V REMOVAL or PHOSPHORUS AND NITROGEN ROM 7 WASTEWATER BY SPRAY IRRIGATION-mum _ :f’ , Dissertation for the' Degreg :o'flPh.‘ A; ' MICHIGAN STATE UNIVERSITY; : ;~ » ' ' ’ DHANANJAIB. SHAH? C This is to certify that the thesis entitled REMOVAL OF PHOSPHORUS AND NITROGEN FROM WASTENATER BY SPRAY IRRIGATION OF LAND presented by Dhananjai Bhogilal Shah has been accepted towards fulfillment of the requirements for Eh.D. degree in Chemical Engineering @4492“ r C Ego: professor DateW" [:1 I775” 0-7639 3 1293 10226 9713 Mil/MM” f” - LI‘IfRAI‘iY i This is to certify that the thesis entitled REMOVAL OF PHOSPHORUS AND NITROGEN FROM WASTEWATER BY SPRAY IRRIGATION OF LAND presented by Dhananjai Bhogilal Shah has been accepted towards fulfillment of the requirements for Eh.D. degree in Chemical Engineering Ago—3C 4. w 7 C unjox professor DateégvtiABn“ 0-7539 25mg \ Q J? \ '1» ABSTRACT REMOVAL OF PHOSPHORUS AND NITROGEN FROM NASTEWATER BY SPRAY IRRIGATION OF LAND By Dhananjai B. Shah Increased attention is being paid recently to the removal of phOSphorus and nitrogen compounds from the wastewater along with organic carbon and biological oxygen demand because high concen- trations of these compounds in our lakes and streams result in algal blooms and create serious other problems. One of the treat- ment methods being considered is spray irrigation of land. Phos- phorus is removed by adsorption to the soils and nitrogen species are converted into atmospheric nitrogen via nitrification and denitrification reactions. In order to design and manage a land treatment facility, mathematical models are needed that describe the movement of vari- ous phosphorus and nitrogen species in soil. This work addresses itself to studying the various reactions such as ph05phorus adsorption, nitrification and denitrification and to developing mathematical models to predict their movements in soil. Results of these models are to be compared with experimental results to test the validity of the models. Dhananjai B. Shah The phosphorus model was derived by taking material balances on water and on phosphorus in the liquid and solid phase. Non-equilibrium conditions were assumed to prevail between phos- phorus concentration in the liquid phase and on the soil. A mass transfer model was used to describe the rate of transfer of phosphorus from the liquid phase on to the solid phase. A Langmuir adsorption isotherm was used to describe the equilibrium relationship between the concentrations of phOSphorus in the liquid and solid phases. Solution of these equations for appropriate initial and boundary conditions showed that the water front moved much faster than the phosphorus front. This enabled the water transport equa- tion to be dropped from the model equations and computations became less complex. Results of the simulation were compared with data from an existing spray irrigation site and they compared remarkably well with one another. These simulation studies showed that the soil system is very efficient in phosphorus removal. Nitrification and denitrification are important micro- biological reactions of nitrogen. Ammonium nitrogen gets converted to nitrate nitrogen by nitrifiers in the presence of dissolved oxygen. This nitrate nitrogen is then reduced by facultative anaerobes to atmospheric nitrogen in the presence of organic car- bon. Kinetics of these reactions were investigated based on a Monod type expression involving two growth limiting substrates, Dhananjai B. Shah u = u -—-£EL-- [——EZL-- m KS1 + 51 [K52 + S2 The following table summarizes the various substrates considered in the two reactions. S1 52 Nitrification : Ammonium nitrogen Dissolved oxygen Denitrification : Nitrate nitrogen Organic carbon Kinetic constants (um, K51, and K52) were evaluated for the nitri- fication and denitrification reactions. Past experimental work was used to determine the constants for the nitrification reaction. For the denitrification reaction, steady state experiments were performed in a stirred tank reactor under conditions such that only one substrate was growth limiting. Steady state values of the substrate in the reactor were determined at various dilution rates. These data were analyzed to obtain the kinetic and stoichiometric constants. From these constants, it was concluded that in the range of nitrate concentrations encountered in wastewater, the denitrification reaction can be considered a first order reaction. It was also found that three times as much organic carbon is required as nitrate nitrogen for complete nitro- gen removal. Using these kinetic expressions, material balance equations were written for ammonium nitrogen and nitrate nitrogen in the Dhananjai B. Shah liquid phase. Material balance equations were also written for all the gas phase components. These equations were solved to obtain some preliminary estimates of the extent of nitrogen removal. The simulation results compared very well with the experimental results. Even at very low flow rates, complete nitrogen removal was not accomplished. The nitrogen removal ability of the soil was found to be of greater importance in selecting a land disposal site than the phosphorus removal capability. Because of great variability in physical, chemical and biological properties of soils, it was estab- lished that some preliminary experimental work would be absolutely essential before a successful land disposal site can be designed and operated. The transport models developed here can give some preliminary estimates on the quantity of phosphorus and nitrogen that can be removed by a spray irrigation site under a given operating policy. REMOVAL OF PHOSPHORUS AND NITROGEN FROM NASTENATER BY SPRAY IRRIGATION OF LAND By . \ -3\ CI "\ ‘ Dhananjai Bi Shah A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1975 To my parents ii ACKNOWLEDGMENTS The author wishes to express his appreciation to Dr. George A. Coulman for his guidance and constant encouragement throughout the course of this work. Appreciation is also extended to the mem- bers of my guidance committee for their participation in this work. The author is greatly indebted to the National Science Foundation (Grant 61-20) and the Division of Engineering Research at Michigan State University for financial support. Special thanks are due to Mr. Don Childs for help with the experimental equipment. The understanding and patience of my wife, Hansa, and her help in preparation of this thesis is sincerely appreciated. iii TABLE OF CONTENTS LIST OF TABLES . LIST OF FIGURES LIST OF APPENDICES Chapter I. INTRODUCTION . Phosphorus and Nitrogen as Pollutants in Wastewater . Advanced Treatment Methods for Phosphorus and Nitrogen Removal . . . . . . . . Land Disposal of Effluent . Phosphorus and Nitrogen Transformations Objectives and Scope of Present Work Organization of Information Provided in This Work II. BACKGROUND Phosphorus Chemistry . Phosphorus Precipitation in Soils Phosphorus Adsorption in Soil . PhOSphorus Adsorption Kinetics Equilibrium Relationship . Rate Expression for Adsorption Sc0pe of Past Work . . Present Work III. MODELING OF PHOSPHORUS MOVEMENT IN SOIL . Physical Situation and Assumptions . Water Transport . . . Development of Model Water Balance Phosphorus Balance Model Parameters . . . Mass Transfer Coefficient and Langmuir Adsorption Isotherm . . . iv Page vii ix xii Chapter Hydraulic Conductivity Capillary Potential Barriered Land Water Renovation System (BLWRS) : Initial and Boundary Conditions Method of Solution . . . Results and Discussion . Numerical Problems . . Surface Boundary Condition for Saturation . Water Transport . . . . . . Phosphorus Transport . IV. NITROGEN TRANSFORMATIONS . Background. Reaction Kinetics Past Work Nitrification Denitrification Experimental Method. . . Suspended Growth Units Vs. Packed Columns . Theory . . . Materials and operating Procedures Analytical Techniques . Experimental Results and Discussion Excess Concentrations Choice of Inoculum Choice of Carbon Source . . . Nitrate Nitrogen Limiting System . Glucose Carbon Limiting System Parameter Values . . Comparison of Parameter Values With Those Obtained From Past Work . V. MODELING OF NITROGEN MOVEMENT IN SOILS Literature Survey and Physical Situation . Method of Attack . . . . . Assumptions . Model . Liquid Phase Gas Phase . Method of Solution Results and Discussion . Chapter Page VI. CONCLUSIONS . . . . . . . . . . . . . . l60 Phosphorus Removal . . . . . . . . . . . l60 Nitrogen Removal . . . . . . . . . . . . l6l NOMENCLATURE . . . . . . . . . . . . . . . . l64 REFERENCES . . . . . . . . . . . . . . . . . I68 APPENDICES . . . . . . . . . . . . . . . . . I75 vi UUUUUUUUOWCDJ: OWNO‘DU'l-th —l LIST OF TABLES Methods of Phosphorus and Nitrogen Removal . Forms of Phosphorus in Water and Soils Solubility Products and Dissociation Constants Used in Developing Figure 2.l . Equilibrium and Approach to Equilibrium Data for Liquid Concentration in Phosphorus Adsorption Growth Media Used in Experimental Studies Average Steady State Data for Nitrogen Limiting System . . Average Steady State Data fbr Carbon Limiting System . Parameter Values Obtained from Experimental Work . Structure of PMODEL Program . Data Required by the FORTRAN Program PMODEL Daily Steady State Data for Experiment N-l . Daily Steady State Data for Experiment N-2 . Daily Steady State Data for Experiment N-3 . Daily Steady State Data for Experiment N-4 . Daily Steady State Data for Experiment N-S . Daily Steady State Data for Experiment N-6 . Daily Steady State Data for Experiment N-7 . Daily Steady State Data for Experiment C-l . Daily Steady State Data for Experiment C-2 . vii Page 14 15 38 92 106 114 119 186 187 227 228 229 230 231 232 233 234 235 Table 0.10 0.11 0.12 D.l3 D.l4 E.l E.2 E.3 Daily Steady State Daily Steady State Daily Steady State Daily Steady State Data for Experiment C-6 . Daily Steady State Data Data Data Data for Experiment C-3 . for Experiment C-4 . for Experiment C-5 . fbr Experiment C-7 . Summary of Solution Methods for the Cases Considered . Structure of Program GASTRAN Data Required by the FORTRAN Program GASTRAN viii Page 236 237 238 239 240 246 247 248 Figure 2.1 LIST OF FIGURES Solubility of VariousBPhosphorus Compounds as a Function of pH [Al Ions Availability Con- trolled by Dissociation of Al(OH)3] . Equilibrium Relationship Between Phosphorus in Liquid Phase and Phosphorus in Solid Phase as Given by Langmuir Equation . . Hydraulic Conductivity VerSus Soil Saturation . Capillary Potential Versus Soil Saturation . Capillary Potential Gradient as a Function of Soil Saturation . . . . . . . Schematic Cross-Section of Barriered Land Water Renovation System (BLWRS) . . . . . Development of Saturation Profile with Constant Surface Saturation . . DeveTOpment of Saturation Profile with Constant Surface Velocity . . . . . . Development of Saturation and Phosphorus Profile During Simulation . . . . . . . Comparison of BLWRS Data With Predicted Results from the Model Effect of Mass Transfer Coefficient on Shock Layer Shape . . . . . . Effect of Dispersion Coefficient on the Advancing Front Thickness . . . Effect of Increasing Application Rate on the X- Profile . . . . . Illustration of Monod Kinetics . ix Page 17 39 41 42 43 44 53 53 55 58 60 61 62 70 4.10 4.12 4.13 4.14 Degree of Nitrification as a Function of Oxygen Concentration . . . . . . . . Rate of Nitrification as a Function of Ammonium Nitrogen Concentration . . . Experimental Setup for the Study of Denitrifica- tion Reaction . . A Typical Calibration Curve for Determining Nitrate Nitrogen . . . . . . . A Typical Calibration Curve for Determining Glucose Concentration . . . . Plot of Bader et al. (l975) to Illustrate How to Take Proper Excess Concentration Plot of Dilution Rate Against Substrate Concentration . . Lineweaver-Burk Plot for Nitrogen Limiting Case Lineweaver-Burk Plot for the Second Order Model for Nitrate Nitrogen Limiting Case . Plot of Microbial Concentration Against Substrate Utilized . . . . . . . . . Monod Plot for Carbon Limiting Case Lineweaver-Burk Plot for Carbon Limiting Case . Microbial Concentration Against Substrate Utilized . . . . Prediction of Stensel's Batch Data B-3 Using Parameters Obtained from This Work . Prediction of Stensel' 5 Batch Data 8- 5 Using Parameters Obtained from This Work . Prediction of Stensel' 5 Batch Data 8- 6 Using Parameters Obtained from This Work . Prediction of Stensel's Batch Data B-2 Using Parameters Obtained from This Work . . Page 75 77 90 96 98 101 107 108 110 112 115 117 118 124 125 126 127 Figure I Page 4.19 Prediction of Stensel's Batch Data B-7 Using Parameters Obtained from This Work . . . . . . l28 5.l Solid-Liquid-Gas Phase Interrelationship . . . . 132 5.2 Concentration Profiles of Ammonium Nitrogen and Nitrate Nitrogen in Liquid Phase . . . . . . 149 5.3 Concentration Profiles of Oxygen in Gas Phase . . . l50 5.4 Concentration Profiles of Nitrogen in Gas Phase . . 151 5.5 Concentration Profiles of Carbon Dioxide in Gas Phase . . . . . . . . . . . . . . . 152 5.6 Gradients of Various Components in Gas Phase Against Soil Depth . . . . . . . . . . . l56 5.7 Diffusive Fluxes of Components in Gas Phase Against Depth . . . . . . . . . . . . . 157 A.l Determination of Mass Transfer Coefficient for Phosphorus Adsorption . . . . . . . . . . 180 xi LIST OF APPENDICES Appendix A. Determination of Mass Transfer Coefficient for PhOSphorus Adsorption from Batch Experiments B. Numerical Method and FORTRAN Program Used for Simulating Phosphorus Movement in Soil C. Pathway for an Enzymatic Reaction S + E + E + P Leading to an Expression for Doub1e +Sugstrate Kinetics . . . . . D. Continuous Feed Experiments,Steady State Data E. Numerical Method and FORTRAN Program Used for Simulating Nitrogen Movement in Soil . xii Page 176 181 221 226 241 CHAPTER I INTRODUCTION Phosphorus and Nitrogen as Pollutants in Wastewater The removal of phosphorus and nitrogen compounds from waste- water is very important because these contaminants, present in high enough concentrations, in an aquatic environment, promote unwanted growth of algae and aquatic plants. The resulting blooms of blue- green algae lead to a higher biological oxygen demand and lower dissolved oxygen levels affecting fish population and would inter- fere with the recreational uses of water. Other problems associ- ated with high algal growth in surface waters include production of objectionable taste and odors and increased chlorine demand. This necessitates the control of the discharge of these compounds into an aquatic environment. Nitrogen compounds of major impor-- tance in water are ammonia, nitrites and nitrates and those of phosphorus include organic phosphorus, inorganic polyphosphates and soluble ortho and metaphosphates. Sources of phosphorus and nitrogen compounds in an aquatic ecosystem are both natural and man-made. Contributions from natural sources include runoff and rainfall. Man-made sources include municipal wastewater, industrial wastes, urban runoff and agricultural runoff from fertilized fields and livestock feedlots. Eliassen et al. (l969), Grundy (l97l) and Ferguson (l968) have tabulated the amounts of phosphorus and nitrogen entering the aquatic environment from each of these sources. Detergents contain phosphates and they account for 30-40 percent of all phosphorus entering the aquatic environment. Industrial wastes contain high concentrations of phosphorus and nitrogen and these concentrations would vary depending on the type of waste. It has been estimated by Ferguson (1968) that of the total quantity of nitrogen contributed to an aquatic ecosystem, one-third can be attributed to municipal sewage effluents and one-half to the runoffs from beef feedlots. Most of the nitrogen in raw municipal sewage is in a form from which ammonia is easily derived. One of the major difficulties in designing for the removal of nitrogen and phosphorus is a lack of reliable information on the critical concentrations of these compounds below which their adverse effects are minimized. Few attempts have been made to quantify limiting concentrations for both nitrogen and phosphorus. Sawyer (1947) and Benoit et al. (1947) concluded from their studies of some lakes that, if at the time of the spring season, the con- ..fentration of inorganic phosphorus exceeds 0.3 ppm, rapid algal growth would occur. On the other hand, some workers (Mackenthum 1962, Fitzgerald et a1. 1965) have stated that of the two, nitrogen is the limiting nutrient and its control is more important. Besides playing a role in the algal bloom, high concentrations of nitrate nitrogen cause problems in industrial and domestic use of water. They are also believed to cause infant cyanosis. In view of these reasons, the U.S. has adopted 10 ppm nitrate nitrogen or less as the standard for drinking water use. Advanced Treatment Methods for Phosphorus and Nitrogen Removal The conventional treatment processes are not capable of removing most of the phosphorus and nitrogen compounds found in wastewater to the required limits. This forces us to modify the existing processes. These advanced treatment methods fall into chemical, physico-chemical and biological classes. These methods are summarized, their main advantages enumerated, and the costs and I efficiencies for phosphorus and nitrogen removal compared in Table 1.1. The conventional treatment plant (first line in Table 1.1) removes only 50 per cent and 30 per cent of the incoming nitrogen and phosphorus, respectively. A slight modification of the above process (third line) involving nitrification and denitrification can remove a high percentage of the incoming nitrogen. It is quite inexpensive and is compatible with phosphorus removal. Of the chemical methods listed in the table, only nitrogen removal by ammonia stripping is inexpensive. Land Disposal of Effluent All the methods in Table 1.1 are treatment methods, except waste disposal by spray irrigation of land. This is the only recycling method which purifies wastes from the treatment plants while it enriches the soil and recharges the groundwater. Land disposal is characterized by the application of sewage effluents TABLE l.l.--Hethods of Phosphorus and Nitrogen Removal.f ‘ Percent Cost Process Type and Mechanism Removed ‘/"1oga‘. Remarks Nitrogen Removal Processes 1. Conventional biologi- Biological 30-50 N 30-100 Sludge disposal problem. P and N cal treatment N. P + Cell Mass lO-3O P removal unsatisfactory. 2. Algae harvesting Biological 50_90 20_35 Final liquid and sludge to be dis- N, P - Cell Mass posed off. P and N renoved siml- taneously. Large land area needed. Requires favorable climate. 3. Aerobic nitrification Biological _ No ultinate waste disposal problem. followed by anaerobic NH4 + 202 + N03 + H20 + H+ 70-95 25-30 Compatible with P removal. 100% denitrification N05 , N2 + £02 + H20 removal not possible. 4. Ammonia stripping Chemical + 80-98 9_25 No ultimate waste disposgl problem. NH; : NH3 + H Problem of increasing NH4 solubility with lower temperature. Air pollu- tion problems. Scaling due to metal . deposits. 5. Breakpoint chlorina- NH; + C12 + NC13, NHCLz, Quite 100_200 High increase in total dissolved tion NHZCl high solids. Nitrate may be a product of chlorination. Phosphorus and Nitrogen Removal Processes 1. Ion exchange Chemical - Quite 100_150 Both P and N can be removed. Prob- NO3 + RC1 Z C1 + RN03 high lem of disposal of regeneration liquid. Pretreatnent required to remove interfering ions. 2. Electra-chemical Chemical Current Sewage + Seawater -—————-—+ _ . . . . . Precipitation of P and u as 80 85 Liquid and solid disposal required. Ca and Mg salts. 3. Electro-dialysis Chemical Problems of chemical precipitation :fi?:;?:e:o;zgngztlog;c”22:9 30-50 100-250 and membrane clogging. High degree selective nenbranes. of pretreatment necessary. 4. Reverse osmosis. Physical Forced passage of water 65-95 250-400 Problems of liquid disposal and mem- through menbranes against brane fouling. osmotic preSSure. 5. Distillation Physical 90-98 Very Can obtain drinking water. Problem Distill off water expensive of liquid disposal. 6. Land application Physico—chemical High removal possible. Large land Chemical and biological fil- 60-90 75_]50 area needed. Advantage of recycling tering action to remove P the nutrients. Management of the and N. system very inportant. Phosphorus Removal Processes 1. Chemical precipitation Chemical Quite Liquid and sludge to be disposedoff. P precipitated by addition hi h 70-90 Can be combined with conventional of alumn, lime, etc. 9 activated sludge process quite easily. 2' “WW“ ””5““ 90-93 40—70 High removal possible. P removed by adsorption. 'Most of the information contained in this table was taken from Eliassen et al. (1969). Stensel (1971) and Sutton et a1. (1975). on forest or crop land in predetermined rates and amounts. It is based on the concept of ”living filter"--letting nature recycle nutrients and water beneficially on land rather than detrimentally through the lakes and streams. The concept of recycling is important because pollution can be viewed as a maldistribution of matter and energy among the three media of the earth: air, water and soil (Bohn and Cauthorn 1972). Nitrogen and phosphorus compounds cause algal blooms in lakes and streams, but in soil they are beneficial to plants. Hot water in a stream can cause thermal pollution but would increase plant growth when applied to soils. Sulfur dust is a pollutant in the atmosphere but can act as a nutrient for plant growth in soils. Hence, the problem of nitrogen and phosphorus pollution in an aquatic environment can be solved by putting effluent on land where these compounds are beneficial to plants and vegetation. Phosphorus and Nitrogen Transformations The ability of the soil to act as a filter is based on the many physical, chemical and biological reactions it can carry out. Chemical functions of the living filter during irrigation include ion-exchange, adsorption and precipitation, and chemical altera- tion. Phosphorus, which is generally present in the form of soluble orthophosphates, can undergo adsorption and precipitation by reaction with calcium, manganese, and iron as the effluent moves down the soil. Along with the phosphorus, some sulfate, boron and heavy metals are also removed from the wastewater by adsorption. The adsorbed phosphorus on the soil can be removed by crapping the soil. The cleaner effluent, then, can recharge the groundwater. Soil has net cation exchange capacity and thus can also adsorb positively charged ions like ammonium. As a biological filter, soil contains microbes. Soil microbes decompose and metabolize biodegradable organic materials to carbon dioxide and water. Nitrogen present in the form of ammonium gets converted via the nitrification reaction to nitrate nitrogen which subsequently is converted to gaseous nitrogen by the denitrification reaction. Both these reactions are micro- biological in nature. The nitrification reaction is carried out by the microbes which oxidize the ammonium nitrogen in the presence of oxygen to nitrate nitrogen. As the wastewater moves down the soil, concentrations of the ammonium nitrogen in the liquid phase and oxygen in the gas phase decrease. When oxygen concen- tration goes down sufficiently to form an anaerobic environment, some microbes utilize nitrate as an alternative electron acceptor in the presence of organic carbon as an energy source. This is termed the denitrification reaction. The top layers of the soil profile are usually the most active sites for biological and chemi- cal filtration. Objectives and Scope of Present Work The soil treatment method can remove phosphorus and nitrogen consistently, only under proper management practices. Application rates of the wastewater should be such as to give sufficient residence times in the soil for complete phosphorus adsorption and nitrogen transformations. High leaching of nitrate, phosphate and other ions is conceivable in intensively irrigated areas. To properly design and manage such systems, enough information is needed about the various chemical and biological reactions involved. . Phosphorus adsorption in different soils has been studied by a number of soil scientists and they have shown that the equilibrium relationship between the two phases can be described by the Langmuir isotherm. Adsorption in packed saturated columns has also been studied by chemical engineers, but in the soil treatment method, water flow through the soil is unsaturated. One of the objectives of the present research has been to study the kinetics of phOSphorus adsorption and develop a mathematical model to simulate the phosphorus movement in soils. Results of this simulation are to be compared with the data from an operating land treatment facility. Nitrification and denitrification have been studied by soil scientists in soil columns. As some nitrification and denitrification does occur in the conventional activated sludge plants, these reactions have also been studied by sanitary engineers, in stirred tank reactors. Until now, rates of these (reactions have been determined as a function of one limiting sub- strate. For nitrification, this limiting substrate is assumed to be ammonium nitrogen and for denitrification it is assumed to be nitrate nitrogen. These rate expressions are valid when other substrates needed for microbial growth are in excess. When they are not in excess, their concentrations also influence the reaction rates. The nitrification reaction requires ammonium nitrogen and dissolved oxygen, and organic carbon is required as an energy source to drive denitrification. If these substrates are also lim- iting, the reaction rates would be greatly affected. An attempt has been made in this work to modify the existing reaction rate expressions involving a single substrate to include the effect of other substrates, if they are not in excess. These modifications are to be made on the basis of past work and some present experi- nental work. Having identified the kinetics, mathematical models are to be developed to predict the movement of various nitrogen Species and compare the simulated results with some experimental data from literature. In short, objectives of the present work have been to (1) summarize the kinetics of (a) phosphorus adsorption, (b) nitri- fication reaction, and (c) denitrification reaction on the basis of past and present work; (2) develop mathematical models describing the movements and transformations of phosphorus and nitrogen; and (3) validate these models by comparing the predicted results with the experimental profiles. It is obvious that the waste-processing capability as well as the design and management criteria for land disposal of wastewater will be strongly dependent upon the characteristics of the terrestrial ecosystem under consideration. Soil characteriza- tion will be an important factor in site selection and long-term operation of the disposal site. The expression of these soil characteristics in modeling equations will be quite important in the design of land waste disposal systems. The increasing scarcity of land will dictate that disposal areas not become merely dumps but be wisely used to allow harvest and recycling of essential plant nutrients. Since the plants and vegetation can take up only a finite amount of phosphorus and nitrogen and soil can process only a fixed amount of phosphorus and nitrogen, this method cannot be used for the disposal of industrial wastes which contain high concentrations of these compounds. The present work can give some indication as to how much of the incoming phosphorus and nitrogen, under a given operating and management practice, leaks into the ground water system. This can help define the upper limit on the application rate, beyond which chemical and biological filtering action is not fast enough to prevent the leakage of the nutrients into the lakes and streams. It can also help determine when the phosphorus adsorption capacity of soil may be exhausted. Double substrate limited kinetic expressions would also be helpful in designing reactors in the activated sludge process for nitrification and denitrification. Organization of Information Provided in This Work This work is mainly concerned with identifying the kinetics of phosphorus adsorption, nitrification and denitrification reactions and using this information to develop mathematical models to simulate the movements of phosphorus and nitrogen in soils spray irrigated 10 by wastewater. Chapters II and III deal with phosphorus trans- fbrmations and its movement, whereas Chapters IV and V are con- cerned with the nitrogen transformations and modeling its movement. Chapter II deals with the phosphorus chemistry. It identi- fies the forms of phOSphorus and their fractions in wastewater, and adsorption and precipitation as the main phosphorus reactions when this wastewater is applied to the soil. It reviews the past work in the area of adsorption columns and discusses the phosphorus adsopriton kinetics. In Chapter III, a mathematical model for the movement of phosphorus has been developed based on a series of assumptions and on the groundwork laid in Chapter II. The numerical method of solution of these equations is also given and the results of simulation are compared with the data taken from an operating land disposal facility. Chapter III also deals with the effect of various physical parameters on the phorphorus profiles in soils. Chapter IV discusses the nitrogen transformations in soils with emphasis on the nitrification and denitrification reactions. Past work in the area of kinetics of these reactions has been sum- marized. The existing kinetic rate expressions based on a single limiting substrate have been modified to include the effect of a second limiting substrate. The constants involved in the nitrifi- cation rate expression have been evaluated by combining the data of various workers. The experimental work done to evaluate the deni- trification rate expression has also been outlined in this chapter. In Chapter V, a mathematical model has been pr0posed for the movement of nitrogen species in soils. It takes into account 11 the important nitrogen transformations and interactions between the solid, liquid, and gas phases. The numerical method used to solve these equations is outlined and the simulation results of the nitrogen movement in soils based on this model have been compared with some experimental data taken from the literature. Chapter VI concludes this work by discussing the results and the pertinent points to be considered while selecting a spray irrigation site and management practice. Wherever possible, the points have been illustrated with example calculations. The appendices following the text contain such things as data used to construct figures in the text and complete descriptions of the com- puter programs used to determine the phosphorus and nitrogen movement in the soils. CHAPTER II BACKGROUND Phosphorus Chemistry Phosphorus, in the form of phosphate, occurs in all the known minerals as orthophosphate, represented as (PO4)'3. Apatites such as hydroxylapatite, Ca]0(OH)2(PO4)6, and fluorapatite, Ca10F2(PO4)6, area major source of phosphorus in soils. Crystalline phosphate minerals in addition to apatites include CaHPO4-2H20 (Brushite), AlPO4-2H20 (Variscite) and FePO4-2H20 (Strengite). There are also some amorphous phosphates containing iron and alu- minium and these, poorly soluble phosphates, may exhibit a wide range of composition when they appear. Dissolved phosphorus may exist in aqueous solution as (l) orthophosphates (PO-3, HPOaZ, H2P0;, H3PO4); (2) complex or inorganic condensed phosphates as pyrophosphate (P20'4, HP20'3, . . .), tripolyphosphate (P3 33, HPBOTS’ . . .) and trimetaphosphate (P3053, HP3052); (3) organic orthophosphates such as sugar phos- phates, phospholipids, phosphoamides, etc.; and (4) organic con- densed phosphates. Complex or the condensed phosphates are largely contributed by man's activities. They are man-made for use in detergents, water treatment, etc., and are discharged with domestic and industrial wastewaters. The condensed phosphates are unstable in water where they are hydrolized to the orthophosphate form. The 12 13 presence of phOSphorus compounds in soils and water can be attribu- ted to biological processes. But in domestic and industrial waste- water, organic phOSphorus may not be present in high concentrations. The total phosphorus in domestic wastewater effluent, not treated Specifically for phosphorus removal, varies from 3 to 10 ppm. Seventy to ninety percent of the total phosphorus in the secondary sewage effluent is present as a soluble orthophosphate. The remainder consists of pyrophosphates, polyphosphates, inorganic condensed phosphates and organic phosphorus species. Table 2.1 summarizes the various forms of phosphorus and their concentrations encountered in water and in soils. Phosphorus Precipitation in Soils Various metal phosphates present in water can precipitate in the soil. The distribution of phosphates in solution is governed by the pH. Given the equilibrium constants for various phosphate acid-base reactions, it is possible to calculate the amount of phosphate in solution at a particular pH. If the solution contains phosphate in concentrations greater than this number, the excess amount will get precipitated. The calculation procedure for deter- mining the solubility relationship is illustrated below. The solubility products and the dissociation constants used in determining the pH-solubility relationship are summarized in Table 2.2.* *Personal communication with Dr. B. G. Ellis, Professor of Soil and Crop Science, Michigan State University, 1973. 14 .Aommpv swam: cw mucmwceaz :o mmupwEEou cowmw>wo Auwpmso cope: mgu mo ucoamms mF—mu meemuomm mommmooca mcwmpocaozamoga masonamoca xoptm mupmo op .mmqumogamoca .muwaw_ mmumcamocqocpco u_cmmco vmucmamzm P . F .m tozam05a .mmumcamoca cmmzm owcmmco _m memo .mmo a .Nmoma: aoaeamoeaepaeeee o_ m o moo mumcamoca m- tocwme01meQ .N mommmuoea .o_ m .o_ m x .0, m N mpmcam02a>_oawce aoeee_oax som-o_ _ademoeo_m m-o a ¢-o a m-o a I moccamoca meU ._ .mpcmmcmpmo mmvowam umpcom momma: . momamu .m=a_o=_0m ee_om a N a we .memeea waxes .e-oma .m-omaz .m-o~a~: aoaeamoeaoesa ”mmumgamoza cwmcmucou owcmmcocfi ap_aeaeom upwomwcm> mmpmzamocq muwpmamco=Fm a . ummcmc aoamzmu mpwumampxxocuzx som ou tcoo we + mamaea _aeae_z-_eom mems_oeesz .+oa:au .mwoa .Nwoaz .-oa~= aoaeamoeaoeoeo Aaaa op"; Pmpopv mmwomam co mucsoaeou wagon mason omega owpom emumzmpmmz moeaom we cowpwmoaeou mace; mscocamozm um>Fommwo e.m_aom use tape: e_ mseoeamoea co meted--._.m msm< II concentration of occupied sites, (2.10) 22 and (Soil) = Q - X = concentration of unoccupied sites. Substituting (2.10) in (2.9) results in dX _ ____ dt'- KKin [Y(Q-X) - Kad] . (2.11) The above equation takes into account both the adsorption and desorption reactions. Gupta and Greenkorn (1973) used this kinetic expression and thought it to be the most representative of the physical situation. Mass transfer kinetics.--This model assumes the rate of adsorption of the solute to be proportional to the driving force. The driving force is dependent on the deviation of the system from equilibrium. The model can be represented as Rate of adsorption = Koa (Y - Y*) . (2.12) Here, Y - Y* departure of the system from equilibrium, Y* = solute concentration in the liquid in equilibrium with solute concentration in the solid phase, mg/l, and K a = constant of proportionality, i.e., volumetric mass transfer coefficient, day'l. Y* will be given by one of the isotherms as a function of X. The basis for using Equation (2.12) for the phosphorus adsorption kinetics will be established later. Novak and Adriano (1975) 23 considered the various kinetic models and concluded that bilinear adsorption kinetics and mass transfer kinetics models adequately express the experimental data in conjunction with the equilibrium relationship given by the Langmuir isotherm. Scope of Past Work As established earlier, the important reactions of phos- phorus in soils are the adsorption-desorption reactions of orthophosphates with the soils. Thus, developing a mathematical model for the phosphorus movement in soils is equivalent to describ- ing the behavior of adsorption columns. One major difference between these columns and the soil adsorption system is the nature of liquid flow. In soil, under the conditions of low application rates, water flow is generally unsaturated. As the time passes, saturation (moisture content of soil) increases. This results in varying velocity of liquid as a function of depth. Most of the adsorption columns studied have been Operated at saturated condi- tions (all the pore spaces occupied by water) and hence velocity in the column is assumed constant throughout. The dynamic response of adsorption, ion exchange and chromatographic columns has been a topic of interest fbr a long time. If a material balance is made for the solute in a thin section AZ of a column, the various components that have to be considered are as follows: rate of incoming solute VAYIZ , across the surface at Z As AZ + Here, 24 rate of outgoing solute VAY|Z + AZ across the surface at Z + AZ rate of adsorption of the §x_ solute by the solid phase AAZpb at a and rate of accumulation of a the solute §{'(AAZY) . Putting all the components together and dividing by AZ gives VAYIZ ‘ VAY|Z+AZ 3X _ a O, the above equation gives 3!. 3_X._.3 32 0b at a L< -V (2.13) r,- = cross-sectional area, cm superficial velocity of the liquid, cm/day = concentration of the solute in the liquid phase, mg/l x -< < > II = solute concentration on the solid phase, mg/kg t = time, day, and ob = bulk density of the soil. The middle term in the above equation represents the rate of increase of the solute on the soils. Since this increase is accomplished only by adsorption, it represents the rate of transfer of the solute from the liquid phase onto the solid phase. The equilibrium relationship, Y* = f(X), along with Equation (2.13) and an expression for 3X/3t, defines the system completely. Inherent 25 in the derivation of the above equations are the following assumptions: 1. Pore spaces are completely occupied by the liquid phase and hence the pore velocity is constant. 2. The percolating fluid displaces this liquid evenly so that the solute concentration is always uniform over any cross section. 3. Nature of the liquid flow is plug-flow and the effect of dispersion and diffusion is not con- sidered. Thomas (1948), using the above assumptions, proposed a model for the chromatographic columns. The velocity through the column was constant and the flow was saturated. For the equilibrium relationship X = f(Y*), he used first order and second order chemi- cal reactions as kinetic models for adsorption and desorption. He also assumed that equilibrium between the two phases is established immediately and the mass transfer resistance is negligible. These assumptions result in Y*=0tX, 1.6., 3X - 131: - 1.21 EYE ' a at ‘ aat' (2'14) Thomas solved his system of equations analytically to obtain the dynamic behavior of an adsorption column. Hiester and Vermuelen (1952) studied the cation adsorption Operation in resin beds. They used second order kinetics in the fOrm of bilinear adsorption to define the rate of cation exchange. In this case, BX/at is given by Equation (2.11). They performed 26 the analysis in dimensionless variables to generalize the earlier results of Thomas. The model of Thomas and that of Hiester and Vermuelen did not consider the effect of dispersion in fluid flow. Lapidus and Amundson (1952) studied the same problem but incorporated the longitudinal dispersion effect which modified Equation (2.13) as fellows, 2 oil-v BZ p1_ ax av 32 “be 3' They used a linear adsorption isotherm and considered the cases of no mass transfer resistance and finite mass transfer resistance. For the latter case, they used BX _ _ pb 5t'- Koa (Y - Y*) and Y* - aX . (2.15) The above cases were solved analytically by Lapidus and Amundson to obtain the dynamic response of an adsorption column. Neilson and Biggar (1962) made a comparative study of the- oretical transport models using a series of carefully conducted soil column experiments. They concluded that none of the models tested agreed quantitatively with experimental results but the approach of Lapidus and Amundson gave the best qualitative prediction. Rhee and Amundson in a series of papers (1971, 1972) derived a model for the adsorption-desorption for saturated flow in columns. Their model consisted of the dispersion equation and the adsorption 27 rate expression (2.15) but used the nonlinear expression of Langmuir to describe the adsorption isotherm. They showed that under certain conditions (dependent mainly on the type of adsorp- tion isotherm used), after some time of operation, the shape of the solute concentration profile in the solid phase becomes con- stant. This solute profile of constant pattern was termed as a shock layer. Once the shock layer is established, it moves down the column with a constant velocity which depends only on the adsorption isotherm and the initial and boundary conditions used. The various physical properties such as dispersion coefficient and mass transfer coefficient do affect the shape of the shock layer, but the velocity of the shock layer is not affected by these constants. They also considered the case of interphase equilibrium and showed that the same results are applicable in this case. Lai and Jurinak (1972) studied the effect of the shape of the equilibrium curve on the concentration profile for a soil column cation adsorption problem. They used an equilibrium model and for the case of convex isotherms they presented data which bear out the shock layer theory of Rhee et al. (1971). Cho et al. (1970) studied phosphorus movement in soil col- umns in which phosphorus adsorption was described as a first order chemical reaction. He demonstrated that the water movement was much faster than the phosphorus movement and that the phOSphorus movement in soils was dependent on the rate of adsorption and the mode of application of phosphorus. II I III 1111 11 11 7| 1 11 11. .‘(.i ‘7 6". 28 Present Work All the above models consider constant pore velocity. This is not necessarily true in the case of a spray irrigation system. As the wastewater is sprayed on the soil, the moisture content in the soil increases. Development of the saturation profile depends on the physical properties of the soil such as hydraulic conduc- tivity (ability of the soil to conduct water) and capillary potential gradient. This gives rise to a varying velocity of water in the soil. This feature has to be included in any attempt to model the phosphorus movement in soils. After sufficient time elapses, flow becomes steady and the model will reduce to the regular adsorption- desorption model. Present work will use the Langmuir adsorption isotherm to describe the equilibrium relationshp between the two phases, and will assume no interphase equilibrium. External film diffusion controlling the adsorption process will be used as the basis for the development of the model. CHAPTER III MODELING OF PHOSPHORUS MOVEMENT IN SOIL Physical Situation and Assumptions The physical situation in a soil column is quite complex. In an unsaturated flow through the soil, three phases exist: (1) gas, (2) liquid, and (3) solid. The solid phase consists of particles and aggregates of particles. The pore spaces existing between the particles are termed micropores and those between the particles and the aggregates or between the aggregates are defined as macr0pores. Liquid, carrying the solute, moves down through the pore spaces. The solute, in order to get adsorbed at the solid surface, has to diffuse from the bulk of the liquid to the solid surface where it is adsorbed. Thus, there are three steps in series. 1. External diffusion: Diffusion of the solute from the bulk of fluid to the outer surface of the solid particle. 2. Internal diffusion: Diffusion of the solute through the pores of the particle to the point where adsorption occurs. 3. Adsorption: Adsorption of the solute on the solid phase- The rate of adsorption will be controlled by the step that offers the greatest resistance to the transfer and hence the step that is the slowest. In this model, it will be assumed that the 29 30 combined resistance of the external and internal diffusion is much greater and, therefore, it is the rate controlling mechanism. In that case, the rate of phosphate adsorption-desorption is defined by 30 ll _ * Koa (Y Y ) where 11 Y* aX/(l - bX) (from 2.7). This is called the mass transfer model. It assumes that diffusion limits the rate of transfer of phosphate between the solution and the solid surface. The solid surface contains the active sites for phosphate adsorption. The rate of adsorption is proportional to the driving force measured by the departure of the system from equilibrium, the overall mass transfer coefficient, and the solid-liquid interfacial area per unit bulk volume of the soil. The overall mass transfer coefficient incorporates both the micro- pore and macr0pore diffusional resistances. The flow of water through the soil deviates considerably from plug flow. This phenonenon is due largely to the wide range of pore sizes which results because of the heterogeneity in the soil particle sizes and shapes. This fact can be accounted for by incorporating a dispersion coefficient in the flow equation. At low flow rates, its value approaches the diffiusion coefficient but at high flow rates, the dispersion coefficient is much larger than the diffusion coefficient (Chung, 1967). Nielson and Biggar's 31 data (1962) at low flow rates indicate dispersion coefficients of the same order of magnitude as diffusion coefficients. Based on the above discussion, the following assumptions are made in the development of the model for phosphorus adsorption in soil. 1. Flow is unidirectional with uniform cross-sectional area. 2. An effective axial dispersion coefficient repre- sents the combined effect of both diffusion and dispersion. 3. Porosity of the soil is assumed constant. 4. The system is isothermal. Water Transport Phosphorus is carried through the soil by water. This necessitates describing the movement of water before one can accurately predict the phosphorus movement through the soil. In developing a model for the two phase water movement in the soil, Novak and Coulman (1972) have shown that a one phase water model is sufficient to describe the soil water movement in irrigated soil over a wide range of non-isothermal conditions. The single phase water movement will be used as a base component of the phosphorus model. The velocity of a liquid in a porous medium like soil is directly proportional to the potential gradient as given by Darcy's law VcS=-Kg—%=-K (gig-1) , (3.1) where 32 V = pore velocity, cm/day, c = porosity of the soil, K = hydraulic conductivity of the soil, cm/day, S = saturation, percent of void space occupied by water, ¢ = total potential, cm of water, 0 = capillary potential, cm of water, and Z = soil depth, cm. Equation (3.1) can be rewritten as 35 l) . (3.2) VcS=-K( 57- we) we Both the hydraulic conductivity and the capillary potential are functions of soil moisture content or soil saturation, S. Development of Model Water Balance various Consider a thin section of soil of AZ thickness. The components of the material balance equation are as follows: rate of incoming water across VcSAIZ , the surface at Z rate of outgoing water across VeSAIZ + the surface at Z + AZ AZ 9 and rate of accumulation of water g%-(AAZ€S) . Adding the various components of the material balance equa- tion and dividing by AZ gives 33 VesAIZ - VeSAIZ + AZ _ a AZ ‘a—t' (AES) . Taking the limit as AZ + 0, gives where VcS is given by Equation (3.2). - 537 (VcS) = @— (e3) 3t Phosphorus Balance (3.3) The various components of the material balance equation for phosphorus in liquid phase are given below: gets rate of incoming phosphorus by diffusion and dispersion across the surface at Z rate of incoming phosphorus by convection across the surface at Z rate of outgoing phosphorus by diffusion and dispersion across the surface at Z + AZ rate of outgoing phosphorus by convection across the surface at Z + AZ rate of adsorption of phosphorus rate of accumulation of phosphorus BY -DA€S ——- , 82 Z VESAYIZ , DAeS 3% z + AZ , VESAYIZ + AZ 9 K0a(Y - Y*)AAZ , and it at (YAAZES) . Adding up all the contributions and dividing by AZ, one I III 1‘(.‘lrl I: I. 7|" 711 1111.1 34 3V BY 2 + AZ Z + AZ AZ .. _3_ - Koa(Y - Y*)A - 3t (YAES) . Taking the limit as AZ + 0, gives av) _ (5'57 g%—(VESY) - Koa(Y - v*) g%-(ves) . (3.4) 57' Phosphorus balance on the soils is quite simple since the rate of increase of the phosphorus concentration on soils is the same as the rate of transfer of the solute from the liquid phase, i.e., 3X _ Pb 5f" K03(Y - Y*) . (3.5) Equations (3.1) through (3.5) along with the Langmuir adsorp- tion isotherm completely define the system. This model can describe the phOSphorus movement in soils at constant or varying velocity, at saturated or unsaturated conditions. When the flow is steady, the model reduces to Equations (3.4) and (3.5) which are of the same form as those of Rhee et al. (1972). However, there are some differences between the definition of the variables in the analogous equations. In the papers bthee et al. (1971, 1972), the pore velocity and time correspond to a saturated flow rate and actual time, respectively. In contrast, this model contains pore velocity and time variabl 35 es, which correspond to the irrigation rate and the cumulative irrigation time, respectively. The mathematical form of the problem can be summarized as follows: 1(esi- - 1(Ves) , 1 at 32 ves=-K(§$ 33-1), be 332- (S 3%) - 537 (Vesv) - Koa (v - Y*) = 53; (Yes) , (3.6) pb-%% = Koa (Y - Y*) , and Y* = 1 fixbx ' J The initial and given below: S(Z,O) Y(Z,0) X(Z,0) = and at Z V(o,t) boundary conditions for solving Equations (3.6) are initial conditions, (3.7) application rate at the surface __ at e- ' K [as oz 13'2 = 0 , V(o,t) = Yi , and boundary _ Yi conditions (3’8) “WU-Wm?- l at Z = L, as _ g!__ 57-- O, and 32 - 0. , In the above equations, X0 and Y0 are in equilibrium and so are Xi and Yi' The physical constants needed to solve the above equations are a. hydraulic conductivity Of the soil as a function of saturation, b. capillary potential of the soil as a function Of saturation, c. overall mass transfer coefficient for the system, and d. Langmuir isotherm constants. TO validate the above model, simulation results are to be compared with data obtained from an actual Operating facility. Such a facility was constructed on the campus of Michigan State University and was called BLWRS (Barriered Land Water Renovation System). A detailed discussion on BLWRS will be given in a later section. 37 Model Parameters Mass Transfer Coefficient and Langmuir Adsorption Isotherm TO determine the mass transfer coefficient and the Langmuir adsorption isotherm for the BLWRS system, an experiment was carried Out in the CrOp and Soil Science Department, Michigan State Uni- versity. The Langmuir isotherm coefficients were Obtained for the BLWRS soil by the method of Olsen and Watanabe (1957). Five grams Of soil was allowed to equilibrate with 40 ml Of solution containing a known concentration Of phosphorus. Equilibrium was assumed to have been reached in eight hours. At equilibrium, the phosphorus concentration in the liquid was determined and the concentration on the soil was calculated by the difference between the initial and the final concentrations in the liquid phase. This process was carried out for five different initial concentrations. During the isotherm determinations, the phosphorus concentrations in solution were also tracked as a function of time, until equilibrium had been attained. The data are given in Table 3.1. The phosphorus concentration on the soil can be calculated by using VL x = x0 + W; (Yo - Y) (3.9) where X = initial concentration on the soil, VL = volume Of the liquid, W = weight of the soil, and Y = initial phosphorus concentration in the liquid. 38 TABLE 3.1.--Equilibrium and Approach to Equilibrium Data for Liquid Concentration in Phosphorus Adsorption. Time hrs Run 1 Run 2 Run 3 Run 4 Run 5 0 2.9 5.55 8.67 11.60 13.57 0.5 1.08 3.09 5.81 7.98 9.69 l 1.07 2.92 5.15 7.46 10.00 2 0.45 1.98 4.77 6.16 8.67 4 0.47 1.76 3.94 5.73 7.73 8 0.38 1.56 2.62 4.70 6.21 The equilibrium relationship is expressed as Y*/X = l/KQ + Y*/Q. A plot Of Y*/X versus Y* will result in a straight line with slope and intercept equal to 1/0 and l/KQ, respectively. Such a plot is shown in Figure 3.1. An ordinary differential equation for the phosphorus con- centration in liquid phase was written and integrated to Obtain the mass transfer coefficient (see Appendix A). The calculated value Of Koa was found tO be 2.0 day'1. Hydraulic Conductivity Hydraulic conductivity, as the name signifies, represents the ability Of the soil to conduct water. For high saturations, the hydraulic conductivity is determined by steady flow experi- ments and Darcy's law. For lower saturations, it is determined from unsteady state flow experiments, and Darcy's equation and water balance equation. Experimental data on the hydraulic 39 .cowpmzam ceasmcmo an cm>ww mm omega UPPom cw mscogamoza use omega venue; :_ maeogamoga cmmZumm awsmcowumpmm EaanPFW:UMtt._.m weaned Egg .t> o.o o.m o.¢ o.m o.~ o.— o a a J . a q rm.o NNFO h ogmocmpcfi <3 maopm 0L x X/rA 40 conductivity on Uplands sand are given in Figure 3.2. The data points were curve fitted using a least squares technique to Obtain an expression for hydraulic conductivity as a function Of saturation.* Capillary Potential Figure 3.3 contains the capillary potential data on Uplands sand. Capillary potential is determined by manometer measurements at high saturations, but at low saturations, it is determined by vapor pressure measurements (Novak, 1972). The experimental data were curve fitted to Obtain an expression for capillary potential as a function of saturation.* From this, a graph Of do/dS versus saturation can be Obtained as shown in Figure 3.4. Hydraulic conductivity and capillary potential data for the Spinks sandy soil which was used in the construction Of BLWRS were not available, hence the data Of Staple (1969) for Uplands sand were used. Barriered Land Water Renovation System (BLWRS) A facility for spray irrigation Of land using wastewater has been Operated at Michigan State University. The soil system was modified to accomplish phosphorus and nitrogen removal within a short distance into the soil. The system is diagrammed in Figure 3.5. It has a mound Of soil underlain by a barrier imper- vious to water. This has the result Of creating aerobic and anaerobic environments in series. On the top of the mound, a thin band of limestone is placed to increase the calcium content Of the *Modified from Novak (1972). Log (Hydraulic Conductivity) 41 2).. 0h— -2)- ‘4‘ Data Reference W. J. Staple, Soil Sci. Amer. PrOC., 33:840 (1969). -6?- l l l i I _ '80 0.2 0.4 0.6 0.8 1.0 S, Soil Saturation Figure 3.2.-~Hydraulic Conductivity Versus Soil Saturation. 4 Data Reference W. J. Staple, Soil Sci._ Soc. Amer. Proc., 33:840 (1969) 3 Log (Capillary Potential) 42 N T 1 0.2 0.4 0.6 0.8 Soil Saturation Figure 3.3.--Capillary Potential Versus Soil Saturation. 1.0 43 \l 05 .b Log (Capillary Potential Gradient) 01 (A) l Data Reference W. J. Staple, Soil Sci. Soc. Amer. Proc., 33:840 (1969). . —-- 0 012 0.4 0:6 S, Soil Saturation 0.8 1.0 Figure 3.4.--Capillary Potential Gradient as a Function Of Soil Saturation. 44 .Ammzbmv seemsm eo_b 1m>ocmm Loam: use; umcmwccmm eo :o_pummtmmocu owumawgomti.m.m wczmwm 1? pm owtov iv“ cmwccmn ucma_ mm mczumwoz mcoN waocmmc< pcmspmem Cw om:N~ we cue \ 85:3 :3 33.75% mocaom x coco Fmpcmampqqam concomnm moccamosa m:o~ ownocm< i mew; umvvm mummz 45 soil. Phosphorus adsorption takes place in the upper part and nitrification and denitrification occur in the aerobic and anaerobic regions. BLWRS was constructed Of Spinks loamy fine sandy soil. Data Obtained from this system after 60 days Of Operation at an average application rate of 2.11 cm/day were used to validate the model developed here. Anaerobic swine waste was spread on the BLWRS at an average rate Of one inch per day. The application rate was reduced during rainy periods. The liquid wastes contained an average Of 40 ppm Of organic and inorganic phOSphorus. Periodically, samples were taken at various depths and were analyzed for their phosphorus content. The detailed description Of the system and the operating procedure can be found in Erickson et al. (1971). When the liquid waste from the anaerobic holding pits was applied to the surface Of the soil, the first reaction to be expected was precipitation Of calcium phosphate. The existing soil pH after Operation of the BLWRS for a Short period Of time was 7.0-7.2 and the calcium content Of both the soil and waste material was sufficiently high to precipitate orthophosphate as calcium phosphate. As discussed in the phosphorus precipitation section, dicalcium phosphate forms rapidly under these conditions, but the other calcium phosphates form more slowly (a few weeks for octa- calcium phosphate and several years for apatite). Since dicalcium phosphate limits the solubility Of phosphorus, the phosphorus con- centration in solution would be from 7—9 ppm total phosphorus in the pH range 7.0-7.2 (from Figure 2.1). As the precipitation 46 phenomenon was not considered in developing the model and approxi- mately 80 percent of the phosphorus added to the BLWRS can be removed by this mechanism, it is very important to establish the phosphorus concentration in solution at the surface. From the application rate, the total time Of irrigation and the quantity Of adsorbed phosphorus, the phosphorus input concentration to the adsorption zone was calculated by material balance. For the BLWRS, it turned out to be 9-10 ppm corresponding to the theoretical value for dicalcium phosphate solubility at pH 7.0. It was verified that precipitation had occurred, as the sur- face soil after several months of operation was found to contain 853 ppm total phosphorus as compared to 132 ppm for the soil at a 5 foot depth. 0f the 853 ppm, only 67 ppm was in the adsorbed state. Thus, during continuous Operation Of the BLWRS, dicalcium phosphate controls the level of phosphorus in solution at 9 ppm. This did not preclude the formation Of less soluble phosphates with time but sug- gested that they would not control the level Of phosphorus in solu- tion leaching into the adsorption zone. Initial and Boundary Conditions Based on the above discussion, the concentration Of 10 ppm phosphorus in solution was used as a boundary condition. The phosphorus concentration from that point onwards was Obtained by numerically solving Equations (3.6) under the following simulation conditions: 47 S(Z,0) = 0.1. X(Z,O) = 4 ppm, (1.05) (3.10) Y(Z,0) = .06 ppm, and S(0,t) = 0.53, ‘ X(O,t) = 63.13, Y(0,t) = 10 ppm, and (B.Cs) (3.11) 02 L BZ L J Here, X(Z,0) and Y(Z,O) are in equilibrium and so are X(O,t) and Y(O,t). The values of the constants in the Langmuir isotherm equation are a = .0122 , and b = .01462. Method Of Solution Equations (3.6) cannot be solved analytically and hence a numerical solution was sought instead. The equations can be divided into two sections: (1) water transport equations and (2) phosphorus transport equations. These two sets Of equations can be solved either separately or simultaneously. In the first method, the water transport equations can be solved first and the saturation profiles computed at different times are stored in the computer.) The phosphorus profile can then be computed from the phosphorus equations and from the computed saturation profiles. The second method would involve solving, at every time interval, 48 the water transport and phosphorus balance equations in succession. The latter method was used in solving the above set of equations. An implicit method was employed to compute the saturation and phOSphorus profiles at the next time interval. All the first order and second order derivatives were approximated by finite difference equations at the next increment in time, resulting in a set of simultaneous equations. These equations were solved, to give the saturation profile and the phosphorus profiles in the liquid and solid phases. Both the water and phosphorus balance equations are nonlinear. In order to follow the above procedure, the equations have to be linearized. Approximate estimates Of saturation and phosphorus profiles were made and an iterative pro- cedure was established. Iterations were continued until the computed and estimated profiles converged to the same values. A general FORTRAN program PMODEL was written to solve the above equations numerically to Obtain the phosphorus profiles. The program is quite general in the sense that another soil system, having different Langmuir adsorption isotherm constants, and dif- ferent physical constants, can be simulated quite easily by changing some parts Of the subprograms. Also, by selecting the proper Option, it can be made to simulate both the water and phosphorus movement or just the phOSphorus movement (this statement will be elaborated later). A complete description of the numerical method used to solve these equations, along with a listing Of the FORTRAN program PMODEL and its associated subprograms, may be found in Appendix B. 49 The following steps illustrate the calculation procedure used to solve the equations numerically. 1. Input the properties of the soil system, the Operating conditions, and the increment sizes of the length and time axes. The program establishes the initial conditions in the soil and the boundary condition at the surface. 2. Compute the saturation profile in the soil. This involves carrying out the following steps. a. Assume a saturation profile at the next time interval. This linearizes the equation and allows us to compute the hydraulic conductivities and the gradients Of capillary potential at the next time interval. b. By using a second order finite difference approxi- mation for the partial derivatives, an equation is written for each grid point resulting in a set of simultaneous linear equations. c. Solve these equations to Obtain the saturation profile at the next time interval. d. Compare the calculated profile with the assumed profile. If they do not match, assume a new profile based on the average of the computed and assumed values at the previous iteration and gO back to step b. If both the profiles match, 90 to step 3. e. Continue this procedure until convergence is obtained within the required limit Of accuracy. phases. 50 3. Calculate the phosphorus profile in the liquid and solid This involves carrying out the following steps. a. Assume a phosphorus profile in the soil at the next time interval based on the past available information. This has the effect Of linearizing the equations. As the X-profile is known, Y* is also known at the next time increment. b. By using a second order finite difference approxi- mation for all the partials, an equation for the phos- phorus concentration in the solution can be written for each grid point resulting in a set of simultaneous linear equations. c. Solve these equations to obtain the phosphorus concentrations in solution at each grid point at the next time increment. d. From the Y profile, the X-profile, i.e., the pro- file Of phosphorus concentrations in the soil, can be computed at each grid point (as Y* at the next time incre- ment is already known). e. Compare the calculated and assumed X-profiles. If they are not converged to the same values within given lim- its, go back to step 3a. If they do, all the required information has been computed. Start the whole cycle again for computing the profiles at the next time increment. 4. All the variables are outputted at the beginning of each computation cycle. 51 Results and Discussion Numerical Problems As the equations in set (3.6) are nonlinear and quite complex, a numerical analysis Of these equations was not possible. The final values of the time and depth increments had to be chosen after some trial and error procedure. In almost all cases, a time increment Of 0.25 day and a depth increment of 0.5 cm or 1 cm were found quite adequate. A very small improvement in the values of the variables compared to the greatly increased computation time did not justify going to smaller increment values. Another problem is the selection of the proper length of soil to simulate at a given time. The soil length should not be too large as this would increase the number of grid points to be used and hence the number of simultaneous equations to be solved. At the same time, it should be large enough so that the boundary condition aY/az = BS/BZ = O at Z = m can be applied realistically enough. In general, a 20 cm or a 40 cm zone was simulated at a time. This depth was sufficiently large so that the concentration values at the lowest point were not greatly different from the initial values. This ensured that the lower boundary condition was applied properly. Surface Boundary Condition for Saturation From Darcy's equation, one can see that when BS/BZ = 0, the saturation is constant and the velocity through the soil is equal to the hydraulic conductivity. The saturation at which the 52 hydraulic conductivity equals the surface application rate of 2.11 cm/day at BLWRS is 0.534512 (from Staple's data on hydraulic con- ductivity as a function of saturation). If the initial saturation is 0.1, then it would be expected that the soil saturation will increase from 0.1 to 0.534512 gradually. There are two surface saturation conditions that can be used as one Of the boundary conditions: constant surface saturation or constant velocity at the surface. Qualitative descriptions for both these situations are depicted in Figure 3.6 which shows the development Of the saturation profile as a function Of time. Figure 3.6a refers to a constant surface saturation, say, at 0.53. This assumes that as soon as the wastewater is sprayed on the land, surface saturation reaches 0.53. In this case, the surface velocity varies from a high value to the surface application rate as the time progresses. Figure 3.6b refers to the case where the surface velocity is constant but not the surface saturation. The surface saturation varies continuously such that it provides the proper saturation and capillary potential gradient to keep the surface application rate constant. The condition Of constant sur- face velocity is more realistic than that of constant surface saturation. Simulation Of water movement with constant surface velocity has been tried but without any success. Childs (1965) reports that mathematical analysis of this case is quite complex. In this work, the case was treated as if the surface saturation was maintained constant at 0.53. 53 .>u_uopm> mumecsm pcmpmcou new: .cowumczomm mommczm accomcou cum: «Femoca comumcaomm yo acmEgoPm>mctt.nm.m we:m_d mpwwoca cavemeapmm eo ucwEQoFm>mott.mo.m weaved cowumcaumm cowumcaumm ”1530 Z momeczm 54 Water Transport As the wastewater starts moving down the soil, the moisture content in the soil increases and so does the phosphorus concentra- tion. If the experiment was being carried out in a soil column of finite length, one would expect that water would start filling the column and after some time, the column would be completely filled with water. Beyond this point, there would be no need to consider the water balance equation and the model reduces to the phosphorus balance equations. Similarly, in a soil system like the BLWRS (infinitely long), one would expect the water front to move much faster than the phosphorus profile. This was verified quite con- clusively by some preliminary runs, and the results Of one Of these runs are shown in Figure 3.7 wherein the Saturation and phosphorus profiles are plotted at different time intervals. After Operating the system for 1-3/4 days, the entire 20 cm of soil length considered shows moisture content at 0.5345. But the phosphorus concentrations in soil are affected only up to 5 cm. The advancing water front is so far ahead Of the phosphorus front that, for all practical purposes, in the region Of the phOSphorus profile, the velocity Of water is constant at 2.11 cm/day and the saturation at 0.534512. After 1-3/4 days, the water balance equa- tion drOps out and the simulation equations reduce to the phosphorus balance equations in the liquid and solid phases. Experimental evidence to support the fact that the water front moves much faster than the phosphorus front comes from Cho (1970). He found that in a soil column, the phosphorus movement is four to eight times slower 2, Depth, cm —.a O 1 ._.1 N 1 55 10 20 30 4O 50 6O t = 1.75 day 14 ’— ll 66 t = 0.50 \\ 18- I- p— 200 . .2 3 A Is .6 S2 Saturation Figure 3.7.--Development Of Saturation and Phosphorus Profile During Simulation. 56 than the water movement. This observation can be easily verified by a simple calculation. The water and phosphorus balances can be established after some application time, and the depths Of the soil to which the water and phosphorus fronts have penetrated can be determined. This would show that the water front is way ahead Of the phosphorus front. For the simulation Of BLWRS system, only the phosphorus balance equations were solved. Another interesting feature Of Figure 3.7 is the extent Of penetration Of the water front in the soil after only six hours and the very small rate Of penetrations thereafter. This is explained easily by the fact that, when a constant surface saturation Of 0.53 is assumed, the instantaneous surface velocity is much higher than the actual 2.11 cm/day. The water profile thus penetrates much farther. After six hours, the saturation gradient is not so steep and the surface velocity is quite close to the actual application rate. This reduces the rate Of the water front advance to reasonable values. Phosphorus TranSport If moisture distribution is neglected for a continuous input of liquid wastes, the calculation procedure is singificantly reduced as the numerical procedure outlined in the previous section is fol- lowed without step 2. The corresponding simulating equations are 2 B Y BY BeSY DES -—§-- VeS -Z-- K a (Y - Y*) = , 57 BX _ pb 5t'- Koa (Y - Y*) , and (3.12) _ ax Y*'1-bx J The numerical solution of Equations (3.12) was Obtained and the results are shown in Figure 3.8. The comparison of the BLWRS data with the simulation results shows remarkable agreement. Even though there are only three data points available at every three inch interval, they lie almost on the predicted curve. This is remarkable, considering the fact that the system simulated here is quite complex. The phosphorus profile has traveled about 12-13 cm in soil after wastewater has been applied for 60 days. The I phosphorus concentration at 25 cm soil depth is around 4 ppm in soil and .06 ppm in solution, indicating almost no leakage from the soil system. Rhee and Amundson (1972) have predicted that under the con- ditions Of favorable equilibrium, the phosphorus profile would attain a constant shape which would move down through the soil. They termed this phOSphorus profile Of constant pattern a shock layer. They also showed that the shape of the shock layer is dependent on the physical constants such as the diSpersion coeffi- cient, the mass transfer coefficient, etc. In simulating the BLWRS system, a provision was made to move the coordinate axes down if the profile approached a constant shape. This occurs when the second point from the top surface reaches the maximum attainable concentration Of 63.13 ppm. During the BLWRS simulation, it was 4 58 7O l 60 U1 0 1 X, P Concentration in Soil, ppm 10L b O 1 (A) O 1 N O r .3. After [I A t = 60 days [3 - BLWRS Data - Predicted from model 0 = 10 cmZ/day _ -1 Koa - 2 day I. m 4 a 12 10 20 211 27 Z, Depth, cm Figure 3.8.--Comparison of BLWRS Data With Predicted Results From the Model. 59 found that after nearly 60 days Of Operating time, the profile approached a constant pattern. The effect Of the mass transfer coefficient on the shape Of the shock layer was investigated and the results are shown in Figure 3.9. It is seen that lower overall mass transfer coefficient results in wider shock layers. This can be easily explained by the fact that with higher mass transfer coefficients, phosphorus will be adsorbed much quicker before it can go too far. Thus, the resulting shock layer would be smaller, and vice versa. The effect of the dispersion coefficient on the shock layer thickness is quite predictable. The dispersion coefficient repre- sents some measure Of deviation from the ideal plug flow. The greater the value Of the dispersion coefficient, the greater is the deviation from the plug flow and this would give greater shock layer width. These arguments are shown to be correct by Figure 3.10. The shock layer width for the case Of D = 10 cm2/day is about 8 cm compared with 4 cm for the case Of D = 2 cmZ/day. Figure 3.11 shows the location of the phosphorus profile in soil when the application rates are different. Because Of a greater input rate Of 4.22 cm/day, the phosphorus profile represented by the curve A is much farther in the soil than the curve B repre- senting the application rate Of 2.11 cm/day. The profiles plotted do not represent the shapes Of the correSponding shock layers because the computations were not carried out for long enough times. Soils, because Of their different compositions and struc- tures, may exhibit different values Of the vairous physical constants. 60 70 60 X, P Concentration in Soil, ppm 10 01 O 1 b O 1 ”:3 N O 1 I Figure 3.9.-~Effect Of Mass Transfer Coefficient 0n Shock Layer Koa, day A 2 B 10 C 50 _ 2 D-—lO cm /day BLWRS Soil 4 12 16 Z, Depth, cm cot- Shape. 61 Figure 3.10.-~Effect Of Dispersion Coefficient on the Advancing 70;r .22\ 2\\ 50L x). iT‘B A E _ c150 \ '8 2 “1 0, cm /day C .,.. 40 c A 10 .2 4,; B 2 S B30 \ é Koa = 10 day"1 \ o. . l S >220F BLWRS 011 \ 10 ‘ 0 1 ....-. 1 1 .-._.1 J L 0 4 8 12 16 20 24 Shock Layer Thickness, cm Front Thickness. 27 62 70 After t = 10 days 60 - _ _EE. A v — 4.22 day _ .132 550 t- B v - 2.11 day Q. T: D = 10 cmz/day O ”1 -1 .540 ’ Koa -- 10 day .§ BLWRS soil 4.: 2 2:30 r O) U C O L) D. .20 ' X 10’. \ 0 2 4 6 8 10 12 Z, Depth, cm Figure 3.ll.--Effect Of Increasing Application Rate on the X-Profile. 63 For this reason, the above discussion on the effect Of various factors on the shock layer shape has been included. For a detailed qualitative discussion on the effect Of various parameters on the shock layer thickness, the reader is referred to Novak et a1 . (1975). There are two important points that need to be considered. This model considered continuous application Of wastewater on the land. This is not necessarily true. When the rains come, the application has to be stOpped so as to prevent ponding on the soil. The rainwater percolates through the soil and some desorption Of phOSphorus is likely to occur from the solid phase to the liquid phase. This could lead to some oscillations in the phosphorus pro- files in soil and in solution. This is just speculation and no experimental evidence has been found to support it. Further work in this area would definitely be helpful. Although a soil system has been found to be very efficient in removing phosphorus from the wastewater, a way must be found to remove this phosphorus from the soil. Otherwise, soil becomes a dumping site for phOSphorus and we have succeeded only in transfer- ring the pollutant from the wastewater to the soil. The best way to remove this phosphorus is to crop the soil and let vegetation use this phosphorus as nutrient. This enables us to recycle the phosphorus rather than let it accumulate in the soil. Thus, a sound ecological land diSposal system would be Operated on a cyclic basis Of spreading the wastewater and cropping the soil. CHAPTER IV NITROGEN TRANSFORMATIONS Background Nitrogen exists in soils in both organic and inorganic forms. It undergoes a number of reactions. The main reactions Of nitrogen are mineralization, nitrification, denitrification and immobilization. All Of these reactions are microbial in nature. There have been a number Of reviews on the nitrogen reactions in soils (Bartholomew and Clark 1965). A brief summary Of the nitrogen transformation processes is given below. Mineralization is the process Of converting organic nitrogen into the inorganic ammonium form whereas immobilization involves converting the inorganic nitrogen into the organic form by assimi- lation and incorporation into microbial cells. Both these reactions occur in Opposite directions but which one will predominate depends on the availability of organic carbon (C) to organic nitrogen (N) ratio. If the ratio is high, immobilization proceeds faster and the reverse would be the case if the C:N ratio is low. If an equilibrium can be assumed between these two reactions in the soil, nitrification and denitrification become the predominant reactions Of nitrogen. Nitrification is a reaction wherein nitrogen in the form of ammonium is converted in the presence Of dissolved oxygen to nitrate 64 65 nitrogen. This process is carried out by chemoautotrophic bacteria. These bacteria Obtain their energy requirement from oxidization Of oxidizable compounds. Nitrification is believed to take place in two steps as given below: + 3 Nitrosomonas; - + NH4+-2-02 rN02+H20+H , (4.1) and - l Nitrobacter, - N02 + 5-02 , N03 . (4.2) The overall reaction is NH+ + 2 0 - N0' + H 0 + H+ (4 3) 4 2 r 3 2 ' ° The second reaction is much faster than the first, therefore nitrite accumulation in the soil is negligible. Nitrosomonas and Nitrobacter are the species of microorganisms that carry out each reaction. They use carbon dioxide as the source for their carbon requirement. The denitrification reaction involves the reduction of nitrate nitrogen to atmospheric nitrogen. This reaction is car- ried out by some facultative bacteria. In an anaerobic environ- ment, these microbes use an alternative electron acceptor such as nitrate in the place Of oxygen. If an energy source such as organic carbon is present, nitrate nitrogen is reduced to nitrogen gas. If glucose is that energy source, denitrification can be written as 66 - denitrifiersk - (4.4) + 6 C02 + 18 H O . 2 In the presence of enough oxygen, the same reaction would proceed as microbes; 6 02 + C6H1206 . 6 (:02 + 6 H20 . (4.5) Under some conditions, it is possible to reduce nitrate to nitrogen chemically. However, Brezonik (1966) has shown that for significant chemical denitrification to occur, soil pH has to be very low. The wastewater to be sprayed on the land disposal site gen- erally contains nitrogen in the form Of ammonium or in the form of proteins, amino acids and urea from which ammonia is easily derived. The main nitrogen component is thus ammonium and the important reactions to be considered are nitrification and denitri- fication. These two reactions have been studied by sanitary engineers and soil microbiologists. Recent interest by sanitary engineers is due tO the fact that a modified activated sludge plant involving nitrification and denitrification has been suggested to remove nitrogen along with the biological oxygen demand. The interest Of soil scientists in nitrogen transformations is under- standable because these are the premier microbial reactions in the soil by which soil nitrogen is lost. Laboratory experiments by soil scientists have been done mainly in soil columns whereas 67 those by sanitary engineers have been carried out mostly in con- tinuous stirred tank reactors. In this work, an attempt will be made to integrate the work done by sanitary engineers and soil scientists. Reaction Kinetics The nitrification and denitrification reactions are biochemical in nature. The biochemical pathway Of each reaction consists of a number of steps in series. Each step is enzymatic in nature and is catalyzed by a very specific enzyme. Overall rate Of the reaction is determined by the slowest step in the series. The most widely accepted model of enzyme kinetics is that of Michaelis-Menten. They represented the reaction S1 +-P as E + 51'::2;E - S]———+ P + E (4.6) where E E enzyme, S1 5 substrate, P 5 product, and E - S E enzyme-substrate complex. The rate of product formation is given by S r = rm (F1571— (Aiba et a1. 1960) (4.7) where 68 r = rate Of product formation, rm = maximum rate Of product formation at very high substrate concentration, and Krn = substrate concentration at which r = rm/Z. Here substrate S1 is assumed to be the limiting substrate. Since nitrification depends on the metabolism of a certain group Of microorganisms, the rate Of product formation would also depend on the growth rate Of microbes and their numbers. Monod (1949), in his study Of bacterial growth in a continuous culture, where there was one limiting substrate, found that his data behaved in a manner typified by the Michaelis-Menten equation and proposed the following equation 51 u = “m K—__:—S- (4.8) S1 1 where um = maximum growth rate when the substrate is present in excess, day—1, u = specific growth rate, day", and KS = saturation constant; i.e., substrate concentration 1 at which u = um/Z. Here = 1. 9A 1‘ th where X = concentration Of microorganisms, mg/l. 69 Equation (4.8) incorporates both the first order and the zero order models. If S1 >> K5], then u = “m 31/31 = um, i.e., the growth rate is constant and is independent Of the substrate concentration. If KS] >> S], then u = “m Si/KS] which indicates that the growth rate is directly proportional to the substrate concentration. At steady state, in a continuous stirred tank reactor, the dilution rate equals the specific growth rate Of the bacteria in the reactor (to be shown later). The chemostat can be Operated at various dilution rates (residence times) and the effluent sub- strate concentration at each dilution rate can be determined. The results can be plotted in two ways as shown in Figure 4.1. In Figure 4.1a, the dilution rate is plotted against the substrate concentration. From this graph, um and KS] can be cal- culated as the dilution rate at large S1 values and the substrate concentration at growth rate equal to um/Z, respectively. The bottom figure illustrates the "washout" phenomenon. If the reactor is Operated at a dilution rate greater than the maximum specific growth rate, the microbes do not have enough time to grow in the reactor and are washed out. The substrate comes out at the initial concentration only. It can be shown that the Michaelis-Menten con- stant and the saturation constant are equal and that rm and “m are related. If the yield coefficients for the microbial reactions are constant, then for a batch system, three differential equations can be written as 70 .AUPHaeeg 66:6: co eoebaeom=F_H--.P.e mesmeu -:apam eoeoapwa .4 A a _m moaeomasm 17.tl‘l|llllt I -0 III'I 1‘ III Is aieJisqns O =r‘l 6193 u0iintt0 S £1')i§‘=“x=“m1< 15 x, (4'9) S1 1 ds1 11'“ 5‘ x f bt ———-= - —- -———————— = rate 0 su 5 rate dt Y1 KS1 + S] (4.10) consumption, and u S QE.=.JB .___J_——- X = rate Of product formation. (4.11) t 2 Ks +51 X Y" (4.12) The maximum specific growth rate and the maximum rate Of product formation are connected by the microbial concentration and the yield coefficient. Most Of the workers have assumed Equation (4.8) to describe the specific growth rate of microorganisms. This expression assumes that only one substrate is limiting. This is true when all the other substrates are in excess. Situations can arise when more than one substrate can become growth limiting. Under these conditions, the Monod expression has to be modified to include the effect Of other substrates. A mechanism (given in Appendix C) has been proposed which is described by the following equation: S 1 2 _________ '___7FT§§ , (4.13) 72 Mahler and Cordes (1968) indicate other mechanisms which are prevalent in bisubstrate enzyme kinetics. Equation (4.13) very conveniently reduces to (4.8) if one of the substrates is in excess. Most of the work on nitrification and denitrification has been done on the basis of single substrate growth limiting kinetics. In a soil column, the concentrationstyfammonium nitrogen and oxygen decrease with length. At some point in the column, both these concentrations can be sufficiently low to be limiting. Thus, it is important to determine the growth rate expression as a function Of two limiting substrates. The constants involved in Equation (4.13) will be evaluated from past work and, in the absence Of any past appropriate work, experiments will be performed to calculate these constants. Past Work Nitrification The substrates required for the nitrification reaction are ammonium nitrogen and dissolved oxygen. One would therefore expect the rate of the reaction to depend on the concentration of both these substrates. At high concentrations Of the substrates, the reaction rate is expected to be zero order. Nakos and Wolcott (1972) car- ried out the nitrification reaction batchwise at ammonium nitrogen concentrations of 400 ppm and higher. The ammonium nitrogen con- centration decreased linearly with time indicating a zero order 73 reaction, but such high concentrations are not encountered in a land disposal system. On the other hand, Wild et al. (1970), in a batch nitri- fication unit at ammonium concentrations Of 30-40 mg/l, still found the reaction rate zero order. The unit was Operated at very high microbial concentration and greater numbers Of microbes could conceivably keep up the ammonium consumption. Knowles et al. (1965) studied the growth rate of nitrifiers as a function Of ammonium concentration as given by the Monod expression. Some Of their results are tabulated below. Temperature °c 10 20 30 Nitrosomonas _] 0.29 0.76 2.0 “m day Nitrobacter 0.59 1.0 1.9 K Nitrosomonas 0.22 0.73 2.4 51 mg/l Nitrobacter 0.30 1.3 5.5 Downing et al. (1964) found the growth rate constant of Nitrosomonas double that Of Nitrobacter. From the above values, it can be shown that the doubling time for nitrifiers is 10-20 hours compared to 2-3 hours for the activated sludge bacteria. This shows that for sufficient nitrification to occur, the detention time in the reactor has to be quite high. Many workers (Mulbarger 1971, Johnson and Schroepfer 1964) have proposed a separate nitri- fication unit from the carbon oxidation unit because Of the slower 74 growing nitrifiers. The nitrification unit is followed by the denitrification unit. These workers have shown quite conclusively that such a system is very efficient in carbon and nitrogen removal. The research efforts mentioned above did not consider the effect Of dissolved oxygen on the rate of nitrification. Most of the work was done under the condition Of a high degree Of aeration. The dissolved oxygen concentration was quite high and it was not the limiting substrate. Wuhrmann (1963) showed that for gOOd nitrification, the dissolved oxygen concentration must be greater than 1 mg/l. .Amer and Bartholomew (1952) studied the effect Of the oxygen concentration in soil air on nitrification. The graph Of rate of reaction versus oxygen concentration is shown in Figure 4.2. This is described by the Monod expression and from the graph, one Obtains K = 0.8 mg/l . (4 14) S1 From the stoichiometric relation [Equation (4.1)], it can be easily seen that for every gm Of ammonium nitrogen oxidized, 4.57 gms of oxygen are required. Wezernak and Gannon (1967) experimentally determined the net oxygen requirement to be 4.33 gms of oxygen per gm Of ammonium nitrogen oxidized. Thus, if not available in sufficient quantities, oxygen can become limiting in the nitrification reaction. Pruel and Schroepfer (1968) carried out nitrification in soil columns under saturated and unsaturated conditions. They I! I'll-111.1 II 7 III-1111111 I 75 .coeuoeacmocou :mmxxo mo compound a we comumupewcumz eo mmemwo11.~.e mesmwu comumcucmucou cwmxxo _\ms m e a N sea sow mp o_ m o 1 1 d |q Pm _\me m.o a x _ M Ammapv m_~ Fe ..edm __om Ego—cgugmm new LwE< me ”mama N\ L meL mm om uotieotjtuitp to 333630 mm oo~ 76 showed that under unsaturated conditions, nitrification was pre- dominant and adsorption Of ammonium was of little significance. Starr (1973) studied nitrogen transformations in a soil column under continuous flow. He measured the concentration of ammonium ions as a function of the soil depth. From this, he com- puted the first and second derivatives and these he plotted against the ammonium concentration to Obtain the first order reaction constant. The method is quite crude (and the author does not agree with the analysis Of his data) but the data plotted in such a fashion do indicate that the reaction is a combination Of zero order and first order reaction (Figure 4.3). The saturation constant and the maximum reaction rate are found to be 10-15 mg/l and 30 pg/cm3/day, respectively. The effect Of various other factors on nitrification has been studied quite extensively. Lower temperatures reduce the rate Of nitrification. As nitrification is accompanied by an increase in the H+ ions concentration, thus reducing the pH, the rate of the forward reaction can be increased by carrying out the reaction at higher pH. In fact, a pH Of 8.5-9.0 has been found to be Optimum. From the above discussion, the approximate values of the various constants can be estimated as follows: 2.5 day", ‘C II 5-15 mg/l (closer to 15 mg/l), and K M d II K52 = 1-2 mg/l. .:owpmcucmucou cmmoepwz Ezwcoee< we comuocad m we co_umuw¥wcuwz we mummtt.m.¢ weaved F\me .cowumcuemocou thzz 77 ca mm on mN ON m_ o_ m o . a a J) mm v . Ar . q P\me N_ u g _m m.N_.. x .m ANNm_V =o_babeamm_o .a.ea ..o .N .eeaom a. ..o_ ”mama .m. l O N 1 L0 N Ken/SMO/fifl ‘UOAAPDLJAJitM JO aied 78 The growth rate expression for the nitrifiers is then S] 52 1.1 = 2.5 m m . (4.15) Denitrification Denitrification was Observed and reported by soil scientists as it sometimes represented the chief route by which the nitrogen in soils could be lost. It was Observed that it takes place in a highly organic environment such as manured soils and progresses slowly in well aerated soils. Denitrification is brought about by facultative bacteria such as Pseudomonas, Achromobacter, Bacillus and Micrococcus. There are two types Of nitrate reduction that can occur: 1. Assimilatory denitrification--In this case, nitrate is reduced to ammonium which enters the pathway leading to the synthesis of protein. The reduction of nitrogen for incorporation into the cell material is called assimilatory denitrification. 2. Dissimilatory denitrification--Here, nitrate is used as an electron acceptor in the absence of oxygen and is reduced to nitrogen gases. This is the type Of denitrification we are more interested in. The rate of denitrification can be expected to be a func- tion of the organic carbon concentration, the nitrate nitrogen concentration, the oxygen concentration and the physical factors such as pH and temperature. 79 The Optimum pH for denitrification lies in the neutral region. The final products Of denitrification depend on the pH. If the pH is below 6, a significant amount of N20 is present but at pH 7, the N20 is reduced to nitrogen and the predominant product is N2. Lower temperatures reduce the rate Of the reaction and the Optimum temperature for the reaction is around 30°C. Denitrifi- cation in soil and the effect Of various parameters on it has been studied in detail by Wijler-and Delwiche (1954) and Nommik (1956). There have been conflicting reports whether complete absence Of dissolved oxygen is required for denitrification to occur. A report Of the Gulf Research Institute (1970) found that denitrification can occur even at dissolved oxygen levels of 4 ppm. On the other hand, Skerman and MacRae (1957) Observed that even very low concentrations Of dissolved oxygen (0.2-0.4 mg/l) inhibited the rate Of denitrification. A number of workers have reported denitrification to occur even in aerobic conditions in the soil. This can be explained on the basis than an anaerobic microenviron- ment exists in spots where denitrification can take place. It has been established quite conclusively that if Oxygen is present, it will be consumed much faster than nitrates (Strickland, 1931). Thus oxygen will be used first and nitrates will be used only after all of the oxygen has been consumed. Denitrification has been accomplished in continuous stirred tank reactors as well as in packed columns. Amant and McCarty (1969) studied the effect Of detention time and various types of packing materials on denitrification. Sand columns worked very 80 well initially but encountered clogging problems later. A deten- tion time Of 1 hour enabled 90 percent reduction of the incoming nitrate nitrogen. DuTOit and Davies (1972) studied denitrifica- tion in both suspended growth and packed column units and found the packed units much more efficient in nitrogen removal than the sus- pended growth units. Residence times in the packed units ranged from 0.5 hour to 4 hours. The quantity Of nitrate nitrogen that can be removed in denitrification depends on the quantity Of the available organic carbon in the system. Organic carbon acts as an electron donor . for denitrification and energy derived by the oxidation of organic carbon is used for cell synthesis. The quantity Of organic carbon that must be added to the system per unit Of nitrogen removal must be known to effectively design the denitrification system. Once the organic carbon requirements are known, the necessary influent methanol or glucose concentration can be determined to remove a given quantity Of nitrogen. Sources of organic carbon can be methanol, glucose, acetic acid, etc. The rate of denitrification will depend on the ease with which these substrates can be degraded. Soils generally have a high fraction of organic carbon. Denitrification would take place even if no energy source is added to the soil. The organic substrates that are added to act as energy sources include glu- cose, methanol, lactic acid, etc. An equation has been developed to predict the quantity Of the methanol required to reduce the nitrate, nitrite and dissolved oxygen (Amant and McCarty 1969): 81 c = 2.47 c -_N + 1.53 c -_N + 0.87 CDO . methanol N03 N02 Sanitary engineers have studied the rate Of denitrification and have generally assumed the rate to be a function of organic carbon concentration as defined by an equation Of the Michaelis- Menten type. Johnson (1972) used the following equation for the rate of denitrification: 2.5 S1 Y‘ = R—S—TST (4.16) l where S1 = limiting substrate concentration in mg/l Of biological oxygen demand (800), and KS = 150 mg/l Of 800. 1 Translated into organic carbon, the value of the saturation constant could be in the range Of 25-50 ppm organic carbon concentration. An exact value cannot be determined without knowing the actual composition Of the substrate used. Stensel (l97l) carried out denitrification in suspended growth units and determined the constants which are given below: 10 day’1 , ‘E’ II 7< 11 50-75 mg/l chemical oxygen demand (C00), (4.17) and yield coefficient 0.15 - 0.18. J 82 The experiments were performed under what Stensel thought were COD limiting conditions. Some of his experiments, though, were performed under conditions when both the COD and nitrate nitrogen could have been limiting. Requa and Schroeder (1972) reported the rate Of denitri- fication as a function Of the nitrate nitrogen concentration with a very small value Of the saturation constant. This essentially reduced the Michaelis-Menten expression to zero order form, with the rate being equal tO about 5 mg nitrate nitrogen reduced/day/l. Starr (1973) studied nitrification and denitrification in a packed column and assumed first order kinetics for the denitrification reaction with the rate constant being equal to 0.08 day“. Soils generally contain a large amount Of organic matter and the rate expression for the growth rate Of microbes becomes zero order with respect to the organic carbon concentration. This explains why soil scientists always worked with nitrate nitrogen as the limit- ing substrate. Both these microbiological reactions are multiple substrate limited but no attempt has been made tO study the growth charac- teristics Of the microbes as a function of these two substrates. For nitrification, a rate expression involving two substrates has been derived but a similar expression for denitrification cannot be derived. For this reason, experiments have been per- formed to estimate um, K51, K52, Y], and Y2. Here, Y1 and Y2 represent the yield coefficients with respect to substrates 1 and 2, respectively. 83 Experimental Method SU§pended Growth Units Vs. Packed Columns Determining the kinetics Of different reactions from field studies is very difficult. Micrometeorological conditions play a vital role in affecting microbial ecology by changing soil temperature and soil moisture. Field studies Of nitrogen trans- formation processes are under conditions Of constantly changing soil temperature and moisture. Under these conditions, all the microbial processes are occurring simultaneously and it is very difficult to differentiate between various processes because of complex interactions. Laboratory studies Of these transformation processes make use Of the ability to control conditions so as to be able to isolate a particular reaction and study its kinetics. As the rate expressions to be estimated are to be used in simulating nitrogen movement in soils, the first temptation is to study the reaction in soil columns. The physical situation in both the cases is quite similar and the results obtained from soil column experiments will be applicable in designing a land disposal system. Soil column studies are analogous to actual field studies. Although soil conditions can be controlled in a labora— tory sOil column, it is still difficult to isolate the effect of a particular reaction. Starr (1973) studied the nitrogen trans- formations in an unsaturated soil column under continuous flow. He measured the concentrations Of various nitrogen species such as nitrogen, ammonium, nitrate nitrogen, etc. Assuming double 84 substrate limited kinetics, one can write a series Of nonlinear second order differential equations involving parameters for the denitrification reaction. Determining these constants then becomes a very lengthy parameter estimation problem (the equations necessary in the analysis Of data will be derived in the chapter on nitrogen modeling). Derivation Of the above equations does not even consider other nitrogen reactions. Thus, the soil column experiment itself is long (steady state conditions are achieved after operating the soil column continuously for three to four months) and analysis of the data is quite difficult. Suspended growth units are continuous stirred tank reactors. They are very easy to use and amenable to easy mathematical analy- sis. Not much sophisticated equipment is required. In the light Of the above discussion, continuous stirred tank reactors were used in this work to evaluate the constants in the rate expression. Theory The specific growth rate Of microbes is defined as the rate Of increase in cell mass per unit cell mass, i.e., g3). (4.18) ><|—‘ u: Taking cell mass balance for a stirred tank reactor gives [incoming rate] - [outgoing rate] + [rate Of generation] = [rate Of accumulation Of cell mass] . 85 Substituting for the various terms gives in - FX + uXV = v §%- (4.19) where F = flow rate, 1/day, Xi = microbial concentration in mg/l, and V = reactor volume, 1. Dividing Equation (4.19) by V throughout gives dX dt'= 0 (xi - X) + uX (4 20) where D = dilution rate, day-1, reciprocal Of residence time. Similar balance equations for substrates 1 and 2 can be written as dS1 0x dt T D (Sli ' 51) ' 11" (4'21) and d5 2 _ uX dt ' D (SZi ' 52) ‘ 12‘ (4'22) where Y] and Y2 are yield coefficients; i.e., they represent the units of cell mass produced per unit consumption of substrates. If steady state conditions are allowed to be reached in the reactor, then 86 -931.-.‘.‘-520 dt dt dt ' Using the above relationship, Equations (4.20), (4.21), and (4.22) can be rewritten as 0 (xi - X) + u I. O o 0 (S11 - $1) - LAX/Y1 II C U (4.23) and D (521 - $2) - uX/Y2 = O . If the incoming cell mass, X], is equal to zero, the first equa- tion of (4.23) simplifies still further, i.e., D = U = u(S]s $2) . At steady state conditions, if there is no cell mass entering with the feed stream, the dilution rate equals the specific growth rate Of the bacteria. Thus, stirred tank reactors provide a very con- venient way of measuring the specific growth rate of the microbes. The value of u is given by S __._1___ 2 + S __ (4.24) 1 Ks2 * S2 Solving Equations (4.23) and (4.24) simultaneously, one (Dbtains the substrate concentrations and the cell mass as follows: r—-——- l S ='B:t 82'4O-Y 1 20 ’ S2 ‘ S2 ' X/Yz 1 where ,._D_ 1.2-_Y_2 11 Y.I Y] Y Y Y D 2 2 2 B = -—- K + S . - -—-S . + ——-K - S . + ——-S . , and um ( S1 11 Y. 21 Y] 52) 11 Y] 21 Y D 2 y:—K (K +S.-_So). “m 82 S1 11 Y1 11 The parameters to be estimated for the above kinetic model are K1net1c parameters: um, K31, K52, and Stoichiometric parameters: Y1, Y2. This can be accomplished by carrying out two different sets of experiments in continuous stirred tank reactors. In one set, the Operating conditions can be maintained such that one of the substrates is present in excess and is not growth limiting. If S2 is present in excess, Equation (4.24) reduces to 51 m KS] + S1 ’ D = H (4.26) 88 Starting with the same initial cOncentrations of S1 and 52, one can operate a stirred tank reactor at different residence times, and determine the concentrations Of the two substrates in the effluent. Thus, a functional relationship between D and S1 is Obtained in terms of a series Of values of D and S]. Similarly, a second set Of experiments can be carried out to Obtain a rela- tionship between D and 52 under the conditions Of excess 5,. Analysis Of these data can be carried out in two ways. The data can be plotted either on a Monod plot or a Lineweaver- Burk plot. In the Monod plot, dilution rate is plotted against the effluent substrate concentration. The shape Of the curve would be Of the same nature as in Figure 4.1a. From this figure, an approximate value of pm is Obtained as the maximum value of u approached asymptotically at very high substrate concentrations. The value Of KS1 is then Obtained as the substrate concentration at which the growth rate equals pm/Z. The Monod plot is very easy to visualize and use, but it is very difficult tO Obtain an accurate estimate Of the parameter values from it. If the experi- ments have not been carried out at a quite high substrate concen- tration, it is very difficult to establish accurately the values of “m and K5]. Another way Of plotting the data is to transform them in such a way that when plotted they fall on a straight line. This is very easily done by transforming Equation (4.26) to KS 1 1 1 1 —=—-+———. (4.27) D 1"m 11m S1 89 A plot of 1/0 against 1/S.l results in a straight line with slope equal to KSl/um and intercept equal to l/um. From these two values, a much better estimate Of the parameters can be Obtained. Both these methods will be used in interpreting the data obtained in this work. Knowledge Of the values of all the kinetic parameters would enable us to predict the effluent concentrations at any Operating conditions and this feature would be very helpful in designing modified activated sludge plants to remove nitrogen. The above model has been tested by growing denitrifiers in a continuous culture on a suitable medium. The required parameters were determined by carrying out sets Of experiments under either carbon limiting conditions or nitrate nitrogen limit- ing conditions at various dilution rates. Materials and Operating Procedures Apparatus.--For the continuous feed experiments, a unit is required that will provide a completely mixed system and a com- pletely air-free system. The experimental unit consisted Of a feed unit, a gas purging unit, a reactor and an effluent collection system. A diagram Of the experimental apparatus is shown in Figure 4.4. Two different chemostats of two liters each were used for this study. The feed system consisted of a cassette tubing pump. The pumping action Of the pump was peristaltic in nature. A certain “Feed rate was required to maintain a desired residence time. The 90 .co_uommm co_umowmweuwcmo mo zuaum on» com asumm —mo:mewcmaxmtt.q.v mczmwm i e 111. c N _ _ Wm asaatm “so e.=_a Y mhmu ou New > ozaeH e_=_a.iin»wi F ee_h m:__ea=m camoeo_z memm> mmmcoum acm=memto couommm xcme umcc_am maoac_ucou u_aoemmcc=u cowumcawpmu pmuwnah e=u cowpmenwpmo —monge <--.m.¢ wcamwu ”\me .cowumepcwocou mmouzpo ow oN om om ow om ON o_ o N n a _ . . N N N._. _L e ‘— 601 L \O F (aoueithsueal) cumcwpm>mz oem we econ cowomcnwpmu 99 dichromate reflux method was not used because of the quite lengthy and time consuming procedure. A carbon analyzer was due to arrive when this work was near completion. It would have been a very convenient instrument to determine the carbon concentration. A "Rapid COD" test was carried out whenever steady state conditions were throught to have been achieved. Dissolved oxygen.--Dissolved Oxygen concentrations of the samples were frequently determined to check for the anaerobic conditions in the reactor. A Yellowsprings Instrument CO., Ltd., polarographic probe was used to measure the dissolved oxygen con- centration. pfi,--The pH in the reactor was monitored quite frequently. It was maintained near the neutral range. A double junction elec- trOde Of Orion Research was used tO measure the pH of the reactor solution. Experimental Results and Discussion Two different sets Of experiments were performed under conditions when (a) the glucose concentration is in excess and only nitrate nitrogen is the limiting substrate, and (b) the nitrate nitrogen is in excess and the glucose concentration is limiting. Runs were made at different residence times and the efflu- ent substrate concentration S1 was determined at steady state conditions. Equation (4.26) was plotted appropriately in terms of 100 D and S1 to Obtain the parameters “m and K5]. Next, a set Of experiments was carried out at conditions in which S1 was in excess and S2 was limiting. From these Observations, “m and K52 were to be estimated. Y1 and Y2 were to be determined from the relationships between the amounts of solids produced and the amounts of substrates utilized. The two liter laboratory scale denitrification reactors were Operated for about 12 months. When steady state conditions were thought to exist, the samples were analyzed in detail. The reactors at steady state were Operated for 2 to 3 days and the average values Of the data at steady state are reported in Appendix 0. Excess Concentrations The most important aspect is the choosing Of proper initial concentrations for the nitrate nitrogen and glucose substrates. The glucose concentration should be such that not only should it be in excess at the start of the experiments but also at the steady state conditions. This has been very vividly illustrated by Bader et al. (1975). It is possible to supply glucose concentra- tion in such a way that it would be in excess at the beginning but towards the end Of the reaction it also could become rate limiting. In Figures 4.7a and 4.7b are plotted contour lines Of constant u on 51-52 axes. As S1 and S2 increase, u also increases. Drawing Figure 4.7 presupposes the knowledge Of the nature Of u as a function of S1 and S2. The shape of the contour lines in Figure Substrate S2 Substrate S2 101 Region a A<--.N.a N4mc:u.11111 = _.I a uneven Fmpcoemgmaxm nu - N we .m P. mmmuxm m Nm z-mcz m _m . m OW 108 S. .mmmo mcwpwewg cmmocuwz coo NoNA xeamtcm>mwzmcmgtt.m.e mczawu 5. mo. mo. no. mo. mo. #0. mo. No. 8. to o N N 1 4 N )N N 1 N J. \11. \\- 1\\\ G \\ al.. no ._.Na 3 w. .w. :8 NGN A r. m I. EJ\—.¥ H MP H OQOFW W. E ‘ . n 1 D. N e . N .m- s: 2.0 h 1P1 n 38.3ch L N m 109 If a smooth curve is made to pass through the experimental points, an S-shaped curve results. This type Of curve is not pre- dicted by a Monod growth model. To account for these deviations at low dilution rates, a different model was considered, 0 = pm —§—————§-. (4.28) Physically, this model predicts a somewhat smaller growth rate up to a certain threshold concentration Of the limiting substrate due to the squared dependence of the growth rate on the limiting sub- strate concentration at low values Of S]. This helps in accounting for the deviations of the experimental data at low growth rates. Beyond this substrate concentration, the model behaves in a manner similar to the Monod model. with “m = 3.7 day-1 and KS1 = 30 mg/l, a smooth curve may be drawn that passes through most of the experi- mental points. A Lineweaver-Burk plot Of this model does smooth out most of the variations encountered in Figure 4.9 (Figure 4.10). This indicates that this model is capable Of fitting the experi- mental data. However, an expression Of the type of Equation (4.28) could not be justified on a sound theoretical basis as in the case Of Equation (4.26). Based on this discussion, the possibility of a different kinetic model controlling the reaction was discounted. For some reason, the nitrate nitrogen was not reduced to the fullest extent at very high residence times. Earlier, the pos- sibility Of selecting a different species at different dilution 110 1/0 I Intercept = = 0.28 um 1 2 SlOpe = -——-= 227 um _ -1 pm - 3.57 day KS = 28.5 mg/l l 0 1 l l 1 4 4 20 4O 60 80 100 120 175$ x 10‘4 Figure 4.lO.--Lineweaver-Burk Plot for the Second Order Model for Nitrate Nitrogen Limiting Case. 111 rates was considered for a continuous stirred tank reactor contain- ing.heterogeneous population. This incomplete reduction occurs at very high residence times which would be expected to give ample time for the growth Of many organism species. It was felt very strongly that some other species could have been growing along with the denitrifiers at these high residence times. The complex interactions between the various species could have been the cause of this incomplete reduction Of the nitrate. Another source Of error could have been due to the problem associated with main- taining low flow rates. Since Equation (4.26) is theoretically sound, it was concluded that the experimental errors were the prime reasons for the discrepancies in the data. Because of the incomplete reduction Of nitrate nitrogen, the points representing the experiments N-5 and N-7 do not lie on the straight line. A straight line was made to pass through the first four points giving “m = 6.7 day-1 and KS] = 88 mg/l. The same four points were curve fitted to a Monod curve and the required parameters were estimated to be “m = 6.8 day"1 and Ks1 = 83 mg/l. These two sets Of values are quite close to one another. From Equation (4.23), one Obtains, X T Y1 (Sli ' $1) ‘ Y2 (SZi ' 52) ° When the microbial cell mass is plotted against the substrate used, the slopes Of the lines would give the yield factors. The lines are plotted in Figure 4.11. From the graph, Y1 = 0.6363 and Y2 = 0.1875. 112 .umNNpNu: mpmcumaam umcwmm¢ cavemepcoocou Nmmnocowz No No_¢11.__.e mcammm N\me ._m - ANN oo_ om om 0N om om o4 om ON o_ o N _ A M _ d N 1 11 3:. w t/fiw ‘x mNNP.o n N> ”ANN - eNmVN> n x Neme.o n _> ”New - e_mv_> n x .ON_ o 3838 n ® z-moz n 0 ® 0 owe com aye com OON co, co. _\me .Nm - NNm 113 The point representing experiment N-7 is way up the nitrate nitro- gen line indicating a very high yield factor, but the same experi- ment gives very reasonable approximation for the glucose line. This indicates that the microbes produced do utilize glucose as an energy source but do not reduce the nitrate. Therefore, there is a strong possibility Of two different populations being present together for the experiment N-7 and some new species invading the reactor contents at high residence times. Glucose Carbon Limiting System Table 4.3 contains the average steady state data obtained from the chemostats. The raw data are given in Appendix D. The nitrate nitrogen concentration chosen for this set of experiments was 250 ppm. The glucose carbon concentration was 100 ppm. For complete glucose oxidation, 50 ppm of nitrate nitrogen may be used. That would still leave about 200 ppm of nitrate nitrogen in the solution and the factor §55299—§5-= 0.7 is fairly close to 1. This will ensure an excess of nitrate nitrogen in the reactor solution. A quick look at the table shows that for residence times greater than 1 day, complete glucose removal takes place. The variations in the influent concentration are due to changing of the feed solution every two days. These data are subjected to the same analysis as the data in Table 4.2. The Monod plot for the system is shown in Figure 4.12. Because Of the absence Of glucose in the effluent in experiments 114 o.m _.o m.o¢ N.mmp ti 0mm cop mpmm.N mtu m.~ N.o o.mm m.mm_ t- omN oo_ mwam.N mtu m.m N.o N.N¢ “.m0N a- omN oo_ cONm._ mtu a.“ m.o m.mm ¢.w0N t- omN oc~ mmNN._ ctu m.m «.0 N.Nm m.m_N m omN CON NNNm.o mtu N.m N.o m.NN m.w_N NN omN ooN Nomv.o Ntu N.N m.o m.“ m.mmN NN omN oo~ NNNN.o Ntu _\mE N\ms z- moz utmmoozpu :1 moz utmmooa—u mxmo :a cmmxxo mcwpom mcwompzo mewsoocN wENH Newmm%muxm um>pommwo nmucmgmam mocmcwmmm N\ms .cowumcpcmucoo .Empmxm acwewswo concmu com mung mpmum Nummpm mmmcm>c=o NmUNchomch mucwoa Nmucmswcqum ~\me a.N_ N _- as a N N W+ WV— E: m N - N _ 116 C-4 through C-7, these four points lie on the Y-axis. A smooth curve can be passed through the remaining three points as shown in the figure. The Lineweaver-Burk plot for the same data is shown in Figure 4.13. Only three points are available. The straight line through these points gives um = 4.0 day‘] and K52 = 17.4 mg/l. Using these parameters, a curve may be drawn on the Monod plot. The three experimental points on the Monod plot lie near the the- oretical curve indicating that both these plots give consistent results. To determine the yield coefficient for the two substrates, the cell mass Obtained is plotted against the respective substrates utilized. The results are shown in Figure 4.14. The values Of Y] and Y2 Obtained from the slopes Of the lines are 0.857 and 0.375, respectively. Parameter Values Table 4.4 summarizes the values of the various parameters evaluated in this work. pm.--The values of “m Obtained from the Lineweaver-Burk plots are more representative than those obtained from the Monod plots. In the carbon limiting system, it was assumed that the S 1 . . . 200 factor K§——;-§—-equaled unity, but it was approx1mately 200-3—80’ 1 l = 0.7. From the value Of “m calculated, correction can be applied to it as follows: 117 .mme mcwuwswg coacmu com uopa xcamtcm>mmzmcwott.m—.e mczmmu Nm> o.N m.P o._ m. o Nm NNNE e.N_ n x 2: mm. n 2...... n 865 x >. . E \\Q\ N- mo 0 e n a E . 1.1m t pamocmpcu mm o 1 _. i O .. m6 .\\\\\- \\ .\\.\ . \\\ \\\\\\ nu . \t\\ - o N OTL =1: Rep ‘amtl aouaptsau 118 cop .OONNNNOO OOOLOAOOO OmeNan OONOOLOOOOOOO NONOOLONZ--.ON.O OLOONN OO ON ON OO Om ON ON ON ON NI NI 1 N 111... . N N n O O. 0 .ON -ON ONN.O n N» NOO.O n N» .Om ANN - _NOON> n x o 3335 t O m z-mOz - a t . OO t/fiw ‘x 119 umms mmm.o mNmF.o apogpmgam N> ms\ . . cwuavoga F “mm o memo o Ppwu > as owgumsowcumoum po_a mmmz Ppmu sogw umcwmpno ¢.~_ m_ -- -- P\ma mmx -- -- mm mm _\ms _m¥ N.m ~.m No.m m.m _-»mu s: u_um=w¥ papa xgam “op; xgzm ugm>mm3mcw4 papa uocoz -Lm>mm3mcw4 pop; coco: .onE»m mg» mcwuwsw4 uummouspu unwaFEPA :mmoguwz Lmuwsmgmm H Empmxm Eogm umcwmpoo .JLOZ mecngwam EOLL. fimcwmuno mwapm> LmHSMLmn—II.¢.¢ unas— 120 apparent “m u$ = pm (0.7) = 4.0, 5.7 day-1. i.e., pm This value is smaller than the one obtained from the Lineweaver- Burk plot for the nitrogen limiting system. The value of “m chosen 1 is 6.8 day' because of the greater accuracy of the nitrogen limiting experiments. K5].--Two different values, 83 mg/l and 88 mg/l are obtained from the Monod and Lineweaver-Burk plots, respectively. The value of 83 mg/l will be chosen as the more representative one. K52.--The two values obtained from the two plots are quite close to one another. The value of 17.4 mg/l will be chosen for K52. Y].--The values of Y1 obtained from the nitrogen limiting system and the carbon limiting system are 0.6363 and 0.857, respectively. Since the analysis of the limiting substrate is more accurate than that of the excess substrate, more weight will be assigned to the first value. The value of Y1 chosen is, therefore, 0.7. Y2.--Similarly, the value obtained from the carbon limiting system is considered more accurate and the value of Y2 is chosen as 0.333. 121 The results of the experiments can be summarized as follows: u = 6.8 day", m KS = 83.0 mg/l, 1 KS = l7.4 mg/l, 2 Y1 = 0.7, and Y2 = 0.333. Comparison of Parameter Values With Those ObtainediFrom Past Work Hadjipetrou (1965) determined yield coefficient for an anaerobic system with nitrates and glucose as the source of carbon. His yield was 0.65 mg cells/gm organic carbon, twice as high as the value obtained in this work. This could be due to the fact that he was working with a pure culture of Aerobacter Aerogenes, whereas a heterogeneous population was used in this work. Stensel's work with the denitrification in a chemostat gave him a value of Y2 = 0.l8 mg cell/mg COD = 0.48 mg cell/mg organic carbon. Chang and Morris (1962), from the studies of the utiliza- tion of nitrate by Micrococcus Denitrificans in an anaerobic system, 1, a value close to 6.8 found the maximum growth rate of 6.3 day- day"1 obtained in this work. This also compared well with the values 3-6 day"1 reported by Stensel (1971). 122 Stensel also reported the values of K52 in the range of 40-75 mg/l of COD, i.e., l5-28 mg/l of organic carbon. This compares well with the value of 17.4 mg/l estimated in this work. All of the work cited above has assumed carbon as the only limit- ing substrate. Moore and Schroeder (l97l) worked with a nitrogen limiting 1, the same as the kinetic model and found the value of “m 3-7 day- one obtained from carbon limiting systems, but their value of K51 was 0.8 mg/l, much lower than 83 mg/l estimated in this work. The best way to validate the double substrate model would be to carry out the reaction when both the substrates are limiting and see how well the experimental outcome and the prediction based on the model would match. This approach presents a problem in the case of a chemostat. The main difficulty arises in choosing the operating conditions such that the concentrations of the sub- strates in the reactor are limiting. An alternative would be to carry out the reaction batchwise and keep track of the substrates' concentrations and the cell mass as a function of time. Model equations can be written for the three variables, S], 52, and X, and they can be integrated to give the three profiles as functions of time. Comparison between the experi- mental and the predicted profiles would give some measure of the validity of the model. Stensel (l97l) carried out a number of batch experiments. His results have been compared with the predicted profiles. The following three differential equations completely defineaabatch system: S :13. = - pm $1 32 X l t 7]— KS + 51 KS + $2 1 2 5 E3 = - 3'3 5‘ 52 x and 2 t Y2 KS + S] KS + 52 l 2 t “m KS + 51 KS + 52 ° 1 2 Stensel used COD as a measure of carbon; therefore, the values of Y2 and K52 obtained in this work have been changed from the basis of organic carbon to COD. The results for the various data are shown in Figures 4.15 through 4.19. Although the data set 8-3 does not fit the model equations well at all, the fit with the data sets B-S, 8-6, 8-2, and 8-7 is remarkable, considering the heterogeneous populations involved, degree of accuracy of the analytical tech- niques, and completely independent sets of experiments. The usefulness of the double substrate model has been illus- trated in the form of example problems for a continuous stirred tank system (Shah et a1. 1975). Activated sludge processes are car- ried out generally in chemostats. This model enables one to determine the effluent concentration of both the substrates at any given Opera- ting conditions. The effect of substrate concentrations on the rate of reaction is accounted for, regardless of whether the substrate is in excess or in limiting supplies. The application of this equation to the design of a land disposal system will be discussed in the next chapter. 124 ----- Predicted 100 \ Experimental \ -1 "m = 6.8 day 30 \\ KS] = 80 mg/l Q \ E _ 45/ v1 = 0.7 560 \ ‘6, +’ 0 g \\ o 8-3 C 3 4O 8 U 20 O 10 20 3O 4O 50 , Time . hours Figure 4.15.--Prediction of Stensel's Batch Data 8-3 Using Parameters Obtained from This Work. Concentration, mg/l 125 30 SuSpended Solids 10 ----- Predicted Experimental B-5 (0 O I l l l O 5 10 15 20 25 Time, hours Figure 4.16.--Prediction of Stensel's Batch Data 8-5 Using Parame- ters Obtained from This Work. 126 30 ----- Predicted Experimental B-6 Concentration, mg/l 0 .....-.........__..... l...,.- ..-. -- I. .... ...-. ......,-L...m. _- _I -.._--.___ .7 ...._1...._...- .-.___... O 5 10 15 20 25 30 » Time, Hours Figure 4.17.--Prediction of Stensel's Batch Data B-6 Using Parameters Obtained from This Work. Concentration, mg/l 127 4o Suspended 5.91151: _ 30 - / ,.. I ’ fl ; / / 20 ----- Predicted Experimental B-2 Time, hours Figure 4.18.--Prediction of Stensel's Batch Data B-2 Using Parame- ters Obtained from This Work. 30 ., 10 30 N O ._I 0 Concentration, mg/l 128 ds __ __ __ __ —-— ----- Predicted Experimental B-7 L 5 10 15 Time, hours 25 Figure 4.19.--Prediction of Stensel's Batch Data B—7 Using Parame- ters Obtained from This Work. CHAPTER V MODELING OF NITROGEN MOVEMENT IN SOILS Wastewater contains nitrogen mainly in the form of ammonium nitrogen and nitrate nitrogen. Proteins, amino acids and urea also occur in abundance but ammonia is readily derived from them. If the wastewater is subjected to primary treatment, most of the nitrogen from proteins, amino acids and urea is converted to the ammonium nitrogen form. If the wastewater effluent is from an activated sludge plant, some ammonium nitrogen could also be con- verted to nitrate nitrogen. The nitrogen in the wastewater, when applied to the land disposal system, gets converted from ammonium nitrogen to atmo— spheric nitrogen via the nitrification and denitrification reactions. An efficient spray irrigation site would maximize the removal of nitrOQen with minimum leakage into the groundwater system. In order to properly design and manage a wastewater land treatment facility, quantitative understanding of the movements of various nitrogen species involved in the nitrogen transformations is required. This chapter presents an attempt to develop a mathematical model to describe the nitrogen movement in the soil. 129 130 Literature Survey and Physical Situation _ Modeling efforts of the past can be divided into two classes: (1) empirical and (2) mechanistic. Duffy and Franklin (1972) took the first approach and develOped a rate expression for nitrification by curve-fitting the data. This rate expression can predict the effect of various factors such as pH, dissolved oxygen concentration, ammonium concentration, etc., on the rate of nitri- fication but has no theoretical basis. Beek and Frissel (1971), using a semi-empirical approach, developed a very detailed model to describe the behavior of nitrogen in the soil. They considered decomposition of organic material, mineralization, nitrification and the physical processes of the movement of water, heat, and salt but considered no denitrification in the system. Several attempts have been made to develop mathematical models to describe the concentration profiles of ammonium and nitrate nitrogen on a theoretical basis. McLaren (1969, 1970) developed a mathematical model to describe the steady state and unsteady state concentration profiles of ammonium,nitrite, and nitrate nitrogen in the absence of ionic dispersion and ion-exchange reaction involving the adsorption of ammonium by the soil. He assumed first order reaction kinetics for both the nitrification and denitrification reactions. Cho (1971) also assumed first order kinetics for these reactions, but he accounted for dispersion and ammonium disappearance due to ion exchange. He derived a set of second order linear partial differential equations and solved them analytically to obtain the steady state and unsteady state I31 concentration profiles of ammonium, nitrite and nitrate. Since nitrification and denitrification require quite Opposite environ- mental conditions, mainly oxygen rich versus oxygen deficient, it is hard to visualize that both the reactions can be carried out in the same equipment. Starr (1973) showed experimentally that using a soil column, it is possible to carry out both the nitri- fication and denitrification reactions simultaneously. He measured concentration profiles of the liquid phase and the gas phase species. The physical situation in a soil column is quite complex. In an unsaturated flow through the soil, three phases exist: (1) gas, (2) liquid, and (3) solid (see Figure 5.1). The solid phase consists of particles and aggregates of these particles. The voids within the aggregates are called micropores and those between the particles and/or the aggregates are called macr0pores. Even if the soil is oxygen rich, it is quite possible to have anaerobic spots or regions, as in micropores, in the soil column. Microbes are attached to these soil particles and aggregates. As the wastewater moves down, the ammonium concentration and the dis- solved oxygen concentration decrease due to the nitrification reaction. If the gas phase and the liquid phase are in equilibrium, some oxygen is transferred from the gas phase to the liquid phase, and thus, oxygen concentration in the gas phase decreases. In the lower part of the soil column where oxygen concentration is suffi- ciently low, denitrification begins to dominate. Even in the upper part of the column, some denitrification does take place in the 132 .ngmcowpapmccmocm manna mmu-uw=a_d-u__om--._.m weaned ”_.,~ r—-> um R2 - K202, K2 - 0 1f X3-— .05. With this assumption, the calculating procedure becomes more complex, since the region from which denitrification begins is not known. All the three sets of equations will have to be solved simultaneously with iterations on the oxygen profile. §g§g_4,--Instead of first order reaction kinetics, a Michaelis-Menten rate expression is used to describe the nitrifi- cation and denitrification reactions, with the added restriction that denitrification would not proceed if the oxygen concentration is above 5 or 10 percent. This is the most cumbersome case of the four cases con- sidered. The calculating procedure involves outer loop iterations with respect to the oxygen profile. Within each of these itera- tions, there are smaller iterations involved for determining the ammonium nitrogen and nitrate nitrogen profiles. Method of Solution The method of solution is quite simple for Case lA (com— pletely analytical) and becomes progressively more complex for 143 Cases 2, 3, and 4. Analytical solution for the other cases was not possible and hence a numerical solution was sought. Equations (5.1) along with the boundary conditions (A) represent a boundary value problem with second order linear or nonlinear differential equation as the case may be. The numerical approach chosen was to solve the second order differential equation in an implicit way. The differential equation is written in the form of a finite difference equation for each grid point resulting in a set of simultaneous equations. These simultaneous equations were solved by using the scientific subroutine ONEDIAG. Equations (5.2) and (5.3) were integrated using Milne's integration technique. To obtain the numerical solution to all the cases, a general FORTRAN program GASTRAN aided by the subroutine ONEDIAG was written. The program was written so that all the input variables are read from data cards. Depending on the value of the option parameters, it would execute any of the above mentioned cases. A complex listing of the finite difference formulae used to approximate the various derivatives and a complete listing of the FORTRAN program and the subprograms can be found in Appendix E. The following is a brief outline of the calculation procedure used in each of the cases. 1. Input the operating conditions and proper values of the option parameters. 2. Divide the soil column length into grid points spaced at every 2 cm. Using smaller sized grid points gave essentially no improvement in the solutions. 144 Case 1A Solve Equations (5.1), (5.2), and (5.3) analytically to obtain the liquid phase and the gas phase concen- trations. a. a. e. a. Case 18 Solve Equations (5.1) and (5.2) analytically to obtain the liquid phase concentrations and the fluxes of the gas components. Solve Equations (5.9) numerically (because of the nonlinear nature of the equations) by Milne's inte- gration method to obtain the gas phase composition. Case 2 Since the reaction rate terms assumed in this case are of Michaelis-Menten type, the resulting Equa- tions (5.1) are nonlinear. To linearize these, assume the profile in question, ammonium nitrogen or nitrate nitrogen. Convert the differential equations into finite dif- ference equations written for each point in the grid and form a diagonal matrix. Solve the simultaneous linear equations to get the computed profile. If the computed and the assumed profiles do not match, assume a new profile and start all over again. Numerically integrate Equations (5.2) to obtain fluxes of the gas components. Solve Equations (5.9) for the gas phase composition. Case 3 Assume an oxygen rofile in the soil. This defines the regions of (11 nitrification alone, and (2) nitrification and denitrification. Solve Equations (5.1) analytically. The differential equation for nitrate nitrogen is split into two equations applicable in the two regions, i.e., 2 d C dC 2 2 K C “T'VETZ‘J' 11 D 2dz - K2C2 = O, with 145 K2 = 0 up to Z = 20 (X3.Z .05). c. Calculate the fluxes from Equations (5.2) by solv- ing them analytically. d. Obtain the concentration profiles from Equations (5.9) by numerical integration. e. Compare the calculated and the assumed oxygen pro- files and if they do not compare well, assume a different oxygen profile and go back to step (b). Case 4 a. Assume an oxygen profile to start with. This would define the regions of (1) no denitrification, and of (2) denitrification, depending on where the cut- off point of 5 percent or 10 percent oxygen concen- tration falls. b. Determine the ammonium nitrogen concentration profile using a trial and error procedure as outlined in Case 2. c. Determine the nitrate nitrogen concentration profile using the iterative technique, taking care to use the right type of equation for each of the two regions. d. Calculate the fluxes of the gas phase components from Equations (5.2) by numerical integration. e. Using these fluxes, the concentration profiles of the gas components are calculated from Equations (5.9). The oxygen profile assumed in step (1) is compared with the oxygen profile calculated. If they do not match within given accuracy, assume a new profile and go back to step (3). Five times as many calcu- lations are required in this case as in Case 3. The program was executed on a Control Data Corporation 6500 digital computer and required only a few seconds of central processor time. 146 Results and Discussion The concentration profiles obtained from the computations in the four cases outlined above are to be compared with the experi- mental results of Starr. The physical parameters chosen are such as to duplicate the physical situation of Starr's column. The kinetic parameters used in the simulation were obtained from other independent sources. The constants for the denitrification reac- tion were taken from this work. The kinetic constants for the nitrification reaction were computed from various sources as shown in Chapter IV. The first order rate constants were taken from Starr's work, so it would come as no surprise if the first order rate model fits Starr's data quite well. The simulation results of the different models will demonstrate the effect of different assumptions. The values used in the simulation study are tabulated below. First Order Reaction Constants: 1 K = 0.3 day-1, and K2 = 0.08 day' . 1 These values were obtained from Starr's data. These constants were not available from other sources and could not be computed from other kinetic constants. Michaelis-Menten Constants: K1 2 umoles/cmB/day, KS1 = l umole/cm3, K2 1 umole/cm3/day, and K52 = 6 pmoles/cm3. 147 The values of K1 and K51 were obtained by reinterpretation of Starr's results. From Figure 4.1, the maximum rate of nitrification varies between 16-30 ug/cm3/day. This translates into 1-2 umoles/ cm3/day. From the same figure, K51 =‘15 mg/l = l pmole/cm3. The value of K52 was taken to be 6 umoles/cm3 based on the present work. The values of K1 and K2 can also be estimated from Equation (4.12), if the maximum specific growth rate, the yield coefficient and the microbial concentration are known. Starr, in his experiments, did not measure the microbial cell mass as a function of soil depth. Hence, accurate estimates of the constants K1 and K2 were not avail- able. Estimates of diffusivities of various components in the liquid and gas phases were obtained on the basis of some experiments carried out by Starr. The same values can be obtained by using theoretical equations. Physical Constants: E 0.4, X = 0.85, L = 100 cm, 1 D2 = 3 cmZ/day, D II 250 cmz/day, D4 = D5 = 150 cm2/day, and U 0) ll 6 cm/day. These constants were obtained on the basis of the physical condi- tion existing in the soil column operated by Starr. 148 Surface Concentrations: C10 — 3.57 umoles/cm3 0.00 C20 C30 - 9.33 umoles/cm3 c 35.155 umoles/cm3 40 50 c 0.013355 umoles/cm3. Surface concentrations of the various gases were taken based on their atmospheric concentrations. Experimental data were available for ammonium nitrogen, nitrate nitrOQen, oxygen, nitrogen and carbon dioxide concentrations. The simulated results are shwon with the related experimental data in Figures 5.2 through 5.5. It is significant to note that the models differ very little in the form of the response. The profiles differ very little in the shape. The deviations could probably be removed by minor adjustments in the parameters. Scientifically, it would seem that the mroe detailed a mathematical model is, the more precise its results will be. Con- sequently, one would surmise that a model which neglects as many mechanisms as number 1 does, would be the least acceptable. In contrast, an engineer would like the simplest model consistent with the accuracy and reproducibility of the data. V The experimental measurements of ammonium and nitrate nitro- gen are well predicted by the simplest model (refer to Figure 5.2) which considers the first order kinetic models. The simulation and experimental results will match because the kinetic parameters were 149 CNH4- mlcromoleslcm3——.— 0 1.0 2.0 3.0 3. 714' case 1A, 18, 3 experimental .‘—————- Z, cm case IA expenmental 100' . T Figure 5.2.--Concentration Profiles of Ammonium Nitrogen and Nitrate Nitrogen in Liquid Phase. 150 02 concentration _____,.. 0 5% 101- 157. 20% I 10 ’ case 1A case 4, 2 experimental T 40 l 50 2, cm 100 Figure 5.3.--Concentration Profiles of Oxygen in Gas Phase. 151 N2 concentration ——-> 0 79 80'7- 85$ 901- .\ 10 I- o o 40- — case 1A «———— 2, cm 8 70 experimental 1(1) Fl gure 5.4.--Concentration Profiles of Nitrogen in Gas Phase. 152 10 20 30 Z, Depth, cm 0" J:- O O 01 D 70 T ‘d_f,,fl. ’v‘" —/ A I Case 1A '— ‘1‘) 13 1 '= 1- ‘: ...m 3° .2 1 r; '5'- ‘21": D- m' L) ifi {3);‘ 90— \ mo - . . . . 1.1 - l. 1 2 3 4 5 6 7 8 9 CO2 % in Air Figure 5.5.--Concentration Profiles of Carbon Dioxide in Gas Phase. 153 obtained by Starr from the analysis of his liquid phase profiles. Thus, validity of the models can be established only by comparing the gas phase profiles and not by comparing the ammonium and nitrate nitrogen profiles. The liquid phase profiles have also been pre- dicted reasonably well by the other models. The various assumptions made in the different models do not affect the ammonium nitrogen profile and hence there are only two curves for it, i.e., for the first order kinetic model and the Michaelis-Menten model. All the nitrate nitrogen profiles peak at the same point but the maximum value in Case 4 is greater than that for Case 2. This is under- standable as Case 4 makes the assumption of no denitrification for soil layers having oxygen concentrations greater than 5 percent. The gas phase profiles of oxygen, nitrogen and carbon dioxide have been plotted in Figures 5.3, 5.4, and 5.5, respectively. All the models predict a much greater oxygen consumption rate than is shown by the experimental data. This could be remedied by using a double substrate kinetic model containing dissolved oxygen as one of the substrates. The rate of nitrification will then decrease with decreasing oxygen concentration. Such a decrease in the oxygen consumption rate would tend to improve the oxygen profile prediction. Significant error appears for all the models in reproducing the nitrogen and carbon dioxide experimental results. The carbon dioxide profiles have the same general form and may simply reflect inaccuracies in data. This does not appear to be the case with nitrogen. The experimental data are in the form of a smooth, monotonically increasing function, while each of the models generates 154 a function which peaks. The peak can be justified since the oxygen profile dr0ps rapidly at the surface whereas the carbon dioxide is not generated until deeper in the soil. Near the surface, nitrogen increases rapidly, whereas in the deeper regions, carbon dioxide increases rapidly. This would make the nitrogen concentration go down a little from the maximum value. It is thus tempting to suggest that better data are needed. However, the quality of the set of data more realistically indicates that we are missing some mechanism. One would h0pe, however, that a significant lowering of the carbon dioxide concentration profile would essentially eliminate the nitrogen deviation. This is numerically true, and hopefully a basic rationale for it can be found. Changing the N2/C02 ratio predicted by Equation (4.4) from 2/1 to 4/1 improved the response form. In calculating the profiles, Stefan-Maxwell equations were generally used to calculate the gas phase compositions. This bypassed the necessity of computing the diffusivity of each Species at every point in the column. Just for curiosity, the same problem was solved by using Equations (5.3) and (5.8) and diffusivity values were printed for each point in the soil column. The diffusivity values of oxygen and carbon dioxide were consistent but in a small region near the nitrogen peak, a region existed where the nitrogen diffusivity was negative. This implied that nitrogen moved in the opposite direction of the concentration gradient. This is a strange phenomenon and can be explained as follows. 155 At every point in the system, X3 + X4 + X5 = l , 01‘ dX dX dX 3 4 5 _ ar+az—*az—'°° From Bird et a1. (1960), a similar equation holds for the diffusive fluxes of all components, i.e., J3 + J4 + J5 = 0 (5.12) where dC. 1. -01.m 371. (5.13) (La ll At the point where nitrogen passes through the maximum, the gradient is zero, i.e., dX4 a-Z—‘=0. If by some way, J4, calculated from the formula J4 = N4 - X4(N3 + N4 + N5) , does not become zero at the same point but becomes zero at a dif- ferent point, then in the region between these two points the signs of J4 and dX4/dZ are the same. For this case, Equation (5.13) indicates a negative diffusivity. This is clearly illustrated by Figures 5.6 and 5.7. Such a phenomenon can only occur in a multicomponent counter-current diffusion system. 156 dXi/dZ x 105 O 400 800 1200 Or*"*‘“’“‘T-‘*”“”"‘ —~—~r— w~~~ ~ ~, 1 Carbon Diox1de f’,///”"" , ,4””’ ./f‘ fi:09§§.=-dx3 / d ’ d2 37' 20" f //7— Area of Negative Diffusivity _‘———-———-'. l— -f —- —- ‘ W 1’ 1’ 30- f / E i / Results from Case 18 U 401’ l 1 1 1 . 501- f g i I 1 i 601- ' 70 L.» --m.-:_1;m-_.- ._. .2--_-H_ . 1 Figure 5.6.--Gradients of Various Components in Gas Phase Against Soil Depth. Z, cm 157 0,, umole/cmzlday 100 200 0 I T I -r'------ r ‘ ' (Nitrogen/ [C b - (D15x13e ve) Oxygen (‘V91 10 - 20 L / Area of Negative Diffusivity 514 = 0: .15 = ".13 30 +- 40 _ Results from Case 18 N4 = 2N5 50 - 60 - 70 Figure 5.7.--Diffusive Fluxes of Components in Gas Phase Against Depth. 158 Some of the assumptions made in the development of the above model can also be relaxed quite easily. The above model can be modified to calculate time dependent profiles. .The solu- tion of the unsteady state problem is lengthy and would be of only academic interest as there is no way to validate the unsteady state model. One of the assumptions made was that no loss of ammonium occurs due to adsorption by the soils. This, in fact, is not true and the ammonium differential equation can be modified to account for ammonium adsorption by the soil as follows: C D 2 NH+-N . §_l_= 8 C _ R1(Cl’ C3) 4 ' 8t 1 + R 322 1 1+R , (5.14) v .32- + R 02 where R represents the ratio of adsorbed ions to solution ions. In deriving Equation (5.14), equilibrium condition was assumed between the adsorbed ion concentration and the solution concentration. At steady state, 3C1/at = O, i.e., 2 0 d C1 _ v dc1 _, R1 = 0 1 + R dzz 1 + R dz 1 + R or dzc1 001 0 -——-- v -——-R = 0 . At steady state, thus, the same concentration profile is obtained whether ammonium adsorption is accounted for or not. Physically, 159 this makes sense because once the capacity of the soil is exhausted, no more adsorption is likely to take place. It was not the purpose of this work to curve fit the data. The purpose was to see how a simplistic model, developed on a the— oretical basis, would do for a very complex system. It has been demonstrated that a very simple model is quite satisfactory for simulation of nitrogen movement in the soil. This does not imply that the simplest model is an accurate reflection of the system. Conditions could conceivably be generated which would be best described by a more complex case. It is, however, a valid tool for the situation studied. Development of a detailed model would gen- erally be expected to be quite helpful in designing a land dis- posal system. Reliable field data for an operating system are needed to validate such models before they can be properly used. Beek and Frissel (1971) had the same problem. Their detailed model could not be verified because of nonavilability of field data. Such models, though, could point to the directions in which new experi- ments are to be carried out to increase the knowledge about a given system. CHAPTER VI CONCLUSIONS The primary objective of this work was to study the feasibility of using land as a waste disposal site to remove the nutrients, mainly phosphorus and nitrogen. Phosphorus is removed by adsorption to the soils and nitrogen by the reactions nitrifi- cation and denitrification. Rate expressions for these reactions were derived and mathematical models for the movement of phosphorus and nitrogen species into the soil were formulated. On the basis of the above work, the following conclusions may be made. Phosphorus Removal With respect to phosphorus removal from the wastewater, the BLWRS system was found to be very efficient. It removed nearly 95-99 percent of the incoming phosphorus. Simulation results obtained by solving the model equations were very good for the BLWRS system and they fell directly on the experimental data points. This proves that a land disposal system can be very efficient in phosphorus removal. The entire system is also amenable to mathe- matical treatment. But after operating the disposal site for a few months, the soil system has to be regenerated in the same way as a packed adsorption column needs to be regenerated. Otherwise, the phosphorus front keeps moving down and, at some point, the soil will 160 161 be completely saturated with ph05phorus. The regeneration can be done by operating the land system in cycles of applying wastewater and cropping. The crops can use the adsorbed phosphorus as a nutrient. With the help of proper management practice, it is possible to use a land disposal system for complete phosphorus removal. Nitrogen Removal To estimate the removal of nitrogen from the wastewater by the soil system, it is important to determine the rate expres- sions for the reactions nitrification and denitrification. Double substrate kinetic models were proposed for the nitrification and denitrification reactions and it was shown that such models can describe the microbial reactions at conditions when two substrates simultaneously affect the growth of microorganisms. The kinetic and stoichiometric parameters involved in such a model were esti- mated from experimental works of past and present. Nitrifiers were found to be slower growing than the activated sludge bacteria. This would require a separate nitri- fication stage, if the traditional activated sludge plants were to be modified for a greater nitrogen removal. From the values of the parameters for the denitrification reaction, it can be con- cluded that in the range of the nitrate nitrogen concentrations encountered in wastewater (20-30 ppm), the reaction is a first order reaction. For complete nitrogen removal, nearly three times as much organic carbon has to be provided. These double substrate 162 kinetic expressions would be very useful in designing the modi- fied activated sludge plants to accomplish the nitrogen removal as well as the biological oxygen demand removal. Solving the equations formulated to describe the movement of nitrogen species shows that even at the very low application rate of 2 cm/day, the exit nitrate nitrogen concen- tration is 11 ppm. This shows that the land disposal system may not be able to accomplish complete nitrogen removal. The success of the entire methodwill depend upon the development of good nitrifying and denitrifying populations. If enough denitrifiers are not available, most of the nitrate nitrogen will leak through the system unaffected and whatever removal of nitrogen occurs would be due to the physical adsorption of ammonium nitrogen by the soil. When the land disposal svstem is started, considerable leakage of nitrogen can be expected initially because of the absence of adequate numbers of microbes. Once the populations are established, nitrogen leakage will decrease. The nitrogen removal ability of the soil is thus more important in designing a land dis- posal system than its phorphorus adsorption capacity. It is important to remember that different soils exhibit different properties and thus different reaction rates for phos- phorus adsorption, nitrification and denitrification. Before any land disposal system can be designed, some preliminary experiments in the laboratory need to be carried out to determine the appro- priate rate constants. A preliminary estimate of the performance 163 of a land disposal system can be obtained by using the FORTRAN programs PMODEL and GASTRAN. It is hoped that this work may represent a step forward in understanding the nitrification and denitrification reactions and, thus, help enable one to design a land disposal site for phosphorus and nitrogen removal with a good deal of theoretical basis. NOMENCLATURE Sometimes the same symbol is used to represent more than one quantity to maintain the established nomenclature in the literature. a Solid-liquid interfacial area, cmzlcm3 A Cross-sectional area, cm2 a, b Langmuir adsorption isotherm constants b Maximum concentration of phosphorus that soil can attain, ppm C Concentration, mg/l in liquid phase, pmoles/cm3 in gas phase 0 Axial dispersion coefficient in phosphorus work, cmzl day 0 Dilution rate in Chapter IV, day"1 D Diffusivity of various species in gas phase, cmzlday F Feed rate in the reactor, l/day J giffusive flux of a component in a gas phase, umole/cmz/ ay K Hydraulic conductivity of the soil, cm/day K Constant in Equation (2.7), ratio of rate constants of adsorption and desorption Ko Overall volumetric mass transfer coefficient, cm/day KKin Rate of forward reaction (2.8) K_1 Rate of backward reaction (2.8) Kad Equilibrium rate constant for reaction (2.8) 164 ><><>dv=-1.1... (8sz + BY W) 0 O The integral can be evaluated quite easily and the final form is given by 11" 8bY2 + 011 - 111+ 01-3/2 1n Y+le5b_5 Yo+B/l6b+6 7 8ng+BYo-yJ 15W Y+B/16b+6 Yo+B/16b-6 where 2 a = (82/256b + Y/8b)1/2. A plot of the left hand side against time should result in a straight line with slope equal to Koa. A small computer program was written to accomplish this and the results are shown in Figure A.l. The points do lie on a straight line but the lines do not pass through the origin as Equation (A.6) indicates. This probably could be due to some inaccuracies in data or due to the variability of the mass transfer coefficient with the change in concentration in the liquid phase. All four lines for the four different experi- mental runs are parallel and the average slope is 3.0. The value of the mass transfer coefficient used in simulation was 2.0 day-1. 180 .comuacomu< ngognmogm Low acmwumewmou gmemcmgh mmmz mo cowumcwELmumo11.P.< mcamwd see .5224 2 _.o o cox I >, to ‘0 :2 m 11 mgopm mmmcm>< . a 11 J . O anleA leufiaaul ‘z APPENDIX B NUMERICAL METHOD AND FORTRAN PROGRAM USED FOR SIMULATING PHOSPHORUS MOVEMENT IN SOIL 181 APPENDIX B NUMERICAL METHOD AND FORTRAN PROGRAM USED FOR SIMULATING PHOSPHORUS MOVEMENT IN SOIL As established in Chapter III, the following equations define the phosphorus movement in soil. 1. The Continuity Equation for Water: 8 211%), ' ‘37 (V85) where =- 3.2.3.5.- VeS K (as 32 1) . The boundary conditions to be used are S = 0.53 at Z = O, and 35/02 = O at Z = L. When Darcy's equation is substituted in the continuity equation, the following equation results, 2 0(es) - a s as 3A gs__ OK at ' KA 3Z2 + K 32 32 + (A 32 I) 32 (3'1) where A = 30/35. 182 183 2. The Continuity Equation for Ph05phorus in the Liquid Phase: 8 BY 8 ——-S ___ ___ BeSY 32 az ‘ 32 De 3 . (V€SY) - Koa (Y - Y*) = with the boundary conditions Y 10 ppm at Z = O, and BY/BZ 0 at Z = L. The above equation, on simplification, gives as 0A I Y LiAa “‘2'+ K 32 32 + (A1):zj - Koa (v - Y*) . (8.2) The soil length of 20 cm or 40 cm was divided into N = 40 intervals of 0.5 cm or 1 cm. The finite difference equations for the first order and second order partials used are given below: f. . - f. . l _gf‘ = 1+l,jil 1-l,j+l OZ i,j+1 2A2 12...: = f1+19j+1 - 2f1 931+] + fi'I 9j+1 (B 3) 2 ’ ' 8Z ,j+1 AZ and a f1.1M ' 11.1 at i,j“1 At 184 Here, the subscript i refers to the location of a point in the 2 direction and j refers to a particular time interval. Equa- tions (E.l) and (8.2) were solved in an implicit way, hence the expansions of the derivatives were written at a future time incre- ment. Equations (B.l) and (8.2) were approximated with the help of the finite difference approximations (3.3) at each grid point in the system, resulting in a simultaneous set of equations. Due to the nonlinear nature of the partial differential equations, the values of S and X had to be estimated at the next time increment. This was accomplished with the help of Taylor's series, = is. Sj+l Sj + at j At , and 8X j + at j At . X ll >< j+l Here, the time derivative of the function was approximated as _ l l l ‘Tij ‘ (é'fj+i + E'fj ' fj-l + E'fj-2)/At ° Substituting the above equations in the Taylor's series gives the express1ons for the estimation of Sj+1 and Xj+]. . .+..+. ., S 2 25 SJ 1 5 SJ_1 0 25 53-2 and 3+1 X I .-. .+.x.+. .. 3+] 2 25 xJ 1 5 J- o 25 xJ_2 185 With these estimates, the set of simultaneous nonlinear equations can be turned into a set of simultaneous linear equa- tions. These equations were solved using the scientific subrou- tine ONEDIAG to obtain S and X at j+l time interval. Iterations were continued until the estimates matched with the computed values. The saturation value at which the hydraulic conductivity equals the application rate was found by using the subroutine CONVERG. To obtain the phosphorus profile as a function of depth and time, a FORTRAN program PMODEL was written and executed (Nl Control Data Corporation 6500. Table B.l contains the list of the subrou- tines used in PMODEL and their functions. The main program was mainly used to command the subroutines. The computing options and the data required for using the program are listed in Table 3.2. A sample output and a complete listing of the program are included in the following pages. 186 TABLE B.l.--Structure of PMODEL Program. Program Functions PMODEL SATURN HYCON DCAPP EQUIL PCONCN OUTPUT ONEDIAG+ CONVERG+ To read in data, establish initial conditions, and command other subroutines in a way so as to achieve desired results. To calculate saturation profile at the next time interval. To calculate hydraulic conductivity if satura- tion profile is given. To calculate derivative of capillary potential at a given saturation. To calculate Y* given the X-profile using an equilibrium relationship. To evaluate phosphorus concentration profile in liquid as well as in solid phase. To output the complete information at a particu- lar time interval. To solve the set of simultaneous linear equa- tions. To find the root of a given equation (two ini- tial estimates on either side of zero are needed). +5. R. Auvil, "A General Analysis of Gas Centrifugation Twith Emphasis on the Countercurrent Production Centrifuge," Ph.D. dissertation, Michigan State University, l974. 187 TABLE B.2.--Data Required by the FORTRAN Program PMODEL. Parameter Description Units YIN Input phosphorus concentration in liquid ppm phase VS Surface application rate cm/day XI Initial phosphorus concentration on soil ppm SI Initial saturation in soil -- EPS Porosity of soil -- BD Bulk density of soil gm/cm3 TC Mass transfer coefficient day“1 ACC Required limit on convergence -- This completes the first data card. Format 8Fl0.0. D Dispersion coefficient of phorphorus in cmZ/day solution AC, BC Langmuir adsorption isotherm constants -- DZ Depth increment used in numerical cm evaluation DT Time increment used in numerical solution day N Number of depth increments -- ITOTAL Total simulation time intervals -- IFREQ Output to be printed every so many time -- intervals IOPT Option parameter = 1; both P and S profiles -- are computed, = 0; assumes constant satura- tion and only phosphorus profile is computed MAX Maximum number of iterations allowed This completes the second data card. 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Mn. . no. . no. . 00. . mm. . m4. 0 05‘ . 4H0 . ma. . m0. . mm. . mm. . mo. . an. . no. . 00. . m4. . mm. . m0. . m4. . No. . N0. . he. . m0. . no lflfi'fi‘h F-‘H'BF‘ ‘6‘. A p— 4 o f. ’.| O -oacoca 44urooJ L0mtu43 “wommua meooos “momma: Jahnuma -udoaw: “024.00 uwnumww omwova 404w0ma uwmaunm unwouov -Uumrrb wmmhkmw mhhoCBL 'mcfi0m4 ”4m4040 ummhoww JhmOOMQ mmmoarw mowfiumw 00mmarw mmuwamm ”whwawo ”admuvw ”Jomuuo haGVuwc pharam0 “HH444 magma” umamwv .quer n««mav hwamum -fuma~ .cwav4HDw-r .Qa om. 00. YD Iv «cur::.n¢>kuna‘o.~ham.:U\mr4¢>ocacaalm :U\0944:m<=-d «.4ucuquv.u.4w¢N(VhJNchJvanJ~Inrwninr)nrnpantn4'J «NnJmONCU‘O '0 oz APPENDIX C PATHWAY FOR AN ENZYMATIC REACTION S1 + S2 + E + E + P LEADING TO AN EXPRESSION FOR DOUBLE SUBSTRATE KINETICS 221 APPENDIX C PATHWAY FOR AN ENZYMATIC REACTION 51 + $2 + E + E + P LEADING TO AN EXPRESSION FOR DOUBLE SUBSTRATE KINETICS Consider the following enzymatic reaction: E+Sl+52—_+P+E. Here, S1 and 52 represent the two substrates, and E and P, the enzyme and the product, respectively. For nitrification and deni- trification, they represent the following. Nitrification Denitrification S1 Ammonium Nitrogen Nitrate Nitrogen $2 Dissolved Oxygen Organic Carbon P Nitrate Nitrogen Nitrogen, Carbon Dioxide, etc. Postulate the following sequence of enzyme reactions: k E+s]%E-s1, (c.1) k + E+$2:k:_2§E-sz, (c.2) 222 E’S]+Sz+‘F3E'S-l-Szg (C.3) £2.40 -4 k+5 E - S] - $2'————+ P + E . (C.5) The above sequence of reactions can be very handily repre- sented as __kiL, + .L. S2 82 N N M + I + I ”U“ k “MU“ k .024» _ +5 where E - S1 = enzyme substrate 1 complex, E - $2 = enzyme substrate 2 complex, E - S1 - S2 = enzyme substrate 1 and substrate 2 complex, k+i = forward reaction rate constants, and k = reverse reaction rate constants. The mechanism postulated is that the enzyme combines with the substrates 1 and 2 to form E - S1 and E - $2 complexes. These complexes then combine with the other substrate to form E - S1 - S2 224 complex which dissociates to give back the enzyme and the product. Let, at the equilibrium conditions, b = concentration of total enzyme, 5] = concentration of substrate 1, $2 = concentration of substrate 2, c = concentration of complex E — S], d = concentration of complex E - $2, and e = concentration of complex E - S1 - $2. The concentration of free enzyme E is, then, represented as b - c - d 4 e. Let K1. K2, K3, and K4 represent the equilibrium constants for the reactions (C.l), (c.2), (C.3), and (C.4), i.e., k k_4 , and K = _ . 7: —J II ”I u 7< N II x. u x (A) II x D 00 3' These, when written in terms of the concentrations of vari- ous species, become S1 (b - c - d - e) I K]: C 9 52(b-c-d-e) K: 2 a ’ (C.7) cS2 d5 3 ‘5'" 6"“ “4:?- J If we further assume that K] = K4 and K2 = K3, it means that neither substrate 1 nor substrate 2 affects the affinity of 225 the enzyme for the other substrate, i.e., the affinity of the enzyme for a substrate is unaffected by the presence of other enzyme substrate complexes. Let K1 = K4 = K.‘ and K2 = K3 = K2. From (C.7), 7< 1e c = ——- and d = ———-. (C.8) Substituting (C.8) in equation for K1 in (C.7) and computing for e, one gets b $152 9 = TK] + 5]) (K2 + 52) ° (C.9) Rate of product formation, v, is k+5e, i.e., k+5 b 5152 v = . If the maximum rate of product formation is denoted by V, then V = k+5b, i.e., 3‘ $2 ( ) v = V -———-——— -——————— . C.IO K1 + Sl K2 * S2 Equation (C.lO) represents the double substrate limited kinetic model that is used in this work. APPENDIX D CONTINUOUS FEED EXPERIMENTS. STEADY STATE DATA 226 .4\02 0.0 u 0040024444 00 00040400 0000 4400 .4\ms 4.0 u 00440400 4000004 40:44 40 0000x0 00>400040 227 mmm 0.04 0404 4.40 4.4 00000000 m4 0N0 40 4.04 4.04 040 0.00 04.4 mm 000 0.4m 0.44 0.44 mom 0.004 mn.0 04 000 mm 0.04 0.04 0404 4.40 40.4 cm 040 0.0m 0.40 m._m 0004 mm.mm 40.4 04 mum mm 0.44 0.44 0004 0.004 00.4 on com 00 4.04 4.04 0404 0.00 00.4 04 com mm 0.00 0.00 emo— 4.40 4.0 4\me 40040< N0 040500 40040< 40 040500 0 0000040 2. moz :4E\PE x 200200 0000040 00004442 0404042 —\mE WWW” 0044044000000 0000 040040c< 040500 .4 u 04004000 0000444: 0404442 404 404004 00440440 .m~ u 04004000 0000040 404 404004 00440440 .4-z 40004400X0 404 .400 04000 400000 44400--.4.0 00044 228 ._\0e 0.40 " 0000040_44 40 00000000 0000 4400 .4\0E 0.0 u 00400400 4000004 40:44 40 0004x0 00>400040 omw m—.©m ooo— cop .mmmummm mm mew em m.mm m.mm mwm 5.50 PN.¢ mm mwm mm m.mm m.mm mwm 0.004 4F.¢ mm m¢m mm N.mm n.mm mmm m.mm mN.¢ om muu Pm m.om m.om mwm n.nm om.¢ 04 mmm mm m.~m m.mm omop o.oo— PN.¢ om omm em m.~m m.~m omo— 4.4m 4N.¢ mm mmm mm n.mm h.mm omop m.mm MN.¢ m4 own om o.wm o.mm omop m.NoF N.¢ _\0E 40auu< 00 040500 40000< 40 040500 0 0000040 2. moz 042445 x 000400 0000040 00004042 0004042 4\0e WWW” 04004004 040500 0040040000000 0000 .4 u 04004000 0000404: 000404: 404 400004 00400440 .00 u 04004000 0000040 404 400004 00400440 .~-z 00004400X0 404 0000 00000 400000 44400--.N.0 00004 229 .4400 0.00 n 0040044444 40 00040000 0000 4400 .4405 0.0 u 00440400 4000004 40:44 :4 :004xo 00>4omm40 000 0.40 .0000000 00 000 0.00 0.00 0.00 0004 0.004 40.0 00 040 0.00 4.40 4.40 0004 4.40 44.0 04 040 0.00 0.00 0.00 0004 0.004 00.0 00 000 0.00 0.00 0.00 0004 0.00 00.0 00 000 0.00 00.04 00.04 0004 0.00 00.0 04 040 0.00 0.00 0.00 0004 0.004 4.0 004 004 0.00 0.00 0.00 0004 4.40 00.0 004 000 00 4.00 4.00 0004 0.00 40.0 4405 40040< 00 040500 40040< 40 040500 0 0000040 2. moz :4EV4E x 000400 0000040 40004442 0004042 4405 WWW” 040440c< 040500 0040040000000 0000 .4 u 04044000 0000444: 0404440 404 400004 00400440 .00 u 04044000 0000040 404 400004 00400440 .0-z 40004400x0 404 0400 00000 400000 44400--.m.0 00044 230 ._\00 0.00 n 0040040_44 40 000_0000 0000 __00 .0\me 0.0 u 00000000 4000004 00044 :0 =0m>xo 00>00mm40 om.m N.MN mw.p .mmmummm mm mmn N.om mm.NN mm.NN mmm N.Nm Rm.P mm m¢n w.mN PN.MN PN.MN mwm w.wm Rm.~ om mNN mm wm.—N em.~N mmm m.mm mm.— om men m.mN em.¢N wm.¢N mmm c.0o— um.F mm mmm ¢.mN o.v~ o.¢N mmop. 0.00— mm.~ mu mmm N.om w.¢N m.¢N mNo— o.oop mm.F om mNN 0N N.NN N.NN mNoP w.mm mm.p ow 0mm mm om.N¢ mo.N¢ mNoF n.mm o.N _\ms 00:00< 00 000500 00000< 00 000000 0 0000000 2. moz :05\PE x 000400 00000—0 00004042 0004042 _\0E WWW” 0040040000000 0000 040000=< 000500 .4 u 00004000 0000400: 000404: 404 400004 00400—00 .00 u 00000000 0000000 404 400004 00400040 .4-z 0000440000 404 0000 00000 >.0003 00_00--.4.0 00000 .4\00 0.00 n 0000040404 40 00000000 0000 4400 .4400 0.0 u 00400400 4000004 40044 04 0000x0 00>4omm40 231 044 4.00 4.00 0004 004 000.4 .0000000 00 044 0.00 0.00 0.00 0004 4.40 00.4 00 044 0.00 0.04 0.04 0004 0.00 00.4 00 004 0.00 4.00 4.00 0004 4.40 40.4 04 044 0.00 4.40 4.40 0404 004 00.4 00 004 0.00 4.00 4.00 040 0.004 00.4 00 004 0.00 0.40 0.40 000 004 00.4 00 000 0.00 0.00 0.00 0004 0.00 00.4 04 000 0.00 4.40 4.40 0004 4.40 00.4 4400 40000< 00 040000 40000< 40 040000 0 0000040 2. moz 040440 x 000400 0000040 00004042 0004042 4400 WWW” 0040040000000 0004 0404400< 040000 .4 u 04004000 00004040 0004040 404 400004 00400440 .00 u 04004000 0000040 404 400004 00400440 .0-z 00000400X0 400 0000 00000 400000 00000--.0.0 00000 232 .0402 0.04 n 0000040000 40 00000000 0000 0000 .0400 0.0 u 00000000 4000004 00000 00 0000x0 00>000000 000 0.00 0.0000 0.000 04.0 00040006 00 000 00 0.00 0.00 000 0.00 04.0 00 000 0.00 0.00 0.00 000 4.40 04.0 00 000 0.00 0.00 0.00 0000 0.00 40.0 04 000 00 4.00 4.00 0000 0.000 04.0 00 040 00 0.00 0.00 000 0.000 00.0 00 004 00 4.00 4.00 0000 0.00 44.0 000 000 00 0.40 0.40 0000 0.00 04.0 000 000 00 0.00 0.00 0000 4.40 04.0 4400 000000 00 000000 000000 00 000000 0 0000000 2. 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