a v i o u r a l S c i e n c e s " M c G r a w - H i l l , N.Y. 1956  46.  S i l v e s t o n , P.L. (1969) " D e s i g n of S e t t l i n g B a s i n s w i t h Allowance f o r R e s i d e n c e Time D i s t r i b u t i o n s " The Canadian J o u r n a l o f Chemical E n g i n e e r i n g V o l . 47, Oct. 1969 pp. 521-524  47.  S i l v e s t o n , P.L. (1972) " S i m u l a t i o n of the Mean Performance of M u n i c i p a l Waste Treatment P l a n t s " Water Research V o l . 6 pp. 1101-1111  48.  Smith, B.W., (1969) " D i g i t a l S i m u l a t i o n of Papermaking P r o c e s s e s " Appita V o l . 22 #6 May 1969 pp. 163-171  49.  Smith, R. (1969) " P r e l i m i n a r y Design of Wastewater Treatment Systems" J o u r n a l o f the S a n i t a r y E n g i n e e r i n g D i v . P r o c e e d i n g s of the American S o c i e t y of C i v i l E n g i n e e r s S A l , F e b r u a r y 1969 pp. 117-145  50.  Smith, R. (1968) " P r e l i m i n a r y D e s i g n and S i m u l a t i o n of C o n v e n t i o n a l Wastewater R e n o v a t i o n Systems U s i n g the D i g i t a l Computer" FWPCA U.S. Dept. of the I n t e r i o r March 1968 P u b l //WP-20-9  51.  Stephenson, J.N. (1950) e d i t o r , " P r e p a r a t i o n and Treatment Pulp" McGraw-Hill N.Y. 1950  52.  Stephenson, J . , and Nemetz, P. (1974) " P r o c e e d i n g s on on Economic i n c e n t i v e s f o r A i r and Water P o l l u t i o n " Research C e n t r e , U.B.C. June 1974  of Wood  Conference Westwater  156  53.  Swedish Steam U s e r s A s s o c i a t i o n , e d i t o r s (1974) Care P r o j e c t " T e c h n i c a l Summary - Stockholm  54.  S u l l i v a n , P.R.  and S c h o e f f l e r , J.D.  (1965)  P r e p a r a t i o n and F o u n d r i n i e r Dynamics" pp. 552-557  "The SSVL E n v i r o n m e n t a l 1974  " S i m u l a t i o n of Stock  TAPPI V o l . 48, #10  October  55.  Takamatsu, T., and N a i t o M. (1967) " E f f e c t s of Flow C o n d i t i o n s on the E f f i c i e n c y of a S e d i m e n t a t i o n V e s s e l " Water Research V o l . 1 1967 pp. 433-450  56.  Terhan, R.J., (1967) " S i m u l a t i o n i n the Pulp and Paper I n d u s t r y " and Paper Magazine of Canada June 1967 pp. T295-T300  57.  Walden, C C , Howard, T.E. and S h e r r i f f , W.J. (1971) "The R e l a t i o n . of K r a f t M i l l O p e r a t i n g and P r o c e s s Parameters to P o l l u t i o n " C h a r a c t e r i s t i c s of the M i l l E f f l u e n t s " Pulp and Paper Magazine of Canada V o l . 72 #2 pp. T81-T87 F e b r u a r y , 1971  58.  W i l c o x , L.R., and C u r t i s , H.J. (1966) "Elementary D i f f e r e n t i a l I n t e r n a t i o n a l Textbook Co., Penn. 1966  59.  Wine, R.L.  (1964)  H a l l , N.J.  1964  "Statistics  f o r S c i e n t i s t s and E n g i n e e r s "  1965,  Pulp  Equations"  Prentice-  157  A-l  APPENDIX I SEMI-MARKOV ANALYSIS OF RELATED SPILLS  In  Chapter I I I a semi-markov approach was  describe a s p i l l  sequence.  approach  c a r r i e d through  w i l l be  i n t r o d u c e d as a c o n v e n i e n t way  In the f o l l o w i n g few pages t h i s to determine  p r o b a b i l i t i e s and passage times.  The  semi-markov  the p r o c e s s e s  limiting  n o t a t i o n and l o g i c o f development i s  borrowed from a s e t o f n o t e s w r i t t e n by R a i f f a and Blaydon I n t r o d u c t i o n to Markov C h a i n s " .  to  called  "An  To the a u t h o r ' s knowledge these notes have  not been p u b l i s h e d , however, the n e c e s s a r y d e f i n i t i o n s a r e i n c l u d e d , i n the development and  the l o g i c should be c l e a r t o a r e a d e r f a m i l i a r w i t h Markov-  Chains.  A  s t o c h a s t i c process  s t a t e space, and a l l n > 0 —  {X  , n = 0,  n  1, 2,  ....}  with a f i n i t e or  countable  i s s a i d to be a Markov c h a i n i f f o r a l l s t a t e s i g , i i , ••• P{X  • n +  . = j X  1  J  =  P  {  X  =  o n  +  i  • X, — i , . . . . , X , o 1 1 ' n-1  l  =  t  = ^| n X  =  A s t o c h a s t i c p r o c e s s which makes t r a n s i t i o n s  i  i  ,, X  n-1  n  _p  i}  =  n  }  from s t a t e t o s t a t e i n  w i t h a Markov c h a i n , but i n which the amount of time spent  i n each  accordance state  b e f o r e a t r a n s i t i o n o c c u r s i s random, i s c a l l e d a semi-Markov c h a i n .  Now  i n the c o n t e x t o f Chapter  s e q u e n t i a l l o c a t i o n of a s p i l l area.  A related s p i l l  I I I we  have a s t a t e b e i n g d e f i n e d as  i n the c u r r e n t r e l a t e d s p i l l  is a spill  i n the same m i l l  the  sequence of an  l o c a t i o n as the immediately  158  preceding  spill  f o r the c u r r e n t major area.  f o l l o w i n g time sequence o f s p i l l s  Time of  i n major a r e a  l o n g , the f o u r t h i s 3 s p i l l s  the system i n s t a t e 1,  the c h a i n from s t a t e 1, r e t u r n s to s t a t e  and  (recovery  1\  2 Jrelated 3>spill 4\sequence  5/ 1 1  sequences. the f i f t h long.  The  is 5 The  first  spills  3 are only long  sequences must always  s t a t e can be missed i n moving  at the end  1  followed  o f a r e l a t e d sequence the  along  system  1.  From the data d e s c r i b e d i n Chapter I I I the f o l l o w i n g t r a n s i t i o n m a t r i x derived f o r s p i l l s  area)  rNrelated 2/spill 3J sequence  1 spill no  the  1 1 1  l o n g and  the s i x t h which i s a g a i n o n l y  have  S t a t e of System  25 13 1 4 9 12 5 4 2 5 20 20  I n the above t h e r e a r e 6 r e l a t e d s p i l l  s t a r t with  1 of the m i l l  Time Difference (hrs)  Spill  0 25 38 39 43 52 64 69 73 75 80 100 120  by  F o r example say we  i n sub  a r e a 3 (weak b l a c k l i q u o r s p i l l s )  See  was  Table A l .  spill  159  State  1  2  3  4  5  6  1  11/31  20/31  0  0  0  0  0  0  0  2  9/20  0  11/20  3  2/11  0  0  9/11  0  0  4  2/3  0  0  0  1/3  0  5  2/3  0  0  0  0  1/3  6  1  0  0  0  0  0  Table A l Note the system has o n l y 6 p o s s i b l e s t a t e s .  From a K-S goodness o f f i t r o u t i n e t h e times between r e l a t e d s p i l l s  f o r sub  area 3 f i t t h e n e g a t i v e b i n o m i a l w i t h p = prob o f s u c c e s s = .288 k = .801 T h i s i m p l i e s a mean r e s i d e n c e time i n t h e s t a t e s , 2, 3, 4, 5, 6 the mean of t h e n e g a t i v e b i n o m i a l  mean  k x (1 - p)  .8 x .71 .29  equal to  distribution:  =  F o r t h e times between u n r e l a t e d s p i l l s  1.95 h r s  a K-S goodness o f f i t t e s t  e x p o n e n t i a l d i s t r i b u t i o n , w i t h mean 0 = 156.4 h o u r s ,  found t h e  t o g i v e a good f i t .  T h e r e f o r e t h e mean r e s i d e n c e time i n s t a t e 1 i s 156.4 hours.  160  Now  i f we take the t r a n s i t i o n m a t r i x g i v e n i n T a b l e A l we  stationary probabilities  t h a t would be o p e r a t i v e i f the p r o c e s s were an  o r d i n a r y Markov c h a i n .  S o l v i n g we g e t : 11 9 Hi = — ni + — 31 20 A  20  "77  112  n  11 — 20  o=  6  and ST1 i  1,1  n  = 1  i  n  =  2  1  can s o l v e f o r the  2 H2 + — * 11  n  2 3 + T 4 3 n  2 +7  n  3  5 +  n  6  161  Solving the above simultaneous equations Iii  =  .414  n  2  =  .266  H  3  =  .22  Jl  k  =-  .12 '.04  n  5  =  n  6  =  .0133  These s i x p r o b a b i l i t i e s then are the l i m i t i n g p r o b a b i l i t i e s of finding system i n each of the states ignoring the state residence times.  the  The  following i s the semi-Markov analysis which w i l l take into account the d i f f e r e n t time  distributions.  Define: S_. x  =  state i expected waiting time f o r a t r a n s i t i o n from S  ±  to S^ given  that the t r a n s i t i o n i s d e f i n i t e l y going to take place.  T1 2  = T  3 1  = Tm  = T  5 1  = T  6 1  = 156.4 hrs  = 1.95 hrs E j j : = p r o b a b i l i t y of a t r a n s i t i o n from S given that a t r a n s i t i o n from S p,  . i s the p r o b a b i l i t y  ±  ±  to S^ by t =  <=° ( i . e .  i s d e f i n i t l y going to occur,  that the system w i l l be going to S )  162  Therefore define = e x p e c t e d w a i t i n g time i n  j Solving f o r a l lthe states Ti  =  PiiTn  + P12T12 =  1 156.4 + | £ x 1.95 31 " ~ " ' 31  Tf  x  w  56.8 h r s P21T21 + P 2 3 T 2 3 =  20  x  1  5  6  ,  4  +  x  1  5  6  '  4  +  x  1 5 6 > A  io  x  1  -  9  5  -  9  5  71.5 h r s T  3  =  P31T31 + P34T34 =  3J  11  x  1  30.0 h r s  f = 4  T  T  5  P  4 1  T  4 1  + P  4 5  T  4 5  =2  =  104.95 h r s  =  P51T51 + P56T56 =  =  104.95 h r s  =  P6lT l  =  156.4 h r s  6  6  + P67T 7 6  =  f  1 x  x 156.4  +  I  x  +|x  1 > g 5  1.95  156.4  Row i f we compute t h e p r o p o r t i o n o f time t h a t t h e p r o c e s s spends i n S^ as t  00  , t h i s s h o u l d be t h e same as t h e l i m i t i n g p r o b a b i l i t y o f b e i n g found  i n t h a t s t a t e o r (b*.  J S i n c e f o r t h e imbedded p r o c e s s t h e l i m i t i n g p r o b a b i l i t y o f a t r a n s i t i o n t o S. i s II. , t h e p r o p o r t i o n o f time spent i n S. s h o u l d e q u a l <j>*. 3  3  3  3  163  <J>* J  Therefore  (Tf^^^) i i i  =  S o l v i n g f o r the s i x s t a t e s  ]Ti TTTTT T-tH.T.  .414  n =  x  -  -266  x 71.5  .22 ^  =  f>3  =  -  _  .04  1 2  -  =  Note t h a t (f>* but  o n l y on  Define step is  the  2  6  6  0  =  _  ~  5  6  -  does not  4  fi  x 105  ^ l  „,, '  9  TTT^  7  ,33  „ . -°  =  x 105 71.5  0 1 3  56.8 71.5  -  x 30 71.5  -  ^  x  _  TTTS—  ~  Ix  =  x x  1  -  =  4  0 5 8 5  .0283  depend on  the mean h o l d i n g  the  form of the h o l d i n g  s t a t e Sy  the Now  l i m i t i n g p r o b a b i l i t y t h a t on arguing  intuitively,  the expected l e n g t h o f s t a y i n S_. then d i v i d i n g 4>^,  of b e i n g Sj on any  i n s t a t e j , by f step  of t h a t  distribution  times.  l i m i t i n g p r o b a b i l i t y ej as  the p r o c e s s i s e n t e r i n g  time  , should  interval.  be  roughly  since  any T\  the l i m i t i n g p r o b a b i l i t y  the p r o b a b i l i t y of  entering  164  Therefore entering  e* = l i m i t i n g p r o b a b i l i t y S. 3  t h a t on any s t e p  the process i s  _ ~  T  3  S o l v i n g f o r the s i x s t a t e s . . . 33 1 " 56.  =  .266 71.5  .0058  .0037  .094  >*  =  105  =  .0585 105  -  Define  iff ! 5  .00167  .00056  =  -  0 0 0 1 8  t h e l i m i t i n g d e s t i n a t i o n p r o b a b i l i t i e s $^* as the l i m i t i n g j o i n t  probability  t h a t on any s t e p  the p r o c e s s i s i n S - and the next  transition  w i l l be t o S.. 3  We know the l o n g run p r o b a b i l i t y  of f i n d i n g  the p r o c e s s i n  i s cj>*.  The  N t o t a l expected h o l d i n g this holding  time i n S  i s T^  ~  ^ i k i k' f t i o n s of K= i Pi • T i • time t h a t i s due t o t r a n s i t i o n s from S^ t o S^ i s —^3 2 P  T  T  n  e  r a c  165  Therefore  T h e r e f o r e we get  P .1.1 nT  x  ,33 x .355 x 156.4 56.8  11  =  .32  12*  =  .0104  21*  =  22*  =  23*  =  .0057  fcl*  31*  =  .087  $56*  Similarly -  .007  .261  =  .172  0  =  .0011  =  .0574  =  .00356  =  .0283  *3-*  *61*  transition  the l i m i t i n g  A g a i n note  p r o b a b i l i t i e s we can  t h a t the l i m i t i n g e n t r a n c e  p r o b a b i l i t i e s do n o t depend on the  h o l d i n g time d i s t r i b u t i o n s but o n l y on t h e expected we were not i n t e r e s t e d probabilities,  h o l d i n g times.  I f however  i n l i m i t i n g p r o b a b i l i t i e s but want i n t e r m e d i a t e  the e x p r e s s i o n s do depend on the h o l d i n g time  T h i s w i l l n o t however be pursued  distributions.  here.  One f i n a l l i m i t i n g parameter o f i n t e r e s t D e f i n e 9•• , t h e expected  step  i s the mean f i r s t  passage  time of passage from s t a t e i t o s t a t e j .  times. For a  166  semi-Markov c h a i n , the mean r e c u r r e n c e time, 0.., i s —, , t h e r e c i p r o c a l o f  l i e *  the l i m i t i n g p r o b a b i l i t y of e n t e r i n g s t a t e j .  3  Therefore 1 e*  174 h r s  =  271 h r s  033 =  327 h r s  e  2 2  600 h r s 855 = 9  66  =  1785 h r s 5550 h r s  From t h i s we can conclude t h e r e w i l l be a s p i l l sequence of s p i l l s . spills  at least  t h a t i n the l o n g r u n (as t -> °°) every 174 hours  i n sub a r e a 3 which c o u l d be the i n i t i a t o r Every  2 spills  long.  sequence of s p i l l s a t l e a s t  These r e s u l t s a l t h o u g h  271 hours t h e r e w i l l Every  3 spills  be a r e l a t e d  327 hours t h e r e w i l l  sequence of  be a r e l a t e d  l o n g and so on.  n o t used i n t h e model developed  u s e f u l f o r an a n a l y t i c examination  of a r e l a t e d  of s p i l l s  i n t h i s study  and t h e i r r e l a t e d  costs.  c o u l d be By  e s t a b l i s h i n g a semi-Markov d e c i s i o n p r o c e s s f o r a l l the major a r e a s w i t h i n the m i l l ,  i t may be p o s s i b l e t o a s s o c i a t e some c o s t s w i t h  the s p i l l s and  optimize the process.  S i n c e a s p i l l has both and  a c o s t consequence  p o s s i b l e above e f f l u e n t  spill  level  (the cost of r e p l a c i n g chemical,  f i n e s ) and a b e n e f i t consequence ( i f a  i s i g n o r e d , maintenance c o s t s , e t c . , a r e r e d u c e d ) ,  the r e s u l t s may be  q u i t e i n f o r m a t i v e as t o t h e t r a d e o f f s i n v o l v e d i n s p i l l m o n i t o r i n g  and p r e v e n t i o n .  167  A-2  APPENDIX I I DERIVATION OF CONVERSION FACTORS TO CONVERT Na S0 2  EQUIVALENT SPILLS TO GALLONS OF CHEMICAL  h  As noted i n Chapter I I I t h e g e n e r a t i o n is  i n terms o f pounds of Na2SG\  determines t h e s p i l l equivalent  (saltcake) equivalent.  s u b l o c a t i o n and c o n v e r t s  number o f g a l l o n s o f c h e m i c a l  Knowing t h e BOD and SS mg/l v a l u e s the s p i l l  The  can be converted  conversion  Libby  1.  model  The model then  the Na2SG\ amount t o t h e  t y p i c a l t o that  sublocation.  f o r each o f t h e c h e m i c a l s  (see T a b l e  3.9),  to i t s BOD and SS e q u i v a l e n t .  f a c t o r s t o convert  pounds Na2S0ij t o g a l l o n s o f c h e m i c a l  the f o u r l i q u o r s a r e d e r i v e d below. C.E.  of s p i l l amounts i n t h e pulp  for  A l l t h e a n a l y s i s f i g u r e s a r e taken from  (1962).  Weak B l a c k L i q u o r equivalent  (W.B.L.)  T o t a l sodium i n W.B.L. taken as N a 2 0  = 49.23 litre  Therefore  s i n c e 1 gm o f Na20 = 2.29 gms Na2S0i  t  for equivalent  of sodium t h e t o t a l sodium i n W.B.L. taken as a Na SOi 2  amounts  equivalent  t  = 49.23 x 2.29 = 112.74 g/1 Therefore  10 - 3 } &  2.  concentration  gm  2 ^ kg  Strong  Black Liquor  x  2  =  by weight = 16%. = 52.9%.  .94  ( i n terms o f N a S 0 ) = 112.74 2  4  x l  i  t  r  e  y ? \ o r 1.06 g a l W . B . L . US g a l o f W.B.L #  (S.B.L.)  T  p  T  1  3.785  x  = 1# N a S 0 2  F o r W.B.L. t h e p e r c e n t a g e o f s o l i d s  F o r S.B.L. t h e p e r c e n t a g e o f s o l i d s by weight  4  168  Assuming t h a t o n l y water i s l o s t a r e t r a n s f e r r e d through,  then t h e d i f f e r e n c e i n % o f s o l i d s i s a consequence  o f the l o s s o f water o n l y . 1 // o f s o l i d s  i n t h e e v a p o r a t o r s and t h a t a l l t h e s o l i d s  Now say we have 1 // o f s o l i d s .  T T =  Then  6.06 // W.B.L.  1/< or  Therefore  ~ ^ =  1.869 // S.B.L.  i n W.B.L. t h e r e a r e 5.06 I, H 0 and i n t h e S.B.L. .869 // H 0. 2  This implies that the evaporators, From L i b b y  2  5 06 — 869 evaporate — ' ^ x 100 = 83% of t h e water  (1962) s p e c i f i c g r a v i t y W.B.L. = 1.087, s p e c i f i c g r a v i t y S.B.L. = 1.325.  Therefore (note:  —^r~  1 g a l W.B.L. = 1.087 x 8.3  1.5// a r e s o l i d s ,  n  =  9.lit  g a l H2O 7.6// a r e H2O)  T h e r e f o r e a f t e r e v a p o r a t i o n t h i s 9. lit of W.B.L. w i l l be reduced t o 9.1// - .83 x 7.6#  — - ?° _ = g a l of W.B.L.  2.8# S.B.L.  H  I T  T  T h i s 2.8// o f S.B.L. w i l l have t h e same Na S0i 2  Now 1 g a l l o n S.B.L.  = 1.325 x 8.3  e q u i v a l e n t as t h e 9.1// o f W.B.L.  4  " „ _ 1 gal H 0  =  11.0//  2  T h e r e f o r e 2.8// S.B.L. 11.0// S.B.L.  .941 // Na SG\ 2  In o t h e r words 1 g a l S.B.L. has a 3.7// Na S0 2  Therefore  3.  1// Na S0, 2  Green L i q u o r  1 f t  3  4  =  (G.L.)  G.L. c o n t a i n s  .941 x ^-r  1 g a l S.B.L.  =  2.7 // N a S 0 2  4  equivalent  t+  .27 g a l S.B.L.  From an example G.L. a n a l y s i s i n L i b b y (1962) Na S  -  1.4// N a 0 e q u i v a l e n t  NaOH  -  1.1// N a 0 e q u i v a l e n t  -  5.9// N a 0 e q u i v a l e n t  2  Na C0 2  3  2  2  2  169  Total a l k a l i content = 8.4// f t as Na 0 3  2  m,. , . . . , Na^SOu equivalent Thxs i s equivalent to 8.4 x 2.290 = 19.2 // — — ; ^ , „ ft° or G.L. Q  0  o o r i  i n  0  c  T  Therefore 1// Na SO, =19.2 0  ^  4.  H  White Liquor (W.L.)  N a  ? ? * ft° S  1  x  1605  « .325 gal G.L. gal  From an example W.L. analysis i n Libby (1962).  In one cubic foot of W.L. there i s  Na S  -  1.4// as Na20 equivalent  NaOH  -  5.5// as _Na2 0 equivalent  Na2C03~  1.5// as Na 0 equivalent  2  2  Total a l k a l i content = 8.4// V 'i** ?, f t o f W.L. 9  T  J  f t -1 = .325 gal 3  Therefore 1// N a S 0 i s equivalent to 19.2// 2  4  N  a  ^3  H  x .1605  170  A3  APPENDIX  III  A LISTING OF THE PULP MILL MODEL (FORTRAN) The l o g i c a l units are assigned i n the model as follows L o g i c a l Unit //l  Task Record of Daily production, water usage and f i b e r losses - i s generated by the model  #2  Record of s p i l l s i n major area 1 - generated by model  #3  Record of s p i l l s i n major area 2 - generated by model  #4  Record of s p i l l s i n major area 3 - generated by model  #6  Record of t o t a l l b s of BOD,  TS and SS generated by  m i l l each hour #7  Input f i l e to be supplied by user f o r d i s t r i b u t i o n parameters and other empirical data needed to run model  #8  Record of BOD,  TS and SS concentrations f o r each  of the 3 o u t f a l l s each hour (mg/1) - generated  #9  by model Record of hourly flows f o r each of the 3 o u t f a l l s (in MUSG) and the hourly production ( i n tons) - generated by model.  Note:  Units #8 and #9 are used as input into the Waste treatment model.  171  kr Ul vr vn i f \ji  Ire -J  OJ  f* lUi  ui u J> J> J*^ 1  IV'  H O j\D CJ -0 O U' J> r  Ul lu  P O Tl 73 n  O ;TT  ;» o  7 n  [<  H  c  n  !  t>  I-I : > .  -i  <r Z  NJ fsj OJ M rvj rsj f\J rvi r\j sNJ IM o; -J o\.r. 4 U-M1 t— O  l»J!UJ Ol OJ [tv> U) tvl M O U  OJ fM  > lo M  c  vr o-  |C/  X- J> 4- Ui  IV-- It  It  H-  n n rr ! o > n i> i L> —  j  ,>• O JT' y v_'  O  r, -H 'in J" y r~ - . —i o • — 1  - j  C~ II 1 C t-- »--  C* >  wX  K  172  nno  or,  |cc ^ o  --j  --J  -j  -J •-.! - i J>  -vt C Ul  fV  O vr.  o o <"* o r 1  C O t— O sT>  i r~) ^ o 0 cj .-. p  Z. ZD •;-}; O  —  |> r, o ii> T I i 1 ~\\r- — II  -si — ;l~ c, >; o :< I o i> |  II m .-, A l i p . „|.  1 JO ^ -  J  n "1  coTl >0 ', ~P O JO t'-i rr O f~i f" 1  -1  j II  11  !o o  r:  -c- i — ^* >  • -H ^ ^  II  I  lo  II  o  o  o  ~- : o  o  y  'C: " r  T.  r  U5TI...G  ILF-  rp H i t  11 7 lit 1 IS 12  1  10  123 12-, J 127 UP 12? 13U Iii 132 123 134 131= 136 13/ 131 i3 ; 14C 1^1 142 14 3 14-t 145 146 147 14S 149 bC 151 152 1 S3 154 155 15o 157  65  1  u  12 5  i  T  R  r  1  v  f  122 129  76  r  J  ZT s < i ) = s i ; )  .2  T  I F ( I J J C ( I ) . b T . S t x { I ) i SAXl vi ! 1 = /. -V K I ; i M i r t C r i ! ) . L T , S c " . I N ( n i S f - ' r . ( : )=/riot i ) :<(:>=.-: 7 s < i) I P ( n < (i J .Ai.UM'lM!-L> L^Jjli ( T.vi; I J =L T S( I ) I f (27 5 ( : ) .L T .ST v 1 >i t I ) j . > IF (ZSS ! i ) .07 . S ? > « ( I ) iSSi-'i ( i ) = I, ( I ) 1 F I / i S 1 1 1 . l. 7 . S M •; ( ! ) 1 (s IS ) 1 1= Z S s. ( I ) GO T G ( l t O , l j j , l 4 C i » I P E A ) ( 2 . i 2o ) T I t ( 1) , 10;. ( 1 i )), i, A i S l i ) J I K 1 ) = .I < 1 )..•! GC r c 1 ) 1 Al) °. L AJ ( 3 i U o I 7 i v. {£) , . } & ; U J . T S U ) T I M ( 2 ) = T l.-ir 1 2 ) +7 GC TC l C I PL AM ( , , i j .•)) 7 ; K . ( > ):o ( .),; . i . ) S(3 ) c  lit l-s, loC  130  161 162 163  135  164  140  It 5 It 6 167 16t loS 17G 171 172 173 174  ( CM 1 NU ' , ( L i , K :, < i ) h .': I I < T L. 'i»( i ), -A ( J ,.U )U 2 i L A ' ( r,U • ( J I , A S •> ( j j F 0 r. ; AT ( ...1 1 o » 1 ^ t - i v . j j i = If 1 [>=0+l I F { J - Ni ) ,r. 1 o 12 (r i t Ai ( 1i 12J ! i I - 1 , ^ ) I ( L C «lTIU)--,rlT( 1 I / >A7T(2 J ' U iH I • ) > (*-> I \ (3 J 16) P R C ) T= f < :>ii« 2 4 . _ * :MJJ t . . ? t . l ^ ) U A T T ( n t = i i J •<")JT, T F J ,•! A T | 1 < , , P'-,. 2 , < L C . i , 1 3 ) CALL tGUL 0 0 1<J 1 = 1,3 7u I .= ( 7 I 1 ) ( .tO.T)GO GO TX Ii CC\ T INL / iCi. ( ! ! : ; ' ( i ) * 2 . 2 Z ? > [ I ) = <?. ; ( i) * 2 . 2  ,v  T  7 IV (3 )=J.l -I.:; ( )_U S P L ( 1 )' = ' >f L ( I ) + 1 CCOTIOL': H H00 ( 1 J -K :s l-;->H ( 1 i HT S( i ) =•1 Si'r ( i ) MS S( 1) =•'SS2ri( 1 ) no i C J •-2. • O-JO, ( 2 ) •-•i • . ' . / ) + •••'0 )->h ( /' / ;. . ( : - i i nl5( 2)=- 7 b ( 2 i T . a y n ( i ) t . T•»( i - u HSS(2)=HS b( ? ) + ^ !  101 15  1  :  ;  : .... )  174  fsj rsj iro ro r\ro < ro N>!rvi ro rojro ro no jro ro roro ro ro tisj ro ro ro ro lr\j ro roro r\j f\j i—i ,—* i—i io r\j ro roro N- r\j jro ro rro o ' t~ o o o o O O vn ^ >T. vO cr: r.: M O vT CO -sj < ^ - OJ iro c Un co -oCT- O " J > o; ro *-* ?• u* \ > > ro OH- CO •vj c v.n -f w ro jt~* o 00  —'  \CJ  1  L>  (/- —«  -7t/i co jrj -i  CO  (/•  "Tl ; i  uo  —1—i <  ; X;  > —- •—•  TJ 5L r.  Ci  A-  —H  C/i  Olo  ~i —  vX' U"> „ ,  r  !t/> C ., ' — O l •"•;IW ; w  —Oo  r-. U — [ • « X |(^ X u - io o  - -i  —  w .  C-  c  r- — •  j  Ti T t—' -—• K~ ! —i O .'"1  jro •  . j"  :r\i r-  *«v  » l jK -J -SI o v vj 1  — — m,  I  |..r.  5  175  vj po r\irv. rv rv |r\> rv rv rv rv r\jro rv rvro i\j f\j |ru iSj r\j ifsj r\j rorv ro ro f\j r\j ro (\J(ro o- rr- vr. ^.n ivr vrvr vr. \. ^ J> |rvj rvj rv |rv> rvrvr.v- rv r\j r\. n -C- -t> 4 -J ;v?- O er-CT- Cr- O u: • Vr ro > — 4 U J rv I- O v T > rs.' t—  i ro tv r\j ;i i (r> or.  O O : in  II  v,.  ;> r~ \  ;T-  IT;  X *  r<  j,-  ;  7  II  !  r*  E> —- i  -4  :r . o  Ci  Hi u  A'  rr f~i  tr,  7 -1 7 7 :7 — 7-  U.  xi •* *  r> c~  "C •* , iO —I - i-— _<; rolr. — > —I- I • — if; - > -. x. —-* ! ii  rn  —* y  »  cr- O : -1  'O  <S  I —  :0  T;  7-. »  •  T  T  ',  ,  :  C Iv. IA > 7 7 7  . * C-H  " f~  -» f.O  UJ iv 7  I— O C. I  X O'r-i  T  7*  A 7, ^ i  I  H  7  >. c-' —  , 1  —  • .-1  j — I  T» II  r  > V  LISTING CF F II. " 29 1 2 92 2 or. 2v4 29:; 296 2', / 29 c 29 9 30 0 301 3C2 30 3 3 04 30b 306 3C 7 360 309 2 10 211 2 12 313 3 14 2 ii3 lc 317 2 1 fa 3 19 220 32 i 3^2 323 224 32 320 327 22b 3 29 220 321 332 32 334 33b 3 36 3 37 33< 2 39 340 341 3 42 34J 344 349 346 34 7 34£ 1  3  r  JL"-  i L : L: A.y .  :-L . ' ( i,* f.))  I F ; :>.i  i:,  .:.  i-,  J i (. v j ^_ ;,.  .-• - v ^ \ ' M - < i c . . v; . ; 0.1 v 2 i  c C TIM:- V. • V .... , i > • L., r • L f. 1J \ ? - h AT-: i J ., i) f- = \ : > I' IKS) M>y i ,•(<•• i ----r(.-..-.,-•, Vf i | u < -co.. ;T..-• o (-'.\ ); , T-. J "; = '-•• S=bS(<r, ) L =K < + -J IF (L :..) TC 9 u CALL ; \ i (•• . o , CT/ r, c, !•<.) TI ( K rx ) =T + i . 0 IF ( T IV F ! KC ) .CT . 1-2 ) TC 1 C 11 T i y t K\ ) =T ; - j- ( y K j T = T «• T 1 ( f i* 1 (ALL ' Mi-'.lt 1- i jTpC-iTiM ,f ) V T ( K< ) = l-i.)0 • L S = C S L H (<•-. K i A AI- T ( < K 1 = -i -1 I ( < ) •• c : \ V1 C S ) 2o co\Ti ,u t> JC ( KK ) =r.r-.!F (LSI*' A-'T( < < K- j T S (\ K ) = 1 S M L 9 1 -• A T (r ) XSS<KK)~SSF I L S I ^ A f T l K M o sP( Kc ) = \ u , C, J TC 1 70, 7 9 ,rtO) ,KF 70 WHITE(2,71)LS, T I M K\),- Ay! | M C ) , A Ci ( » M , T i U . < ] , / A S 1 I- K. ) G J T j 9C • yCLT ( Kri) XCK<) i( "K. ) 75 y I r L ( 3 . 7 1 i L S , T }•> [ K. < j, ,/ •*A ts i , T ; ,( GC TC 9 0 ,XbS(KK) ii 0 R I I C ( <, , 71 ! L A , T I M , < -\) ,. , i\CL> ITH M( ,^ 7 K J S ( KK) 71 F () 4 AT ( 1X , I 'j , 1 1 0 , 4 F 1 3 . -. J 90 I F ( i .3 F . I T I y. ) CC TC HU GO TJ 1 100 f.CMIN LA 'V E T 0 R \ CMC C c su-i-c-oTiyc »'.TCJ (PS j o i , v>-Ur r <,i... »iT,nAT,W) c C WATfH U S A G E " y CAY A r ';, M,T C 0IM D 1 V: N i 1 • • \ . • < ,i T ( 3 ) , v T F - ". ( 2 , i i , 2 KCAL !-iA!i;T N= l :  ;  r  R  ;  :  ,;  r :  v  r  n  D  Ki'4L'= H A'\ ; ( 0 . 0 ) DC tC 1-2,1) 1 F ( X NO . C E . A A Tt - A ( , I , i j . . y :1: . ^ t " , I-1,1) ) L = - ! - l ) . AC,lv 0.WAT 40 CCM IMU 43 T»A :AY = ; A TC <•< I y, c, 2 * +( i.. AT C - •i, A (L> i,2 > — - AT:: -f-(- , C, 2 ) ) / ( - A T ' (• , 1 , 1) ) 11, 1) - ATI M !, L , i ) ) ) *< t- .,D---.TH k ^ T = T •. i\ 0 A Y / 2 "i . CO ,'C K = l 1  ;  1  rt  -  I ^  i. 1 .y , L +  177  * ^ -r-  X-  o o  o IO O O O Ul 4> |IU M -  J> O  OJWWW  U)  o J"  *n  UJ sO  U> U J U ) U ) U l U J vO sO  vri vr -J>  U ) IvJ I U ) U l  rr:  Ul  ui ui: ui  UJ  Co -J cr ;<_- 4> M  u. ro  UJ  u  - C ' C C s l  1  UJ  -0  UJ u w *-i o C- lUJ LU lo ro O r" I-J c-  UJ ' •  U] OJ tv) . U J u.  O  r"  oo o h» TD ji.o —< t— • —< 1—I - jf/— iv s, —1 • i *— — O II (--.Ci rr • T> ——• *— II - — >- i: , L s. li •—. r~ ~ — —" —• n '/ • : ^ — i ;r — s ; /-ij r~ —< _j C {/i r~ « r* C. «• 1/1 o —4 —1 »— .—. — >-; f~* —•— -„^ ~» Js." —1 "J i; — O s. X '->> w + > — • Il •T T >J — . s. ix. > •i - ^ . s. s. -TT. — -—f r. J"*"; > i~ ~Z•* i.r i'sj i r• n —i c :r, <rI'—t -.' .— •— I C j — J !/•• —• Cs". \*— -• ! — s. —• s. * « —~ * " >s. c. -< —i - X.—. _r • —( X j—J r; —> — '" ,X v • s,_ j. r~ *TJ </• •* | T - •• — T- ir. *~ —i —! TJ  —* <•/•  ir  o o  c —<  l~  '•  1  s.  O  *T  *  "II  2  n o, — r 11 r t i -i ^:  x- o n  oa  —  O  "->-  i/0  r  ll  _  w  ro - M 7,  —i  r  -  I  ty —  s/ —-  —  i—  c  r-v  —p l*—  I—  ->  .•->  -  C • ;>'~  -*  *— I—.  c *-  7-' •* sC —-* i —  — — s.  * -v.. c h  —i  L-  r-  — i  ir- — j. —- ;•/• —1 is c j<.!(/• — —— { « / • . T, k!— TJ —1 Z, r-ss < .<~ - — I !•*" ' — )i •s. ^. <^ i. ; _> !w — 1 *— r .- •—'U •-• •-" |—i w > s. 's, M U > — * —.' —- • •fc- ;.—. • • -SJ —v. — >; c -is s.* l+jv'. - .—. w u; J> -I"". i.r. is J. c • —i --j ( A V' , ; j—i *_ —1 ' —• —t 4^ '  — — — s— »• •— —1  rr  —-  C  A  o r~  r  C" w  1  1  o  t"  { *— •n  —1 z  T —t  C  h  H  l;> i. j—'  "If  tjO l>_  rv O"  ii  c  C  UJ  L U UJ U-l U- O-J V U~ m '  UJ I  O  1  LJU  IJJ  KP  V  H- C  US  sT  178  |j> x-  JN J>|. JN > .  !> Js |j». 4> J>  Irr v-r j> jui ru  IN) I—  —  o o  ui i .  i  JN  Ul V i V vl OJ IV |  > i> >|r\j r\j r\  >  II  It  c. ct  c:  TJ -Hi  r":  —i  •> X II II * 1^ 7- II - ,L -I'? A X | _ I. V,:  XT- X X| —n — t [ n i> - •' • •< IIn UJ « i H x [ i • -I X I !:-, VjJ - | • —rc_.il rv: i if •  Kr  x  o  J> J> J>  c. -j  r~, cz  179  A4  APPENDIX IV A LISTING OF THE WASTEWATER TREATMENT MODEL The  l o g i c a l u n i t s are assigned  i n the model as f o l l o w s  Logical Units #5  Task To s e t the d e s i g n parameters f o r the c u r r e n t experiment  #6  Record o f h o u r l y e f f l u e n t  from t h e m i l l i n mg/l and  l b s / T o n a t the end o f each day #7  A f i l e o r i n t e r a c t i v e d e v i c e which can answer the questions regarding f a c t o r  #8  The i n f l u e n t i n mg/l.  #9  concentrations  T h i s i s read  loadings f o r the 3 o u t f a l l s  each hour by the model  The p u l p m i l l p r o d u c t i o n and water usage r e c o r d as i n p u t i n t o the model  The  d e s i g n v a r i a b l e s which can be a l t e r e d by the user and read  from u n i t #5 a r  TIME = time s t e p f o r lagoon model = 1 hr A = s e t t l i n g r a t e constant  d e r i v e d i n t e x t = .104 cm  DET = d e s i r e d d e t e n t i o n time f o r c l a r i f i e r  (3 h r s )  QQ = t h e o r e t i c a l h y d r a u l i c l o a d which c l a r i f i e r w i l l have as i n f l u e n t (35,000,000 USG f o r ICOMB =2,3,4) H = depth of c l a r i f i e r = 15 f t T I = time s t e p f o r c l a r i f i e r model = 3600 sees ICOMB = system l a y o u t d e s i r e d f o r r u n = 1,' too4 Ak = dummy v a r i a b l e TEMP = Lagoon o p e r a t i n g temperature = °C AREA = a r e a o f Lagoon i n a c r e s DEPTH = depth o f Lagoon i n f t  180  Ul Ul ui Ul Ul Ul Ul Ul Ul > •o-- .p* OJ I— o  re  C- Ui  |UJ M  h-  J> u  |£ -  t> -n  ^  U) l_ tU f\J |ro i\j ro rvi rv ro ro  ui -r- t_;  O  |-i II  —t >• rr.  IM I—  t\j i o •  ~J  C-  Ul  '  •x>  w U- Jt tOi ) Ulw U) K l  PI  o  II  o • o II  o o  ~  n •  ml<:  Ii  1  IT.  |_ < x-  ier)  | * ro  rf  >|t- * Co-  O  I-J  • fl ^-  ,\j -  i-  —  l-J  LISTING 59 60 61 62 6j 64 _CJ> 67 66 69  ^  A.M.  ^  14  I H A N S . s n . O . JGiJ TJ=0. ST- = 0. FACT r = .!. . CYCI.F-C. CO n j i ' , •: > • . : {;,:,)  6  F 0 PA A f ( I X , • I r-jPt T~ 1 J M 7 O ~ ' 1 iT"" \ -j _h:,.0«T  .  19, 1 9 7 9  • t,  = JM  T  (  Td 1-  :  F A• j ( /, 7J TJ , ]-IP FCP-1AT ' WP. I TP ((2F0.Q) 7,0) 8 FUFA.AT ( IX, I IFCT F.,CTU-' POP V W C K IX AOS F•_>.J ' ) °.t AO (7 . A) F A C. rCFA 9 FOR'-'AT (1-9. 0! WP 1 1 0 ( 7 , 1 1 ) 11 FORMAT ( I X , ' IOPQT CYCLF I A. F . . . ' l P F A O ( 7 , 1 2 ) 0 YC LC 12 FOPMAT ( F i .0) 13 w'P IT F. ( 6 ,2 i A ,Oi:T ,9 J, H , ICC , 2 FORM AT ( IX , • A = ' , F 5 . 3 , 5X , ' OF T'= ' , F . . I , 5X, ' 0 0=' , F 1 0 . 0 , 9X , H = ' , F 5 1 .2 ,9X , • ICCMB= ' , 13,/ ) WR IT I: < . .3 ) AK , T C in , APF A , PLP1 II ,KK , VL AG 3 FORM AT ( IX , * AK = ' , FC . 5 ,4X , ' T F MP = ' , F9 . 0 , t X, ' APEA=' , F6 .0 ,4X , ' I'JbPTri= ' 1F4 .'J ,'tX , ' KK = • , Fi;.9 ,4X, ' VLAC= , F 1 . . 1 ,//) u'RI TP ( 6 ,1 0) TJ . FACT CP , S TCP .CYCLE ; 10 FORM AT ( LX , ' T J = ', FO .0 ,5X , 'F ACT.) <= • , Ft:. 0 ,9 X, ' S T _ ° = * , FO.O, u X , • CYCL L i.FS.O,///) C__ 7  70 71 72 Vi 74 79 76 77 78 79  1  1  ec  81 82 83 84 Gi> £6  1  87  C READS  oa  ^6 S7 98 99 ICC 10 1 102 103 104 1051C6 1C71C8 1C9 110 U l 112 113 114  *A S T E-1-1:10 P |.  iJ  66  89 90 91 92 93 94  CF F I L E  c  100  '  40 C C FLOW , C 65  70  " 75  76  THE CAILY '/.' ATI- P FLGw  •  FO* 3 A=*EAi  1 Al ML, SO / HR — A N C  CONTIMUE RE AO (9 , 40, EH|)= 20C) ( WAT T ( I) , 1 =1 , 1 ) , PHUO F C M A T ( I X , 3 F O . 0 , F10 .0) 3  AFRANGcMcN TS  IN RESPONSE  TO i CU MB  GC' TQ( 69, 7 0 , 7 9 , 7 6 ) , ICOi'B 01=(HATT(I)fWATT(I)+WATT(i)) 02=0. 03 = 0. GO TG 80 01 -yiATT(2) * AATT (3) 0 2 =W A T T ( 1 ) 03=0. GO TC 80 Q1 = ,JATT(2) Q2 = .1 AT T ( 1 ) + U AT T ( 2 ) 03=0. GO TC 30 Cl=OATT(2)+WATT(3) 02=0. G3 = M . ' AT T ( 1) CCMIMCE  -0 C C LAGC.CN 24 PP, PARAMETER S C  115  FLAG = ,;H-Q;  116  T T = 7 T / (KLA_*3.*/££*1£6)  DAILY  PULP P  f  LISTING  CF  CN 00  V  i : i  A . . , .  iv.  JOG.  1,75  Wi-f-M:  D  13  119 120  Ul  122 123 124 125' 126 127 128 125 130 131 122 133 134 135 136 137 13 8 135 140 141 142 143 144 145 146 147 1.48 149 150 151 152 153 154 155 156 15/ 158 • 159 160 161 162 163 16> 165 166 167 16 8 165 17C 171 172 173 174  L  A L r • IT A = 1 . +K K = .= T T E = h XP ( (-ALf'H 1 A ) ---T S "C-/ r ! ) = T I f't" / T T KfcT \= ( Al. Ciir A / T T - l . / T T ) i; X X = L A F i - T i KL / i i ) 0 = ;a+02  117  lie  V ?  wASrfc'-.M'MFt.  FILE  c  C C L A R I F I F P 24 O00-' P./'.»Av;;r.=  C  CuC=!,'l/ !oOO . :  E S T = V V / ( 10 ••• 1 b 6 ) PH = ( ! . *• C K - P t i T ) EE-EXPi ( -AL°M* n / H E S H )  P.  AL  ;EX ••..<•>I-T! / \  :  c 81  :  s"!  CCMI.MLE T=T+1.  0 = t> 1 .  c  C RfcADS I O F L U K O T COOC E N T AT I 1 — ,"-'G /L OF UOI) A ;\ j S S F K U M t A C H OF 3 C I L L C P t Aij ( 3 , j 3 , t = 2 C Ci ( C t<00 ( ! ) , 1= i , 3 ) , < C S S < J ) , J = 1,3 ) 35 F 0 Ri"i A T t l X i & F l O . C J C. C INFLUENT CCoC 1N RCSFCNSc T C SYSTE". L A Y O U T -- ICOOB C C 1N1=CLAK ! FI FIX S S 10 F LUr. N T — O G /L C C S S C T H = SS IN S T = . = fK T l - A T i.iYPASSCS C L A P I F I E K — MG/L C • I t>INCL=rtO.) I N T O C L A P I F I C P .iOO T02N TO L A GC I. Ai - - M G / L C Z=L!OC INTO LAGOON »..UCH i.YPASSfcu C L A F. i F i ;- K — f.G/L C CSSfiYO = S S OF S TPS AC hr. I C H B Y P A S S E S C O M P L E T E 'SYSTEM-- l-Ui/L C CBOCi.U = BC;j O F STREAM WHICH liY PASSES C C M F L E T E S Y S T F . M — M G / L GO TCI 8 2 . 3 3 , c!4- »fc3 J i ICO0ii 82 C 101 =( CSS ( i ) *f, A T T ( 1 ) K.$S (2 ) *WATT (z ) +CS S ( 3 )* .-.ATi ( 3) ) / Q l CSSOTH=0. C8 IOCL = ( C 600( 1 ) "WATT ( 1 ) + CHOC (2 ) ^ w A T T ( 2 ) +CBGO( 3 ) * *A T T ( 3 ) ) /O 1 l-C. CSSi>YE = 0. COCi)ijY=0. . GO TC £5 83 C 1 M1 = ( CSS (2.)"W-WT< 2 ) + C S S < 3 ) * / < A T T ( 3 ) ) / O l CS-S.HH = CSS< 1) CU I"jCL = (CMC ( 2 ) *WATT (2 ) +CfJOD (3 ) * W A T T ( 3 ) ) / 01 ' Z=C30C!i) CS.StlYE=0. CbCOBY=C. GO TO ti5 84 CIM=CSS(2I C S SO T H = ( C S S ( 1 ) < w A T T ( I) + C S S ( 3 ) - A T T ( 3 ) ) / C 2 C B IOC L = L BCD ( 2 ) z = <;: BCD (11 *wAT T (11 rcnoi: ( 3)-*ATT I'.3) i / c * CSSGYE=0. CECCBY=0. GO TO 63 •  ARIAS  •  ;  86  C I M=  ! C S S (2  )= W A T T ( 2 ) + C S S (  CSSOTH=0. CB IfwCL = (C30D ( 2 )  Z=C.  * ' » A T T  3  )='  . . A T T ( 3 ) )/O  (2 ) +C400  (3 )  1  * «AT  T (  3  ) )/.U  •  f  V  > — • —  I  LISTING 175 170 1 77 170 179 130 131 182 183 . 184 165 18t 187 188 189 190 191 192 193 194 . 195 19o 197 . 198 199 2GC 201 2 02 203 204 205 20, 207 2C8 • 2C9 ' 210 211 212 213 2 14 215 2 16 2 17 2 18 2 19 220 22 1 222 223 224 225 226 227 228 229 230 . 231 232  CF  In A S T E - .100 E L  11:31  CSS-YF-CSSi 1 ) (. t)COGY=L : i l "J ( 1 ) CCI\ n \ L  •  FILt  85 C C A R T I F I C I A L SHOCK c c c TREAT l i t I S P O U R S C T'< = T J + STE-' : :  ro i i CC N f INCH •  _ > ! . S il'-IR  IS  A.M.  AOS.  19,  1975  I0=MT2_  "  Ad  i \ !• L J E NT  GO  36  AC  OS  =3  . /if  j  . (c  I M » 0  I * C S S C T M ' 02  i *<  F A C T . J A -  1 . )  ' AO D C = 3. 785 CiA I NCL -•'02 )'••(-' AC T C - k - l . ) .vOLCCV-M.CO/ ( .••)3_7*3.7;ci ) C 1 M = FACTOR*C 1 'U C 3 I N C L = FACT0-*CI)I.JCL CSS )T-i = CS.vjTri=i-FACTCR • C S S 0 Y E = 0 S S ti Y 0 * F A C T C R C 3 C 0 t Y = CH.aCtiYv FACTOR _=FACTCRvZ I F (T .F|0. TK) T J= T K + C Y C L t i:  87  90  CCtNTINLE CALL TREAT vvR ITE ( 6, 70) CI N i ,CS2 .CSSCTh ,CrilAtC.L , Z ,CB'JCOT , T FORMAT ( I X , 6 1 F 8 . 1,4X) , F y . C )  C C D A I L Y INPUT - OCTROI S T A T I S T I C S GET E P R 1 RE C c DAYriCD = CAVBGC.+ (CfcP0 3T~'C +C tJOG 0 Y -'0 3 J * . . 7 d S SSS = (C I M * T 1 / ( AlFri*-*2) I M i . - i EE ) + (C Z ERG i« R c _ T / ( A I _ P H *I* J_ M E E - l . ) 1 + ( CZ ERI)2*RtST / ALPli ) * (1 . - FE )-GZ ER G 1 v T I *E 11 AL P H SSS=SSS/3oOC.. . GAYS S = OAYSS+( S S S * G H - C S S C T H - C ^ i - C S S-Y-"U.).*3. 7b9 0 I i\B_0*D 1 N s C » + (CI; I NCL*0 1 *l "Q 2 + CO 00 b.Y *<} 3 ) <3 . 785 01 ,\SS = i)l R9S *- ( C l M * 0 i + C S S C T n * C 2 +C SS OY t *03 )* 3 . 785 B l R = B I M C r i l N 0 L * G l + Z*q2 bCLT = ;3Cl;T+CfiG-.3UO F L =F L + 0 U02 SIi\=SIi\ + C I N l * 0 1 SCLT = S C U T + SSS*'.l SSLA = SSLA*S SS*C SS0Tri»-0 2 -3. ?<i5 BBLA = f--KL A • ( C6 INCL*Q 1 +Z ' C 2) »' 3 . 7u5 IF ( 0 . K E . 2 4 . )G0 TC SI BOOTCN = :)AYiJOU*2.205/W C0 J  :  :  S S T C N = CAYSS"2.2G5/P'RL(J  b I M'LN = OI RiOOO*2 . 2 0 5 / P R C C S I i\TCN = :)T .\l-.v*2 . 205/PPOO S5AV = S S L A / ( C' 3 .705*24. ) DBAv=BBLA/(0-3. 7o5*24. i S S I A G * . 1 2 M SSAV + C'.rt A y ) / ( 1 . + . > T T * . 1 2 -j ) SSEXT= S S L A 0 * 0 * 2 4 . / P S CO W R IT E ( 6 , 9 1 ) S IN TO\, S i TO N , RI N T'jiv , 3 C.J TCN , S S I AG . SS. X T FORMAT ( / , F 9 . 2 , V X , F i . 2, 16 X, F 8 . i , 1 6 X , F 3 . 2 , 10 X , F 8. 2 , 1F0 8.2 X, , / ) :  91  ;  D = C. CAYOCO=C. OAYSS=C.  184  UJ oJ O J OJ UJ Ul U J U J U J U J j> J> .J> J> J> J - V.J co -< r I\J  > — o  UJ  UJ  UJ  OJ OJ 'viJ U J C' U '  UJ UJ  [UJ  OJ  OJ  r\j  UJ 10  UJ  UJ  UJ  M  ui OJ UJ OJ K :  o vc cc'  UJ  iu ui  UJ OJ IvJ I O l u U J UJ l o l  ^ l*\> f\J KJ f\) i\j UNj ' r »j i - O  ^ o- w  UJ OJ  UJ  |oJ OJ  OJ UJ  UJ  o  Ul -l> u  o  C o c  o O O  rsj r-oivj -.n  INJ  rvj rvj r\j r\j rvj *o u-i  o  in  CD n  o  o  j> 1  o TJ  ~  >  O rn r  >  >  II  II  Tl in ro o .  io  n  JJ >  IT  r~ r n o o o  —  CD II  o 1> o  o o  O O  o  II  -0  I  —  •  —i  a -i  —t  >  -4 —4 II  •  <  m  en —i  —.  •  T  r~  O  n  cr.  C_> X-  o o  r~  7> <T> r~ i  [ o p n  —<  |;v  u: j> -• <r C O •  ,T; -V.  *  —  c -H  •  4-  -C  J  •* <y  cV  j> •*  •  I  o  N  'JH/l  n  1 o i—  . CHAIN LIMITED  185  tU LU  

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