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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 in Partial Fulfillment of the Requirements for the Degree of Masters of Science in Business Administration in the Faculty of Commerce and Business Administration We accept this thesis 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 at the U n i v e r s i t y of B r i t i s h Columbia I agree that the l i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r re f e r e n c e and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my department, or 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 ain s h a l l not be allowed without my w r i t t e n permission. Department of Commerce and Business A d m i n i s t r a t i o n The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, B.C. August, 1975 i i 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 biochemical oxygen demand e f f l u e n t s of a k r a f t pulp m i l l was developed by superimposing st o c h a s t i c chemical s p i l l s and normal process discharge. The e f f l u e n t generated i s input into a v a l i d a t e d c l a r i f i e r aerobic s t a b i l i z a t i o n lagoon waste treatment model. U t i l i z i n g cost r e l a t i o n s h i p derived from the l i t e r a t u r e , c a p i t a l and operating costs for various system configurations and s i z e s were determined. Numerous experiments were run to evaluate the waste treatment system's s e n s i t i v i t y to i n f l u e n t concentration, temperature and h y d r a u l i c load. A l e a s t cost system configuration was determined f o r any desired e f f l u e n t l e v e l . The implications of a s p i l l basin and increased s p i l l frequency were evaluated. I t was concluded that the models could be a valuable planning t o o l to pulp m i l l management. TABLE OF CONTENTS ± i i r Page INTRODUCTION 1 CHAPTER I - THESIS DEFINED AND LITERATURE REVIEW. . 4 1.1 THE PULP MILL MODEL '. . . . . i 4 1.2 THE WASTE TREATMENT MODEL 7 1.3. WASTEWATER TREATMENT PLANT COSTS 10 CHAPTER II - SYSTEMS IDENTIFICATION . . . . . . . . 12 2.1 THE PULP MILL: FUNDAMENTAL PROCESSES AND RESULTING WASTEWATER 12 2.1.1 Biochemical Oxygen Demand (BOD) 17 2.1.2 Suspended Sol ids (SS) 18 2.2 THE WASTE TREATMENT PLANT 19 2.2.1 Introduction 19 2.2.2 The C l a r i f i e r . . . . . . . . 22 CHAPTER II I - SYSTEMS ANALYSIS . . . . 27 3.1 THE PULP MILL. 27 3.1.1 S p i l l Data 28 3.1.2 S p i l l Data Analys is . . . 29 3.1.3 Production and Water Usage. . . 39 3.1.4 Regular E f f l u e n t . . . . . . . 42 3.2 WASTE TREATMENT. . . . ' 43 3.2.1 The C l a r i f i e r . . 45 3.2.2 The Lagoon. . 55 3.2.3 Waste Treatment General izat ion 59 3.2.4 Discussion. 63 3.3 CAPITAL AND OPERATING COSTS OF WASTE TREATMENT 63 CHAPTER IV - MODEL DEVELOPMENT 74 4.1 PULP MILL MODEL DESCRIPTION. 74 4.1.1 Generating Chemical S p i l l s . .'• 78 TABLE OF CONTENTS (Cont'd) 'Page 4.1.2 Production and Water. 84 4 .1 .3 Bringing i t a l l Together. .' 88 4.1.4 V a l i d a t i o n of Pulp M i l l Model 91 4.2 WASTE TREATMENT MODEL 97 4.2.1 The General Structure 97 4.2.2 The Model 99 4 .2 .3 Subroutine TREAT. . . . . . . . . . . . . . . . . . . 104 4.2 .4 The COST Subroutine . 105 4.2.5 Waste Treatment Model V a l i d a t i o n 105 CHAPTER V - MODEL EXPERIMENTS . . 116 5.1 DESIGN VERSUS COST . . . . . . . . . 116 5.1.1 The Lagoon Cost Curves 116 5.1.2 S e n s i t i v i t y Tests on Lagoon Cost Curves . . . . . . 121 5.1.3 The C l a r i f i e r Cost Curves 134 5.2 SHOCK LOAD EXPERIMENTS . . . . . 140 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 . 148 BIBLIOGRAPHY 151 i LIST OF TABLES Table No. Page 2.1 Typical BOD and SS Levels for Kraf t M i l l Sewers. . . 19 3.1 Major and Minor S p i l l Locations in Pulp M i l l Model . 30 3.2 Goodness of F i t Results for S p i l l Amounts (units of 1000 lb) . 32 3.3 Goodness of F i t Results for Time Between Unrelated S p i l l s (units of hours). . . . . . . . . . . . . . . 32 3.4 Related S p i l l Count for 3 Major Areas. . . . . . . . 34 3.5 Goodness of F i t Results for Time Between Related S p i l l s (units of hours). . . . . . . . . . . . . . . 35 3.6 Related S p i l l Count for Each S i te 36 3.7 Related S p i l l Decision Matrix for Recovery Area (#1) 37 3.8 Related S p i l l Decision Matrix for Recaust Area (#2). 37 3.9 BOD, TS and SS of M i l l Liquor Samples. . . . . . . . . 38 3.10 Pounds Na 2 S0 4 Equivalent to Gallons of Liquor Conversion Factors . . . . . . . . . . . . . . . . . 39 3.11 Two Empirical D i s t r i b u t i o n s for Dai ly Water Usage Determined by Level of Production. . . . . . . . . . 40 3.12 Empirical D i s t r i b u t i o n for Dai ly Production in A i r Dry Tons 40 3.13 BOD, TS and SS Means and Standard Deviations f o r the Six M i l l Areas . 44 "3.14 Proportions of Total Hydraulic Flow from the Six M i l l Areas . . . . . . . . . . . . . . 44 4.1 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 4.2 Production, Water Flow and Fiber Loss Data Generated by the Pulp M i l l Model . . . . . 89 4.3 Summary of k-s Tests f o r Simulation Generated and Real Data Ef f luent for Di f ferent Steady State Time Interval and Temperature Combinations. . '.. . . . . . 112 5.1 Lagoon Capital Cost and Operating Costs for Combination 3 and Combination 4 Systems -Standard M i l l E f f luent . . . . . . . . . . . . . . . 117 LIST OF TABLES (Cont'd) Table No.. Page 5.2A Lagoon Capital Cost and Operating Costs for Combination 3 and 4 Systems - Standard Inf luent Load, Temp = 30°C 123 5.2B Lagoon Capital Cost and Operating Costs for Combination 3 and 4 Systems - Standard Inf luent Load, Temp = 40°C 124 5.3A Lagoon Capital and Operating Costs for Combination 3 and Combination 4 System - Standard Hydraulic Load X .9 . "126 5.3B Lagoon Capita l and Operating Costs for Combination 3 and; Combination 4 Systems - Standard Hydraulic Load X 1.1 127 5.4A Lagoon Capital Cost and Operating Cost for Combination 3 and 4 Systems - Standard Influent Load X .9 129 5.4B Lagoon Capita l and Operating Costs f o r Combination 4 Systems - Standard Influent X 1.1. . . .. . . . . 130 5.5 Lagoon Capital and Operating Cost for Combination 3 and Combination 4 Systems - Increased S p i l l Frequency in Recovery Area of M i l l . . . . 135 5.6 C l a r i f i e r Capital and Operating Cost for the Combination 1 and 2 Systems with Di f fe rent C l a r i f i e r Detention Time • 137 5.7 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 Ef f luent Loads ±10% of Standard 139 5.8 BOD lbs/Ton Ef f luent from a Combination 2 System for Various Factor Shock Loads over Various Time Interva ls . . 141 5.9 Table Showing Lagoon Maximum Concentrations and Recovery Times as a Consequence of Various Shock Loads 143 v i i LIST OF FIGURES Figure Number Page 2.1 Schematic Outl ine of Bleached Kraft 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 for Pulp M i l l Dai ly 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 . 47 3.3 Dispersion Curve for Center Feed C l a r i f i e r . . . . . 49 3.4 Properties of Age D i s t r i b u t i o n in Tank and of Outflows for Various Flows . . 50 3.5 Schematic of Generalized Model 60 3.6 Capita l Cost VS. Flowrate at Various % Removal of BOD: Aerated Lagoon 65 3.7 Annual Operating Cost VS. % Removal of BOD: Aerated Lagoon . . . . . . . . . . . . . . 67 3.8 Capital Cost VS. C l a r i f i e r Area: Primary & Secondary C l a r i f i e r . . . . . . . . . 69 3.9 Annual Operating Cost VS. Flow: Primary & Secondary C l a r i f i e r . . . . 71 4.1 Diagram of Waterborne Ef f luent Streams Included in Model Indicat ing S p i l l and Regular E f f luent 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 . . . . . . . . . . . 86 4.4 BOD Val ida t ion for Pulp M i l l Model. Real E f f luent and Simulation Generated Ef f luent with Ident ical Input 96 4.5 SS V a l i d a t i o n f o r Pulp M i l l Model. Real E f f luent and Simulation Generated Ef f luent with Ident ica l Input 96 v i i i LIST OF FIGURES (Cont'd) -Figure Number • Page 4.6 Four Wastewater Treatment Plant Configurations Possible 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 Ef f luent (using same i n f l u e n t ) for Steady State Operation Time, t = 1 hr and t = 24 hr . . . . . 107 4.9 Plot 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 for Simulation Generated Ef f luent and Real Data Ef f luent Using Di f fe rent Steady State Time Interval and Temperature Combinations I l l 5.1 Lagoon Capital Operating Cost Curves for Combination 3 and Combination 4 Systems. Numbers Beside Data Points Indicate Lagoon Area in Acres . . 118 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 f o r Indicated Temperature 125 5.3 Lagoon Capita l and Operating Cost Curves for 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 in Acres . . . 128 5.4 Lagoon Capita 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 in Acres . . . . . . . . 131 5.5 Lagoon Capital and Operating Cost Curves for 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 5.6 C l a r i f i e r Capital Cost Curves for Combination 1 and Combination 2 Systesm. Numbers Beside Data Points Indicate Theoretical Detention Time . . . 138 5.7 Lagoon Response Curves for Shock Interval of 24 Hours 142 ix LIST OF APPENDICES Appendix Number Page I Semi-Markov A n a l y s i s o f Related S p i l l s A - l II D e r i v a t i o n o f Conversion Factors to Convert Na2S04 Eq u i v a l e n t S p i l l s to Gallons of Chemical . A-2 III A L i s t i n g o f the Pulp M i l l Model A - 3 IV 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 Columbia f o r h i s invaluable guidance and encouragement i n the development of t h i s t h e s i s . A s p e c i a l thanks to Dr. J : Stephenson, also at the U n i v e r s i t y of B r i t i s h Columbia. I am also very indebted to Rolf Serenius and Dr. T. Howard of B.C. Research f o r t h e i r patience and encouragement i n guiding me through the complexities of the k r a f t pulping process. This work was supported by a Fellowship from the B r i t i s h Columbia Research Council. The author i s g r a t e f u l for the assistance and back-up given by the Council's s t a f f . S p ecial thanks to Mrs. D. Dove for analyzing the m i l l samples and Mrs. V. Coates and her l i b r a r y s t a f f f o r a l l t h e i r assistance. I would a l s o l i k e to thank the following personnel f o r t h e i r assistance and co-operation: 1) Mr. N. Eckstein, MacMillan Bloedel, Harmac 2) ,Mr. Horwood, MacMillan Bloedel, Head O f f i c e , Vancouver 3) Mr. D. H i l l , B.C. Forest Products, Crofton 4) Mr. M. Hague and Mr. Zagar, Weyerhaeuser, Kamloops. 1' INTRODUCTION Pulp and paper i s a major industry i n B r i t i s h Columbia. In 1973 there were 22 pulp m i l l s i n the province, 18 of which use the k r a f t pulping process. Their t o t a l production for 1972 was 1,853,000 tons of wood pulp accounting f o r 37% of the provinces f o r e s t exports. In 1969 the f o r e s t industry employed 17,500 people and had manufacturing sales of 1.7 b i l l i o n d o l l a r s (Stephenson and Nemetz, 1974). B r i t i s h Columbia exports i t s f o r e s t products to over 40 countries of which Japan, the United States and Great B r i t a i n are the biggest customers, accounting f o r 43% of the exports. The pulp and paper market has about the same number of customers with the United States being the l a r g e s t . A majority of the exports i s newsprint (approx. 79.8%) while the remainder i s p r i m a r i l y bleached pulp. The pulp and .paper process generates a considerable amount of a i r and water p o l l u t i o n . The s e v e r i t y of the problem was emphasized i n a recent study by the Swedish Environment P r o t e c t i o n Board. They state that as of 1972 the f o r e s t industry was responsible f o r more than 80% of the t o t a l p o l l u t i o n , expressed as BOD (biochemical oxygen demand), from domestic and i n d u s t r i a l waste i n Sweden, and 80% of the f o r e s t industry c o n t r i b u t i o n was from pulp m i l l s (Lekander, 1972). The proportions f o r Canada are probably very s i m i l a r since both countries have a s i m i l a r dependence on the f o r e s t industry. 2 Before 1950 the industry f e l t that the pulping e f f l u e n t s would be e a s i l y absorbed by the environment and l i t t l e thought was given to. waste t r e a t -ment. As a r e s u l t tons of t o x i c chemicals and wood f i b e r were released i n t o the n a t u r a l water systems each day. However in the f i f t i e s and s i x t i e s pulp m i l l operation costs rose and i t became economically advantageous to develop more e f f i c i e n t ways of r e c y c l i n g the process chemicals and the l o s t f i b e r s . During t h i s same period the lakes and r i v e r s became i n c r e a s i n g l y more respected as resources to be protected and maintained. As a consequence of t h i s combined economic and environmental push the pulping industry has become i n c r e a s i n g l y more concerned with m i l l wastes and t h e i r subsequent treatment. Over the past decade hundreds of t e c h n i c a l and economic studies have been c a r r i e d out pn treatment of pulp m i l l wastes. Groups such as the National Council of Paper Industry for A i r and Stream Improvement Inc. (NCASI), B.C. Research, the Canadian Department of the Environment, and the U.S. Environmental Pr o t e c t i o n Agency have a l l been.active i n t h i s area. However, despite a l l the new information being generated by these groups, m i l l management considering waste treatment a l t e r n a t i v e s can s t i l l not be sure 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 given waste treatment system. There i s great v a r i a b i l i t y i n m i l l e f f l u e n t q u a l i t y both between m i l l s and within a s i n g l e m i l l from day to day. Over one t h i r d of the t o t a l chemical and f i b e r losses are due to 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 are usually due to f a u l t y equipment, i n c o r r e c t c o n t r o l or the human factor (negligence, e t c . ) . I t i s these a c c i d e n t a l surges of tox i c chemicals and wood f i b e r which represent a threat to the s t a b i l i t y of operation of a waste treatment system. They are also hard to design against. A waste treatment system which can handle such operational transients e f f i c i e n t l y may be many times the s i z e of a system needed for normal operating conditions and exponen-t i a l l y more expensive. M i l l management therefore faces a d i f f i c u l t tradeoff problem, namely r e l i -a b i l i t y of the system i n meeting required discharge l e v e l s versus costs of the waste treatment plant. Management obviously would l i k e to minimize costs but also wants to be sure that the investment i s e f f e c t i v e i n meeting i t s o r i g i n a l purpose. The problem i s to study the systems behaviour i n response to t y p i c a l inputs and determine subsequent costs and e f f i c i e n c i e s of operation. There are techniques which f a c i l i t a t e bringing the r e a l world s i t u a t i o n into the laboratory. These permit the d e c i s i o n maker to experiment with d i f f e r e n t 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 without worrying about design f a i l u r e s . The techniques r e f e r r e d to are computer simulation and mathematical modelling. They have been applied to many i n d u s t r i a l processes with varying amounts of success. Their development and use can g r e a t l y increase the understanding of the problem and provide invaluable information on f e a s i b i l i t y of proposed so l u t i o n s . 4 CHAPTER I THESIS DEFINED AND LITERATURE REVIEW This study had two o b j e c t i v e s : 1. Develop two computer simulation models. The f i r s t of the waterborne e f f l u e n t s generated by a k r a f t pulp m i l l and a second of the e f f l u e n t s subsequent modification i n a waste treatment plant. Both models function on a one hour time step to give reasonable representation of the systems dynamic behaviour. 2. Use published cost r e l a t i o n s h i p s to study cost v a r i a b i l i t y of waste treatment as a function of d i f f e r e n t system designs, e f f i c i e n c i e s and inputs. In the following three sections the h i s t o r y of the above, as r e f l e c t e d i n the l i t e r a t u r e , i s reviewed and i t ' s implications on t h i s study are discussed. 1.1 THE PULP MILL MODEL Past computer simulation studies i n the pulping industry have, been p r i m a r i l y ~ concerned with c o n t r o l and process problems of a chemical engineering nature. For example, S u l l i v a n and Schoeffler (1965) presented a technique for simulating stock preparation and f o u r d r i n i e r dynamics permitting evaluation of d i f f e r e n t c o n t r o l schemes i n response to process modifications and system tra n s i e n t s . Tehrar (1967) gave a more general approach to simultion i n the pulp and paper industry. He discussed simulation and i t s p o t e n t i a l to the industry and then developed a model of the wet end of a paper machine to 5 study basis weight changes and t h e i r c o n t r o l . B.W. Smith (1969) developed a d i g i t a l simulation of paper making systems. Using both dynamic and steady state models Smith simulated process concentration f l u c t u a t i o n s as a consequence of flow surges i n storage tanks and connecting pipes. A s i m i l a r approach was taken by Henrickson and Meinander (1972) to evaluate various process design p o s s i b i l i t i e s . The published l i t e r a t u r e reveals very few attempts to model the k r a f t pulping process and no attempts at the complete m i l l (pulping and bleaching) In C a r r o l l (1960) the k r a f t cooking k i n e t i c s are measured, the k r a f t pulping process i s modelled and a non-linear technique for optimizing plant operation costs i s developed. System balance equations with s i x independent c o n t r o l v a r i a b l e s can be modified i n order to maximize the obje c t i v e function. Boyle and Tobias (1972), developed a new model reportedly 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 i n C a r r o l l ' s model. None of the above models deal with waterborne e f f l u e n t s generated i n a pulp m i l l operation. However there have been numerous data studies made i n the past few years which t r y to e s t a b l i s h the main sources of m i l l e f f l u e n t and possible operational c o r r e l a t i o n s . Howard and Walden (1971) analyzed over 1000 samples c o l l e c t e d over a AO-day period from major process streams of seven B.C. k r a f t pulp m i l l s . Means and variances f o r B0D 5 and t o x i c i t y were determined although no r e l i a b l e c o r r e l a t i o n was found. 6 In a l a t e r study, Walden, Howard and S h e r i f f (1971) used m u l t i p l e regression techniques to c o r r e l a t e B O D 5 and t o x i c i t y with m i l l operating data. Some i n t e r e s t i n g in-plant c o r r e l a t i o n s were obtained, however, c o r r e l a t i o n s for combined m i l l o u t f a l l s were poor. The Swedish Steam Users A s s o c i a t i o n (1974) made one of the f i r s t attempts to look at dynamic aspects of pulp m i l l losses. They looked at a pulp m i l l operation on d i f f e r e n t time scales with i n t e r v a l s ranging from .25 hrs to 1 hour. Their primary state v a r i a b l e was the v a r i a t i o n of sodium s a l t s concentration i n the e f f l u e n t s . Using t h i s as a measure of a c c i d e n t a l discharges i n the m i l l , they found that i n many sewers there were temporary discharges ( s p i l l s ) of l e s s than one hour duration over 50% of the time. A more extensive study, Gove (1974), described a c o n t r o l strategy and some analog simulation r e s u l t s of the impact of above normal loadings on a waste treatment plant. For t h i s study a "black b o x " a p p r o a c h was used to develop the pulp m i l l e f f l u e n t model. Regular process losses for various m i l l areas were generated s t o c h a s t i c a l l y , based on empirical data. Superimposed upon t h i s was a sequence of s p i l l s generated from a derived d i s t r i b t u i o n . The "black box" approach eliminates the need for a d e t a i l e d model of the process. 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 exact model. The "black box" d e s c r i p t i o n i s a general term applied to an input-output device. The black box represents a f u n c t i o n a l transform which gives the e f f e c t of input changes on output. The contents of the black box are not of i n t e r e s t as long as the t r a n s i t i o n i s achieved i n a way that r e f l e c t s a c t u a l system behaviour. 7 This approach i s supported by a statement i n the Swedish Steam Users A s s o c i a t i o n (1974) report which states: "The t o t a l discharge from a pulp or paper m i l l can be divided into normal process discharges, dependent on the design of the process and the equipment being used, and temporary or a c c i d e n t a l discharges caused by disturbances to the process". 1.2 THE WASTE TREATMENT MODEL With the growing concern for the environment i n the l a s t 10 years, waste treatment models have become an i n c r e a s i n g l y more popular t o o l f o r design and management of wastewater treatment systems. They o r i g i n a l l y were dire c t e d towards domestic sewage but i n recent years many i n d u s t r i a l l y oriented models have been developed. Montgomery (1964) developed a model of a sewage treatment system which allowed e f f l u e n t storage and low-flow augmentation i n the r e c e i v i n g stream. The t r e a t -ment plant was represented as an e f f i c i e n c y of operation r e l a t i o n s h i p , and i t s i n f l u e n t was an empirical time trace which the model sampled every two hours. The i n t e r a c t i o n s within the model were treated as a system of queues and service f a c i l i t i e s . The model determined the dissolved oxygen concentration implications on the r e c e i v i n g stream for d i f f e r e n t r i v e r flow l e v e l s . R. Smith (1969) developed a model for design and evaluation of waste water treatment systems using e m p i r i c a l l y derived r e l a t i o n s h i p s f o r operational 8 e f f i c i e n c y and costs. The model permitted s p e c i f i c a t i o n of various component combinations and modelled t h e i r steady state operation. However a l l the inputs and outputs assumed continued steady state and gave no f e e l for the dynamic implications of the system. Similar approaches to waste treatment design have been developed by E i l e r s and R. Smith (1973), R. Smith (1968) and Chainbelt Inc. (1972). In recent years various models have been developed for s p e c i f i c components of waste treatment systems. Many of these models have t r i e d to represent the dynamic behaviour of the component as a consequence of load v a r i a t i o n s . Takamatsu and Naito (1967)'developed a number of mathematical models of hydraulic flow i n a sedimentation basin enabling them to simulate e f f i c i e n c y v a r i a t i o n as a function of turbulence and changing hydraulic loads. Naito, Takamatsu and Fan (1969) developed a mathematical model of the ac t i v a t e d sludge process to f a c i l i t a t e optimizing the system's c a p i t a l cost. S i l v e s t o n (1969, 1971) developed residence time d i s t r i b u t i o n s of s e t t l i n g basins and used them i n a simulation of mean performance of a municipal waste treatment plant. Some reasonable f i t s to r e a l data were found. In Sakata and Si l v e s t o n (1974) a f i r s t order chemical re a c t i o n was assumed to represent s e t t l i n g of a non - f l o c c u l a t i n g suspension and an exponential r e l a t i o n s h i p for s e t t l i n g v e l o c i t y was derived and v e r i f i e d . In Beak-Environment Canada (1973) various mathematical models of residence time d i s t r i b u t i o n s f o r aerated lagoons were derived and v e r i f i e d against 9 three operational lagoons. Other operational c h a r a c t e r i s t i c s of the lagoon operation are also discussed and a considerable amount of summary data i s presented. However, the report does not t r y to model the systems response to changes i n input over time. Bodenheimer (1967) i s a summary paper of the treatment systems a v a i l a b l e for pulp m i l l wastes discussing many primary and secondary systems and t h e i r costs. A more de t a i l e d discussion of the design and operation of secondary waste treatment systems i s contained i n a report published by the C i t y of Austin, Texas (1971). The p r i n c i p l e s of secondary waste treatment are summarized and the design of four major b i o l o g i c a l treatment systems (activated sludge, aerated lagoon, t r i c k l i n g f i l t e r s and waste s t a b i l i z a t i o n ponds) are discussed i n considerable d e t a i l . The need for dynamic models of wastewater treatment processes was r e c e n t l y emphasized i n Andrews (1974). On page 263, he sta t e s : "....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 should be emphasized that the development of dynamic models f o r wastewater treatment processes and the use of . these models for the improvement of c o n t r o l s t r a t e g i e s i s a d i f f i c u l t task and i s presently i n i t s infancy". Some be n e f i t s of dynamic models c i t e d by Andrews are: 1. Performance - one can study range of plant e f f i c i e n c y l e v e l s rather than j u s t average. 10 2. The development and evaluation of better c o n t r o l systems. 3. One can study start-up behaviour and evaluate a l t e r n a t e s t a r t -up procedures. 4. One can evaluate the process s t a b i l i t y and study i t s response to system t r a n s i e n t s . For t h i s study a f i r s t order model of a wastewater treatment system., common to a number of B.C. pulp m i l l s , was developed. Certain steady state assumptions were made i n the model which prevent i t from being dynamic i n the true sense of the word. The model operated on the same time scale as the pulp m i l l model and gave a reasonable representation of the system's response to the pulp m i l l e f f l u e n t over time. 1.3 WASTEWATER TREATMENT PLANT COSTS Numerous papers and manuals are a v a i l a b l e f or evaluating the costs of a wastewater treatment plant. Some even complement the costing aspects with a steady state approximation of the systems performance and allow the user to experiment with d i f f e r e n t component arrangements. [ E i l e r s and R. Smith (1973), R. Smith (1968), Logan et a l (1962)]. They are p r i m a r i l y f or use with domestic sewage a p p l i c a t i o n s . A comprehensive report on wastewater treatment systems f o r pulp m i l l s was prepared by the U.S. Department of the I n t e r i o r (1967). I t gives the r e s u l t s of a n a t i o n a l study of operational pulp m i l l s with ranges of treatment 11 costs experienced i n the industry for d i f f e r e n t treatment processes versus m i l l production and age. Reports published by NCASI have also dealt with the costs of pulp m i l l treatment f a c i l i t i e s [Edde (1968), Gehm and Gove (1968)] as have other papers by Haynes (1968), White (1968), Eckenfelder and Barnard (1971) and Bower (1971). For the purposes 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 i n Bower (1971) were used. They represent a summary of much of the published data and f a c i l i t a t e the determination of cost as a function of flow and e f f i c i e n c y . Bower's aerated lagoon cost curves were the only ones that could be found i n the published l i t e r a t u r e . 12 CHAPTER II SYSTEMS IDENTIFICATION 2.1 THE PULP MILL: FUNDAMENTAL PROCESSES AND RESULTING WASTEWATER Pulping i s the process by which wood i s reduced to a fibrous mass. In other words i t i s the means of rupturing the bonds between the f i b e r s of wood This task can be accomplished mechanically, thermally, or chemically. In t h i s study a m i l l using the p r i m a r i l y chemical process known as the k r a f t process i s modelled. A flow chart of a bleached k r a f t m i l l operation can be found i n Figure 2.1. F i r s t introduced by C. S. Dahl i n 1879, the k r a f t process separates the c e l l u l o s e f i b e r s from the l i g n i n materials by using a d i g e s t i o n mixture c o n s i s t i n g of caustic soda and sodium sulphide, together known as white liquo The wood, which at t h i s point i s i n the form of small chips, i s cooked i n a pressure v e s s e l (the digester) with white l i q u o r for approximately two to three hours. The l i g n i n i s dissol v e d forming a black, t o x i c substance known' as black l i q u o r . Black l i q u o r contains approximately 50 percent of the o r i g i n a l wood weight i n the form of wood ex t r a c t i v e s and s o l u b i l i z e d l i g n i n . The black l i q u o r i s then separated from the c e l l u l o s e f i b e r by washing the unbleached pulp (brownstock) i n a number of counter current wash stages. The black l i q u o r extracted from the pulp during the i n i t i a l washing stages i s returned to the chemical recovery system. Overflow from the l a s t washer i s discharged as the main process sewer from the pulping s e c t i o n of the m i l l , (unbleached white water overflow, i . e . UWW). The combined black l i q u o r s are 13 FIGURE 2.1 SCHEMATIC OUTLINE OF BLEACHED KRAFT MILL OPERATION WOOD V CHIP PREPARATION >-DIGESTER -A WHITE LIQUOR A WEAK B L A C K LIQUOR M U L T I P L E E F F E C T E V A P O R A T O R S W e r j CWJ e ^ i mv* «--r> 11 CONDENSATE 0 B L A C K LIQUOR OXIDATION fl S A L T C A K E n ADDITION „ , X > «rr» c-=, c&J V R E C O V E R Y F U R M A C E n U G R E E N I) LIQUOR I RECAUSTICIZ ING FILTRATION P U L P WASHING TO B L E A C H P L A N T V CHLORINATION U V/ VV V OVERFLOW V _ CAUSTIC I  1st E X T R A C T I O N v/ CHLORINATION i! V IL» SECONDARY 1 st C H L O R I N A T I O N i! CAUSTIC 0 v"; EXTRACTION V l L ™ ^ = > S E C O N D A R Y E X T R A C T I O N W A S H I N G , DRYING, BALING cr=2» t.T^~3> <anr=* *t: MARKET B L E A C H E D P U L P 14 concentrated i n m u l t i p l e e f f e c t evaporators to produce strong black l i q u o r which i s burned i n a recovery furnace to r e t r i e v e pulping chemicals. The smelt from the recovery furnace i s redissolved to give "green l i q u o r " . The green l i q u o r i s r e c a u s t i c i z e d , adjusted to strength and c a l l e d "white l i q u o r " . The "white l i q u o r " i s reused i n the digester together with v a r i a b l e proportions of added black l i q u o r . Approximately 95% of the pulping chemicals are recycled and most of the soluble organic m a t e r i a l extracted from the wood during d i g e s t i o n i s burned i n the chemical recovery furnace. The volume of e f f l u e n t from the pulping s e c t i o n of a k r a f t m i l l (UWW) i s normally between 8,000 and 12,000 gal/ADT (ADT = a i r dry ton of pulp production) with a pH of 7 to 10. Howard and Walden (1971) reported from a survey of seven B. C. bleached k r a f t m i l l s that the unbleached white water e f f l u e n t was the most toxic of the d i f f e r e n t e f f l u e n t streams. The dark color and coarse nature of unbleached k r a f t pulp l i m i t i t s market usage. Consequently, most m i l l s further process the unbleached f i b e r s to white bleached pulp. The bleaching process involves c h l o r i n a t i o n of the washed pulp and e x t r a c t i o n of the c h l o r i n a t i o n products i n an a l k a l i n e e x t r a c t i o n stage. Because of the detrimental e f f e c t continued exposure of the f i b e r s to c h l o r i n e has on the r e s u l t a n t pulp's strength, bleaching i s c a r r i e d out as a multistage process. B a s i c a l l y the system involves c h l o r i n a t i o n , at about 20°C, of the r e s i d u a l l i g n i n materials remaining a f t e r d i g e s t i o n and brownstock washing by contacting the pulp at a consistency of 3 - 3.5% f o r one h a l f to one hour with c h l o r i n e . This i s followed by washing and then by 15 c a u s t i c e x t r a c t i o n ( i n NaOH) of the pulp at a consistency of 10 - 12 percent for one hour at a temperature of approximately 60°C. The a l k a l i n e extracted pulp i s subsequently washed with water and treated with further c h l o r i n e , hypochlorite and/or ch l o r i n e dioxide stages with intervening washing. F i n a l l y the pulp i s dried and baled. Bleaching causes further losses of organic material from the pulp which amounts to 5 to 10 percent of the unbleached stock. These losses are discharged from the plant with the e f f l u e n t . The f i r s t c h l o r i n a t i o n e f f l u e n t normally has a volume of 15,000 - 25,000 gal/ADT pulp with a pH of 2 to 3. The f i r s t c a u s t i c e x t r a c t i o n e f f l u e n t has a flow volume of between 5,000 - 8,000 gal/ADT pulp with a pH of 9 to 11. Both these sewers represent a very high percentage of the m i l l s t o t a l p o l l u t i o n load. . Although the process streams mentioned above do not account f o r the t o t a l l i q u i d losses i n a k r a f t pulp m i l l they do represent the main sources of p o l l u t i o n . Superimposed upon these streams are losses from f a u l t y equipment, process 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 chemical. E f f l u e n t s from a bleached k r a f t pulp m i l l are usually discharged through two o u t f a l l s . F i r s t the a l k a l i n e (or general pulping) o u t f a l l which includes the a l k a l i n e bleaching e f f l u e n t , the unbleached Whitewater and r e s i d u a l s from 16 the pulping and recovery areas. Second the acid o u t f a l l containing the c h l o r i n a t i o n stage bleach plant sewers. Large q u a n t i t i e s of foam can be produced when these sewers are combined. Consequently, i n m i l l s without treatment f a c i l i t i e s the o u t f a l l s are e i t h e r a considerable distance apart or are combined and fed through a foam tank before f i n a l discharge. The recovery process mentioned earlier,which receives the black l i q u o r from the digestor and the brown stock washers,has the p o t e n t i a l of being and often i s one of the main p o l l u t e r s i n the k r a f t pulp m i l l . A l l the chemical l i q u o r s used i n the k r a f t process are extremely to x i c and have high p o l l u t i o n contributions. Although the recovery process i n theory i s a nearly closed system the c a u s t i c nature of the l i q u o r s and other f a c t o r s p r e c i p i t a t e frequent process s p i l l s . The basic c y c l i c stages involved i n the recovery system are: 1 . Separation of the spent l i q u o r (black l i q u o r ) from the pulp. 2. Evaporation of the l i q u o r to a concentration of 50 - 60 percent s o l i d s . 3. Combustion of the concentrated l i q u o r i n a s u i t a b l y designed furnace for separating the l i g n i n and other organic compounds from the sodium s a l t s by burning, for reduction of the sulphur-containing s a l t s mostly Na2S04 ( s a l t cake) to sodium sulphide and for u t i l i z i n g the heat produced to generate steam. 4. Withdrawal from the furnace of the sodium s a l t s i n molten condition and t h e i r s o l u t i o n i n water g i v i n g green l i q u o r . 17 5. Treatment ( c a u s t i c i z i n g ) of the green l i q u o r with calcium hydroxide to convert the sodium carbonate in the smelt to sodium hydroxide while at the same time calcium hydroxide i s converted to calcium carbonate, which i s a p r e c i p i t a t e , according to the following r e a c t i o n : Ca(OH) 2 + Na 2C0 3 • CaC03+ + 2NaOH 6. Withdrawal of the c a u s t i c i z e d and c l a r i f i e d s o l u t i o n (white l i q u o r ) for use i n another cycle. The calcium carbonate separated i n step 5 i s usually converted to CaO i n a k i l n together with make up lime and then i s slaked, with the green l i q u o r and i s converted by the water to calcium hydroxide and reused i n step 5. The two most widely used measures of pulp m i l l e f f l u e n t q u a l i t y are b i o -chemical oxygen., demand and suspended s o l i d s . These are now defined since they w i l l be used extensively throughout the remainder of the study. 1. Biochemical Oxygen Demand (BOD) BOD i s a qu a n t i t a t i v e t e s t , usually done on a 5-day b a s i s , which i n d i c a t e s the rate at which oxygen i s used by organic wastes in the e f f l u e n t . Oxygen i s used by b a c t e r i a to degrade organic constituents to carbon dioxide, water and other non-organics. For pulp m i l l s the BOD l e v e l i s p r o p o r t i o n a l to the amount of dissolved wood constituents i n the water. 18 BOD has serious implications to the n a t u r a l aquatic l i f e i n the r e c e i v i n g stream since i t too depends on the dissolved oxygen concentration i n the water. If a high BOD e f f l u e n t enters the stream, most of the d i s s o l v e d oxygen w i l l be used by the b a c t e r i a i n degrading the organic wastes. As a r e s u l t the natural aquatic l i f e w i l l not survive. The amount of BOD that a n a t u r a l system can t o l e r a t e depends on the volume of the r e c e i v i n g water and i t s rate of flow. I t s unit of measurement i s mg/1 or pound of BOD/ADT of pulp. 2. Suspended Sol ids (SS) This r e f e r s to a l l material which can be f i l t e r e d out of a l i q u i d . It i s also often c a l l e d t o t a l suspended s o l i d s since i t includes s e t t l e a b l e s o l i d s ( s o l i d s which s e t t l e i n one hour) and v o l a t i l e suspended s o l i d s ( l o s t on i g n i t i o n at 5 7 5 ° C ) . The suspended s o l i d s are composed mostly of f i b e r . They must be removed because being organic they represent a very high t o t a l oxygen demand (although not a high BOD). As a consequence they can g r e a t l y decrease 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 allowed to b u i l d up. If dumped d i r e c t l y into the r e c e i v i n g stream SS s e t t l e and become a major threat to the aquatic l i f e and also g r e a t l y a f f e c t the a e s t h e t i c appeal of the area. I t s usual u n i t of measurement i s mg/1 or pound of SS/ADT of pulp. The t y p i c a l BOD and SS l e v e l s experienced at the main k r a f t m i l l sewers are summarized i n Table 2.1. 19 TABLE 2.1 TYPICAL BOD AND SS LEVELS FOR KRAFT MILL SEWERS Sewer BOD SS Pulping (U.W.W.) 1st C h l o r i n a t i o n 1st Caustic E x t r a c t i o n 12 - 30 lb/ADT ^25 lb/ADT ^20 lb/ADT 10 - 15 lb/ADT 1 - 2 lb/ADT 2 - 4 lb/ADT The b r i e f d e s c r i p t i o n given here does not r e f e l c t a l l the f a c t o r s a f f e c t i n g a pulp m i l l s BOD and SS l e v e l s . The wood species used v a r i e s between m i l l s and has widely varying c h a r a c t e r i s t i c s , i h terms of i t s content of extractable materials,both seasonally and due to the trees l o c a t i o n when harvested. M i l l procedures are also v a r i e d to s u i t product requirements. M i l l design also v a r i e s . A combination of these f a c t o r s , a l l of which are designed to produce a product of r i g i d 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 v a r i a b l e c h a r a c t e r i s t i c s . 2.2 THE WASTE TREATMENT PLANT 2.2.1 Introduction In t h i s study two processes are modelled, a primary sedimentation tank (or c l a r i f i e r ) and a 5-day aerobic s t a b i l i z a t i o n lagoon. The two q u a n t i t a t i v e measures of e f f l u e n t loading and system e f f i c i e n c i e s are BOD and SS. The c l a r i f i e r removes p r i m a r i l y SS while the aerobic s t a b i l i z a t i o n lagoon removes p r i m a r i l y BOD. Since the SS loading can greatly a f f e c t lagoon operation the c l a r i f i e r precedes the lagoon. 20 FIGURE 2.2 CIRCULAR CLARIFIER WITH CENTER FEED 21 The c l a r i f i e r and aerobic s t a b i l i z a t i o n lagoon were chosen because of t h e i r proven r e l i a b i l i t y and e f f i c i e n c y . With the current emphasis on p r o t e c t i o n and improvement of the environment and the increased use of e f f l u e n t l i m i t s with respect to BOD and SS i n the discharge to public water systems, there has developed a need for r e l i a b l e , continuous performance, high rate processes. As mentioned e a r l i e r , s p i l l s are a major f a c t o r i n the pulping industry and occur at a s u f f i c i e n t frequency to r e s u l t i n c o s t l y v i o l a t i o n s of desired discharge l e v e l s . Therefore a r e l i a b l e system i s one which can absorb sudden shocks. The system must also be equipped to e f f i c i e n t l y remove both SS and BOD. The c l a r i f i e r , p o ssibly followed by a s e t t l i n g pond, i s the most e f f i c i e n t and e f f e c t i v e way of removing suspended s o l i d s . It has found wide acceptance for both municipal and i n d u s t r i a l waste. On the average c l a r i f i e r s i n the pulping industry are of centre feed, c i r c u l a r type with an i d e a l r e t e n t i o n time of 3 hours and a depth of no more than 15 f t . The aerobic s t a b i l i z a t i o n lagoon,which p r i m a r i l y removes BOD,was chosen because of i t s r e l i a b i l i t y and capacity to absorb short term s p i l l s with l i t t l e or no r e f l e c t i o n i n output. As a consequence of t h i s i t has found wide acceptance i n the pulping industry [see Rand (1972) and Bodenheimer (1967)]. I t s main disadvantage i s the land area needed to provide an adequate detention time (4 to 10 days). A m i l l of the type being modelled i n t h i s study, with an average water flow of 65 MUSGD, requires a 15' deep lagoon 22 of about 75 acres surface area to provide the needed r e t e n t i o n time. Maintenance can also be a problem since b i o l o g i c a l o x i d a t i o n generates suspended s o l i d s . Often t h i s i s solved by following the lagoon with a secondary c l a r i f i e r or a s e t t l i n g pond. Generally input pH should be kept at 7.0 ± 2.0 i n order to ensure b a c t e r i a l s u r v i v a l . Also water temperature should not drop too low so as to 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 r e a c t i o n . Despite these complications however, with s u f f i c i e n t process c o n t r o l , aerated lagoons function e f f i c i e n t l y i n many areas of B.C. 2.2.2 The C l a r i f i e r The purpose of a c l a r i f i e r i s to remove suspended s o l i d s (SS). B a s i c a l l y c l a r i f i e r operation involves detaining wastewater i n a large basin f o r a s u f f i c i e n t length of time so that the SS can s e t t l e to the bottom of the basin. Settled sludge i s continuously removed using a motor driven revolving rake mechanism to c o l l e c t and concentrate the sludge (see Figure 2.2). The c l a r i f i e r design common to pulp m i l l s i s the c i r c u l a r type i n which the waste flow enters i n the centre and leaves v i a an overflow weir running around the circumference of the tank near the upper rim. In t h i s study the e f f i c i e n c y of SS removal was assumed to be a function of the detention 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 of the waste being treated. Design of a c l a r i f i e r i s based on f i b e r slowly s e t t l i n g through quiescent water. To be removed, the f i b e r must s e t t l e f a s t e r than the r i s e rate of the water i n the c l a r i f i e r . Large f i b e r s may s e t t l e at speeds of 10 to 23 15 feet per hour. As they become smaller t h e i r s e t t l i n g r a t e decreases. About 92% of the p a r t i c l e s w i l l s e t t l e f a s t e r than 3 1/2 f t per hour (Bodenheimer, 1967). The c a p i t a l cost of a c l a r i f i e r i n general i s p r o p o r t i o n a l to i t s surface area (Bower,1971). To ensure an adequate detention time (Detention time = volume ^ volume must be kept constant (for an assumed steady state flow rate flow rate) implying an inverse r e l a t i o n s h i p between depth and cost f or any given volume. In Chapter I I I , an exponential approximation f o r the s e t t l i n g rate i s developed. For pulp m i l l wastes a nominal detention time i s from 3 to 4 hours and depth i s 12 to 15 f t . For a 3 hour detention time and a 15 f t deep tank with an average flow of 35 M.U.S.G.^^ day, the volume required would be, 35 x 1 0 6 MUSG Vol = J J • day x 3 hrs = 4.4 x 10 6 US gal 24 ^ day with a depth of 15 f t , the diameter would be, D = 2x \J 4.4 x 10 6 g a l x .134 x j ^ r j r x - y - £ 224 f t 2.2.3 The Aerated Lagoon The primary purpose of the lagoon i s to remove soluble BOD using b i o l o g i c a l treatment. B a s i c a l l y the process provides an environment i n the lagoon ^M.U.S.G. = m i l l i o n U.S. gallons 24 which permits b a c t e r i a to use the organic m a t e r i a l as a substrate for growth and energy. In the aerobic s t a b i l i z a t i o n lagoon dissolved oxygen assim-i l a t e d by micro-organisms i s supplied by mechanical aerators. The b i o l o g i c a l reactions taking place i n the lagoon are summarized i n the following equations: org material + 0 2 + NH3 + P -» New c e l l s (C5H7N02') 1 o p + c o 2 + H 2 ° The degradation of c e l l m a t e r i a l then occurs as follows: (C 5H 7NO 2) 1 0P + 0 2 +C02 + H 20 + NH3 + Polysaccharides Both reactions require oxygen and the 5-day rate at' which oxygen i s required i s the BOD5 of the w a s t e . In the C i t y of Austin, 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 described. They state that i f oxygen and BOD concentration i n the aerobic s t a b i l i z a t i o n lagoon are high, the b i o l o g i c a l r e a c t i o n rate, K, can be assumed constant. For a s u f f i c i e n t l y aerated lagoon t h i s i s a reasonable assumption for pulp m i l l e f f l u e n t . I t i s also assumed that the aerator mixing i s s u f f i c i e n t to keep a l l the SS i n the lagoon i n suspension. To obtain a reasonable BOD reduction e f f i c i e n c y , the minimum recommended retention time for a lagoon i s 5 days, (Bodenheimer, 1967). Lagoons vary from 6 f t to 15 f t i n depth. The deeper the lagoon the stronger must be the aerators to function e f f i c i e n t l y . However, f o r a given detention time (and therefore volume) the surface area a v a i l a b l e w i l l d i c t a t e the depth. For the remainder of t h i s study BOD w i l l be written f o r B O D 5 . The f i v e days w i l l be understood. 25 The SS generated by the oxidation i n the aerobic 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 aterial which i t s e l f has a 5-day BOD equivalent. For pulp m i l l wastes, Bower (1971), claims that t h i s b i o l o g i c a l sludge i s produced at a rate of .15 lb for each pound of BOD removed and that i t contributes approximately .1 lb of BOD per pound of sludge generated. E f f e c t s of temperature on BOD removal have been documented for many b i o -l o g i c a l waste treatment processes i n laboratory studies. The maximum removal rate generally occurs around 37°C which i s the optimum temperature fo r the b a c t e r i a (Beak-Environment Canada, 1973). In most systems operating in colder climates the temperature becomes a major f a c t o r a f f e c t i n g the system's treatment e f f i c i e n c y . L i t t l e has been published on temperature e f f e c t s i n f u l l scale aerobic s t a b i l i z a t i o n lagoons however the l i q u i d temperature within an aerobic s t a b i l i z a t i o n lagoon w i l l depend upon the rate at which heat i s l o s t and the extent of mixing which e x i s t s . Beak-Environment Canada (1973) found lagoons with a large length-width r a t i o to have a roughly l i n e a r temperature decrease through the 5-day lagoon. Therefore the mean lagoon temperature can be taken as the arithmetic mean between lagoon i n f l u e n t and e f f l u e n t temperature. Nutrients such as nitrogen and phosphorus often must be added to a lagoon to maintain the b a c t e r i a l i f e c y c l e . The dosage required i s governed by the concentration of these chemicals already present and by the BOD strength of the wastewater. In t h i s study a l l necessary n u t r i e n t s are assumed a v a i l a b l e . 26 Another important f a c t o r i n the operation of a lagoon i s i n f l u e n t pH. The pH should i d e a l l y . b e between.6 and 8 f o r optimum BOD reduction of pulp m i l l wastes (Beak-Environment Canada 1973). To accomplish 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 before entering the lagoon. If t h i s i s not s u f f i c i e n t , p ossibly due to a bleach plant shut down, chemicals may be added as needed. The i n f l u e n t pH can experience sudden s h i f t s as a r e s u l t of s p i l l s i n the m i l l but unless the s p i l l i s of major proportions (100,000 gallons of weak black l i q u o r i s a major s p i l l ) the lagoon can usually absorb these t r a n s i e n t s . However a continued s p i l l over a number of 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 shock to the system.can destroy the b a c t e r i a i n the lagoon and r e s u l t i n a system f a i l u r e f o r a number of days. In Gove (1974), i t i s recommended that s p i l l basins be constructed and m i l l o u t f a l l s be monitored with conductivity probes. It would then be possible to d i v e r t s p i l l s to the basin and release them l a t e r at a rate which can be handled e f f i c i e n t l y by the lagoon. Although s p i l l s are considered i n t h i s study i t was not possible 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 typical water borne effluent time trace by sampling each hour empirical BOD and SS distributions for each of the main sewers within the m i l l and multiplying the results by hourly hydraul-ic flows. Superimposed upon this normal effluent stream is a sequence of model generated s p i l l s . To establish the above distributions a considerable amount of data were re-quired. Most of the data were supplied by one B. C. pulp m i l l . The data made available are the following: 1. Six months of conductivity charts at the mill's main outfalls with notes indicating s p i l l locations (not complete). 2. Typical daily m i l l flow values for main m i l l sewers. 3 . Some BOD and SS sampling results for the same sewers as #2. 4. Twelve months of m i l l daily operating summaries, six months of of which overlap with / / l . 5. BOD and SS readings taken at main outfalls as required by Pollution Control Branch for 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 liquor 3 . White liquor 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, faulty control or equipment failu r e . Spills present a very real prob-lem to m i l l management since they are next to impossible to predict and re-present a financial loss as well as a pollution problem. To incorporate s p i l l s in the model, six months of continuous conductivity charts for the main sewer outfall were analyzed. Each day m i l l personnel collected the charts, wrote comments as to s p i l l locations and summarized,' the past 24 hours total chemical losses expressed as Na^SO^ per ton of pro-duction equivalent , tons of fiber lost, and water usage for that day. It i s common practice i n the pulp mills to measure chemical losses in terms of i t s Na2S0^ equivalent. The conductivity reading is proportional to the Na +, S 0 4 = and S = concentrations and since sodium and sulphur are necessary constituents in the white liquor (NaOH and Na2S) they must be re-placed. Usually N a 2 S 0 4 -(salt cake) is added in the recovery cycle to replace lost sodium and sulphur, thus the term "Na2S04 equivalent". 29 By establishing a Na 2 S04 loss per ton of production base level for a clean operating day the Na^O^ 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 fraction of the total area of a l l s p i l l s for each day. These fractions are the prop-ortion of the above base level loss that each individual s p i l l represents. By multiplying each fraction by the total above normal Na 2 SOi + loss for that day, the Na 2 SOi 4 equivalent for each s p i l l was estimated. This was done for a total of 178 days. About 70% of the chart indicated s p i l l s were identified as to location, although the Na^SO^ equivalent of most s p i l l s could be determined. Approximately three weeks of m i l l opera-tion 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 in the data base since the conductivity charts did not supply enough information. Their possible implications on the waste treat-ment system w i l l be considered later. Two items to note are that: 1. Although a s p i l l on the conductivity chart may last over an hour, i t s effect is. recorded as only being f e l t during the hour in which i t was ini t i a t e d . Very few s p i l l s were over an hour in length. 2. The extra hydraulic load created by the s p i l l was assumed negligible since even a large s p i l l of say 100,000 gallons represents less than 3% of the hourly m i l l flow. 3.1.2 SPILL DATA ANALYSIS S p i l l locations were broken down into three major locations with 12 sublocations. (The 12 sublocations belong to one of the three major locations). 30 Table 3.1 summarizes these. TABLE 3.1 MAJOR AND MINOR SPILL LOCATIONS IN PULP MILL MODEL MAJOR AREA RECOVERY-//1 RECAUST-//2 PULP ING-// 3 Sub Loc 'n Name &/or Liquor Sub Loc n Name &/or Liquor Sub Loc 'n Name &/or Liquor 3 Weak black l i q u o r 5 Green l i q u o r 1 Wood Prep'n 4 P r e c i p i t a t o r s -strong black l i q . 6 White l i q u o r 2 Knots-W.B.L. 12 Condensates -strong black l i q . 7 White l i q u o r 11 Kamyr Spills-W.B.L. 8 Slaker-Green l i q u o r 13 14 B.S. Washers-W.B.L. Kamyr Condensates The recovery, recaust and pulping locat i o n s represent nearly 100% of the s p i l l s recorded i n the data. The recovery area alone accounts f o r nearly 71% of a l l s p i l l s recorded. Goodness of f i t t e s t s were run f o r the s p i l l amounts^^and the time between (2) successive s p i l l sequences for each of the three major areas. The computer ^^Note: The s p i l l amounts data were expressed i n u n i t s of 1000 l b s of Na2S0^ equivalent. The time data i s i n hours. (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 the next few pages. The time d i f f e r e n c e s analyzed here were the time ( i n hours) between the l a s t s p i l l of a sequence and the next s p i l l i n the area which has the p o t e n t i a l of i n i t i a t i n g a new sequence. . 31 program used was one developed at UBC which uses the Kolmogorov-Smirnov (K-S) and the Chi-square goodness of f i t t e s t s f o r f i t t i n g given data to 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 Morley, 1973). These i n c l u d e : 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. E x p o n e n t i a l 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 to sample s i z e and i s gen-e r a l l y accepted as a more powerful t e s t ( S i e g e l , 1956). The t e s t determines the g r e a t e s t d i s t a n c e between the data and the t h e o r e t i c a l cumulative d i s -t r i b u t i o n s and compares i t to a t a b l e of c r i t i c a l . v a l u e s f o r a given s i g -n i f i c a n c e l e v e l . I f the d i s t a n c e i s l e s s than the c r i t i c a l l e v e l , then the n u l l hypothesis i s accepted, ( i . e . , we cannot r e j e c t the hypothesis that the d i s t r i b u t i o n s are the same). For a more complete d i s c u s s i o n of the K-S t e s t see Fishmann (1973) or S i e g e l (1956). The r e s u l t s of the t e s t s are found i n Table 3.2 f o r the s p i l l amounts, and Table 3.3 f o r the i n t e r -a r r i v a l times. The K-^ S r o u t i n e estimates the d i s t r i b u t i o n parameters from the sample data. I f these parameters are ones of s c a l e or l o c a t i o n , however, the K-S c r i t -i c a l values become d i s t r i b u t i o n dependent (Fishmann, 1973) . L i l l i e f o r s (1969) gives a t a b l e of K-S c r i t i c a l values f o r the 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 estimated mean. Comparing these values to a standard K-S t a b l e , i t TABLE 3.2 GOODNESS OF FIT RESULTS FOR SPILL AMOUNTS (units of 1000 lb) Area # of Observations Gamma Negative Binomial Log Normal K-S Adjusted R X D KS (.05) P K D KS (.05) M S D KS (.05) #1 Recovery 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 1.55 .078 .301 5.47 2.85 .214 .301 .246 TABLE 3.3 GOODNESS OF FIT RESULTS FOR TIME BETWEEN UNRELATED SPILLS (units of hours) Area # of Observations Gamma Distribution Negative Binomial Log Normal K-S Adjusted R X D KS (.05) P K D KS (.05) M S D KS (.05) //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 1.25 .197 .361 13.8 2.9 .170 .361 .297 Note: See Table 3.5 for definitions of parameters CO to 33 is seen that the 0.05 significance level critical values for Lilliefors' table are about the same as the critical 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) is increased. In the context of this study, a type II error is more serious. A suitably adjusted K-S critical values table could not be found for the gamma, log-normal or negative binomial distributions, therefore, the K-S standard critical values were also determined for ^  = .2. These are found in 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 in the s p i l l data, a sequence of up to six spills 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". Table 3.4 summarizes the number of related spills for each sub location. The goodness of f i t routine results can be found in Table 3.5. Since not a l l spills are part of a related sequence i t was necessary to es-tablish a related s p i l l decision strategy. Each s p i l l , i f not imbedded in an already initiated sequence, is a potential initiator of a related sequence. TABLE 3.4 RELATED SPILL COUNT FOR 3 MAJOR AREAS INTERVAL AREA TIME 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 U f M X K C b U L / i b t U K l i n t B t i W t t l N K£,L.A1CX) 5riJ-,l_,a V.U1NJ.XJ u r n u u n o ; Area # of Observations Gamma Negative Binomial Log Normal K-S Adjusted R X D KS (.05) P K D KS (.05) M S D KS (.05) #1 Recovery #2 Recaust #3 P u l p i n g 67 16 1.24 2.04 .447 .528 .191 .220 .166 .328 N .287 .392 3 RELAT .722 1.86 ED SPII .041 .136 LS .166 .328 1.62 2.45 1.77 1.92 .268 .211 .166 .123 .267 NOTE (FROM KITA AND MORLEY (1977) 1. Gamma D i s t r i b u t i o n f 00 - < x R " 1 e - x / B f o r x > 0 f o r x <. 0 where k = R = eKf(R) _ 2 x o=2 X = 1 = x o 2 2, Negative Binomial D i s t r P(x) = x ! ( K - l ) ! (K+x-1)! q X p k where k = P = m = k = # of successes prob success i n 1 t r i a l average # of success before k t n success ,2 .2 m SD SD2"- nT 2 3. Log Normal M = i l i l o g i o x i n S = . | 1 ( l o g 1 0 X i - M ) i n-1 SD = standard dev'n of # of f a i l u r e s before K t n success. CO 36 Using empirical data i t was possible to establish a decision matrix of probablilities that a related s p i l l w i l l occur. An interesting 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 location in a re-lated sequence, (i.e., the f i r s t s p i l l in the sequence puts the system in sta 1, a second s p i l l in a sequence puts the system in state 2, etc.). Table 3.6 is a summary of related s p i l l sequences for each of the three major areas. For each state i , the count.represents the number of s p i l l s that occurred as the i-th s p i l l in a related sequence. For example, in the re-covery area, state 3 has a count of 14. This means that of the52 i n i t i a l -izing 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 in Tables 3.5 and 3.6, the pulping area did not have any "related" s p i l l s . TABLE 3.6 RELATED SPILL COUNT FOR EACH STATE State Major Area 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 is a stochastic process which makes transitions from state to state in accordance with a Markov chain but in which the time spent i n each state before a transition occurs i s random. 37 Using the data of Table 3.6, i t is now possible to construct the related s p i l l decision matrices. For the recovery area, the following matrix re-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 .467 0 0 0 0 3 .285 0 0 .714 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 7 1. 0 0 0 0 0 0 Similarly for the recaust area, the following matrix results: TABLE 3.8 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 5 1. 0 0 0 0 Notice, given the sequence i s in state i , only two jumps are possible, to state i + 1, or back to state 1. This provides sufficient structure for 38 the semi-Markov process. The results summarized i n Table 3.5 provide a time distribution between related states (i.e., state i to state i + 1) while the results summarized in Table 3.3 provide a time distribution between the end of a related sequence and the beginning of a new potential sequence (i.e., state i to state 1). Using these results i t i s possible to determine lim-i t i n g probabilities of being in any state, mean f i r s t passage times and limiting transition probabilities. An analysis of this sort can be found in Appendix I. To translate a s p i l l amount in terms of i t s Na2SO^ equivalent into an equi-valent BOD and SS load, liquor samples from the m i l l were analyzed and are summarized in Table 3.9 TABLE 3.9 BOD, TS AND SS OF MILL LIQUOR SAMPLES Liquor BOD m g / l TS m g / l ss m g / i Weak Black Liquor 36,700 176,148 272 Strong Black Liquor 131,250 624,127 800 White Liquor 0 unreliable 300 Green Liquor 0 i t 2021 The Na SO, equivalent to volume of liquor conversion factors were deter-2 4 mined from the literature and the calculations can be found in Appendix I I . A summary of the results are: 39 TABLE 3.10 POUNDS Na 2S0 4 EQUIVALENT TO GALLONS OF LIQUOR CONVERSION FACTORS US gal of liquor/lb of Na^O^ Weak black liquor 1.063 Strong black liquor .270 Green liquor .325 White liquor .325 To convert a Na^SO^ equivalent to a BOD loading: , , me BOD , „ ,gal's of liquorv lbs BOD = (lbs Na 2S0 4 Equiv.) X ( I i t r / o f l i q u o r > X (« l b p f ) X 10"6 ^ X 2.2 ^ X - B f i -mg kg 3.785 l i t r e 3.1.3 PRODUCTION AND WATER USAGE Daily production in air dry tons and water usage in U. S. gallons per day were transcribed from monthly operating sheets and used to establish empir-i c a l distributions. It was originally hoped that there would be a reasonably good correlation between water usage and production; however, this proved not to be the case. The highest correlation for various combinations of complete runs was about .26. The data did indicate, however, that days with lower production tend-ed to use less water. This also f i t s the intuitive feel of their relation-ship. Consequently, two empirical distributions for water usage were de-veloped, one for production greater than 1,000 a i r dry tons per day and one for less. The two distributions are given i n Table 3.11 and their cum-ulative distributions are plotted i n Figure 3.1. TABLE 3.11 TWO EMPIRICAL DISTRIBUTIONS FOR DAILY WATER USAGE • DETERMINED BY LEVEL OF PRODUCTION AO Production ^1000 Tons MUSGD 51 53 55 57 59 61 63 65 67 69 71 73 Count 11 1 1 1 A 3 2 3 A 1 3 1 Total=35 Cumulative Prob. .31A .3A3 .371 .4 .51A .6 .657 .7A3 .857 .886 .971 1.0 Production >1000 Tons MUSGD 57 59 61 63 65 67 69 71 73 Count 2 1 1 3 7 11 28 2A 9 Total=86 Cumulative Prob. .023 .035 .0A7 .081 .163 .291 .616 .895 1.0 TABLE 3.12 EMPIRICAL DISTRIBUTION FOR DAILY PRODUCTION IN AIR DRY TONS Production ADT Count Cumulative Prob. 0 - 500 12 .0819 500 - 600 5 .090 600 - 700 9 .114 700 - 800 4 .147 800 - 900 10 .180 900 - 1,000 16 .286 1 , 0 0 0 - 1,100 10 .367 1,100 - 1,200 32 .573 1,200 - 1,300 50 .893 1,300 - 1,400 24 1.000 » "Prod'n <1000 tons ,Prod'n >1000 tons FIGURE 3.1 CUMULATIVE DISTRIBUTIONS FOR PULP MILL DAILY WATER USAGE 42 An empirical distribution for production was similarly established and is summarized in Table 3.12. Since the empirical distributions for water and production give a daily figure and the intent is to run the model on an hourly basis, i t i s as-sumed that the production and water per hour w i l l be constant for any given day. In other words, T> , /i Day production Production/hr = — i r r^, n 24 hrs/day H , O F W h r = ; f l ° W 2 24 hrs day 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 effluent. A c t i v i t i e s such as debarking, dreg and mud washings, brown stock washers, screening and bleaching a l l result i n liquid residuals. This "regular" effluent was grouped according to origin into six areas or streams. These six areas and their resulting effluent streams represent, i n several cases, quite a large portion of the mill's operation. However, the breakdown is a f a i r l y standard one (see Bower, 1971). The six streams and what they include are: 1. Acid stream - the bleaching area 2. Alkaline (general) stream - brown stock washers, digestors, blow tanks, screen rooms 3. Recovery - recovery boilers, precipitators, black liquor storage, evaporators, Na^SO^ storage. 4. Flyash c l a r i f i e r 43 5. Recaust stream - lime kilns, white liquor and green liquor 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 effluents were assumed to be normally dis-tributed. This is a f a i r l y standard assumption in 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 results are summarized in Table 3.13. By sampling from these distributions each hour i t is possible to generate hourly "regular" BOD and SS concentrations for each of the streams. Multi-plying these concentrations by the water flow in the stream the actual BOD and SS loads for that hour can be determined. The water flow for each stream is a proportion of the hourly m i l l flow as'summarized in Table 3.14. 3.2 WASTE TREATMENT Most models of waste treatment systems consider only steady state operation. Therefore, given a constant hydraulic load and concentration, i t is possi-ble to determine the average performance of a system. This is the common approach used in engineering design. However, in recent years more inter-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 effects the effluent detention time. Detention time is 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 AREA BOD mg/l TS mg/l SS mg/l MEAN ST. DEV. MEAN ST. DEV. MEAN ST. DEV. ACID STREAM 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 MACH. ROOM 9 .2 58 15 26 5 TABLE 3.14 PROPORTIONS OF, TOTAL HYDRAULIC FLOW FROM THE SIX MILL AREAS AREA FLOW PROPORTION GAL/MIN OF TOTAL ACID STREAM 22,400 .477 ALKALINE " 18,750 .400 RECOVERY " 2,900 .063 FLYASH CLAR. 900 .019 RECAUST STREAM 700 .014 MACH. ROOM " 1,250 .027 TOTAL 46,900 1.00 4 5 reduction are a function of the length of time a given unit of polluted water i s in residence. The waste treatment model in this study enables a pulp m i l l manager to study some of the dynamic effects of pulp m i l l oper-ation on the clarifier-lagoon 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 settling is directly proportional to the concentration of suspended solids in the c l a r i f i e r at any time t. This results in an exponential relationship for the weight fraction of SS removed i n the basin by time t. Sakata and Silveston (1974) developed a f i r s t order reaction assumption for settling. For the f i r s t order reaction assumption, they state: X(t) = 1 - exp (-kt) eqn 3.1 where X(t) = weight fraction of SS removed i n the basin by time t k = apparent sediments removal coefficient (rate of reaction) -1 sec t = time (sec) h If we let t = — where h = depth of c l a r i f i e r i n cm v D = threshold settling velocity cm/sec T i l ~ v Threshold velocity v Q i s a lower bound on the settling velocity. Any particles with settling velocity v £ v Q w i l l settle in the time = ~. If h ^ we let vo= detention time, then v Q is the minimum velocity any particle starting at a distance h from the bottom of the c l a r i f i e r must have to ensure settling. 46 -hk we get X(t) = 1 - exp (——) v o Note: v D = | 3 where Q = f l u i d flow rate into c l a r i f i e r in 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 distribution of the settling velocity 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 distribution of v This implies for any suspended matter, i f the settling velocity curve is fi t t e d by equation 3.2, the fractional 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 settling velocity for pulp m i l l wastes in a 6 f t column is presented. (This is reproduced as Figure 3.2). By f i t t i n g equation 3.2 to this graph the parameter "a" for pulp m i l l wastes was estimated (i.e., equation 3.2 was evaluated at 3 points on the graph c n i iteratively, u n t i l a reasonable f i t was found). A value of a = .104 f i t the plot quite well. Therefore, for any given depth of c l a r i f i e r i t was possible to determine the parameter k for pulp m i l l wastes. Namely: .6 % Suspended Solids with S e t t l i n g V e l o c i t y Equal or Less than V(D) FIGURE 3.2 DISTRIBUTION OF TERMINAL SETTLING VELOCITIES FOR PULP MILL WASTES 48 .104 C m a , J- U H sec .104, -1 V = — = — ; - — : — s e c h h cm h In Figure 3.3 is seen a copy of a typical residence time plot for a center-feed c l a r i f i e r (Chainbelt Inc. 1972). The output has a quick response to the change in inflow concentration. To mathematically model this kind of behaviour a technique popular i n the f i e l d of chemical reaction engineering was used. Basically, the problem is 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 in influent concentration. Levenspiel (1972), i n his 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 in the direction of flow as a separate element. The plots i n Figure 3.4 should help in understanding these concepts. By linking a number of tanks in series i t is possible to approximate a part i a l l y mixed system. The greater the degree of mixing the less the number of tanks in series (Note: an i n f i n i t e number of tanks i n series i s equivalent to plug flow). 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 series, where the total 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 Therefore, take the following system Q(t) - 9Stl C I N ( t ) I t c^t) / 'A Q(t) C,<t) V v„ 1 2 where Q(t) = hydraulic flow at time t . C i ( t ) = concentration of SS i n tank i at time t V i = volume of tank i . (Note: V^ and V^ are assumed to be equal and V^ + = volume of c l a r i f i e r . Also the volume of l i q u i d retained i n each tank remains constant independent of Q ( t ) ) . F i r s t perform a mass balance on tank 1 at time t over a time span of A t (a) Change i n mass from time t to time t + A t = M(t +.A t) - M(t) - Q(t)C ( t ) A t - Q ( t ) C 1 ( t ) A t - V 1 C 1 ( t ) k c A t inflow mass of SS outflow mass mass of SS which s e t t l e s of SS i n time At -1, k = sediments removal c o e f f i c i e n t (sec ) c = f i r s t order " r e a c t i o n " rate .104 5 2 (b) Now d i v i d i n g by At we get M(t+At)-M(t) = Q(t) C (t) At Q(t) C L ( t ) - V 1 C 1 ( t ) k r Mas s Using 77-^ = concentration 0 Volume (c) we can express (b) as AC, (t) T T 1 = V l ~At - Q ( t ) C I N ( t ) " *M C l ( t ) " V l C l ( t ) k c V Defining QTJTS, = detention time = T(t) d i v i d i n g (c) by V^and taking the l i m i t as At + 0 We get dc 1(t) c I N ( t ) . c 1 (t) - k.C, (t) T(t) T(t) c 1 rearranging dC 1(t) 4 F - + ciV 1 + k T(t) T(t) ° I N ( t ) T(t) eqn. 3.3 Equation 3.3 i s a l i n e a r d i f f e r e n t i a l equation of the general form, & + P(x)y = Q(x) which has a s o l u t i o n Y = e ^ P ( x ) d x r Q ( x ) e ^ ( x ) d x dx + Ce ^ P < x ) d x (Wilcox and Curti s (1966)) Applying t h i s to equation 3.3 we get C 1 ( t ) = e l+kr.T(t) d t T(t) r t C I N ( t ) e T(t) m<m) dt T(t) dt + 0 e. l+k rT(t) d •T(t) whereJT^ = i n t e g r a t i o n constant for end conditions. eqn. 3.4 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 in equation 3.4 greatly simplifies the sol-ution. Since the pulp m i l l model cycles on an hourly basis, l i t t l e resol-ution should be lost as a consequence. Therefore assuming T(t) = T = constant for each 24-hour period c Q(t) = Q = " " 11 " " n — r — " II II T II II C I N U ; " CIN~ 1 and solving eqn. 3.4, we get c i s ( t ) = C l N 1+k T c c -(1+k T )£-1 - e c c 1 c + CA0)e~(1+kcTc)T eqn. 3.5 1 c where C.^ = inflow concentration of SS for any given hour (mg/l) T = detention time (for each tank) for current 24-hour period (sec c „ Vol of tank i.e., T = -C^(0) = concentration of SS i n tank 1 at t = 0 (mg/l) For the two-tank situation, a d i f f e r e n t i a l equation similar to equation 3.3 was derived, only i n this case the feed concentration from tank 1 to tank 2 is 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 for the outflow concentration of tank 2 was then dC2<fc> . C 2(t) l1+\Tc d t • \ T C , c i s ( t > eqn. 3.6 Applying the general solution indicated earlier '2S (t) = e " J < KT c > £ f\(t). J ( l + k c T c ) ^ J\ I -= c +Le - V J T 2 ° c s u b s t i t u t i n g equation 3.5 f o r C^Ct) and s o l v i n g C 2 S ( t ) " IN (1+k T )' c c' -(1+k T )±-- c c 1 1-e c c c T +e c t C I N ( t ) c 2 ( 0 ) + C ; L ( 0 ) f - ^ L - -c c c eqn. 3.7 Looking at equation 3.7 notice that: at t = 0, we get C_(t) = C 9(0) as expected. Now as t increases the term t - Cl+k T )—— e c c T decreases implying that the second term in 3.7 has less effect on C 2(t) as t increases. As t approaches i n f i n i t y , 3.7 becomes C 2 ( t ) = _ J L C l n (1+k T ) 2 c c implying that with a constant input concentration and no changes in T, the. output concentration C 2(t) approaches a constant and the system has there-fore a limiting efficiency. For an instantaneous shock load = 0 and C^(0) mass of shock load vol. of tank 1 55 and C 2(0) = 0, we get the theoretical response curve of the c l a r i f i e r model. C s 2 ( t ) - C l ( 0 ) f e - ^ c V f c which has a shape similar to that of Figure 3.3. 3.2.2 THE LAGOON In Chapter II, the biological oxidation process occurring in 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 directly pro-portional to BOD concentration at time t. To model the temperature depend-ence of K^, an empirical relation expressing as a function of temperature was used (Beak - Environment Canada (1973)). T-20 The function i s : Kj* - .256 (1.032) Where T = temperature, °C K_ * ='lagoon removal rate, day ^ J-i (Since the model is run on an hourly basis the resultant K^ * must be divided by 24). In Beak-Environment Canada (1973) and i n City of Austin, Texas (1971), the tanks i n series model was found to give reasonable representation of a lagoon's response time curve. As far as BOD reduction was concerned however, they only looked at the long term steady state operation and did not try to model lagoon performance variations as a function of changing hydraulic loads and input concentrations. In other words, for steady state, they claimed: 56 -1. BOD cone, out BOD cone, i n ( 1 + K ^ ) 3 where: = lagoon removal rate (hr ) = detention time of each of the tanks f o r three equal volume tanks i n s e r i e s . For the purposes of t h i s study, a three-tanks-in-series model of the lagoon's behaviour over time was developed. Schematically the model i s : Q c B l ( t ) CINBUD CR2(t) p£B3<t> Q Note: = V 2 = V 3 ' V l + V2 + V 3 = v o-'- u m e o f l a g o o n Q = hydraulic flow, assumed constant f o r each 24-hour period (1/sec) CINBOD = concentration of i n f l u e n t BOD constant f o r any given hour ( / l ) Setting up mass balance r e l a t i o n s h i p f or each tank,relationships i d e n t i c a l to eqns. 3.3 and 3.6, except with d i f f e r e n t constants, r e s u l t . Using the r e s u l t s of s e c t i o n 3.2.1, i t was only necessary to carry the s o l u t i o n one more step and solve for the output from tank 3 i n terms of the s o l u t i o n already developed i n the c l a r i f i e r model f o r tank 2 (eqn. 3.7). 57 Applying a mass balance to tank 3 r e s u l t s i n the following l i n e a r d i f f e r e n t i a l eqn. + C B 3 ( t ) = c B ? ( t ) TL Using the general s o l u t i o n and s u b s t i t u t i n g equation 3.7 for C g 2 ( t ) (with the necessary parameter changes) c B 3 ( t ) CINBOD r -at • 1-e T L + e -at ICRI (0 ) _ t 2 L B 1 2 T ~ 2 + C B 2 ( 0 ) t „ + C R 3 ( 0 ) - CINBOD t 2a T Eqn. 3.8 CINBOD t where a = (1 + K LT L) (subscript L i n d i c a t e s lagoon parameters) C- (0) = concentration of BOD (mg/l) in tank 1 at t = 0 Bl Cg 2(0) = concentration of BOD (mg/l) i n tank 2 at t = 0 C B 3 < 0 > concentration of BOD (mg/l) in tank 3 at t = 0 = BOD removal rate constant (hr *) = detention time for each tank for any given 24 hour period Volume of tank g a l . = TTZ • n — (hrs) gal/hr inflow = time i n hours For steady state operation as t approaches i n f i n i t y equation 3.8 reduces to C R (t) 1 = 1 CTEOTJ a 3 (1 + K ^ ) 3 which i s i n complete agreement with Beak-Environment Canada (1973) report. 58 To model the suspended s o l i d s generated as a byproduct of the b i o l o g i c a l oxidation process an approximation developed i n Ci t y of Austin, Texas (1971) was used. If the complete lagoon i s treated as a completely mixed basin and the sludge age i s assumed equal to the detention time; = a*(Sp + X n) 1 + b * t . where X = e f f l u e n t SS concentration mg/l X 0 = i n f l u e n t SS concentration mg/l a = lbs of SS generated per lb of BOD removed b = rate 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 ( l b / l b - day) Values f or the constants were obtained from two separate papers a = .15 lb SS/lb BOD removed Bower (1971) b = .2 day" 1 Kormanik (1972) This r e l a t i o n has no d i r e c t time dependence and d i f f e r s with the BOD lagoon model i n i t s mixing structure and therefore was used only as an SS i n d i c a t o r on a d a i l y b a s i s . The SS generated also contributes BOD to the lagoon. For each pound of SS generated .1 pounds of BOD i s created (Bower, 1971). T h i s was incorporated i n a change of the rea c t i o n rate constant as follows The sludge generation rate = k L* = .15K^ 'amount of sludge generated^ j = k^* x volume x concentration (t) x At ,in'each tank over time At / 59 Rewriting the mass balance equation f or tank i AM(t) = Q C I N ( t ) A t - QC. (t) - K LV ± C ± (t)At + .1 k L*V ± C ± (t)At gi v i n g AM(t) At and d i v i d i n g through by V i (K^ - .lk*) C ± (t) T where - .Ik* = .985 Therefore, with the appropi'iate change i n K , equation 3.9 i s s t i l l v a l i d . 3.2.3 Waste Treatment General izat ion In most m i l l s , as with the one modelled i n t h i s study, the acid and a l k a l i n e (or general) e f f l u e n t sewers were kept separate and were not linked u n t i l j u s t before the waste treatment plant. When f i n a l l y l i n k e d they were 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 (pH - 7 ± 2) i n f l u e n t i n t o the lagoon. In some cases only the general sewer was fed to the c l a r i f i e r and the two sewers were mixed just, before the lagoon. This r e s u l t e d i n the BOD i n the general sewer feed to the lagoon being buffered by the c l a r i f i e r as a r e s u l t of i t ' s 2 or 3 hour detention time. In other words 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 on the lagoon buffered and somewhat dispersed by the c l a r i f i e r . 60 To f a c i l i t a t e various combinations of i n f l u e n t into the lagoon a more generalized model was developed. Schematically t h i s model looks l i k e FIGURE 3.5 SCHEMATIC OF Q l CBOD(t) CINB« i t i t Q l V c l Z GENERALIZED MODEL Q2 c l a r i f i e r lagvoon The two main changes were f i r s t the lagoon i n f l u e n t BOD concentration was made a function of time and second the m i l l h y d raulic load was s p l i t between the c l a r i f i e r and lagoon feeds ( i e . , Ql and Q2). To solve for C_ 0 (t) i n terms of the knowns ( i e . , Ql, V„. , V „ , V T, , VT , CNIB U-J LI LZ LI LZ V Z, 02) f i v e d i f f e r e n t i a l equations one for each of the tanks were developed i n the same manner as i n the l a s t two sections, remembering that the BOD i n the c l a r i f i e r i s . only mixing and not taking part i n the f i r s t order s e t t l i n g "reaction", [ i t i s assumed that 10% of the BOD t r a v e l l i n g through the c l a r i f i e r s e t t l e s out (private communication - T. Howard)] then s t a r t i n g with the f i r s t tank i n the sequence, the equations are solved successively, the s o l u t i o n for each tank i n turn being s u b s t i t u t e d i n t o the d i f f e r e n t i a l equation for the next tank. The f i n a l s o l u t i o n for CjgCt) i n terms of the known parameters, i s 61 fCINB*Ql + Z*Q2] " -a_t • 1-e T L -tvt +e T L _J-Lt +2*TT^)^ t e ^ f l + G \. Gt where J = C Ro(0) + B 3 v u , T F + G L = CBINCL*Q1 Z Q l _ H a2*Q ° ~ a 2 QCBINCL Ql a Q Ql 1 1 H = C B 2 ( 0 ) - — (1J2 g A + B Eqn. 3.10 Q ( T L ) 2 3 Ql Q (T L)' — + —o D = -Ql QTT C?*(0) C T * ( 0 ) _ C B I N C L _ C B I N C L "If + C B 1 < ° > B = A = C l l i O ) _ CBINCL T c3 T c3 - C , * ( 0 ) C T * ( 0 ) _ CBINCL _ CBINCL B + "TTF 3 TBZ and a = (1 + kT c) 62 Q = t o t a l flow into lagoon (1/sec) Ql = flow into c l a r i f i e r (1/sec) Q2 = Q-Ql = flow which bypasses c l a r i f i e r CBINCL = concentration of BOD into c l a r i f i e r (mg/l) Z = concentration of BOD i n Q2 (mg/l) T c = detention time for each tank i n c l a r i f i e r model (sees) = detention time for each tank i n lagoon model (hrs) C_. *(0) = i n i t i a l concentration of BOD i n tank i of c l a r i f i e r at t = 0 (mg/l), i = 1, 2 (0) = i n i t i a l concentration of BOD i n tank j of lagoon at t = 0; (mg/l) j = 1,2,3, If i t i s assumed that the c l a r i f i e r i s completely bypassed by a l l the sewers, implying C ± *(0) = 0, i = 1,2 Q = Q2 ( i e . Ql = 0) a = 1 1 3 = T L CBINCL = 0 Z = t o t a l BOD concentration from m i l l T c = 0 then equation 3.10 reduces to equation 3.8. 63 3.2.4 Discussion In the l a s t three sections a mathematical model was developed for a c l a r i f i e r and aerobic s t a b i l i z a t i o n lagoon waste treatment system. The dynamics of the system to which t h i s study was d i r e c t e d should be r e f l e c t e d i n the one hour r e s o l u t i o n the model operates under. It should be stressed that the f i n a l model i s not dynamic i n the true sense of the word. The model i n f a c t functions' i n a kind of quasi-steady state. Each hour the various parameters assumed to be constant are set and the clock s t a r t i n g at t = 0, runs the model i n steady state for one hour. At the end of the hour the f i n a l state of each tank becomes i t ' s i n i t i a l state for the next hour. The parameters are changed accordingly and the model i s run again f o r one hour. The changes i n concentration each hour, and i n hydraulic load each 24 hours, although not smooth t r a n s i t i o n s , should r e f l e c t o v e r a l l system behaviour. 3.3 CAPITAL AND OPERATING COSTS OF WASTE TREATMENT Two of the major f a c t o r s i n any management dec i s i o n are the c a p i t a l cost of that decision and the future costs i t may create. Waste treatment systems are no exception. The two processes modelled here, a c l a r i f i e r and aerobic s t a b i l i z a t i o n lagoon,represent a very large investment i n space, time and money. To cost a structure as large as a lagoon accurately an i n t e n s i v e engineering f e a s i b i l i t y study would almost surely have to be completed f i r s t . However i n using t h i s model as a management a i d , f i g u r e s of t h i s accuracy are not e s s e n t i a l . What i s more c r u c i a l i s to get a f e e l of the magnitude of cost changes as a r e s u l t of changes i n the basic design of the system. 64 In Figures 3.6, 3.7, 3.8 and 3.9 can be seen graphs of the c a p i t a l and operating costs for a center feed c l a r i f i e r and an aerobic s t a b i l i z a t i o n lagoon (Bower, 1971). Using the p l o t s i t i s possible to develop e x p l i c i t cost r e l a t i o n s for use i n the model. These w i l l now be developed, a) Lagoon C a p i t a l Costs In Figure 3.6 lagoon c a p i t a l costs are a function of lagoon e f f i c i e n c y and flow i n MUSG/day. Since each of the 8 p l o t s for the d i f f e r e n t e f f i c i e n c i e s are l i n e a r on a l o g - l o g p l o t , the cost r e l a t i o n s h i p w i l l have the following form: CC = A*(FLOW) 5 where A = cost intercept for flow = 1. mgd B = slope of log-log curves Since the p l o t s are l i n e a r and p a r a l l e l , the B c o e f f i c i e n t w i l l be i d e n t i c a l for a l l e f f i c i e n c y l e v e l s . The A i n t e r c e p t s however w i l l be d i f f e r e n t . To determine B, take the 40% curve In 8.1 x 10 5 - In 3.1 x 10k = 2.092 + 11.51 - (1.131 + 9.21) l n 100 - l n 1.0 4.61 - 0 = .708 The A i n t e r c e p t s (The CC value for Flow = 1 mgd) are e f f i c i e n c y intercept .40 $3. x 104 .5 6 x 10 4 .6 9 x 10h .7 12 x 104 .8 18.8 x 10 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 e f f i c i e n c y intercept .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 intercept for the .4 curve i s used. For lagoon e f f i c i e n c i e s between any 2 consecutive data points the A intercept i s determined by l i n e a r i n t e r p o l a t i o n . For example i f the e f f i c i e n c y (EFF) i s between .8 and .85, then the A intercept i s calculated as follows: GA = log (18.8 x 10 4) + [(EFF - .8)/(.85 - .8)]*[log (23 x 10 4) - log (18.8 xlO then A = EXP(GA) The c a p i t a l cost of the lagoon i s then evaluated as CC L = A*(FLOW)' 7 0 8 Note: EFF = lagoon e f f i c i e n c y , determined at the completion of the experiment gpp _ t o t a l BOD into lagoon - t o t a l BOD out of lagoon t o t a l BOD into lagoon where t o t a l s are taken for the complete experiment. b) Lagoon Operating Costs Figure 3.7 i s a semi-log p l o t of lagoon operating costs (per(MUSG/day) flow) versus lagoon e f f i c i e n c y . For any given e f f i c i e n c y operating costs are a l i n e a r function of lagoon flow. Namely Operating Costs = OC = C*FL0W where C = constant dependent on e f f i c i e n c y . 68 The constants C were determined for the same e f f i c i e n c y l e v e l s used f o r c a p i t a l costs. The data points taken from Figure 3.7 are: e f f i c i e n c y .4 .5 .6 .7 .8 .85 .9 .95 C 1480 2400 4100 7600 14700 21500 33000 53000 If lagoon e f f i c i e n c y f a l l s between any 2 consecutive data points C i s determined using l i n e a r i n t e r p o l a t i o n . For example, for an e f f i c i e n c y between .8 and .85 GC = log (14700) + [(EFF-.80)/(.85-.8)]*£log (21500) - log (14700) ] N then C = EXP(GC) The operating costs are then OC = C*FL0W d o l l a r s . c) C l a r i f i e r C a p i t a l Costs Figure 3.8 i s a log-log p l o t of c l a r i f i e r c a p i t a l costs versus c l a r i f i e r surface area. The r e l a t i o n s h i p w i l l have the following form: . . ' C a p i t a l Costs = C C c L = D*(AREA) E 2 where D = Cost intercept at Area =1. f t E = slope of log-log curve To evaluate D i t i s necessary to extrapolate the curve beyond that shown on the p l o t , g i v i n g D = $29.5 FIGURE 3.8 69 CAPITAL COST VS. 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P1 • .Lj_U.-.i..T. ' i :L ."!'.-! 1. | i -r:r i .ii. 1 ' j PP; ... -i . i •!-: I T T P 1" i -1 i p : ; i ; " " " 1 •" I 1 , . iPT.: 1 j • . i:.' -p ..Li " r ...r_ r j ~ -J J } o ' i 3 4 i 6 7 9 10 1,000 2 3 4 5 6 10, 000 3 s 1Q0 1 C l a r i f i e r Area, f t 70 To evaluate E E = s lope = In (2 x 10 5) - In (2 x 10 J) In (1.5 x 10 H) - In (10 z) A ^ 6 = . 9 2 therefore c l a r i f i e r c a p i t a l costs = C C c L = 29.5*(Area i n f t 2 ) 2,-92 Knowing the depth of the c l a r i f i e r d a i l y flow and t h e o r e t i c a l detention time, the surface area can be determined. D a i l y flow. f t3 24 ^ day Surface Area = -d-^- x detention time (hrs) depth ( f t ) d) C l a r i f i e r Operating Costs Figure 3.9 shows a log - l o g p l o t of c l a r i f i e r operating costs versus c l a r i f i e r d a i l y flow. Due to i t s l i n e a r nature i n the area of i n t e r e s t i n the model (10 MUSGD/day to 100 MUSGD/day) the p l o t was l i n e a r i z e d (dashed l i n e ) . The mathematical form f o r the c l a r i f i e r operating costs i s 0 C c L = F*(FL0W) G where F = cost intercept f o r flow = 1. mgd G = slope of log-log p l o t FIGURE 3.9 71 ANNUAL OPERATING COST' VS. FLOW : PRIMARY & SECONDARY CLARIFIER Flow, ingd 72 The constants were evaluated as F = $3600 in (3.2 x IP*4) - in (3.6 x 10 2) = S l ° p e = in (20)- in (1) = .726 Therefore ti 726 c l a r i f i e r operating costs = 3600* (FLOW) ' dollars where FLOW is in MUSG/day. A l l the cost relationships are in 1970 dollars. To determine the operating costs the following relation 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 in the costs are: 1. C l a r i f i e r a. Capital Costs - concrete structure, sludge pumps, rakes b. Operating Costs - power, administration, maintenance, sludge removal. 2. Aerated Lagoons a. Capital Costs - floating aerators, PVC lining, power supply (the land was assumed to be already available) b. ' Operating Costs - power, operating labour, maintenance, nutrients, administration. 73 The following assumptions were made by Bower i n the development of the cost data: 1. A l l f a c i l i t i e s operate for 350 days per year. 2. Primary c l a r i f i e r i s of the c i r c u l a r type with center upflow feed. C l a r i f i e r diameter depends on flow r a t e , s e t t l i n g v e l o c i t y of suspended matter and detention time. 3. C l a r i f i e r sludge i s assumed to have 5% s o l i d s . 4. Chemical a d d i t i v e s were assumed not required i n the c l a r i f i e r . 5. The aerated lagoon i s assumed to be water t i g h t . 6. Aerators are of the f l o a t i n g type and have s u f f i c i e n t horse power to maintain a l l s o l i d s i n suspension. 7. The lagoon feed i s assumed to be n e u t r a l i z e d . This can u s u a l l y be accomplished by combining the general and a c i d i c sewers. However, often chemical a d d i t i v e s such as ammonia or lime must be used. The costs of the mixing s t a t i o n and these chemicals are not included i n the model. Bower does i n d i c a t e however that the c a p i t a l costs for the holding tanks and chemical feeders are around $10,000. The operating cost i s nominally around $65/ton of ammonia required. 8. Sludge d i s p o s a l i s not included. 74 CHAPTER IV MODEL DEVELOPMENT 4.1 PULP MILL MODEL DESCRIPTION The model described herein i s concerned with 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 pulp m i l l . It i s p r i m a r i l y a s t o c h a s t i c model sampling from e m p i r i c a l l y derived d i s t r i b u t i o n s each hour. The computer program i s written i n FORTRAN (a l i s t i n g can be found i n Appendix I I I ) . The model was not designed to be used as a pulp m i l l design a i d . I t ' s purpose i s to generate a t y p i c a l pulp m i l l e f f l u e n t time trace to be used as input i n t o the waste treatment model. I t i s possible to change the d i s t r i b t u i o n parameters i n the model and thereby create a better or worse than normal time trace. Figure 4.1 provides a general flow chart of the pulp m i l l as v i s u a l i z e d i n the model. Notice that each of the s i x e f f l u e n t streams have a regular e f f l u e n t c o n t r i b u t i o n while only three streams have a s p i l l c o n t r i b u t i o n . The streams combine and e x i t from the m i l l modelled as i n d i c a t e d . These three e f f l u e n t o u t f a l l s from the m i l l are maintained i n the model and a l t e r n a t e combinations of them are a v a i l a b l e as i n f l u e n t to the waste treatment plant. Figure 4.2 i s an o v e r a l l schematic of the model's str u c t u r e g i v i n g the generation sequence and the model de c i s i o n points. In the following pages the model w i l l be discussed i n d e t a i l with a d i s c u s s i o n of the r e s u l t s of chapter III. ICAL SOURCE OF EFFLUENT S = SPILLS R = REGULAR CHIPS DIGESTORS SCREEN ROOM BLEACH PLANT MACHINE ROOM PRODUCTION 75 MILL OUTFALLS FLYASH CLARIFIER Sewer #4 RECAUST I I RECOVERY FURNACE S.R Sewer #5 S,R I Sewer #3 EVAPORATION Sewer #2 S,R Sewer #1 Sewer #6 R 1 = ACID OUTFALL 2 = ALKALINE (GENERAL) OUTFALL 3 = MACH. ROOM OUTFALL 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 Spi 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 Fi 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 to Regular E f f l u e n t For Indicated Area Read Time and Amount For Next S p i l l i n Area Which Just Had S p i l l Write BOD Cone. - 3 O u t f a l l s CSS Cone. - 3 O u t f a l l s for Current Hour No _ Is Hour = 24? Yes Write Days - BOD/ton - SS/ton - Prod'n - T o t a l Water Has experiment run for ITime hours? Yes I 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 data acquired from a B.C. m i l l was presented i n a summarized form. Using the r e s u l t s shown there, i t was possible to generate both re l a t e d and unrelated s p i l l s i n the model. Looking at Tables 3.2 and 3.3 the n u l l hypothesis for the gamma, negative binomial and log-normal d i s t r i b u t i o n s cannot be rejected f o r both the s p i l l amounts and times between unrelated s p i l l s . The Kolmogorov-Smirnov D s t a t i s t i c for both the s p i l l amounts and the times between unrelated s p i l l s was the smallest or second smallest f o r the gamma d i s t r i b u t i o n . Consequently i t was used i n the model to generate 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 supplied by the goodness of f i t program. (Note for the s p i l l amounts the v a r i a t e s units are i n terms of 1000 lbs of Na2S0tt). The gamma d i s t r i b u t i o n has the following density function: a-1 oo ^ x > 0, a and 3 are constants. x e where T (cx) = gamma function and a = shape parameter 6 = a scale parameter (the mean rate) Note when a = 1, f(x) becomes the density function f o r the exponential decay d i s t r i b u t i o n . As a increases beyond 1, the 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 quickly as the number of sample points increases. 79 By c a l c u l a t i n g the sample mean, x, and sample variance S 2, the parameters a and 3 can be estimated since E(x) = a3 var(x) = a3 2 Therefore solving for a and 3 A = £ 2 & = ~ t r e f - P h i l l i p s and Beightler (1972)] P h i l l i p s and Beightler (1972) presented a new algorithm for generating gamma v a r i a t e s with integer or non-integer parameters, c a l l e d " P h i l l i p s technique". I t appeared to have more s t a t i s t i c a l r e l i a b i l i t y for gamma d i s t r i b u t i o n s with ct<l and equal r e l i a b i l i t y f o r a>l when compared to other techniques for generating gamma v a r i a t e s . P h i l l i p s technique employs a numerical approximation to generate the gamma va r i a t e over v a l i d ranges of a and B. Using stepwise regression, f u n c t i o n a l r e l a t i o n s h i p s f or d i f f e r e n t ranges of a were determined. These permit generation of gamma v a r i a t e s f or 0 < a < °°. The method has a great computational advantage over other methods i n that i t requires the gener-at i o n of only one random v a r i a b l e each time the algorithm i s used. Also for any given a and 3 parameter set, the f u n c t i o n a l r e l a t i o n s h i p s need only be determined once and the r e s u l t s then stored f o r any future c a l l s for the same parameter set. This algorithm was programmed for the model and can be found i n the program l i s t i n g i n Appendix III as subroutine GAMMA. 80 As list e d in the appendix i t is only valid for 0 £ a £ 2. If a higher range is needed, the required functional expressions can be found in Ph 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 fitt e d by the negative binomial distribution. The negative binomial distribution i s based on the number of .independent Bernoulli t r i a l s (K + x) which occur before a given number of successes K are observed (It is x that has the negative binomial distribution). The probability mass function i s : Therefore the probability that x failures are encountered prior to the K success i s : , N ,k + x-lx k,- >x (k + x-1)! k,.. .x p(x) = ( x ) p (1-p) = (x!)(k-l)! P ( 1 " P ) where p = probability, of;success in one t r i a l k = number of successes x = number of failures Using the moments method the goodness of f i t routine discussed in Chapter III determined the distribution parameters list e d in Table 3.5. 81 Note, when K = 1, the negative binomial reduces to the geometric d i s t r i b u t i o n . In the model s i t u a t i o n K was not an integer and therefore the concept of the k*"*1 success becomes somewhat meaningless. However by making use of a r e l a t i o n s h i p between the negative binomial, Poisson and gamma d i s t r i b u t i o n s a negative binomial d i s t r i b u t e d x was generated for a non-integer K as follows. ' Suppose X i s from a Poisson d i s t r i b u t i o n with 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 with parameters a = K and 3 = 1-p , where K and p are as previously defined, then X i s a negative P binomially d i s t r i b u t e d v a r i a t e . In other words f(X=x/Y) = e~ YY X x = 0,1, and f , , ,K K-1 -Xy where A 1-P then f(X=x) =JfQ(=x/Y) fy(y)dy o = T(x+K) . A K. 1 x r(x+l)r(K) ^ 1 + A ; = T(x+K) K x r(x+l)r(K) P U p ; which i s the density function f o r the binomial distribution.[Fishman (1973)] subroutine NEGBIN then looks l i k e : P X = -= 1-p GENERATE Y = GAMMA (a=K,(3=X_1) S = 1 I A = e" Y X = 0 i Generate Ux+1 " random number YES DONE! 83 Note p and k are given parameters to the routine. The l i s t i n g for subroutine NEGBIN can be found in appendix III. The two distributions, gamma and negative binomial, were used in sub-routine SPILL to generate three typical m i l l chemical s p i l l time traces, one for each the 3 major areas. The subroutine SPILL is only called once by the main program. In that one c a l l i t generates the s p i l l sequences for the number of hours previously defined in the main program. In determining the s p i l l time traces, the following procedure is followed for each of the major areas (recovery, recaust, pulping) in turn. 1. Determine time interval (in hours) and amount (in //Na2S0i1 equiv.) of next unrelated s p i l l using Gamma dist. 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 for chemical typical of sublocation determined in 2. 4. Convert gallons of s p i l l into BOD, TS and SS equivalents (kgs) 5. Record location, time interval, amount (in gals) and BOD, TS and SS equivalents of s p i l l . 6. If current clock time i s equal to specified number of hours for current experiment go to 10, otherwise continue 7. Determine i f current s p i l l i s to be followed by a related s p i l l . If No, then return to 1. If YES, continue. 8. Determine time interval (subroutine NEGBIN) and amount (subroutine GAMMA) of related s p i l l . 84 9. Return to 3 10. Repeat 1 to 9 for next major area, returning clock to 0. A copy of a model generated s p i l l sequence f o r the recovery area can be found i n Table 4.1. In Figure 4.3 i s a flow chart of subroutine SPILL showing more e x p l i c i t y how the various d i s t r i b u t i o n s and d e c i s i o n matices are used i n the model. 4.1.2 PRODUCTION AND WATER Production serves two functions i n the model. F i r s t as a pointer to decide which water d i s t r i b u t i o n to use and second as a f a c t o r to determine the pounds of e f f l u e n t per ton of production. The production data described i n Chapter H I w a s used to e s t a b l i s h an empirical d i s t r i b u t i o n f o r production. The cumulative d i s t r i b u t i o n i s read into the model as 11 data points (see Table 3.12). To determine a day^s production, a uniformly d i s t r i b u t e d random v a r i a b l e i s generated and located i n an i n t e r v a l of the cumulative d i s t r i b u t i o n . The production i s then determined by i n t e r p o l a t i o n . This i s accomplished i n subroutine PRODN which returns the d a i l y and hourly production i n a i r dry tons. In the model the two cumulative d i s t r i b u t i o n s f or the water usage are read i n as empirical data points (see Table 3.11). The correct water d i s t r i b u t i o n corresponding to production i s determined and a uniformly 85 TABLE 4.1 A SEQUENCE OF SPILLS GENERATED BY THE PULP MILL MODEL FOR THE RECOVERY AREA ib Time (hr) Gal of BOD Equiv TS Equiv SS Equiv it ion Interval Liquor in KGS in KGS in KGS 12 17 242.6849 J.20. o!44 5 7 3.2217 0. 7 23 1 12 2 2 3 7 0 4 . 7 5 7 8 1 1 7 8 1 . 2 6 1 7 5 5 9 9 0 . 6 4 8 4 71. 1143 12 1 95.3940 47. +1 Ob 2 25 .3207 0.286 2 4 i l 7 6 7.6257 381.5098 1313.132 3 2. 3C2 9 4 2 3 2 4 1 . 4 9 3 J 1 6 1 1 . 0 2 4 4 7 6 5 6 . 4 180 9. 7245 3 o l 5 4 8 5 6 . 2 4 2 2 60 0 . 4 4 6 7 3 234.2 573 4.8 56 2 3 8 2 2 3 0 l o 9 3 7 5 3 J 3 3 o-jt 3 0 148 5 3 . -<898 2 2.3C1 9 4 1 1 1 9 6 t . 2 0 7 1 "'976.2 5 50 4 6 3 9 . 6 6 8 a 5 . 892 9 "" 4 3 63 2 3 „ 2 9 3 0 3 142. 6 7 62 14 935.6172 16.9699 4 2 4 6 o « 7 3 7 5 2 3 1 o 9 6 8 6 1 1 J 2 . 4 3 4 1 1 . 4 0 0 2 3 9 5 4 6 5 2 . 9 3 3 6 6 3 2.79cib 3 J 9 8 . t 5 3 o 4 . 6 5 2 9 -• 5 9 o 2 3 j. 0 i o 2 5 5 5 6 0 1 4 8 4 0.009 2 4 2 5 2 2 7.6367 1 1 3 . 1 3 5 5 3 3 7 « o 7 8 ^ 0 . 6 82 9 4 1 8 4 2 . 4 7 5 6 418. 71 J2 i 9 3 v . 9 2 7 5 2 . 5 27 4 ~ 3 4 19 7 1 . 1 5 4 i 9 7 9 . 6 6 3 3 4 6 5 5 o 8 6 3 3 5 . 9 1 3 5 1 0 8 9 7 0 7 . 7 695 1 3 2 j . 2 5 0 3 t +bj . 3 7 1 1 9 . 7 27 8 J 7 2 2 6 1 , J . o914 3 J 7 3 . 6 934 1 5 0 3 2 o 0 5 b 6 2 2 . 6 0 0 7 - 1 6 6 9 5 , 9 0 2 3 9 1 U o t 4 2 3 4 4 5 9 . 4 6 8 8 6 . 695 9 3 5 6 8 6 . 5 4 6 1 9 . 3 . 3 7 03 4 3 7 . 2 3 9 5 0 . 6 86 5 3 1 6 2 1 0 . 2 3 3 3 8 4 4 e 5 9 2 0 4 1 3 6 . 0 1 5 6 6.210 2 2 ••I <i 402 5 1 0 2 5 4 / 4 . 9 3 7 5 2 6 S l i d w 1 6 40.2 56 9 3 4 l O O - t . 5 8 6 7 1 3 o « 5 9 o 6 6 6 o .9 2 1 4 1. JC4 4 4 1 8 3 3 7 3 3 . 5 6 7 9 1 8 5 5. 5 8 3 0 3 3 1 9 . 6 8 7 5 11 .200 7 3 1 1 0 8 1 2 2 o 2 352 i 1 0 4 . 6 3 J 4 5 4 0 9 . 4 4 1 4 8 .122 3 3 2 3;.io05 .3 4 3 3 t 162. 3 2 4 2 2 u 3 8 3 . 1 5 6 3 3 0 . 6 0 5 3 3 _ i O 6 8 4 2 o b 3 o 7 93Oo 6 3 2 3 4 5 5 7 . 2 5 9 4 6 . 8 4 2 9 3 l . » J 4 1 1 9 9 . 9 7 80 1 6 3 . 1 9 IJ 7 9 9 . 1 8 5 3 1. 2 0 3 0 3 5 4 4 4 3 . 3 J 0 8 6 J 4 . 9 6 8 3 2 962 .5681 4.448 3 ^ 1 164S io 0234 2 2 4 3 o 3667 1 J 9 3 o . 3 4 7 7 16.4 99 0 3 2 2 9 2 6 . 1 9 0 9 3 9 7 . V 6 17 1 9 4 8 . 8 -r3 J 2. 926 2 4 1 5 4 4 5 2 . 5 6 6 4 2 2 1 2 . 9 2 5 3 H ) 5 1 6 . 9 6 0 9 1 3 . 3 5 7 7 4 1 4 2 1 2 0 l 6 o l 0 6 0 3 9 7 2 o 0 3 5 2 2 8 3 3 2 . 1 9 1 4 36.0485 4 2 7 6 3 5 . 3 5 5 5 3 7 9 4 . 7 7 15 1 8 0 3 4 . 7 1 J 9 2 2 . 9 06 1 4 5 4 2 7 . 0 3 2 3 2 1 2 . 6 5 8 J I 0 i 0 . 6 6u4 1.2 63 6 4 5 2 3 0 4 3 3 2 1 2 o 6 4 3 3 6 3 . 0 7 3 1 0.076 3 •t 21 37 1 3 .6 3 9 9 1348. 1638 8783 .425o 11.1559 4 4 9 7 5 . 9 7 0 5 4 o 5 o 05 II 2 3 05.2427 2.9279 •t 1 6 1 7555 . 1 367 3 75 4 . 9 0 2 6 1 7 3+ 5.234^ 22. 665 4 3 ^ 3 4 186 3 5 . 16 J 2 2534.3813 12411 . 0 1 5 6 1 8 . 6 35 1 :> ? 4 4 9 5 . 1 2 8 9 6 x 1 . 3 3 7 4 2993.7559 4. 495 1 3' 9.5 a 1 2 . 3 6 9 9 1 1 0 . 4 3 2 3 5 4 1 . 0 382 O . 8124 3 1 14J 2045 3 . 2 2 2 7 2 781.63 7 7 13621.8438 20.453 2 4 1 2 2 0 6 2 . 6 8 6 0 1 J 2 5 o 1 5 4 8 4 8 7 2 . 0 6 2 5 6 . 1 8 8 1 + 2 1 5 1 3 . t 2 i o 7 5 2 . 1 7 0 4 3574.702-+ 4. 540 3 -+ 3 106.2967 52. 8 3 0 4 2 5 1 . 0 7 7 6 0.3189 4 3 9 J . 4 5 2 0 4 4 . 9 5 4 6 213 . 6 4 7 6 0.2714 + 93 6 5 1 . 2 3 u 0 3 2 3 . 6 o l l 1536 .2053 1.9537 4 5 3 7 9 3 . 2 J 6 5 i 885.2234 8959.5547 11. 3 79 6 4 3 12821 . 8 5 9 t o 3 7 2 . 4 6 09 3U 285.2344 38.4656 4 32 7 3 4 3.3 6 79 169.1628 303.9493 1.021 1 4 54 1280.6885 636.5u20 3)24.9866 3. 842 1 3 9 3 1533. 75 32 76 2 . 2 / 3 7 3622.718b 4 . 6 C 13 FIGURE 4.3 FLOW CHART .OF SUBROUTINE SPILL 86 Clock = 0 KK = 1 E s t a b l i s h Parameters f o r S p i l l Quantity Gamma Variates V NSP(KK) = 0? NO KES E s t a b l i s h Parameters for Unrelated S p i l l I n t e r a r r i v a l Time Gamma Variate RELATED SPILL SEQUENCE Generate a Uniform R.Vv(RN2) Determine PRQB. of T r a n s i t i o n NSP(KK) ->• NSP(KK) + 1 = RPROB(KK) Yes Is RN2 > RPROB(KK)? No Set NSP(KK) = 0 C a l l Gamma (Time) (Generates Time Between Last S p i l l and Next S p i l l ) Unrelated C a l l Gamma (Amt.) (Generates the ^ £ 8 0 ^ Equivalent f o r the Amount' of S p i l l i n Thousands of lb) E s t a b l i s h Parameters For Related S p i l l I n t e r a r r i v a l Time -(Negative Binomial Variate) t C a l l NEGBIN (Time) (Generates Time Between Last S p i l l and Next Related S p i l l ) C a l l Gamma (Amt.) Convert # Na 2S0 [ t Into Gallons of Chemical Equiv. f o r the Current Sublocation Clock = Clock + Time 87 Generate a Uniform R.V. - RN1 I Determine RNl's Interval Loc'n i n the Sublocation Cumulative Distr. for 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 Typical of Sublocation Just Determined Convert Gals of Chem. into Its BOD and SS Equivalent kg's. NSP(KK) + NSP(KK) + 1 KK+1 No Record S p i l l Data According to Major Area Clock > I Time? I Yes No KK = 3? Yes Return to Main 88 d i s t r i b u t e d random number i s located within a d i s t r i b u t i o n i n t e r v a l . The water usage i s then determined by i n t e r p o l a t i o n between the i n t e r v a l end points. In subroutine WATER, the d a i l y and h o u r l y ^ a ^ y . ) w a t e r usage l e v e l s are determined. Also the hourly flows f o r the s i x m i l l streams are c a l c u l a t e d - using the proportions presented i n Table 3.14. The r e s u l t s of c a l l i n g the two subroutines PRODN and WATER f o r each simulated day are recorded for the number of days s p e c i f i e d at the s t a r t r . ,# of hours of experiment , . . A ^ . , ^  of the experiment. ( • :— c 1- 1). A copy of t h i s data as computed by the model i s i n Table 4.2. A complete record of t h i s data for the s p e c i f i e d number of days i s created by the model before the ac t u a l experiment i s run. 4.1.3 BRINGING IT ALL TOGETHER Having created the s p i l l production and water usage data f o r the s p e c i f i e d number of days the model uses t h i s information, combined with hourly data generated by subroutine REGUL, to generate the m i l l e f f l u e n t time trace. Subroutine REGUL i s c a l l e d by the main program each hour of simulated time. It creates a regular e f f l u e n t stream to account f o r chemical and f i b e r losses not c l a s s i f i e d as s p i l l s since by the very nature of the pulping process, a c e r t a i n amount of e f f l u e n t i s generated no matter how adequate Production Day Ton/Hr; 6 7 3 9 1 ) 1 1 . l 3 14 1 5 IS 17 13 19 2) 2 1 22 23 2 4 25 2.1 2 f 23 29 3 J J 1 32 3 3 34 33 36 j>7 33 3 9 5 J. 32 37o9i 15.40 56. 74 47.80 54. 92 41.31 18.63 46. 78 2 1 o i i 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 Fiber Losses (Tons/Hr) 1 2 3 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 0 a 3 3 3.53 0. 5 J 3.17 0. 6 7 0. 08 0.03 0.04 0. 03 0.08 0 . U 3 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. O o J. 03 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. 04 0.04 0 .04 0. J4 J . J4 • J . J J ^ _ 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 0 4 0 , •J. 04 04 j4 0 . 34 0.21 Area 1 1 .34 1.18 1.32 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-_?A6_ I. 18 .1.33 lo44 29 1, 1.39 1. 45 29 39 1.48 .1 .26 1.14 1 . 38 1. 34 Water Flows (xlO 6 Gal/Hr) 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. 13 1.16 0. 85 1. 11 1.10 1 . 1 3 1.12 1.0 7 l o l l 1.18 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 Area 3 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 0.1 8 0.18 0.1 7 o-LL 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 Area 4 0.05 0.05 0.C5 0.06 Area 5 0.04 0.04 0.04 0.04 . 0 o 06 0.06 0.04 0.04 0.04 0.03 0.04 0. 06 0.04 0.0 3 0.04 0.03 0.06 0 .06 0.-35 0.05 0.06 0.06 0. 04 0.05 0.04 0.04 0.04 0.04 0.04 0.05 0.05 0.03 0.0 4 0.04 0 . 0 6 0.05 0.05 0.04 0.04 0. 04 0.05 0.06 _0_.05_ 0.05 0.04 0.04 0.04 0.06 0.04 0.04 0.04 0.05 0.06 0 .06 0.04 0.04 0.05 0.05 0.06 0.06 0.04 0. 04 0.04 0. 06 0.05 0o 05 0.05 0.04 0.04 0.06 0.05 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 . M 0.08 ° 0.07 90 the process control. To account for this the regular effluent flows for the six major effluent streams were s t a t i s t i c a l l y modelled by assuming a normal distribution with empirically determined means and standard deviations for each of the streams. (These parameters can be found in section 3.1.4). Sampling stochastically each hour from these normal distributions a reasonable representation of the mill's regular effluent concentration i s generated. To determine actual effluent loads the sub-routine multiplies each of the six stream variates by their corresponding water flows for that hour and returns the BOD and SS levels in pounds for each of the streams (see Figure 4.1). To get a true m i l l representation, the 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 mill's f i n a l effluent. (see also Figure 4.2) 0) T = 0 1) Read day number, hourly production and hourly water flow for six streams for current day 2) Determine water flows (MUSG/hr) for 3 main outfalls for current day (see Figure 4.1) 3) Generate this hours regular effluent levels ( lbs/hr) CLOCK = CLOCK +1 T = T +1 4) Is there a s p i l l this hour in any of the 3 major areas? If No go to 7 If YES continue 91 5) Add BOD and SS l e v e l s of s p i l l to the corresponding regular e f f l u e n t stream 6) Read time and amount of next s p i l l i n area which j u s t had 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 to be t o t a l l e d on a d a i l y basis 8) Add BOD and SS for the streams, which make up the three m i l l o u t f a l l s , together 9) Convert lbs/hr of e f f l u e n t for the three o u t f a l l s into conc-ent r a t i o n units mg/1 10) Record BOD and SS f o r each main o u t f a l l 11) If CLOCK = s p e c i f i e d number of hours f o r current experiment stop otherwise continue 12) If T = 24 (has current day ended) go to 14,otherwise continue 13) Go to 3 14) Record BOD and SS as lbs/ton along with production, and t o t a l water usage for current day 15) T = 0 16) Go to 1. 4.1.4 VALIDATION OF PULP MILL MODEL The v a l i d a t i o n of a simulation model i s d e f i n i t i e l y a "pandora's box". I p h i l o s o p h i c a l l y represents the a c i d t e s t f o r any model but i n r e a l i t y cannot absolutely be solved. This i s a consequence of the lack of a 9 2 technique or groups of techniques which can establish beyond reasonable doubt that the model i s a true representation of reality. There is also the problem of real i t y i t s e l f since once data is gathered and inter-pretated we have taken the "reality" out of i t s natural environment and imposed our own conceptual interpretation. However in approaching this seemingly impossible task the original purpose of the model must be kept in mind. Often a major simplification of a system can give a reasonable 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 is 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 resulting in an axle fracture. This example is rather extreme but the major point is a l l too often forgotten. You can't get more than you put in and don't put in more than you need! y Before validating the overall simulation tests were made on the various distributions used in the model to check that they were functioning as designed. Goodness of f i t tests were run for the gamma distribution to insure that the routine used was indeed generating gamma variates with the given 93 parameters. Subroutine GAMMA was used to generate 250 v a r i a t e s f o r s p i l l Na2S0i + amounts and compared to the t h e o r e t i c a l gamma d i s t r i b u t i o n with the same parameters as those used to generate the v a r i a t e s . The r e s u l t s are summarized below; Area R A kS(.05) D s t a t . Recovery .414 .024 .086 .039 Recaust .515 .045 .086 .028 Pulping 1.19 .064 .086 .034 For a l l three areas the D s t a t i s t i c <kS(.05) implying that the d i s t r i b u t i o n s are the same. S i m i l a r l y 250 time i n t e r v a l s between unrelated s p i l l s were generated for the three areas using subroutine GAMMA and goodness of f i t comparison were run. These r e s u l t s are l i s t e d below: Area R A kS(.05) D s t a t . Recovery .511 .0019 .086 .080 Recaust .807 .0017 .086 .061 Pulping 1.101 .001 .086 .073 Again the d i s t r i b t u i o n s are the same at the .05 s i g n i f i c a n c e l e v e l . The subroutine GAMMA therefore i s creating the expected v a r i a t e s adequately. 94 Next, subroutines PROD and WATER were checked. I t would be expected t h a t the r e a l data and the data created' by the model would correspond f o r pr o d u c t i o n and water s i n c e the 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 of f i t t e s t was done f o r both production and water i n order to r e i n f o r c e confidence i n the model technique. The r e s u l t s are summarized below: D i s t r i b u t i o n kS(.05) D(N,M) P r o d u c t i o n .1923 .051 Water .1923 .073 N = 100 M = 100 To t e s t the complete model using the technique of h i s t o r i c a l v e r i f i c a t i o n ^ r a t h e r than generate 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 of pro d u c t i o n and water f l o w s , r e a l m i l l data was used as in 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 world s i t u a t i o n represented averages over a peri o d of days. By f o r c i n g the model to average over the same time span as the r e a l data, a comparison of the r e s u l t s was p o s s i b l e . The inputs to the model were: 1. E m p i r i c a l s p i l l sequences f o r the three major a r e a , converted to chemical and BOD and SS e q u i v a l e n t s i n the same manner as described e a r l i e r . 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 the model and the r e a l world f o r the same i n p u t s . 95 2. D a i l y water usage for the s i x m i l l streams and the corresponding production, a l l taken from m i l l operating summaries, for the same time span as the s p i l l s . The regular e f f l u e n t generation was untouched since no corresponding r e a l data for t h i s time span was a v a i l a b l e . For each simulated day the lbs/ton of BOD and SS were determined and averaged over a c e r t a i n number of days to correspond to the " r e a l world" data. In the m i l l s i t u a t i o n the samples analyzed represented mixtures of samples taken over 4 to 7 days. The r e s u l t s for BOD and SS are p l o t t e d i n Figure 4.4 and 4.5. These plo t s i n d i c a t e a reasonable congruence of behaviour between model and m i l l data. Both p l o t s have numerous i n t e r s e c t i o n s of the r e a l and simulated r e s u l t s . Also the n o t i c a b l e or "unusual" peaks generally coincide. There i s some disagreement i n magnitude for the f i r s t high peak (data point at time 4); however, looking at the r e a l data, t h i s time i n t e r v a l includes a m i l l s t a r t up for which a considerable amount of the s p i l l data could not be deciphered from the conductivity charts. Also the model was not designed with the a b i l i t y to generate a m i l l s t a r t up e f f l u e n t time trace. Kolmogorov-Smirnov two sample goodness of f i t tests were run for both SS and BOD for these runs. The r e s u l t s are summarized below: D(N,M) kS(.05) SS .327 .414 BOD .207 .414 N = 22, M = 22 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 9 7 The f i n a l v e f i f i c a t i o n test f o r the pulp m i l l model consisted of a K-S goodness of f i t between r e a l world and model e f f l u e n t data using model generated s p i l l sequences. The model was run for 100 days and the BOD and SS, expressed as pounds per ton, were averaged for every 5 out of 7 days. The goodness of f i t r e s u l t s are as follows: D(N,M) KS(.05) SS .471 .482 BOD .124 .482 N = 17, M = 15 Therefore we cannot r e j e c t the hypothesis that the two d i s t r i b u t i o n s are d i f f e r e n t . 4 . 2 WASTE TREATMENT MODEL 4 . 2 . 1 The General S t r u c t u r e In Chapter I I I the waste treatment model's mathematical development was discussed and generalized solutions f o r BOD e f f l u e n t from the lagoon and SS e f f l u e n t from the c l a r i f i e r were derived (see eqns 3.7 and 3.10). These equations were programmed i n FORTRAN and a l i s t i n g can be found i n Appendix I V . Although the model was designed to use the pulp model's output as input, i t i s completely independent of the pulp m i l l model structure and can be used to model the systems behaviour for any given i n f l u e n t . The program requires c e r t a i n system parameters (such as the lagoon area, depth, and c l a r i f i e r depth) as input before an experiment can be run. These are l i s t e d i n the appendix with t y p i c a l values and u n i t s i n d i c a t e d . The model was designed to function as an aid to m i l l management i n designing a c l a r i f i e r - l a g o o n 98 treatment system. Consequently, e s s e n t i a l design parameters can be changed e a s i l y . The program also determines c a p i t a l costs and yearly operating costs for both c l a r i f i e r and lagoon i n each run. A v a r i a t i o n of the program was. written which permitted a r t i f i c i a l l y increased hourly loads to the system for any given time span (up to 24 hours). The increased load 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 being considered as the normal operating i n f l u e n t time trace. For example, the pulp m i l l model creates a t y p i c a l BOD and SS e f f l u e n t time s e r i e s on an hourly ba s i s . This i s then given to the treatment model as i n f l u e n t . On prompting from the program, the user can specify a m u l t i p l y i n g f a c t o r , i t s a c t i v e time span and the hour,to s t a r t the increased load. For example i f the user gives a f a c t o r of 10 for a time span of 5 hours s t a r t i n g at hour 100 the program w i l l m ultiply the BOD and SS i n f l u e n t concentrations by 10 for the hours from 100 through to 105 and use these as i n f l u e n t data f o r those hours of simulated operation. It then returns to the o r i g i n a l time trace f o r the remainder of the run. This procedure gives the user considerable v e r s a t i l i t y to experiment with the systems response to various degrees of shock loading. It also provides some i n t e r e s t i n g information on the systems recovery times. This feature was prompted by a NCASI study published i n 1974 (Gove, 1974). The model permits the user to combine the three m i l l o u t f a l l streams into 4 d i f f e r e n t i n f l u e n t combinations to the treatment model. This was i n t r o -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 various 99 m i l l s . Some m i l l s combine the general and acid o u t f a l l s between the c l a r i f i e r and the lagoon, others only feed the general and machine room streams into the treatment system and completely bypass the system with the acid stream. The combination desired i s s p e c i f i e d at the beginning of a run (see appendix; IV l i s t i n g and v a r i a b l e d e f i n i t i o n ) . Schematics of the 4 possible combinations are shown i n Figure 4.6. The d i f f e r e n t combinations r e s u l t in' various hydraulic loadings to the system and therefore provide an opportunity to experiment with al t e r n a t e f a c i l i t i e s and observe t h e i r e f f l u e n t outcomes. 4.2.2 The Model The waste' treatment model i s a mathematical model evaluating the equations developed i n Chapter 3, for t = 1 hour. This assumes that the system operates i n a steady state over each hour. (The hydraulic load and i n f l u e n t concentration are constant). At the end of the hour, the f i n a l concentration of each tank i n the se r i e s model i s made the i n i t i a l concentration f o r the next hour. The next hour's hydraulic load and i n f l u e n t concentration are determined, system parameters such as detention time are a l t e r e d ( i f the hour begins a new day) as required and the system i s run again f o r another hour. The process i s repeated for the s p e c i f i e d number of hours. At the end of each hour the model records the follow i n g : 1. Influent SS concentration into c l a r i f i e r (mg/1) 2. SS concentration of stream which bypasses c l a r i f i e r (mg/1) 3. SS concentration of c l a r i f i e r e f f l u e n t (mg/1) 4. BOD concentration into c l a r i f i e r (mg/1) 5. BOD concentration of stream which bypasses c l a r i f i e r (mg/1) 6. BOD concentration of lagoon e f f l u e n t (mg/1). ACID GENERAL "ACID ROOM COMBINATION 1 GENERAL ROOM LAGOON COMBINATION 2 ACID ROOM ACID GENERAL COMBINATION 3 ROOM LAGOON COMBINATION 4 FIGURE 4.6 FOUR WASTEWATER TREATMENT PLANT CONFIGURATIONS POSSIBLE IN WASTE TREATMENT MODEL o o 101 At the end of each 24 hour period the model records the t o t a l amounts of SS and BOD which entered and l e f t the treatment system expressed as pounds per ton of m i l l production. Also lagoon generated SS i s given as the mg/1 average f o r the day as w e l l as lbs/ton. The model i s composed of three parts, the MAIN program, subroutine TREAT and subroutine COST. Subroutine TREAT i s c a l l e d every simulated hour by MAIN while subroutine COST i s c a l l e d once at the end of the run. A general flow chart of the model can be found i n Figure 4.7. i n running the model, the user has c o n t r o l over c e r t a i n design parameters. : include: a. Steady state time i n t e r v a l f o r c l a r i f i e r ( in sees) and lagoon ( i n hour b. The rate of s e t t l i n g as a f i r s t order l i n e a r r e a c t i o n ( m sec ) c. C l a r i f i e r detention time (hours) d. Estimated average d a i l y flow i n t o c l a r i f i e r (MUSGD) e. C l a r i f i e r depth ( f t ) f. Treatment system layout (1 to 4) 8- B i o l o g i c a l r e a c t i o n rate i n lagoon (hr ^) h. Lagoon water temperature °C i . Lagoon surface area (acres) 3 • Lagoon depth ( f t ) . To c a l c u l a t e the precise mass of e f f l u e n t which i s discharged over a time i n t e r v a l TI the following expression must be evaluated; FIGURE 4.7 FLOW CHART OF WASTE TREATMENT MODEL 102 T=0 DD=0 Set Design Parameters C r i t i c a l Constants etc. Calculated Program Requests Info, on A r t i f i c i a l Loads, TJ, Step, Factor Cycle Reads Water Flow for 3 O u t f a l l s and Days Prod'n (Unit #8) Determines Water Flows for Desired Treatment Layout Calculates 24 hr Parameters for C l a r i f i e r and Lagoon-Detention Time, Flows, etc. DD=0 J Yes Reads Influent BOD SS Concentrations For 3 Input Streams - Unit #9 t Determine Cone, of System Inputs As Result of System Layout Is TJ < T ^ TJ + Step? Yes M u l t i p l y System Input Cone, by Factor For Step I n t e r v a l C a l l Treatment Which Returns E f f l u e n t Cone's. Is T=24? Yes No Calculate Influent and E f f l u e n t S t a t i s t i c s f o r 24 Hour Periods and Run Averages t C a l c u l a t e SS Generated i n Lagoon on D a i l y Basis No IS DD=24? T=T+1 DD=D0+1 i s T=Run Time? Yes Ca l c u l a t e E f f i c i e n c i e s and C a l l Cost End 103 Maes of po l l u t a n t past any point over the i n t e r v a l of time 0 to TI TI Q*C(t)dt TI Q \ C(t)dt i f we assume Q i s constant f o r the time 0 to TI, where C(t) = the d i s t r i b u t i o n of po l l u t a n t concentration over time Q = hydraulic flow at point of i n t e r e s t i n equivalent u n i t s Due to the c l a r i f i e r ' s short detention time i t may experience large changes i n e f f l u e n t concentration over the period of one hour. Consequently, t h i s expression was evaluated f o r the c l a r i f i e r SS e f f l u e n t . By s e t t i n g C(t) equal to equations 3.7 we get .TI -at Mass of SS(kgs) = 1-e Tc -at + e C 2(o) + C t \L _ CIN(t.) 1 ^0)TQ Tc(l+kcTc)J -IN |. -aTI T 1+e c + C 2(0)Tc a u -aTI T ' 1-e 4C|0)T^ a 2" -aTI T e C - l -aTI Tc -C-£0)TI e Where Q i n i n l i t r e s / s e c a = 1 + k * T c TI = 3600 sees. Eqn. 4.1 For the lagoon i t was assumed the 5 day detention time would buffer system surges r e s u l t i n g i n very small BOD e f f l u e n t concentration changes within one hour. The hourly mass of BOD e f f l u e n t i s therefore the product of BOD concentration at time t = 1 hr times h y d r a u l i c flow f o r that 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 model-are determined. The model determines a new one tank detention time parameter every 24 hours. This i s : T £ = REST = c l a r i f i e r tank's detention time = Volume of tank 1 (or tank 2) i n l i t r e s flow into tank i n l i t r e s / s e c = residence time i n sees. The l i n e a r "reaction r a t e " s e t t l i n g constant i s .104 CK c l a r i f i e r depth i n cm ( s e e c h a P t e r I I I ) S i m i l a r l y f o r the lagoon the model determines the detention times f o r each of the three equal volume tanks. T^ = TT = lagoon tanks detention time Volume of a tank i n l i t r e s flow i n t o tank i n l i t r e s / h = time i n hours and then the BOD removal rate constant KK according to the r e l a t i o n KK =[(1.256) * ( 1 . 0 3 2 ) ] T E M P / 2 4 discussed i n Chapter I I I . 4.2.3 Subroutine TREAT Subroutine TREAT reads the c l a r i f i e r and lagoon i n f l u e n t concentrations each hour and evaluates the system's e f f l u e n t concentrations. The f i n a l 105 concentrations f o r each tank are made the i n i t i a l concentrations f o r the next hour. The present structure of the subroutine uses the generalized model developed i n section 3.2.3 f o r the lagoon and the model developed i n s e ction 3.2.1 for the c l a r i f i e r . Although the primary purpose of the c l a r i f i e r i s to remove SS; some BOD i s removed as SS. To accommodate t h i s , the model assumes that 10% of the BOD which passes through the c l a r i f i e r s e t t l e s out and i s not, passed on to the lagoon. 4.2.4 The COST Subroutine-Using the r e l a t i o n s h i p s developed i n section 3.3 the subroutine COST evaluates the four cost r e l a t i o n s h i p s at the end of the simulation experiment. These are recorded and comprise the f i n a l statements i n the output of the 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 of the complete waste treatment model was not poss i b l e due to lack of a v a i l a b l e data. The data which was used f o r h i s t o r i c a l v a l i d a t i o n was supplied by Weyerhaeuser, Kamloops f or t h e i r operational aerobic s t a b i l i z a t i o n lagoon. The two months of data obtained consisted of d a i l y BOD concentration, expressed i n mg/1, at the entrance to the sedimentation ponds and the e x i t of the lagoon, and the d a i l y h y d r a u l i c load to the lagoon i n MUSGD. The sedimentation ponds are the f i n a l stage i n SS removal before entering the lagoon and have a detention time of a few hours. The i n f l u e n t concentration to the lagoon was assumed to be equal to the sedimentation 106 ponds i n f l u e n t . Using t h i s data i t was possible to v a l i d a t e tha lagoon section of the model. Referring to Figure 3.5, by making Ql = 0 Q2 = lagoon hydraulic load (1) Z = i n f l u e n t BOD concentration (mg/1) the lagoon formulation, as expressed i n equation 3.8, can be obtained from equation 3.10. Lagoon area i s 74 acres and i t ' s depth i s 15 f t . Input temperature was approximately 40°C and the e f f l u e n t 30°C, therefore the average temperature of 35°C was used. Since the data was on a d a i l y b a s i s the model could be run e i t h e r on an hourly b a s i s (t = 1 hour) using the same input concentration f o r each of the 24 hours, or on a d a i l y b a s i s , using each input concentration and hydr a u l i c flow only once and running the model f o r t = 24 hours. In Figure 4.8 are p l o t s of a) recorded e f f l u e n t data f o r the a c t u a l lagoon, b) the simulation run on an hourly basis (the point p l o t t e d i s the concen-t r a t i o n at hour 24 of each day) and c) the simulation run on a d a i l y b a s i s . Sixty data points are p l o t t e d . As seen from the f i g u r e the model, s t a r t i n g at i n i t i a l concentrations of zero i n a l l three tanks, took approximately 8 days to reach reasonable operating l e v e l s . Both the t = 1 and t = 24 pl o t s appear to give a resonable f i t to the data. The model following 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 hr 108 the sudden drop i n concentration for days 50 to 56 comes as a consequence of s i x low flow and zero pulp production days at the m i l l . The flows on day 53 f e l l to 16.2 MUSG/day (normal i s approximately 60 MUSG/day). There are c e r t a i n implications i n using the model i n a steady state for t = 1 hour. As seen i n eqn. 3.8, there are a considerable number of exponential terms with time i n t h e i r exponent. I t e r a t i n g the model each hour, only a very small portion of the exponential decay curve i s a c t u a l l y A t y p i c a l negative exponential p l o t looks as follows: used. where f = e - c t and c = constant t = t ime For the lagoon model a t y p i c a l value of C would be: c = - = 1 + k T,TT, = 1+. 0169*40. " T L T L . 40-= .025 + .0169 = .0419 Therefore f o r i u P -.0419*1 -t = 1 hour f = e = .96 while for 0 . . , -.0419*24 -t = 24 hour f = e = .37 109 Looking at equation 3.8 for t = 1 hour the f i r s t term becomes quite i n s i g -n i f i c a n t while the second term i s very much the dominating element. In f a c t i f the i n f l u e n t BOD concentration i s considerably l a r g e r than the i n i t i a l concentrations of the three.tanks, the C (t) value could a c t u a l l y experience a drop from i t s previous value although the i n f l u e n t i s high. (This predicted drop i n the e f f l u e n t concentration due to a sudden increase i n the i n f l u e n t concentration a c t u a l l y did occur when the model was run using a r t i f i c i a l shock loads. The model recovered within 3 hours however and s t i l l r e f l e c t e d the time delayed response of the system). .This counter i n t u i t i v e r e s u l t comes from the steady state assumptions made in 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 term while the impact of the second term i s reduced by about 60%. As t approaches i n f i n i t y , the output concentration approaches a lower l i m i t . , . \~i / \ CINBOD l i m C ( t ) - • cr 5 y co Using t y p i c a l values, the time u n t i l C_. 0(t) = . 99*CINBOD B3 - 3 — or would be - 40 / r t - 3 -49 x 4.6 - 123^|}ours - 5 days • - TT t TT ( i e . .99 = 1-e In.01 = - a - or t = — * (-In.01) J. La (X or the f u l l lagoon detention time. This i s an u n r e a l i s t i c extreme and would not give a very dynamic representation of the lagoons operation. 110 K-S goodness of f i t t e s t s were done for both the t = 1 hour and t = 24 hour e f f l u e n t data against the ac t u a l data. The r e s u l t s are seen below: Time D(N,M) KS(.05) KS(.Ol) t = 1 t = 24 .334 .251 .268 .268 .321 .321 N = it of r e a l world observations = 49 M = // of simulated observations = 53 The n u l l hypothesis that the t = 24 run and the r e a l data are equivalent at the .05 s i g n i f i c a n c e l e v e l cannot be reject e d . However, for the t = 1 hour run the n u l l hypothesis i s r e j e c t e d . This implies that there i s a time i n t e r v a l between t = 1 and t = 24 which represents a threshold of a c c e p t i b i l i t y f o r using the steady state assumption i n the model. Some experiments were run using the same lagoon i n f l u e n t for various time i n t e r v a l s and temperatures and K-S goodness of f i t te s t s performed on the r e s u l t s . These are summarized i n Table 4.3 A p l o t of time i n t e r v a l versus temperature can be found i n Figure 4.9. There i s a threshold boundary 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 which i s a function of the time i n t e r v a l and temperature. Beak-Environment Canada (1973) state that the r e a c t i o n rate reaches a maximum at about 37°C and f a l l s o f f for higher temperatures. The impli c a t i o n s of t h i s are seen i n Figure 4.9. The dotted l i n e represents a symmetrical drop i n the I l l O l : : •  3 5 3 6 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 Int e r v a l 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 reaction rate with increasing temperature beyond 37°C. The minimum time i n t e r v a l which i s accepted by the K-S test i s t = 12 hours with a lagoon operating temperature of 37°C. Despite the r e j e c t i o n of the n u l l hypothesis f o r t = 1 hour, i t was decided to proceed as o r i g i n a l l y intended. The reasons for doing so are: 1. The K-S test i s not an absolute test and the plot s i n Figure 4.8 ind i c a t e that the t = 1 hour model gives a reasonable represent-a t i o n of r e a l i t y . 113 The intent of the model i s to t r y and observe the more dynamic aspects of the treatment system's behaviour. This would be l o s t i f the model were i t e r a t e d every 12 or 24 hours. The t = 1 f i t i s bad p r i m a r i l y because i t f a i l s to f i t r e a l data low points i n the day = 24 to day =? 52 region. If the temperature gradient along the lagoon were accounted for i n the model, the t = 1 p l o t may drop s u f f i c i e n t l y to f i t the r e a l data. The model as i t i s now structured can not incorporate a temperature gradient r e l a t i o n s h i p . Some BOD w i l l s e t t l e out i n the sedimentation ponds i n the " r e a l world" s i t u a t i o n while the model does not take t h i s into account. This w i l l r e s u l t i n the model e f f l u e n t being somewhat higher in concentration. For the c l a r i f i e r model v a l i d a t i o n data was not a v a i l a b l e . The only data acquired were SS readings on composite samples of 5 days of operation. In order to perform a reasonable v a l i d a t i o n , data would be needed on an hourly basis due to the c l a r i f i e r s short detention time. The c l a r i f i e r model does not s u f f e r from the exponential cut o f f experienced with the lagoon model fo r the t = 1 steady state approximation. For the c l a r i f i e r the constant _ 1 + k c T c  C T c 1 + .104 * 4753.5 = 15.*12*2.54  4753.5 2 2 = 4753.5 = 4.52 x 10~4 114 Therefore for t = 1 hour = 3600 sees -4.52 x 1 0 - 4 x 3.6 x 10 3 f = e = e - 1 * 6 3 = .1959 Referring to eqn. 3.7, the implications of the second term on C2(t) are greatly reduced by the exponential f a c t o r . In fac t t h i s implies that the c l a r i f i e r i s t y p i c a l l y running at about .8 of the maximum e f f i c i e n c y as determined by the model structure. The maximum e f f i c i e n c y p o s s i b l e i s „ , C ? ( t ) _ , 1 max e f f = 1 - - 1 - ( 1 + k c T c ) 2 Jl_ (3.2)' = 1 - - 7 ^ 2 = 90% Therefore the c l a r i f i e r i s operating at approx. .8 x 90% = 72% e f f i c i e n c y . This w i l l vary each day as a r e s u l t of the change i n detention time. In the model, c l a r i f i e r e f f i c i e n c y i s determined f o r a completed run as follows; i -f ee- • SSTlN - S S T o n r c l a r x f x e r e f f i c i e n c y = - — — S S T I N Where S S T J ^ J = t o t a l suspended s o l i d s which entered c l a r i f i e r over complete experiment SST ^ = t o t a l suspended s o l i d s which l e f t c l a r i f i e r over out v complete experiment In a simulated 15 day experiment, the c l a r i f i e r e f f i c i e n c y was determined as 77%. This i s a t y p i c a l value f o r SS% removed f o r c l a r i f i e r s with detention times between 2.5 to 3.0 hours (Bower, 1971). The data given 115 by Bower, acquired from NCASI Tech. B u l l e t i n #190, i s reproduced below: Detention time % removal of SS 2.5 hrs 75 3.5 88 A.O 90 5.0 92 6.0 96 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 model some experiment runs were run for d i f f e r e n t design detention times. The r e s u l t s can be seen below. Detention time % removal of SS 3 77 4 83 5 87 6 90 The c l a r i f i e r model appears to give a somewhat conservative reduction i n SS when compared to the NCASI data. However the NCASI data represents i d e a l maximum e f f i c i e n c i e s corresponding to long term steady state design models. The model developed here i t e r a t e s every hour so i t does not operate the c l a r i f i e r model at maximum steady state e f f i c i e n c y . 1 1 6 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 for each of the four wastewater treatment plant combinations changing c l a r i f i e r detention time and lagoon area s e q u e n t i a l l y . The same inputs, c o n s i s t i n g of 65 days of pulp m i l l model e f f l u e n t , were used f o r each of the experiments. At the end of each experiment the mean and variance of the lb BOD/ton and lb SS/ton for 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. Also K-S goodness of f i t te s t s were performed comparing d a i l y e f f l u e n t time s e r i e s for each of the experiments to a standard d a i l y time s e r i e s . The standard chosen was for a system with a 3 hour c l a r i f i e r detention time and a 75 acre -15' deep lagoon operating at 35°C. This standard i s maintained throughout t h i s chapter. 5.1.1 The Lagoon Cost Curves The f i r s t 3 combinations (see Figure 4.6) provide almost i d e n t i c a l i n f l u e n t to the lagoon, therefore only the r e s u l t s for combinations 3 and 4 w i l l be discussed. Keeping a l l other factors i d e n t i c a l to the standard, experiments were run fo r lagoon areas ranging from 20 acres to 125 acres. The costs, e f f i c i e n c y , mean and variance of input and output, and the K-S t e s t r e s u l t s were generated for each of the experiments. These are summarized i n Table 5.1. The costs versus mean lb BOD/ton are p l o t t e d i n Figure 5.1. The shaded areas 117 TABLE 5.1 LAGOON CAPITAL COST AND OPERATING COSTS FOR COMBINATION 3 AND COMBINATION 4 SYSTEMS - STANDARD MILL EFFLUENT Lag Area Lag CC Lag OC Lag Lag In BOD ///ton Out BOD ///ton Lag Out Eff. Flow 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 Tf 40 2,586,116 633,013 .83 33.9 58.13 373.9 26.5 59.3 .938 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 II 70 4,053,501 1,476,957 .93 33.9 58.13 373.9 22.8 46.2 .938 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 fo 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 effluent means for capital 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 "Pollution Control Objectives for the Forest Products Industry" (Department of Lands, et a l , 1971). The objective BOD effluent levels 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 level A applies to new mills and is the level they must meet immediately. It is to this level that the results of this chapter w i l l be directed (Note the effluent mean lb BOD/ton includes a l l the outfalls. 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 in capital and operating costs of an aerated lagoon with a change in mean effluent level. One of the most striking results i s the cost dominance of combination 3 over combination 4 for any effluent mean. Given an effluent level which management wants to meet i t is always less costly to construct a combination 3 system, (i.e. feed a l l the m i l l outfalls through the lagoon) than a combination 4 system (bypass the lagoon with the acid effluent). In other words, given a lagoon area, the effluent quality possible i s always better with a combination 3 system and at less 120 capital and operating cost. The reason for this i s that i t i s not necessary to operate a combination 3 lagoon at such a high efficiency in order to obtain the same quality effluent as with a combination 4 system. Operating a lagoon at high efficiencies is 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 privilege of dumping acid wastes, since i t is the acid effluent that i s putting a lower bound on the lb/ton level which a combination 4 system can attain. For the given m i l l , the combination 4 system would not be able to attain level A at any cost. Another way to look at the plot i s , given a certain amount of capital which management is willing to invest in an aerated lagoon, a higher quality effluent w i l l always result with a combination 3 system. A combination 3 system requires a neutralization mixing basin ahead of the lagoon. However such a basin w i l l cost approximately $10,000.00, a small investment relative to lagoon capital costs. To meet the level A requirements with a combination 3 system, the capital investment w i l l be approximately 2.7 x 10 5 dollars and expected operating costs would be about $600,000.00 per year. At an operating temperature of 35°C the lagoon size needed i s approximately 55 acres - 15' deep. Since this 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 this level. If this i s of concern i t may be advisable to work along the p + a curve. This would require a capital investment of approximately 3.5 x 10 6 dollars with operating costs at about 121 1 x 10 6 dollars per year. At an operating temperature of 35°C this would mean a lagoon size of approximately 65 acres - 15' deep. Although management may be willing to invest i n the larger lagoon, land av a i l a b i l i t y could well be a limiting factor preventing construction of the more reliable system. As indicated earlier these results 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 for the standard system and the results were similar. The lagoon efficiency was slightly reduced (approximately 1%) and the lagoon capital costs dropped to about 3.9 x 10 6 dollars. (From Table 5.1 the 65 day run resulted in lagoon CC = 4.01 x 10 6 dollars). S ince the results are almost identical, 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 sensitivity of the curves in Figure 5.1 experiments were run with each of the following changes. (Note: For each of the following only the variable indicated was altered. The other variables were l e f t as they were in generating Figure 5.1). a. Temperature Two experiments were run 1. temperature = 30°C 2. temperature = 40°C 122 b. Hydraulic Load Two experiments were run. Hourly flows f o r a l l 3 o u t f a l l s were .1. increased by 10% 2. decreased by 10% c. E f f l u e n t Load Two experiments were run. The hourly SS and BOD concentration from the 3 o u t f a l l s were 1. increased by 10% 2. decreased 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 loads f o r the waste treatment system, expressed as lb/ton, were compared to the established standard system using the K-S goodness of f i t routine. Results of these experiments are summarized i n Tables 5.2 A and 5.2 B and Figure 5.2 f o r temperature , Tables 5.3 A and 5.3 B and Figure 5.3 f o r hydraulic load, and Tables 5.4 A and 5.4 B and Figure 5.4 for e f f l u e n t load. Looking at Figure 5.2 the cost curves generated f o r the changes i n lagoon operating temperatures are i d e n t i c a l to those i n Figure 5.1. The mean lb BOD/ton i s i n essence a measure of the lagoon's e f f i c i e n c y and the e f f i c i e n c y f o r any given lagoon volume i s a function of hydraulic flow and temperature. Therefore, since the flow i s not a l t e r e d i n the temperature runs, the 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 flow l i n e on Figure 4.8. No matter what the temperature of the lagoon model, i t w i l l s t i l l follow the same flow l i n e and therefore generate the same cost versus e f f i c i e n c y curve. The TABLE 5.2A LAGOON CAPITAL COST AND OPERATING COSTS FOR COMBINATION 3 AND 4 SYSTEMS - STANDARD INFLUENT LOAD,TEMP = 30°C Comb Lag Area Lag CC Lag OC Lag E f f Lag Flow In BOD ///ton Out BOD ///ton Lag Out D In Lag D In CL D Out CL Mean Var Mean Var D(N,M) KS(.05) 3 20 582,576 97,195 .39 65.4 58.1 373.9 35.2 166.7 1.0 .238 0 0 0 30 1,221,460 168,478 .51 •" II 28.1 86.0 .969 •" II II-40 1,755,114 274,445 .60 "• it 22.7 47.1 .908 50 2,143,343 421,343 .67 it 18.7 29.3 .831 60 2,618,152 595,452 .73 " " ti 15.6 19.8 .554 70 3,173,116 789,827 .77 II 13.1 14.1 .538 it 80 3,693,615 995,000 .80 II 11.1 10.4 .215 100 4,543,221 1,468,835 .86 ti 8.2 5.98 .307 125 5,504,752 2,094,492 .896 II 5.9 3.2 .369 4 20 30 40 50 60 70 80 1,057,085 1,567,784 2,230,943 2,757,697 3,250,358 3,664,426 4,011,143 133,395 287,804 483,299 714,697 968,576 1,213,780 1,447,091 .59 .72 .80 .85 .88 .91 .93 33.9 58.1 37.3.9 ii IT Tl II II II 35.5 30.8 27.8 25.9 24.5 23.6 22.9 117 79.2 63.6 55.5 50.8 47.9 45.9 .984 .985 .985 .938 .938 .938 .938 II » „ TABLE 5.2B LAGOON CAPITAL COST AND OPERATING COSTS FOR COMBINATION 3 AND A SYSTEMS - STANDARD INFLUENT LOAD,TEMP = 4Q°C Comb Lag Lag Lag Lag Lag In BOD ///ton Out BOD ///ton Lag Out D In D In D Out Area CC OC Eff Flow Mean Var Mean Var D(N,M) KS(.05) Lag CL CI 3 20 1,019,959 143,642 .48 65,4 58.1 373.9 30.0 117.7 .985 .239 0 0 0 30 1,779,258 282,608 .61 IT II II 22.6 56.1 .908 it II it II 40 2,296,200 488,449 .70 II II II 17.4 • 28.7 .646 it II II it 50 3,044,594 743,269 .76 II II II 13.7 16.2 .554 II II II it 60 3,747,094 1,022,340 .81 II II ti 10.9 9.9 .169 II II it tt 70 4,323,528 1,338,975 .83 II IP II 8.9 6.5 .154 it II it tt 80 4,886,945 1,680,806 .87 II II II 7.36 4.4 .323 i i II tt tt 100 5,844,085 2,349,295 .91 II it it 5.2 2.2 .415 II i i ti II 125 6,737,215 3,097,800 .94 II i i it 3.5 1.1 .415 II n II ti 4 20 1,397,832 236,747 .69 33.9 II II 31.9 97.3 .985 II tt it tt 30 2,268,214 495,210 .80 it II II 27.7 67.5 .985 II II tt it 40 2,969,456 819,554 .86 i i it II 25.3 55.7 II it it it tt 50 3,571,540 1,154,664 .90 •t II II 23.8 49.9 .938 II it it tt 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 IZ f+ Ho 18 2 0 2 2 . Z(+ 2 6 2<S 3 0 32. 3 ^ - 3 6 3 8 4 0 System Mean BOD lb/ton 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 .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 • Out BOD ///Ton Lag Out D Lag In D CL In & Out Mean Var Mean Var D(N,M) KS ( 0 . 5 ) 3 75 4 , 0 1 3 , 0 4 3 1 , 1 6 3 , 4 4 4 . 8 3 6 5 . 4 5 8 . 1 3 7 4 . 0 9 . 9 6 8 . 1 5 0 0 3 2 0 6 5 7 , 8 3 9 1 1 1 , 0 1 5 . 4 1 7 1 . 9 6 0 . 2 3 9 7 . 7 3 6 . 5 1 8 2 . 7 . 9 8 5 . 2 3 9 . 2 0 0 . 2 4 6 . 2 1 5 3 0 1 , 4 0 1 , 7 2 8 2 0 3 , 3 2 4 . 5 3 it I I ti 2 8 . 9 9 6 . 6 . 9 6 9 ti ii 4 0 1 , 9 7 4 , 1 6 1 3 3 6 , 1 8 3 . 6 2 ti II I I 2 3 , 2 5 2 . 8 . 9 0 8 it ti 5 0 2 , 4 0 6 , 0 3 5 5 1 3 , 9 2 1 . 6 9 ti I I it 1 8 . 9 3 1 . 6 . 8 1 5 it I I 6 0 3 , 0 0 5 , 4 7 5 7 2 6 , 4 8 4 . 7 4 it ti ti 1 5 . 6 2 0 . 5 . 5 5 4 ti ti ! 7 0 3 , 6 2 3 , 3 4 0 9 5 6 , 1 7 5 . 7 8 i ' II it 1 3 . 1 1 4 . 0 . 5 3 8 I I it 75 4 , 0 1 2 , 0 4 9 1 , 1 2 6 , 3 9 7 . 8 1 ti ii n 1 1 . 5 1 3 . 1 . 3 3 8 II it 8 0 4 , 1 6 9 , 6 5 5 1 , 2 1 1 , 2 8 1 . 8 2 it ti ti 1 1 . 1 1 0 . 0 . 2 0 0 it • ft 1 0 0 5 , 1 1 7 , 1 3 1 1 , 7 7 7 , 0 6 5 . 8 7 ii- tt ti 8 . 1 5 . 5 . 3 0 8 I I • ti 1 2 5 6 , 1 4 2 , 2 1 5 2 , 4 9 6 , 7 6 0 . 9 1 ti n it 5 . 7 2 . 8 8 . 3 8 5 it ti 4 2 0 - 1 , 2 0 0 , 0 7 4 1 6 2 , 4 3 9 . 6 1 3 7 . 3 6 0 . 2 3 9 7 . 7 3 6 . 9 1 3 2 . 3 . 9 8 4 -. 239'' 3 0 1 , 8 0 1 , 8 0 8 3 5 1 , 7 3 2 . 7 3 II ti ti 3 2 . 2 9 0 . 8 . 9 8 4 » 4 0 2 , 5 2 7 , 5 4 4 5 8 7 , 1 9 9 . 8 1 it ii ii 2 9 . 3 7 3 . 6 . 9 8 4 » 5 0 3 , 1 0 6 , 9 1 1 8 6 5 , 2 1 8 . 8 6 it it it 2 7 . 5 6 4 . 8 . 9 8 4 » ; 6 0 3 , 6 3 5 , 8 4 0 1 , 1 5 6 , 9 7 6 . 8 9 ti it it 2 6 . 2 5 9 . 8 . 9 3 8 ) 7 0 4 , 0 7 7 , 2 0 1 1 , 4 4 1 , 0 8 7 . 9 2 it ii it 2 5 . 3 5 6 . 7 . 9 3 8 75 4 , 3 3 5 , 0 5 8 1 , 6 2 3 , 6 2 3 . 9 3 tt ti it 2 4 , 8 5 3 . 1 . 9 3 8 8 0 4 , 4 3 5 , 2 6 7 1 , 6 9 7 , 4 1 1 . 9 3 it it ii 2 4 , 7 5 4 . 6 . 9 3 8 » 1 0 0 4 , 8 4 4 , 9 8 3 1 , 9 9 0 , 6 9 9 . 9 6 it tt tt 2 3 . 8 5 2 . 2 . 9 3 8 " 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 3 75 4,013,043 1,163,444 .83 3 20 858,525 120,765 .47 3 30 1,572,301 233,563 .59 3 40 2,047,783 403,529 .68 3 50 2,669,224 615,209 .75 3 60 3,316,581 846,445 .80 3 70 3,851,704 1,115,489 .83 75 4,191,905 1,307,630 .85 3 80 4,349,930 1,400,199 .86 3 100 5,239,442 1,976,666 .90 3 125 6,092,680 2,650,693 .93 4 20 1,246,026 195,298 .67 30 1,997,521 412,605 .79 40 2,639,093 680,808 .85 50 3,200,079 972,175 .89 60 3,649,124 1,252,717 .92 70 3,992,827 1,492,375 .94 Lag Flow 65.4 58.8 30.5 ii In BOD #/Ton Mean 58.1 56.1 Variance 56.1 n Out BOD #/Ton Lag Out 373. 350, 350.9 Mean 9.96 28.8 21.9 16.9 13.5 10.8 8.9 7.7 7.4 5.21 3.6 30.5 26.1 23.6 22.0 21,0 20.4 Variance 9.96 103.9 48.3 25.3 14.9 9.6 6.5 6.2 4.5 2.39 1.2 . 84.0 57.3 46.8 41.5 38.6 36.9 D(N,M) 0 .969 .908 .600 .538 .138 .185 .338 .338 .415 .415 .989 .938 .938 .938 .938 .892 KS(0.5) 0 .239 ti it Lag In • Stand .154 CL Out .16+ u o Q io O J2S Temp. = 35° Factor X Hydraulic Load Cost Cost O 2. 4- 6 8 /o. "71 7£ 71" 71 20 2Z 2JT~2G 2-8 30 3 Z 3fc 36 3§ % System Mean BOD lb/ton . 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 Lag CC Lag OC Lag Eff Lag Flow In BOD ///Ton Out BOD ///Ton Lag Out D In D In CL D Out CL Mean Var Mean Var D(M,M) KS(.05: Lag 3 20 744,249 115,300 .44 65.4 63.9 452.4 35.9 170.4 .985 .239 .246 .277 .215 30 1,479,950 217,095 .56 " tt 27.9 84.3 .954 II 40 2,010,533 367,296 .65 ti 22.0 45.0 .908 II tt 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 tt 10.0 8.3 0.0 ti tt 100 5,196,483. 1,882,857 .88 ti 7.2 4.5 .338 ti 125 6,145,002 2,590,265 .92 it 5.04 2.3 .415 it 4 20 1,222,553 177,606 .64 33.9 tt 37.1 129.3 .985 tt 30' 1,898,313 .381,223 .76 tt 32.1 88.3 .985 tt 40 2,586,126 633,017 .83 ti 29.1 71.8 .985 ti 50 3,164,641 921,892 .88 it 27.2 63.5 .969 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 to vO LAGOON CAPITAL AND OPERATING COSTS FOR COMBINATION 3 AND COMBINATION 4-SYSTEMS STANDARD INFLUENT X 1.1 Lag Lag Lag Lag Lag In BOD ///Ton Out BOD ///Ton Lag Out D In Lag D In CL D Out CL ' Comb Area CC OC Ef f Flow Mean Var Mean Var D(N,M) KS(.05) 3 75 4,013,043 1,163,444 .83 65.4 58.1 373.9 9.96 8.15 0 .239 S tandard 20 744,086 115,282 .44 ti 52.32 302.9 29.4 114.1 .984 it .277 .308 .169 30 1,479,887 217,083 .56 it it II 22.8 56.5 .907 it tt II tt 40 2,010,499 367,302 .65 II II it 18.0 30.1 .738 II tt tt it 50 2,512,810 560,583 .72 II it ti 14.5 17.9 .554 II ti II tt 60 3,159,880 784,990 .77 tt II ti 11.9 11.5 .385 n ti ti n 70 3,756,650 1,027,186 .81 it ti it 9.8 7.9 .015 II ti II tt 75 4,106,861 1,215,264 .83 it it it 8.6 7.5 .200 .239 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 4 20 1,222,499 177,589 .64 33.9 it ti 30.4 86.6 .984 .239 .277 .308 .153 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 i i 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 O I i : : : : O 2 <r 6 8 'O 12. If- /fe /8. 20 22- Of- 2& 28 3 ° 32. 3<£ 36 38 4 0 System Mean BOD lb/ton FIGURE 5.4 LAGOON CAPITAL AND OPERATING COST CURVES FOR COMBINATION 3 SYSTEM WITH STANDARD INFLUENT LOAD MULTIPLIED BY 1.1 AND .9. i NUMBERS BESIDE DATA POINTS INDICATE LAGOON AREA IN ACRES. * 132 expected difference however is that the efficiency of any given size lagoon has gone up for higher temperatures and down for lower. The data points on Figure 5.2 are labelled according to lagoon temperature and size. Notice also that the capital costs of any given sized lagoon increase with tempera-ture. With an increased reaction rate more oxygen is required in order to maintain f i r s t , the biological activity and, second, the assumption that the reaction rate i s constant, therefore more aerators and/or more power are needed, resulting in increased capital cost. From these results, we would therefore anticipate the change in flow and effluent load to enclose the curve in Figure 5.1. Looking at Figures 5.3 and 5.4 we see that this i s the case. The higher load and higher flow curves are both above the standard curve and similarly 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 is not changed significantly (at .05 significance level), according to the K-S test, for the 10% change in flows (.200 <.239). Similarly the output from the 80 acre lagoon is not significantly different 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 influent into the lagoon differs significantly for both factor loading experiments. The effluent i s significantly identical for a 70 acre lagoon with a .9 factor loading and for an 80 acre lagoon with a 1.1 factor loading. 133 Referring to Tables 5.3 A and 5.4 A, despite the lower mean and variance for the i n f l u e n t i n Table 5.3 A (and noticeably i t s s i g n i f i c a n t s i m i l a r i t y to the standard i n f l u e n t ) , lagoon e f f i c i e n c i e s f o r any given area are l e s s i n Table 5.3 A than i n 5.4 A as are also the means and variances of lagoon e f f l u e n t . This implies the lagoon model i s more s e n s i t i v e to change i n flow than changes i n i n f l u e n t concentration. The cause.is probably the decreased residence time with increased flow r e s u l t i n g i n a lower operation e f f i c i e n c y . To t e s t the impli c a t i o n s of s p i l l frequency on the waste treatment cost curves, an experiment was run using a pulp m i l l e f f l u e n t trace with s p i l l frequency d r a s t i c a l l y increased. A l l c h a r a c t e r i s t i c s of the m i l l were maintained except f o r the "time between unrelated s p i l l s " d i s t r i b u t i o n f o r the recovery area. For the standard m i l l trace the time between unrelated s p i l l s ( i n the recovery area) had a mean of 207.45 hours and a standard deviation of 290.13 hours. To increase s p i l l frequency the mean and standard d e v i a t i o n were both changed to 100 hours. To accomplish t h i s the gamma d i s t r i b u t i o n parameters had to be changed. From K i t a and Morley (1973), the parameters are r e l a t e d as A - - 2 - 100 = .01 (100) 2 and 8 = ( a ) 2 = 1.0 134 These changes were introduced i n t o the pulp m i l l model, a new e f f l u e n t time s e r i e s was generated and was given as i n f l u e n t to the waste treatment model. 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 , expressed as l b BOD/ton, were compared to the standard system t r e a t i n g the standard 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 of f i t t e s t . The r e s u l t s are summarized i n Table 5.5 and Fig u r e 5.5. Comparing Tables 5.1 and 5.5 we can see that the increased number of s p i l l s had l i t t l e e f f e c t on lagoon e f f i c i e n c y and costs f o r a given lagoon area, although i t d i d in c r e a s e the mean and v a r i a n c e of the l b BOD/ton of the lagoon e f f l u e n t . As a consequence, the s i z e of lagoon necessary to mainta i n a below 15 l b BOD/ton e f f l u e n t average inc r e a s e s s i g n i f i c a n t l y . This i s more e a s i l y seen i n Fi g u r e 5.5. For the increased s p i l l s experiment a 70 acre lagoon i s r e q u i r e d at a c a p i t a l cost of 3.75 m i l l i o n d o l l a r s , w h i l e f o r the standard m i l l a 55 acre lagoon i s s u f f i c i e n t a t a cost of 2.7 m i l l i o n d o l l a r s , a saving of up to 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 Table 5.6 i s a summary of experiments run f o r d i f f e r e n t c l a r i f i e r d e t e n t i o n times f o r system combinations 1 and 2. The cost curves are p l o t t e d i n Figure 5.6. The c l a r i f i e r doesn't have the c l e a r dominance property that was observed f o r the lagoOn model. The c a p i t a l cost curves i n t e r s e c t at a mean of 11.6 l b SS/ton w i t h a c a p i t a l cost of approximately 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 AREA OF MILL ~omb Lag Area Lag CC Lag OC Lag Eff Lag Flow In BOD ///Ton Out BOD ///Ton Lag Out Mean Var Mean Var D(M,M) KS(.05) 3 20 734,982 114,920 .43 66 76.0 542.1 43.7 189.2 .923 .239 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 4 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 U i 0 2 ^ 6 ' /o /2 /</ ' <6 /8 2D Z 2 Z¥- 2 6 2 8 5 0 32. 3<r- 3 6 3 8 to 4 2 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. TABLE 5.6 CLARIFIER CAPITAL AND OPERATING COST FOR THE COMBINATION 1 AND 2 SYSTEMS WITH DIFFERENT CLARIFIER DETENTION TIME Comb Det. Time Hrs C l a r . CC Clar. OC Cla r . E f f . In SS ///Ton Out SS ///Ton CL Out Mean Var Mean Var D(M,M) KS(.05) 3 3 584,190 47,566 .82 42.6 187.7 9.96 8.2 0 0 1 2 711,020 74,555 .69 42.6 187.7 12.7 13.0 .092 .238 4 1,345,351 74,555 .85 II II 6.1 2.9 .938 II 5 1,651,934 Tl .89 II II 4.7 3.1 .923 II 6 1,953,617 II .91 ii if 3.7 2.7 .938 II 7 2,251,286 11 .93 it II 3.0 2.6 .938 it 2 2 402,300 47,566 .70 42.6 187.7 17.1 24.9 .538 .238 4 761,199 II .86 ii ti 11.5 11.7 .262 II 5 934,663 II .90 ii II 10.3 9.5 .523 it 6 1,105,355 it .92 ii II 9.5 8.2 .723 II 7 1,273,776 ti .94 it ii 8.9 7.3 .830 II O / 2 • 3 • £ S 6 ? 8 9 to II /Z. IS rf 15 Z6, If 18 Effluent Mean SS lb/ton FIGURE 5.6 CLARIFIER CAPITAL COST CURVES FOR COMBINATION 1 AND COMBINATION 2 SYSTEMS. NUMBERS BESIDE DATA POINTS INDICATE THEORETICAL DETENTION TIME. 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. Output Clar KS Tests Mean Var Mean 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 Standard 3 42.6 187.7 13.4 15.7 140 levels greater than or equal to 11.6 lb SS/ton the combination 2 cost curves dominate since both i t s capital and operating costs are least. 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 for a 3 hour detention time c l a r i f i e r in a combination 3 system. K-S goodness of f i t tests were performed against the earlier described standard. The results are summarized in Table 5.7. In a l l cases the null 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 intensities and over various time periods. These are summarized in Table 5.8. A l l the experiments were monitored for 11 days after the shock was initiated and the daily levels represent lb BOD/ton. A l l the experiments peak on day six as a consequence of the exponential form of the lagoon model. Remember i t was assumed that the hydraulic flow i s not altered by s p i l l s (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 in 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 effluent 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 results in an effluent concentration 30 x normal for 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 48 HOUR 24 HOUR 10- HOUR 5 HOUR 1 HOUR Day Factor 5 10 100 5 10 50 100 10 100 5 100 100 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 . 8 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 10.6 142 Shock Interval O 2.0 <fO 60 g o /oo /2.0 fao /fco /60 200 Z2x> 2Ho 2&a Time - Hours FIGURE 5.7 LAGOON RESPONSE CURVES FOR SHOCK INTERVAL OF 24 HOURS 143 TABLE 5.9 TABLE SHOWING LAGOON MAXIMUM CONCENTRATIONS AND RECOVERY TIMES  AS A CONSEQUENCE OF VARIOUS SHOCK LOADS Si z e Time Time to Max Time From Normal of Fac t o r I n t e r v a l Max Cone. Max to Normal Cone 100 1 54 hrs 81 mg/1 244 hrs 21 mg/1 100 5 53 hrs 185 mg/1 270 " 50 ti ti 105 " 250 " " 100 10 43 " 300 mg/1 300 hrs » . 10 1  54 " 50 " 176 " 100 24 44 hrs 700 mg/1 306 " " 50 II ti 350 mg/1 294 " 10 II it 90 mg/1 230 11 " 100 48 29 hrs 1230 mg/1 337 hrs 10 II 29 140 mg/1 264 " " 144 which according to the r e s u l t s i n Gove (1974) w i l l almost surely r e s u l t i n a f i s h k i l l . (Note a s p i l l of t h i s s i z e i s somewhat u n l i k e l y since i t would represent several hundred thousand gallons of weak black l i q u o r ) . Some other response curves are summarized i n Table 5.9. Their implications on the environment however, are not int e r p r e t e d here. To test 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 i n a s p i l l basin and then r e l e a s i n g i t over time makes a considerable d i f f e r e n c e on a lagoon's perfor-mance, two experiments were run. The f i r s t with a f a c t o r of 10 x normal fo r 10 hours and the second with a f a c t o r of 2 x normal f o r 70 hours. (The 10 x normal s p i l l f o r 10 hours represents, a s p i l l equivalent to approximately 100,000 gallons of weak black l i q u o r , the 2 x normal for 70 hours represents approximately the same BOD loading). The r e s u l t s are presented below. Experiment Normal Cone. (mg/l) Max. Cone. Reached (mg/l) Time of Max. Time Max. to Normal lb/ t o n Max. Out lb/ton Max. In 10 x 10 hr 20 40.9 33 hr 178 hr 32.7 102.1 2 x 70 hr 20 23.0 33 hr 170 hr 21.0 106.3 Both experiments reached maximum concentration at the same time and took the same length of time to recover. However, the 2 x 70 experiment r e s u l t e d i n considerably lower e f f l u e n t concentrations over the same time span. This implies that i f adequate s p i l l monitoring i s maintained enabling a s p i l l 145 to be diverted to a collection basin, releasing i t at controlled levels over time w i l l greatly decrease the s p i l l ' s impact on the treatment system and the receiving stream. 5.3 SUGGESTED DATA COLLECTION SCHEMES AND MODEL IMPROVEMENTS 5.3.1. The Pulp M i l l Model One definite improvement for the pulp m i l l model is a better data base. The following i s a l i s t of the ideal data base that would f a c i l i t a t e the develop-ment of a better pulp m i l l model. 1. Hourly samples from the six major m i l l sewers indicated in Chapter III, determination of their BOD and SS loadings, and pH Also a record of the hourly flow past each of the monitored points. Continue for one week of operation. 2. For a period of 2 to 4 months daily samples at the same locations determining their BOD and SS loadings, pH and daily flows. 3. Complement #1 and ill with conductivity charts for each of the six sewers with complete identification of s p i l l locations and the chemical spilled. 4. Possibly make a more extensive study of the related s p i l l concept developed in Chapter III. Such things as repetitive equipment failures can often be modelled very well 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 in 1, 2 and 3. 146 6. Monitor 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 adequately s i n c e they represent a sever shock to secondary waste treatment systems. 7. For the same periods 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 determining t h e i r BOD and SS l o a d i n g s , pH, temperature and flow. Another p o s s i b l e improvement i s an increase i n the number of major areas considered by the model. However, i g n o r i n g the increased data requirements t h i s would e n t a i l , i t may a l s o destroy the v a l i d i t y of the s t o c h a s t i c " b l a c k box" approach used. To maintain the model's v a l i d i t y , development of more exact transform f u n c t i o n s to generate the r e g u l a r e f f l u e n t would probably be necessary. This then gets back to the problems of modelling the k r a f t and b l e a c h i n g process d e t a i l s . Such an approach should give a more d e f i n i t i v e model but may not i n c r e a s e the a p p l i c a b i l i t y of the model to the purposes at hand. 5.3.2. The Waste Water Treatment Model Data was not as c r u c i a l to development of the waste treatment model s i n c e i t was a mathematical model of the process. However a b e t t e r data base i s needed f o r model v a l i d a t i o n . The i d e a l data base here would be the f o l l o w i n g . 1. Hourly a n a l y s i s of i n f l u e n t and e f f l u e n t f o r both the c l a r i f i e r and lagoon, r e c o r d i n g BOD and SS l o a d i n g s , pH, temperature and flow. For the c l a r i f i e r one week of data should s u f f i c e . For the lagoon at l e a s t two weeks i s recommended. A l s o the c l a r i f i e r should have samples taken every 10 or 15 minutes over one or two days to get a 147 better p i c t u r e of i t s dynamic behaviour. 2. This should be complemented with continuous conductivity charts of the i n f l u e n t and e f f l u e n t f o r both c l a r i f i e r and lagoon. One improvement of the waste treatment model would be the i n c l u s i o n of models and cost curves for other process often used to tr e a t pulp m i l l wastes, ( i . e . , A c t i v a t e d sludge, t r i c k l i n g f i l t e r s , etc.) By making i t po s s i b l e for a user to experiment with various process combinations, other r e l i a b l e systems, within a m i l l s budget and/or space l i m i t a t i o n s could be explored. These models could be of a steady state nature, i t e r a t i n g on a reasonable dynamic time scale. Of course the v a l i d i t y of the steady state approach would have to be explored. Another improvement would be the development and v a l i d a t i o n of a b e t t e r c l a r i f i e r model. It. appears from a recent communication with Dr. S i l v e s t o n , at Waterloo U n i v e r s i t y that the l i n e a r r e a c t i o n assumption f o r c l a r i f i e r s e t t l i n g may be an oversimplication of the process. S i l v e s t o n i s c u r r e n t l y developing another approach to modelling the dynamic operation of a c l a r i f i e r . 148 CONCLUSIONS ' The purposes of t h i s study as stated at the beginning of Chapter I I were to: 1. Develop two simulation models, one of the wastewater from a k r a f t pulp m i l l and another of a t y p i c a l waste modification system common to the pulping industry. 2. Study the cost v a r i a b i l i t y of waste treatment as a function of d i f f e r e n t system designs. It i s f e l t that these purposes were s a t i s f i e d . The f i r s t four chapters describe the development, structure and v a l i d a t i o n for the two models i n #1. Chapter V describes a sequence of experiments run with the models to determine the waste treatment systems s e n s i t i v i t y both i n terms of cost and q u a l i t y of e f f l u e n t , f u l f i l l i n g purpose #2. The models developed are not perfect by many means and often represent s i m p l i f i c a t i o n s of the processes involved. They have however served a number of u s e f u l functions. These are now summarized: 1. A "black box" approach was s u c c e s s f u l l y used to provide a reasonably dynamic approximation of the water borne e f f l u e n t s from the pulping process. 2. A f i r s t attempt was made to analyze chemical s p i l l data and t r y and incorporate the e f f l u e n t implications of the s p i l l s i n a model of the m i l l ' s e f f l u e n t production. 3. A reasonably w e l l v a l i d a t e d model of a lagoon was developed and found to be more s e n s i t i v e to changes i n flow than i n f l u e n t 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 lagoon. 4. The frequency of s p i l l s , which although observed to have l i t t l e effect on the efficiency of a lagoons performance, greatly affected the mean lbs BOD/ton of the effluent. The cost implications of this were found to be quite substantial. Also the size of lagoon required to meet the Pollution Control Boards Level A was also greatly affected. 5. A clear cost dominance relationship was found for three of the four waste treatment system configurations experimented with. When attempting to satisfy any effluent BOD quality level i t was always less expensive, 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 outfalls through the lagoon rather than bypass the lagoon with the acid sewer. 6. The level A standard for c l a r i f i e r operation was demonstrated to be satisfied with less cost, by feeding only the general and machine room outfalls to the c l a r i f i e r . These are the major results. Many more observations and conclusions can be drawn from the experiments run. Also the experiments described in Chapter V do not exhaust the p o s s i b i l i t i e s available with the models as they now stand. For example shock load experiments for different size 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 different s p i l l distributions to determine the 150 marginal costs of reducing the mean l e v e l s , etc. I t would appear i n conclusion that the techniques employed i n t h i s study could be of considerable use to pulp m i l l management i n making a waste treatment system investment decision. The trade o f f s become much c l e a r e r and a l t e r n a t e designs can be examined without the " r e a l world" consequences. The imperfections of the models should be kept i n mind but only as i n d i c a t o r s f o r future development. Through continued experimentation and development, the v a l i d i t y of a model and therefore i t s usefulness grows. It i s hoped that t h i s study has provided another step i n that d i r e c t i o n . BIBLIOGRAPHY 152 1. Andrews, J.F. (1974) "Dynamic Models and' c o n t r o l Strategies f or Wastewater Treatment Processes." Water Research, Vol 8, 1974 pp. 261-289 2. Beak - Environment Canada (1973) " B i o l o g i c a l Treatment and T o x i c i t y Studies".Economic and Technical Review Report EPS3-WP-73-6 3. Bodenheimer, V.B. (1967) "Factors to Consider i n Waste Treatment Systems Evaluation" Southern Pulp and Paper Manufacturer, Feb 10, 1967 4. Bower, B. (1971) - Residuals- M o d i f i c a t i o n - D e s c r i p t i o n of Procedures and Data Sources - Resources for the Future Report - 1971 5. Boyle, T.J., and Tobias , M.G. 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(1973) "Wastewater Treatment Plant Cost Estimating Program' Documentation" U.S. Environmental Protection Agency, NTIS, PB-222-762 16. E i l e r s , R.G. and Smith, R. (1973) "Executive D i g i t a l Computer Program For Preliminary Design of Wastewater Treatment Systems Documentation" U.S. Environmental Protection Agency, NTIS PB-222-71 17. Erickson, L.E., Ho, Y.S. and Fan, L.T. (1968) "Modelling and Optimiz-ati o n of Step Aeration Waste Treatment Systems" Journal W.P.C.F. Vol. 40, #5, Part 1 May, 1968 pp. 717-732 18. Fan, L., Mushra, P.N., and Chen, K.C., (1972) " A p p l i c a t i o n of Systems Analysis Techniques" in B i o l o g i c a l Waste Treatment" Proceedings IV IFS: Fermentation Technology Today pp. 555-562, 1972 19. Fishman, G.S. (1973) "Concepts and Methods i n Discrete Eyent D i g i t a l Simulation", John Wiley & Sons, N.Y. 197 3 20. Gehm, H.W., and Gove, G.W. (1968) "Kraft M i l l Waste Treatment i n the U.S. - a Status Report", NCASI Tech. 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(1972) "Environmental Care at Pulp M i l l s , Results and Expectations" Svensk Papperstidning #1 15 January 1972 pp. 5-14 28. Levenspiel , 0. (1972) "Chemical Reaction Engineering - 2nd E d i t i o n " John Wiley & Sons Inc., N.Y., 1972 29. Libby, C.E., "Pulp and Paper Science and Technology", Volume I-Pulp McGraw H i l l , N.Y. 1962 30. L i l l i e f o r s , H.W. (1969) "On the Kolmogorov - Smirnov Test for the Exponential D i s t r i b u t i o n with Mean Unknown", American S t a t i s t i c a l A s s o c i a t i o n Journal, March 1969, pp. 387-389. 31. Logan, J.A. et a l , (1962), "An Analysis of the Economics of Wastewater Treatment" Journal WPCF, Vo l . 34 #9, Sept. 1962 pp. 860-882 32. McCabe, B.J., and Eckenfelder, W.W., e d i t o r s , (1956), " B i o l o g i c a l Treatment of Sewage and I n d u s t r i a l Wastes" Reinhold Publ. N.Y. 1956. 33. McKeown, J.J.,.and Gellman, I., (1974) "Characterizing E f f l u e n t V a r i a b i l i t y from Paper Industry Wastewater Treatment Processes. Employing B i o l o g i c a l Oxidation" NCASI Special Report. 34. Mishna, P.N., et a l . " B i o l o g i c a l Wastewater Treatment System Design - Parts I and I I " The Canadian Journal of Chemical Engineering, Vol. 51, December 1973, pp. 694-708. 35. Montgomery, M.M., and Lynn, W.R. (1964) "Analysis of Sewage Treatment Systems by Simulation" Journal of the Sanitary Engineering Div., Proc. of the American Society of C i v i l Engineers, SA1, February 1964, pp. 73-97. 36. Naito , M., et a l . (1969) "Optimization of the Activated Sludge Process -Optimum Volume Ratio of Aeration and Sedimentation Vessels." Water Research Vol. 3 pp. 433-443. 37. Naylor., T.H. et a l . , (1966) "Computer Simulation Techniques" John Wiley & Sons, N.Y., 1966. 38. P h i l l i p s , D.T. and B e i g h t l e r , C.S. (1972) "Procedures f o r Generating Gamma Vanates with Non-Integer Parameter Sets" Journal of S t a t i s t i c a l Computation and Simulation V o l . 1, #3 J u l y 1972. 155 39. R a i f f a , H. and Blaydon - unpublished manuscript "An Introduction to  Markov Chains" AO. Rand, G.H., (1972) "Elements of S e l e c t i o n f or Secondary Waste Treatment Systems" TAP PI,- V o l . 55, #8 Aug 1972 pp. 1192-1194 41. Romans, H., (1970) "Process Modelling and Analysis i n the Wood Pulping Industry: Wood Pulping, Pulp Bleaching and Stock Preparation" U n i v e r s i t y of Idaho Ph.D. 1969 42. Ross, S.M., "Applied P r o b a b i l i t y Models with Optimization A p p l i c a t i o n s " Holden Day, San Francisco, 1970 43. Sakata, N., and S i l v e s t o n , P.L., (1974) "Technical Note - Exponential Approximation for S e t t l i n g Rate" Water Research V o l . 8 pp. 491-492, 1974 44. S e r v i z i , J.A. and Gordon, R.W. (1973) "De t o x i f t e a t i o n of Kraft Pulp M i l l E f f l u e n t by an Aerated 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 Parametric S t a t i s t i c s f o r the Behavioural Sciences" McGraw-Hill, N.Y. 1956 46. S i l v e s t o n , P.L. (1969) "Design of S e t t l i n g Basins with Allowance for Residence Time D i s t r i b u t i o n s " The Canadian Journal of Chemical Engineering V o l . 47, Oct. 1969 pp. 521-524 47. S i l v e s t o n , P.L. (1972) "Simulation of the Mean Performance of Municipal Waste Treatment Plants" Water Research V o l . 6 pp. 1101-1111 48. Smith, B.W., (1969) " D i g i t a l Simulation of Papermaking Processes" Appita Vol. 22 #6 May 1969 pp. 163-171 49. Smith, R. (1969) "Preliminary Design of Wastewater Treatment Systems" Journal of the Sanitary Engineering Div. Proceedings of the American Society of C i v i l Engineers SAl, February 1969 pp. 117-145 50. Smith, R. (1968) "Preliminary Design and Simulation of Conventional Wastewater Renovation Systems Using 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 Publ //WP-20-9 51. Stephenson, J.N. (1950) e d i t o r , "Preparation and Treatment of Wood Pulp" McGraw-Hill N.Y. 1950 52. Stephenson, J . , and Nemetz, P. (1974) "Proceedings on Conference on Economic incentives f or A i r and Water P o l l u t i o n " Westwater Research Centre, U.B.C. June 1974 156 53. Swedish Steam Users Ass o c i a t i o n , e d i t o r s (1974) "The SSVL Environmental Care P r o j e c t " Technical Summary - Stockholm 1974 54. S u l l i v a n , P.R. and Schoeffler, J.D. (1965) "Simulation of Stock Preparation and Foundrinier Dynamics" TAPPI V o l . 48, #10 October 1965, pp. 552-557 55. Takamatsu, T., and Naito M. (1967) " E f f e c t s of Flow Conditions on the E f f i c i e n c y of a Sedimentation Vessel" Water Research Vol. 1 1967 pp. 433-450 56. Terhan, R.J., (1967) "Simulation i n the Pulp and Paper Industry" Pulp 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 Kraft M i l l Operating and Process 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 Vol. 72 #2 pp. T81-T87 February, 1971 58. Wilcox, 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 Equations" In t e r n a t i o n a l Textbook Co., Penn. 1966 59. Wine, R.L. (1964) " S t a t i s t i c s for S c i e n t i s t s and Engineers" Prentice-H a l l , N.J. 1964 157 A - l APPENDIX I SEMI-MARKOV ANALYSIS OF RELATED SPILLS In Chapter I I I a semi-markov approach was introduced as a convenient way to describe a s p i l l sequence. In the following few pages t h i s semi-markov approach w i l l be c a r r i e d through to determine the processes l i m i t i n g p r o b a b i l i t i e s and passage times. The notation and l o g i c of development i s borrowed from a set of notes written by R a i f f a and Blaydon c a l l e d "An Introduction to Markov Chains". To the author's knowledge these notes have not been published, however, the necessary d e f i n i t i o n s are included, i n the development and the l o g i c should be c l e a r to a reader f a m i l i a r with Markov-Chains. A s t o c h a s t i c process {X , n = 0, 1, 2, ....} with a f i n i t e or countable n state space, i s said to be a Markov chain i f for a l l states i g , i i , ••• n _ p X = i • X, — i t , . . . . , X , = i , , X = i } o o 1 1 ' n-1 n-1 n = P { X n + l = ^| Xn = i } and a l l n > 0 P{X • . = j — n + 1 J A s t o c h a s t i c process which makes t r a n s i t i o n s from state to s t a t e i n accordance with a Markov chain, but i n which the amount of time spent i n each state before a t r a n s i t i o n occurs i s random, i s c a l l e d a semi-Markov chain. Now i n the context of Chapter I I I we have a state being defined as the sequential l o c a t i o n of a s p i l l i n the current r e l a t e d s p i l l sequence of an area. A r e l a t e d s p i l l i s a s p i l l i n the same m i l l l o c a t i o n as the immediately 158 preceding s p i l l f o r the current major area. For example say we have the following time sequence of s p i l l s i n major area 1 of the m i l l (recovery area) Time State of Time of S p i l l D i fference System (hrs) 0 1 25 25 1 38 13 1 39 1 rNrelated 43 4 2 / s p i l l 52 9 3J sequence 64 12 1\ 69 5 2 Jrelated 73 4 3>spill 75 2 4\sequence 80 5 5/ 100 20 1 120 20 1 In the above there are 6 r e l a t e d s p i l l sequences. The f i r s t 3 are only 1 s p i l l long, the fourth i s 3 s p i l l s long and the f i f t h i s 5 s p i l l s long followed by the s i x t h which i s again only 1 s p i l l long. The sequences must always s t a r t with the system i n state 1, no state can be missed i n moving along the chain from state 1, and at the end of a r e l a t e d sequence the system returns to state 1. From the data described i n Chapter I I I the following t r a n s i t i o n matrix was derived f o r s p i l l s i n sub area 3 (weak black l i q u o r s p i l l s ) See Table A l . 159 State 1 2 3 4 5 6 1 11/31 20/31 0 0 0 0 2 9/20 0 11/20 0 0 0 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 only 6 p o s s i b l e states. From a K-S goodness of f i t routine the times between r e l a t e d s p i l l s f o r sub area 3 f i t the negative binomial with p = prob of success = .288 k = .801 This implies a mean residence time i n the states, 2, 3, 4, 5, 6 equal to the mean of the negative binomial d i s t r i b u t i o n : mean k x (1 - p) .8 x .71 .29 = 1.95 hrs For the times between unrelated s p i l l s a K-S goodness of f i t t e s t found the exponential d i s t r i b u t i o n , with mean 0 = 156.4 hours, to give a good f i t . Therefore the mean residence time i n state 1 i s 156.4 hours. 160 Now i f we take the t r a n s i t i o n matrix given i n Table A l we can solve for the stationary p r o b a b i l i t i e s that would be operative i f the process were an ordinary Markov chain. Solving we get: 11 9 2 2 2 Hi = — n i + — H2 + — n 3 + T n4 + 7 n 5 + n6 31 A 20 * 11 3 3 20 1 1 2 "77 1 , 1 11 n o = — n 2 20 6 and ST1 n i = 1 i = 1 161 Solving the above simultaneous equations Iii = .414 n 2 = .266 H 3 = .22 Jlk =- .12 n 5 = '.04 n 6 = .0133 These six probabilities then are the limiting probabilities of finding the system in each of the states ignoring the state residence times. The following is the semi-Markov analysis which w i l l take into account the different time distributions. Define: S_. = state i x expected waiting time for a transition from S± to S^  given that the transition i s definitely going to take place. T 21 = T 3 1 = Tm = T 5 1 = T 6 1 = 156.4 hrs = 1.95 hrs E j j : = probability of a transition from S± to S^  by t = <=° (i.e. given that a transition from S± i s definitly going to occur, p, . is the probability that the system w i l l be going to S ) 162 Therefore define = expected w a i t i n g time i n j S o l v i n g f o r a l l the s t a t e s 1 31 " ~ w " ' 31 Ti = P i i T n + P12T12 = T f x 156.4 + |£ x 1.95 56.8 hrs P21T21 + P23T23 = 20 x 1 5 6 , 4 + i o x 1 - 9 5 71.5 hrs T 3 = P31T31 + P34T34 = 3J x 1 5 6 ' 4 + 11 x 1 - 9 5 30.0 hrs f 4 = P 4 1 T 4 1 + P 4 5 T 4 5 = 2 x 1 5 6 > A + I x 1 > g 5 = 104.95 hrs T 5 = P51T51 + P56T56 = f x 156.4 + | x 1.95 = 104.95 hrs T 6 = P 6 l T 6 l + P 6 7 T 6 7 = 1 x 156.4 = 156.4 h r s Row i f we compute the p r o p o r t i o n of time that the process spends i n S^  as t 0 0, t h i s should be the same as the l i m i t i n g p r o b a b i l i t y of being found i n that s t a t e or (b*. J Since f o r the imbedded process the l i m i t i n g p r o b a b i l i t y of a t r a n s i t i o n to S. i s II. , the p r o p o r t i o n of time spent i n S. should equal <j>*. 3 3 3 3 163 Therefore <J>* = ( T f ^ ^ ^ ) J i i i Solving for the s i x states = n ] T i = .414 x 56.8 TTTTT 71.5 T-tH.T. x 1 x x ,33 - -266 x 71.5 _ „,, ~ TTTS— - ' 2 6 6 .22 x 30 „ 0. ^ = 71.5 = - ° 9 4 f>3 = - 1 2 x 105 = fi 71.5 I x _ .04 x 105 _ - T T T ^ ~ - 0 5 8 5 ^ = - 0 1 3 7 ^ l 5 6 - 4 = .0283 Note that (f>* does not depend on the form of the holding time d i s t r i b u t i o n but only on the mean holding times. Define the l i m i t i n g p r o b a b i l i t y ej as the l i m i t i n g p r o b a b i l i t y that on any step the process i s entering state Sy Now arguing i n t u i t i v e l y , since T\ i s the expected length of stay i n S_. then d i v i d i n g 4>^, the l i m i t i n g p r o b a b i l i t y of being i n state j , by f , should be roughly the p r o b a b i l i t y of entering Sj on any step of that i n t e r v a l . 164 Therefore e* = l i m i t i n g p r o b a b i l i t y that on any step the process i s entering S . _ 3 ~ T 3 Solving f o r the s i x states . . . 33 1 " 56. .266 71.5 = .0058 .0037 .094 >* = = .00167 105 .0585 105 .00056 - i f f 5 ! = - 0 0 0 1 8 Define the 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 p r o b a b i l i t y that on any step the process i s i n S - and the next t r a n s i t i o n w i l l be to S.. 3 We know the long run p r o b a b i l i t y of f i n d i n g the process i n i s cj>*. The N t o t a l expected holding time i n S i s T^ ~ ^ P i k T i k' T n e f r a c t i o n s of K= i P i • T i • t h i s holding time that i s due to t r a n s i t i o n s from S^ to S^  i s —^3 2 165 Therefore Therefore we get = .32 P n T .1.1 x 11 ,33 x .355 x 156.4 56.8 S i m i l a r l y 1 2 * = .0104 * 3 - * - .007 2 1 * = .261 = .172 2 2 * = 0 = .0011 2 3 * = .0057 fcl* = .0574 3 1 * = .087 $ 5 6 * = .00356 * 6 1 * = .0283 the l i m i t i n g t r a n s i t i o n p r o b a b i l i t i e s we can Again note that the l i m i t i n g entrance p r o b a b i l i t i e s do not depend on the holding time d i s t r i b u t i o n s but only on the expected holding times. If however we were not interes t e d 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 intermediate step p r o b a b i l i t i e s , the expressions do depend on the holding time d i s t r i b u t i o n s . This w i l l not however be pursued here. One f i n a l l i m i t i n g parameter of i n t e r e s t i s the mean f i r s t passage times. Define 9•• , the expected time of passage from state i to state j . For a 166 semi-Markov chain, the mean recurrence time, 0.., i s —, , the r e c i p r o c a l of l i e * 3 the l i m i t i n g p r o b a b i l i t y of entering state j . Therefore 1 e* e 2 2 = 271 hrs 033 = 327 hrs 600 hrs 855 = 1785 hrs 9 6 6 = 5550 hrs 174 hrs From t h i s we can conclude that i n the long run (as t -> °°) every 174 hours there w i l l be a s p i l l i n sub area 3 which could be the i n i t i a t o r of a r e l a t e d sequence of s p i l l s . Every 271 hours there w i l l be a r e l a t e d sequence of s p i l l s at l e a s t 2 s p i l l s long. Every 327 hours there w i l l be a r e l a t e d sequence of s p i l l s at l e a s t 3 s p i l l s long and so on. These r e s u l t s although not used i n the model developed i n t h i s study could be use f u l for an a n a l y t i c examination of s p i l l s and t h e i r r e l a t e d costs. By es t a b l i s h i n g a semi-Markov d e c i s i o n process f o r a l l the major areas within the m i l l , i t may be possible to associate some costs with the s p i l l s and optimize the process. Since a s p i l l has both a cost consequence (the cost of r e p l a c i n g chemical, and possible above e f f l u e n t l e v e l f i n e s ) and a ben e f i t consequence ( i f a s p i l l i s ignored, maintenance costs, etc., are reduced), the r e s u l t s may be quite informative as to the tradeoffs involved i n s p i l l monitoring and prevention. 167 A-2 APPENDIX II DERIVATION OF CONVERSION FACTORS TO CONVERT Na2S0h EQUIVALENT SPILLS TO GALLONS OF CHEMICAL As noted i n Chapter I I I the generation of s p i l l amounts i n the pulp model i s i n terms of pounds of Na2SG\ (saltcake) equivalent. The model then determines the s p i l l sublocation and converts the Na2SG\ amount to the equivalent number of gallons of chemical t y p i c a l to that sublocation. Knowing the BOD and SS mg/l values for each of the chemicals (see Table 3.9), the s p i l l can be converted to i t s BOD and SS equivalent. The conversion f a c t o r s to convert pounds Na2S0ij to gallons of chemical for the four l i q u o r s are derived below. A l l the ana l y s i s f i g u r e s are taken from C.E. Libby (1962). 1. Weak Black Liquor (W.B.L.) T o t a l sodium i n W.B.L. taken as Na20 equivalent = 49.23 l i t r e Therefore since 1 gm of Na20 = 2.29 gms Na2S0i t f o r equivalent amounts of sodium the t o t a l sodium i n W.B.L. taken as a Na 2SOi t equivalent = 49.23 x 2.29 = 112.74 g/1 Therefore concentration ( i n terms of Na 2 S 0 4 ) = 112.74 l i t r e x 3.785 x - 3 } & x 2 2 ^ = .94 # y ? \ T p T or 1.06 g a l W . B . L . = 1# Na 2 S 0 4 1 10 gm kg US g a l of W.B.L 2. Strong Black Liquor (S.B.L.) For W.B.L. the percentage of s o l i d s by weight = 16%. For S.B.L. the percentage of s o l i d s by weight = 52.9%. 168 Assuming that only water i s l o s t i n the evaporators and that a l l the s o l i d s are transferred through, then the d i f f e r e n c e i n % of s o l i d s i s a consequence of the l o s s of water only. Now say we have 1 // of s o l i d s . Then 1 // of s o l i d s T T = 6.06 // W.B.L. 1/< or ~ ^ = 1.869 // S.B.L. Therefore i n W.B.L. there are 5.06 I, H 20 and i n the S.B.L. .869 // H 20. 5 06 — 869 This implies that the evaporators, evaporate —' ^ x 100 = 83% of the water From Libby (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 1 gal W.B.L. = 1.087 x 8.3 —^ r ~ n = 9.lit gal H2O (note: 1.5// are s o l i d s , 7.6// are H2O) Therefore a f t e r evaporation t h i s 9. lit of W.B.L. w i l l be reduced to 9.1// - .83 x 7.6# — - H ? ° I T _ T = 2.8# S.B.L. ga l of W.B.L. This 2.8// of S.B.L. w i l l have the same Na 2S0i 4 equivalent as the 9.1// of W.B.L. Now 1 ga l l o n S.B.L. = 1.325 x 8.3 " „ _ = 11.0// 1 g a l H 20 Therefore 2.8// S.B.L. .941 // Na 2SG\ 11.0// S.B.L. 1 g a l S.B.L. .941 x ^-r = 2.7 // Na 2S0 4 In other words 1 gal S.B.L. has a 3.7// Na 2S0 t + equivalent Therefore 1// Na2S0,4 = .27 gal S.B.L. 3. Green Liquor (G.L.) From an example G.L. an a l y s i s i n Libby (1962) 1 f t 3 G.L. contains Na 2S - 1.4// Na 20 equivalent NaOH - 1.1// Na 20 equivalent Na 2C0 3 - 5.9// Na 20 equivalent 169 Total a l k a l i content = 8.4// f t 3 as Na20 m,. , . . . Q , 0 o o r i i n 0 Na^SOu equivalent Thxs i s equivalent to 8.4 x 2.290 = 19.2 // — c — ; ^ , „ T  ft° or G.L. Therefore 1// Na0SO, =19.2 N a ? S ? 1 * x 1605 « .325 gal G.L. ^ H ft° gal 4. White Liquor (W.L.) From an example W.L. analysis in Libby (1962). In one cubic foot of W.L. there is Na2S - 1.4// as Na20 equivalent NaOH - 5.5// as _Na2 0 equivalent Na2C03~ 1.5// as Na20 equivalent Total a l k a l i content = 8.4// V 'i**9?, T f t J o f W.L. Therefore 1// Na 2S0 4is equivalent to 19.2// N a ^ 3 H x .1605 f t3 -1 gal = .325 170 A3 APPENDIX III A LISTING OF THE PULP MILL MODEL (FORTRAN) The logical units are assigned in the model as follows Logical Unit Task / / l Record of Daily production, water usage and fiber losses - i s generated by the model #2 Record of s p i l l s in major area 1 - generated by model #3 Record of s p i l l s in major area 2 - generated by model #4 Record of s p i l l s in major area 3 - generated by model #6 Record of total lbs of BOD, TS and SS generated by m i l l each hour #7 Input f i l e to be supplied by user for distribution parameters and other empirical data needed to run model #8 Record of BOD, TS and SS concentrations for each of the 3 outfalls each hour (mg/1) - generated by model #9 Record of hourly flows for each of the 3 outfalls (in MUSG) and the hourly production (in tons) - generated by model. Note: Units #8 and #9 are used as input into the Waste treatment model. 171 kr Ul vr Ire -J f* Ul lu vr o-P O Tl |C/ n c ;» o [< t> Z - i H <r -vn i f \ji lUi OJ ui u1 J> J> J*^  IV' H O j\D CrJ -0 73 n IV-- It It H-O U' J> O ;TT 7 ! n I-I : > . X- J> c 4- Ui l»J !UJ Ol OJ M O U [tv> U) tvl OJ fM OJ M rvj rsj f\J o; -J o n n rr ! o > n i> i L> — j C~ - j II 1 C t-- »--rvi r\j NJ \.r. 4s U-1 IM NJ fsj M t— O ,>• O JT' yv_' O r, -H 'in J" y r~ - . —i o •—1 > lo M K C* > w X 172 n n o 0 cj .-. p — |> r, o ii> TI i - 11 ~\\r- — II -si — ;l~ c, >; o :< I o i> | 1 JO ^ - II m .-, A l i p .J „|. n "1 |cc ^ o j II 11 r: ! o o II -c- i — *^ > Z. ZD •;-}; O co or, --j - -J - j -J •-.! -vt C Ul - i J> fV I II l o o Tl >0 ', ~P O JO t'-i rr O f~i f"1 • -H ^  ^ o o ~ - : o O vr. i r~) ^  o o o 1 <"* o r C O t— O sT> o 'C: r" y T. r U5TI...G rp H i t ILF-1 1 7 l i t 1 IS 1 2 1 123 12-, 127 U P 12? 13U I i i 132 123 134 131= 136 13/ 131 i 3 i ; 14C 1^1 142 14 3 14-t 145 146 147 14S 149 b C 151 152 1 S3 154 155 15o 157 l i t l-s, l o C 161 162 10 J 65 ( C M 1 N U ' h .': I I < T L. -A ( J ,.U L A ' ( r , U F 0 r. ; AT ( ... i = If 1 1 ' i » ( i ) , 1 o » 1 ^ t ) U 2 i - iv . j j , ( L i , K :, < i ) • ( J I , A S •> ( j j 12 5 [>=0+l I F { J - Ni u t A i ( 1 i 1 2 J ! i «lTIU)--,rlT( /> A 7 T ( 2 J ) ,r. 1 o L C 12 1 ( r i 1 I I • ) > \ T r ( 3 J 122 129 ' U i H  R 16) P R C ) T= f <1 :>i « v 2 4 . _ * :MJJ t . . ? t . l ^ ) U A T T ( n f t = i r F J ,•! A T | 1 < , , P'-,. 2 , < L C . i , 1 3 ) CALL JtGUL 0 0 1<J 1 = 1,3  (*-> I I - 1 , ^ ) I ( : .... ) i J •<")JT, T 76 I .= ( 7 I 1 ( GO TX Ii C C \ T I N L -/ iCi. ( ! ! : Z ? > [ I ) = <?. ).tO.T )GO 7u ; ' ( i ) * 2 . 2 ; ( i) * 2 . 2 Z T s< i )= T s i ; ) . 2  IF (I JJC( I ) .bT. S t x { I ) i S vi i M i r t C r i ! ) . L T , S c " . I N ( n i S f - ' I P ( n < (i J .Ai.UM'lM!-L> L^Jjli If (27 5 ( : ) .L T .ST v 1 >i t I ) j .> T.vi; IF (ZSS ! i ) .07 . S ? > « ( I ) iSSi-'i AXl ! 1 = /. -V K I ; r . ( : )=/riot i ) :<(:>=.-: 7 s < i) 130 135 1 F I / i S 1 1 1 . l. 7 . S c M •; ( ! ) 1 s S 1 1 GO TG(ltO,ljj,l4Ci»I P E A ) ( 2 . i 2o ) T I ,v t ( 1) , 10;. ( 1 ) , i J I K 1 ) =T.I < 1 )..•! GC r c 1)1 °. 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  ( I J = L T S ( I ) ( i ) = I, ( I ) ( I ) = Z S s. ( I ) i ) , A i S l i ) Al) 163 GC TC l C I 164 140 PL AM ( , , i j .•)) 7 ; K . ( > ) It 5 7 IV (3 )=J.l -I.:; ( ! )_U It 6 101 S P L ( 1 )' = '> f1 L ( I ) + 1 167 15 C C O T I O L ' : 16t H H00 ( 1 J -K :s l-;->H ( 1 i loS 17G 171 172 173 174 :o ( .),; . i . ) S(3 ) HT S( i ) =• MS S( 1) =•' no i C J : O-JO, ( 2 ) -• nl5( 2)=-1 Si'r ( i ) SS2ri( 1 ) •-2. • • i • . ' . /) +;•••'0 )->h ( 7 b ( 2 i T . a y n ( i ) t . /' / ;. . ( : - i i T•»( i - u HSS(2)=HS b( ?)+^ 174 lr\j ro ro io M O L> CO uo (/- —« (/• —1 — i -7 t/i co jrj < -i > —- •—• ro r\j f\j r\j ro ro vT CO -sj fsj rsj iro ro r\< ro N- r\j jro ro ro <?• u* -\>  ro H-1 ro ro N> r o ' O CO !rvi ro ro i—i ,—* i—i •vj c v.n jro ro no jro ro ro t~ o -f w ro jt~* o 00 "Tl ; i TJ 5L ; X; Ci A-r-. U [—• « X |(^ X u - i o - o T i j T t—' -—• K~ ! —i O .'"1 jro • . j " ro ro ro tisj ro ro o o o \CJ O O ^ - OJ ro ro iro c Un co -o vn CT- O " J > ^ >T. o; ro *-* vO cr: r.: —' r. O l o —H !t/> —- C ., ' — Oo O l •"•;IW ; w C/i ~ i — vX' U"> „ , r 5 :r\i r- *«v c- -i — r- — • w-. 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' ( i,* f.)) i:, J i (. v j ^_ ;,. .-• - v ^ \ ' M - < i c . . v; . ; 0.1 v 2 i > 29:; 296 2', / c C TIM::- V. • V .... , i > • L., r; • L f. 29 c 29 9 30 0 1J \ ? - h AT-: i J ., i) f- = \ :> I' IKS) M>y i ,•(<•• i ----r- (.-..-.,-•, Vf i | 301 3C2 30 3 u < -co.. ;T..-•r o (-'.\ ); ,R T-. J "; = '-•• S=bS(<r, ) 3 04 30b 306 L =K < + -J IF (L :.;.) TC 9 u CALL ; : \ i (•• . o , CT/ r, c, !•<.) 3C 7 360 309 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 2 10 211 2 12 T = T «• T 1 ( f i* 1 (ALL ,;' M i - ' . l t 1- i jTpC-iTiM ,f ) VT( K< ) = r : l-i.)0 • 313 3 14 2 ii-L S = C S L H (<•-. K i A AI- T ( < K 1 = -i -1 I ( < ) •• c : \ V1 C S ) 2 o c o \ T i , u 3 lc 317 2 1 fa t> JC ( KK ) =r.r-.!F (LSI*' A-'T( <  K- j T S (\ K ) = 1 S M L 9 1 -• A v T (r ) XSS<KK)~SSF I L S I ^ A f T l K M 3 19 220 32 i o sP( Kc ) = \ - u , C, J TC 1 70, 7 9 , rtO ) ,KF 70 WHITE(2,71)LS, TIM K\),- Ay! | M C ) , A Ci (»M,TiU.<] , / A S 1 I- K. ) 3^2 323 224 G J T rj 9C 7 5 y I r L ( 3 . 7 1 i L S , T }•> [ K. < j, / A y T ( ts i GC TC 9 0 , •*• CL Kri) , T ; ( K<) , XC i( "K. ) 3 2 1 320 327 ii 0 R I I C ( <, , 71 ! L A , T I M ,< -\) ,. \ > T ( ^  K J 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 i CL I H M , 7 S ( KK) ,XbS(KK) 22b 3 29 220 GO TJ 1 100 f.CMIN LA 'V E T 0 R \ 321 332 3 2 3 CMC C c 334 33b 3 36 su-i-c-oTiyc »'.TCJ (PS j o i , v>-Ur r <, c C WATfH U S A G E " y CAY A r ';, M,T nC 0IM i... »iT,nAT,W) 3 37 3 3 < 2 39 D 1 V: N i 1 • • \ .•< ,i T ( 3 ) , vT F - ". ( 2 , i i , 2 KCAL D!-iA!i;T N = l 340 341 3 42 Ki'4L'= H A'\ ; ( 0 . 0 ) DC tC 1-2,1) -34J 344 349 1 F ( X NO . C E . A1 A Tt ;- A ( , I , i j . A v 0 . y 1 40 CCM IMU -43 T»A :AY = ; A TC <•< I y, c, 2 * +( i.. AT C - A ( ) . C,l .WAT : : . ^ t " , I •i, L> i,2 > — - AT:: -f--1,1) ) L = - ! - l (- , C, 2 ) ) / ( - A T I ^ i. 1 .y , L + 346 34 7 34£ 11, 1) -rt ATI M !, L , i ) ) ) *< t- .,D---.T-H k ^  T = T •. i\ 0 A Y / 2 "i . CO ,'C K=l ' 1 ( • , 1 , 1 ) ) * ^ -r-o o o O Ul 4> X- J> U) OJ IO O O O |IU M - o J" O r" WWW *n vri vr UJ U> UJ sO vO sO -J> u. ro U) U) U l UJ U) IvJ I U ) U l U l rr: Co -J cr ;<_- 4> T J o c —< s. o o o h» TD O —* <•/• o l~ *T ji.- o i r '• * —< t— • —< - jf/-— iv 1 s, —1 • i 1—I -*— — O II (-. Ci rr • T> — *— >- ,L —- —• li II -— •—. r~ i: ~ s. —" n '/ • ;r — —• : ^ — i -ij - — s ; /- r~ —< {/i -« r*_ «• _j r~ C 1/1 o »— C. .—. —4 —1 —- >-; f~* — - Js." "J i; —1 •— ~» w — O s. X „^ w '->> + >—• T - >J — . i> • -T- — Il •T T . s. x. i - ^ . s. s. J- f r. —- "*"; > i~ i r • ~Z- i'sj c •* i.r n - —i :r, <r- —t I'-.'r - .— •— j — —• C J !/•• \*— - I C s". -• ! — —• * « —~ "> I — s. s. * c. -< s. - X. —. _r —i • —( X j—J r; X —> v • s,_ — '" , j. r~ *- </• •* |T- •• C • ;>'~ T J —i T- ir. i— — —! *— I—. *~ ty s/ c r - —p l*— c 7-' •* sC —- -v -* *- —- r- i — -* — — I — -> .•-> — i h* v.. L- —i c - — — — — rr —- j. A ir- — —- ;•/• s. C !(/• — is — 1 c j<.-s— o —-— {/•. « »• •— r~ TJ !— T, - k-—1 —1 r-ss Z, < .<~ - !•*" '—) i •s. — I !w ^. i. ; _> <^ *— r .- •—' U —1 •-• |—i w > M •-" 's, s. U >—* —.' —- • •fc- ;.—. • • c - * jv'. -SJ —v. >; — is -w u; J> -I"". i.r. - s. l+ .—. c is J . • --j (A V' —i , ; j—i *_ —1 4^  ' r ' —• —t C" w o t" { *— h H "If tjO 1 • n T l;> l>_ 1 —1 z —t j — ' i. 177 U J ui ui: ui U J u 1 M - C ' C C s l "II x- o 2 n C n o , — r 11 r t i -i ^: U J UJ ' -0 • U J u w *-i o C-o O r" lUJ LU U] lo r-I-J c-OJ tv) . U J U J U J I u. C O LU UJ U-l U- O-J 1 V U~ m ' LJU IJJ U S KP V H- C sT o a O "->- i/0 r 7, —i ll ro - M rv ii O" c 178 |j> x- !> Js IN) I— |j». 4> J> Irr v-r j> jui ru — II It > TJ -Hi JN J>|. o o JN > . ui i . i JN Ul V i V vl OJ IV | > i> > |r\j r\j r\ c. -j J> J> J> r~, cz c. ct c: r": — i •> X II II * 1^  7- II - ,L -I'? A X | _ I. V,: •< II XT- X X| n UJ « i H x [ i • -I X I !:-, VjJ - | i if • Kr x o —n —t [ n i -> '• • • —rc_.il rv: 179 A4 APPENDIX IV A LISTING OF THE WASTEWATER TREATMENT MODEL The l o g i c a l units are assigned i n the model as follows L o g i c a l Units Task #5 To set the design parameters f o r the current experiment #6 Record of hourly e f f l u e n t from the m i l l i n mg/l and lbs/Ton at the end of each day #7 A f i l e or i n t e r a c t i v e device which can answer the questions regarding f a c t o r loadings #8 The i n f l u e n t concentrations f o r the 3 o u t f a l l s i n mg/l. This i s read each hour by the model #9 The pulp m i l l production and water usage record as input i n t o the model The design 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 ar TIME = time step f o r lagoon model = 1 hr A = s e t t l i n g rate constant derived i n text = .104 cm DET = desired detention time f o r c l a r i f i e r (3 hrs) QQ = t h e o r e t i c a l h y draulic load 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 for ICOMB =2,3,4) H = depth of c l a r i f i e r = 15 f t TI = time step f o r c l a r i f i e r model = 3600 sees ICOMB = system layout desired f o r run = 1,' too4 Ak = dummy v a r i a b l e TEMP = Lagoon operating temperature = °C AREA = area of Lagoon i n acres DEPTH = depth of Lagoon i n f t 180 Ul Ul ui Ul Ul Ul •o-- .p* OJ Ul Ul Ul I— o > C- Ui |UJ M h--•x> t> -n |£ - ^ —t >• rr. re ' PI o II o II • o J > u w o o U t t i ) w -J O Ul U) Kl U) l_ tU f\J O |ro i\j ro rvi rv ro ui -r- t_; ro I M t\j i I— o • ~ J C - U l | - i ml-II <: ~ Ii 1 n • IT. | * ro r f >|t- * Co-x-ier) |_ < O I - J • fl ^-,\j - — i - l-J LISTING CF F I L E *A S T E-1-1:10 P |. ^ A.M. ^ . 19, 1979 • t,J =M T ( 59 IHANS . s n.O. JGiJ Td 1-60 TJ=0. 61 ST- i J = 0. 62 FACT r = .!. . e c 81 6 j CYCI.F-C. 6 4 CO nj i ' , _CJ> 14 •: >• . : {;,:,) :  6 6 6 F 0 PA Af (IX, • I r-jPt T~ 1 JM7O~'1 iT"" \ -j _h:,.0«T 67 F A• j ( /, 7J TJ , ]-IP 66 7 FCP-1AT (2F0.Q) 69 ' WP. I TP ( 7,0) 70 8 FUFA.AT ( IX, 1 I IFCT F.,CTU-' POP VWCK IX AOS F •_>. J ' ) 71 °.t AO (7 . A) F A C. rCFA  7 2 9 FOR'-'AT (1-9. 0! Vi WP 110(7,11) 74 11 FORMAT (IX,' IOPQT CYCLF I A. F . . . ' l  79 P F AO(7,12)0 YC LC 76 12 FOPMAT ( F i .0) 77 13 w'P IT F. ( 6 ,2 i A ,Oi:T ,9 J, H , ICC , 78 2 FORM AT ( IX , • A = ' , F 5 . 3 , 5X , ' OF T'= ' , F. . I , 5X, ' 0 0=' , F 1 0 . 0 , 9X , 1 H = ' , F 5 79 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= ' 82 1F4 .'J ,'tX , ' KK = • , Fi;.9 ,4X, ' VLAC= 1 , F 1 . . 1 ,//) 83 u'RI TP ( 6 ,1 0) TJ . FACT CP , S TCP .CYCLE ; 84 10 FORM AT ( LX , ' T J = ', FO .0 ,5X , 'F ACT.) <= • , Ft:. 0 ,9 X, ' ST_° = * , FO.O, u X , • CYCL L Gi> i.FS.O,///) £6 C__ 87 C READS THE CAILY '/.' ATI- P FLGw FO* 3 A=*EAi 1 Al ML, SO / HR — A N C DAILY PULP P o a c • 89 100 CONTIMUE 90 RE AO (9 , 40, EH|)= 20C) ( WAT T ( I) , 1 =1 , 1 ) , PHUO 91 40 FC 3MAT (IX,3FO.0 , F10 .0) 92 ' C 93 C FLOW AFRANGcMcN TS IN RESPONSE TO i CU MB 94 , C GC' TQ( 69, 70,79,76) , ICOi'B  ^6 6 5 01=(HATT(I)fWATT( I)+WATT( i ) ) S7 02=0. 98 03 = 0. 99 GO TG 80 ICC 70 01 -yiATT(2) * AATT (3) 10 1 0 2 = W A T T ( 1 ) 102 03=0. 103 GO TC 80 104 " 75 Q1 = ,JATT(2) 105- Q2 = .1 AT T ( 1 ) + U AT T ( 2 ) 1C6 03=0. 1C7- GO TC 30 1C8 76 Cl=OATT(2)+WATT(3) 1C9 02=0. 110 G3 = .M' AT T ( 1) U l -0 CCMIMCE 112 C 113 C LAGC.CN 24 PP, PARAMETER S 114 C 115 FLAG = ,;H-Q; 116 T T = 7 T / (KLA_*3.*/££*1£6) CN 00 f LISTING CF F I L E wASrfc'-.M'MFt. L i : i A . . , . JOG. i v . 1,75 Wi-f-M: V 117 l i e 119 120 A L r • IT A = 1 . +K K =.= T T E D=h XP ( (-ALf'H 1 A ) ---T S "C-/ r ! ) 13 = T I f't" / T T KfcT \= ( Al. Ciir A / T T - l . / T T ) ? U l 122 123 i; X X = L A F i - T i KL / i i ) 0 = ;a+02 c 124 125' 126 C CLARIF I F P 24 O00-' P./'.»Av;;r.= C CuC=!,'l/:!oOO . 127 128 125 P. E S T = V V / ( 10 •• 1 b 6 ) AL PH = ( ! . *• CK - P t i T ) 130 131 122 EE - E X P i ( -AL°M* n/HESH ) :;EX ••..<•>I-T! /\ : s"! c 133 134 135 81 CCMI.MLE T = T + 1 . 0 = t> 1 . 136 137 1 3 8 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 tACH OF 3 CILL ARIAS C 135 140 141 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. 142 143 144 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 CSSCTH = SS IN S T = . = fK T l -A T i.iYPASSCS C L A P I F I E K — MG/L 1 4 5 146 147 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 1.48 149 150 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 82 .33 , c!4- » fc 3 J i ICO0ii 82 C 101 =( CSS ( i ) *f, A T T ( 1 ) K.$S (2 ) *WATT (z ) +CS S ( 3 )* .-.ATi ( 3) )/Ql 151 152 153 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. 154 155 156 CSSi>YE = 0. COCi)ijY=0. . GO TC £5 15/ 158 • 159 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 ' • 160 161 162 Z=C30C ! i ) CS.StlYE=0. CbCOBY= C . 163 16> 165 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 2 166 167 16 8 C B IOC L = L BCD ( 2 ) • z = <;: BCD (11 *wAT T (11 rcnoi: ( 3)-*ATT I'.3) i /c* CSSGYE=0. 165 17C 171 CECCBY=0. GO TO 63 • 86 C I M= ! C S S ( 2 ) = W A T T ( 2 ) + C S S ( 3 )=' . . A T T ( 3 ) )/O 1 V 172 173 174 CSSOTH=0. CB IfwCL = (C30D ( 2 ) * ' » A T T (2 ) +C400 (3 ) * «AT T ( 3 ) )/.U Z=C. f LISTING C F F I L t In A S T E - .100 E L 11:31 A.M. AOS. 19, 1975 I0=MT2_ V 175 170 1 77 170 C CSS-YF-CSSi 1 ) (. t)COGY=L : i l "J ( 1 ) 8 5 CCI\ n \ L : : • " > — • — 179 130 131 C c c ARTIFICIAL SHOCK _ > ! . S il'-IR I S A d 182 183 . 184 c C TREAT litIS P O U R S i \ !• L J E NT T'< = TJ + STE-' 165 18t 187 GO ro i i 36 CC N f INCH • . 188 189 190 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 -•'i:02 )'••(-' AC T C - k - l . ) .vOLCCV-M.CO/ ( .••)3_7*3.7;ci ) 191 192 193 C1M= FACTOR*C 1 'U C3INCL = FACT0-*CI)I.JCL CSS )T-i = CS.vjTri=i-FACTCR • 194 . 195 19o C S S 0 Y E = 0 S S ti Y 0 * F A C T C R C3C0tY = CH.aCtiYv FACTOR _=FACTCRvZ 197 . 198 199 I F (T .F|0. TK) T J= T K + C YCLt 87 CCtNTINLE CALL TREAT 2GC 201 2 02 C vvR ITE ( 6, 70) CI Ni ,CS2 .CSSCTh ,C ril AtC.L , Z ,CB'JCOT , T 90 FORMAT (IX,6 1 F8. 1,4X) ,Fy.C) 203 204 205 C c DAILY INPUT - OCTROI STATISTICS GET E P R 1 RE C DAYriCD = CAVBGC.+ (C fcP 0 3T~'C +C tJOG 0 Y -'0 3J*..7dS 20, 207 2C8 • SSS = (C I M * T 1 / ( AlFri*-*2) I M i . - i EE ) + (C Z ERG i« R c _ T / ( A I _ P H * * _ 1 + ( CZ ERI)2*RtST / ALPli ) * (1 . - FE )-GZ ER G 1 v T I *E 11 AL P H SSS=SSS/3oOC.. . I J M E E - l . ) 2C9 ' 210 211 GAYS S = OAYSS+( SSS * G H-CSSCT H - C ^ i - C S S-Y-"U.).*3. 7b9 0 I i\B_0*D 1 NsC» + (CI; I NCL*0 1 *l "Q 2 + CO 00 b.Y *<} 3 ) J<3 . 785 01 ,\SS = i)l R9S *- ( C l M*0i+CSSCTn*C2 +C SS OY t *03 )* 3 . 785 212 213 2 14 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 U 02 215 2 16 2 17 SIi\=SIi\ + C I Nl*01 SCLT = S C U T + SSS*'.l SSLA = SSLA*S SS*C SS0Tri»-0 2 :-3. ?<i5 2 18 2 19 220 BBLA = f--KL A • ( C6 INCL*Q 1 +Z ':C 2) »' 3 . 7u5 IF (0.KE.24. )G0 TC SI BOOTCN = :)AYiJOU*2.205/W C0 22 1 222 223 S S T C N = C A Y S S " 2 . 2 G 5 / P ' R L ( 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 224 225 226 S5AV = SSLA/( C':3 .705*24. ) DBAv=BBLA/(0-3. 7o5*24. i S S I A G * . 12M SSAV + C'.rt A y ) / ( 1 . + . > T T * . 1 2 -j ) 227 228 229 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 91 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 , 1 0 X , F 8.2 , / ) I 230 . 231 232 D = C. CAYOCO=C. OAYSS=C. UJ oJ O J j> J> .J> co -< r OJ UJ Ul U J U J U J J> J> J -I\J >— o U J U J U J V.J UJ OJ OJ UJ 'viJ UJ UJ C' U ' o j> 1 T J ~ o > O rn r > > II II — 1> o [ U J O J U J U J U J ui 1 0 U J M K : O J r\j o vc cc' o in r-o o . o o o 184 OJ UJ OJ KJ f\) ^ o- w i o n JJ > II r~ r n o o o U J iu ui i\j Nj ^ l U ' r»j UJ OJ IvJ *\> f\J i - O o C D - 0 I II — • IO l u UJ UJ lo l Ul -l> u IT cr. o o O O o a —i - i UJ OJ U J |oJ OJ U J o o OJ UJ O O C rsj r-o o -.n c o ivj INJ rvj rvj r\j r\j rvj *o u-i in —t - 4 > —4 • II O < m n —< en —i —. • T r~ u: C_> j> -• X- <r C O , T ; • r~ -V. 7> <T> * r~ i — c • -H •* <y c-j> V •* • [ o p n o N ' J H / l n 1 |;v o i— 4- -C J CD n Tl I . CHAIN LIMITED 185 tU LU 

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