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Development of an analytical tool for anaerobic digestion of organic wastes Wang, Yu 2010

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DEVELOPMENT OF AN ANALYTICAL TOOL FOR ANAEROBIC DIGESTION OF ORGANIC WASTES  by  Yu Wang  B.A. The University of British Columbia, 2007   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  The Faculty of Graduate Studies  (Chemical & Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  February 2010  @ Yu Wang, 2010  ii ABSTRACT  Anaerobic digesters decompose organic matter biologically in the absence of oxygen. In some cases, in addition to waste management, the purpose of anaerobic digestion (AD) is to produce methane, which can be used for energy. In the Fraser Valley region, potentially 30 MW of energy can be generated through AD with the additional benefits of reduced odour, green house gas (GHG) emissions and soil and water contamination, which is produced currently from artificial fertilizers.  The main goal of this research project is to develop an anaerobic digestion calculator that would assist farm and herd owners in the Lower Fraser Valley in making decisions on choosing suitable anaerobic digestion technologies for their own farms. The calculator is developed from Excel spreadsheets and graphical user interfaces (GUIs). These user interfaces take inputs, send the inputs to the corresponding spreadsheet cells, and block invalid inputs from causing calculation error.  The new calculator uses the Lawrence and McCarty kinetic model to calculate substrate consumed during AD. This calculator takes hydraulic retention time (HRT) and feed, via animal counts, single-defined flow or mixing several waste sources, as inputs. From these inputs and default kinetic parameters, which can be modified, reactor size, biogas production rate, effluent characteristics, capital cost and revenue of the AD plant are calculated and summarized for users. Users can select one of the three possible digester configurations: completely-mixed, plug-flow and mixed plug-flow and heat and electricity co-generation or biogas upgrading. Currently the calculator is valid for simulating AD in the mesophilic temperature range only. Further modifications are needed to include other kinetic models, input more feed types and simulate thermophilic AD.   iii TABLE OF CONTENTS  ABSTRACT.......................................................................................................................................................... ii TABLE OF CONTENTS ..................................................................................................................................... iii LIST OF TABLES................................................................................................................................................. v LIST OF FIGURES.............................................................................................................................................. vi LIST OF SYMBOLS AND ABBREVIATIONS................................................................................................. vii ACKNOWLEDGEMENTS ................................................................................................................................. ix 1 INTRODUCTION......................................................................................................................................... 1 1.1 History of anaerobic digestion........................................................................................................ 1 1.2 Project background......................................................................................................................... 1 1.3 Environmental benefits of AD technologies................................................................................... 3 1.4 Project Objectives........................................................................................................................... 3 2 LITERATURE REVIEW .............................................................................................................................. 5 2.1 Reactions of anaerobic digestion.................................................................................................... 6 2.2 Optimum conditions for anaerobic digestion ................................................................................. 7 2.3 Organic waste properties ................................................................................................................ 9 2.4 Existing anaerobic digestion technologies and suppliers ............................................................. 11 2.41 Dry vs. wet digestion........................................................................................................... 14 2.42 Mesophilic vs. thermophilic digestion................................................................................. 15 2.43 Completely Mixed vs. MPF ................................................................................................ 16 2.44 Co-generation vs. biogas upgrading .................................................................................... 17 2.5 Existing kinetic models of anaerobic digestion ............................................................................ 17 2.51 Multi-step models................................................................................................................ 17 2.52 Overall kinetic models......................................................................................................... 19 2.6 Valid ranges of Lawrence & McCarty’s model ............................................................................ 21 2.7 Capital cost estimation ................................................................................................................. 22 3 EXISTING AD CALCULATORS .............................................................................................................. 27 3.1 Coefficient-based software ........................................................................................................... 27 3.2 Kinetic-based calculators.............................................................................................................. 29 4 DEVELOPMENT OF THE NEW AD CALCULATOR............................................................................. 32 4.1 Design rationale............................................................................................................................ 32 4.2 Digester models ............................................................................................................................ 33 4.3 Biogas utilization model............................................................................................................... 38 4.4 Model calibration and parameter estimation ................................................................................ 40 4.5 Economic analysis method ........................................................................................................... 47 4.6 Interface design ............................................................................................................................ 48 4.7 Error handling............................................................................................................................... 51 5 DEMONSTRATION CASE STUDIES ...................................................................................................... 53 5.1 Baldwin Dairy .............................................................................................................................. 53  iv 5.2 Bell Farms .................................................................................................................................... 54 5.3 Deere Ridge Dairy........................................................................................................................ 54 5.4 Stencil Farm.................................................................................................................................. 55 5.5 Five Star Dairy ............................................................................................................................. 56 5.6 Predictive case study .................................................................................................................... 57 5.7 Predicted results and analysis of mixed wastes ............................................................................ 58 6 DISCUSSION AND CONCLUSIONS ....................................................................................................... 64 6.1 Discussion .................................................................................................................................... 64 6.2 Conclusions .................................................................................................................................. 68 6.3 Further research ............................................................................................................................ 70 BIBLIOGRAPHY ............................................................................................................................................... 72 APPENDICES..................................................................................................................................................... 79 Appendix A: A case study using AD calculator........................................................................................... 79 Appendix B: A list of AD technology suppliers .......................................................................................... 88 Appendix C: Material balance of CSTR ..................................................................................................... 89 Appendix D: Material balance of PF digester ............................................................................................. 91 Appendix E: Material balance of MPF digester .......................................................................................... 93 Appendix F: A list of substrates’ biogas yields............................................................................................ 96 Appendix G: A list of active AD sites ......................................................................................................... 99 Appendix H: Sample calculation for CSTR with co-generation ............................................................... 102 Appendix I: Sample calculation for MPF with biogas upgrading ............................................................. 109               v LIST OF TABLES Table 1: Reactants and products involved in the three phases of anaerobic digestion .................................. 6 Table 2: Recommended C:N:P feed ratio for anaerobic digestion ................................................................ 8 Table 3: N, P and K content of common organic wastes ............................................................................... 8 Table 4: Summary of common organic wastes biogas yields...................................................................... 10 Table 5: A summary of digester characteristics ........................................................................................... 14 Table 6: Results of Garcia-Ochoa et al.'s study........................................................................................... 19 Table 7: A brief summary of one-step models............................................................................................. 20 Table 8: A summary of case studies for capital cost estimation .................................................................. 23 Table 9: General information of selected sites for calibration..................................................................... 43 Table 10: Values of kinetic parameters........................................................................................................ 44 Table 11: Calibration results obtained from calculator................................................................................ 46 Table 12: Baldwin Dairy case study results summary................................................................................. 53 Table 13: Bell Farms case study results summary....................................................................................... 54 Table 14: Deere Ridge Dairy case study results summary .......................................................................... 55 Table 15: Stencil Farm case study results summary.................................................................................... 56 Table 16: Five Star Diary case study results summary................................................................................ 56 Table 17: A summary of 450 cattle case study ............................................................................................ 57 Table 18: Computed AD system performance for 450 cows with 20% food wastes................................... 59 Table 19: Computed AD system performance for 450 cows without food wastes...................................... 60 Table 20: Results of economic analysis for 450 cows with 20% food waste .............................................. 63 Table 21: Summary of power generation from anaerobic digestion of cow manure................................... 64              vi LIST OF FIGURES Figure 1: A scheme of anaerobic digestion pathways.................................................................................... 5 Figure 2: Definition of various solid contents............................................................................................. 11 Figure 3: General layout of a biogas plant .................................................................................................. 12 Figure 4: Six common digester configurations ........................................................................................... 13 Figure 5: Capital cost vs. number of cattle.................................................................................................. 25 Figure 6: Capital cost vs. maximum power output...................................................................................... 25 Figure 7: Simple web-based calculators...................................................................................................... 27 Figure 8: Spreadsheet of the AD Community software............................................................................... 29 Figure 9: Calculator from Biorealis Systems, Inc. ...................................................................................... 30 Figure 10: FarmWare from US EPA............................................................................................................ 31 Figure 11: VBA interface between users and Excel spreadsheets ............................................................... 32 Figure 12: Diagram of CSTR model ........................................................................................................... 34 Figure 13: Diagram of PF model................................................................................................................. 35 Figure 14: Diagram of MPF model ............................................................................................................. 36 Figure 15: Bacteria growth in a two-stage MPF ......................................................................................... 37 Figure 16: Calibration range summary........................................................................................................ 45 Figure 17: Files included in the calculator .................................................................................................. 48 Figure 18: A list of spreadsheet used in the calculator ................................................................................ 48 Figure 19: Colour-coding of spreadsheet cells ............................................................................................ 49 Figure 20: Interface organization diagram .................................................................................................. 50 Figure 21: S/6000 vs. HRT.......................................................................................................................... 68              vii LIST OF SYMBOLS AND ABBREVIATIONS  ATCF      After tax cash flow ($) AD       Anaerobic Digestion BC       British Columbia CM       Completely Mixed DM       Dry Matter FDS      Fixed Dissolved Solid FOG      Fat, Oil and Grease FSS      Fixed Suspended Solid FVRD      the Fraser Valley Regional District GHG      Greenhouse Gas HRT      Hydraulic Retention Time MPF      Mixed Plug-flow Digester OC       Operation cost ($) PF       Plug-flow Digester PV       Present value ($) SRT      Solid Retention Time TS       Total Solid TVS      Total Volatile Solid USEPA      United States Environmental Protection Agency VBA      Visual Basic for Application VDS      Volatile Dissolved Solid VS       Volatile Solid, which is equivalent to TVS VSS      Volatile Suspended Solid  a       Growth yield constant (mg/mg)  viii b       Decay rate (1/day) C       Capital cost ($) Cp       heat capacity (kJ/kg ℃) E       Energy (kJ/day) k       Maximum rate of substrate utilization (mg/mg day) ki       Reaction constant of reaction i KS       Half-growth velocity (mg/L) m       Maintenance coefficient (1/day) m&        Mass flow rate (kg/day) ri       Reaction or rate of reaction i S       Substrate concentration (mg/L) t       Time (day) T       Temperature (℃) v       Volumetric flow rate (m3/day) V       Digester volume (m3) VA       Volatile acid concentration (mg/L) X       Bacteria concentration (mg/L) Yi       Yield of reaction i  μ       Growth rate of bacteria (1/day) ρi       Density of i (kg/m3) η       Efficiency (%)        ix   ACKNOWLEDGEMENTS  I offer my enduring gratitude to the faculty, staff and my fellow students at the UBC, who have inspired me to continue my work and study in this field. I thank Dr. S. Baldwin and Dr. A. Lau for their advice, support and guidance throughout this project, and also for enlarging my vision of technologies and future of this field. I thank Matt Gordon and Gustav Rograstrand from the British Columbia Ministry of Agriculture and Lands for their valuable input. The British Columbia Ministry of Agriculture and Lands as well as Life Sciences British Columbia are acknowledged for providing funding for this project.         1 1 INTRODUCTION  1.1 History of anaerobic digestion Anaerobic digestion (AD) is the decomposition of organic matter in the absence of oxygen. During this decomposition, which is due to microbial activity, a gaseous mixture of methane, carbon dioxide and trace amounts of hydrogen sulfide and hydrogen is produced. Hence, AD systems are often referred to as "biogas systems". This process can be found in many naturally occurring anoxic environments including watercourses, sediments, waterlogged soils and the mammalian gut. It can be used to produce biogas from a wide range of wastes including industrial and municipal wastewater, agricultural, municipal, food industry wastes, and plant residues.  One of the earliest reports of gas production in decomposing organic wastes was made by Van Helmont in 1630. But, it was only in 1804 when John Dalton eventually established the chemical composition of methane. After World War I, the British became interested in producing methane from farm wastes, but were not able to make much progress. In the 1940s, many municipal sewage treatment plants in the United States were already able to use anaerobic digestion while at the same time generating heat and electricity for the plant. This was the beginning of sustainable waste management and pollution control. After World War II, many nations developed biogas generation to enhance their economic recovery (Maramba 1978). In the oil supply crisis of the 1970’s and 1980’s AD again become popular and in 1986, gas from the decomposition of sewage was used to light a street in Exeter, England. There was a lull in interest in AD until the most recent world-wide concerns about energy availability, sustainability and pollution control, which means that anaerobic digestion technologies once again are becoming relevant.  1.2 Project background The Fraser Valley region is located in southwestern British Columbia (BC). It consists of two  2 regional districts: an urban region, Metro Vancouver (MV), and a rural region, the Fraser Valley Regional District (FVRD). In the report “Feasibility Study – Anaerobic Digester and Gas Processing Facility in the Fraser Valley, British Columbia” by Electrigaz Technologies Inc. (Electrigaz Technologies Inc. 2008), it is estimated that activities in the Fraser Valley region generate 3.3 million tonnes annually of organic wastes suitable for anaerobic digestion. These consist of 82% agricultural wastes, 8% food wastes and 10% municipal wastes. Among these wastes, 85% (2.9 million tonnes) are estimated to be readily available for anaerobic digestion.  The most probable scenario for the development of anaerobic digestion in BC was concluded to be on-farm manure-based systems accepting some off-farm food processing wastes as opposed to large centralized complexes. The environmental benefits of adapting anaerobic digestion include: odour control, pathogen reduction, improved water quality and reduced greenhouse gas (GHG) emissions. The economic benefits of adopting anaerobic digestion include: power generation, fertilizer or compost production and reduced landfill usage, with power generation being the most attractive feature of anaerobic digestion. The overall potential for energy generation from biogas through anaerobic digestion in the Fraser Valley is estimated to be 30 MW.  However, the electricity portion of the BC energy market is mostly made up of inexpensive and clean hydroelectric power produced by BC Hydro. Although there are some programs available for electricity sales, such as BC Hydro Net Metering Program, BC Hydro Standing Offer Program and BC Hydro Clean Power Call, the profits through these electricity sales programs for small biogas plants are very limited. Thus, upgrading the methane in biogas to natural gas grade would be far more economically appealing to biogas plans in BC. The disadvantages of upgrading biogas are the increased capital and operation costs and also the possibility of releasing pollutants, such as CO2 and H2S, to the atmosphere depending on the upgrading method.    3 1.3 Environmental benefits of AD technologies Due to rising energy prices and dwindling supplies of oil and gas, governments around the world are promoting renewable energy technologies. Anaerobic digestion technology has the advantage of being relatively inexpensive, easy to construct and operate with few constraints on the location.  Although agriculture is generally considered to be a green industry, agricultural activity is a major source of greenhouse gas emissions. In fact, 52% and 84% of global anthropogenic methane and nitrous oxide emissions, respectively, come from agricultural activity (Smith 2007). Most of the methane emitted is due to on-land decomposition of animal wastes and other on-farm organic wastes. Therefore, by applying AD technology to treat these animal and organic wastes, the methane gas produced can be captured and used to produce energy instead of polluting the air. Also, during the collection and purification of methane gas, trace amounts of hydrogen sulfide are removed, which eliminates another air and odour pollutant.  Furthermore, since AD creates very little new biomass while destroying high loading rates of organics, there is a significant reduction in the volume of solid wastes needing disposal. In fact, many farms use residual solid wastes from AD as bedding material for their barns, which also reduces the farm’s operating costs. The liquid portion of AD effluent is rich in nitrogen, phosphorus and potassium. As a result, this liquid can be used as an effective fertilizer after pathogens and other harmful micro organisms are destroyed.  1.4 Project Objectives The main goal of this research project is to assist farm and herd owners in the Fraser Valley region in making decisions on choosing suitable AD technologies for their own farms. This goal can be separated into two connected objectives. The first objective is to inform potential users of the currently available technology options for both anaerobic digestion and biogas utilization.  4 The second object is to accurately model the selected AD and biogas utilization technology. The models used should be relatively simple yet providing a fair estimation on vital biogas plant parameters, such as biogas yield, digester volume, capital cost, annual income and etc.  In order to achieve these two objectives, the calculator developed must include the follow features: 1. The ability to input amounts of different types of wastes including animal, food, agricultural and municipal wastes. 2. A user-friendly interface for choosing a digester configuration and for selecting whether to use cogeneration or biogas upgrading. 3. A model parameter input interface, which should provide default values for average users, but also allow advanced users to input their own parameters to match their particular feed or design. 4. Detailed output including all the input information, model parameters used and calculated results. Users should be able to export and save this output as another file, so that it can be viewed as a report. 5. Help documentation for both basic and advanced users.  The first phase of this project was a literature review of the reactions involved in AD, the properties of organic wastes, kinetic models that have been developed for anaerobic degradation of these wastes and available reactor configurations for AD. Existing AD-related calculators also were compared and contrasted. During the second phase of this project, an Excel-based calculator with a windows-like interface was developed. Finally, this calculator was tested against several case studies collected during the literature review. The calculator’s advantages, limitations and possible further improvements were reported after the tests.    5 2 LITERATURE REVIEW The composition of organic wastes most suitable for AD is not clear and varies from one literature source to another. All organic wastes contain proteins, fats, fibers and inert material that cannot be digested. Digestion of complex organic materials takes place in three overall stages: hydrolysis, acetogenesis and methanogenesis. During the hydrolysis stage, complex organic polymers are broken down into their monomer intermediates: amino acids, volatile fatty acids (VFA) and sugars as shown in Figure 1. Reactions that lead to the production of N2 and H2S are not included because they account only for a small portion of the biogas produced and organic wastes consumed. During acetogenesis, these intermediates are converted into acetate with carbon dioxide and hydrogen as by-products. Finally in the methanogenesis stage, hydrogen and acetate are converted into methane and carbon dioxide.   Figure 1: A scheme of anaerobic digestion pathways   6 2.1 Reactions of anaerobic digestion Table 1 is a brief summary of the main reactants and products during each step. In general, the microorganisms involved in hydrolysis and acetogenesis grow more rapidly than the microorganisms involved in methanogenesis. As a result, methanogenesis tends to be the rate-limiting step. However, for some materials, such as grasses and newsprint, which contain more recalcitrant celluloses, hydrolysis may be very slow and rate-limiting (Rittmann & McCarty 2001).  Table 1: Reactants and products involved in the three phases of anaerobic digestion Step Reactants Products Hydrolysis Organic Material C6H12O6, volatile acids C6H12O6 CH3COOH, CO2, H2 Acetogenesis CO2, H2 CH3COOH CH3COOH CH4, CO2 Methanogenesis CO2, H2 CH4  The stoichiometry equation describing overall AD varies with reactants (Cheremisinoff 1994, Buvet et al. 1982):  Acetic acid: 423 CHCOCOOHCH +→      (1)  Fat, oil:  422610654 75.3825.1525 CHCOOHOHC +→+   (2)  Lipids:  2425106 33 COCHOHOHC +→+     (3)a  Proteins: 3275242103716 2.07.51.92 NHNOHCCOCHOHNOHC +++→+ &&&   (4)b Urea:  32222 2)( NHCOOHNHCO +→+    (5) Stearic acid: 3 2 16 2 4 2( ) 8 13 5CH CH COOH H O CH CO+ → +  (6) a, b  Coefficients in Equation 2 and 4 have been corrected from their original values.  7 During the last century, researchers have developed many overall stoichiometry equations for an arbitrary substrate. Assuming very little new biomass is generated through AD, the following stoichiometry equation (Buswell & Neave 1930) is fairly accurate:  → −−+ + OHdcbaNOHC dcba 24 324   324 8 324 8 324 dNHCOdcbaCHdcba +++−+−−+   (7) Using general formula for proteins, carbohydrates and fats in Equation 7, the theoretical methane yields for these three types of biochemicals are 0.7, 0.83-0.96 and 1.4 m3/kg DW respectively. In addition to increased yields, the composition of methane is higher in biogas produced from fats (71% versus 50% for carbohydrates and 38% for proteins).  2.2 Optimum conditions for anaerobic digestion For methanogens, the optimum pH range is from 6.6 to 7.6. Beyond these pH limits, digestion is able to proceed but with less substrate conversion due to a lower rate (Cheremisinoff 1994). As shown in Figure 1, acetic acid is produced during acetogenesis and consumed as the main source of food during methanogenesis. At steady state, the rate of acetic acid production and consumption should be the same. If the pH is not controlled properly, it may drop below pH 6.0 or rise above pH 8.0 until complete failure of digestion (Demuynck et al 1984). However, more recent studies have shown that methanogenesis can occur in an acidic environment. Certain methanogenicbacteria, such as Methanosarcina barkeri and Methanosarcina vacuolata, can grow well at pH as low as 5. It seems that some microbiological pathways are altered by pH when certain substrates, such as methanol, are available. This observation suggests that the options of pH value of methanogensis have not been fully examined (Malina & Pohland 1992).  Organic carbon and nitrogen, various vitamins, amino acids, and trace metals elements are essential to microorganism growth. Since in anaerobic digestion complex organic wastes are used, these combined nutrients are always available. However, several optimal C:N:P ratios for the influent have been recommended and some of these are listed in Table 2. On average, the  8 recommended C:N:P ratio is about 125:5:1.  Table 2: Recommended C:N:P feed ratio for anaerobic digestion Ratio Value Organic Loading Reference COD:N:P 400:7:1 High Malina and Pohland 1992 COD:N:P 1000:7:1 Low Malina & Pohland 1992 C:N 10-30:1 N.A. Timbers & Marshall 1981 C:N:P 100:6:1 N.A. Cheremisinoff 1994 COD:N:P 1000:5:1 Low (0.5g/g) Buvet et al 1982 COD:N:P 250:5:1 High (0.15g/g) Buvet et al 1982 C:N:P 330:5:1 Low (0.5g/g) Buvet et al 1982 C:N:P 130:5:1 High (0.15g/g) Buvet et al 1982  Table 3: N, P and K content of common organic wastes  N w.% P w.% K w.% Reference Beef Manure 0.60-4.90 1.27-1.60 0.05-4.00 Smil 1982 Dairy Manure 1.50-3.90 0.31-1.60 1.40-2.20 Smil 1982 Swine Manure 2.00-7.50 0.56-2.50 1.50-4.90 Smil 1982 Poultry Manure 1.10-11.00 0.38-6.30 0.73-5.20 Smil 1982 Pig Manure 7.5 2.5 3 Seadi 2001 Cattle Manure 4 1.2 4 Seadi 2001 Poultry Manure 7 2 2 Seadi 2001 Soup Processing Waste 0.58 0.8 0.12 Zhang et al 2007 Cafeteria Waste 0.51 0.14 0.50 Zhang et al 2007 Commercial Kitchen Waste 0.55 0.14 0.50 Zhang et al 2007 Fish Farm Waste 1.33 0.16 0.14 Zhang et al 2007 Grease Trap Waste 0.21 0.04 0.02 Zhang et al 2007  9  Table 3 is a summary of the nitrogen, phosphorus and potassium content of some organic wastes. Nearly all of the organic wastes listed in Table 3 have a N:P ratio exceeding the recommended 5:1; and all of these organic wastes are rich in organic carbon. As a result, the recommended C:N:P ratio (125:5:1) may not be satisfied in most cases. However, none of the biogas plant sites encountered through literature review reported any problems with lack of or inhibition by nitrogen or potassium. As a result, it could be beneficial to investigate how flexible these nutrient ratios can be.  Similar to most chemical reactions, biochemical reactions are dependent also on temperature. For estimating the dependence of reaction rate on temperature the Arrhenius equation can be used. In practice, there are two temperature ranges for AD processes: mesophilic (near 35℃) and thermophilic (55℃~60℃). Within the intermediate range between 40℃ and 50℃, the activity and growth of neither bacteria involved in acetogenesis nor methanogenesis is favoured. The total biogas production rate is higher in the thermophilic than the mesophilic range. The methane composition at high organic loading rates (> 9 g VS/L digester volume per day) is higher in the thermophilic than the mesophilic range. However, at lower organic loading rates (< 6 g VS/L digester volume per day), the methane composition is higher in the mesophilic than the thermophilic range (Mackie & Bryant 1995). Due to the high energy costs of thermophilic operation, its feasibility very much depends on the efficiency of thermal energy production from methane. Furthermore, nearly all farm-size methane digesters encountered through this literature review operate in the mesophilic range of 30℃ to 40℃. Consequently, both temperature ranges were examined but the calculator was calibrated from mesophilic plants.  2.3 Organic waste properties Animal manures from cattle, hog, and poultry and agriculture wastes such as corn and grass  10 silage are commonly used for anaerobic digestion. More recently, food processing wastes such as grease trap, fats and baking wastes, municipal wastes such as water treatment sludge and organic garbage are being used as feeds for AD (Spencer 2007). It is important to know what the potential biogas yield per wet or dry tonne is for different types of organic wastes. Table 4 is a summary of all the biogas yields of common organic wastes encountered during the literature review. A more detailed list with references is in Appendix F: A list of substrate biogas yields. As shown in Table 4, biogas yield of a particular substrate is usually given as a range. The solids contents of substrates affect their biogas yields greatly. For example, at 50% TS, the biogas yield is 500 m 3/wet tonne, whereas at 100%, the biogas yields is 1390 m3/wet tonne. Food wastes are commonly added together with animal wastes to enhance biogas production due to their relatively high biogas yields. However, depending on the source of the food waste, its biogas yield can still vary (50 m3/wet tonne for kitchen wastes and 110 m3/wet tonne for soup processing wastes). Consequently, these values should only be used as indicative values for initial estimation with caution (Birse 1999).  Table 4: Summary of common organic wastes biogas yields Substrate Biogas Yield (m3/wet tonne) Cattle Manure 25 Pig Manure 15-35 Sheep Manure 26 Hen Manure 90-150 Food Waste 46-225 Yard Waste 60-90 Yard and Food Waste 89-102 Fish Farm Waste 472 Grease Trap and Fat Waste 275-1390 Corn/Grass Silage 175-200  11  Aside from biogas, the effluent from AD can be used as fertilizer or compost. Therefore, the nitrogen, phosphorus and potassium content of the wastes must be known. Most of these elements are not converted into gases, but incorporated into the newly formed biomass. As a result, the solid portion of the effluent tends to be richer in nutrients, such as N, P and K, than the original waste.  The last important characteristic of organic wastes is the solid content and organic matter content. Organic matter content is measured typically as volatile solids (VS), which is the change in mass on combustion of the material. It should be noted that not all volatile solids are digestible. As shown in Figure 2, the dry matter (DM) or total solid (TS) content can be further categorized into four components: volatile suspended solids (VSS), fixed suspended solids (FSS), volatile dissolved solids (VDS) and fixed dissolved solids (FDS). Through this literature review, it was concluded that TVS or VS is commonly used to represent the substrates.   Figure 2: Definition of various solid contents  2.4 Existing anaerobic digestion technologies and suppliers Figure 3 illustrates the general layout of a biogas plant, which consists of pretreatment, digestion,  12 biogas utilization (co-generation or biogas upgrading) and effluent disposal. The effluent of digestion can be separated into solid and liquid products. For biogas plants on farm sites, the solid product can be used for bedding and the liquid product can be spread as fertilizer. Due to the long history of anaerobic digestion, there are many types of anaerobic digesters around the world.   Figure 3: General layout of a biogas plant  Figure 4 summarizes the 7 most common digester configurations that are still active. Details, such as construction material, height-to-width ratio of the digester, recirculation scheme and wasting location, may vary from site to site. Other variations include addition of pretreatment and downstream processing units, or connecting these digesters in series or parallel. Through a review of recently constructed farm-sized anaerobic digesters, the most effective ones are the completely-mixed digesters (CSTR, Figure 4a) and mixed plug-flow digesters (MPF, Figure 4f & g). There are also some active plug-flow digesters (PF, Figure 4e), but problems were encountered maintaining their operation. Table 5 is a brief summary of the characteristics for these common digesters. It should be noted that for higher solids contents, it is more common to use mechanical mixing than passive gas mixing.  13    a. CSTR (mixing may also be mechanical) b. Upflow Anaerobic Sludge Blanket (UASB)   c. Covered Lagoon d. Fed Batch Digester (may or may not include mechanical mixing)   e. Plug Flow Digester f. Rotary Mixed Plug Flow Digester   g. Dual Chamber Mixed Plug Flow Digester (left) and Its Top View (right) Figure 4: Six common digester configurations  14  Table 5: A summary of digester characteristics Temperature Operation Digester Type Size Total Solid Retention Time Mesophilic Thermophilic Continuous Feed Batch CSTR All Range 8%-20%+ High Y Y Y Y MPF Farm <12% Medium Y Y Y N PF Farm <10% Low Y Y Y N  There are many active suppliers of AD technology and biogas producers in North American and European markets. This section will briefly compare some of them with respect to several key design concepts. A more complete list of suppliers can be viewed in Appendix B: A list of AD technology suppliers. In the following section, the main differences in digester configuration and operation are discussed according to dry vs. wet digestion, mesophilic vs. thermophilic operating conditions, CSTR vs. MPF configuration, and co-generation vs. biogas upgrading.  2.41 Dry vs. wet digestion Feed to the digester consists of aqueous slurry. In some cases this results from the way in which waste is collected. For example, in the case of manure, material is washed out of the barn area with water into a holding tank resulting in low solid content slurry. In other cases, where drier materials are collected, such as food waste, water may need to be added to achieve a desired percent solids or a dry digestion process may be favoured. In general, dry digestion refers to an AD process with TS over 20%, whereas wet digestion refers to an AD process with less than 20% TS. Among the current large scale AD plants, roughly 62% of them are wet digestions (Beck 2004). Smaller biogas plants, such as the ones located on farm sites, normally operate around 10% TS (Van Buren 1979). However, AD is generally not economically feasible if the total solids content is lower than 5% since the material will likely have low energy content (Strategic Policy Unit 2005). When the TS content is too high, agitation and pumping could be an issue, especially  15 for dry digestion systems (Millen 2008). The majority of biogas plants studied in this project operates between 8% and 12% TS. From this literature review, the biogas yields (based on m3 per tonne VS) of dry and wet digestion do not differ much. Although wet digestion has a shorter HRT, its digester volume is smaller due to the higher influent volumetric rate.  GHD (Chilton, W.I., U.S.) is a major supplier of wet AD technology. It offers a specialized U-shaped two-chamber MPF design (as shown in Figures 5g and h) that operates at lower than 15% TS (GHD 2009). BIOTHANE (Camden, N.J., U.S.) also offers similar MPF digesters of similar configuration, but it also provides completely mixed (CM) digesters. Although farm-sized digesters are dominated by wet digestions, there are some active suppliers of dry AD technology. PlanET (St. Catherine’s, O.N., Canada), for example, offers a dry digestion completely mixed digester with a paddle inside for mechanical mixing. Another active supplier, Kompogas (Glattbrugg, Switzerland), offers horizontal MPF digesters that are optimized at around 30% TS (Kompogas 2009).  2.42 Mesophilic vs. thermophilic digestion Generally speaking, digesters are more stable and need less process heating when operated in the mesophilic temperature range, but they are larger than those required in thermophilic processes (Wilkie 2005). Due to the additional heating requirements, thermophilic digestion is therefore only economically viable at high organic loading rates (Mackie & Bryant 1995, Demuynck et al 1984). Some studies have shown that biogas yields are higher in the thermophilic temperature range (Svoboda 2003), and that dry digestion is more favourable for thermophilic processes (Beck 2004). A study of Danish centralized anaerobic digestion plants installed during 1980’s and 1990’s found that special construction materials needed for thermophilic digestors (i.e. steel) increase their costs above those for mesophlic digestors (which are made out of concrete) (Hjort-Gregerson 1999).   16 Most of the AD technology suppliers offer digesters that operate in mesophilic range. For example, GHD’s U-shaped two-chamber MPF digesters and Alvesta’s (Devon, U.K.) dual chamber completely mixed bio-digester systems both operate within the mesophilic temperature range. For thermophilic digesters, Kompogas offers horizontal MPF digesters that operate at 30% TS. Microgy (Tarrytown, N.Y.) is the only supplier encountered in this study that is specialized in thermophilic digestion in the North America market.  2.43 Completely Mixed vs. MPF The most common continuous digesters for AD are completely mixed (CSTR in Figure 4a) and plug flow digesters (Figure 4e). However, due to the difficulty in maintaining ideal plug flow and problems with sand and other solids accumulating inside the digester (Dennis & Burke 2001), AD technology suppliers developed MPF digesters (Figure 4f). A partially mixed plug flow digester’s HRT and volume are less than that for a completely mixed digester, but not as low as for a plug flow digester. It can be viewed as a compromise between the stability of a CSTR and the efficiency of a plug flow digester. Based on the literature review, both completely mixed and MPF digesters are very popular on farms (combined they account for 95% of the digesters reviewed). However, the completely mixed configuration seems to be the only feasible choice for larger capacity operations (centralized digesters).  Many active suppliers of AD technology, such as BTA (Pfaffenhofen, Germany), HAASE (Chicago, I.L., U.S.), and RCM (Parsippany, N.J., U.S.) produce completely mixed digesters with different mixing methods, digester shapes and gas capturing methods. Plug flow digesters are advertised by the following companies, RCM, OWS (Dayton, O.H., U.S.), and Alliant Energy (Madison, W.I., U.S.). Major suppliers of MPF digesters are GHD, Kompogas and BIOTHANE. Among these three suppliers, GHD MPF digesters were encountered most often in this literature review.   17  2.44 Co-generation vs. biogas upgrading Most of the AD plants currently operating use biogas to generate electricity and heat. The two primary types of power generation equipment are microturbines and reciprocating gas engines. Microturbines are small gas engines that burn methane mixed with compressed air. Reciprocating gas engines are essentially natural gas engines that have been transformed to handle the larger volumes of biogas because of its higher CO2 content (Goldstein 2006). However, because electricity in BC comes from inexpensive and clean hydro electric power, upgrading biogas to natural gas grade methane increases the economic feasibility of AD in BC (Electrigaz 2007).  Many engine vendors, such as Entec (Salt Lake City, U.T., U.S.) and Linde-KCA (Dresden, Germany) supply farm-sized co-generation engines. In farm-sized co-generators, 30% to 40% of the total heat of combustion is converted to electricity and around 50% is captured as usable heat. Very few biogas upgrading systems exist at AD operations in North America currently. However, one company, QuestAir Technologies (Blainville, Q.C., Canada), has patented technologies for farm-sized biogas upgrading systems. Thus, biogas upgrading technology is available for incorporation at AD installations of the future. Examples of co-generation and biogas upgrading are given below.  2.5 Existing kinetic models of anaerobic digestion In order to accurately predict AD performance, an accurate mathematical model for substrate uptake rate is needed. Most existing models for AD can be categorized into two types: multi-step and overall Monod-type models. In these sections, both types will be discussed and compared.  2.51 Multi-step models Detailed models include all the main steps in AD (as shown in Figure 1), where each step is described by one overall stoichiometric equation and has its own rate expression. The overall  18 rates of substrate uptake and methane production can be calculated by solving the equations for all steps simultaneously. Garcia-Ochoa et al. developed such a model (Garcia-Ochoa 1999). In their model, the six reaction steps are: hydrolysis of waste (r1), growth of acetogenic bacteria (r2), production of organic acids (r3), consumption of substrate for acetogenic bacteria maintenance (r4), growth of methanogenic bacteria (r5), and organic acids consumption for methanogenic bacteria maintenance (r6). From this reaction scheme, they formulated the following model (modified for pseudo-steady state and t less than 22):  Substrate mass balance:   1rdt dS −=            (8)  Volatile acid mass balance:   5533 rYrYdt dVA −=           (9)  Reaction rates:   )( 643221 rrrrYr +++−=−         (10)   agbXkr 22 =            (11)   agbXkr 33 =            (12)   agbagbS Xmr ,4 =           (13)   VAXkr met55 =           (14)   metmetS Xmr ,6 =           (15) where S is the substrate concentration (g/L), t is time (days), VA is the volatile acid concentration (g/L), Yi is the yield of biomass or VA per VA or substrate in reaction i (g/g), ri is the rate of reaction i (g/Lday), ki is the reaction constant of reaction i (units varies according to the order of the reaction), mS is the maintenance coefficient (1/day), X is the concentration of bacteria (g/L), subscripted agb denotes acetogenic bacteria and subscripted met denotes methanogenic bacteria. Using experimental data fitted to this model they obtained the parameter values shown in Table 6. In 2005, Sotemann et al. have also developed a multi-step modeling for treating sludge  19 (Sotemann et al. 2005). However, due to the complexity of the models, neither of them was used in other reports studied in this literature review. Due to the lack of unsteady-state laboratory data, the accuracy of these two models cannot be verified.  Table 6: Results of Garcia-Ochoa et al.'s study Parameter Value Lower Limit Upper Limit k2 0.0839 0.0838 0.0840 k3 0.454 0.452 0.455 mS,agb 0.713 0.981 1.187 k5 0.0151 0.0150 0.0152 mS,met 0.551 0.292 0.809 Y2 2.548 2.888 15.000 Y3 1.758 1.741 1.775 Y5 7.885 7.288 8.422  2.52 Overall kinetic models Although anaerobic digestion is carried out by many groups of bacteria in several stages, it is more common to model the substrate uptake kinetics with an overall growth dependent reaction rate. As shown in Table 7, in these overall growth models, the cell specific growth rate (µ) is a fraction of the maximum growth rate of bacteria (µmax). The maintenance activity of the bacteria is modeled by the decay factor (b) in most of these models.  Barthakur et al. (1991) suggested that when substrate hydrolysis is poor and rate limiting, as would be the case for fibrous materials, the Contois-type equation is more applicable, whereas a Monod-type relationship better represents the kinetics for soluble substrates. In practice, kinetic models’ accuracy may vary depending on the configuration of digesters, but Lawrence & McCarty’s model has been used in studies of anaerobic methane production (Sanchez et al 2004).  20 Furthermore, Lawrence & McCarty’s model can predict kinetics of anaerobic bacterial growth accurately (Kumar et al 2007). On the other hand, Chen & Hashimoto model is particularly accurate for two-phase AD of fruit and vegetable wastes (Viturtia & Alvarez 1996), membrane anaerobic system (Lai et al 1999), membrane aerobic system (Nour et al 2010) and AD of palm oil mill effluent in UASFF (up-flow anaerobic sludge fixed film) bioreactor (Zinatizadeh et al 2006). Overall Lawrence & McCarty’s model appears to be more suitable for the configurations and organic wastes of this project through literature review.  Table 7: A brief summary of one-step models Name Model Reference Grau b S S −= 0 maxµµ Grau et al 1975 Contois b SBX S − + = maxµµ  Contois 1959 Chen & Hashimoto b SKKS S − −+ = )1(0 maxµµ  Chen & Hashimoto 1979 Lawrence & McCarty b SK akS S − + =µ Lawrence & McCarty 1967 Linke 1 0 − = S S kµ  Linke 2006 Note: μ is the growth rate of bacteria (1/day), μmax is the maximum growth rate of bacteria (1/day), S is the concentration of substrate (mg/L), S0 is the initial concentration of substrate in digester (mg/L), a is the growth yield constant (mg/mg), k is the maximum rate of substrate utilization (mg/mg day), KS is half-growth velocity (mg/L), X is the bacteria concentration (mg/L), b is decay rate (1/day) and B, K, Y are constant parameters developed for their corresponding model.    21 2.6 Valid ranges of Lawrence & McCarty’s model Although the Lawrence & McCarty model can be used to model anaerobic digestion, it still has certain limitations. As in all continuous-operation bioreactors with no solids retention, washout can occur where the HRT is too short for the bacteria to multiply inside the reactor. To prevent users from choosing HRTs where washout would occur, a minimum HRT must be calculated. According to Equation 16, if 1)( ≤− bakHRT , then the value of S is negative, which is impossible in practice: 1)( )1( −− + = bakHRT bHRTKS S           (16) In order to avoid a negative S, the range of HRT must be limited for a set of fixed kinetic parameters: bak HRT − > 1            (17)  01 >= µ HRT            (18)  0>− + b SK akS S            (19) Equation 19 reveals another limitation of the Lawrence & McCarty model. In this model, both growth and endogenous metabolism are represented. However, at low substrate concentrations inside the bioreactor, the growth rate may decrease below the endogenous metabolism rate. This means that there is not enough food for maintenance of the existing bacteria population, which would then decline. Therefore, total conversion of substrate in the bioreactor is not possible. Consequently, the maximum conversion (Conv.), the portion of substrate consumed, attainable can be calculated. Since KS+S and b are always positive, Equation 19 can be written as:  SbKSbak >− )(            (20) Since specific growth rate (ak) is always greater than specific death rate (b), Equation 20 can be written as:  22  bak bKConvSS S − >−= .)1(0         (21) Thus, the maximum conversion attainable is:  )(1. 0 bakS bKConv S − −<          (22)  2.7 Capital cost estimation Accurate estimation of a farm-sized biogas plant’s capital cost is important so that users can decide on the economic feasibility of installing AD systems. To increase the economic feasibility of AD, some farm owners receive various supports from local agencies, construct part of the plant by themselves or share part of the facility with another farm, electricity or natural gas vendor. Ghafoori and Flynn (2006) summarized capital cost data in terms of biogas production rate. In their report, different curves were generated using cost indexing to 2005 US dollars and plotted for centralized plants in Denmark (1999-2002). Although the types of reactor are not cited in their study, in general, the capital costs exhibit economy of scale, and the exponent 0.60 usually adopted for processing plants was found to be valid for AD systems. Lazarus (2009) at the University of Minnesota performed an economic analysis and confirmed the economy-of-scale via cost-capacity relationship for dairy farm digesters.  According to the USEPA (United States Environmental Protection Agency) AgSTAR program, as-built costs generally are not available. Nevertheless, based on vendor quotes between 2005 and 2008, they analyzed AD system capital cost data for 28 dairy farms for which itemized cost estimates for the digester, the engine-generator set, engineering design, and installation were available. The AD systems included 10 complete mix digesters, 16 plug flow digesters, and 2 covered lagoons. Systems designed for co-digestion with other wastes were excluded from their analyses. They are also aware of the fact that not all reported costs include the same equipment, thus introducing variability in the reported costs of digesters. To analyze costs on a common basis,  23 they excluded costs of system components that were not included in all of the available cost estimates. These components were post-digestion solids separation, hydrogen sulfide reduction systems, and utility charges including line upgrades and interconnection equipment costs and fees. With the aforementioned items excluded, the remaining capital costs were then scaled to August 2008 dollars using the Chemical Engineering Plant Cost Index (CEPCI). As a result, they proposed linear regression equations for estimating digester capital costs based on number of dairy cows. For rough estimations, linear regression equations can be further simplified into the following two forms: CowsCostPerCowCapital ×=        (23)  erOutputMaximumPowCostPerKWCapital ×=    (24)  These linear regression equations typically do not include factors for economy of scale. Thus, at best, they are only valid for a certain range of inputs, which depends on the data used to generate the equation. For the purpose of this project, 11 case study sites were selected to include a wide range of cows on site and maximum power output. Table 8 is a brief summary of the relevant site information.  Table 8: A summary of case studies for capital cost estimation Name Location Cattle Power (kW) Digester Type Adjusted Capital (U.S.$) Reference AA Dairy N.Y. 1000 130 PF 292,000 Martin 2004 Crave Brothers Farm W.I. 1000 200 CSTR 1,500,000 Ballenger 2008 Gordondale W.I. 860 135 MPF 650,000 Martin 2005 Green Valley Dairy A.Z. 2500 600 CSTR 2,550,000 Jacobs 2007  24 Name Location Cattle Power (kW) Digester Type Adjusted Capital (U.S.$) Reference Haubenschild M.N. 850 135 PF 423,000 Lazarus 2006 Noblehurst Farms N.Y. 1300 130 PF 747,700 Wright and Ma 2003 Spring Valley Dairy N.Y. 236 25 PF 143,650 Wright and Ma 2003a Patterson Farms N.Y. 1000 250 CSTR 1,508,630 Curt Gooch and Inglis 2008 Ridgeline Dairy N.Y. 525 130 CSTR 740,800 Pronto and Curt Gooch 2008a Sunny Knoll Farms N.Y. 1400 230 PF 1,084,500 Pronto and Curt Gooch 2008b SheLand Farms N.Y. 560 125 CSTR 1,199,717 Pronto and Curt Gooch 2008c Vander Haak Dairy W.A. 1200 285 MPF 1,200,000 Goldstein 2004  The data in Table 8 were plotted in two figures: capital cost vs. cattle (Figure 5) and capital cost vs. maximum power output (Figure 6). As shown in Figure 5, when plotting against the animal heads on site, the scale factor for completely mixed digesters (CSTR) and MPF (or PF) digesters are 0.6655 and 1.0684 respectively. In Figure 6, when plotting against the animal heads on site, the scale factor for completely mixed digesters (CSTR) and MPF (or PF) digesters are 0.6304 and 0.8753 respectively. The scale factor for completely mixed digesters is closer to 0.6 in both cases (Ghafoori and Flynn 2006), whereas the scale factor for MPF (or PF) digesters is only valid when plotting against the maximum power output.   25  Figure 5: Capital cost vs. number of cattle   Figure 6: Capital cost vs. maximum power output  Consequently, for this project, the capital costs for installing AD processes are estimated as:  Completely Mixed Digesters:  6304.046594 erOutputMaximumPowCapital ×=    (25)  MPF (PF) Digesters:  26  8753.09.7635 erOutputMaximumPowCapital ×=    (26)  Equation 25 and 26 suggest that MPF systems are less expensive than CM systems. This is in line with the factsheets published by Cornell University’s Manure Management Program (www.manuremanagement.cornell.edu) based on survey of individual dairy farms. On the other hand, data compiled by the USEPA AgStar program about capital costs of AD systems suggests the opposite. There are also studies suggesting that the economic differences between the low-solids CM systems with complete mixing and the high-solids PF systems without mechanical devices within the reactor are small (Verma 2002). Because of the uncertainties in the relative capital costs for CSTR versus PF systems, the estimated capital cost in our study should be further verified when more up-to-date data become available.                  27 3 EXISTING AD CALCULATORS  3.1 Coefficient-based software Many AD calculators are already available on the Internet. Most of them are simple calculators as shown in Figure 7. These software are very easy to use and require only a few inputs about the quantities of organic wastes. However, the results obtained from these calculators are limited. The Renewable Energy Concepts (http://www.renewable-energy-concepts.com) software (as shown in Figure 7b) only provides the electricity and thermal energy generation through a co-generation system. The AD Community (http://www.anaerobic-digestion.com/index.php) software (as shown in Figure 7a) provides a bit more information including methane production and total income (gross).   a. AD Community Software (Last 2009) b. Renewable Energy Concepts Software (Renewable Energy Concept 2009) Figure 7: Simple web-based calculators  As a trial use of these two calculators, 1,000 dairy cattle was input into each one. The electricity production predictions were very different, assuming 360 operating days per year: 314,040  28 kWhr/year by AD Community software and 76,320 kWhr/year Renewable Energy Concepts software. Since the algorithm behind the Renewable Energy Concepts calculator is usually hidden from users, it is not possible to determine the reliability of its calculations.  The AD Community website provided a separate spreadsheet file to illustrate its calculator’s algorithm. As shown in Figure 8, different coefficients are assigned to each type of livestock (Column B for dairy cattle, Column C for other cattle, Column D for pig and Column E for poultry). In order to obtain the digester volume and methane production for a dairy farm, the calculator multiplies the number of dairy cattle by a factor for the size of digester per dairy cow (as shown in the red cell, B34, in Figure 8). Similarly, the algorithm for calculating methane generation is to multiply the total amount of VS in the feed by a methane yield per kg of VS (as shown in the green cell, B36, in Figure 8), assuming 100% conversion of the VS. For a mixed feed from dairy cattle, other cattle, pig and poultry manure, it calculates the digester volume and methane yield for each type of livestock individually. The sum of individual results is the overall result. The fundamental concept of this algorithm is that the digester volume and methane yield are proportional to the number of livestock with an additional assumption that all the VS are digested to completion. As a result, the accuracy of the results primarily depends on how accurate and reliable the coefficients are.  There two important disadvantages of this type of software. The first disadvantage is that it is impossible to achieve 100% conversion. In practice, the ultimate biodegradable fraction of dairy manure is approximately 40% (Wilkie, 2005). The most economically feasible approach is to find an optimal digester volume (or HRT) that achieves the treatment requirements and provides the best biogas production per unit digester volume. Unfortunately, coefficient-based software cannot accurately predict the biogas production at various digester volumes. The second disadvantage is that users cannot select different digester types or biogas utilization systems. The two calculators shown in Figure 7 do not show users what kind of digester is used and users cannot compare the  29 differences in methane production and annual income between different digestion technologies. Furthermore, these two calculators both assume co-generation to be the biogas utilization method. However, for this project, the efficiency, capital costs and energy consumption of biogas upgrading treatment must be included due to low sale price of electricity in BC.   Figure 8: Spreadsheet of the AD Community software  In conclusion, coefficient-based software is relatively easy to construct and use, but it provides limited information on the digester type, methane yield, biogas utilization and capital costs. More importantly, it does not help users to decide which technology is more suitable for their own cases.  3.2 Kinetic-based calculators Kinetic-based calculators are developed using bacterial growth models. Figure 9 is a web-based kinetic-based calculator from Biorealis Systems, Inc. (http://biorealis.com). It can handle  30 different types of wastes and allow users to manipulate some operating conditions such as water content and temperature. In the output section, it provides information about the digester volume, digester cost, methane yield and energy production. However, this software assumes that only thermal energy is produced through biogas utilization.   Figure 9: Calculator from Biorealis Systems, Inc.  A far more advanced AD calculator is FarmWare (as shown in Figure 10) developed by the U.S. Environmental Protection Agency (EPA) under the AgStar Program (http://www.epa.gov/agstar/). This software was developed only for livestock manure feeds. It offers selection of a wide range of designs for equipment used in pretreatment and effluent treatment. The advantage of this calculator is that once users go through the whole simulation, they will have a detailed layout of the overall process including all the equipment needed. The biggest disadvantage is that its feed is limited to animal manure. Future practice will include addition of off-farm organic wastes to ADs so as to improve the biogas yield and economic incentives for AD processes. Therefore,  31 FarmWare is of limited application for this project, where the AD feed for this project could contain up to 20% (weight) of off-farm organic wastes together with animal manure. Another minor disadvantage is that it requires installation on users’ computers, thus compatibility becomes an issue. The newest version of FarmWare is compatible with Windows XP, 2000 and 98, but not compatible with Windows VISTA and Apple Macintosh systems at the moment. In order to solve this issue, this software requires constant updates with common operating systems.   Figure 10: FarmWare from US EPA  Although the kinetic model and calculations are hidden, US EPA provided a user manual (http://www.epa.gov/agstar/resources/handbook.html) with this software. In the user manual, it states that the kinetic model used by FarmWare is the Chen & Hashimoto Model.    32 4 DEVELOPMENT OF THE NEW AD CALCULATOR  4.1 Design rationale There are several key principles that guided development of the new AD calculator. The calculator software had to be open-source to allow users to view and modify the code. A simple user interface was required for the typical user, such as a farmer, who may not be familiar with computers or AD technologies.  In order to achieve these goals, the software was developed and tested using Microsoft Excel 2003, but it is compatible with Excel 2007. For complicated calculations, it is not simple for users to find the connections between and the meaning of individual cells. In order to overcome this problem, VBA (visual basic for application) coding was used to create easier to use graphical user interfaces that guide users through the Excel spreadsheet.   Figure 11: VBA interface between users and Excel spreadsheets  As shown in Figure 11, typical users will only see these graphical user interfaces (GUI) constructed with VBA codes. Code running in the background assigns users’ inputs to the corresponding cells in the Excel spreadsheets. Once the current spreadsheet calculations are complete, these results are passed back to the GUI, which presents the output figures in a more clear and informative way to the user. A big advantage of this approach is that the GUI checks the user input and therefore can reject inappropriate inputs. If this happens, the GUI will inform users of the error and not pass the inappropriate data onto the spreadsheets, which would otherwise  33 result in crashing of the program or calculation of misleading results. On the other hand, if more expert users want to bypass the GUI and perform manipulations directly on the spreadsheets, they can do so by accessing the spreadsheet directly. Another advantage of having an Excel-based calculator is that spreadsheets can be viewed in most operating systems. The common operating systems, such as Windows 98, 2000, XP, VISTA and Mac OS X will need to upgrade their Excel program with their systems’ updates to ensure that Excel files edited in early version are compatible with the newest version. As a result, compatibility will not be a problem.  As discussed in Section 2.52, the bacterial growth kinetic model chosen for this project was the Lawrence & McCarty’s model. The digester models used are discussed in detail in the next section, 4.2 Digester models, where the conservation of mass and energy principles were followed. As discussed in Section 2.6, the economic models determined from the literature review did not provide satisfactory estimations of the capital costs. Therefore, a more accurate economic model was constructed as described in upcoming Section 4.4.  Finally, after the AD calculator was completed, it was tested to compare predicted performance with data from actual operating biogas plants. This was used to evaluate the accuracy, stability and limitations of the software.  4.2 Digester models The bacteria growth kinetic model chosen for this project is the Lawrence & McCarty’s model. For this model, the solid retention time (SRT) is linked to the cell specific growth rate (µ) (Lawrence & McCarty 1967):  µ= SRT 1             (27) Since for digesters that do not recirculate solids, the values of HRT and SRT are the same, and the volume of a digester can be calculated by:  vSRTV ×=             (28)  34 where V is digester volume (m3), v is the volumetric flow rate of the feed (m3/day). In order to apply this kinetic model to the CSTR, PF and MPF digesters, mass balances where performed with the following assumptions: 1. The volumetric flow rate of influent and effluent are considered equal to each other since typically 85%~90% of the feed is water. 2. Inert (I) portion of the influent such as sand, remains unchanged through the process. 3. The biogas produced only contains methane and carbon dioxide. We assume that any water vapour lost with the gases is returned to the digester. Trace amount of H2S and N2 are neglected. 4. The only products of anaerobic digestion are methane, carbon dioxide, new biomass and ammonium. 5. Phosphorus, potassium and other trace nutrients are not taken into account in mass balance.   Figure 12: Diagram of CSTR model  For a CSTR with flows labeled as shown in Figure 12, the concentrations of bacteria (X) and substrate (S) inside the digester are the same as they are in the effluent. Therefore, the differential mass balance is:  vXbX dt dS aV dt dXV −−= )(         (29) At steady state, this equation can be reduced and modified to:  35  )(11 bX dt dS a XV v HRT −==         (30) From the extension of the Laurence & McCarty’s model:  SK kS dt dS X S + = 1            (31) Therefore, the direct calculation for S is:  1)( )1( −− + = bakHRT bHRTKS S           (32) From this equation, the concentration of un-digested organics inside the digester (i.e. S) can be calculated for a chosen HRT, which is a design parameter. Then, the amount of organics in the feed that have been digested is known and from this the production rates of biogas, ammonium and bacteria produced can be calculated as:  ii yieldvSSR ××−= )( 0          (33) where Ri is production rate (kg/day) and yieldi is the mass of product produced per mass of substrate consumed (kg/kg). The subscript i refers to methane, CO2, ammonium or biomass.  Figure 13: Diagram of PF model  The bacteria growth kinetics in an ideal PF digester as shown in Figure 13 is very similar to the CSTR example. The difference is that the concentrations of bacteria and substrate inside the digester changes gradually as it flows from the entrance to the exit of the digester. In order to adapt the CSTR equations for a PFR, estimated average values of substrate and bacteria concentrations are used. The log mean average S is:  36  eff eff SS SS S lnln 0 0 − − =           (34) Substituting this expression of substrate concentration into the Lawrence & McCarty model, it becomes:  b SSKSS SSak HRT effSeff eff − −+− − = )ln(ln)( )(1 00 0      (35) Although an analytical solution for the effluent substrate concentration, Seff, cannot be derived, numerical solution can be calculated via the goal-seek function in Excel. Once the effluent substrate concentration is calculated, the biogas, ammonia and bacteria production rates can be calculated using Equation 36.   Figure 14: Diagram of MPF model  Figure 14 is a simplified illustration of a two-stage MPF digester. The feed spends half of the HRT in the first tank, in which some mixing occurs due to rising biogas bubbles, and then spends the other half of the HRT in the second tank, where some additional mixing takes place also due to rising biogas bubbles. Depending on the strength of the organic wastes being processed and the activity of the bacteria, some solid material is separated from the effluent and re-fed back into the second tank.  As shown in Figure 15, bacteria in the second tank are in the stationary phase, therefore:  23 XX =             (36)  37 Since there is no change of bacteria concentration in tank 2, the substrate consumption is entirely for bacteria maintenance. As a result, the substrate concentration in effluent (S3) can be calculated as:  akHRTeX Activity XX 5.0021 1 ==        (37)  a XXSS 0101 − −=           (38)  12 SS =              (39)  2 2 23 HRTkXSS −=           (40)   Figure 15: Bacteria growth in a two-stage MPF  The overall biogas production rate from both tanks is then:  )()( 32110 SSvyieldSSvyieldRbiogas −×+−×=     (41) The biogas yield coefficients from substrate in the two tanks are assumed to be equal. It is also reasonable to assume that the substrate concentration in the recirculation flow is low (S1 = S2)  38 because, at the exit of tank 2, most of the substrate will have been consumed, during a successful digestion. Since the main purpose of the recirculation flow is to increase the bacteria concentration in tank 2 (X2 = X3), the volumetric flow rate of the recirculation stream is much less than the volumetric flow rate of the influent or effluent, which can be assumed to be equal, i.e. v = v1. As a result, the biogas production rate can be further simplified into:  )( 30 SSvyieldRbiogas −×=         (42) which makes sense, because the overall biogas production should just be the product of yield times substrate consumed during the process.  4.3 Biogas utilization model Two options are presented for biogas utilization: cogeneration for heat and electricity production and upgrading to natural gas grade methane. In the case of co-generation an internal combustion engine is used to produce heat and power for electricity generation. The overall energy produced through combustion of biogas is calculated first:  combustionmethanecombustion CHmE η×∆×= 4&       (43) where Ecombustion is the energy produced through combustion (kJ/day), methanem&  is the mass flow rate of methane (kg/day), ΔCH4 is the heat of combustion for CH4 (kJ/kg) and η is the combustion efficiency (%). The heat (Ethermal) and electricity (Eelectrical) produced through co-generation are calculated as:  thermalcombustionthermal EE η×=         (44)  electricalcombustionelectrical EE η×=         (45) where ηthermal is the efficiency of thermal energy recovery (%) and ηelectrical is the efficiency of electrical energy conversion (%).  Heat is generated for use in the anaerobic digestion process in two ways. Firstly, heating is  39 required (Eheating) to bring the influent’s temperature up to the operating temperature. This can be calculated as:  )( feedoperatefeedwaterheating TTmCpE −××= &      (46) where Cpwater is the heat capacity of water (kJ/kg ℃), feedm&  is the mass flow rate of influent (kg/day), Toperate is the operating temperature (℃) and Tfeed is the influent temperature (℃). The influent’s heat capacity was assumed to be the same as that for water since most (85%~90%) of the feed is water. Additional heat is required to counteract losses due to natural convection from the outside of the digester (Eloss) to the environment, which is calculated as:  ))(( ambientoperatesoilsoilairairloss TTAUAUE −+=      (47) where Uair and Usoil are the overall heat transfer coefficients for heat transfer from the digester walls to the surrounding air and soil (kW/m2 ℃), Aair and Asoil are the surface areas of the above ground and underground portions of the digester (m2) and Tambient is the surrounding temperature. It is assumed that the ambient temperature of air and soil are equal. The heat of reaction is neglected due its relatively low value. As a result, the net thermal energy produced that is available for other heating purposes is:  lossheatingthermal net thermal EEEE −−=        (48)  The other option for biogas utilization is to upgrade the gas to pipeline-grade methane. However, in many cases a small portion of the biogas produced must be used to satisfy the thermal energy requirements of the digester, which are calculated as before. The amount of methane consumed for these heating requirements, Ethermal, is calculated as:  )( feedoperatefeedwaterheating TTmCpE −××= &      (49) ))(( ambientoperatesoilsoilairairloss TTAUAUE −+=      (50) lossheatingthermal EEE +=          (51)  40 The remaining biogas is sent to the methane purification unit.  4CH E m combustionthermal thermalburned methane ∆ = ηη &        (52) Thus, the amount of biogas treated through biogas upgrading system is:  methanemethane burned methanemethaneupgrade biogas V mmV %ρ && − =         (53) Where ρmethane is the density of methane gas (kg/m3) and V%methane is the volume fraction of methane in the biogas (%).  4.4 Model calibration and parameter estimation There are four parameters in the Lawrence & McCarty model: a, k, KS and b. The values of these parameters can be obtained from experimental data using graphical methods. From the Lawrence and McCarty model, the following equation is obtained:  SK kXSSS V v t S dt dS S + −=−= ∆ ∆ ≈ )( 0        (54) which can be modified to:  kSk K SSv XV S 11 )( 0 += −          (55) Therefore, by plotting )( 0 SSv XV −  vs. S 1  the slope equals k K S  and the intercept equals k 1 . From these, the values of KS and k can be calculated. Similarly, the following equation for the biomass mass balance:  X V vbX dt dS a dt dX −−−=          (56) can be simplified to:  )( V vb tX S a tX X +− ∆ ∆ −= ∆ ∆          (57) or  41 )()()( 00 V vb XV vSS a XV vXX +− − = −        (58) Therefore, the value of a and V vb +  can be obtained by plotting XV vXX )( 0−  vs. XV vSS )( 0 − . From these, the values of a and b can be calculated. It is important to note that these equations are setup to have positive values for the kinetic parameters. In the case where batch reactors are used in experiment, the value of V v can be estimated by reaction time in days.  However, since this project does not include any experimental work, the values of these parameters must be obtained through either literature review or calibration from existing biogas plants. In total, three sites were selected for the calibration (four cases).  Walford College Farm (CADDET 1997) Walford College Farm is a 260 hectare mixed farm owned and operated by Walford College near Shrewbury in the UK. There is a herd of 130 dairy cows and young dairy stock, 160 pigs and beef cattle, which together produce about 3,000 tonnes of manure annually. In 1990, the college decided to introduce an integrated farm slurry management system based on anaerobic digestion. In October 1994, an anaerobic digestion system with an engine-generator and a composting unit, at a total construction cost of 133,649 UK pound, was commissioned as part of a three-year demonstration project.  The Walford College Farm digester is a 335 m3 completely-mixed digester sitting above ground. In summer, 12 m3 of mixed slurry is fed into the digester daily at a hydraulic retention time of 16~20 days. This process yields 450 m3 of biogas per day, which produces 18.22 kW of electricity for 19.5 hours and enough heat to maintain the digester at a temperature of 35~37℃. The effluent’s liquid portion is passed to a 950,000 litre storage tank and then spread onto the grass fields due to its high nutrient value (2.32 kg nitrogen, 1.32 kg phosphate, and 5.3 kg potash  42 for each 1,000 litre). The effluent’s solid portion is made into compost for the college’s own use, and for sale to garden centers and other customers.  Linsbod Biogas Reactor in Pucking, Austria (Steffen 2005) Linsbod Biogas Reactor is a 12-year old farm-scale plant located in Pucking, Austria. Its feedstock is a mixture of poultry manure, poultry bedding and hog manure. The mixture is homogenized to a liquid with a solid content of 10~14%, and is fed into the digester four times a day at 1.5 m3 per time.  The reactor consists of an outer concrete cylinder 6 m in diameter and 9 m in height and an inner concrete cylinder 3 m in diameter and 11 m in height. The volume between the inner and outer cylinder has an airtight concrete roof and a volume of 270 m3. As biogas is produced in between the inner and outer cylinder, the pressure builds up until it is strong enough to push biogas into the inner cylinder. This system operates at 35~37℃, and produces 200~300 m3 of biogas per day with a methane content of 60~65%. Due to the sand in poultry manure, this digester requires sand cleanup every few years.  Davinde Biogas Plant in Denmark (Al Seadi 2000) Davinde biogas plant, built in 1987, is the first example of a centralized biogas plant established and operated by 11 farmers. The aim of this project is to produce and sell renewable energy from the supplied animal manures and straws supplied by farmers. The manures are from 3 pig farms and 3 cattle farms with small amounts of sludge and fish waste from 2 fish processing industries in the area.  The plant is small scale and rather simple, which keeps operational costs low. The digester is a single 750 m3 completely-mixed digester operating at mesophilic temperature range (36℃). It treats 28 tonnes of organic mixture per day (25 tonnes animal manure and 3 tonnes alternatives)  43 and produces 0.3 million Nm3 of biogas annually.  Table 9 is a summary of the inputs obtained from these four case studies. Among these parameters, manure flow rate, HRT and feed TS were used as inputs to the calculator; biogas production rate is the primary output for comparison. The digester size varies from 270 m3 to 1332 m3, which covers most of the farm-size digesters’ volumes. The influent dry material (DM) weight percentage varies from 5.5% to 14%, which is a typical range for wet-digestion. In the Davinde cases, the influent DM weight percentage is not given in the report. As a result, the default values within the calculator are used for calibration.  Table 9: General information of selected sites for calibration Manure Digester HRT Feed TS Effluent TS Biogas Methane Site m 3/day m3 Day w.% w.% m3/day v.% Walford College Summer 12 335 20 14 8.4 450 N.A. Walford College Winter 18 335 20 9 5.5 450 N.A. Linsbod 6 270 45 12 N.A. 250 62.5 Davinde 28 750 27 N.A. N.A. 882 N.A.  Table 10 is a list of the kinetic parameter values found from literature for the Lawrence & McCarty model. The value of KS is an indication of the degradability of the substrate. As shown in Table 10, a simple substrate such as acetate has a KS value of less than 400 mg/L. On the other hand, a more complex substrate such as the mixture of dextrose, bacto-tryptone and bacto-beef extract has a KS value of 13000 mg/L. For calibration purpose, the selected range is between 3000 mg/L and 13000 mg/L with a step size of 1000 mg/L. In the anaerobic digestion kinetic study by Barthakur et al. (Barthakur et al. 1991), they proposed the following model:  44 SKXk K K S S h S ++ = maxµµ           (59) where Kh is the substrate hydrolysis rate coefficient (1/day) and X is the concentration of active cell biomass (g/L). Comparing this model with Lawrence and McCarty’s model, the inhibitions are S h S KXk K K +  for Barthakur’s model and KS for Lawrence & McCarty’s model. From the values reported by Barthakur et al., the value of KS for Lawrence and McCarty’s model should be around 5000 mg/L (assuming 40% VSS reduction through anaerobic digestion).  The growth yield constant, a, is also the yield of biomass. As shown in Table 10, its range is 0.04-0.1 g/g with a step size of 0.01 g/g. The range for b, the decay rate, is 0.01-0.03 1/day with a step size of 0.001 /1day. The feasible range for k, the maximum rate of substrate utilization, is 0.9-1.6 g/g day with a step size of 0.1 g/g. A summary of the ranges and step sizes used in the calibration section of the calculator are shown in Figure 16.  Table 10: Values of kinetic parameters Substrate k KS a b Reference 1.07  13000 0.104 0.02 Dextrose, bacto-tryptone, bacto-beef extract daylbsVSS lbsCOD ×  L mgCOD  lbsCOD lbsVSS  day 1  Agardy et al. 1963 0.77-6.67   105-3180  0.04-0.11 0.01-0.015 Long chain fatty acid daygVSS gCOD ×  L mgCOD  gCOD gVSS  day 1  Palvostathis and Giraldo-Gomez 1991 1.33-70.6 22.5-630 0.14-0.17 6.1 Carbohydrates daygVSS gCOD ×  L mgCOD  gCOD gVSS  day 1  Palvostathis and Giraldo-Gomez 1991  45 Substrate k KS a b Reference 5.5-12.3 100-207 0.04-0.042 0.01-0.019 Acetate daygVSS gCOD ×  L mgCOD  gCOD gVSS  day 1  Lawrence and McCarty 1967 2.6-11.6 11-421 0.01-0.054 0.004-0.037 Acetate daygVSS gCOD ×  L mgCOD  gCOD gVSS  day 1  Palvostathis and Giraldo-Gomez 1991 N.A. 6.0-25.4 0.62-3.61 N.A. Acetate (thermo) N.A. L mgAcetate  molAcetate gCell  N.A. Mladenovska and Ahring 2000    Figure 16: Calibration range summary  The calibration is a trial and error process. The calculator repeats the calculation with every combination of the parameters and reports the combinations that provide a result (biogas yield) within the defined tolerance range. For the calibration of the default parameters, the defined ranges (shown in Figure 16) yield 1848 combinations for each of the four case studies.  From all these 7392 trials, 768 combinations yield results within the tolerance range. Among these 768 combinations, many of them appear repeatedly in many cases. The default set of  46 parameters must yield an acceptable result for all four case studies. Parameter combinations that satisfy this criteria are tabulated in Table 11. Since the value of KS has been calculated to be around 5000 mg/L from Barthakur’s model, the best set of kinetic parameter value is 0.026 1/day (b), 1.4 g/g day (k), 0.06 g/g (a) and 6000 mg/L (KS).  Table 11: Calibration results obtained from calculator b k a KS 1/day g/g day g/g mg/L 0.026 1.4 0.06 6000 0.025 1.2 0.06 7000 0.029 1.3 0.07 8000 0.028 1.3 0.07 9000 0.011 1.4 0.05 9000 0.012 1.1 0.06 10000 0.027 1.3 0.06 10000 0.011 1.1 0.06 11000 0.026 1.3 0.06 11000 0.019 1.3 0.08 12000 0.025 1.3 0.07 12000 0.014 1.3 0.06 13000 0.019 1.4 0.07 13000 0.024 1.3 0.07 13000  For a feed of mixed organic wastes, it is expected that the overall KS can be estimated as the sum of weighted KS values of every organic waste in the feed, which will be discussed later in 6.2 Discussion. Sample calculations of this method are included in Appendix H: Sample calculation  47 for CSTR with co-generation and Appendix I: Sample calculation for MPF with biogas upgrading.  4.5 Economic analysis method The economic calculation is done by a table of cash flow. For every year of operation, the operation cost is calculated as a fraction ( OCf ) of the capital cost of the plant:  OCfCapitalOC ×=           (60) During the first few years (n) of operation, the annual debt repayment (A) of principle (P) and interests (i) is calculated using the capital recovery factor:  1)1( ])1([ −+ + = n n i iiPA            (61) The revenue consists of two parts, the sales of electricity (or methane gas), 1S ; and the savings from heating, fertilizers and bedding materials, 2S . As a result, the before-tax cash flow (BTCF) is:  yCostElectricitOCSBTCF −−= 1       (62) Thus, the taxable income (TI) is:  AonDepreciatiBTCFTI −−=        (63) Annual tax is calculated as:   TITaxRateTax ×=           (64) Therefore, the after tax cash flow (ATCF) is:  TaxASBTCFATCF −−+= 2        (65)  Net present value (NPV) of the project is the sum of the present values of the annual cash flows, which are computed with the MARR (minimum acceptable rate of return) specified. In this study, MARR is assumed to be 10%. The smallest value of N (number of years of operation) that yields a  48 non-negative net present value is the discounted payback period (DPP), which measures the time required to recover the initial investment from the discounted production cash flows. Simple payback period (PP) is similar to DPP, except that the time value of money due to MARR is not taken into consideration.  Finally, the internal rate of return (IRR) is computed as the break-even interest rate or discount rate, i, that makes NPV of a project equal to 0, such that:  ∑ = = + N t t t i CF 0 0)1(            (66) where CFt is the tth year’s cash flow. In general, a project is economically viable if its net present value is positive or its internal rate of return is greater than MARR.  4.6 Interface design The calculator developed consists of three groups of files: supplementary files, Excel spreadsheets and graphical user interfaces (GUIs). As shown in Figure 17, the supplementary files are documentation files in the Help folder and in the Image folder are the GUI images used by the Visual Basic VBA program. These files can also be accessed directly as word files and image files.  Figure 17: Files included in the calculator    Figure 18: A list of spreadsheet used in the calculator   49 The MSExcel spreadsheets and the VBA code for the GUI are combined in the calculator itself as a Microsoft Excel file: CalculatorDevelope1020. The spreadsheets are used to store data and perform calculations. As shown in Figure 18, there are nine spreadsheets in total. Spreadsheet “Start” contains the macro to initiate the calculator when the MSExcel file is first accessed. As a result, users will not see the spreadsheets when the calculator is running. Spreadsheet “Feed” and “Rate” are used to store users’ inputs on feed properties and kinetic parameters. Spreadsheet “CSTR”, “PlugFlow” and “MPF” contain calculations for their corresponding type of digester. Spreadsheet “Energy Balance” contains calculations on co-generation and biogas upgrading. Spreadsheet “Econ” contains calculations for economical analysis. Finally, spreadsheet “Calibration” is used to help user select optimal kinetic parameters from their own experimental data.   Figure 19: Colour-coding of spreadsheet cells  Figure 19 is the screenshot of part of Spreadsheet “Feed”. As indicated in the spreadsheet, yellow cells contain users’ inputs and green cells are calculated results. The part shown in Figure 19 is used specifically for inputting feed properties by supplying the head-counts of each livestock available at the farm site. Once the numbers are entered, using default manure property data, all the properties for each manure waste and the final combined feed are calculated.  50   Figure 20: Interface organization diagram  There are many GUIs used in this calculator. The general links between each interface are shown in Figure 20. The diamonds indicate a selector interface where a user must select only one of the several possible following interfaces. The rectangles indicate a standard interface where certain inputs or outputs are requested or given. The black line indicates standard design mode. The red and green lines indicate calibration mode and quick-start mode. Sometimes the red and green lines merge with the black lines. This means that the upcoming interface is shared by different modes. At the end of “Calibration” and “Results” interface, there is an option to go back to the “Mode Selection” interface to start a new simulation. A more detailed demonstration of each  51 interface and how they are connected can be viewed in Appendix A: A case study using AD calculator.  4.7 Error handling There are two types of errors that may rise during the application of this software. The first type of error is an input error. If invalid data are input into the spreadsheet, they may cause calculation errors such as no-value (a character is used as a number in an equation) or divide-by-zero (the denominator of an equation is 0). Therefore, before users can go to the next interface, all inputs of the current interface are checked for these errors. Other error checks include for missing input values, input format check and input value check. The missing input error check will, for example, interrupt the program and give a warning if a user forgot to input the amount of animals on the farm site. The input format check detects any inputs that are not in the correct format. For example, this check will interrupt the program and give a warning if a user enters a word instead of a number for the desired digester HRT. The input value check is only available for some inputs. For example, if a user enters a combustion efficiency over 100%, this check will provide a warning. On the other hand, if a user enters the wrong ambient temperature, 250℃ instead of 25 ℃ for example, there is no check written to detect this error. This is because this error is very unlikely to cause serious calculation error that may crash the program. However, in all of the GUIs, “default” buttons are available to help users restore all inputs to their default values.  The second type of error is fatal error that causes the program or Excel to crash. Some unforeseen events may lead to this type of error, but it is not clear how to prevent these events from occurring. Several mechanisms are adapted for this project to improve the stability of the software. The first mechanism is to hide the spreadsheet while interfaces are running. Therefore, users cannot modify the same cell in two different ways, which may lead to inconsistency. The second mechanism is to only allow users to turn off the program at certain GUI. This prevents data from a previous case study over-writing the current case. Finally, if all these fail and a fatal  52 error does occur, the program will terminate its current application without saving any of the user inputs.                           53 5 DEMONSTRATION CASE STUDIES In order to test the stability, performance and accuracy of the calculator software, several case studies were conducted. Each case involves an operating digester about which sufficient information has been published in the literature. By inputting feed information for each case, the predicted performance of the digester is calculated using the calculator. These results are compared with the reported biogas production rate and digester volume. A more detailed guide of how to use the calculator to run a simulation can be viewed in Appendix B: A case study using AD calculator.  5.1 Baldwin Dairy Baldwin Dairy is located in Baldwin, Kansas. It has a herd size of 1,050, which produces about 113 cubic meter of manure and water waste at about 8% total solid. Initially, this site did not have a generator. Some biogas is used to heat the process and the rest is flared. In 2008, this farm has reached an agreement to supply biogas to a nearby farm and a greenhouse complex for heating. The AD system is a MPF digester designed by a local company in Wisconsin, Bob Komro. The design operating temperature is between 35℃ and 37℃; and the designed HRT is about 21 days.(Kramer and Krom 2008a)  Table 12: Baldwin Dairy case study results summary  Digester Type Temperature ℃ Cattle Flow Rate m 3/day HRT days Total Solid Biogas m 3/day Site MPF 35-37 1050 113 21 8% 3681 Simulation One MPF 35 1050 - 21 8% 1492 Simulation Two MPF 35 - 113 21 8% 2739  The information obtained for this site and the calculator’s results are shown in Table 12. For this  54 case study, the first simulation used animal count (1050 cattle) and calculated how much influent is available from default values. On the other hand, the second simulation directly used the influent flow rate provided in the report. Consequently, result from the second simulation is much closer to the reported value. For this case study, both simulations assume that the influent contains only cattle manure.  5.2 Bell Farms Bell Farms with 5,000 sows is located in Thayer, Iowa. During the first six months of operation, the total biogas produced was 64,250 m3. Its 80kW co-generation engine operates 77% of the time, and annually produces about $46,600 worth of electricity at $0.09 per kWhr. (Moser 2003)  Table 13: Bell Farms case study results summary  Digester Type Temperature ℃ Sow HRT days Total Solid Biogas m 3/day Site CM 37 5000 N.A. N.A. 357 Simulation CM 35 5000 26 8% 294  The information obtained for this site and the calculator’s results are shown in Table 13. The HRT used for simulation was a common value for CSTR, and the total solid was the default value for sow manure. The predicted biogas production rate is close to the reported biogas production rate. This simulation assumed that the influent contains only sow manure.  5.3 Deere Ridge Dairy Deere Ridge Dairy is located in Nelsonville Ohio. It currently has a herd size of 850. The average total solid content of the collected manure is about 8~9%. This site uses a 140kW Caterpillar net engine generator to produce electricity, which is sold to Alliant Energy. Captured heat from the engine is used for heating the digester, milk parlor and facility water. The AD system on this site  55 is a MPF digester designed by GHD, Inc. The design temperature is within mesophilic range, and the design HRT is 22 days. Passive mixing is done by recirculation of biogas at the bottom of the digester. (Kramer and Krom 2008a)  Table 14: Deere Ridge Dairy case study results summary  Digester Type Temperature ℃ Cattle HRT days Total Solid Electricity kW Site MPF Meso 850 22 8-9% 140 Simulation MPF 35 850 22 8.5% 123  The information obtained for this site and the calculator’s results are shown in Table 14. The estimated electricity production rate is close to the reported value. This simulation assumed that the influent contains only cattle manure.  5.4 Stencil Farm The Stencil Farm in Denmark has a herd size of around 1,300 heads, but only between 700 and 1000 heads regularly send manure to the digester. As a result, the volume and the total solid content vary depending on which barn the manure came from. The AD system at Stencil Farm is a below grade, concrete, straight plug-flow system designed by RCM Digesters, Inc.. This system operates at around 37℃ with a designed total solid of 9 to 12 percent. (Kramer and Krom 2008b)  The information obtained for this site and the calculator’s results are shown in Table 15. For the simulation, both of the herd size and the total solid values were assumed to be the average values of the site’s records (rounded up). The HRT was not given in the report, thus, a common value for PF digester (25 days HRT) was used. The site’s reported and the calculator’s estimated values of electricity production rate are in good agreement. This simulation assumed the influent contains only cattle manure.  56  Table 15: Stencil Farm case study results summary  Digester Type Temperature ℃ Cattle HRT days Total Solid Electricity kW Site PF 37 700-1000 N.A. 9-12% 123 Simulation PF 35 850 25 10.5% 95  5.5 Five Star Dairy Five Star Dairy is located in Elk Mound, Wisconsin with a herd size of 850 heads. The dairy entered into an agreement with Microgy, Inc. that Microgy would install the digester in 2000 with no cash outlay from the dairy owner; the owner would pay off the debt through biogas sales to Dairyland Power, which provides the generator. This Microgy AD system is an above ground, carbon steel CSTR digester. It has a design HRT of 20 days, and operates at 52℃. In addition to the dairy wastes on site, this system also treats about off-farm food wastes (roughly 10% of the total feed). (Environmental Law & Policy Center 2009)  Table 16: Five Star Diary case study results summary  Digester Type Temperature ℃ Cattle HRT days Total Solid Electricity kW Site CM Thermo 850 20 N.A. 775 Simulation CM 35 850 26 10% 78  The information obtained for this site and the simulation’s results are shown in Table 16. The digester on this site is operating at thermophilic temperature range, whereas the simulation can only run in mesophilic range at this point. As a result, the HRT used in the simulation was a common value (26 days) for CSTR in mesophilic range. The difference of electricity production between the reported and estimated values is large. However, in the previous two cases (Deere  57 Ridge Dairy and Stencil Farm), wastes from 850 cattle only require 140 kW and 123 kW engine respectively, which is quite close to the predicted 133 kW. Through literature review, AD processes from Microgy often have much oversized engines. As a result, the calculator’s result is reasonable, but further investigation on applying this calculator in thermophilic range should be conducted.  5.6 Predictive case study A fictitious 450-cow dairy farm located in the Lower Fraser Valley was used for performing overall technical and economic feasibility analyses, so as to assess project viability. Fresh cow manure is considered an ideal feedstock for anaerobic digestion since it has a balanced carbon-to-nitrogen ratio, a good buffering capacity and is rich in anaerobic bacteria (Electrigaz Inc., 2007 and 2008). Off-farm organic waste is not included in the influent (feedstock) to the anaerobic digester. Calculations were performed for CM (three different HRTs) and MPF (three different HRTs) systems. Inputs used in the calculator are 25 m3 manure/day (or, equivalent to 0.055 m3/cow.d, per ASAE Standards, 2008) at 12.5% TS. The TS will be diluted to 10.0% prior entering the digester to include the water used during manure collection. The results are tabulated in Table 17.  Table 17: A summary of 450 cattle case study Digester Type CM Digester MPF Digester HRT (days) 25 28 30 20 22 25 Digester volume (m3) 1005 1126 1207 644 708 804 Effluent TS (%) 8.21 5.49 4.74 5.77 5.02 3.73 VSS Reduction (%) 23.4 56.5 65.3 53.8 62.4 77.1 Biogas Production CO2  (tonne/day) 0.4 1.0 1.1 0.9 1.1 1.3 CH4  (tonne/day) 0.2 0.5 0.5 0.5 0.5 0.6  58 Co-generation Heat Production (106 kWhr/year) 0.237 0.925 1.102 0.908 1.080 1.383 Digester Type CM Digester MPF Digester Power Production (106 kWhr/year) 0.298 0.717 0.827 0.681 0.790 0.975 Power Purchased (106 kWhr/year) 0.015 0.036 0.041 0.034 0.040 0.049 Cow Power (kW/cow) 0.08 0.18 0.21 0.18 0.20 0.25 Biogas Upgrading Purified CH4 (m3/day) 163 567 671 556 659 836 Power Purchased (106 kWhr/year) 0.027 0.095 0.113 0.093 0.111 0.140  Several input parameters, such as electricity price, methane sale price, debt interest and savings, affect the economic analysis greatly. As Electrigaz’s study (Electrigaz Technologies Inc. 2008) suggested, at the current electricity price in the Lower Mainland, biogas upgrading is more profitable than co-generation. However, the market price of natural gas fluctuated during 2009 (http://tonto.eia.doe.gov/oog/info/ngw/ngupdate.asp), thus users must use the most updated prices and outlooks of natural gas for their economic analysis.  5.7 Predicted results and analysis of mixed wastes General assumptions are the same as the predictive case study (450 cows). In scenario No. 1, off-farm food waste is not included in the influent (feedstock) to the anaerobic digester. Then, simulation is extended to scenario No. 2, with food waste added to the feedstock, resulting in a mixture of 80% dairy manure and 20% food waste. Calculations were performed for CSTR and MPF, with different HRTs. Inputs and assumptions used in the calculator are summarized as follows: • Without food waste, manure/slurry generation is 25 m3/day (or equivalent to 0.055 m3/cow day); TS 12.5% (with 10% VSS). The manure will be diluted from TS 12.5% to TS 10.0%. • Digester operating temperature:  35oC (mesophilic)  59 • Average annual ambient temperature:  13.8oC • Digester configuration:  Diameter-to-length ratio is 1.5:5.0 • With food waste, the mixture has an original volume of 31 m3/d or tonne/day, and again diluted to TS 10%, resulting in an influent feed rate of 39 tonne/day. • Heat recovery efficiency: 50% • Power or electricity recovery efficiency: 40% • Combustion or engine efficiency: 90% • Utility fraction (percent co-generated power used to heat the digester): 5% • Heat recovery efficiency: 70% Predicted AD system performance results are summarized in Tables 18 and 19 for the two scenarios, dairy manure with food waste and dairy manure without food waste, respectively.  Table 18: Computed AD system performance for 450 cows with 20% food wastes CSTR MPF HRT HRT  HRT  HRT HRT  HRT   25 d 28 d 30 d 20 d 22 d 25 d Digester volume (m3) 1261 1412 1513 1009 1110 1261 Biogas Production CH4 production (tonne/day) 0.39 0.71 0.80 0.64 0.74 0.91 CO2 production (tonne/day) 0.71 1.30 1.46 1.17 1.36 1.68 Biogas yield (m3/tonne feed) 24.4 44.9 50.3 40.3 46.8 57.8 Co-generation Heat production (106 kWhr/year) 0.658 1.459 1.665 1.310 1.558 1.981 Power production (106 kWhr/year) 0.774 1.424 1.595 1.279 1.485 1.833 Engine size (kW) 89.6 164.8 184.6 148.1 171.8 212.1 Power per cow (kW/cow) 0.199 0.366 0.410 0.329 0.382 0.471 Power purchased (106 kWhr/year) 0.029 0.053 0.060 0.048 0.056 0.069  60 CSTR MPF HRT HRT  HRT  HRT HRT  HRT   25 d 28 d 30 d 20 d 22 d 25 d Biogas Upgrading Purified CH4 (m3/day) 415 886 1007 798 943 1192 Power purchased (106 kWhr/year) 0.096 0.197 0.223 0.177 0.209 0.262 Effluent TS (%) 7.38 5.04 4.40 5.61 4.85 3.52 VS (%) 77.7 66.6 61.5 70.1 65.1 51.4 VS reduction (%) 33.7 62.1 69.7 55.9 64.9 80.1  Table 19: Computed AD system performance for 450 cows without food wastes CSTR MPF HRT HRT  HRT  HRT HRT  HRT   25 d 28 d 30 d 20 d 22 d 25 d Digester volume (m3) 813 910 975 650 715 813 Biogas Production CH4 production (tonne/day) CO2 production (tonne/day) Biogas yield (m3/tonne feed) 0.07 0.14 7.30 0.23 0.43 22.9 0.28 0.51 23.0 0.26 0.48 25.4 0.30 0.55 29.5 0.37 0.68 36.4 Co-generation Heat production (106 kWhr/year) Power production (106 kWhr/year) Engine size (kW) Power per cow (kW/cow) Power purchased (106 kWhr/year) < 0 0.149 17.3 0.04 0.006 0.363 0.469 54.2 0.120 0.018 0.462 0.553 64.0 0.142 0.021 0.450 0.519 60.1 0.134 0.020 0.548 0.603 69.8 0.155 0.023 0.716 0.744 86.1 0.191 0.028  61 CSTR MPF HRT HRT  HRT  HRT HRT  HRT   25 d 28 d 30 d 20 d 22 d 25 d Biogas Upgrading Purified CH4 (m3/day) 2.48 232 290 283 340 439 Power purchased (106 kWhr/year) 0.006 0.055 0.068 0.065 0.078 0.099 Effluent TS (%) 8.73 5.93 5.17 5.51 4.75 3.43 VS (%) 76.9 65.3 60.0 62.6 56.4 39.1 VS reduction (%) 16.8 52.9 62.4 58.6 68.1 84.1  The computed results indicate that, among all configurations involved in the simulations (CM with HRT of 25, 28 and 30 days; MPF with HRT of 20, 22 and 25 days), a MPF system with HRT of 25 days gives best system performance. With mixed waste (80% dairy manure and 20% food waste), the methane production rate is 0.91 tonne/day, leading to power production of 212 kW, which is equivalent to 0.47 kW/cow. The corresponding biogas yield is 58 m3/tonne feed (wet basis). Percent volatile solids reduction is also the highest, at 80%, When compared to the digestion of dairy manure alone, expected biogas yield would be doubled, whereas power production would be greater by 2.5 times.  By comparison, Electrigaz Technologies Inc. (2007) presented a case study regarding biogas energy potential in their report. The fictitious feedstock comprises 30 tonne/day cow slurry (7% TS) and 20% by weight or 6.3 tonne/day fats oil and grease (FOG, 15% TS). Assuming biogas yield of 15.7 m3/tonne and 347.8 m3/tonne for manure and FOG respectively, the overall biogas yield was estimated to be 58.7 m3/tonne feed. The estimated power production was 293 kW (assuming power recovery efficiency is 40%). In a follow-up report (Electrigaz Technologies Inc. 2008), the feedstock comprises 88 tonne/day cow slurry (10% TS) and 24% by weight of food  62 waste (11 tonne/day, 23% TS) and FOG (10 tonne/day, 36% TS). Assuming biogas yields of 22.4, 71.7 and 361 m3/tonne for manure, food waste and FOG respectively, the overall biogas yield was again estimated to be 58.2 m3/tonne feed. This amount of biogas is equivalent to 250 m3/hr, which could power a 500 kW co-generation plant. This value is also deemed to be the minimum biogas production rate to justify a biogas upgrading plant. It shall be noted that the estimated results are dependant on the various key assumptions, including biogas yield and power recovery efficiency.  The major assumptions used in the economic analysis include the following: • Project life (period of analysis): 10 years • 70:30 equity/debt financing structure • Loan compound interest rate: 6% per annum • Minimum acceptable rate of return MARR: 10% • Electricity purchased at 5 cents/kWhr and sold at 9 cents/kWhr • Sales revenue is only due to power generated • No revenue from gate fees nor expenses related to the treatment of off-farm wastes • No revenue from carbon credits or government grants/incentives • Revenue due to biogas upgrading, processing of digestate to compost, and fiber recovery are not considered in this example • Tax rate: 13.5% (federal and provincial rates for small business) • No investment tax credits from SR&ED activities • Capital cost allowance (CCA rate, Class 43.1 Income Tax Act) for depreciable assets: 30% (for high efficiency AD co-generation systems, this rate is increased to 50% after the first year)  Results derived, as shown in Table 20, suggest that MPF systems are less expensive than CSTR systems. For co-generation, if the selling price of the electricity is at 9 cents per kWhr, none of the configurations investigated are economically feasible based on ATCF, since for all cases, net  63 present values are negative. However, if economic feasibility is based on BTCF, then the net present values associated with MPF systems having HRT of 20 to 25 days are positive, and hence the internal rates of return are greater than MARR of 10%. Under these circumstances, simple payback period of 7-8 years is achievable. This concluded that for a 450 cow farm (with 20% off-farm food wastes) located in the Fraser Valley region, a MPF system is the best choice.  Table 20: Results of economic analysis for 450 cows with 20% food waste CSTR MPF HRT  HRT  HRT  HRT   28 d 30 d 20 d 25 d Electricity (106 kWhr/year) 1.859 2.077 1.653 2.368 Electricity sale ($/year) 167,298 186,929 148,737 213, 099 BTCF ($/year) 94,970 109,205 107,710 156,701 Cost Capital cost ($) 1,376,845 1,476,600 758,579 1,039,175 Operating cost ($/year) 68,842 73,830 37,929 51,959 Electricity purchase ($/year) 3,485 3,894 3,099 4,439 Profitability Indicators Based on BTCF Net present value NPV, $ -353,700 -334,137 145,448 255,468 Internal rate of return IRR, % 1.0 2.1 15.9 17.5 Simple payback period PP, year 10 10 5 5 Based on ATCF Net present value NPV, $ -726,066 -736,435 -84,370 -63,876 Internal rate of return IRR, % <0 <0 6.1 7.9 Simple payback period PP, year N.A. N.A. 8 7   64 6 DISCUSSION AND CONCLUSIONS  6.1 Discussion  Table 21: Summary of power generation from anaerobic digestion of cow manure Power Generation (kW/cow) 1997-2002a 2002-2008b, c PF Digester 0.08-0.17 0.16-0.21d MPF Digester 0.15-0.23 0.16-0.28e CM Digester (CSTR) 0.15-0.23 0.23-0.32f a  USEPA - AgSTAR Handbook (http://www.epa.gov/agstar/resources/handbook.html) b  AgSTAR Program - Guide to anaerobic digesters (http://www.epa.gov/agstar/operational.html) c Cornell University – Manure management Program (http://www.manuremanagement.cornell. edu) d  RCM Digesters Inc/RCM International Inc. e mostly GHD Inc. f various suppliers and sites as shown in Appendix B: A list of AD technology suppliers and Appendix G: A list of active AD sites.  As shown in Table 21, CM digesters had the highest power generation per cow. Although MPF digesters from GHD generate less power per cow, their capital costs for farm sized operation are much lower than CM digesters. It is not yet clear what the maximum capacity of MPF digesters is and how well they perform treating food wastes, FOG or MSW. Consequently, centralized plants that treat a variety of organic wastes from surrounding communities still prefer completely mixed digesters due to the high feed loading rate. Considering the capital cost estimation model (Equation 28 and 29), a centralized digestion plant shared by its nearby farms and communities is very likely to be more profitable, but the transportation costs (the price of diesel fuel) will greatly  65 impact operating costs (Swanson 2005). Another advantage of investing in a centralized digestion plant is that the capital cost is shared by several owners, thus, the financial burden can be reduced significantly comparing to constructing one AD system on each individual farm. Although currently most AD sites in North America are constructed for single farm application, some community shared plants, such as Tillamook Digester, are already in operation. People that are interested in adapting AD process should look into the possibility of a shared digestion plant first.  The future trend of AD is to include organic wastes from many sources together with animal wastes. Some new AD plants are designed to treat organic wastes from municipal sources only. As shown in Table 3, the biogas yields of food and yard wastes are considerably higher than the biogas yields of animal wastes. Thus, a biogas plant that takes in only municipal organic wastes would produce much more biogas per tonne of wastes. However, as shown in Table 4, the nutrition values (N, P and K content) of animal wastes are generally higher than the nutrition values of municipal wastes. As a result, the effluent from treating animal wastes is a better fertilizer. Since AD process is quite flexible with the organic wastes input, most sites will load any organic wastes that do not interrupt the digester’s stability into their digesters to boost the biogas production. Consequently, co-digestion must be considered in the design of any anaerobic digesters.  Kinetic parameters of the Lawrence & McCarty model vary according to the organic waste composition of the feed. By assuming quasi-steady-state, Shuler and Kargi (Shuler and Kargi 2002) have illustrated how to determine the overall kinetic parameters of a mixture from its individual component’s kinetic parameters. The general concept is to assume rapid equilibrium or quasi-steady-state of an intermediate; and then through algebraic manipulation, rewrite the overall reaction to find the overall inhibition term, which is usually a function of each individual component’s inhibition. Another approach is proposed by O’Rourke (1968):  66 ∑ = −− + = n i iiii iiiS bkaHRT HRTbK S 1 , 1)( )1(         (67) According to Equation 67, the substrate concentration is the sum of each individual organic waste’s concentration after digestion. In most cases, it can be assumed that all the organic wastes share the same HRT. The challenge of applying these two methods is how to categorize the components of an organic waste mixture. It is convenient to use animal wastes, agricultural wastes, FOG etc. However, a more scientific and accurate way is to use proteins, fibers, fats, carbohydrates etc. as components of an organic waste mixture. Also, both methods will require individual inhibition or kinetic parameters for each organic waste source.  Furthermore, anaerobic digestion can be considered to have three stages: hydrolysis, acetogenesis and methanogenesis. Among these three stages, acetogenesis can be considered as intermediate, whereas hydrolysis experiences inhibition from initial substrates and methanogenesis experiences inhibition from the products of acetogenesis (CH3COOH) (Barthakur et al. 1991). It is beyond the scope of this project to determine the most accurate expression of the overall inhibition and other kinetic parameters from individual components. However, since anaerobic digestion in one digester is mostly carried out by three groups of bacteria, it is reasonable to use one set of values of a, k and b for the overall digestion.Thus, Equation 67 can be estimated as: ∑ = −− + = n i total iSi m Km bakHRT bHRTS 1 , 1)( )1( & &        (68) which means the KS of a mixture can be calculated as: ∑ = = n i total iSi mixtureS m Km K 1 , , & &           (69) Due to the scope of this project, there is not enough data to verify this estimation. However, Equation 70 is used in the calculator as a suggested KS value for a waste mixture of manure, food and FOG.   67 As shown in Table 17, the difference in biogas production between a CM with 25 days HRT and another with 28 days HRT are large. This is because according to the Lawrence & McCarty model, the value of HRT (a user input) will greatly affect biogas production and the biogas plant’s economic analysis. As shown in the substrate concentration calculation through the Lawrence & McCarty model: 1)( )1( −− + = bakHRT bHRTKS S           (70) HRT has direct effect on the effluent’s substrate concentration. Since biogas yield is calculated according to Equation 36, HRT also directly affects the biogas production rate. For the calibrated parameters, Equation 68 can be rewritten as:  1058.0 1026.06000 − + ×= HRT HRTS          (71)  Therefore, as shown in Figure 21, after 35~40 days, the effluent’s substrate concentration stabilizes. This suggests that a longer HRT (35~40 days) will have the highest biogas yield per tonne of organic wastes. However, as the total biogas yield increases, the required co-generation engine size also increases which according to Equation 28 and 29, will cause the capital cost to increase. In order to be economically feasible, the choice of HRT has to be a value that produces reasonable amount of biogas but does not lead to a very high capital cost. From the reports and sites encountered through literature review, for PF and CM digesters, a reasonable HRT is between 25 and 30 days for treating an influent that is primarily livestock manure.  It is also important to point out that biogas is not the only useful product from AD process. The solid portion of the effluent can be used as compost or bedding material for livestock. In the case of using the solids for composting, it may be beneficial to have a slightly longer HRT that further breaks down the solids. On the other hand, if the solids are used as bedding materials, it may be better to have a slightly shorter HRT that soften but not necessarily break down the fibers in the influent.  68   Figure 21: S/6000 vs. HRT  The capital cost model used in the calculator is developed from co-generation AD sites. The construction and operating costs of biogas upgrading is known to be more expensive than cogeneration (Electrigaz Technologies Inc. 2008), since boilers (thermal energy only) are much cheaper than co-generation. Due to the lack of reported data from biogas upgrading and boiler AD sites, capital cost models of combining these two biogas utilization with AD technologies cannot be developed. As a compromise, during the economic analysis, it was assumed that the capital costs of all three biogas utilization method are within the same magnitude, thus the capital cost of co-generation is used in all three cases. However, the energy production and/or upgraded methane production results are valid. Therefore, the estimated annual before and after tax incomes are still accurate. However, the capital cost (if biogas upgrading or boiler is the chosen biogas utilization method) and the payback period should be only used as a reference for comparison purpose.  6.2  Conclusions Anaerobic digestion offers one solution to help reduce GHG emissions while at the same time providing alternative energy. It is especially applicable in the Fraser Valley region, where  69 potentially 30 MW of energy can be generated with the additional benefits of reduced odour, GHG emissions and soil and water contamination from artificial fertilizers. As a result, it is necessary to educate local farm owners about AD technology and to enable them to estimate the benefits of adopting AD on their farm, hence the motivation for this calculator.  Although this AD calculator has limited temperature range, it allows the user to input different feed types, select from several bioreactor configurations and it provides reasonable estimations of biogas production rate, the energy produced and most importantly the capital costs and revenue of adopting AD technology. So as to produce a calculator compatible with both PC and Mac computers and to have an accessible algorithm, this software is constructed on Microsoft Excel spreadsheets with simple user interfaces coded via VBA. This software has surpassed most of the AD technology assisting tools available at the moment.  Since experimental work was not part of this project, all the data used for calibration and testing were obtained from reports, articles and websites gathered during a literature review. Therefore the model kinetic parameters used by the calculator are only relevant for the types of feeds used in the studies used to calibrate the model. Since, in some future applications, feeds other than manure will become common, the calculator can be used to derive model kinetic parameters for these other feeds. More experimental data are needed to allow calibration of a more accurate calculator applicable to many feed types. Therefore, results provided by this calculator should be considered as the average values that best represent the performance and capital cost of biogas plants specified by users during the simulation. Users should keep in mind that this software does not provide enough information to be used as an actual design of a biogas plant. The intent of this software is to show people how beneficial and how much it costs to adapt AD technology with fairly accurate and realistic values, which means that in some cases, it will not be feasible or beneficial to apply AD technology.   70 On the other hand, this software helps more sophisticated users. The algorithms, parameters (with their default values) and logics of all the calculation involved can be viewed and modified in spreadsheet. For people with the knowledge of more accurate and site-specific data or a specific idea of a new digester configuration, they can modify some parameter values via the GUI or directly in the appropriate cells in the spreadsheet to improve the performance of the calculator. So far, there has been no kinetic-based AD technology simulation program that allows users to view all the details and calculations behind the user interfaces.  It should also be noted that the capital cost of typical farm-size biogas plant is still a burden to most farm owners. Support from government officials and suppliers in any form, such as grants, permits or co-ownership, are extremely important to encourage farm owners to upgrade their current manure management systems to a more economically beneficial and environmental friendly technology.  6.3 Further research Through this project, several interesting questions are not clearly answered. These questions are generally related to the microbiology of anaerobic digestion and the growth pattern and conditions of the bacteria involved. However, if answered, they could enhance the performance of the calculator.  At this point, the calculator can still be improved with further researches. Aside from the Lawrence & McCarty model, the Chen & Hashimoto model is also a popular kinetic model for AD. Further development of the calculator should include both models and allow advanced users to select the preferred model for their simulations. The temperature effects on the kinetic parameters of both models are not fully investigated in this project. A more complete calculator should be able to adjust these parameters based on the operating temperature from users’ inputs. Finally, the current calculator requires HRT as a user input. However, as shown in Equation 16  71 and 21, it is also reasonable to use conversion instead of HRT. This could be another feature to be added into the calculator.  The second question is if digester configurations have effects on the values of the kinetic parameters. The answer is most likely to be no if there is only one group of bacteria involved. However, since there are three groups of bacteria involved in anaerobic digestion, the kinetic parameters’ values for digester configurations that mix and separate the three groups are expected to be different. The difference in HRT requirement between CSTR and MPF seem to support this idea.  The third question is how to provide access of this program to farmers and other users. Offering free online download is one quick method, but through a progress discussion, it was suggested that an online accessible version of the calculator should be developed. This could be done through some coding on a server that provides interface compatible with internet cookies but still performs the same calculations as the current software on the server. As a result, with the advanced graphics handling, the software can be more entertaining and user friendly, which is very important in educating people about AD technology and its benefits.  The last and perhaps the most important question is how to accurately predict the capital costs of any combination of AD technologies and biogas utilization methods. The prices of similar designs from different vendors are very likely to be different, but as illustrated in this project, it is possible to produce a model for estimation. 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Volume 41, No. 5 (2006).                       79 APPENDICES  Appendix A: A case study using AD calculator This case study is done for the Baldwin Dairy case shown in 6.0 Case Studies. The given information are: 1050 cattle, 8% total solid in feed, 35℃~37℃ operating temperature, MPF digester, 21 days HRT and the biogas production rate, 3681 m3/day.  The first interface is shown in Figure A1. Users can choose “Start” to continue or “Quit” to terminate the current application. Figure A2 is the following interface, which is a disclaimer. Although the information has not been filled yet, users must select agree to continue.   Figure A1: Welcome interface   80  Figure A2: Disclaimer interface   Figure A3: Mode interface  81  Figure A3 is the mode selector (interface sequencing can be viewed in Figure 11). In this case study, since the only feed information we know is the herd size, we can select “Digester Design” then select “Input via Animal Count” or just select “Quick Start” here. Either way will bring us to the interface show in Figure A4.   Figure A4: Input via Animal Count  After entering 1050 cattle, press confirm to continue or press previous to go back to the previous interface. Figure A5 is the next interface, parameter input. Users can modify any of the parameters used for this simulation, and they can also press “Reset” to restore the parameters to their default value. In this case, since we are not given any information on the parameters, we will use the default parameters and press “Confirm” to continue.   82  Figure A5: Parameter input   Figure A6: Digester selection  83  Figure A6 is the digester selection interface. In this case, we select “Mixed Plug Flow Digester” then press “Confirm” to continue. The interface shown in Figure A7 is the design interface for mixed plug flow digester. In here, users can modify the designed HRT, initial bacteria concentration and desired total solid. In this case, we will modify the design HRT to 21 days and desired total solid to 8% according to the information given, then press “Confirm” to continue.   Figure A7: MPF interface  In the energy production method or biogas utilization method interface, we will select co-generation, even though this particular site does not have either co-generation or biogas purification on site. Figure A9 shows the temperature profile and thermal parameters used for co-generation energy production. The yearly temperature profile is for Lower Mainland, BC only. Users in other region must adjust the values accordingly.   84  Figure A8: Energy production method   Figure A9: Temperature profile interface  85   Figure A10: Co-generation parameters interface  Figure A10shows the parameters involved for performing the energy balance for co-generation. Depends on the dimension and position of the digester, users can adjust the radius to length ratio and the underground surface area fraction of the digester. The electricity utility covers the entire electricity requirement by the digestion systems, such as pumping, sensors, mixing and etc.  Figure A11 and Figure A12 shows the parameters involved for capital estimation and economic analysis. The capital cost of the plant is already calculated and shown. From this value, users can adjust their debt information, which is defaulted at 30% of the capital cost with 6% interests and 5 years payback. Users can also adjust the methane sale price, electricity sale and purchasing prices. As discussed in the discussion section, the market price of methane fluctuates a lot, it is very important for users to check out the most recent local price. The annual savings can be from bedding materials, local heating, and fertilizers; in some cases, this can also include carbon  86 credits or tax returns. Since this value varies from one site to another, the default value is 0.  Figure A11: Capital estimation input interface  Figure A13 shows the final results, in this case, the biogas production rate is 3616 m3/day (comparing to the reported value 3681 m3/day). As previously assumed, without including any savings as part of the revenue, the payback period of this investment is estimated to be 14 years. If savings from bedding materials, local heating and fertilizer are included, the payback period will be more competitive. Finally, users can press “Detail” to export the whole simulation into another spreadsheet for later viewing or press “View Excel” to view the current case in spreadsheet without the interfaces. Users can also start a new case by selecting “New Case” or terminate the current application by selecting “Quit”   87  Figure A12: Economic analysis input interface   Figure A13: Brief outputs interface  88 Appendix B: A list of AD technology suppliers    89 Appendix C: Material balance of CSTR   Figure C1: Flow diagram of CSTR model  General assumptions: 1. Volumetric flow rates of feed and effluent are the same. 2. Gas phase contains only CO2 and CH4. 3. Bacteria concentration in the feed is zero.  Mass balance on inert, N and P:  ieffifeed mm ,, && =            (C1)  ][][ iviv efffeed =            (C2) Thus, the weight fraction of component i (inert, N or P) is:  eff feed m iv & ][              (C3) Effluent substrate concentration:  1)( )1( −− + = bakHRT bHRTKS Seff          (C4)  90 Effluent biomass concentration:  ActivitybHRT SSa X efffeedeff 1 1 )( + − =         (C5) where Activity is the portion of bacteria that is active (%). Gas phase mass flow rate calculation:  feedefffeedCOCO vSSYm )(22 −=&         (C6)  feedefffeedCHCH vSSYm )(44 −=&         (C7)  42 CHCOGas mmm &&& +=           (C8) Gas phase volumetric flow rate:  4 4 2 2 CH CH CO CO Gas mm v µµ && +=           (C9) Volumetric composition of CO2 and CH4 in gas phase:  Gasi i i v mV µ & =%            (C10) The overall mass flow rate of effluent:  Gasfeedeff mmm &&& −=           (C11) Ammonia production rate:  feedefffeedNHNH vSSYm )(33 −=&         (C12)          91 Appendix D: Material balance of PF digester   Figure D1: Flow diagram of PF model  General assumptions: 1. Volumetric flow rates of feed and effluent are the same. 2. Gas phase contains only CO2 and CH4. 3. Bacteria concentration in the feed is zero.  Mass balance on inert, N and P:  ieffifeed mm ,, && =            (D1)  ][][ iviv efffeed =            (D2) Thus, the weight fraction of component i (inert, N or P) is:  eff feed m iv & ][              (D3) Effluent substrate concentration:  b SSKSS SSak HRT efffeedSefffeed efffeed − −+− − = )ln(ln)( )(1     (D4) Since there is no analytical solution obtained from this equation, the value of Seff is solved numerically via goal-seek function provided by Microsoft Excel. Effluent biomass concentration:  92  ActivitybHRT SSa X efffeedeff 1 1 )( + − =         (D5) where Activity is the portion of bacteria that is active (%). Gas phase mass flow rate calculation:  feedefffeedCOCO vSSYm )(22 −=&         (D6)  feedefffeedCHCH vSSYm )(44 −=&         (D7)  42 CHCOGas mmm &&& +=           (D8) Gas phase volumetric flow rate:  4 4 2 2 CH CH CO CO Gas mm v µµ && +=           (D9) Volumetric composition of CO2 and CH4 in gas phase:  Gasi i i v mV µ & =%            (D10) The overall mass flow rate of effluent:  Gasfeedeff mmm &&& −=           (D11) Ammonia production rate:  feedefffeedNHNH vSSYm )(33 −=&         (D12)           93 Appendix E: Material balance of MPF digester   Figure E1: Flow diagram of MPF model General assumptions: 1. Volumetric flow rates of feed1, feed2 and effluent are the same. 2. Gas phase contains only CO2 and CH4.  Mass balance on inert, N and P:  ieffifeedifeed mmm ,,2,1 &&& ==          (E1)  ][][][ 21 iviviv efffeedfeed ==          (E2) Thus, the weight fraction of component i (inert, N or P) is:  2 1 ][ feed feed m iv &              (E3) eff feed m iv & ][1              (E4) Feed2 biomass concentration:  akHRT feedfeed eXActivity X 5.012 1 =        (E5) where Activity is the portion of bacteria that is active (%).  94 Effluent biomass concentration:  2feedeff XX =            (E6) Feed2 substrate concentration:  a XX SS feedfeedfeedfeed 12 12 − −=         (E7) Effluent substrate concentration:  HRTkXSS feedfeedeff 22 5.0−=         (E8) Gas phase mass flow rate calculation:  11 )(22 feedefffeedCOCO vSSYm −=&         (E9)  11 )(44 feedefffeedCHCH vSSYm −=&         (E10)  4221 CHCOGasGasGas mmmmm &&&&& +=+=       (E11) 1211211 )()( 42 feedfeedfeedCHfeedfeedfeedCOGas vSSYvSSYm −+−=&  (E12) 12122 )()( 42 feedefffeedCHfeedefffeedCOGas vSSYvSSYm −+−=&   (E13) Gas phase volumetric flow rate:  4 4 2 2 21 CH CH CO CO GasGasGas mm vvv µµ && +=+=        (E14)  4 4 2 2 121121 1 )()( CH feedfeedfeedCH CO feedfeedfeedCO Gas vSSYvSSY v µµ − + − =  (E15)  4 4 2 2 1212 1 )()( CH feedefffeedCH CO feedefffeedCO Gas vSSYvSSY v µµ − + − =   (E16) Volumetric composition of CO2 and CH4 in gas phase:  Gasi i i v mV µ & =%            (E17) The overall mass flow of feed2:  112 Gasfeedfeed mmm &&& −=          (E18)  95 The overall mass flow rate of effluent:  Gasfeedeff mmm &&& −= 1           (E19) Ammonia production rate:  11 )(33 feedefffeedNHNH vSSYm −=&        (E20)                         96 Appendix F: A list of substrates’ biogas yields  Substrate Biogas Yield Units Ref. Dairy Manure 0.04-0.9 Smil 1982, pp 352, 353 Swine Manure 0.26-1.05 Smil 1982, pp 352, 353 Poultry Manure 0.1-0.56 Smil 1982, pp 352, 353 Pig Slurry 0.25-0.50 Seadi 2001, p 13 Cattle Slurry 0.20-0.30 Seadi 2001, p 13 Poultry Slurry 0.35-0.60 Seadi 2001, p 13 Whey 0.35-0.80 Seadi 2001, p 13 Grass Silage 0.56 Seadi 2001, p 13 Straw 0.15-0.35 Seadi 2001, p 13 Food Waste 0.50-0.60 Seadi 2001, p 13 Fruit Waste 0.25-0.50 m 3/kg VSS Seadi 2001, p 13 Cattle Slurry 25 Birse 1999, p18 Pig Slurry 26 Birse 1999, p18 Laying Hen Litter 90-150 Birse 1999, p18 Broiler Manure 50-100 Birse 1999, p18 Food Processing Waste 46 Birse 1999, p18 Pig Slurry 15 Monnet 2003 Yard Waste 69-90 Beck 2004 Yard Waste & Food Waste 89-102 Beck 2004 Potato Processing Waste 850 Linke 2006 Soup Processing Waste 112 Zhang et al 2007 Cafeteria Waste 150 Zhang et al 2007 Kitchen Waste 53 m 3/tonne feed Zhang et al 2007  97 Substrate Biogas Yield Units Ref. Fish Farm Waste 472 Zhang et al 2007 Grease Trap 275 Zhang et al 2007 Sheep Waste 26 Patel 2006 Goat Waste 26 Patel 2006 Poultry Waste 120 Patel 2006 Fat 1390 WestStart-CALSTART 2004 Proteins 650 WestStart-CALSTART 2004 Carbohydrates 840 WestStart-CALSTART 2004 Cow Manure (9%TS) 25 Electrigaz Technologies 2007 Pig Manure (7%TS) 25 Electrigaz Technologies 2007 Potato/Vegetable Wastes (10%TS) 60 Electrigaz Technologies 2007 Corn/Grass Silage (25%TS) 175 Electrigaz Technologies 2007 Food Waste (20%TS) 225 Electrigaz Technologies 2007 Fats and Grease (50%TS) 500 Electrigaz Technologies 2007 Cow Manure  25 Preusser 2006 Pig Manure  35 Preusser 2006 Potato/Vegetable Wastes 70 Preusser 2006 Corn/Grass Silage 200 Preusser 2006 Food Waste 175 Preusser 2006 Fats and Grease  980 Preusser 2006 Cow Manure  25 Kramer and Krom 2008b Pig Manure  30 Kramer and Krom 2008b Potato/Vegetable Wastes 39 Kramer and Krom 2008b Corn/Grass Silage 185 Kramer and Krom 2008b Food Waste 265  Kramer and Krom 2008b  98 Substrate Biogas Yield Units Ref. Fats and Grease  961  Kramer and Krom 2008b   99 Appendix G: A list of active AD sites  Farm and Location Number of cows Manure Generation m3/cow.d Co-digestion feedstock Reactor type Supplier Biogas production m3/d Biogas yield m3/t Power Generation  kW     kW/cow Year Blue Spruce VE 1200   MPF GHD   240 0.20 07 Green Mountain  1050   MPF GHD 3270  300  07 Montagne  1200     3740  300  07 Pleasant Valley  1950     6230  600  06 AA NY 600   HPF 1 RCM 1214 35.7 130 0.21 Emerling  1200   HPF RCM   230 0.19 Patterson  1000  Cheese whey CSTR RCM   250 0.25 05 Ridgeline  525  Milk products waste   9700 73.5 120 0.23 01 Sunnyside  6100   MPF GHD   1600 0.27 08 Cayuga regional enterprise  1255  Food waste, FOG, potato wastewater sludge CSTR EcoTech Solutions and GBU 6110  625 0.50 08 Baldwin WI 1050 0.143  MPF 2 Komro 3680 28   06 Clover Hill  1250   MPF GHD   300 0.24 07 Double S  1100 0.13      200 0.18 04 Gordondale  850 0.16     40 140 0.16 02 Crave Brothers  800 0.14 Cheese whey 10% CSTR    230 0.29 07 Five Star  850  Food waste (esp. FOG) 10% CSTR Microgy   750 0.89 05 Green Valley  2100 0.20  CSTR Biogas Direct   600 0.29 07 Lake Breeze  2550 0.21 Corn syrup waste     600 0.24 06 Norwiss  1240  Food waste 10% CSTR Microgy   850 0.68 06  100 Farm and Location Number of cows Manure Generation m3/cow.d Co-digestion feedstock Reactor type Supplier Biogas production m3/d Biogas yield m3/t Power Generation  kW     kW/cow Year Suring  950 0.12  CSTR Ambico   250 0.26 06 Vir-Clar  1200 0.10 On-farm organic waste CSTR Biogas Direct   350 0.29 04 Haubenschild MN 850   HPF RCM   135 0.16 99 Scenic View MI 2200  Syrup stillage CSTR Phase 3/ Biogas Direct 13460  700 0.32 05 Van der Haak4 WA 1100a 750b  20% food and fish processing waste MPF GHD   285a 450b 0.26 0.60 05 Qualco Energy  2000  Food waste/whey   5750  450 0.23 08 G DeRuyter  3500   Flush system PF GHD 12420  1200 0.34 08 Tillamook #1          #2 OR 2000 2000   HPF RCM   250 300  07 Brabaker PA 900   CSTR RCM 2060  160 0.18 Dovan  400   HPF RCM 1250  100 0.25 Fair Winds  650   HPF RCM 1160  140 0.21 Hill Crest  1150   HPF Team Ag 1390  130 0.11 Mains  600   CSTR EMG   90 0.15 Mason Dixon 5  2300   HPF Energy Cycle   600 0.25 Penn Englad  800   CSTR RCM/ Team Ag 1420  130 0.16 Reingrid  800   CSTR RCM   130 0.16 Wanner’s  400   CSTR RCM 1720  160 0.40  101 Farm and Location Number of cows Manure Generation m3/cow.d Co-digestion feedstock Reactor type Supplier Biogas production m3/d Biogas yield m3/t Power Generation  kW     kW/cow Year Wild Rose  880 0.17 Food waste CSTR Microgy   750 0.85 05    102 Appendix H: Sample calculation for CSTR with co-generation   Figure H-1: Overall calculation flow chart  Feed Property Calculation  User inputs:   25 /manurem tonne day=& 325 /manurev m day=   6 /foodm tonne day=& 36 /foodv m day=  %10=feedTS   Default values:  %23=foodTS  %21=foodVSS  %80 , =reductionfoodVSS   %10=manureTS  %8=manureVSS  %60 , =reductionmanureVSS   Mixed feed property:  foodmanuremix mmm &&& +=    25 6 31 /mixm tonne day= + =&  103  foodmanuremix vvv +=   daymvmix /31625 3 =+=   mix foodfoodmanuremanure mix m mTSmTS TS & && ×+× =   %52.12 31 6%2325%10 = ×+× =mixTS   mix foodfoodmanuremanure mix m mVSSmVSS VSS & && ×+× =   %52.10 31 6%2125%8 = ×+× =mixVSS   mixmix reductionfoodfoodfoodreductionmanuremanuremanure reductionmix mVSS VSSmVSSVSSmVSS VSS & && × ××+×× = ,, ,   %7.67 31%52.10 %806%21%6025%8 , = × ××+×× =reductionmixVSS  In order to achieve the targeted 10% TS prior entering digester, dilution is required. The feed’s property after dilution is:  feed mix mix feed TSTS VSSVSS ×=   %4.8%10 %52.12 %52.10 =×=feedVSS   mix feed mix feed mTS TS m && ×=   12.52% 31 38.8 / 10%feed m tonne day= × =&  water mixfeed mixfeed mm vv µ && − +=   daymv feed /8.381 318.3831 3=−+=   Kinetic Parameter Estimation  Default values:  104  gga /06.0=  1026.0 −= dayb  gdaygk /2.1=    LmgK manureS /6000, =   LmgK foodS /600, =  3 , 25 /biogas manureY m tonne=   4 , 60%CH manureF =  3 , 200 /biogas foodY m tonne=   4 , 60%CH foodF =  Weighted KS of the final feed:  mix food foodS mix manure manureSfeedS m m K m m KK & & & & ×+×= ,,,    LmgK feedS /495531 6600 31 256000 , =×+×=  Modified yield coefficients:  mix foodbiogasfoodmanurebiogasmanure feedbiogas m YmYm Y & && ,, , ×+× =   3 , 25 25 6 200 58.9 / 31biogas feed Y m tonne× + ×= =  feedbiogasmix foodCHfoodbiogasfoodmanureCHmanurebiogasmanure feedCH Ym FYmFYm F , ,,,, , 44 4 × ××+×× = & &&   %60 9.5831 %602006%602525 ,4 = × ××+×× =feedCHF   reductionmixmix CHfeedCHfeedbiogas CH VSSVSS FY Y , ,, 44 4 × ×× = µ   gVSSgCHEY CH /337.0%7.67%52.10 368.0%609.58 44 = × −×× =   reductionmixmix COfeedCHfeedbiogas CO VSSVSS FY Y , ,, 24 2 )1( × ×−× = µ   gVSSgCOEY CO /619.0%7.67%52.10 387.1%)601(9.58 22 = × −×−× =   Digester Mass Balance  User inputs:  105  dayHRT 28=   Default values:  %90=Activity   Substrate mass balance:  1)( )1( −−×× ×+× = bkaHRT HRTbKS Seff  LmgSeff /297301)026.02.106.0(28 )28026.01(4955 = −−×× ×+× =   feed feedfeed v mVSS S &× =0   3 0 8.4% 38.8 0.084 / 84000 / 38.8 S tonne m or mg L×= =  ActivityHRTb SSa X effeff 1 1 )( 0 × ×+ −× =   LmgX eff /2093%90 1 28026.01 )2973084000(06.0 =× ×+ −× =   Biogas generation:  44 )( 0 CHefffeedCH YSSvm ×−×=&   4 138.8 (84000 29730) 0.337 0.71 / 1000 1000CH m tonne day= × − × × = × &   22 )( 0 COefffeedCO YSSvm ×−×=&   2 138.8 (84000 29730) 0.619 1.3 / 1000 1000CO m tonne day= × − × × = × &  Energy Balance  User inputs:  5:5.1: =LengthRadius  %10=iedSurfaceBur   Default values:  %90=combusionη  %50=thermalη  %30=electricalη   106  CmWU air °= 2/53.1  CmWU soil °= 2/63.0  %5=Utility   CToperate °= 35   CT °= 61  dayPeriod 901 =  CT feed °= 251,   CT °= 102  dayPeriod 602 =  CT feed °= 252,   CT °= 143  dayPeriod 603 =  CT feed °= 253,   CT °= 204  dayPeriod 1504 =  CT feed °= 254,   Energy generation through co-generation:   combustionmethanecombustion CHmE η×∆×= 4&  kWEcombustion 411%90243600 1000891 16 100071.0 =× × ×××=    thermalcombustionthermal EE η×=  kWEthermal 205%50411 =×=    electricalcombustionelectrical EE η×=  kWEelectrical 123%30411 =×=   electricalUtility EUtilityE ×=   kWEUtility 17.6123%5 =×=   Digester surface area:  HRTvV feed ×=   310922839 mV =×=   3/1 2 )( LengthRadius VUnitLength ×× = pi   mUnitLength 14.3) 55.114.3 1092( 3/12 =××=   107  22 2)(2 UnitLengthLengthRadiusRadiusUnitLengthArea ××××+×××= pipi   222 60314.355.114.32)5.114.3(14.32 mArea =××××+×××=   Energy balance:  )1( iedSurfaceBurAreaUUA airair −××=   CWUAair °=−××= /830%)101(60353.1   iedSurfaceBurAreaUUA soilsoil ××=   CWUAsoil °=××= /38%1060363.0   waterfeedoperatefeedairsoiloperateperiodheating CpTTmUAUATTE ×−×++×−= )()()( 1,1, 1 &   kWE periodheating 44360024 10002.4)2535(39 1000 1)83038()635( 1, = × ××−×+×+×−=    Similarly, the heating requirements of the other three time periods are calculated to be:  kWE periodheating 412, =  kWE periodheating 373, =  kWE periodheating 324, =   4,3, 2,1, )()( )()( 43 21 PeriodEEPeriodEE PeriodEEPeriodEEE periodheatingthermalperiodheatingthermal periodheatingthermalperiodheatingthermal net thermal ×−+×−+ ×−+×−=   150)32205(60)37205(60)41205(90)44205( ×−+×−+×−+×−=netthermalE   kWhrkWdayOrE netthermal 144864060360=   )( 4321 PeriodPeriodPeriodPeriodEE electricalsaleelectrical +++×=   kWhrkWdayOrE saleelectrical 106272044280)150606090(123 =+++×=   )( 4321 PeriodPeriodPeriodPeriodEE Utilitypurchaseelectrical +++×=   kWhrkWdayOrE purchaseelectrical 533092221)150606090(17.6 =+++×=  Economics  User inputs:  %30=Debt  %6=Interest  yearDebtTime 5=   108  Default values:  CapitalOperation %5=  CapitalHardware %10=   kWhrySaleElectricit /$09.0=  kWhryPurchaseElectricit /$08.0=   %13=TaxRate  %13=MARR  yearSavings /$0=   Revenue calculation:  yPurchaseElectricitESavingsySaleElectricitEIncome purchaseelectrical sale electrical ×−+×=   yearIncome /$9138008.053309009.01062720 =×−+×=   Capital calculation:  kWEEngine electrical 123==   6304.046594 EngineCapital ×=   967845$12346594 6304.0 =×=Capital   Debt yearly payback:  DebtTime DebtTimeInterestDebtCapitalDebtPay )1( +×××=   yearDebtPay /$91.75491 5 )15%6(%30967845 = +××× =  The table of annual cash flow, which varies from one year to another, is constructed according to Equation 63 to 67. The payback period is the first year that yields a positive overall present value.          109 Appendix I: Sample calculation for MPF with biogas upgrading   Figure I-1: Overall calculation flow chart  Feed Property Calculation  User inputs:   25 /manurem tonne day=& 325 /manurev m day=   6 /foodm tonne day=& 36 /foodv m day=  %10=feedTS   Default values:  %23=foodTS  %21=foodVSS  %80 , =reductionfoodVSS   %10=manureTS  %8=manureVSS  %60 , =reductionmanureVSS   Mixed feed property:  foodmanuremix mmm &&& +=    25 6 31 /mixm tonne day= + =&  110  foodmanuremix vvv +=   daymvmix /31625 3=+=   mix foodfoodmanuremanure mix m mTSmTS TS & && ×+× =   %52.12 31 6%2325%10 = ×+× =mixTS   mix foodfoodmanuremanure mix m mVSSmVSS VSS & && ×+× =   %52.10 31 6%2125%8 = ×+× =mixVSS   mixmix reductionfoodfoodfoodreductionmanuremanuremanure reductionmix mVSS VSSmVSSVSSmVSS VSS & && × ××+×× = ,, ,   %7.67 31%52.10 %806%21%6025%8 , = × ××+×× =reductionmixVSS  In order to achieve the targeted 10% TS prior entering digester, dilution is required. The feed’s property after dilution is:  feed mix mix feed TSTS VSSVSS ×=   %4.8%10 %52.12 %52.10 =×=feedVSS   mix feed mix feed mTS TS m && ×=   12.52% 31 38.8 / 10%feed m tonne day= × =&  water mixfeed mixfeed mm vv µ && − +=   daymv feed /8.381 318.3831 3=−+=   Kinetic Parameter Estimation  Default values:  111  gga /06.0=  1026.0 −= dayb  gdaygk /2.1=    LmgK manureS /6000, =   LmgK foodS /600, =  3 , 25 /biogas manureY m tonne=   4 , 60%CH manureF =  3 , 200 /biogas foodY m tonne=   4 , 60%CH foodF =  Weighted KS of the final feed:  mix food foodS mix manure manureSfeedS m m K m m KK & & & & ×+×= ,,,    LmgK feedS /495531 6600 31 256000 , =×+×=  Modified yield coefficients:  mix foodbiogasfoodmanurebiogasmanure feedbiogas m YmYm Y & && ,, , ×+× =   3 , 25 25 6 200 58.9 / 31biogas feed Y m tonne× + ×= =  feedbiogasmix foodCHfoodbiogasfoodmanureCHmanurebiogasmanure feedCH Ym FYmFYm F , ,,,, , 44 4 × ××+×× = & &&   %60 9.5831 %602006%602525 ,4 = × ××+×× =feedCHF   reductionmixmix CHfeedCHfeedbiogas CH VSSVSS FY Y , ,, 44 4 × ×× = µ   gVSSgCHEY CH /337.0%7.67%52.10 368.0%609.58 44 = × −×× =   reductionmixmix COfeedCHfeedbiogas CO VSSVSS FY Y , ,, 24 2 )1( × ×−× = µ   gVSSgCOEY CO /619.0%7.67%52.10 387.1%)601(9.58 22 = × −×−× =  Digester Mass Balance  User inputs:  dayHRT 22=   112  Default values:  %90=Activity  LmgX /10000 =   Substrate and bacteria mass balance:  20 1 HRTka eff eActivity XXX ×× ×==   LmgeXX eff /2453%90 1000 2 222.106.0 1 =×== ××   feed feedfeed v mVSS S &× =0   3 0 8.4% 38.8 0.084 / 84000 / 38.8 S tonne m or mg L×= =  a XXSS 0101 − −=   LmgS /59783 06.0 10002453840001 = − −=   21 HRTXkSS effeff ××−=   LmgSeff /274032 2224532.159783 =××−=   Biogas generation:  44 )( 0 CHefffeedCH YSSvm ×−×=&   4 138.8 (84000 27403) 0.337 0.74 / 1000 1000CH m tonne day= × − × × = × &   22 )( 0 COefffeedCO YSSvm ×−×=&   2 138.8 (84000 27403) 0.619 1.36 / 1000 1000CO m tonne day= × − × × = × &  Energy Balance  User inputs:  5:5.1: =LengthRadius  %10=iedSurfaceBur   Default values:  113  %90=combusionη  %70=thermalη  %30=electricalη   CmWU air °= 2/53.1  CmWU soil °= 2/63.0  %5=Utility   CToperate °= 35  3/27.0 mkWhrPPSA =   CT °= 61  dayPeriod 901 =  CT feed °= 251,   CT °= 102  dayPeriod 602 =  CT feed °= 252,   CT °=143  dayPeriod 603 =  CT feed °= 253,   CT °= 204  dayPeriod 1504 =  CT feed °= 254,   Energy generation through co-generation:   combustionmethanecombustion CHmE η×∆×= 4&  kWEcombustion 429%90243600 1000891 16 100074.0 =× × ×××=    thermalcombustionthermal EE η×=  kWEthermal 300%70429 =×=  Although there is no electricity generated in biogas upgrading, its value must still be calculated according to co-generation’s default values in order to determine the utility power requirements.   electricalcombustionelectrical EE η×=  kWEelectrical 129%30429 =×=   electricalUtility EUtilityE ×=   kWEUtility 4.6129%5 =×=   Digester surface area:  HRTvV feed ×=   38582239 mV =×=   114  3/1 2 )( LengthRadius VUnitLength ×× = pi   mUnitLength 9.2) 55.114.3 858( 3/12 =××=   22 2)(2 UnitLengthLengthRadiusRadiusUnitLengthArea ××××+×××= pipi   222 5149.255.114.32)5.19.2(14.32 mArea =××××+×××=   Energy balance:  )1( iedSurfaceBurAreaUUA airair −××=   CWUAair °=−××= /708%)101(51453.1   iedSurfaceBurAreaUUA soilsoil ××=   CWUAsoil °=××= /32%1051463.0   waterfeedoperatefeedairsoiloperateperiodheating CpTTmUAUATTE ×−×++×−= )()()( 1,1, 1 &   kWE periodheating 40360024 10002.4)2535(39 1000 1)70832()635( 1, = × ××−×+×+×−=    Similarly, the heating requirements of the other three time periods are calculated to be:  kWE periodheating 372, =  kWE periodheating 343, =  kWE periodheating 304, =  Comparing the four values, the highest one is used as the heating requirement, which is satisfied through a boiler. 4 , 1 4 CH E m thermalcombusion periodheatburn CH ∆×× = ηη &  4 40 24 3600 16 0.0985 / 90% 70% 891 1000 1000 burn CHm tonne day × × = × = × × × &  burn CHCH pure CH mmm 444 &&& −=  4 0.74 0.0985 0.6415 /pureCHm tonne day= − =& feedCHCH pure CHupgrade biogas F m v ,44 4 × = µ &   115 daymvupgradebiogas /3.15721000%6068.0 6415.0 3 =× × =   )()( 4321 PeriodPeriodPeriodPeriodPvEE PSAupgradebiogasUtilitypurchaseelectrical +++××+=   kWhrE purchaseelectrical 20812324)150606090()27.024 3.15724.6( =×+++××+=  Economics  User inputs:  %30=Debt  %6=Interest  yearDebtTime 5=   Default values:  CapitalOperation %5=  CapitalHardware %10=   3 4 /$25.0 mSaleCH =  kWhryPurchaseElectricit /$08.0=   %13=TaxRate  %13=MARR  yearSavings /$0=   Revenue calculation:  )( 4321 4 4 4 PeriodPeriodPeriodPeriod m v CH pure CHsale CH +++×= µ &   yearmv saleCH /65.339617)150606090(68.0 10006415.0 3 4 =+++× × =   yPurchaseElectricitESavingsSaleCHvIncome purchaseelectrical sale lCH ×−+×= 44   yearIncome /$57.6825408.0208123025.065.339617 =×−+×=   Capital calculation:  kWEEngine electrical 129==   8753.09.7635 EngineCapital ×=   537353$1299.7635 8753.0 =×=Capital   Debt yearly payback:  DebtTime DebtTimeInterestDebtCapitalDebtPay )1( +×××=   116  yearDebtPay /$53.41913 5 )15%6(%30537353 = +××× =  The table of annual cash flow, which varies from one year to another, is constructed according to Equation 63 to 67. The payback period is the first year that yields a positive overall present value.                        

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