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Modeling of steady state heat release, oxygen profile and temperature profile in circulating fluidized… Ju, Dale Wen-Ching 1995

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MODELING OF STEADY STATE HEAT RELEASE, OXYGEN PROFILE AND TEMPERATURE PROFILE IN CIRCULATING FLUIDIZED BED COMBUSTORS By Dale Wen-Ching Ju B.A.Sc., University of British Columbia, 1989  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA May 1995 © Dale Wen-Ching Ju, 1995  In  presenting  degree at the  this  thesis in  University of  partial  fulfilment  of  the  requirements  for  an advanced  British Columbia, I agree that the Library shall make it  freely available for reference and study. I further agree that permission for extensive copying of this thesis for department  or  by  his  or  scholarly purposes may be granted her  representatives.  It  is  by the head of  understood  that  copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  Jft  t  11  ABSTRACT  A computer model, using the Monte Carlo method, was developed to predict heat release, oxygen profiles and temperature profiles in Circulating Fluidized Bed (CFB) combustors. The model includes initial devolatilization of the coal feed, a correction in the evolved volatiles region based on the plume model, char combustion, an oxygen mass balance to determine the oxygen profile, and an energy balance to detenriine the temperature profile. The highly non-linear energy balance equation includes conduction, particle and gas convection and radiative heat transfer terms. A number of studies were conducted to observe how the model's prediction changes with superficial gas velocities of 6 m/s and 7 m/s, and solids recirculation rates of 15, 30 and 50 kg/m s, for both the UBC CFB and the Studsvik CFB. 2  A validation of the model's partial pressure of oxygen profile predictions compared to experimental data was made for the UBC CFB test case.  Ill  TABLE OF CONTENTS  Page ABSTRACT  ii  LIST OF TABLES  vii  LIST OF FIGURES  viii  ACKNOWLEDGMENT  xi  CHAPTER 1 INTRODUCTION 1.1  1  DESCRIPTION OF CIRCULATING FLUIDIZED BEDS  CHAPTER 2 PREVIOUS MODELS OF CFBs  6 11  2.1  INTRODUCTION  11  2.2  OVERALL MODELS  11  2.3  HYDRODYNAMICS  13  2.3.1  Senior's Hydrodynamic Model  15  2.3.1.1 Assumptions  16  2.4  HEAT TRANSFER  22  2.4.1  Film Theory  22  2.4.2  General Comments on the Film Theory  24  2.4.3 Penetration Theory  25  2.4.4  28  Gas Film - Emulsion Packet Theory  2.4.5 Radiative Heat Transfer 2.4.5.1  Chen's Model  28 31  2.4.5.2 Radiative Contribution in Heat Transfer Model 2.4.6 Heat Transfer in Overall Model  34 35  CHAPTER 3 MODELLING OF HEAT RELEASE. OXYGEN PROFILES 3.1  AND TEMPERATURE PROFILES OF CFBs  37  MODEL ASSUMPTIONS  37  iv 3.2  DESCRIPTION OF MODEL APPROACH AND SUBROUTINE EQUATIONS  39  3.2.1  39  Devolatilization  3.2.2 Plume Model  42  3.2.3  44  Char Combustion  3.2.4 Monte Carlo Approach 3.2.5  Comparison of Monte Carlo Approach with Analytic Technique  3.3  47 48  3.2.6 Monte Carlo Approach within the Program  48  3.2.7  Heat Transfer Model  52  3.2.7.1  52  Cell to Cell Heat Transfer  3.2.7.2 Differences with Chen's Model  54  3.2.7.3  56  Finite Difference Formulation  3.2.7.4 Wall to Cell Heat Transfer Equation  58  3.2.7.5  58  Cyclone and Standpipe  DESCRIPTION OF MODEL PROGRAM  59  3.3.1  59  Input and Output Files  3.3.2 Program Steps  61  3.3.3  64  Model Tuning  3.3.4 Discontinuity of Temperature Profile  66  3.3.5  69  Convergence  3.3.6 Numerical Stability of Partial Pressure of 3.3.7  Oxygen Profile  69  RunTime  72  CHAPTER 4 DISCUSSION OF RESULTS AND VALIDATION 4.1 4.2  4.3  ...75  INTRODUCTION  75  4.1.1  76  Initial Test Runs  STUDSVIK CFB  79  4.2.1  General Description  79  4.2.2  Sensitivity Analysis  79  4.2.3  Results  83  4.2.3.1 Heat Release Profiles  83  4.2.3.2 Partial Pressure Profiles  87  4.2.3.3  92  Temperature Profiles  UBC PILOT CFB  95  4.4  4.3.1  Description  95  4.3.2  Test Run  98  4.3.3  Results  98  VALIDATION  CHAPTER 5 CONCLUSION AND RECOMMENDATIONS  108 Ill  5.1  CONCLUSION  Ill  5.2  RECOMMENDATIONS FOR FUTURE WORK  112  NOMENCLATURE  113  REFERENCES  115  APPENDLX A  PROGRAM LISTING  119  APPENDIX B  SAMPLE INPUT FILES  154  B. 1  HYDRODYNAMIC INPUT FILE LISTING  154  B.2  USER INPUT FILE LISTING  157  OUTPUT FILES  158  shO  159  shl  165  sh2  171  sh3  177  sh4  183  sh5  189  sh2b  195  sh700  201  sh900  207  uhO  213  sh6  219  LIST OF VARIABLES  225  D. 1  INPUT FILE FROM HYDRODYNAMIC MODEL  225  D.2  USER INPUT FILE.  226  D.3  PROGRAM VARIABLES  226  APPENDIX C  APPENDIX D  vi  APPENDIX E  E N T H A L P Y B A L A N C E SPREADSHEETS  Vll  LIST OF TABLES  Page Table 1.1  Comparison of CFB With Other Types of Boilers [Basil and Fraser, 1991]  Table 2.1  Predictions of Overall CFB Models [Sanderson, 1993]  Table 3.1  Comparison of Predicted Burnout Times with Particle Diameters  Table 3.2  4 12  46  Description of Convergence Loops and Tolerances used in Program  61  Table 4.1  Characteristics of Highvale Coal [Grace et al., 1989]  81  Table 4.2  Particle Size Distribution of Highvale Coal and Bed  81  Table 4.3  Major Parameters in the Sensitivity Analysis Cases  Table 4.4  (Studsvik CFB, base case shO)  82  Parameters in Baseline Test  99  VI11  LIST OF FIGURES  Page Figure 1.1  Coal Production and Consumption in Canada, 1986 [Energy, Mines and Resources Canada, 1987]  Figure 1.2  Heat Transfer Surfaces of a CFB Boiler [Basu and Fraser, 1991]  Figure 1.3  2 5  A Typical Commercial CFB [Kullendorf and Andersson, 1985]  8  Figure 1.4  Various CFB Configurations [Yang, 1992]  9  Figure 1.5  Common Non-Mechanical Valves [Yang, 1992]  Figure 2.1  Illustration of Solids Distribution in a CFB Riser [Senior, 1992]  Figure 2.2  10  14  Regions and Flow Patterns Assumed by a 2-Zone Core/Annulus Modelling Approach in a CFB [Brereton, 1987]  Figure 2.3  Observed Gas and Solid Flow Patterns in a Sharp CFB Riser Exit [Brereton, 1987]  Figure 2.4  17 20  Apparent Suspension Density Profile as a Function of Riser Exit Geometries [Senior, 1992]  21  Figure 2.5  Film Theory  .23  Figure 2.6  Penetration Theory  26  Figure 2.7  Gas Film - Emulsion Packet Theory  29  Figure 2.8  Radiative Heat Transfer Model [Chen, 1988]  32  Figure 2.9  Schematic Cross-Section of a Membrane Waterwall Surface [Bowenetal., 1991]  Figure 3.1  36  Devolatilization Time as a Function of Temperature Predicted by Equation 3.1  40  Figure 3.2  Plume Model of Volatiles Dispersion [Stubington, 1980]  43  Figure 3.3  Probability of a Particle Leaving a Cell  50  Figure 3.4  Particle Paths in a Riser  51  ix Figure 3.5  Direction Convention used in Cell to Cell Heat Transfer Equation  55  Figure 3.6  Model Algorithm  60  Figure 3.7  Net Mass Flowrate From the Core to the Streamer vs Height for the UBC CFB  Figure 3.8  67  Temperature Distribution of Core Cells (before and after curve smoothing)  Figure 3.9  Temperature Convergence for Various Initial Temp. Guesses (Studsvik CFB, case shO)  Figure 3.10  71  Partial Pressure of 02 vs Height (Studsvik CFB, Combustion of Highvale Coal with U=7 m/s and Gs=15 kg/m2s)  Figure 4.1  70  Temperature Profile of Case shO (for various initial temperature guesses)  Figure 3.11  68  73  Pressure of Cells at a Height of 1 m Above Secondary Air (Studsvik CFB; case shO)  78  Figure 4.2  Schematic of Studsvik CFB [Kobro, 1984]  80  Figure 4.3  Volatiles Heat Release vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2) ....84  Figure 4.4  Char Heat Release vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2) ....85  Figure 4.5  Char Heat Release vs Height (Combustion of Highvale Coal with U = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5) ....86  Figure 4.6  Changes in Core Density in Secondary Zone for Various Solids Recirculation Rates - Primary Zone Density = 315 kg/m3 (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  Figure 4.7  Char Heat Release Distribution vs Height (Combustion of Highvale Coal, Studsvik CFB; cases shO and sh3)  Figure 4.8  88 89  Partial Pressure of 02 vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2) ....90  Figure 4.9  Partial Pressure of 02 vs Height (Combustion of Highvale Coal with U = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5) ....91  Figure 4.10  Temperature vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  Figure 4.11  Temperature vs Height (Combustion of Highvale Coal with  93  U = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5) Figure 4.12  94  Comparison of Wall Temperature Gradient at a Height of 2.4 m Above Secondary Air with Other Experimental and Theoretical Works  96  Figure 4.13  Simplified Schematic Diagram of UBC Pilot-Scale CFB  97  Figure 4.14  Volatile Heat Release (Combustion of Highvale Coal with U = 7 m/s and Gs = 30 kg/m s)  100  2  Figure 4.15  Char Heat Release (Combustion of Highvale Coal with U = 7 m/s and Gs = 30 kg/m s)  101  2  Figure 4.16  Char Heat Release for Various Mean Particle Diameters (UBC CFB, Combustion of Highvale Coal with U = 7 m/s).. 103  Figure 4.17  Partial Pressure of O2 vs Height (Combustion of Highvale Coal with U = 7 m/s and Gs = 30 kg/m s)  104  2  Figure 4.18  Temperature vs Height (Combustion of Highvale Coal with U = 7 m/s; UBC CFB; case uhO)  Figure 4.19  106  Enthalpy Balance for Core Cell at Height = 3.36 m (UBC CFB, case uhO)  Figure 4.20  107  Oxygen Concentration Profiles for Highvale Coal Conditions: Zhao (T=891 °C, U=8.26 m/s, 0 influegas=2.9%) 2  Anthony (T=830 °C, U=7 m/s, 0 influegas=3.7%) 2  Agarwal & Davidson (T=830 °C, U=7 m/s, 0 influegas=3.7%) 2  109  xi  ACKNOWLEDGMENT  I would like to thank Dr. Clive Brereton for his continual guidance and encouragement throughout the course of this work. The success of this thesis could not have been achieved without his invaluable insights and support. I would also like to thank Dr. John Grace, Dr. Jim Lim and Dr. Serge Julien for their prompt comments given the short notice. Thefinancialsupport of ABB Combustion is also gratefully acknowledged. Most of all, thank You Jesus! To You be the Glory, forever.  1  CHAPTER 1 INTRODUCTION  In Canada, the major uses of coal are for the generation of electricity and for coking coal in the steel industry. Because coal is very expensive to transport compared to its energy value, its popularity as an energy source is usually only for the provinces with substantial coal reserves. In addition to transportation costs, environmental concerns are also a factor in coal's competitiveness. Combustion of coal releases sulfurous gases, NOx, unburnt trace elements [Energy, Mines and Resources Canada, 1987], and more carbon dioxide than the combustion of natural gas. Since 1973, coal production in Canada has steadily increased.  In 1985, coal  production was estimated to be 60.7 million tonnes, 9 4 % of which was mined in Western Canada. Presently, coal is Canada's third largest mineral export, after oil and natural gas. Coal consumption as a fuel in power generation is mainly in four provinces, Alberta, Saskatchewan, Ontario and Nova Scotia, with Alberta consuming the largest percentage at 47%.  In fact, 9 2 % of Alberta's electrical energy production is from the consumption of  coal. See Figure 1.1 [Energy, Mines and Resources Canada, 1987]. The future outlook of coal consumption shows Canada with a large remaining reserve of coal, which is 1.5 times as large as oil and gas reserves. At the present rate of coal production, the proven reserves will last more than 100 years. The major competition for thermal coal is from nuclear sources, since nuclear energy production releases little or no gas emissions. Therefore, the challenge in using thermal coal is to develop more cost effective clean coal technologies. Circulating Fluidized Bed Boilers (CFBBs) have a number of advantages over other solid fuel fired boilers.  Some of these advantages include fuel flexibility, high  combustion efficiency, in-situ and low cost sulphur removal, low NOx  emissions and load  turndown capabilities. In addition, CFBs are part of some advanced cycles, such as  2  Figure 1.1  80000  Coal Production and Consumption in Canada, 1986 [Energy, Mines and Resources Canada, 1987]  COAL M CANADA, 1986.  60000  40000 \ -  20000 H  D0MESTIC PRODUCTION  CONSUMPTION  3  topping cycles, which have higher cycle efficiency. Less coal is used for the same amount of thermal energy production; therefore, less carbon dioxide is released. There are very good gas-solid and solid-solid mixing in CFBs and there are many inert solids present in the bed; therefore, fuels that enter CFBs quickly mix with the bed solids without a significant drop in the bed temperature. This results in CFBs* ability to burn many different fuels without the support of auxiliary fuel. Compared to bubbling beds, which have combustion efficiencies of 90% to 96%, CFBs have a combustion efficiency of approximately 97.5% to 99.5% [ Basu and Fraser, 1991]. The high combustion efficiencies are mainly due to good gas-solid mixing and the fact that unburnt fuel is returned back into the riser. Sulphur capture in CFBs is also better than in bubbling beds. CFBs can capture approximately 90% of the sulphur dioxide released during combustion, using less sorbent than in bubbling beds, where in both cases the beds are made up of sorbent. Sulphur capture reaction is slow; therefore, the longer residence time of particles in the CFB, approximately 3 to 4 sec, makes it more effective compared to 1 to 2 sec. in an average combustion zone. CFBs also have low NOx emissions.  CFBs have the capability to provide the  combustion air in stages. Fuel nitrogen is usually released with the volatiles near the base of the riser. If not enough oxygen is supplied in the primary air, the fuel nitrogen will form molecular nitrogen before it reaches the secondary air and form NOx.  Once molecular  nitrogen is formed, it will not normally form NOx at the relatively low CFB temperatures of850 °C. Finally, the ability to control heat absorption allows the CFB to respond quickly to changes in loads. Therefore, CFBs are known to have good turndown capabilities. All of the mentioned advantages make CFB's ideal for certain operations, depending on the type of fuel available and environmental concerns. Table 1.1 shows a comparison of a typical CFB with other types of boilers.  4  Table 1.1 Comparison of CFB With Other Types of Boilers [ Basu and Fraser, 1991]  Stoker  Bubbling  CFB  Pulverized  Height (m)  0.2  1-2  15-40  27-45  U(m/s)  1.2  1.5-2.5  4-8  4-6  Excess air (%)  20-30  20-25  10-20  15-30  Grate Heat Release Rate  0.5 - 1.5  0.5-1.5  3-5  4-6  Coal size (mm)  6-32  0-6  0-6  Turndown ratio  4: 1  3: 1  3-4:1  85-90  90-96  95-99  99  400 - 600  300 - 400  50 - 200  400 - 600  none  80-90  80-90  small  Characteristics  (MW/m2)  Efficiency (%) NOx emission (ppm) S02 capture (%)  <0.001  There are several possible locations and arrangements of heat transfer surfaces in a typical CFB boiler, some of which are shown in Figure 1.2 [ Basu and Fraser, 1991]. Generally, heat is removed through vertical membrane wall surfaces, located around the outer reactor wall above the secondary air. For large commercial CFBs, additional internal heat transfer tubes may be added in the reactor or heat may be removedfromthe cyclone or external heat exchangers. In order to design an appropriate CFB, designers need to know the heat transfer coefficients for varying operating condition; however, experimental data for CFB operations are few and fundamental understanding of CFBs trails considerably behind commercial advances, making scale-up from pilot plant data a difficult task. Therefore, there is a need for a better understanding of the hydrodynamics and heat transfer mechanism in CFBs.  5  Figure 1.2  FLUIOIZIHO AIR  Heat Transfer Surfaces of a CFB Boiler [ Basu and Fraser, 1991]  ASH  (  6  CFBs dynamics are complex and many variables affect heat transfer to the membrane walls, some of which include particle size distribution, thermal conductivity of the particle and gas, heat capacity of the particle and gas and wall surface temperature, just to name a few. There are actually more than 31 variables that affect heat transfer in CFBs [Wu, 1989]. It is the goal of this thesis work to develop a model to predict heat release, partial pressure of oxygen profiles and temperature profiles in a CFB given the geometry and hydrodynamic properties of the CFB and the physical and chemical properties of the fuel. This model will also be used to observe changes in the CFB's operating conditions when variables such as superficial gas velocity and solids recirculation rate are changed. This model will aid in selecting the appropriate locations for heat transfer surfaces in CFBs, so that a CFB unit can be optimized for turndown and fuel flexibility. This thesis consists of the results of a literature search into various overall models of CFBCs heat transfer and hydrodynamics, including a description of Senior's hydrodynamic model, described in chapter 2. Chapter 3 consists of a detailed discussion of a model, which was developed in this thesis to predict heat release and heat transfer in CFBs. In addition, this chapter includes a discussion of the various assumptions and convergence problems encountered throughout the model's development stages. And finally in chapter 4, there is brief discussion of the test results from the model and a qualitative comparison of the predicted results with measured experimental data for the UBC CFB. Thefindingsfromthis research work are then summarized in chapter 5.  1.1  Description of Circulating Fluidized Beds CFBs are a subset offluidizationoperations, called fast fluidization, that lie  between turbulentfluidizationand pneumatic transport regimes.  In other words, the  superficial gas velocity through the bed is larger than the transport velocity of the  7  particles, but is small enough that some particles travel downwards or fall back in a region close to the outer wall of the CFB. Figure 1.3 shows a schematic of a typical CFB. A CFB consists of a "riser", where combustion principally occurs. It is a tall column of relatively small cross sectional area compared to stoker and bubbling bed boilers. Combustion air is normally split into a primary and a secondary air feed. The primary air enters the base of the riser and the secondary air is injected anywhere from 1 m to 10 m above the base. The region below the secondary air ports is usually called the primary zone and the region above the primary zone is called the secondary zone. The superficial gas velocity in the primary zone ranges from 2 m/s to 6 m/s. In the secondary zone, gas velocities rangefrom5 m/s to 10 m/s. The total height of the riser can range anywherefrom10 m to 20 m or higher, and the mean particle size is approximately 50 p.m to 500 urn. There are many different arrangements of CFB systems. A few of the more common configurations can be seen in Figure 1.4. Solids in a CFB are comprised mainly of ash, sand during startup and fresh calcined and spent sorbent. There is considerable carryover of particles from the riser, depending on the exit geometry. Therefore, solid separators such as cyclones are used to separate the solidsfromthe riser exit gas stream. The solidsfromthe cyclone are returned continuously through a return leg near the base of the riser. Most return legs include a non-mechanical valve such as L-valve, J-valve, V-valve and seal pot, shown in Figure 1.5. Non-mechanical valves do not contain any moving parts. The solids that flow through the return leg are controlled by aeration and the geometry of the pipe. The primary zone can be designed to have different geometries, such as a tapered or a constant cross-sectional area, which will affect the acceleration of particles in the primary zone as well as fuel mixing.  8  Figure 1.3  A Typical Commercial CFB [Kullendorf and Andersson, 1985]  CAS  HOT  PRIMARY AIR 40-10%  9  Figure 1.4  Various CFB Configurations [Yang, 1992]  Expanded Riser  CFB with Seal Pot & Expanded Section  CFB with Mechanical  Valve  \7» Slow Bed  L-Valve  CFB with Slow Bed a n d L—Valve  SI  LT ft  External Fluid Bed Heat Exchanger  • CFB with External Heat E x c h a n g e r  10  Figure 1.5  Common Non-Mechanical Valves [Yang, 1992]  Solids  Solids  Solids  -Aeration  -Aeration  -Aeration  Fluidizing Gas Loop-Seol  J-Valve  L-Valve 1  Solids  Solids  1  Solids  -Aeration  V  Aeration  Fluidizing Gas  Fluidizing Gas Reverse  Seal  V-Valve  Seal Pot  11  CHAPTER 2 PREVIOUS M O D E L S OF CFBs  2.1  INTRODUCTION There have been several models of fluidized beds and CFBCs developed within  the last 10 years. A summary of fluidized bed models can be found in [Saxena et al., 1981] and a summary of CFB models can be found in [Sanderson, 1993]. These models describe various fluidized bed phenomena, in order to gain a better understanding of CFB operations and to predict transient behavior and control of disturbances. A practical model can be as complex as the power of one's computing system; however, a more complex model does not necessarily mean a more accurate one. In fact, the philosophy of modeling is to include only enough detail to adequately predict the important parameters, since it is usually unrealistic to study all possible parameters. Therefore, deciding the level of complexity needed to obtain an adequate model is highly subjective and depends on what variables the model intends to predict.  2.2  OVERALL MODELS Overall models of CFBC are complex in nature, since there are many  interrelated processes taking place. Generally, a complete overall model will include hydrodynamics, combustion reactions and heat transfer. In addition, the cyclone, particle size distribution, attrition, agglomeration and exit/inlet geometries should be taken into account.  /  Several overall models, listed in Table 2.1 [Sanderson, 1993], will be briefly described.  The assumptions that each model has made in regards to their  hydrodynamics and heat transfer models will be mentioned in the following sections. These models vary in complexity and in the variables they predict, such as  12  hydrodynamics, combustion, pollutant emissions, temperature and response to disturbances. Model 1 focuses mainly on predicting combustion efficiencies, while model 2 is concerned with predicting operating parameters such as hydrodynamics, heat transfer, chemical reaction kinetics and cyclone performance. Model 3 focuses on predicting pollutant emissions and model 4 considers hydrodynamics and oxygen concentration profiles. Models 7 and 9 are steady state models while models 5, 6, 8 and 10 describe static and dynamic behaviors.  Table 2.1  Predictions of Overall CFB Models [Sanderson, 1993]  1  2  3  4  5  6  7  8  9  10  Hydrodynamics  X  X  X  X  X  X  X  X  X  X  Combustion  X  X  X  X  X  X  X  X  X  X  Emissions  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  Heat Transfer Miscellaneous (e.g. L-valve, additional heat exchanger)  13  Models: 1 2 3 4 5 6 7 8 9 10  Ahlstrom Pyroflow (1987) Basu (1991) 1ST (1993) Haider & Datta (1993) Zhang (1991) Xu & Mao (1993) TEA (1993) Mori (1991) Lin & Li (1993) Siegen (1987)  2.3  HYDRODYNAMICS In order to predict heat release and heat transfer in CFBs, knowledge of the  flow patterns of solids within the riser must be known. Experimental observations have shown some characteristic hydrodynamics found in CFBs.  Some of these  observations are a downward flow of dense streamers near the walls of the riser, otherwise known as the annulus region, and an upwardflowof dilute suspension in the middle of the riser, known as the core region [Yerushalmi et al., 1978], [Brereton et al., 1986] and [Yang et al., 1991], shown in Figure 2.1. It has also been observed that the core has regions of higher and lower voidages, which seem to suggest "clustering". Clustering is the phenomenon where a group of particles are loosely locked in some random configuration and engulfed in gas. The cluster, sometimes referred to as a "packet" or "streamer", acts as an individual entity, occasionally losing and gaining a few particles. Models 1, 2, 3, 4 and 6, noted in the previous section, use the core/annulus structure of the riser. The overall models that did not use the core/annulus structure characterized a section of the CFB riser at a given height as a lumped-parameter section. In other words, gas and solids are ideally mixed in each cell and each cell has  14  Figure 2.1  Illustration of Solids Distribution in a CFB Riser [Senior, 1992]  15  chemical reactions, particle attrition and cell to wall heat transfer occurring. None of the models simulated the clustering phenomena. From previous experimental and modelling work, it was found that reactor geometry affects the hydrodynamics [Senior, 1992]. Sharp riser exits result in a higher suspension density at the top of the riser. In addition, the presence of a membrane heat transfer surface will affect the thickness of the streamers formed near the wall. It has also been shown that the position of the solids return entry and the shape of the primary zone tapering affects the solids acceleration in the developing zone. None of the CFB models incorporate reactor geometry effects.  2.3.1  Senior's Hydrodynamic Model The heat release and heat transfer model developed in this thesis work is based  on a mechanistic model of CFB hydrodynamics by Senior [1992]. This hydrodynamic model predicts the suspension density profiles and hydrodynamics of the wall and core regions. The accuracy of the predicted suspension density profile is approximately ± 20% and was based on comparisons with experimental data, obtained from the UBC pilot CFB and the Studsvik CFB.  For the UBC CFB, experimental data were  measured for superficial gas velocities of 6 m/s to 10 m/s, solids recirculation rates of 20 kg/m s to 170 kg/m s and for various primary/secondary air splits. 2  2  For the  Studsvik CFB, experimental data were collected for superficial gas velocities of 4 m/s to 8 m/s, solids recirculation rates of 40 kg/m s to 90 kg/m s and for various air splits. 2  2  Although solids flow in a two-dimensional or a three-dimensional model will be more representative of an actual CFB riser, than a simple core/annulus model, increased dimensional models are more complex, significantly more difficult to solve and may not necessarily give more accurate results than a lower dimensional model. It was found that a model where the riser was split into a one-dimensional core and an annulus region, which is called the two-zone, core/annulus approach, gave reasonable  16  trends. The two zones interact with one another by radial interchange of solids across the zone boundary, see Figure 2.2. Axially, Senior's CFB model was divided into 20 core cells and 20 annulus cells along the height of the riser, above the secondary air. The primary zone is represented as a single cell. The hydrodynamic results from Senior's models show that fewer cells can be used near the middle section of the riser, where suspension densities are quite uniform; however, the top and the bottom of the riser may be regions of steep suspension density gradients and more cells may be needed to accurately predict the densities. Comparing this model to the overall models shows that the overall models had different number of cells along the height of the riser. Some models divided the riser into 2, 3 or many cells, and one model (DBA) took the entire riser as being one cell. Some of the model differences resultfromdifferent number of cells being needed to predict different phenomena. For example, a riser where the solids are well mixed will require only a single cell to sufficiently predict the overall solids mixing. However, to understand the details of the density profile, more axial cells may be needed.  2.3.1.1 Assumptions The assumptions made in Senior's model are: (i)  The hydrodynamics is represented by a two-zone, core/annulusflowstructure, which is described above.  (ii)  The riser is isothermal. Typically, a riser's temperature ranges from 850 °C to 1000 °C, and is not isothermal in practice; however, these temperature variations will not significantly affect the hydrodynamics but will affect heat release and heat transfer in the riser. Test runs conducted using Senior's model and varying bed temperaturesfrom850 °C to 1000 °C show less than a 10%  17  Figure 2.2  Regions and Flow Patterns Assumed by a 2-Zone Core/Annulus Modelling Approach in a CFB [Brereton, 1987]  DOWNFLOW  UPFLOW C O R E  [ernal x  18  difference in the mass flowrate of air; therefore, the hydrodynamic results are almost the same. Gas and solid densities are constant. The solid suspension densities, however, vary along the height of the riser and in each zone. The behavior of the particles is represented by particles with the sauter mean particle size. The particles in the fully-developed region in the core travel up the riser at a constant velocity. This velocity is equal to the superficial gas velocity minus the sauter mean particle terminal velocity. This assumption is valid for dilute systems. There are no clusters in the core above the secondary air feed ports. The primary zone is in the developing flow region near the bottom of the riser, and the assumptions on the behavior of the particles, listed above, do not apply in this region; therefore, only the bulk density was predicted in the primary zone. For simplicity, the height of the top of the developing flow region is also the secondary air feed port height. In reality, the top of the developingflowregion is usually 0.5 m to 1.5 m above the secondary air. The region above the secondary air is in fully-developed flow. The developing flow region is the region near the bottom of the reactor, where there is a steep decline in the density profile and large core to wall flux of solids.  In the fully developed region, there is less interchange of solids  between the core and the annulus. The interface between these two regions are described in more detail in Senior's thesis. In the developing flow region, an exponential decaying profile is assumed for the bulk suspension density.  19  (x)  The average streamer velocity in the annulus is assumed to be -1.1 m/s. The average velocity of the falling streamer usually ranges from -0.5 m/s to -1.8 m/s, and this velocity is dependent on the suspension density. This range of  streamer  velocity  was  found  experimentally  using  high  speed  cinematography by Wu [Wu et al., 1990], and is the same order of magnitude as suggested by other researchers such as Glicksman [1988]. Another  observation  that  was  included in  Senior's  model  is  the  non-homogeneous nature of the annulus. Some wall sections contain streamers and others are exposed to the dilute upwards flow of particle suspension in the core. Both of these conditions were modeled in the annulus, by computing the thickness of the streamer and the fraction of the wall coverage by the streamers as a function of riser height. Some limitations in Senior's model include the assumptions made in the developing flow region or the primary zone, and the assigned reflection coefficient, which is presently modeled as not a function of solids recirculation rate, superficial gas velocity, gas viscosity, gas density, particle density, particle size distribution and exit geometry. The reflection coefficient is defined as the fraction of solids traveling upwards at the exit height that are returned down the walls of the riser. Figure 2.3 shows the gas and solids flow patterns at a sharp riser exit [Brereton, 1987] and Figure 2.4 shows the effects of riser exit smoothness on a suspension density profile [Senior, 1992]  20  Figure 2.3  Observed Gas and Solid Flow Patterns in a Sharp CFB Riser Exit [Brereton, 1987]  Crossf lowing; solids layers on roof  I  Gas streamlines —  Solids streamlines  21  re 2.4  Apparent Suspension Density Profile as a Function of Riser Exit Geometries [Senior, 1992]  T = 850 °C, U = 6.5 m/s  T = 850 °C, U = 9.0 m/s  HEIGHT IN RISER (m)  22  2.4  H E A T TRANSFER Presently, there is a lack of experimental data from commercial operating CFBs  that is not considered proprietary; however, a few researchers have made their data available [Werdermann et al., 1993], [Couturier et al., 1991] and [Leckner et al., 1992]. The majority of other CFB data that are available are for CFBs with either small heat transfer surfaces, small diameter CFBs or for CFBs operating at room temperatures, for example [Bi et al., 1990] and [Furchi et al., 1988]. In addition, most experimental data do not include radiative heat transfer and when compared with each other are often scattered. Generally speaking, heat transfer models fall into three categories depending on how they treat the solid suspension near the riser wall. Theses categories are as follows: (1) Film theory (2) Penetration theory (3) Gasfilm-emulsionpacket theory  2.4.1  Film Theory The film theory was first proposed by Dow and Jacob [Dow et al., 1951]. They  conducted experiments with various particle sizes and column diameters to study the heat transfer mechanism between a fluidized bed and a heat transfer surface. In their model there is an air film between the downward moving solids and the wall of the riser. Adjacent to this air film, the solid suspension is treated as discrete particles that move down the film, and discrete hot particles move up through the center of the bed. See Figure 2.5. The particle to surface contact is assumed to be negligible and heat is transferred through this film, which may be as thin as 0.01 mm thick. As expected, there is a temperature gradient across the film, and there is also a temperature gradient near the distributor as the cold primary air mixes with the hot particles in the bed; however, the rest of the bed is at a uniform temperature. In reality, this film layer is not continuous, but it is scoured by particles at irregular intervals.  23  Figure 2.5  Film Theory  air out  I  _Crr*_  I 2-  !  4  |  wall layer in which solids move downward  distributor  iL /^v  /S.  air in  /S.  24  Leva [1952] used the same model as Dow and Jacob, but assumed that the air film thickness is strongly dependent on the gas viscosity. In addition, as the particles scour the air film, the film's resistance decreases; therefore, the particle's velocity should also be included in the heat transfer equation. Leva, derived an equation that contains the thermal conductivity and the viscosity of the gas as well as the mass and velocity of the particles, and a new dimensionless variable called the "fluidization efficiency" was defined. The fluidization efficiency value was determined byfittinga derived bed to wall heat transfer coefficient with experimental data. Levenspiel and Walton [Levenspiel et al., 1954] also used the film theory, but did not assume that the airfilmwas continuous along the wall. They assumed that a fresh film starts at every point on the heat transfer wall where a solid particle touches the surface; thereby, producing severalfilmsand predicting a smaller total resistance to heat transfer. The total resistance is expressed as an "equivalentfilmthickness".  2.4.2  General Comments on the Film Theory Thefilmtheory emphasizes the role of thermal conductivity of the gas and neglects  thermal capacity of the solid particles.  Also, the air film is scoured by solids which  decreases the thickness of the film. The results of this theory may appear reasonable; however, the assumption that the role of the solid particles in heat transfer are insignificant is not seen experimentally. This model wrongly suggests that at minimum fluidization the heat transfer is zero, because an anomaly in the derived equation at minimumfluidizationgives zero equivalent film thickness, which leads to zero heat transfer. Therefore, the heat transfer value at minimumfluidizationmust be extrapolated from a higher value. In addition, extrapolation of heat transfer values for higherfluidizationranges must also be done. Most models using the film theory predicts that radiation heat transfer is insignificant at temperatures less than 1000 °C. Radiation heat transfer was shown, by  25  subsequent researchers [Szekely et al., 1969], [Botterill et al., 1970], [Baskakov, 1985] and [Han et al., 1992], to be significant at much lower operating temperatures.  2.4.3 Penetration Theory Mickley and Trilling [Mickley et al., 1949] werefirstto develop the penetration theory for fluid bed heat transfer. Emphasis was placed on the transport of heat by the solid particles, which suggests that because the heat transport by the solids is fast, the temperature gradient is present only in a thin layer near the heat transfer surface. In addition, the effective thickness of this layer is reduced by the motion of the particles and heatflowsby conduction and convection. Mickley and Fairbanks [Mickley et al., 1955] were the first to represent the solid suspension as a packet. They recognized the heat transfer mechanism to be unsteady conduction and they researched the role of heat capacity of solid particles. The packet resides within a thin layer near the wall and the physical properties of the packet are the same as that of the bed. The packet has afinitelife span before it is re-entrained into the core of the riser, and is replaced by afreshpacket. A continuous flow of such packets is the chief mechanism of heat exchange. See Figure 2.6. The boundary conditions are such that the packet instantaneously attains the temperature of the wall when it comes into contact with it, i.e., there is zero resistance or an infinite heat transfer coefficient between the packet and the wall. Mickley and Fairbanks considered two models for bed dynamics. (i)  Slug model - all the packets move down the wall at a uniform velocity. They all have the same residence time and behave alike.  (ii)  Side mixing model - there is a radial exchange of packets between the surface and the bed.  26  Figure 2.6  Penetration Theory  After time t  27  From their experiments, they showed that the heat transfer coefficient was proportional to the square root of the thermal conductivity of the packet, assuming constant packet density and heat capacity. Their model also explained how heat transfer increases due to a decrease in the particle size, because smaller particles circulate at surfaces more rapidly than larger particles. The disadvantage of this model is that it predicts infinite heat transfer coefficients as the contact time approaches zero. The model also assumes that the bed is homogenous, which is not the case, since there are porosity changes. Baskakov [1964] used the packet model of Mickley and Fairbanks, but he included addition thermal resistance between the wall and the packet to account for changes in porosity. His model is essentially a combination of the film theory and the penetration theory. Changes in porosity are significant near walls where gas layer thicknesses are approximately one particle radius. Baskakov's model gives finite values of the heat transfer coefficient as the contact time approaches zero, as compared to Mickley and Fairbanks model. In addition, this additional thermal resistance seems to suggest a gap between the fluidized bed and the membrane wall. Gorelik [1967] used a model similar to Baskakov's except the packet that reaches the wall is divided into a higher and a lower porosity zone. The higher porosity zone is close to the wall, and the lower one is equal to the bed porosity. However, the heat transfer problem becomes the unsteady heating of two zones, each having different thermal properties due to different porosities.  Two  zones with different thermal  conductivities causes a temperature gradient at their interface. The difficulty then is to determine the thermal properties of the two zones.  28  2.4.4  Gas Film - Emulsion Packet Theory  The gasfilm-emulsionpacket theory, also called the "alternate-slab model", proposed by Gabor [1970], assumes that the solid suspension near the riser wall is made up of alternate slabs of gas and solid. See Figure 2.7. Many investigators [Vedamurthy et al., 1974], [Bhattacharya et al., 1977] and [Kolar et al., 1979], using this theory assume that radiation only occurs between adjacent plates along with conduction through the gas film between the plates. The bed and heat transfer surface are considered grey and the gas is assumed to be transparent [Kolar, 1979]. The properties are evaluated at an average temperature equal to the mean of the temperature of the two bounding slab surfaces. The radiation incident on each slab is assumed to undergo reflection, radiation, and scattering. The limiting values of these parameters as the number of slabs approaches iminity are considered to be the effective bed values. The predictions from this model over predicts the heat transfer coefficient values at high temperatures; however, the maximum prediction error using this model is less than +35%, which is remarkably good considering its simplifying assumptions. All of the above models were initially developed for bubbling beds. Many have subsequently been adapted for CFBs.  2.4.5  Radiative Heat Transfer  Most studies on heat transfer in CFBs only deal with particle convective heat transfer or overall heat transfer. Although an investigation by Jolley [1949] showed that radiative heat transfer term is significant at operating temperature of 1000 °C, experimental measurements of the radiative heat transfer contribution is difficult. There are many views as to the contribution of radiation to the overall heat transfer in a CFB. One point of agreement is that it is insignificant at low temperatures; however, there is no agreement as to what temperatures are considered "low" and what are  29  Figure 2.7  Gas Film - Emulsion Packet Theory  30  considered "high" temperatures. According to Han's experimental measurements [Han et al., 1992], the contribution of radiative heat transfer to the total heat flux can range from 5% to 50% for suspension temperatures from 200 °C to 600 °C. In addition, there is uncertainty as to how other variables, such as particle diameter, particle surface temperature, fluidizing velocity, and effective bed and surface emissivities, affect the radiative heat transfer term. It is therefore necessary for a model of heat transfer in CFB to predict the radiative contribution in high temperature beds as a function of various parameters and operating conditions. The additional heat transfer in the packet due to radiation using the penetration theory was studied by several researchers, such as work done in model 3. Another more complex model, by Chen [1988], involves developing a model of the heat transfer process by a non-linear differential formulation of the simultaneous radiative-conductivefluxin the packet. In Chen's model, the radiative flux is split into an absorption and a scattering flux in both the forward and backward directions. The general limitation of the penetration theory is that a number of the mean packet properties must be known, such as effective packet thermal conductivity, packet residence time and bubble fraction. In addition, for Chen's model, the packet's absorption and scattering cross-sections must also be known, which are difficult to evaluate. One assumption in the penetration theory is the packet's surface adjacent to the wall is assumed to immediately attain the wall temperature; in other words, there is zero resistance. Other assumptions include the packet leaves the wall before the thermal wave penetrates the packet, and the packet and the bed are assumed to have the same thermal properties. The penetration theory gives predictions that are only accurate for long contact times. As time approaches zero, the heat transfer coefficient predicted approaches infinity.  31  2.4.5.1 Chen's Model Chen developed a model that represents the interactive convective and radiative heat transfer process in a CFB. In the past, radiative heat transfer models usually treat the two-phase suspension as an opaque grey body with an effective suspension emissivity. The radiative heat transfer coefficient is then added to the convective heat transfer coefficient to obtain the overall heat transfer coefficient.  In reality, radiative and  convective heat transfer occur simultaneously throughout the suspension and are nonlinear.  The resulting equation is non-linear and has not been solved analytically.  Numerical methods were used to solve the general case. Chen's model considers an axial segment of the riserfromthe wall to the center of the riser. See Figure 2.8. Solid suspension is characterized by local parameters such as volume fraction of solid particles, temperature, heat generation rate, effective thermal conductivity, absorption cross-section,  back-scattering cross-section,  axial particle  velocity and axial gas velocity. For steady-state conditions, an energy balance can be made for the control volume. The general formulation is given in Equation 2.1.  !(*» f ) "  1  ( +  (  l  " > a  A  " « ] f  (2.1) - i  (  1  -  J  )  =  -  G  -  32  Figure 2.8  Radiative Heat Transfer Model [Chen, 1988]  .Center of riser  k I  L  ^ positive x direction  si/ positive y direction  *  33  where, y x kgff T otp pp Cp Up p c Ug I J G  distance in the axial direction (m) distance in the transverse direction (m) effective thermal conductivity (W/mK) absolute temperature (K) volume fraction of the particle density of the particle (kg/m ) specific heat of the particle (J/kg-K) velocity of the particle (m/s) density of the gas (kg/m ) specific heat of the gas (J/kg-K) velocity of the gas (m/s) radiative flux in the positive y direction (W/m ) radiativefluxin the negative y direction (W/m ) heat source intensity per unit volume (W/m ) 3  3  g  g  2  2  3  v  From the energy balance equation, Chen's model ignores the axial conductive and axial radiativefluxesas well as radial convection of the particles and gas. The photon transport equations for the radiant energy passing through the solid suspension by absorption and back-scattering are given below.  ^  + S )l  = -U  + S J + Ar&T  (2.2)  4  r  r  r  ax ^ = (A ax  S )j-S I-A cxT  (2.3)  4  r  r +  where, A S a  r  r  radiation absorption cross-section / unit volume back-scattering cross-section / unit volume Stefan-Boltzman constant (W/m K )  r  r  2  4  and A and S are calculated by: r  A  r  • C  r  L  —  (2.4)  ^  p  j  .  = q  .3to,0-«,) d  p  (  2  5  )  34  where, CL 8p dp b  dimensionless proportionality factor emissivity of the particles diameter of the particles (m) back-scattering coefficient  The boundary conditions used are:  T(0,y) = T  w  §(L,y) ax  =0  T(x,0) = T  t  I (0,y) = w  o-T:+{1-£ )J  £w  W  W  J (L,y) = h L  where the subscripts representation are, w wall condition i initial condition L condition at the center of the reactor column  2.4.5.2 Radiative Contribution in Heat Transfer Model  The convective and radiative heat transfer process in a CFB in reality is interactive. The equations are highly non-linear and difficult to solve numerically. Initially, Chen's equations were used in the heat transfer model developed in this work. The riser was divided into 20 axial cells and 2 radial cells. The annulus cell and the core cell were separated as individual control volumes, and the finite difference method was used to solve Equation 2.1. Temperature convergence was difficult to achieve; therefore, a less sophisticated non-interactive convective and radiative heat transfer equation was used to solve for the temperature profile in this thesis work. Due to the modular nature of the program developed, the heat transfer subroutine can be replaced with a more sophisticated heat transfer equation at a later date.  35  2.4.6  Heat Transfer in Overall Model  There are various models developed to describe high temperature heat transfer processes in CFBs and all of them use the penetration theory. Models 2, 3, 5, 6, 7, 8 and 10, listed previously include a heat transfer model. Model 2 uses a heat transfer model according to Nag [Nag et al., 1991], which includes particle and gas convection to all of the neighboring cells. Model 3 uses a more complex heat transfer model that includes conduction, convection and radiative heat transfer. The overall heat transfer in this model is determined by a mass and energy balance on all solid and gas phases. Model 5 uses an enthalpy balance on each chemical species and a constant wall heat transfer coefficient to determine the heat transfer in the CFB. Models 6 and 8 are similar to model 5's treatment of heat transfer; however, the wall heat transfer rates are determined by energy balances at the furnace wall. Model 7 calculates the amount of chemical heat generated using the Delft SURE Model [Lin et al., 1989]; however, this model does not include bed to wall heat transfer to be implemented into an overall model. Finally, model 10 determines the amount of chemical heat generated by solving a mass balance for each gas species and assuming a constant wall temperature, a heat balance is done according to a model by Martin [1980]. None of the overall models look at heat transfer to a membrane waterwall surface, which consists of tubes connected by longitudinal fins [Bowen et al., 1991], see Figure 2.9.  36  Figure 2.9  Schematic Gross-Section of a Membrane Waterwall Surface [Bowenetal, 1991]  high temperature gas—solid suspension  37  CHAPTER 3 MODELLING OF HEAT RELEASE. OXYGEN PROFILES AND TEMPERATURE PROFILES OF CFBs  In this chapter, a detailed description of the model, developed in this thesis work, to predict heat release, oxygen and temperature distributions in CFB combustors will be discussed. The equations used are simple exponential equations for devolatilization and char combustion. The oxygen partial pressure profile is determined by a mass balance for each cell, given the initial oxygen pressure, and the temperature is determined by solving a nonlinear partial differential equation with the temperature term to the 4th power. The program code is modular, so that each subroutine can be easily replaced by other equations. The heat release and heat transfer subroutines are coupled, which is required to solve for the temperature distribution.  3.1  M O D E L ASSUMPTIONS The assumptions used in the heat release and heat transfer subroutines are as  follows. (i)  The heat capacity of the gas is assumed to be constant and equal to the heat capacity of the gas at a temperature of 850 °C. The heat capacity of the gas is recognized to be a function of temperature. However, this assumption was made to simplify the heat transfer equation to show, at this initial stage, that the program gives reasonable predictions. The program can be easily modified to include more sophisticated energy balances, including a heat capacity term that is a function of temperature.  (ii)  The heat capacity of the particle is assumed to be constant.  (iii)  The density of the particle is assumed to be constant.  (iv)  The density of the gas is assumed to be constant.  38  Velocity changes of the gas due to combustion are neglected. Realistically, the variables in assumptions (iv) and (v) are both a function of temperature and gas velocity does change as more combustion gas is produced. However, this assumption is consistent with the hydrodynamics model used. In Senior's model, the mass flux of the gas is assumed to be constant. Since the mass flux of the gas is the product of gas density and gas velocity, both of these values were taken as constants.  In the absence of a hydrodynamic model that is a  function of temperature, these assumptions were made. Fragmentation and attrition of coal particles were assumed to be insignificant. In practice, the reaction of coal in CFBs, namely devolatilization and char combustion where heat is released, may be complicated by fragmentation that typically occurs near the end of devolatilization and by attrition, which occurs throughout char burning. The mass transfer rates of oxygen to the char particle and carbon dioxide away from the particle are assumed to be rapid [Howard, 1983]. Therefore, the limiting step is the kinetic rate of char combustion. This assumption is valid for high gas velocities or good gas-solid mixing, which is a characteristic of CFBs [Basu and Yan, 1993]. The char is assumed to be completely burned to form carbon dioxide, i.e., no carbon monoxide present. No heat release occurs in the standpipe, since there is very little oxygen present to support combustion. The gas and particles in each cell are well mixed and at the same temperature. The higher heating value of the fuel was used for both the volatile and the char combustion. This neglects some of the complexities at the local heat balance, and more detailed balances are needed for further development of the work.  39  (xii)  The modelfirstcalculates the enthalpy needed to dry all the moisturefromthe fuel before the coal undergoes combustion. The amount of moisture in each cell is calculated based on thefractionalheat released within the cell.  (xiii)  The particle heat up rate is assumed to be infinite. In other words, the volatiles immediately start being released from the coal particles upon entering the primary zone.  (xiv)  There is 100% combustion of the coal particles. This is easily modified.  3.2  DESCRIPTION O F M O D E L A P P R O A C H AND SUBROUTINE EQUATIONS  3.2.1  Devolatilization  Several devolatilization expressions were considered.  These expressions were  developed by Jia [Jia et al., 1993], Anthony [Anthony et al., 1975], and a combined devolatilization expression by Agarwal [ 1986] and Davidson [Davidson et al., 1985]. The devolatilization expression by Anthony, shown in Equation 3.1, was determined by heating up to 950 °C, in a helium environment, monolayer samples of lignite and bituminous coal supported on wire mesh. Devolatilization was found to be a function of time and temperature and not a function of particle diameter. For bituminous coal, the correlation was found to have a standard deviation of approximately 3 wt%. Figure 3.1 shows how the correlation predicts the time to devolatilize as a function of temperature.  (3-1)  40  Figure 3.1  0.9  0.8  0.7 +  Devolatilization Time as a Function of Temperature Predicted by Equation 3.1  41  where,  V fraction of volatiles released at time t V* initialfractionof volatiles in coal (from proximate analysis) t time (s) T temperature (K) ko = 706 s E = 11.8kcal/mol R = 1.978xl0- kcal/mol.K 0  3  The devolatilization expression by Jia, shown in Equation 3.2, is a function of particle diameter; however, it is not a function of time.  t = S.lOxlO ^- - ^ - ^ 1 0  1  9 5  1  6  (3-2)  0 8 6  d  where,  t^ T dp P  b  0  devolatilization time (s) bed temperature (K) particle diameter (m) partial pressure of oxygen (atm.) must be within the range 0.01 atm. to 0.14 atm.  Very recently, a third devolatilization expression, which is a combination of the expressions by Agarwal and Davidson, was used. This devolatilization expression is both a function of particle diameter and time.  The equations and results are listed and  compared in the following chapter. Although for all of the test cases, the devolatilization expression by Anthony was used, due to the modular nature of the program, Equation 3.1 can be easily replaced by another equation which may incorporate pressure, heating rate and particle size.  42  3.2.2  Plume Model Experimentally, in both large and small CFBs, volatile plumes are found. These  plumes are caused by poor radial mixing of gas, and the effect of the plume is that volatiles are not necessarily burned at the location where they are released. Clearly, as shown in Figure 3.2, this is a 2 or 3 dimensional mixing problem; however, the core/annulus model is only 1 dimensional. In order to superimpose the 2 dimensional phenomenon upon the 1 dimensional model, it is necessary to perform separate computations and then transfer the results into the 1 dimensional case. In this model, the volatiles are assumed to burn at their point of release; therefore, the plume phenomena was handled by looking at the volatiles release as a function of height, and then transferring some fraction of the volatiles to the cell above. This transfer simulates the poor mixing, which prevents volatiles from releasing their heat of combustion at their point of evolution. Devolatilization is rapid and generally takes place 3 to 20 seconds after the coal is fed into a CFB. Since the volatile matter will dispersefromthe fuel feed point rapidly in the axial direction, but only slowly in the radial direction, the volatiles evolution region forms an axial symmetric region centered on the fuel feed point [Stubington, 1980] and [Park et al., 1981]. If the fuel feed point is located at the wall, then the evolution region's axis of symmetry will be centered at the wall. The volatiles must mix with oxygen for combustion to occur. Therefore, oxygen availability can be the limiting factor in volatile combustion, if the oxygen concentration is less than stoichiometric in the region near the fuel feed. This is more prevalent in large CFBs, where the volatiles burn higher up the riser. As the volatiles travel up the height of the bed, they also diffuse a significant radial distance, which is given by Einstein's diffusion equation [Stubington, 1980].  x =2Dj 2  (3.3)  43  Figure 3.2  Plume Model of Volatiles Dispersion [Stubington, 1980]  Mean concentration of  volatiles released  Coal  !  I  :  Air  i •I  Volatiles evolution region for short devolatilization time  Mean concentration of  volatiles  released  Coal  Coal  I  1  I  ! Air  Volatiles evolution region for long devolatilization time  44  where, rv  t  average displacement squared radial volatile diffusion coefficient = 0.01 m /s time (s) 2  To correct for the volatile dispersion, the above equation was solved for t, then knowing the velocity of the gas in the axial direction, the height h above the coal feed point where we observe fully radial mixing of volatiles is calculated. Fully radial mixing is achieved when the volatile evolution region spans the full cross-sectional area of the riser. For any cells below this height h, the amount of volatiles released is corrected for by transferring a fraction of the total volatiles to the cell above. This fraction is called the volatiles transfer fraction and is set at 0.3, which seemed to produce reasonable results. The current volatiles release rate, calculatedfromEquation 3.1, is very fast and mainly occurs in the primary zone. The effects of using the plume model is not clearly seen, including the effect of various volatile transferfractionvalues.  3.2.3  Char Combustion  After devolatilization, the char particle that remains may take several minutes to burn out, depending on the size of the particle. Since the mass transfer rate of oxygen to the coal particle was assumed to be rapid and the limiting step is char combustion, the Arrhenius equation was used to express char combustion. Assuming afirst-orderreaction, the following equation was used [Howard, 1983].  k =A exp R  c  -  (3.4)  45  k Tg E Ac R  where,  R  A  reaction rate (kg/m satm) surface temperature (K) = 150,000 kJ/kg = 7260 kg/m satm = 8.314 kJ/kg-K 2  2  The char combustion equation was also included in a separate subroutine within the program; thereby, making replacement expressions of the char combustion rate an easy task. The time for burnout of a particle is given by:  (3.5)  where,  diameter of the char particle (m) reaction rate (kg/m satm) partial pressure of oxygen (atm) density of the char particle (kg/m ) burn-out time (s) 2  Pc x  3  From Table 3.1, we can compare the predicted burnout times and riser residence times for various particle diameters. It should be noted that the devolatilization time, calculated from Equation 3.1 [Anthony et al., 1975], is not a function of particle diameter. Also, the average particle residence times, given in Table 3.1, are determined based on a single pass.  46  Table 3.1  Comparison of Predicted Burnout Times with Particle Diameters Studsvik CFB Bed Temperature = 850 °C Particle Surface Temperature = 900 °C Partial Pressure of O2 = 0.05 atm Particle Density = 1400 kg/m Superficial Gas Velocity = 7 m/s 3  Time (s) Devolatilization [Anthony et al., 197511 Devolatilization [Jia et al., 1993] Devolatilization [Agarwal, 19861 Char burnout Average single pass particle residence in theriserabove the secondary air Average single pass particle residence in the primary zone  dp = 100 um  dp = 1 mm dp = 3 mm dp = 1 cm 4  1.8xl0-  5  0.047 0.784  1.1  6.5  44.9  1.5  7.8  47.4  784  2352  7840  30 10  Comparing the devolatilization time prediction by Anthony with Jia shows that Anthony's formulation over predicts the devolatilization time for small particle diameters and under predicts the time for large particles. Therefore, there is a limited range of particle size (approximately 2 mm) where this correlation is valid. The model assumes that the fuel particle travels through the bed in the same way as the bed particles. Then the single pass residence time for the primary and secondary zone is independent of the particle diameter. This assumption is valid for small diameter particles that are approximately the same size or smaller than the bed particles. For larger diameter particles, this assumption breaks down. However, typical coal particle diameters in CFBs are no more than approximately 4 mm, compared to an average bed particle of 0.5 mm [Senior, 1992].  47  By comparing the char combustion time with the single pass residence time in the secondary zone, for large diameter particles, we can conclude that the coal particle will pass through the riser many times before it is completely burnt out. The heat release distribution for large particles will then be similar to the density distribution. Therefore, there is a potential for simplification in the heat release model for large particles, by setting the heat release distribution to equal the density distribution. Finally, by comparing the devolatilization time with the single pass residence time, for small diameter particles, we can conclude that if the devolatilization time is much less that the residence time in the primary zone, then most of the volatiles will be released in this zone. In addition, from Figure 3.1, most of the volatiles are released within the first few seconds from when the fuel enters the riser; therefore, most of the volatiles will be released in the primary zone, according to Anthony's correlation.  3.2.4  Monte Carlo Approach  The Monte Carlo Method is a class of mathematical methods first used by scientists in the 1940s. The essence of this method is the use of random or pseudo random numbers to study some phenomena.  Although the problem may be non-  probabilistic, an individual event that makes up the problem has the structure of a stochastic process, a sequence of states determined by random events.  Therefore,  although the answers obtained are statistical in nature and subject to the laws of chance, the average value of the answer isn't. In order to determine how accurate the answer is or to obtain a more accurate answer more experiments can be conducted. In this program approximately 100 particles will give reasonable heat release distributions due to char combustion. Many people use the Monte Carlo Method and it has become an accepted part of scientific practice in many fields. Some advantages are convenience, ease and directness  48  of the method.  In addition, Monte Carlo Methods are computationally effective,  compared with deterministic methods when treating many dimensional problems. For the Monte Carlo method to be effective, a source of randomness is needed. Unfortunately, the random functions supplied with different computers are pseudo random, which is to say that they are deterministic but niimic the properties of independent uniformly distributed random variables.  3.2.5  Comparison of Monte Carlo Approach with Analytic Technique  An alternative method to the Monte Carlo Approach is to solve the heat release and the heat transfer equations simultaneously by formulating mass and energy balance equations for each particle size within each cell. There are approximately 40 cells and the greater the number of particle sizes considered in the mass and energy balances the more accurate thefinalresult. Assuming that there are 20 particle sieve sizes considered, which is the number in the fuel feed's particle size distribution, there would be over 800 simultaneous non-linear equations that must be solved for each time step. This very large and sparse matrix must then be iterated until afinalconverged value is reached. Such an approach will be time consuming, and due to the nonlinear nature of the energy balance equation, the solution may be difficult to converge. The Monte Carlo approach was chosen because it seems to be a simpler method to program than the analytic technique method. In addition, using the Monte Carlo method, CFB systems of hundreds or thousands of particles can be treated quite routinely.  3.2.6  Monte Carlo Approach within the Program  In this program a large number of coal particles are individually traced throughout the bed riser and solids recirculation system. In each cell, the coal particle's probability of being transferred to the wall, from the wall, up the riser or down the riser is simply the ratio of the flow of particles out of the cell in a given direction, to the cell mass. The time  49  steps were selected such that at any given time step, the probability of the coal particle leaving the cell is set at 10%. See Figure 3.3. This probability value of 10% was chosen after initial experiments, using various probability values, showed that at higher probability values the accuracy of representing particle movement within the riser decreased. At lower probability values, accuracy increased; however, total run time also increased. A probability value of 10% seemed to be the optimum value. Several hydrodynamic assumptions were made in this program. The particles in the core were assumed to move only up the riser or to the streamer, and the particles in the streamer were assumed to only move down the streamer or to the core. See Figure 3.4. This assumption is the same as in Senior's hydrodynamic model. In addition, the coal particles were assumed to move in the same way as the bulk ash and sand particles. A fraction of the particles that hit the top of the riser is reflected back into the streamer, based on a given reflection coefficient in the CFB. The rest of the coal particles that leave the top of the riser enter the cyclone, which is treated as a CSTR with a residence time of 0.3 seconds. This cyclone model can be replaced by alternative models. The coal particles less than 50 urn exit with the flue gas while larger particles leaving the cyclone are returned to the CFB's primary zone through the standpipe. As the coal particle move throughout the riser, it first undergoes devolatilization then char combustion. In addition, to tracking the path of the particle, the Monte Carlo method also follows in which cell and at what time heat is released. Ultimately, this form of "bookkeeping" produces a heat release distribution. The resultant heat release distribution is a function of temperature and partial pressure of oxygen, which must be initially guessed. However, once the heat release distribution is determined a new partial pressure of oxygen profile can be calculated and then a new temperature profile. The Monte Carlo method is repeated until a converged heat release distribution, partial pressure of oxygen profile and temperature profiles are obtained.  50  Figure 3.3  Probability of a Particle Leaving a Cell  Variables: m mass of particles in cell Fy flow across Ay (kg/s) Fx flow across Ax (kg/s) t time step (s)  Ay  Ax Fx< Annulus Cell  m Core Cell  0 Probability of a particle moving vertically:  Py = Fy . t / m  Probability of a particle moving horizontally:  Px = Fx . t / m  Probability of a particle staying within the cell: Pm = 1- Py - Px  51  Figure 3.4  Solid Particle Paths in the Riser  4^ 4^  4Standpipe  Primary Zone  52  In order to validate the predicted particle paths throughout the riser, based on the Monte Carlo method, a test run was conducted. In this experiment one large "theoretical" particle, with a diameter of 1 m, was introduced into the primary zone and was traced as it underwent devolatilization and char combustion. The large size of the particle ensures that it will move through all of the cells many times before it is finally consumed. If the particles that hit the top of the riser are assumed to all reflect back down the streamer and the riser's temperature and oxygen concentration are constant, then the resultant heat release distribution should equal to the density distribution of the CFB. The expression for devolatilization time chosen for this test is from Jia [Jia et al, 1993], since the time for volatiles release in this expression is given as a function of bed temperature and particle diameter. However, the devolatilization rate was assumed to be constant. The devolatilization time expression for Highvale coal is shown in Equation 3.2. The char combustion rate used is from Howard [1993] and was shown previously in Equations 3.4 and 3.5. The resultsfromthis test, assuming a constant riser temperature of 850 °C, is that the heat release distribution due to volatiles and char combustion was indeed found to be the same shape as the density distribution.  3.2.7  Heat Transfer Model Two types of heat transfer were considered in the model; cell to cell heat transfer  and cell to wall heat transfer.  3.2.7.1 Cell to Cell Heat transfer The overall cell to cell heat transfer equation, given below, includes conduction, convection and radiative heat transfer of both particles and gases.  53  -{F c +p c v )A {T x  p  g  g  g  w  -T )0  w  MP /wXfc C  +  -soApTp +eoA T£ w  [F c + p c v )A {T x  p  g  g  g  E  E  - T°)  +P c u )A {T - T°) g  g  g  s  s  + eoAjJZ + soA T^ + ecxA T^ +G=0 N  s  (3-6)  G  thermal conductivity of the cell (W/mK) surface area of one side of the cell (m ) temperature (K) distance in the transverse direction (m) distance in the axial direction (m) mass flux of particles in the transverse direction (kg/m s) mass flux of particles in the axial direction (kg/m s) heat capacity of particles (J/kg-K) density of gas (kg/m ) heat capacity of gas (J/kg-K) represents the mass exchange of gas in the transverse direction due to turbulent mixing (m/s) velocity of the gas in the axial direction (m/s) emissivity of the cell Stefan-Boltzman constant (W/m K ) source term in the cell (W/m)  subscripts,  W E N S P  west east north south control volume  superscripts,  0  reference  where,  k A T y Fx F  y  °P  Pg c  g  v  g  u  g  8 CT  2  2  2  3  2  4  54  Figure 3.5 shows an enlarged riser cell cross-section, to indicate the direction convention used in the overall cell to cell heat transfer equation.  3.2.7.2 Differences with Chen's Model  The differences between the above heat transfer equation and the one used by Chen, besides the fact that the above equation does not couple the radiative and the conductive heat transfer terms are, the equation above includes heat conduction not only in the radial direction but also in the axial direction. Secondly, in Chen's model only convective heat transfer in the axial direction is considered; whereas, the above equation includes convection in the radial direction. In Chen's model, the entire riser width is treated as a uniform gas solid suspension. The average suspension properties must be known to solve the steady-state finite differences formulation. However, in this model, the properties of the annulus and the core sections have different properties; therefore, the riser is split into a number of core and annulus cells along the riser height.  55  Figure 3.5  Direction Convention used in Cell to Cell Heat Transfer Equation north  east  west 4r south  T  Wall  Tw  1  N  Tp  Ts  (a ) Core Cell as Control Volume  T  Wall  N  TP  Te  Ts  (b) Annulus Cell as Control Volume  56  3.2.7.3 Finite Difference Formulation  Since the heat transfer equation is not conducive to analytical solution, numerical methods were used to solve the equation. More specifically, finite differences with the control volume method was used. The width of the riser was divided into four cells: the wall cell, the annulus, the core and the axis of symmetry of the riser. Each cell had different boundary conditions and had to be treated separately.  The finite difference  formulation of the heat transfer equation for each cell is given below. For the wall cell, a constant temperature boundary condition was used. The wall temperature was set at 250°C. This assumes that the limiting rate of heat transfer is on the hot gas side, so that the cooling water temperature is equal to the wall temperature. The annulus cell had the followingfinitedifference formulation.  +F c A {T  - T°)-p c u A {T  -FysC A (T  - T°) + c u A {T  yn  p  N  P  s  N  P  g  Pg  g  g  s  s  N  s  P  s  - r°)  ~ T°)  -eaApT* + soAyX/ + saA T^ + eoA T^ + £oA Tf E  N  s  +G=0  (3.7) where, subscripts,  h ne xe yn ys  cell to wall heat transfer coefficient (W/m K) north face of the cell to the east of the control volume transverse direction of the cell to the east of the control volume (m) axial direction of the cell to the north of the control volume (m) axial direction of the cell to the south of the control volume (m) 2  57  For the core cells, the finite difference formulation is as follows.  - T ) -r^-(T -  f-iT  M  P  w  -(F c + c v )A {T x  p  Pg  g  g  T ) - ^-{T  P  w  p  N  - T)  p  s  - T°) + {F c +p c v )A {T xw  p  g  g  g  w  w  - T°)  -soApTp* + soA T^ + eoA T£ + eoA Tf + G = 0 w  N  s  .(3.8)  The finite difference formulation for the core to annulus conduction terms, in Equations 3.7 and 3.8, estimates the temperature gradient as the difference in the core and annulus temperatures divided by their distance apart. This estimation is more valid for small CFB risers, where the distance between the core and annulus is much smaller. In larger CFB units, this estimation assumes that there is a constant gradual temperature gradient between the core and the annulus, when in actuality, the temperature gradient in a CFB is very steep in the annulus and becomes less steep near the core and annulus boundary. The center of the riser symmetry is handled by setting the temperature gradient across the symmetry point to zero. The temperature of the center symmetry point, within thefinitedifference formulation, is set to equal to the core temperature at the same riser height. This boundary condition becomes less valid near the top and bottom of the riser, where the solids exit and entry points are not symmetric.  58  Using the given equation and boundary conditions, a temperature profile of the riser was obtained.  3.2.7.4 Wall to Cell Heat Transfer Equation The wall heat transfer coefficient term used is from a Studsvik report [Morris, 1988]. This term was obtained by fitting experimental data on the Studsvik C F B unit. A linear relationship between the furnace side heat transfer coefficient and the furnace solids bulk density was observed to be the following.  (3.9)  ft, = 1 . 8 A  where,  hf Pt,  furnace side heat transfer coefficient (W/m K) furnace solids bulk density (kg/m ) 2  3  3.2.7.5 Cyclone and Standpipe The cyclone is treated as adiabatic. The total amount of devolatilization and char combustion is recorded and an overall heat balance is calculated. There are two possible selections for the solids return particle temperature. The first selection is assuming that a heat exchanger is placed between the cyclone and the standpipe, the solids return particles are assumed to re-enter the riser at a constant temperature, set by the user. The second selection is to set the temperature of the solids return equal to the operating temperature of the cyclone. The second selection was chosen in the sensitivity analysis cases. The solids return particles are initially mixed with the combustion air and the fuel feed. The initial temperature of this mixture is used as the boundary condition of the surface temperature of the south face of the primary zone. Since this surface temperature is usually not equal to the temperature of the primary zone, there is heat loss due to conduction and radiative heat transfer through this surface. The magnitude of the heat  59  loss is less than 0.5% of the total heat transfer through the membrane wall; therefore, this loss does not affect the accuracy of the heat balance equation and the final temperature results. However, better alternative to this boundary condition, is to set the boundary condition as being an adiabatic surface. In this way, there would be no heat loss through this surface.  3.3  DESCRIPTION O F M O D E L P R O G R A M  3.3.1  Input and Output Files  The model's algorithm is seen in Figure 3.6, a description of the convergence loops and tolerances used are listed in Table 3.2, and the program listing is included in appendix A.  Initially, input and output files are assigned.  There are 2 input files included in  appendix B; one containing the CFB initial conditions and specifications, most of which are output values obtainedfromSenior's CFB model. The other inputfileincludes the fuel specifications, the relaxation parameters used in the specific case and the number of particles in the Monte Carlo method. The four outputfilesgenerated by the program are listed below. (i)  Afinaloutputfileincluded in appendix C  (ii)  Afilethat contains the temperature distributions at every iteration  (iii)  Afilethat contains information used in the enthalpy balance check  (iv)  A file that contains the temperature of one cell at every iteration, which show whether of not convergence has been achieved.  A description of the input and output variables used in the program are listed in appendix D.  60  Figure 3.6  (initial Oxygen Profile)  Model Algorithm (initial Temperature)  {Senior's Hydrodynamic Model)  New Heat Release Profile) faew Oxygen Profile)  Loop 3  New Temperature Profile )  61  Table 3.2  Convergence Loop 1 2  3  Description of Convergence Loops and Tolerances used in Program Description  Tolerance  Relaxation  Partial pressure of oxygen profile convergence for the core cells only Temperature profile convergence  Absolute 0.001 atm. Relative 1%  0.7  Heat Transfer Subroutine convergence is met by monitoring the convergence of 1 core cell's temperature at every call to the heat transfer subroutine calculation, or comparing the temperature profile with the previous iteration's profile, until the absolute error is less than the set tolerance.  0.7  Absolute approx. 0.01 °C —  3.3.2  Program Steps  (i)  The program initially reads the inputfilesand creates the output files.  (ii)  The riser is divided into core and annulus cells, and cell dimensions are then determined. For all the test cases, theriserwas divided into 20 core cells and 20 annulus cells, which have equal height and corresponds to the cell divisions used in Senior's model. Also there is a cell that represents the primary zone and a cell that represents the cyclone.  (iii)  Given the gas velocities, the combustion efficiency and the excess oxygen value of the gas and the ultimate analysis of the fuel, the air and fuel feedrates are calculated.  (iv)  The transverse and radial mass fluxes for all the cells are converted into mass flowrates.  (v)  The mass flowrate values are used in a mass balance where the axial mass flowrates of particles in the core cells were changed to ensure conservation of mass throughout the riser. Due to the nature of Senior's mass fluxes output  62  values, the mass balance for each cell in the riser was not entirely balanced. The error in the mass balance varies from + 4% near the bottom of the riser to - 5% at the top of the riser. Although this did not pose problems to Senior's hydrodynamic model, the enthalpy balance is very sensitive to the mass balance. A mass balance was needed to solve the temperature distribution in this model. Next a uniform initial value of 21% partial pressure of oxygen was set for the riser, and a uniform temperature of 850 °C was guessed for the bed. In addition, the user was prompted by the program to specify whether the solids return temperature will be equal to the cyclone temperature or a set temperature, specified by the user. A probability matrix is then set up using the mass flowrate information. This matrix is used to determine how a coal particle will travel within the CFBriserduring devolatilization and char combustion. Next the total membrane surface area is determined if a CFB design approach is used. Given an initial operating temperature of the bed, the program will calculate the fractional heat transfer area needed to achieve that temperature. If a rating approach is used, the user can specify the heat transfer area and the program will then calculate the operating temperature. Presently, the program sets the heat transfer surface as evenly distributed on all sides and along the full height of the riser above the secondary zone. The location of the heat transfer surface can be easily set at specific locations, at a later date. The devolatilization subroutine is called. This heat release profile due to devolatilization is corrected by using a volatile transferfractionterm, which assumes that the unburnt volatiles travel up the riser in a plume until they reach a cell with more oxygen, or until the volatiles are radially fully mixed with other gases. This phenomena is discussed in more detail in Section 3.2.2.  63  (xi)  The heat release due to devolatilization is determined, by summing up the total volatiles released in each cell and assuming the volatiles have the same higher heating value as for char.  (xii)  The subroutine to determine the partial pressure of oxygen profile is called. A mass balance is done to determine the oxygen profile.  The secondary air is  introduced into both the core and the annulus cells just above the primary zone. The split is determined on the core and the annulus cross-sectional area. In this way, the mean gas velocities in the core and annulus will be constant and equal to the gas velocities set in the user input file. (xiii)  This updated partial pressure profile of oxygen is compared with the previous iteration's profile to determine if convergence has been met. If convergence has not been met, the heat release due to char combustion is recalculated using the updated partial pressure of oxygen profile.  (xiv)  The subroutine to calculate the temperature profile of the CFB riser is called. Finite differences with a control volume formulation was used to conduct an enthalpy balance around each cell to determine the temperature profile.  (xv)  The updated temperature profile is determined.  (xvi)  The temperatures for the core and annulus cells at a height that corresponds to the beginning of the developing zone are altered to smooth the temperature profile. The other cell's temperatures were not altered.  This discontinuity in the  temperature profile is discussed in the Section 3.3.4. (xvii) The updated temperature profile is compared to the previous iteration to ensure convergence is reached. If convergence has not been achieved, the heat release due to devolatilization and char combustion and the partial pressure of oxygen subroutines are recalculated. (xviii) A printout of the output is generated.  64  3.3.3  Model Tuning  The major parameters in the user input file, found in appendix B, that can be varied for convergence reasons are listed below. (i)  Number of particles in the Monte Carlo method. The greater the number of particles used, the heat release distribution, the oxygen partial pressure profile and the temperature profile will be more smooth. The errors associated with not enough particles become more evident in the oxygen partial pressure profile in the annulus. A coal particle does not travel through many annulus cells, especially near the bottom of the riser; therefore, as the number of particles increases, more particles will travel though any given cell. Initial tests of the Monte Carlo method showed that approximately 100 particles are needed for reproducible results, in the core cells, which do not significantly change as more particles in the Monte Carlo method are used. More than 400 particles are needed to produce smooth profiles in the annulus cells. However, as more particles are used, the total run time increases linearly.  (ii)  Tolerance used in the partial pressure of oxygen profile calculation. This value is used in convergence loop 1, which is shown in Figure 3.6 and Table 3.2. The tolerance is an absolute tolerance, set at 0.001 atmospheres, which corresponds to a relative tolerance of 1% to 2.5%, and is based on the partial pressure of oxygen in the core. The change in the partial pressure of oxygen in the core was used as the basis, because there is very little oxygen in some parts of the annulus and its' absolute and relative tolerance errors would be too small to be meaningful. Conversely, the absolute and relative variations in the partial pressure of oxygen in the core is not large, and this iterative calculation converges steadily, normally within 10 iterations if an under relaxation factor of 0.7 is used.  (iii)  Tolerance used in the temperature profile calculation  65  This is a relative tolerance, used in convergence loop 2 which is shown in Figure 3.6 and Table 3.2, and is set at 1% of any cell's temperature compared to the cell's temperature in the previous iteration. This calculation is very rapid, using an under relaxation factor of 0.7. Tolerance in the heat transfer subroutine. This value is used in convergence loop 3, which is shown in Figure 3.6 and Table 3.2. Normally, the temperature for 1 core cell was monitored to determine whether a steady-state temperature had been reached; however, the user may also specify a temperature tolerance to determine whether convergence is achieved. For the test runs conducted, by monitoring the temperature of 1 core cell until convergence has been achieved, thefinalabsolute temperature tolerance was less than 0.01 °C. Relaxation parameter in the partial pressure of oxygen calculation. This under relaxation factor is set to 0.7. Relaxation parameter in temperature profile calculation. This under relaxation factor is set at 0.7 and prevents this subroutine from diverging. The relaxation parameters used in the partial pressure of oxygen and the temperature calculations are used to prevent the profile predictionsfromdiverging. Even if increasing the relaxation parameters does not cause the profile predictions to diverge, this will not significantly decrease the program's computation time, since the limiting calculation is the Monte Carlo method. Residence time of the cyclone. This value is set at 0.3 seconds, and can be easily replaced with a more sophisticated cyclone model, if necessary.  66  3.3.4  Discontinuity of Temperature Profile There is a discontinuity in the temperature profile calculated by this model, which  varies for different CFBs and initial conditions.  The position and magnitude of the  discontinuity coincides with the boundary between the developing and the fully-developed zone.  The discontinuity results from the hydrodynamic model, which uses different  equations to predict the mass fluxes for the developing and the fully-developed zones. Figure 3 . 7 , shows a plot of mass flowrate versus height for the UBC CFB, and the discontinuity can be seen clearly. Since the discontinuity does not significantly affect the hydrodynamic code, but affects the temperature profile, and since only 1 cell is affected, namely the boundary cell, a curve smoothing subroutine was used to correct for this one point. From Figure 3 . 8 , it can be seen that the curve smoothing subroutine does not change the results of the other points or affect the temperature prediction in subsequent iterations. Several other methods to correct for the discontinuity were considered. Initially, subdividing the riser into more cells in the axial direction was tested. The result of this test is shown in Figure 3 . 7 .  By increasing the number of axial cells, the bounds of the  discontinuity location were constricted and the magnitude of the discontinuity was reduced; however, by increasing the number of cells, the run time increased. Secondly, the tolerance in the hydrodynamics code that controls the convergence of the boundary massfluxesprediction was decreased. This caused the discontinuity to decrease, but not to an extent that the temperature profile would be continuous. In fact, if the tolerance was decreased too much, the hydrodynamic code would not converge.  67  68  Figure 3.8  Temperature Distribution of Gore Cells (before and after curve smoothing)  880 - r  870  0  2  3  4  5  height above secondary air (m)  69  Since this discontinuity also affected the heat generation profile slightly, smoothing the heat generation profile was considered.  This reduced the magnitude of the  discontinuity; however, it was still present. The best method found to date to deal with the discontinuity is to smooth the temperature profile directly, at every iteration.  3.3.5  Convergence Due to the non-linear nature of the equations, it takes several hundred iterations  until a final converged solution is obtained.  In practice, several test runs were first  conducted at different initial temperature guesses, to determine the bounds of the final temperature solution. These bounds, within + 20 °C were then used in the final run. In this way, the initial guess of the temperatures is close to the final solution, so that convergence is achieved in less than 100 iterations. If the test runs were not conducted, it may take more than 600 hundred iterations to obtain the final converged result. Figure 3.9 shows that there is indeed afinaltemperature solution, since a higher or a lower initial temperature guess will still converge on the samefinalvalue. Repeatability of the results was also studied by running the same conditions several times, starting with different initial temperature profiles. The results, shown in Figure 3.10, were such that each run produced effectively identical profiles, provided that sufficient time was given for convergence; therefore, the repeatability of the program is good.  3.3.6  Numerical Stability of Partial Pressure of Oxygen Profile An analysis was done to determine if and when instabilities arose in the partial  pressure of oxygen profile iteration and in the temperature profile iteration. For the partial pressure of oxygen profile, it was shown that the greatest relative variation in the amount  70  Figure 3.9  Temperature Convergence for Various Initial Temp. Guesses (Studsvik CFB, case shO)  950 - r  0  200  400  600  number of iterations  800  1000  71  Figure 3.10 Temperature Profiles of Case shO (for various initial temperature guesses)  900  T  72  of oxygen was in the annulus cells. This suggests that because only 100 particles were used in the Monte Carlo method, and the volume and residence time in the annulus is small compared to the core cells, if one extra coal particle enters an annulus cell, the oxygen partial pressure profile can be significantly different. A test run was conducted for the Studsvik CFB, in which the number of particles in the Monte Carlo method was increased from 100 particles to 400 particles, see Figure 3.11. From thisfigurewe see that with 400 particles the partial pressure profile in the annulus is more smooth, but clearly more particles are needed to obtain afinalconverged annulus profile. This error in the partial pressure of oxygen in the core cells was small compared to the streamer and seemed to reach a converged value quickly, as will be shown in the next chapter, Figure 4.1.  3.3.7 RunTime The run time required for convergence could be slightly improved by varying the relaxation parameters and the convergence tolerance values.  However, as mentioned  previously, the limiting subroutine in the program was generating the heat release distribution using the Monte Carlo method. Decreasing the minimum number of particles needed in the Monte Carlo method, can significantly decrease the overall run time of the program. For the test cases studied, which are rating problems, initially several quick runs of approximately 10 minutes each were conducted using only 10 particles in the Monte Carlo method and starting each run at a different initial temperature guess, to determine the range of the final converged temperate profile. Then using relaxation parameters of 0.7 for both the partial pressure of oxygen profile and the temperature profile calculations, setting 0.001 atmospheres for the absolute tolerance value of the partial pressure of oxygen and 0.01 °C for the absolute tolerance of the heat transfer subroutine, and using  73  Figure 3.11 Partial Pressure of 02 vs Height (Studsvik CFB, Combustion of Highvale Coal with TJ = 7m/s and Gs = 15 kg/m s) 2  0.07  T  0.01 +  0 -I 0  1  1  1  2  4  6  height (m)  74  100 particles in the Monte Carlo method, the program took approximately 2.5 minutes per iteration. With a initial guess of the final temperature of the riser, which is close to the final converged temperature, program convergence can be obtained within 20 iterations; however, with most of the test runs, the program was allowed to run for 200 iterations to ensure that convergence has been met.  The total run time for 200 iterations was  approximately 8 hours. If more particles are used in the Monte Carlo method, then the total run time of the program would increase linearly in proportion to the number of particles. For a design problem, where we wish to find the total heat transfer area needed to achieve a given average operating bed temperature, initial quick test runs were also conducted using a different heat transfer area for each test. The design problem was found to take just as long to run as a rating problem. The program was executed on Sun workstations, which is approximately 3 to 4 times as fast as a 33 MHz 486 PC.  75.  CHAPTER 4 DISCUSSION OF RESULTS AND VALIDATION 4.1  INTRODUCTION The goal of a Circulating Fluidized Bed Boiler's operation is to generate steam for  energy production. In a typical day, the demand for energy varies, with a higher demand early mornings and early evenings. Since the CFB boiler is unable to store any energy, the operation of the C F B will have to be changed to meet the various steam demands throughout the day. The basic strategy for meeting varying steam demands is to vary the heat flux from the boiler The basic heat flux equation is given below.  Q - UAAT  (4.1)  Since the heat transfer area, A, is constant and the temperature difference, AT, cannot change significantly, this implies that the heat transfer coefficient, U, must be varied. Some parameters must be kept within certain operating ranges. One of these parameters is the percentage of air leaving with the flue gas. Ideally, this value is kept at a minimum, usually between 1 0 % and 3 0 % excess air, or just enough air is added for complete combustion; thereby, minimizing heat loss by heating the excess air. Secondly, the average temperature of the bed is kept within the operating range of 750 °C to 900 °C. A temperature greater than this range will cause more NOx to be generated, decrease sulphur capture and cause other operating problems. Operating temperatures considerably less than 750 °C will hinder coal combustion. The exact temperature will depend upon fuel reactivity. The above arguments assume that the reactor is approximately isothermal. At low load, the gas velocity may be low and the circulation rate may drop correspondingly. In this case, the primary zone  76  must be held at the desired operating temperature; therefore, there may be a significant drop in the upper furnace temperatures. In order to change the heat transfer coefficient to meet the steam demands, the suspension density profile of the CFB must be varied. There are several parameters that can be changed to achieve the desired heat transfer coefficient.  The typical parameters  include air feedrate, solids recirculation rate andfluegas recycle rate. To verify that CFB control can be effectively modeled using the program developed here, results were obtained for both the Studsvik CFB and for the UBC CFB using various superficial gas velocities and solids recirculation rate inputs. The model does not considerfluegas recirculation; therefore, the effects of this parameter on a CFB's operations were not studied.  4.1.1  Initial Test Runs To ensure that a random number was generated with each call to the random  number generator, when the program was executed on a 486 PC, a new seed was selected with each call for a random number. The results of several Studsvik CFB runs, shO, with the same initial inputs were conducted with similar, but not identical results. When this program was executed on the Sun Workstation, it was not possible to generate a random seed with each call to the random number generator; however, the random numbers generated are sufficiently random, such that different initial starting points of the same test case gave the same, but not identical profile predictions. From previous testing of the model, it is clear that the temperature profile changes affect the pressure profile to a larger extent than the pressure profile causing changes in the temperature profile calculations.  The reason for this is that the high solids  recirculation rates tend to smooth out the temperature profile, making the temperature more uniform throughout the riser. This effect masks changes in the heat release and partial pressure of oxygen profiles under the conditions studied. Therefore, test runs were  77  conducted to ensure that the CFB's partial pressure of oxygen profile had indeed converged before the program called the subroutine to predict the temperature profile. On average, the program conducted 10 to 20 iterations of the partial pressure of oxygen profile before the tolerance was met and the temperature profile could then be predicted. There was some concern that the tolerance was not tight enough for the pressure convergence.  In one test, the partial pressure of oxygen calculation was allowed to  continue for 200 iterations, tracking the pressure of oxygen in a core and streamer cell at a height which shows the greatest pressure variations.  The height chosen, based on  behaviour in previous runs, was 1 m above the secondary air. Figure 4.1 shows that the partial pressure of oxygen in the core cell quickly reached a steady value of approximately 0.04 atm. within the first 10 iterations, while the streamer cell's partial pressure of oxygen did not converge but varied around an average value of 0.02 atm. The reason, which was previously mentioned, is that the number of Monte Carlo particles used may not be large enough so that if one extra particle enters an annulus cell, its oxygen partial pressure profile can be significantly changed. Therefore, more particles in the Monte Carlo method will be needed. This will cause the total run time to increase. A third test run was conducted to show that the Monte Carlo Method was simulating the path of the coal particle as it traveled throughout the CFB, based on the CFB's hydrodynamics. For this test, a very large "theoretical" particle with a diameter of 1 m was introduced into the primary zone of the CFB and tracked throughout its devolatilization and combustion. Theriserwas assumed to be at a constant temperature and partial pressure of oxygen. In addition, the devolatilization expression used was from Jia, which is a function of particle diameter. Since the primary zone is normally much larger and denser than a core or streamer cell, a small coal particle will devolatilize and combust before it has the chance to travel up the riser. A large coal particle should have a long enough combustion time for it to travel through all of the cells many times over. In these circumstances, the percentage of the total heat release in each cell should be the  78 Figure 4.1 0,  .  Oxygen Partial Pressure of Cells at a Height of l m Above Secondary Air (Studsvik CFB; case shO)  79  same as the cell's percentage suspension density. This was indeed found to be the case; thereby, showing that the Monte Carlo Method was working as the program intended. 4.2  STUDSVIK CFB  4.2.1  General Description The Studsvik 2.5 MW thermal prototype CFB is a boiler that is 6.1 m tall with a  square cross-sectional area of 0.65 m by 0.65 m. There are membrane surfaces on all four sides of the riser. The riser has a smooth exit geometry with a riser top reflection coefficient of 0.1 [Senior, 1992]. A schematic of the Studsvik CFB is shown in Figure 4.2.  4.2.2  Sensitivity Analysis A set of sensitivity analysis was conducted for the Studsvik CFB to study the  effects of varying superficial gas velocity and solid recirculation rates, while combusting Highvale coal. An analyses of Highvale coal is given in Table 4.1, and the particles size distribution of the Highvale coal and the bed are given in Table 4.2. The inputs and the operating conditions of the six cases studied in the sensitivity analysis are listed in Table 4.3. The three different solids recirculation rates studied were 15 kg/m s, 30 kg/m s and 2  2  50 kg/m s. In addition, two superficial gas velocities cases of approximately 7 m/s and 2  6m/s were also studied. In practice, a commercial CFB may have a "turndown", a reduction in the load, as low as 3:1, or a corresponding decrease in the superficial gas velocity from a full load value of 7m/s to as low as 2.5 m/s.  It would be useful to model a case where the  superficial gas velocity is 2.5 m/s, to observe changes in the temperature distribution. However, it was found that at superficial gas velocities less than approximately 5 m/s, the hydrodynamic model breaks down.  Low gas velocities in the hydrodynamic model,  coupled with the existing "wall disturbance factor", which is a valuefittedto experimental  80  Figure 4.2  Schematic of the Studsvik CFB [Kobro, 1984]  81  Table 4.1  Characteristics of Highvale Coal [Grace et al, 1989]  Proximate Analysis Volatile Matter Fixed Carbon Ash Moisture Ultimate Analysis - Dry Basis (%) Carbon Hydrogen Nitrogen Sulphur Oxygen Ash Higher Heating Value (MJ/kg)  Table 4.2 Particle Size (mm) 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0  (%) 30.5 42.1 12.2 15.2 62.4 3.6 0.8 0.2 18.7 14.3 24  Particle Size Distribution of Highvale Coal and Bed Highvale Coal (%) 9.25 10.92 13.18 12.11 11.09 8.73 7.75 5.48 4.75 3.74 3.41 3.99 1.29 0 0 0 0 0  Lime (%) 0 0 0 0.34 0.61 1.36 0.95 4.33 14.06 13.33 13.19 20.54 19.76 7.02 2.91 1.51 0 0  Bed (%) 0 0 0 0 0 2.0 4.44 3.7 3.27 10.78 28.29 23.72 14.33 5.95 1.54 0.66 0.57 0.75  82  Table 4.3  Major Parameters in the Sensitivity Analysis Cases (Studsvik CFB, base case shO)  sh2 sh3 sh4 sh5 shO shl cases: 6 6 6 7 7 7 superficial gas velocity (m/s) 50 15 30 50 15 30 solids recirculation rate (kg/m s) 898 812 764 859 835 852 solids return temperature (°C) 389 403 341 335 396 347 fuel feedrate (kg/hr) 3018 3129 2644 2599 3070 2694 air feedrate (kg/hr) 3.3 2.5 2.8 2.5 2.5 3.0 height of developed zone (m) yes yes yes yes yes yes Highvale coal 1400 1400 1400 1400 1400 1400 Fuel density (kg/m ) 2800 2800 2800 2800 2800 2800 bed density (kg/m ) 2.89 2.89 2.89 2.89 2.89 2.89 average particle size (mm) 20 20 20 20 20 20 excess air (%) 100 100 100 100 100 number of particles used in the Monte 100 Carlo Method 2  3  3  data over a limited range, produced unreasonable core-wail flux calculations. Therefore, only a 15% reduction in the maximum load has been studied to this point. In order to study the effects of turndown by decreasing the superficial gas velocity to a value of 3.3 m/s, the wall disturbance factor was increased from 310 to 470. However, there is insufficient  experimental hydrodynamic data to validate this  modification. The resultsfromthis low superficial gas velocity test, sh6, for the Studsvik CFB, is presented at the end of appendix C. Clearly, further work is needed to extend the hydrodynamic model to cover a greater operating range. Initially, the heat transfer area needed to give an average operating temperature of 850 °C was calculated. The heat transfer area calculated was approximately 70 % of the total wall area. This percentage wall area was used for all the runs in the sensitivity analysis. The actual heat transfer area of the CFB can be modified depending on the type of fuel combusted by installing refractory, but is approximately 50% of the total wall area.  83  As expected, the heat transfer area calculated using the model was larger than the actual heat transfer area. This is a result of two major reasons. The model assumes that the membrane surfaces are smooth and not made up of membranes, or parallel tubes connected longitudinally by fins. Therefore, the actual total membrane surface area is greater than the area calculated in the model.  The model  corrects for this inconsistency by calculating the total heat transfer area based on the steady state bed temperature one would like the model to operate at. In this way, the total heat transfer area would be equivalent to the actual heat transfer area of a membrane surface. Further work on the details of the membrane wall heat transfer would aid in the calculation of the cell to wall heat transfer rate. The performance of the membrane surface should include an effectiveness factor. Secondly, the model does not include heat lossfromthe riser. However, based on a rough overall energy balance on the Studsvik CFB, assuming 50% heat transfer area, the surface of the CFB is at 35 °C, the heat transfer coefficient from the CFB surface to the surrounding air is 15 W/m^C, the surrounding air is at 20 °C and a coal feedrate of 400 kg/hr, the heat lossfromthe riser is less than 10 % of the total heat generated.  4.2.3  Results The following figures of heat release, oxygen partial pressure and temperature  profiles are for conditions above the secondary air. At a height of 0 m, this point indicates the condition in the primary zone.  4.2.3.1 Heat Release Profiles The results from the sensitivity analysis, Figures 4.3, 4.4 and 4.5, show that the volatiles and char heat release is mainly in the primary zone.  This is because the  devolatilization expression used releases the volatiles quicklyfromthe coal upon entry into the primary zone. In addition, the density and size of the primary zone is large compared  84  Figure 4.3 Volatiles Heat Release vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  0.4  T  0.35  0.3 4 * — Gs = 15 kg/m2s (streamer) 0.25  ~o-  Gs = 30 kg/m2s (streamer) " Gs = 50 kg/m2s (streamer)  0.2  Gs = 15 kg/m2s (core) Gs = 30 kg/m2s (core)  0.15 -H  Gs = 50 kg/m2s (core) 0.1  0.05  4  2  3  height (m)  85  Figure 4.4 Char Heat Release vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  1  T  0.1 • G s = 15 kg/m2s (streamer)  a> u  _o  G  s =  3  0  k g / m 2 s  (streamer) (0  ro  Gs = 50 kg/m2s (streamer) 0.01  co  o  Gs = 15 kg/m2s (core)  c o  Gs = 30 kg/m2s (core)  o ro  Gs = 50 kg/m2s (core) 0.001  0.0001 2  3  height (m)  86  Figure 4.5 Char Heat Release vs Height (Combustion of Highvale Coal with U = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5)  0.1  41  Gs = 15 kg/m2s (streamer) Gs = 30 kg/m2s (streamer) Gs = 50 kg/m2s (streamer) 0.01  Gs = 15 kg/m2s (core) Gs = 30 kg/m2s (core) Gs = 50 kg/m2s (core)  0.001 +  0.0001 -I  1  1  1  1  0  1  2  3  4  height (m)  1  5  87  to other cells in the riser, and the residence time in the primary zone compared to other cells is considerably larger. The primary zone is approximately 6 to 8 times larger than a core cell and 6 to 50 times as dense. The second observation from these figures is that the char heat release profiles for various solid recirculation rates are almost the same; however for higher solid recirculation rates, the fraction of heat release in the primary zone is less; thereby, a larger percentage of heat is released in the riser and cyclone. This is because as more solids are being added to the riser, the primary zone begins to become saturated with solids, and the percentage density increase in that zone is not great. The density of the primary zone stays almost constant at approximately 315 kg/m^. Instead, the solids are transferred up the riser and the percentage density change of the riser in the secondary zone is significantly increased, causing more heat to be released further up the riser. The density changes can be seen in Figure 4.6. In addition, the case with a higher superficial gas velocity show a slightly lower fraction of heat release near the bottom the riser.  The higher gas velocity seem to  contribute to carrying the particles from the primary zone up the riser, consequently releasing the heat in the secondary zone. This can be seen by comparing the heat release resultsfromruns shO and sh3, shown in Figure 4.7.  4.2.3.2 Partial Pressure Profiles  From the partial pressure of oxygen profiles, shown in Figures 4.8 and 4.9, a higher partial pressure of oxygen was shown for higher solid recirculation rates and for higher gas velocities. However, the higher oxygen concentration in the core meant fewer oxygen in the streamer cells. The total amount of oxygen in the streamer is very small, approximately 1.5% of the total oxygen in the riser. In addition, the oxygen profile in the streamer varied from iteration to iteration. It is difficult to obtain a converged oxygen profile, as can be seen in Figure 4.1.  88  Figure 4.6  Changes in Core Density in Secondary Zone for Various Solids Recirculation Rates - Primary Zone Density = 315 kg/m (Combustion of Highvale Coal with TJ = 7 m/s; Studsvik CFB; cases shO, shl & sh2) 3  70  60  4-  50  co E  40  (A  c a>  TJ  "HJ u Oi  30  o u  20  10 +  89  Figure 4.7 Char Heat Release Distribution vs Height (Combustion of Highvale Coal, Studsvik CFB; cases shO and sh3)  0.1  41  U = 7 m/s (streamer) U = 7 m/s (core) 0.01  U = 6 m/s (streamer) U = 6 m/s (core)  0.001  0.0001  90  Figure 4.8 Partial Pressure of 02 vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  0.08  T  0.07  0.06 Gs = 15 kg/m2s (streamer) |  0.05  -—D-  c w  — Gs = 50 kg/m2s (streamer)  > X  o o 0.04 CD  Gs = 15 kg/m2s (core)  k_ (A V>  t CO Q.  0.03  IJO-D-O-CHIJJ*  ** 0.02  k  UJ  Ii  Id  /  4  + 2  Gs = 30 kg/m2s (core) Gs = 50 kg/m2s (core)  e7  TJ  0.01  Gs = 30 kg/m2s (streamer)  4 height (m) .  91  Figure 4.9 Partial Pressure of 02 vs Height (Combustion of Highvale Coal with TJ = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5)  0.08  T  0.07  0.06  4|  Gs = 15 kg/m2s (streamer)  I  o.o5  -HI  c  > x o 0 a)  —  Gs = 30 kg/m2s (streamer) — Gs = 50 kg/m2s (streamer)  0.04  4-  w  3  (A V)  Gs = 15 kg/m2s (core)  01 (0  '€  (0  0.03  •L  Gs = 30 kg/m2s (core) Gs = 50 kg/m2s (core)  0.02  0.01 4-  92  As the superficial gas velocity decreased, there seems to be even less oxygen in the annulus cells. In fact, there are cells where there is no oxygen, near the bottom of the riser. The partial pressure of oxygen in the core cells, however, seems to change very little. The variation in the partial pressure of oxygen in the streamer cells is due to the insufficient number of particles used in the Monte Carlo method. From Figure 3.11, when more particles are used, we see less fluctuations in the partial pressure predictions.  4.2.3.3 Temperature Profiles From the temperature profiles, Figures 4.10 and 4.11, we see that although various solids recirculation rates and superficial gas velocities were used in these test cases, the temperature profiles were similarly shaped and uniform; however, they are displaced by approximately 50 °C. This is due to the significant contribution of the heat release distribution to the overall temperature distribution. However, the high internal circulation rates tends to smooth out huge maldistributions in the heat release distribution. Although approximately 80% of the heat release occurs in the primary zone, there are sufficient recirculating solids that there is still only a 50 °C temperature change throughout the riser. It is then understandable that the heat release distributions are similar, and subsequently the temperature profiles will also be similar although the pressure profiles may not be. Pressure has less of an affect on temperature as the reverse situation. Another interesting phenomena is that the temperature of the streamer increases near the top of the riser, which is due to the nature of the energy balance. The volume of the streamer at the top of the riser is small; approximately 0.0003 m , or 0.3% of the core 3  volume at the top. Therefore, hot particles from the core and particles that are reflected off the top of the riser cause the streamer cells to heat up to temperatures that are greater than the core temperatures.  93  Figure 4.10 Temperature vs Height (Combustion of Highvale Coal with U = 7 m/s; Studsvik CFB; cases shO, shl & sh2)  1000 T  950  — » — Gs = 15 kg/m2s (streamer) Gs = 30 kg/m2s (streamer)  900  O  - Gs = 50 kg/m2s (streamer)  CO a  (O k. Q.  Gs = 15 kg/m2s (core)  E  Gs = 30 kg/m2s (core)  850 -a  800  750  -+-  2  3  height (m)  Gs = 50 kg/m2s (core)  94  Figure 4.11 Temperature vs Height (Combustion of Highvale Coal with TJ = 6 m/s; Studsvik CFB; cases sh3, sh4 & sh5)  950  900  Gs = 15 kg/m2s (streamer) —D-  850 + o  Gs = 30 kg/m2s (streamer) — Gs = 50 kg/m2s (streamer)  3 •*-» <0  w o.  Gs = 15 kg/m2s (core)  E 0)  800  Gs = 30 kg/m2s (core) Gs = 50 kg/m2s (core)  750  700  95  The temperature of the core cells is a steady decreasing curve, but the streamer cells have temperatures approximately 50 °C less than the core. This thermal boundary layer near the wall follow the same trends as experimental measurements [Leckner, 1991] and theoretical equations [Brewster, 1984], shown in Figure 4.12. Although the model's temperature gradient predictions matches Leckner's experimental measurements very well, this is not an indication of the sophistication of the heat transfer model, since a number of simplifying assumptions have been made. However, this does indicate that the average temperature predictions of the model can be used as a starting point to predict combustion and heat transfer rates in the streamer and might be extended to predict the production of certainfluegases such as NOx and  4.3  UBC PILOT CFB  4.3.1  Description The  SO2.  detailed description of the UBC pilot-scale circulating fluidized bed  combustion facility can be found in Grace [Grace et al, 1989]. A schematic of the major components can be seen in Figure 4.13. The reactor column is 7.32 m high and has a cross-section of 152 mm by 152 mm. Primary air flows through the bottom of the CFB,  through a distributor plate into a  tapered primary zone. The secondary air enters the CFB through 2 opposed air ports located 0.9 m above the distributor plate. The solids and gas leaving the top of the CFB are separated in a refractory lined primary cyclone with 0.31 m ID, andfinerparticles are captured in a secondary cyclone with a 0.2 m ID.  The solids from the primary cyclone are  returned through the standpipe located 0.4 m above the distributor.  96  Figure 4.12  Comparison of Wall Temperature Gradient at a Height of 2.4 m Above Secondary Air with Other Experimental and Theoretical Works  97  Figure 4.13  Simplified Schematic Diagram of UBC Pilot-Scale CFB  PNEUMATIC FEED PORT PRIMARY AIR  98  4.3.2  Test Run  A test case, uhO, was conducted using the model of the UBC CFB, to see how well the model predicts operating parameters in a pilot-scale CFB as compared to a commercial CFB.  In addition, experimental data are available for the UBC CFB for  various load control parameters. These data can be used to qualitatively validate the model. The baseline conditions for case uhO are superficial gas velocity of 7.03 m/s and a solids recirculation rate of 30 kg/m2s. The heat transfer area calculated by the model, which gave a corresponding CFB operating temperature of 850 °C is 35% of the total wall area. The model assumes that the heat transfer area is evenly distributed on all four sides of the CFB riser and no heat transfer or heat loss from the primary cyclone and standpipe. The UBC CFB's actual heat transfer area is only approximately 5% of the total wall area located in a small section near the top of the riser. However, the UBC CFB has high heat lossfromall four sides of theriserandfromthe primary cyclone and standpipe. The heat lossfromtheriseris evenly distributed throughout the full height of the riser, and as much as 50% of the heat loss isfromthe primary cyclone and standpipe. For this CFB, the heat transfer assumptions made in the model, would reasonably represent the actual heat transfer and heat loss from the CFB, except that the high capacitance of the refractory and the axial heat transfer through the refractory would tend to make experimental temperature results more uniform.  4.3.3  Results  The heat release results from run uhO compared to that from case shO of the Studsvik CFB, listed in Table 4.4 of baseline conditions, shows the volatiles completely devolatilizing in the bottom 3 m of the .riser in the UBC CFB; whereas, in the Studsvik  99  CFB, the volatiles are released within thefirstmeter upon entering the riser. The volatiles and char heat release profiles are shown in Figures 4.14 and 4.15. From Figures 4.14 and 4.15, we can see that the fraction of heat released in the streamer is higher than in the core for TJBC's CFB, but in the Studsvik CFB the reverse is seen. In the Studsvik CFB, the annulus region's average cross-sectional area is approximately 0.9 % of the total cross-sectional area; whereas in the UBC CFB, the average annulus region is approximately 3 % of the total cross-sectional area. While even 3% may not seem significant in terms of total cross-sectional area occupied, the annulus region contains approximately 80% of the total solids in the cross-section. Therefore, the streamer is much more significant in terms of its effect upon combustion and pollutant formation behaviour in small cross-sectional CFB risers.  Table 4.4  Parameters in Baseline Test  cases: superficial gas velocity (m/s) solids recirculation rate (kg/m s) solids return temperature (°C) fuel feedrate (kg/hr) air feedrate (kg/hr) height of developed zone (m) Highvale coal fuel density (kg/m ) bed density (kg/m ) average particle size (mm) excess air (%) number of particles used in the Monte Carlo Method 2  3  3  uhO (UBC) 7 30 793 23 177 3.2 yes 880 2650 2.89 20 100  shO (Studsvik) 7 30 859 396 3070 2.8 yes 1400 2700 2.89 20 100  100  Figure 4.14 Volatile Heat Release (Combustion of Highvale Coal with TJ = 7 m/s and Gs = 30 kg/m s) 2  0.25 4  . .—  UBC (streamer)  B  - UBC (core) »--.••-  —  u  (0  0.1 -H  0  0.2  0.4  0.6  0.8  height of cell / height of riser  1  Studsvik (streamer) Studsvik (core)  101  0.0001 4  1  1  1  0  0.2  0.4  0.6  height of cell / height of riser  1 0.8  102  In terms of modelling, because the streamer's influence on combustion and emissions is less for a large cross-sectional  CFB riser, a one dimensional  combustion/pollutant model that considers the core cells only will be faster to converge, and properly applied, the temperature and pressure profile results may still be valid. A core annulus model for heat transfer is still vital, since heat transfer occurs in the wall layer. For this test run, most of the volatiles are released in the primary zone, because the primary zone in the UBC CFB is approximately 2.3 times as large as a core cell and 12 to 35 times as dense. Therefore, the residence time in this zone is more than 10 times aslong as any other cell in the riser. From Figure 4.14, we see that for the UBC CFB, the fraction of volatiles released near the bottom of the riser is greater than in the Studsvik CFB. This may be due to the smaller riser diameter of the UBC CFB. In the UBC CFB, the volatile plume that forms, quickly spans the full diameter of theriser;therefore, there is enough oxygen present, near the bottom of theriser,for volatiles combustion. The char heat release profiles with various particle diameters, at a constant temperature profile, can be seen in Figures 4.16. Thisfigureshows that the solids in the UBC CFB is well mixed; therefore causing the char heat release profiles to stay the same regardless of particle diameter. If larger particles are combusted, not only would the devolatilization expression used be invalid, but the assumption that the fuel particle behave in the same way as the bed particles would also be invalid. The heat release profiles would then be different. Comparing UBC's partial pressure of oxygen profiles with the profile from case shO, Figure 4.17, shows that for UBC's CFB, the pressure profile in the streamer cells is more smooth and uniform. Again, this is due to the streamer's significance in a smaller cross-sectional CFB. The amount of oxygen present in the annulus is approximately 5% of the total oxygen in the UBC CFB; whereas in the Studsvik CFB, there is only 1.5% oxygen in the annulus. If additional coal particles were to combust in the Studsvik CFB's  103  Figure 4.16 Char Heat Release for Various Mean Particle Diameters (UBC CFB, Combustion of Highvale Coal with U = 7 m/s)  1  T  -a  mean dp = 2.7 mm (streamer) ~ 2.7 mm (core)  r—  4.4 mm (streamer) ~ 4.4 mm (core)  A  " 7.9 mm (streamer)  &  7.9 mm (core)  •  2 cm (streamer) ~ 2 cm (core)  0.001  -\  1  1  1  '  0  2  4  6  8  height (m)  104  Figure 4.17 Partial Pressure of 02 vs Height (Combustion of Highvale Coal with U = 7 m/s and Gs = 30 kg/m s) 2  0.12  T  0 -I 0  1  1  1  1  1  0.2  0.4  0.6  0.8  1  height of cell / height of riser  105  annulus, the oxygen partial pressure profile results can be quite different. Combustion in the cyclone for both the UBC CFB and the Studsvik CFB are insignificant, less than 0.5% of the total heat release, in this model. The temperature profile, Figure 4.18, shows the UBC's CFB to give temperature in the streamer and core that are 50 °C apart near the bottom of the riser, but quickly become only 10 °C apart further up the riser. In the Studsvik CFB, the streamer's temperature is much less than the core's temperature. In addition, for UBC's CFB, we do not observe the temperature of the streamer heating up near the top of the riser. The "kink" in the temperature profile of the streamer is due to the discontinuity in the temperature profile prediction, as discussed in Section 3.5. Although the temperature at the discontinuity point has been smoothed, by just averaging the temperatures in the adjacent cells, at times the streamer temperature profile is not as smooth as is desirable. Finally, similarly to the Studsvik CFB, there is a high solids recirculation rate in the CFB, which causes the temperature profile to become more uniform; however, for the UBC CFB, the dense annulus region, causes the average bed density for a given riser height to be greater than for the Studsvik CFB and therefore, the heat transfer coefficient is also greater. As more heat leaves through the heat transfer surface, the CFB temperature cools considerably. Figure 4.19 shows the magnitude of the particle convective term compared to the conduction and radiative terms.  106  Figure 4.18 Temperature vs Height (Combustion of Highvale Coal with U = 7 m/s; UBC CFB; case uhO)  900  T  107  Figure 4.19  Enthapy Balance for Core Cell at Height = 3.36 m (UBC CFB, case uhO)  nonth C, Pc, Gc, R  west C, Pc, Gc, R  —>  core cell  G  C, Pc, Gc, R south  Heat Transfer (W) Temperature (C) G : heat generation C : conduction Pc: particle convection Gc: gas convection R : radiation Total Enthapy Balance  core cell 826 447  west  north  south  -2 -5681 -37 -263  0 -1016630 -46664 -35  0 1022077 46779 8  -1  108  4.4  VALIDATION The oxygen partial pressure profiles for the UBC CFB were computed using two  different devolatilization expressions. Thefirstexpression of Anthony et. al. was shown in Equation 3.1, and the second expression is a combination of expressions by Agarwal [1986] and Davidson et. al. [1985], which are shown below. The expression by Anthony, is not a function of particle diameter and is valid for small particles with diameters less than 2 mm.  This expression is not valid for larger particles; therefore, the second  expression by Agarwal and Davidson was also looked at to observed the differences. The results were compared with experimental partial pressure of oxygen values measured by Zhao [1992]. Experimental and predicted profiles are shown in Figure 4.20. The devolatilization time and rate are given by the following expressions by Agarwal and Davidson, respectively.  The equation presented by Davidson is the  prediction of a shrinking core model with diffusion control. r =k d d  v  (4.2)  n p  where, dp kv n  devolatilization time (s) particle diameter (mm) constant (s/mm ) = 1.5 constant = 1.5 n  - U 1-3(1-/)'+2(1-/)  («)  *d  where,  t f  time (s) devolatilization time (s) fractional yield of volatiles  Differences in the predicted partial pressure of oxygen profiles and experimental data may be due to several reasons. The combustion conditions used in the model and by Zhao are not identical. In addition, the devolatilization expression by Anthony is not a  109  Figure 4.20 Oxygen Concentration Profiles for Highvale Coal Zhao (T=891 °C, U = 8.26 m/s, 0 in flue gas = 2.9%) Conditions: Anthony (T=830 °C, U = 7 m/s, 0 in flue gas = 3.7%) Agarwal & Davidson (T=830 °C, U = 7 m/s, 0 in flue gas = 3.8%) 2  2  2  0.14  Agarwal & Davidson (annulus) Agarwal & Davidson (core) -*  Anthony (annulus) Anthony (core)  -*  data from Zhao (wall) Zhao (midpoint)  -*  2  4  6  height above secondary air (m)  Zhao (center)  110  function of particle diameter. Results using Anthony's expression shows most of the volatiles being released in the primary zone and not further up the riser. This is reflected in less oxygen near the bottom of the riser. The devolatilization expression by Agarwal is a function of particle diameter. This expression shifts the volatiles release further up the riser and also causes the oxygen partial pressure profile to be shifted up. This prediction is closer to the experimentally measured results. The oxygen profile in the annulus is also predicted better in this case. In addition, accurate experimental oxygen measurements are extremely difficult to obtain, and the experimental measurements show oxygen concentrations at the wall, the center and a point midway between the wall and the center of the riser.  These  measurements were conducted on a square cross-sectional area riser with entrance/exit effects.  In this model, oxygen profiles are calculated for the core and annulus of an  equivalent circular cross-sectional riser, without considering entrance/exit effects. Therefore, only a qualitative comparison can be done. Figure 4.20 does show the effects of a core/annulus structure in a CFB. Secondly, the expression by Agarwal and Davidson predicts approximately the correct combustion in the primary zone. The shape of the partial pressure of oxygen curve in the annulus was also correctly predicted by Agarwal and Davidson. There are some differences in the partial pressure of oxygen curves in the core; however, these differences may be due to the reasons stated above or due to experimental errors.  Ill  CHAPTER 5 CONCLUSION AND RECOMMENDATIONS  5.1  CONCLUSION In this thesis, a computer model was developed to predict heat release partial  pressure of oxygen profiles and temperature profiles in a CFB combustor, given the geometry, hydrodynamic properties of the CFB and the physical properties of the fuel. This model can be used for designing purposes to predict the heat transfer area needed to operate at a given temperature or it can be used in a rating problem to predict the temperature profile given the heat transfer area of the CFB. The program structure is modular, with separate subroutines for devolatilization, plume model, char combustion, oxygen profile and temperature calculations. Several test cases were conducted to observe how the model predictions change with various inputs of superficial gas velocities and solid recirculation rates. In addition, comparisons were made between the U B C CFB, a pilot scale CFB with a cross-sectional area of 0.15 m by 0.15 m, and the Studsvik CFB, a 2.5 M W thermal prototype CFB with a cross-sectional area of 0.65 m by 0.65 m. A qualitative validation was made between the model predictions of the U B C CFB and experimental data.  The results from this  validation seems to suggest that the model can predict the correct trends, with a more representative devolatilization model. There are some limitations to the operating cases the model can predict and the accuracy of the predictions. They are listed below. (i)  The primary zone and the cyclone are both treated as CSTRs (Continuous Stirred Tank Reactors).  (ii)  Superficial gas velocities below 5 m/s were not studied. Due to the limitations in the hydrodynamic code as discussed in Section 4.2.2, hydrodynamic predictions for low velocity cases were not possible.  112  (iii) Combustion air was not recycled back into the riser. (iv) Incomplete combustion to for CO was not looked at. (v)  The devolatilization equation used is not a function of particle diameter.  (vi) A simplified energy equation was used, where the radiative and convective heat transfer terms are not coupled. Due to the highly non-linear nature of the energy balance equation, convergence was extremely difficult to achieve and it took many iterations to arrive at the final output, even with a good initial guess of the temperature. In addition, the particle convective term is orders of magnitude larger than the other terms, see Figure 4.19.  Therefore, any changes in heat release,  oxygen profile or temperature within a cell will take many iterations for that disturbance to affect the whole riser. An attempt to converge an equation where the convective and radiative heat transfer terms are coupled was unsuccessful. (vii) Radiative heat transfer from one cell was assumed to affect its adjacent cells or surface only. This assumption is valid for a annulus cell, where there are dense particles; however, for the dilute core cells, this assumption may not be valid.  5.2  RECOMMENDATIONS FOR FUTURE WORK Future work can be done on the model to remove the limitations listed in the  previous section.  Some of the limitations to the devolatilization and char combustion  equation can be easily programmed due to the modular nature of the program. In addition, incorporating this model as a subroutine to Senior's hydrodynamic model, and changing the hydrodynamics code so that the temperature profile output from the model can be placed back into the hydrodynamics code and iterated until a final converged solution is achieved. Finally, the addition of a NOx and SO2 emissions model would make the overall CFB program complete.  113  NOMENCLATURE Units Variables y x kgjj T Op Pp Cp Up Pg c u I J G A S a CL e dp b V V* t R  distance in axial direction distance in radial direction effective thermal conductivity absolute temperature volume fraction of particles density of particle specific heat of particle velocity of particle density of gas specific heat of gas velocity of gas in the axial direction radiative flux in the positive x direction radiative flux in the negative x direction heat source intensity per unit volume radiative absorption cross-section per unit volume back-scattering cross-section per unit volume Stefan-Boltzman constant dimensionless proportionality factor emissivity of the particles diameter of the particles back-scattering coefficient fraction of volatiles released at time t initial fraction of volatiles in coal (from proximate analysis) time gas constant  t(j Tjj PQ x Djy k T d p T k A F  devolatilization time bed temperature partial pressure of oxygen average displacement squared radial volatile diffusion coefficient reaction rate surface temperature diameter of char particle density of char particle burnout time thermal conductivity of the cell surface area of one side of the cell mass flux of particles in the transverse direction  g  g  v  r  r  p  2  R  s  c  c  x  m m W/m-K K kg/m J/kg.K m/s kg/m J/kg-K m/s W/m W/m W/m 3  3  2  2  3  W/m K 2  4  m  s kJ/kg-K kcal/mol-K s K atm.  kg/m -s-atm K m kg/m s W/m-K m2 kg/m s 2  3  2  114  F V  y  g  8 G h hf Pt, U Q f  mass flux of particles in the axial direction represents the mass exchange of gas in the transverse direction due to turbulent mixing emissivity of the cell source term in the cell cell to wall heat transfer coefficient furnace side heat transfer coefficient furnace solids bulk density overall heat transfer coefficient heat transfer fractional yield of volatiles  kg/m s 2  m/s W/m W/m2K W/m2K kg/m W/m-K W 3  Subscripts w i L W E N S P NE xE yN yS  wall initial condition at the center of the reactor column west east north south control volume north face of the cell to the east of the control volume transverse direction of the cell to the east of the control volume axial direction of the cell to the north of the control volume axial direction of the cell to the south of the control volume  Superscripts 0  reference  m m m  115  REFERENCES Agarwal, P.K., "A Single Particle Model for the Evolution and Combustion of Coal  Volatiles", Fuel, Vol. 65, p. 803-810, June 1986. Anthony, D.B., Howard, J.B., Hottel, H.C. and Meissner, H.P., "RapidDevolatilization of Pulverized Coal", Symp. Int. Combust. Proc., 15, p. 1303-1317, 1975. Baskakov, A.P., "The Mechanism of Heat Transfer Between a Fluidized Bed and a  Surface", Int. Chem. Eng., 4(2), p. 320-323, 1964. Baskakov, A.P., "Radiative Heat Transfer in Fluidized Beds", Fluidization. 2nd ed.,  Academic Press, London, Ch. 13B, p. 465-472, 1985. Basu, P. and Fraser, S.A., Circulating Fluidized Bed Boilers: Design and Operations. Butterworth-Heinemann, 1991. Basu, P. and Yan, J., "Characterization of the Fine Char Particle Combustion in CFBs",  Fluidized Bed Combustion, Volume 1, A S M E 1993. Bhattacharya, S.C. and Harrison, D., "Heat Transfer in High Temperature Fluidized  Beds", European Congress on Particle Technology, Nuremburg, p. 23, session K2, 1977. Bi, H., Jin, Y., Yu, Z. and Bai, D., "An Investigation on Heat Transfer in CFB",  Circulating Fluidized Bed Technology III, 1990. Botterill, J.S.M. and Sealey, C.J., "Radiative Heat Transfer Between a Gas-FluidizedBed  and an Exchange Surface", British Chem. Eng., Vol. 15, No. 9, p. 1167, 1970. Bowen, B.D., Fournier, N. and Grace, J.R., "Heat Transfer in Membrane Waterwalls",  Int. J. Heat Mass Transfer, Vol. 34, No. 4/5, p. 1043-1057, 1991. Brereton, C. and Stromber, L., "Some Aspects of the Fluid Dynamic Behavior of Fast  Fluidized Beds", CFB Technology. Pergamon Press, Toronto, 1986. Brereton, C, "Fluid Mechanics of High Velocity Fluidized Beds", Ph.D. Dissertation,  Department of Chemical Engineering, U.B.C., 1987. Brewster, M.Q., "Effective Emissivity of Fluidized Bed", A S M E Heat Transfer Division, Vol. 40, p.7-13, 1984. Chen, J.C., Cimini, R.J. andDou, S., "A Theoretical Modelfor Simultaneous Convective and Radiative Heat Transfer in Circulating Fluidized Beds", Circulating Fluidized Bed  Technology II, p. 255-262, 1988.  116  Couturier, M.F. and Stevens, D., "Measurements ofHeat Transfer, Temperature, Solids Mass Flux, Gas Concentration and Cyclone Capture Efficiency in the Chatham CFB Unit", Energy Conversion Engineering Group, University of New Brunswick, 1991. Davidson, J.F., Cliff, R. and Harrison, D., Fluidization. 2nd ed., Academic Press, 1985, p. 642. Dow, W.M. and Jakob, M., "Heat Transfer Between a Vertical Tube and a Fluidized AirSolidMixture", Chem. Eng. Prog., 47(12), p. 637-648, 1951. Energy, Mines and Resources Canada, Energy in Canada : A Background Paper. November 1987. Furchi, J.C.L., Golstein Jr., L., Lombardi, G. and Mohseni, M., "Experimental Local Heat Transfer in a CFB", Circulating Fluidized Bed Technology H, 1988. Gabor, J.D., "Wall-to-Bed Heat Transfer in Fluidized and Packed Beds", Chem. Eng. Progress Sym. Series, 66(105), p. 76-86, 1970. Glicksman, L.R., "CFB Heat Transfer", CFB Technology II. 1988. Gorelik, A.G., "Mechanism ofHeat Exchange Between Surfaces and a Fluidized Bed", J. Eng. Phys., 13(6), p. 495-498, 1967. Grace, J.R., Brereton, C , Lim, C.J., Legros, R., Zhao, J., Senior, R.C., Wu, R.L., Muir, J.R. and Engman, R., "Circulating Fluidized Bed Combustion of Western Canadian Fuels", Final Report Prepared for Energy, Mines and Resources Canada under contract 52SS.23440-7-9136, 1989. Han, G.Y., Tuzla, K. and Chen, J.C., "Radiative Heat TransferfromHigh Temperature Suspended Flows", Institute of Thermo-Fluid Engineering and Science, 1992. Howard, J.R., Fluidized Beds. London: Applied Science, p. 62, 1983. Jia, L., Becker, H.A. and Code, R.K., "Devolatilization and Char Burning of Coal Particles in a Fluidized Bed Combustor", The Canadian Journal of Chemical Engineering, Vol. 71, Feb. 1993. Jolley, L.J., "Heat Transfer in Beds ofFluidized Solids", Fuel Research 28(5), p. 114115, 1949. Kobro, H. "Description of Studsvik's Fast Fluidized Bed Prototype", Studsvik Report, Studsvik/EM-84/3, 1984.  117  Kolar, A.K., Grewal, N.S. and Saxena, S.C., "Investigation of Radiative Contribution in a High Temperature Fluidized-Bed Using the Alternate-Slab Model", Int. J. Heat Mass Transfer, Vol. 22, p. 1695-1703, 1979. Leckner, B., "Heat Transfer in Circulating Fluidized Bed Boilers'', Circulating Fluidized Bed Technology BI, p. 27-37, 1991. Leckner, B. and Andersson, B.A. "Characteristic Features ofHeat Transfer in CFB Boilers", Powder Technology, 70, p. 303-314, 1992. Leva, M., and Grummer, M., "A Correlation of Solids Turnover in Fluidized Systems - Its Relation to Heat Transfer", Chem. Eng. Prog. 48(6), p.307-313, 1952. Levenspiel, O., and Walton, J.S., "Bed-Wall Heat Transfer in Fluidized Systems", Chem. Eng. Prog. Symp. Ser. 50(9), p. 1-13, 1954. Lin, W., and Van den Bleek, C M . , "The SOx/NOx Emissions in CFB Combustion of Coal", Proc. of the 3rd Int. Conf. on CFB, p. 545-550, 1989. Martin, H., "Warme-und Stoffubertragung in der Wirbelschicht", Chem-Ing-Tech, 52, nr 3, s. 199/209, 1980. Mickley, H.S. and Fairbanks, D.F., "Mechanism ofHeat Transfer to Fluidized Beds", A.I.Ch.E. Journal, 1(3), p. 374-384, 1955. Mickley, H.S. and Trilling, C.A., "Heat Transfer Characteristics ofFluidized Beds", Ind. Eng. Chem. 41(6), p. 1135-1147, 1949. Morris, M., "Furnace-Side Heat Transfer Coefficient Within Circulating Fluidized Beds", Studsvik Report, p. 110, 1988. Nag, P.K. and Moran, M.N., "Prediction ofHeat Transfer in Circulating Fluidized Beds", Proc. of the 3rd Int. Conf. on CFB, 1991. Park, D., Levenspiel, O. and Fitzgerald, T.J., "A Modelfor Large Scale Atmospheric Fluidized Bed Combustors", The American Institute of Chemical Engineers Symp. Series, 77(205), p. 116-126, 1981. Sanderson, W.E., "A Review of Overall Models of Circulating Fluidized Bed Combustors -A Literature Study", Technische Universiteit Delft, September 1993. Saxena, S.C. and Gabor, J.D., "Mechanisms ofHeat Transfer Between a Surface and a Gas-FluidizedBedfor Combustion Application", Prog. Energy Combust. Sci., Vol. 7, p. 73-102, 1981.  118 Senior, R., "Circulating Fluidized Bed Fluid and Particle Mechanics: Modeling and Experimental Studies with Application to Combustion", Ph.D Dissertation, Department of Chemical Engineering, U.B.C., 1992. Stubington, J.F., "The Role of Coal Volatiles in Fluidized Bed Combustion", Journal of the Institute of Energy, p. 191-195, 1980. Szekely, J. and Fisher, R.J., "Bed to Wall Radiative Heat Transfer in a Gas-Solid Fluidized Bed", Chemical Engineering Science, Vol. 24, p. 833-849, 1969. Vedamurthy, V.N. and Sastri, V.M.K., "An Analysis of the Conductive and Radiative Heat Transfer to the Walls of Fluidized Bed Combustors", Int. J. Heat Mass Transfer, 17, p. 1-9, 1974. Werdermann, C.C. and Werther, J., "Heat Transfer in Large-Scale CFB Combustors of Different Sizes", Technical University Hamburg, 1993. Wu, R.L., "Heat Transfer in Circulating Fluidized Beds", Ph.D. Dissertation, Department of Chemical Engineering, U.B.C., August 1989. Wu, R.L., Grace, J.R., and Lim, C. J., "A Modelfor Heat Transfer in Circulating Fluidized Beds", Chemical Engineering Science, Vol. 45, No. 12, p. 3389-3398, 1990. Yang, W., "The Hydrodynamics of CFBs", Encyclopedia of Fluid Mechanics Supplements. Gulf Publishing, 1992. Yang, Y., Jin, Y , Yu, Z., Wang, Z. and Bai, D., "The Radial Distribution of Local Particle Velocity in a Dilute Circulating Fluidized Bed", CFB Technology HI. Pergamon Press, Oxford, 1991. Yerushalmi, J., Cankurt, N.T., Geldart, D. and Liss, B., "Flow Regimes in Vertical GasSolid Contact Systems", A.I.Ch.E. Symp., Series No. 176, Vol. 74, 1, 1978. Zhao, J., "Nitrogen Oxide Emissions from Circulating Fluidized Bed Combustion", Ph.D. Dissertation, Department of Chemical Engineering, U.B.C., 1992.  119  APPENDIX A PROGRAM LISTING j 2  3 4 5 6  7 8  ^ c  *  11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  28 29 30 31 32 33 34 35 36 37 38 39 40  *  c c  * *  C  c c  H E A T G E N E R A T I O N and H E A T TRANSFER P R O B L E M  *  c  rev. 8.1, 1995 Feb. 8 by.D.W. Ju  *  * * *  3fc  c c c c c c c c c c c c c c c  * * *  *  *  Q  10  *************** j j g A T F ******************  ?|c 3§C 3|C ifC 3|C ?|C  3|C 3§C 3|C S|C 3|C 3§C 3§C 3|C 3fC 3fC3fC3fC3|C3{(34c3fC3fC ?|C 3|( 3fC 3|C 3fC 3fC  ifc 3fC 3$C 3$C 3|c ]fc 3§C  This program uses the Monte Carlo Method to compute the heat release, oxygen and temperature profile in a CFB riser. Initially, the y-dir flux of the core cells had to be recalculated to force a mass balance. The devolatilization rate is calculated as a function of bed temperature. The program also incorporates char combustion assuming only kinetic rates and a first order reaction. It calculates the partial pressure of oxygen along the streamer and core by assuming air enters at 2 1 % 02. Dispersion of air in the radial direction has been corrected for using the plume model. Some of the particles that leave the top of the riser is returned to the CFB after passing through a cyclone with a residence time of RT sec. The streamer cross-sectional area varies along the CFB riser. The heat transfer subroutine uses a simplified radiation heat transfer term. The temperature profile was smoothed for 1 point at every iteration. The control-volume method was also used.  C C  implicit real*8(a-h,o-z) real*8 mcyc,k character*65 titlel,title2,cyclon common/blka/acell(300),o2feed,x,fuel,uc,us common/blkb/cycv,npart,dt(300),pmatt(300),pmatl(300),rc, 1 volf,valh,rt,distv(300),siv(20),pdist(20) common/blkc/heatc(300), dpcut, presc(300), press(300), denp, coeff common/blkd/heat(300),total, dycell,cross,presc2(300),press2(300), conO, 1 oxyclc,mcyc,pair common/blke/vtf,nfeed cornmon/blkf7to(5,300),k,at,twall,tair,vg,tref,cp,cg,afeed,fin common/blkg/flux(300,5),dx(5,300),dy(5,300),f,emiss,denb(300) common/blkh/acinit,asinit,acfin,asfin  120 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85  corrrnion^lki/areaw(5,300),areae(5,300),arean(5,300), 1 areas(5,300),areat(5,300),e^ 2 v5,v6,cyc,gcyc dimension fluxc(300,5),heatv(300),ult(7) dimension pmat2(300),tempo(300),temp(300) c Unit 1 and 2 are inputfiles,and 3,7,8,9 are output files. open(unit=l,file=sh0.dat ) open(unit=2,file='hl4.inp') open(unit=3,file='sh0.plt') open(unit=7,file=sh0.xls') open(urut=8,file=sh0.out') open(unit=9,file=sh0.txt,form='print) ,  1  ,  ,  ,  ,  l  data nx,dpcut/2,5.d-5/ datapo2,cp,cg/0.21d0,800.d0,1172.d0/ datadeng,sbc/0.3d0,5.67d-8/ pi=4.d0*datan(l.d0) c Error handler during generation of the executable file. ieeer=ieee_handler('set', 'common', SIGFPEDEFAULT) if (ieeer.ne.O) print *, 'could not establish fp signal handler' c Read inputfile1.  900 910  read(1,900) title 1 ,title2 format(lx,a65,/lx,a65,/) read(l,910) ny,at,rc,per,primev,dbavg,devh,pair,tb,twall format(lx,i3,/lx,8(fl0.6,/lx),fl0.6) tinit=855.d0 read(l,*) read(l,*) read(l,*) primeh=primev/at ncell=ny*nx+l  920  do i=l,ncell read(l,920) (flux(ij)j=l,4) format(8x,f6.2,3fll.4)  121  86  enddo  87  88 89 90 91 92 93 94 95 96 97 98 99 100 101 102  930  read(l,*) read(l,*) read(l,*) read(l,930) asinit acinit=at-asinit do i=l,ny read(l,930) acell(ny+i) format(14x,fl0.6) enddo read (1,930) asfin acfin=at-asfin do i=l,ny acell(i)=at-acell(ny+i) enddo acell(ncell)=at  103  104 105 106 107 108 109 no 111 112 113 114 115 116 117 118 119 120 121 122 123  940  941  942  943  read(l,*) read(l,*) read(l,*) do i=l,7 read(1,940) ult(i) format(lx,fl0.3) enddo read(l,*) read( 1,941) volf,denp format(lx,fl0.3,/lx,fl0.3) volf=volf/100.d0 read(l,*) read(l,941) uc,us read(l,942) sug,fluxr,k,emiss format(lx,fl0.5,3(/lx,fl0.5),///) doi=l,18 read(l,943) siv(i),pdist(i) format(lx,fl0.3,5x,fl0.3) enddo close(l)  124  125  recirc=fluxr*at  126  127  c Calculate the furnace solids bulk density as a function of height.  128  129 130  do i=l,ny+2 denb(i+2Hflux(i,4)*acell(i)+flux(i+ny,4)*acell(i+ny))/at  122  131 132  enddo denb(2)=flux(ncell,4)  133 134  135  c Read input file 2.  136  137 138 139 140 141 142  read(2,945) cl,c2,valh 945 format(//lx,f8.2,5x,f8.2,/lx,f8.1) read(2,946) npart,perc,rifeed,eps,eps2,eps3,rf2,rf,cross,vtf,rt,exair,cefF,tsp, 1 tair,tref,constl 946 format(/lx,il0,/lx,fl0.6,/lx,il0,14(/lx,n0.6)) close(2)  143  144  vg=cross  145  146  c Set dx and dy values for each cell.  147  148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169  dyceU=flux(2,l)-flux(l,l) r=dsqrt(at/pi) doj=l,ny+3 dx(lj)=0.d0 dx(4j)=0.d0 enddo doj=3,ny+2 rcore=dsqrt(acell(j-2)/pi) ra=r-rcore dx(2,j)=ra dx(3j)=rcore enddo rcore=dsqrt(acinit/pi) ra=r-rcore do i=l,2 dx(2,i)=ra dx(3,i)=rc enddo rcore=dsqrt(acfin/pi) ra=r-rcore dx(2,ny+3)=ra dx(3,ny+3)=rc  170  171 172 173 174 175  do i=l,4 dy(i,l)=0.d0 dy(i,2)=primeh doj=3,ny+2 dy(i,j)=dycell  123  176 177 178  enddo dy(i,ny+3)=0.d0 enddo  179  180  c Call subroutine to determine air and fuel feedrates.  181  182  call feed(tb,po2,ceff,exair,ult)  183  184 185  c Multiply the massfluxmatrix (TLTJX) by the dimensions of the riser and store c in the massflowratematrix (FLUXC).  186  187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207  do i=l,ny-l fluxc(i,l)=flux(U) fluxc(i,2)=flux(i,2)*dycell*per fluxc(i,4)=flux(i,4)*dycell*aceU(i) enddo fluxc(ny, 1 )=flux(ny, 1) fluxc(ny,2)=flux(ny,2)*dycell*per fluxc(ny,4)=flux(ny,4)*dycell*acell(ny) fluxc(ny+l,l)=flux(ny+l,l) fluxcfay+l^^uxfay+l^dycel^per fluxc(ny+l,3)=flux(ny+l,3)*asinit fluxc(ny+l,4)=flux(ny+l,4)*dycell*acell(ny+l) do i=ny+2,ncell-l fluxc(i,l)=flux(i,l) fluxc(i,2)=flux(i,2)*dycell*per fluxc(i,3)=flux(i,3)*(acell(i)+acell(i-l))/2.d0 fluxc(i,4)=flux(i,4)*dycell*acell(i) enddo fluxc(ncell, 1 )=flux(ncell, 1) fluxc(ncell,2)=0.d0 fluxc(ncell,4)=flux(ncell,4)*primeh*at  208  209  c calculate axialfluxof the core cells to ensure a mass balance.  210  211 212 213 214 215  fluxc(ncell,3)=recirc+fluxc(ny+l ,3) fluxc( 1,3)=fluxc(ncell,3)-fluxc( 1,2)+fluxc(ny+1,2) doi=2,ny fluxc(i,3)=fluxc(i-l,3)-fluxc(i,2)+fluxc(ny+i,2) enddo  216  217 218 219 220  flux(ncell,3)=fluxc(ncell,3)/acinit doi=l,ny-l flux(i,3)=fluxc(i,3)/((acell(i)+acell(i+l))/2.d0) enddo  124  221 222  flux(ny,3)=fluxc(ny,3)/acfin afeed=o2feed/32.d0/.21d0*29.d0  223  224  c Set initial guess of pressure and temperature.  225  226 227 228 229  do i=l,ny+2 press(i)=0.21d0 presc(i)=0.21d0 enddo  230  231 232 233 234 235 236 237 238 239 240  do i=l,ncell temp(i)=tinit tempo(i)=temp(i) enddo doj=2,ny+3 to(lj)=twall do i=2,4 to(ij)=tinit enddo enddo  241  242 243 244  c Input solids return temperature. It can be set to equal the cyclone c temperature, calculated by the program, or set at a bed temp, set c by the user (normally 850C).  245  246 247 248 249  2 1 950  print*, 'Select solids return temperature. (C=cyclone, B=temperature selected by user)' read(*,950) cyclon format(a3)  250  251  iffcyclon.ne.'C.and. cyclon.ne.B') goto 2  252  253 254 255 256 257 258  if(cyclon.eq.'B') then print*, 'Enter temperature of inlet particles (C)' read(*,*)tp endif tcyc=tp fin=fuel/at  259  260 261  c Determine the time step and the probabilities of how the particle c will move, depending on the location of the particle.  262  263 264 265  do i=l,ncell pmatl(i)=fluxc(i,2)/fluxc(i,4) pmat2(i)=fluxc(i,3)/fluxc(i,4)  125  266 267  pmatt(i)=pmatl(i)+pmat2(i) dt(i)=perc/pmatt(i)  268  269 270 271 272  pmatl(i)=pmatl(i)*dt(i) pmat2(i)=pmat2(i)*dt(i) pmatt(i)=pmatl(i)+pmat2(i) enddo  273  274 275  c Calculate thefractionof the wall covered by membrane tubes (f), or c set it at a specified wall area.  276  277 278 279 280 281  c c c c c  htarea=(fnel*valh*1000.d0/2.5d0)/(constl*dbavg*(tmit-twall) 2+ermss*sbc*((tinit+273.15d0)**4-(twall+273.15d0)**4)) rarea=per*(primeh+flux(ny,l)+dycell/2.d0) if(htarea.le.0.dO) htarea=0.d0 f=htarea/rarea  282  283  f=0.7d0  284  285  c Initialize heat distribution terms  286  287 288  5  iter2=0 iter2=iter2+l  289  290  c Determine the areas.  291  292 293 294 295 296 297 298 299 300  doj=l,ny+3 do i=l,4 areaw(ij)=0.dO areae(ij)=0.dO arean(i,j)=0.dO areas(ij)=0.d0 areat(ij)=0.dO enddo enddo  301  302 303 304 305 306 307 308 309 310  areaw(l,2)=primeh*per*f areae(l,2)=primeh*per*f areaw(2,2)=primeh*per*f areae(2,2)=primeh*per do i=3,4 areaw(i,2)=primeh*per areae(i,2)=primeh*per enddo doj=3,ny+2  126  311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350  areaw(lj)=dycell*per*f areae(lj)=dycell*per*f areaw(2j)=dycell*per*f areae(2j)=dycell*per do i=3,4 areaw(ij)=dycell*per areae(ij)=dycell*per enddo enddo doj=3,ny+l arean(3JHacellO-2)+acellO-l))/2.dO arean(2j)=(acell(j-2+ny)+acell(j-l+ny))/2.d0 areas(3j+l)=arean(3j) areas(2,j+l)=arean(2j) enddo arean(3,ny+2)=acfin arean(2,ny+2)=asfin arean(3,ny+3)=acfin arean(2,ny+3)=asfin arean(3,l)=acinit arean(2,l)=asinit arean(3,2)=acinit arean(2,2)=asinit areas(3,3)=acinit areas(2,3)=asinit areas(3,2)= acinit areas(2,2)=asinit areas(3,1 )=acinit areas(2,l)=asinit areas(3,ny+3)=acfin areas(2,ny+3)=asfin doj=2,ny+2 areat(lj)=areaw(lj) areat(2j)=areae(2j)+areaw(2j)+arean(2j)+areas(2j) areat(3j)=areaw(3j)+arean(3,j)+areas(3j) enddo areat(2,1 )=areas(2,1) areat(3,1 )=areas(3,1) areat(2,ny+3)=arean(2,ny+3) areat(3,ny+3)=arean(3,ny+3) =  351  352  cycv=0.d0  353  354 355  c Call subroutine to calculate volatilization heat distribution  127  356  call volat(ny,heatv,tdvol,totv,ncell,cl,c2,temp,pi)  357  358  coeff=7.26d3*exp(-1.5d5/(8.314d0*(tsp+273)))  359  360  c Call subroutine to correct for volatile dispersion  361  362  call vdisp(heatv,ncell,ny,pi,flux)  363  364 365  c Count the number of iterations and call subroutine to calculate c the char heat distribution  366  367 368  10  iter=0 iter=iter+l  369  370  call char(ny,cyc,pi,ncell,ult)  371  372  cycc=cyc-cycv  373  374  c Calculate fraction of the total heat generated in each cell.  375  376 377 378  do i=l,nmax heat(i)=0.d0 enddo  379  380 381 382 383 384 385  total=0.d0 do i=l,ncell heat(i)=heatv(i)+heatc(i) total=total+heat(i) enddo total=total+cyc  386  387 388 389  do i=l,ncell heat(i)=heat(i)/total enddo  390  391  c Call subroutine to calculate the 02 partial pressure profile  392  393  call pres(ny,cyc,pi,po2,ncelf)  394  395  c Check that the errors in the pressure of the core cells are less than EPS.  396  397 398 399 400  ermax=0.d0 do i=l,ny+2 errorc=abs(presc(i)-presc2(i)) if(errorc.gt.ermax) then  128  401 402 403 404  ermax=errorc ic=i endif enddo  405  406  c Print the error and the iteration number.  407  408  print*,iter,error',iter,ermax ,  409  410  c Update the pressures.  411  412 413 414 415  do i=l,ny+2 press(i)=press(i)+rf* (press2(i)-press(i)) presc(i)=presc(i)+rf*(presc2(i)-presc(i)) enddo  416  417 418  c Decide whether convergence has been met. If not, go back c to statement number 10.  419  420 421  if(ermax.gt.eps) goto 10 erl=ermax  422  423  c Set the temperature of the solids return.  424  425 426 427 428 429  ifCcyclon.eq.'C) then trec=tcyc else trec=tp endif  430  431 432 433 434 435  tin=(afeed*cg*tair+fhel*cp*tref+recirc*cp*trec)/(afeed*cg+fo 1 recirc*cp) do i=l,4 to(i,l)=tin enddo  436  437  c Call subroutine heat to determine temperature profile.  438  439  call htrans(ncell,ny,eps3,per,rf2,recirc,ult)  440  441 442  print*, "No. of iterations in htrans-, iter2 write(8,*) 'No. of iterations in htrans-, iter2  443  444 445  c New temperatures  129 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483  doj=ny+2,3,-l temp(j-2+ny)=to(2j) temp(j-2)=to(3,j) enddo temp(ncell)=to(3,2)*acinit/at+to(2,2)*asinit/at c Smooth temperature profile for 1 point (at the boundary between c developing and fully developed region). do i=l,ny if(devh.le.flux(i,l))then i=i-l ratio=(temp(i+l)-temp(i-2))/(flux(i+l, l)-flux(i-2,1)) temp(i)=ratio*(flux(i,l)-flux(i-2,l))+temp(i-2) temp(i-l)=ratio*(flux(i-l, l)-flux(i-2, l))+temp(i-2) i=i+l+ny ratio=(temp(i+1 )-temp(i-3))/(flux(i+1,1 )-flux(i-3,1)) temp(i)=ratio*(flux(i, l)-flux(i-3, l))+temp(i-3) temp(i-l)=ratio*(flux(i-l, l)-flux(i-3,1 ))+temp(i-3) temp(i-2)=ratio*(flux(i-2,l)-flux(i-3,l))+temp0^ goto 20 endif enddo c Write the temperature to output 20 960  965  file.  write(8,960) (to(i,ny+3),i=l,3) format(3(lx,fl0.2)) doj=ny+2,3,-l write(8,965) tAvall,tempG+ny-2),tempG-2),effh(j) format(4(lx,fl0.2)) ifij.eq.7) then write(3,*) tempO-2) endif enddo write(8,965) (to(i,2),i=l,3),effh(2) write(8,960)(to(i,l),i=l,3) call flush(3)  484  call flush(7)  485 486 487 488 489 490  call flush(8) c Calculate the temperature of the cyclone. tcycn=temp(ny)+gcyc/(afeed * cg+recirc* cp)  130  491 492  c Set the number of iterations in the temperature profile subroutine to c ensure that a converged solution is obtained.  493  494  if(iter2.ge.200) goto 50  495  496  c Check the convergence of the temperature.  497  498 499 500 501 502 503 504 505 506 507 508 509 510 511 512  error=0.d0 ermax=0.d0 ierr=0 do i=l,ncell error=dabs(temp(i)-tempo(i)) if(error.gt.ermax) then ermax=error ierr=i endif enddo error=dabs(tcycn-tcyc) if(error.gt.ermax) then ermax=error ierr=ncell+l endif  513  514 515 516 517 518 519 520 521 522 523  print*,'eps2,ermax,ceir,eps2,ermax,ierr write(8,*) 'eps2,ermax,ceir,eps2,ermax,ierr if(ierr.eq.(ncell+l)) then print*, 'tempo,temp',tcyc,tcycn write(8,*) 'tempo,temp',tcyc,tcycn else print*, 'tempo,temp',tempo(ierr),temp(ierr) write(8,*) 'tempOjtemp'jtempo^e^jtemp^err) endif write(8,*)  524  525 526  c Update temperature and check that convergence has been met. c If not, go back to statement number 5.  527  528 529 530 531 532 533 534 535  if(ermax.gt.eps2) then rf3=l.d0 do i=l,ncell tempo(i)=tempo(i)-rf3 * (tempo(i)-temp(i)) tcyc=tcyc-rf3 * (tcyc-tcycn) enddo goto 5 endif  131  536  537  c Calculate average partial pressure of 02 leaving riser and cyclone (atm).  538  539 540  50  pout=presc(ny+2)*acfir^at+press(ny+2)*asfin/at pcyc=(oxyclc-mcyc*x)/(uc*acfin+us*asfin)*po2/con0  541  542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562  c Print output results to unit 9.  800 1 2 3 4 5 6 7 8 802 1 2 3  804  563  564 565 566 567 568  806 1 2 3  write(9,800) titlel,title2 format(45x,'page 1 of 6',//////15x, 'CFB HEAT RELEASE AND HEAT TRANSFER MODEL',/15x, y/isx,  •RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION l.r,/15X, •WRITTEN BY: DALE W.C. JUy//15x,a65,/15x,a65,///15x, •FUEL PHYSICAL PROPERTIES AND COMPOSITIONyi5X, •  'J/lSx,  •PROXIMATE ANALYSIS'/A 5x,Weight %') write(9,802) (ult(i),i=l,7) fonnat(15x,f8.3,5x,'AshVl5x,f8.3,5x,MoistureV15x,ffi.3,5x, Sulphur',/15x,f8.3,5x,'Hydrogen,/15x,f8.3,5x,Carbon',/15x, f8.3,5x,Nitrogen,/15x,f8.3,5x,'Oxygen',//15x, •PARTICLE SIZE DISTRIBUTION',//15x,5x,'mm,13x,'wt %') doi=l,18 write(9,804) siv(i),pdist(i) format(15x,fl0.3,5x,fl0.3) enddo ,  ,  ,  ,  l  ,  write(9,806)npart,f*100.d0 format((" 1 "),45x,'page 2 of GJill III 5x, 'COMBUSTION CONDITIONS',/15x,' '# of particles in Monte Carlo Method',4x,i 10,/l 5x, '% of total wall area with membranes',5x,fl0.1,' %')  ',//15x,  569  570 571 572 573 574 575 576  808  810  ifTcyclon.eq.'C) then write(9,808) tree format(15x,'Solids return temp, equals cyclone temp.',fl0.1,' C) else write(9,810)trec format(15x,'Solids return temp, set at',14x,fl0.1,' C) endif  577  578 579 580  1 812  write(9,812) recirc,fluxr,cross,cefPl00.d0,exair*100.d0,vtf, rrfeed,fuel*3600.d0,afeed*3600.d0,pair*100.d0,rt,rc,devh format(15x,'Solids recirculation rate',16x,fl0.3,'kg/s',/15x,  132  581 582 583 584 585 586 587 588 589  1 2 3 4 5 6 7 8 9  'Solids recirculation flux',15x,fl0.3,'kg/m2s',/15x, 'Gas cross-flow coefficient', 14x,fl0.3,' m/s',/15x, 'Combustion efficiency', 19x,fl0.1,' %',/15x,'Excess air',30x,fl0.3,' %',/15x, 'Volatile transferfraction',14x,fi0.3,/15x,Number of fuel feed points', 14x,ilO,/15x,Tuel feedrate',27x,fl0.3,' kg/hr',/15x,'Air feedrate',28x, fl0.3,' kg/hr',/15x,'% of total air that is primary', 10x,fl0.1,' %',/15x Residence time of particles in cyclone'^XjflOJ,'sec.',/15x, *Reflectioncoefficient',18x,fl0.3,/15x, Height at which developed zone begms',3x,fl0.3,'m')  590  591 592 593 594 595 596 597  814 1 2 3 4 5  write(9,814) uc,us,sug,tb format(//15x,'GAS VELOCITIES',/l5x,' ',//15x, 'Core insterstitial gas velocity',9x,fl0.3,' m/s',/15x, 'Streamer interstitial gas velocity*,6x,fl0.3,' m/s',/15x, 'Superficial gas velocity',16x,fl0.3,'m/s',//15x, TBed temperature used in calculating ,/17x, 'heat transfer area and gas velocities',3x,fl0.1,' C) 1  598  599 600 601 602 603 604  816 1 2 3 4  write(9,816) format((" 1 "),45x,'page 3 of 6',//////l 5x, *HEAT RELEASE DISTRIBTJTION ,/15x, ' ',//15x,*Height',8x, Traction of Total Heat Release',/34x,' Volatiles', 16x, 'Char',/17x,'(m)',9x,'Streamer',4x,Core',6x,'Streamer',4x,'Core',/) 1  ,  605  606 607 608 609 610 611 612 613 614 615  818  1 820  822 1  write(9,818) fluxc(ncell,l),heatv(ncell)/total,heatc(ncell)/total format(15x,f5.2,12x,fl0.6,12x,fl0.6) do i=l,ny write(9,820)fluxc(i,1 ),heatv(i+ny)/total,heatv(i)/total,heatc(i+ny)/total, heatc(i)/total format(15x,f5.2,6x,3(lx,fl0.6),2x,fl0.6) enddo write(9,822) cycv/total,cycc/total,totv/total,(total-totv)/total format(15x,'Cyclone',10x,fl0.6,12x,fl0.6,//15x,'TOTAL*,12x,fl0.6,12x, fl0.6)  616  617 618 619 620 621 622 623 624 625  824 1 2 3 4  826  write(9,824)fluxc(ncell,1 ),press(2) format(("l"),45x,'page4of6',//////15x, 'OXYGEN PARTIAL PRESSSURE DISTRffiUTION', /15X,' V/lS^Height'^x, 'Partial Pressure of Oxygen (atm.)717x,'(m)',9x, 'Streamer',4x,'Core',//15x,f5.2,12x,fl0.6) do i=l,ny write(9,826) fluxc(i,l)+dycell/2.d0,press2(i+2),presc2(i+2) format(15x,f5.2,6x,2(lx,fl0.6))  133 626 627 628 629 630 631 632 633 634 635 636 637 638 639 .640 641 642 643 644 645 , 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 6^7 668 669 670  828 1 2 3  830 1 2 3  832  834 1 2 836 1 2 3 4  838  100  c  enddo write(9,828) erl,po2,pout,pcyc format(//15x,"Pressure convergence tolerance', 10x,fl0.4,' atm.', /15x,"Partial pressure of oxygen entering',5x,fl0.6,' atm. ",/15x, "Partial pressure of oxygen leaving riser",fl0.3,' atm.',/15x, Tartial pressure of oxygen leaving cyclone',f8.3,'atm.') write(9,830) fluxc(ncell,l),temp(ncell) format(("l"),45x,'page5of6",//////15x, 'TEMPERATURE DISTRIBUTION',/15x, ' ,//15x,'Height,8x,'Temperature(C)', /17x,'(m)',9x,'Streamer,4x,'Core',//15x,f5.2,llx,fl0.1) do i=l,ny write(9,832) fluxc(i,l),temp(i+ny),temp(i) format(15x,f5.2,4x,2(lx,fl0.1)) enddo write(9,834) trec,ermax,tcyc,twall format(//15x,'Solids return temperature', 15x,fl0.1,' C',/15x, 'Temperature convergence tolerance',7x,fl0.3," C',/15x, 'Cyclone temperature',21x,fl0.1,' C',/15x,Wall temperature',24x,fl0.1,' C) ,  ,  ,  write(9,836) format((" 1 "),45x,"page 6 of &,//////! 5x, HEAT TRANSFER COEFFICIENTS',/15x, ' ',//15x,'Height',2x,'Density', 2x,'Core Temp.",2x,Heat Transfer Coefficient (W/m2C)', / l 7x,*(m)',3x,'(kg/m3)',5x,'(C)*,6x,'Radiative",2x,'Convective',3x,'Overall',/) write(9,838) fluxc(ncell,l),flux(ncell,4),temp(ncell),effr(2),effc(2),efih^ do i=l,ny denav=(flux(i,4)*acell(i)+flux(i+ny,4)*acell(i+ny))/at write(9,83 8) fluxc(i, l),denav,temp(i),effr(i+2),effc(i+2),effh(i+2) format(15x,f5.2,2x,f8.3,2x,f7.1,3(2x,fl0.1)) enddo close(9) close(3) close(7) close(8) Stop end  ********************** subroutine feed ************************* subroutine feed(tb,po2,ceff,exair,ult) c Subroutine to calculate the coal feedrate (fuel), given c the ultimate analysis of the coal and the gas velocity in the  134  671  c streamer and the core (us and uc).  672  C  673 675 676 677 678 679 680 681  c c c c c c c c c  gg2  c  674  Variables are: fuel coal feedrate (kg/s) o2feed oxygen feedrate (kg/s) o2need oxygen feedrate needed for every 1 kg/s of coal feed (kg/s) ult ultimate analysis of coal uc gas velocity in the core (m/s) us gas velocity in the streamer (m/s)  ********************************************  683  684 685 686 687  implicit real*8(a-h,o-z) cornmon/blka/acell(300),o2feed,x,fuel,uc,us conimon/blkh/acinit,asinit,acfiri,asfin dimension ult(7)  688  689  c Calculate the 02 feedrate (kg/s)  690  691 692  1  o2feed=101.325d0*(uc*acinit+us*asinit)/8.314d0/(273.15d0+tb)* po2*32.d0  693  694  c Calculate the 02 feedrate needed for 1 kg/s fuel (kg/s)  695  696 697  x=(ceff*(ult(3)/32.d0+ult(4)/4.d0+ult(5)/12.d0)*32.d0-ult(7))/10 o2need=exair*x+x  698  699  c Calculate the fuel feedrate (kg/s)  700  701 702 703 704  705 706 707 708 709  fuel=o2feed/o2need return end £********************** subroutine volat ************************* subroutine volat(ny,heatv,tdvol,totv,ncell,cl,c2,temp,pi) c Subroutine to determine the heat release distribution due to c devolatilization (heatv). Q*****************************************************************  710  711 712 713 714 715  implicit real*8(a-h,o-z) common/blkb/cycv,npart,dt(300),pmatt(300), 1 pmatl(300),rc,volf,valh,rt,distv(300),siv(20),pdist(20) common/blkc/heatc(300),dpcut,presc(300),press(300),denp,coeff dimension heatv(300),temp(300)  135  716  717  c Intialize heatv.  718  719 720 721 722  voli=0.dO do i=l,ncell heatv(i)=0.d0 enddo  723  724  c Main loop over the number of particles.  725  726  do 30 ii=l,npart  727  728 729  c Determine the initial size of the particle based on the particle c size distribution.  730  731 732 733 734 735 736 737 738 739  rval=d_lcran() totwt=0.dO doi=l,18 totwt=totwt+pdist(i)/100.d0 irTrval.le.totwt) then dpinit=siv(i)/1000.d0 goto 5 endif enddo  740  741 742  5  volp=pi*dpinit**3/6.d0 pmas=denp*volp  743  744 745 746 747 748  vol=voli voldifM.dO time=0.d0 icell=ncell icello=icell  749  750 751  c Generate a random real number between [0,1] to determine the position c of the particle.  752  753  10  time=time+dt(icell)  754  755 756 757 758  itTyoldif.le. 1 .d-6) then tdvol=time-dt(icell) goto 30 endif  759  760  rval=d_lcran()  136  761  762 763 764 765  if(icell. eq. ncell) then if(rval.le.pmatt(icell)) icell=l goto 20 endif  766  767 768 769 770 771 772 773 774  iflYval.le.pmatl(iceU)) then if(icell.le.ny) then icell=icell+ny else icell=icell-ny endif elseif(rval.le.pmatt(icell)) then if(icell.eq.ny) then  775  776 777 778  c If the particle exits the top of theriser,another random number c is generated to determine whether the particle is transferred to c the streamer or is removed to the cyclone.  779  780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805  1  1  rval=d_lcran() if(rval.le.rc) then icell=ncell-l goto 20 else voldif=volf*(l.d0-dexp(-cl*time*dexp(-c2/ (1.987d-3*(273.15d0+temp(iceUo))))))-vol vol=vol+voldif heatv(icello)=heatv(icello)+valh*voldif*pmas time=time+rt voldif=volf* (1. d0-dexp(-c 1 *time* dexp(-c2/ (1.987d-3*(273.15d0+temp(icello))))))-vol vol^vol+voldif cycv=cycv+valh*voldif*pmas icell=ncell icello=icell goto 10 endif elseif(icell.lt.ny) then icell=icell+l elseif(icell.eq.ny+l) then icell=ncell else icell=icell-l endif endif  137  806  807  c Add the heat generation due to volatiles to each cell.  808  809 810 811 812 813 814 815  20 1  30  voldif=volf*(l.d0-dexp(-cl*time*dexp(-c2/ (1.987d-3*(273.15d0+temp(icello))))))-vol vol=vol+voldif heatv(icello)=heatv(icello)+valh* voldifpmas icello=icell goto 10 continue  816  817  c Calculate the heat distribution.  818  819 820 821 822 823 824 825 826 827 828 829 830 831 832 833  g34 835 836 837 838  839 840  841 842 843 844 845  40  50  totv=0.d0 do 40 i=l,ncell totv=totv+heatv(i) continue distv(l)=heatv(l)/totv do 50 i=2,ncell sum=0.d0 do j=l,i sum=sum+heatv(j) enddo distv(i)=sum/totv continue return end  £********************** subroutine vdisp ************************ subroutine vdisp(heatv,ncell,ny,pi,flux) c Subroutine which uses the plume model to correct for volatile c dispersion c. c Variables are: c c nfeed Number of feed points. c height Height above the feed where there is full radial mixing c sdisp Average displacement in the radial direction (m) c tdisp Time (sec.) c r Radius (m)  847  848 849 850  implicit real*8(a-h,o-z) cornmoriMka/acell(300),o2feed,x,fiiel,uc,us common/blkb/cycv,npart,dt(300),pmatt(300),  138  851 852 853 854  1  pmatl(300),rc,volf,valh,rt,distv(300),siv(20),pdist(20) common/blke/vtf,nfeed dimension r(300),heatv(300),flux(300,5) datadrp/0.015d07  855  856 857 858  r(nceli)=dsqrt(acell(ncell)/pi) ndiv=l if(nfeed.ne. 1) ndiv=(nfeed-2)*2+2  859  860 861  sdisp=r(ncell)/ndiv tdisp=sdisp**2/(2.d0*drp)  862  863 864  c Calculate the height where the volatiles are fully mixed in the c radial direction.  865  866  height=uc*tdisp  867  868 869  c Transfer afraction(vtf) of the volatiles to the cell above where c the volatiles are released.  870  871 872 873 874 875 876 877 878 879  heatv(ncell)=heatv(ncell)-vtf* heatv(ncell) if(flux(l,l).ge.height) return heatv(l)=heatv(l)+vtf*heatv(ncell) heatv(l)=heatv(l)-vtf heatv(l) do i=2,ny-l ifTflux(i, 1 ).ge.height) return heatv(i)=heatv(i)+vtPheatv(i-l) heatv(i)=heatv(i)-vtf*heatv(i) enddo  880  881 882 883 884 885 886 887  ggg 889 890 891  892 893  894 895  if(flux(ny,l).ge.height) return heatv(ny)=heatv(ny)+vtf*heatv(ny-1) heatv(ny)=heatv(ny)-vtf*heatv(ny) cycv=cycv+vtf*heatv(ny) return end subroutine char ************************* subroutine char(ny,cyc,pi,ncell,ult) c Subroutine to determine the char heat release distribution. c c Variables are: c c cmass Mass of char particle c eye Total heat released in the cyclone  139  896 897 898 g99 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940  c dp Particle diameter (m) c icell Position of the particle at a given time c volmas Mass of volatiles ***************************************************************** c  1  implicit real*8(a-h,o-z) common/blkb/cycv,npart,dt(300),pmatt(300), pmatl(300),rc,volf,valh,rt,distv(300),siv(20),pdist(20) cornmon/blkc/heatc(300),dpcut,presc(300),press(300),denp,coeff dimension ult(7)  c Intialize the heat due to char combustion vector to zero, and the c heat released in the cyclone to equal the heat released due to c devolatilization. do i=l,ncell heatc(i)=0.d0 enddo cyc=cycv c Main loop over the number the particles. do 30 ii=l,npart c Determine the initial size of the particle based on the particle c size distribution. rval=d_lcran() totwt=0.d0 doi=l,18 totwt=totwt+pdist(i)/100.d0 if(rval.le.totwt) then dpinit=siv(i)/1000.d0 goto 5 endif enddo 5  volp=pi*dpinit**3/6.d0 pmas=denp*volp volmas=pmas*volf ashmas=pmas*ult(l)/100.d0 cmas=pmas-volmas-ashmas  c Determine diameter of a particle of fixed carbon only.  140 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985  dp=(6.d0*cmas/(denp*pi))**(l.d0/3.d0) c Generate a random real number between [0,1] to determine the initial c position of the char particle based on the devolatilization heat c released distribution. rval=d_lcran() icell=l do i=l,ncell-l iflrval.ge.distv(i)) icell=i+l enddo icello=icell  10  time=0.d0 time=time+dt(icell) rval=d_lcran() if(icell.eq.ncell) then if(rval.lt.pmatt(icell)) icell=l goto 20 endif if(rval.le.pmatl(icell)) then if(icell.le.ny) then icell=icell+ny else icell=icell-ny endif elseif(rval.le.pmatt(icell)) then if(icell.eq.ny) then  c If the particle exits the top of the riser, another random number c is generated to determine whether the particle is transferred to c the streamer or is removed to the cyclone. rval=d_lcran() if(rval.lt.rc) then icell=ncell-l else if(dp.gt.dpcut) then fi=coeff*pi*(dp**2)*presc(icello+2)*dt(icello)* cmas2=cmas-fi irTcmas2.1e.0.dO) then heatc(icello)=heatc(icello)+cmas2*valh goto 30  12.d0  141  986 987 988  endif heatc(icello)=heatc(icello)+fi * valh cmas=cmas-fi  989  990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006  time=time+rt fi=coeff*pi*(dp**2)*presc(ny)*rt*12.d0 cmas2=cmas-fi if(cmas2.1e.0.d0) then cyc=cyc+cmas2*valh goto 30 endif cyc=cyc+fi*valh cmas=cmas-fi dp=(6.dO*cmas/(denp*pi))**(l.dO/3.dO) icell=ncell icello=icell goto 10 else goto 30 endif endif  1007  1008 1009 1010 1011 1012 1013 1014 1015  elseif(icell.lt.ny) then icell=icell+l elseifTJcell. eq. ny+1) then iceli=ncell else icell=icell-l endif endif  1016  1017 1018  c Calculate the heat generation due to char combustion, assuming first c order reaction. From: Howard, J.R.  1019  1020 1021 1022 1023 1024 1025 1026 1027 1028  20 if(icello.le.ny) then fi=coeff*pi*(dp**2)*presc(icello+2)*dt(icello)* 12.d0 elseif(icello.eq.ncell) then fi=coeff*pi*(dp**2)*presc(2)*dt(icello)* 12.d0 else fi=coeff*pi*(dp**2)*press(icello-ny+2)*dt(icello)* 12.d0 endif heatc(icello)=heatc(icello)+fi*valh icello=icell  1029  1030  c Mass balance to determine the new particle diameter, DP.  142  1031  1032 1033 1034 1035 1036 1037 1038 1039  1040 1041 1042 1043 1044 1045 1046  1047 1048  1049 1050 1051 1052 1053 1054 j055 1056  1057 1058 1059 1060 1061 1062 1063  30  cmas=cmas-fi if(cmas.lt.0.dO) goto 30 dp=(6.d0*cmas/(denp*pi))**(l.d0/3.d0) goto 10 continue return end  ^********************** subroutine pres ************************** subroutine pres(ny,cyc,pi,po2,ncell) c Subroutine to determine the partial pressure of oxygen profile. c Secondary in injected into the core and the streamer cells to c keep the gas velocities in the streamer and core at a constant c value. c c Variables are: c c cc Concentration of oxygen in the core c cs Concentration of oxygen in the streamer c mcyc Mass of fuel in the cyclone (kg) c mfuel Mass of fuel in each cell (kg) c o2prim Oxygen feed in the primary air c rcore Radius of the core £*****************************************************************  implicit real*8(a-h,o-z) real* 8 mfiiel,mcyc common/blka/acell(300),o2feed,x,fuel,uc,us common/blkd/heat(300),total dycell,cross,presc2(300), 1 press2(300),con0,oxyclc,mcyc,pair corrimori/blkh/acinit,asinit,acfin,asfin dimension mfuel(300),conc(300) >  1064  1065 1066 1067  c Assume time duration is 1 sec. c Calculate the mass of fuel in each cell (kg) based on the fraction c of heat released.  1068  1069 1070 1071 1072  do i=l,ncell mfuel(i)=heat(i)*fuel enddo mcyc=cyc/total*fuel  1073  1074 1075  c Calculate the concentration of 02 in each cell (kg/m3)  143  1076 1077  con0=o2feed/(uc*acinit+us*asinit) cprim=o2feed * pair-mfuel(ncell)*x  1078  1079 1080  c Addition of secondary air, in both the streamer and core, c after the primary zone.  1081  1082 1083 1084 1085 1086  if(cprim.le.0.d0) then conin=(o2feed*(l .dO-pair))/(uc*acinit+us*asinit) else conin=(o2feed-rrmiel(ncell)*x)/(uc*acirut+us*asiriit) endif  1087  1088 1089 1090  conc(ncell)=conin oxyc=conin*uc*(acell( 1 )+acell(2))/2. dO oxys=conin*us*(acell(ny+l)+acell(ny+2))/2.d0  1091  1092 1093 1094 1095 1096  do i=l,ny-l rcore=dsqrt(acell(i)/pi) frac=cross* 2. dO *pi* rcore* dycell cc=(acell(i)+acell(i+l))/2.d0*uc cs=(acell(ny+i)+acell(ny+i+l))/2.d0*us  1097  1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109  1  oxys=(oxys-rrifuel(ny+i)*x+frac*(oxyc-mme^ (cc+frac))/(l.d0+fiW^ oxyc=(oxyc-mfhel(i)*x+frac*oxys/cs)/(l .dO+frac/cc) ifToxys.lt.O.dO) oxys=0.d0 ilToxyc.lt.O.dO) oxyc=0.dO conc(i)=oxyc/cc conc(ny+i)=oxys/cs enddo rcore=dsqrt(acell(ny)/pi) frac=cross*2.d0*pi*rcore*dycell cc=acfin*uc cs=asfin*us  1110  1111 1112 1113 1114 1115 1116 1117 1118  1  oxys=(oxys-rrifuel(ny+ny)*x+frac*(oxyc-mfu (cc+frac))/(l.dO+frac/cs-fr^^ oxyc=(oxyc-rniuel(ny)*x+frac*oxys/cs)/(l.dO+frac/cc) ilToxys.lt.O.dO) oxys=0.dO if(oxyc.lt.0.dO) oxyc=0.dO oxyclc=oxys+oxyc conc(ny)=oxyc/cc conc(2*ny)=oxys/cs  1119  1120  c Calculate the partial pressure of 02 in each cell  144  1121  1122 1123 1124 1125  press2(l)=po2 presc2(l)=po2 press2(2)=conc(ncell)*po2/con0 presc2(2)=press2(2)  1126  1127 1128 1129 1130  do i=3,ny4-2 presc2(i)=conc(i-2)*po2/con0 press2(i)=conc(ny+i-2)*po2/con0 enddo  1131  1132  return end  1133 1134  H25 1136 1137 1138 1139 1140 1141  1142 1143  1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 U59  1160 1161 1162 1163 1164 1165  g************************ subroutine htrans ************************ subroutine htrans(ncell,nycell,eps,per,rf2,recirc,ult) c Subroutine to calculate the temperature profile given the partial c pressure of oxygen profile and heat release distribution. c To aid convergence, the particle convective term entering the riser c is set to equal the term leaving the riser. c c Variables are: c c a,b,c,r Entries in the tridiagonal matrix c eg Heat capacity of the gas (J/kgK) c cp Heat capacity of the particles (J/kgK) c deng Density of the gas (kg/m3) c emiss Emissivity cf Fraction of the wall covered by membrane c fx Matrix of massfluxin the radial direction (kg/m2s) c fyn Matrix of massfluxin the north direction (kg/m2s) c fys Matrix of massfluxin the south direction (kg/m2s) eg Matrix of source term for each cell (W) c heatev Heat of evaporation of water at 25 C (J/kg) c sbc Stefan-Boltzmann constant (W/m2K4) c t Temperature matrix for present iteration c to Temperature matrix for previous iteration cu Solution vector from subroutine tridag c  *******************************************  1  implicit real*8(a-h,o-z) real*8 k common/blka/acell(300),o2feed,x,fuel,uc,us common/blkb/cycv,npart,dt(300),pmatt(300), pmatl(300),rc,volf,valh,rt,distv(300),siv(20),pdist(20) common/blkd/heat(300),total,dycell,cross,presc2(300),  145  1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176  1 press2(300),conO,oxyclc,mcyc,pair corrunonMkf/to(5,30 common^lkg/flux(300,5),dx(5,300),dy(5,300),f,erm common/blkfi/acirut,asinit,acfin^ corrrnioa03lki/areaw(5,300),areae(5,300),arean(5,300), 1 areas(5,300),areat(5,300),effh(300),deng,sbc,constl, 2 effc(300),effr(300),v2,v5,v6,cyc,gcyc dimension t(5,300),fyn(5,300),fys(5,300),fx(5,300) dimension a(300),b(300),c(300),r(300),u(300),heat(300) dimension g(5,300),ult(7) data heatev/2.44d6/  1177  1178 1179  ny=nycell+3 nx=4  1180  1181  c Convert temperaturesfromC to K  1182  1183 1184 1185 1186 1187 1188  do i=l,nx doj=l,ny to(ij)=to(ij)+273.15d0 t(ij)=to(ij) enddo enddo  1189  1190  c Determine fx, fyn and fys values.  1191  1192 1193 1194 1195 1196 1197 1198  doj=l,ny do i=l,nx 6c(ij)=0.d0 fyn(ij)=0.d0 fys(ij)=0.d0 enddo enddo  1199  1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210  doj=3,ny-l fx(3j)=flux0'-2,2) fx(2j)=flux0-2+nycell,2) enddo fx(2,2)=flux(nyceU+l,3)*asinit/(dy(2,2)*per) fx(3,2)=0.d0 doj=4,ny-2 fyn(3j)=flux0-2,3) fys(3,j)=flux0-3,3) fys(2j)=flux0-2+nycell,3) fyn(2,j)=flux(j-l+nyceil,3)  146  1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255  enddo fys(2,3)=flux(nycell+l,3) fyn(2,3)=flux(nycell+2,3) fyn(2,2)=flux(nyceU+l,3) fyn(3,3)=flux(l,3) fys(3,3)=flux(ncell,3) fyn(3,2)=flux(ncell,3) fys(3,2)=(recirc+fuel)/acinit fyn(3,ny-l)=flux(nycell,3) fys(3,ny-1 )=flux(nycell-1,3) fys(2,ny-l)=flux(ncell-l,3) ryn(2,ny-l)=flux(nycell,3)*acfin*rc/asfin c Calculate heat generation term (W), subtracting the heat loss due c to the evaporation of water at (25 C). g(2,2)=heat(ncell)*(fuel*valh*1000.d01 (foel*ult(2)+mel*ult(4)/2.dO*18.dO)/100.dO*heatev)*asinityat g(3,2)=heat(ncell)*(tuel*valh*1000.d01 (fuel*ult(2)+fuel*ult(4)/2.d0* 18.d0)/l 00.d0*heatev)*acinit7at doj=3,ny-l g(2j)=heatO-2+nycell)*(fuel*valh*1000.dO1 (fuel*ult(2)+fuel*ult(4)/2.d0* 18.d0)/100.d0*heatev) g(3j)=heatO-2)*(fuel*valh*1000.dO1 (mel*ult(2)+fiiel*ult(4)/2.d0*18.d0)/100.d0*heatev) enddo gcyc=cyc/total*£uel* valh* 1000. dO c Start N-S sweep  10  iter=0 iter=iter+l do 100j=2,ny  C Calculate A,B,C and R. a(l)=0.d0 b(l)=l.d0 c(l)=0.d0 r(l)=twall+273.15d0 iflj.eq.ny) then do i=2,4 a(i)=0.d0  147  1256 1257 1258 1259 1260 1261  b(i)=l.dO C(i)=0.d0 r(i)=t(3j-l) enddo goto 50 endif  1262  1263  c Set an upper limit of the heat transfer coefficientto 100.  1264  1265  h=consl*denb(j)  1266  1267  if(h.ge.l00.d0)h=100.d0  1268 1269  i=2 11=(fx(2j) * cp+deng* eg* vg) * areae(i j) t2=(fx(3j)*cp+deng*cg*vg)*areae(ij) t3=fyn(ij)*cp*arean(ij) t4=deng*cg*us*arean(ij) t5=fys(ij)*cp*areas(ij) t6=deng*cg*us*areas(ij)  1270 1271 1272 1273 1274 1275 1276  1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292  1293 1294 1295 1296  1 1 1 2 3  ae=-k*areae(i j)/((dx(i j)+dx(i+1 J))/2. dO) an=-k*arean(ij)/((dy(ij)+dy(ij+l))/2.d0) as=-k*areas(i,j)/((dy(i j)+dy(i j - l))/2.d0) s=-g(ij) ap=ae+an+as a(i)=h*areaw(i j)+emiss*sbc*areaw(i j)*to(i-1 j)* *3 b(i)=ap-h*areaw(ij)*arean(ij)/at-erniss*sbc*areat(ij)*to(i,j)**3tl-t4-t5 c(i)=-ae-h*areaw(ij)*arean(i+l j)/at+emiss*sbc*areae(i,j)*to(i+l,j) **3+t2 r(i)=an*to(ij+l)+as*to(ij-l)+s-emiss*sbc*arean(ij)* to(ij+l)**4-erniss*sbc*areas(ij)*to(ij-l)**4+ (-tl+t2-t4-t5)*(tref+273.15d0)-t3 *(to(i j+l)-(tref+273.15d0)) -t6*(to(ij-l)-(tref+273.15d0)) i=3 tl=(fx(3,j)*cp+deng*cg*vg)*areaw(ij) t2=(fx(2j)*cp+deng*cg*vg)*areaw(i,j) t3 =(fyn(i j) * cp+deng* cg*uc) * arean(i j) t4=(fys(ij)*cp+deng*cg*uc)*areas(ij)  1297  1298 1299 1300  aw=-k* areaw(i j)/((dx(i j)+dx(i-1 j))/2. dO) an=-k*arean(ij)/((dy(ij)+dy(ij+l))/2.d0) as=-k*areas(ij)/((dy(ij)+dy(i,j-l))/2.d0)  148  1301 1302 1303 1304 1305 1306 1307 1308  S=-g(ij) ap=aw+an+as a(i)=-aw+emiss*sbc*areaw(ij)*to(i-lj)**3+t2 b0) ap-emiss*sbc*areat(ij)*to(ij)**3-tl-t3 c(i)=0.d0 r(i)=an*to(ij+l)+as*to(ij-l)+s-erniss*sbc*arean(ij)* to(ij+l)**4-emiss*sbc*areas(ij)*to(ij-l)**4+ (-tl+t2-t3)*(tref+273.15d0)-t4*(to(i j - l)-(tref+273.15d0)) =  1 1  1309  1310  ifljeq.2) r(i)=r(i)+gcyc  1311 1312  i=4 aw=l.d0 ap=aw a(i)=-aw b(i)=ap c(i)=0.d0 r(i)=0.d0  1313 1314 1315 1316 1317 1318 1319  1320  50  call tridag(a,b,c,r,u,nx)  1321  1322 1323 1324  do i=l,nx t(ij)=u(i) enddo  1325  1326  c Update temperature solution.  1327  1328 1329 1330  90  do i=l,4 to(ij)=to(ij)-rf2*(to(ij)-t(i,j)) enddo  1331  1332  100  continue  1333  1334  c Calculate the temperature of the cyclone.  1335  1336  tcyc=to(3,ny)+gcyc/(afeed*cg+recirc*cp)  1337  1338 1339 1340 1341 1342 1343 1344 1345  error=0.d0 ermax=0.d0 itab=0 jtab=0 doj=2,ny do i=l,nx error=dabs(t(ij)-to(ij))/t(ij) if(error.gt.ermax) then  149  1346 1347 1348 1349 1350 1351 1352  ermax=error itab=i jtab=j endif enddo enddo print*, 'ij,iter,error',itabjtab,iter,ermax  1353  1354  c Calculate the new mixing temperature.  1355  1356 1357 1358 1359 1360  tmix=(afeed*cg*(tair+273.15d0)+fuel*cp*(tref+273.15d0)+ 1 recirc*cp*tcyc)/(afeed*cg+fuel*cp+recirc*cp) do i=l,4 to(i,l)=tmix enddo  1361  1362  if(ermax.gt.eps) goto 10  1363 1364  C  1365  c Check the energy balance (for debugging purposes).  1366  1367 1368 1369 1370  vl=0.d0 v2=0.d0 v3=0.d0 v4=0.d0  1371  1372 1373 1374 1375 1376 1377  900  doj=ny-l,2,-l do i=2,3 gen=g(ij) vl=vl+gen write(7,900) i,j,t(i,j),gen format(il5,2x,il5,2x,fl5.4,2x,fl5.4)  1378  1379  c Set upper limit of the heat transfer coefficient.  1380  1381  h=constl*denb(j)  1382  1383  if(h.ge.l00.d0)h=100.d0  1384  1385 1386 1387 1388 1389 1390  1  if(i.eq.2) then condw=-h*areaw(ij)*((t(i,j)*arean(ij)+t(i+l,j)* arean(i+lj))/at-t(i-lj)) conde=-k*areae(ij)/((dx(ij)+dx(i+lj))/2.d0)*(t(ij)-t(i+l,j)) v2=v2+condw else  150  1391 1392 1393 1394 1395 1396 1397 1398 1399 1400  1  910  condw=-k*areaw(ij)/((dx(ij)+dx(i-lj))/2.d0)* (t(ij)-t(i-lj)) conde=0.dO endif condn=-k*arean(ij)/((dy(ij)+dy(ij+l))/2.d0)*(t(ij)-to(i,j+l)) conds=-k*areas(ij)/((dy(i,j)+dy(ij-l))/2.d0)*(t(ij)-to(ij-l)) ifTj.eq.ny-1) v3=v3+condn ifij.eq.2) v4=v4+conds write(7,910) condw,conde,condn,conds format(4(fl5,4,2x))  1401  1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435  1 1  1 1 2  if(i.eq.2) then convwp=0.d0 convwg=0.d0 convep=-fx(2j)*cp*areae(ij)*(t(ij)-298.15dO)+ fx(3j)*cp*areae(ij)*(t(i+lj)-298.15d0) conveg=-deng*cg*vg*areae(ij)* (t(ij)-298.15d0)+deng*cg*vg*areae(ij)*(t(i+lj)-298.15d0) convnp=fyn(i j)*cp*arean(i j)*(to(i j+l)-298.15d0) convng=-deng*cg*us*arean(ij)*(t(i,j)-298.15d0) convsp=-fys(ij)*cp*areas(ij)*(t(ij)-298.15d0) convsg=deng*cg*us*areas(ij)*(to(ij-l)-298.15d0) ifTj.eq.ny-1) htop=cohvng+convnp ifTj.eq.2) then convsg=0.d0 convsp=0.d0 endif else convwp=-fx(3 J)*cp*areaw(ij)*(t(i,j)-298.15d0)+ fx(2j)*cp*areaw(ij)*(t(i-lj)-298.15d0) convwg=-deng*cg*vg*areaw(ij)* (t(ij)-298.15d0)+deng*cg*vg*areaw(i,j)* (t(i-lj)-298.15d0) convep=0.d0 conveg=0.d0 convnp=-fyn(i j)*cp*arean(i j)*(t(i j)-298.15d0) convng=-deng*cg*uc*arean(i,j)*(t(i,j)-298.15d0) convsp=fys(ij)*cp*areas(ij)*(to(ij-l)-298.15d0) convsg=deng*cg*uc*areas(ij)*(to(iJ-l)-298.15d0) ifTj.eq.ny-1) htop=htop+convng+convnp ifTj.eq.2) then convsg=0.d0 convsp=-htop-(vl+v2)+gcyc endif endif  151  1436  iffj.eq.ny-l) v3=v3+convnp+convng  1437  ifTj.eq.2) v4=v4+convsp+convsg  1438 1439  write(7,910) convwp,convep,convnp,convsp write(7,910) convwg,conveg,convng,convsg  1440  1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453  radv^-erruss*sbc*areaw(ij)*(to(ij)**3*t(ij)-to(i-lj)**3* radn=-emiss* sbc*arean(i j)*(to(i j)* *3 *t(i j)-to(i j+1)* *4) rads=-emiss*sbc*areas(ij)*(to(ij)**3*t(ij)-to(ij-l)**4) if(i.eq.2) then rade=-emiss*sbc*areae(ij)*(to(ij)**3*t(ij)to(i+lj)**3*t(i+lJ)) v2=v2+radw else rade=0.d0 endif ifij.eq.ny-1) v2=v2+radn ifijeq.2) v2=v2+rads write(7,910) radw,rade,radn,rads  1454  1455 1456 1457  if(i.eq.2) then effc(j)=-condw/areaw(i J)/(to(i j)-to(i-1 j)) efrx(j)=-radw/areaw(i j)/(to(i j)-to(i-1 j))  1458  efmO)=effcO)+effrO)  1459 1460 1461  endif enddo enddo  1462  1463 1464 1465 1466  V5=vl+v2+v3+v4 v6=v5/vl*100.d0 print*, vl,v2,v3,v4,v5 write(8,*) VI - v5',vl,v2,v3,v4,v5  1467  1468 1469 1470 1471 1472 1473 1474  print*, 'heat balance % diff. of heat gen. = ',v6 write(8,*) 'heat balance % diff. of heat gen. = ',v6 zl=vl z2=v2 z3=v3 c  1475  1476  c Convert the temperatures back from K to C.  1477  1478 1479 1480  doj=l,ny do i=l,nx to(i,j)=to(i,j)-273.15d0  152  1481 1482 1483  enddo enddo return end  1484 1485  1487 1488 14g5 1490  subroutine tridag(a,b,c,r,u,n) c Subroutine to solve a nxn tridiagonal matrix. c  1491 1492 1493 1494  *******************************************  implicit real*8(a-h,o-z) dimension gam(300),a(300),b(300),c(300),r(300),u(300) bet=b(l) u(l)=r(l)/bet  1495  1496  c Decomposition and forward substitution.  1497  1498 1499 1500 1501 1502  doj=2,n gam(j)=c(j-l)/bet bet=bO)-aO)*gamO) uG)=(r(J)-aO)*uG-l))/bet enddo  1503  1504  c Backsubstitution.  1505 1506  do j=n-1,1,-1  1507 1508 1509  uO)=uO)-gamO+l)*uO+l) enddo return end  1510 1511  1512 1513 1514  C  ******** I E E E error handling routine ************ integer function commonhandler (sig, sip, uap) integer sig  1515  1516  c define the structure siginfo, as in < sys/siginfo.h>  1517  1518 1519 1520 1521 1522 1523 1524 1525  structure/fault/ integer address end structure structure/siginfo/ integer sisigno integer sicode integer sierrno record /fault/ fault  153  1526 1527 1528 1529 1530 1531 1532 1533 1534  end structure record /siginfo/ sip c for error codes see p 89 numerical computation guide  10  write (0,10) sip.si_code, sip.fault.address format('ieee e x c e p t i o n i l , ' occurred at address ', z8 ) end  154  APPENDIX B SAMPLE INPUT FDLES  B. 1  HYDRODYNAMIC INPUT FILE LISTING  COMBUSTOR: CASE:  Studsvik Prototype shO  20 425000 0.100000 2.607681 0.680000 107.334949 2.777500 0.719603 849.850000 106.850000  —  cell#  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21  no. of cells in y-dir — x-sectional area (m2) — reflection coeff. — perimeter of riser (m) — primary zone volume (m3) — average bed density (kg/m3) — height of start of dev. zone (m) — frac. of total air that is primary - — bed temperature (C) — wall temperature (C)  height(m) flux out X-dir.  flux out Y-dir.  .13 .38 .63 .88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 .13  49.3334 238.1944 151.6668 30.4128 104.8062 20.3644 78.2123 14.7241 62.7280 11.4609 53.5793 9.5401 48.1274 8.3980 44.8620 7.7148 42.9003 7.3047 41.7035 7.0580 40.8774 6.9041 40.1386 6.7814 39.3816 6.6567 38.6006 6.5280 6.3953 37.7956 6.2585 36.9665 36.1136 6.1177 35.2373 5.9729 34.3383 5.8243 33.4162 5.6720 1247.4000 1134.0000  76.6772 46.5892 28.5548 17.6849 11.0329 6.9686 4.5322 3.0692 2.1894 1.6597 1.3395 1.3410 1.3169 1.2920 1.2663 1.2398 1.2126 1.1847 1.1560 1.1266 12.1690  densities  155  22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41  .38 .63 .88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 .00  7.6581 5.0597 3.5054 2.4755 1.8042 1.4154 1.1882 1.0542 .9746 .9262 .8862 .8467 .8063 .7650 .7229 .6801 .6367 .5929 .5489 .0000  height (m)  Aa (m2)  .00 .13 .38 .63 .88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.1.7 4.42 4.67 4.92  .089157 .072131 .044831 .028355 .018412 .012411 .008790 .006604 .005285 .004489 .004009 .003708 .003469 .003225 .002972 .002712 .002444 .002167 .001882 .001589 .001288  1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 1247.4000 369.1127  1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 1134.0000 316.9441  156  5.05  .001136  Particle Physical Properties and Composition Weight % Fuel 12.200 15.200 .170 3.050 52.900 .680 15.800  ash moisture sulphur hydrogen carbon nitrogen oxygen  40.000 1400.000  % volatiles yield particle density (kg/m3)  7.122 3.567 6.95850 30.00000 .07921 .85000  mean core gas velocity (m/s) mean streamer gas velocity (m/s) superficial gas velocity (m/s) solids recirc.flux(kg/m2s) thermal conductivity of gas particle radiation emissivity  'article Sieve Sizing wt% mm 7.925 5.613 3.962 2.794 1.981 1.397 .991 .701 .495 .351 .246 .175 .124 .088 .053 .045 .038 .000  9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 .000 .000 .000 .000 .000  157  B.2  USER INPUT F I L E LISTING  INPUT FILE FOR HEAT.F Constants Used With the Devolatilization Rate Equation bituminous coal 11.8 706.0 higher heating value (kJ/kg) 24000.0 100 0.1 1 0.001 1.0 0.01 0.7 0.7 0.1 0.3 0.3 0.2 1.0 900.0 25.0 25.0 1.0  number of particles in the Monte Carlo method frac. of particles that exit a cell within dt number of feed points tolerance for partial pressure of 02 (atm) tolerance for bed temperature (C) convergence tolerance in subroutine heat relaxation factor in subroutine heat relaxation factor for partial pressure of 02 mass transfer crossflow coefficient volatile transfer fraction residence time in the cyclone (sec.) excess air combustion efficiency particle surface temperature (C) temperature of inlet air (C) reference temperature (C) const, in wall convective heat transfer coeff. term  158  APPENDIX C OUTPUT FILES  159 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case : shO (base case) Superficial gas velocity = 6.96 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION  PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  160 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recuxulation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 858.6 C 12.750 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 395.687 kg/hr 3070.295 kg/hr 72.0 % 0.300 sec. 0.100 2.777 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  7.122 m/s 3.567 m/s 6.958 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  161 page 3 of 6  HEAT RELEASE DISTRIBUTION Height (m) 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone TOTAL  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core 0.337328 0.001086 0.077952 0.003157 0.017585 0.000082 0.004516 0.000003 0.001274 0.000000 0.000414 0.000004 0.000233 0.000001 0.000448 0.000007 0.000271 0.000001 0.000200 0.000000 0.000257 0.000000 0.000123 0.000000 0.000076 0.000000 0.000039 0.000000 0.000063 0.000000 0.000079 0.000000 0.000027 0.000000 0.000017 0.000000 0.000007 0.000000 0.000007 0.000000 0.000051 0.000037 0.502019  0.464242 0.017981 0.007278 0.009128 0.004215 0.006292 0.002686 0.004353 0.001962 0.003025 0.001509 0.002080 0.001248 0.001675 0.001108 0.001341 0.001003 0.001087 0.000910 0.000996 0.000883 0.000947 0.000874 0.000874 0.000818 0.000898 0.000825 0.000825 0.000822 0.000860 0.000781 0.000751 0.000779 0.000686 0.000754 0.000564 0.000716 0.000491 0.000709 0.000364 0.000670 0.004644 0.497981  162 page 4 of 6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION  Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.068524 0.031904 0.053800 0.018193 0.046472 0.012646 0.043154 0.011824 0.041219 0.015730 0.039964 0.021778 0.039116 0.025567 0.038457 0.027828 0.037964 0.029310 0.037572 0.029630 0.037212 0.029585 0.036890 0.029795 0.036598 0.029436 0.036308 0.029658 0.036025 0.029217 0.035742 0.029720 0.035482 0.030067 0.035238 0.030834 0.035020 0.031302 0.034815 0.032164 0.034630  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0040 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  163 page 5 of 6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  889.4 891.4 883.8 833.4 888.0 830.3 884.5 881.0 827.6 825.1 877.8 822.9 875.0 821.1 872.5 870.2 819.8 818.7 868.1 817.9 866.3 820.9 864.5 823.9 862.8 826.9 861.4 827.3 860.2 828.4 859.0 830.4 858.0 834.2 857.2 841.1 856.7 853.3 856.7 876.3 857.4  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  858.6 C 0.004 C 858.6 C 106.8 C  164 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  316.944 233.423 146.824 94.664 63.214 44.242 32.797 25.889 21.720 19.205 17.688 16.738 15.982 15.211 14.412 13.591 12.744 11.869 10.968 10.042 9.091  889.4 891.4 888.0 884.5 881.0 877.8 875.0 872.5 870.2 868.1 866.3 864.5 862.8 861.4 860.2 859.0 858.0 857.2 856.7 856.7 857.4  110.3 109.9 98.1 97.4 96.8 96.2 95.7 95.3 95.0 94.8 94.6 94.8 96.6 96.6 96.7 97.0 97.4 98.3 99.8 102.6 108.0  100.5 100.8 106.9 101.4 67.7 47.4 35.1 27.7 23.2 20.5 18.9 17.8 16.8 15.9 15.1 14.2 13.2 12.2 11.2 10.1 8.9  210.8 210.7 205.0 198.7 164.5 143.6 130.9 123.1 118.3 115.3 113.5 112.6 113.4 112.6 111.8 111.1 110.6 110.5 111.0 112.7 116.9  165 page 1 of6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: shl Superficial gas velocity 6.96 m/s Solids reciculation rate 50 kg/m2s Highvale coal(mean dp 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  166 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 835.1 C 21.250 kg/s 50.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 388.886 kg/hr 3017.519 kg/hr 72.0 % 0.300 sec. 0.100 2.525 m  GAS VELOCrnES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity Bed temperature used in calculating heat transfer area and gas velocities  7.187 m/s 3.600 m/s 6.958 m/s 849.9 C  167 page 3 of 6  HEAT RELEASE DISTRIBUTION Height (m) 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone TOTAL  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core 0.330548 0.008532 0.072786 0.001237 0.016510 0.004695 0.005423 0.000078 0.001387 0.000033 0.000365 0.000000 0.000267 0.000010 0.000123 0.000000 0.000287 0.000000 0.000080 0.000000 0.000029 0.000000 0.000027 0.000000 0.000054 0.000000 0.000017 0.000000 0.000013 0.000000 0.000005 0.000000 0.000036 0.000000 0.000022 0.000000 0.000006 0.000000 0.000005 0.000000 0.000006 0.000012 0.497612  0.451193 0.022746 0.007294 0.012063 0.004265 0.006954 0.002901 0.004356 0.002131 0.002992 0.001742 0.002187 0.001434 0.001822 0.001301 0.001637 0.001168 0.001444 0.001182 0.001286 0.001070 0.001289 0.001105 0.001260 0.001052 0.001123 0.001092 0.001082 0.000990 0.000949 0.000990 0.000831 0.000929 0.000781 0.000890 0.000678 0.000875 0.000565 0.000847 0.000489 0.000803 0.005618 0.502388  168 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.072215 0.023893 0.057783 0.012219 0.049493 0.000000 0.045156 0.002534 0.042749 0.010056 0.041216 0.018399 0.040186 0.023755 0.039461 0.026177 0.038872 0.027334 0.038395 0.028038 0.037992 0.027895 0.037594 0.027771 0.037204 0.028304 0.036830 0.028480 0.036482 0.029135 0.036152 0.029855 0.035846 0.030160 0.035557 0.030736 0.035289 0.031467 0.035042 0.031969 0.034815  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0039 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  169 page 5 of6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  854.0 855.4 849.5 852.4 803.1 802.2 849.6 846.9 801.8 844.5 802.5 842.6 804.0 841.0 806.1 839.7 808.6 838.8 811.2 837.9 812.6 837.1 814.0 836.4 815.4 835.7 815.6 816.2 835.1 834.6 817.3 834.2 819.2 822.2 833.9 827.2 833.8 833.9 835.5 850.3 834.4  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  83 5.1 C 0.004 C 835.1 C 106.8 C  170 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  383.621 288.739 185.084 122.702 85.097 62.419 48.736 40.479 35.495 32.488 30.757 29.504 28.167 26.773 25.316 23.795 22.212 20.559 18.840 17.052 15.196  854.0 855.4 852.4 849.6 846.9 844.5 842.6 841.0 839.7 838.8 837.9 837.1 836.4 835.7 835.1 834.6 834.2 833.9 833.8 833.9 834.4  102.3 101.7 91.4 91.2 91.2 91.3 91.6 92.1 92.6 93.2 93.4 94.2 94.1 94.1 94.3 94.5 94.9 95.6 96.7 98.5 101.9  100.3 100.6 106.3 106.3 90.3 66.1 51.4 42.5 37.0 33.7 31.8 30.4 29.0 27.5 26.0 24.4 22.7 20.9 19.0 17.0 14.9  202.6 202.4 197.7 197.6 181.5 157.4 143.0 134.5 129.7 126.9 125.3 124.6 123.1 121.7 120.2 118.9 117.6 116.5 115.7 115.6 116.8  171 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case : sh2 Superficial gas velocity = 6.96 m/s Solids reciculation rate = 15 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION  PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  172 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 897.8 C 6.375 kg/s 15.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 403.300 kg/hr 3129.367 kg/hr 72.0 % 0.300 sec. 0.100 3.283 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity Bed temperature used in calculating heat transfer area and gas velocities  7.064 m/s 3.536 m/s 6.958 m/s 849.9 C  173 page 3 of6  HEAT RELEASE DISTRIBUTION  (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.368394 0.001269 0.078107 0.000458 0.017016 0.000093 0.004032 0.000300 0.001880 0.001258 0.000603 0.000767 0.000655 0.000000 0.000138 0.000000 0.000029 0.000000 0.000006 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000  Height  TOTAL  0.535547  0.466610 0.013888 0.006876 0.004697 0.003829 0.001244 0.002424 0.002026 0.001628 0.001626 0.001121 0.001453 0.000861 0.001174 0.000704 0.000887 0.000586 0.000704 0.000569 0.000578 0.000531 0.000482 0.000497 0.000427 0.000482 0.000402 0.000471 0.000394 0.000451 0.000375 0.000466 0.000358 0.000451 0.000272 0.000433 0.000236 0.000428 0.000252 0.000440 0.000199 0.000413 0.003048 0.464453  174 page 4 of 6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.064113 0.024916 0.048143 0.024727 0.042146 0.034367 0.039890 0.033023 0.038603 0.024529 0.037719 0.022326 0.036985 0.027596 0.036556 0.029910 0.036262 0.030934 0.036028 0.031514 0.035833 0.031949 0.035666 0.032133 0.035514 0.032136 0.035370 0.032060 0.035230 0.032083 0.035092 0.032094 0.034959 0.032669 0.034841 0.032881 0.034731 0.032650 0.034617 0.032975 0.034515  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0020 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  175 page 5 of6  TEMPERATURE DISTPJBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  960.6 954.2 963.3 897.2 959.3 954.8 892.0 950.2 886.8 945.9 881.2 875.4 941.6 869.3 937.4 933.2 863.3 929.0 857.8 924.7 852.8 920.5 848.5 845.4 916.7 844.4 912.7 908.8 843.5 905.2 842.5 901.9 842.7 898.9 845.6 896.5 853.5 895.2 871.4 896.2 910.2  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  897.8 C 0.002 C 897.8 C 106.8 C  176 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  244.887 176.105 108.381 67.562 42.946 28.095 19.131 13.725 10.462 8.491 7.304 6.586 6.153 5.899 5.709 5.503 5.295 5.083 4.871 4.656 4.440  960.6 963.3 959.3 954.8 950.2 945.9 941.6 937.4 933.2 929.0 924.7 920.5 916.7 912.7 908.8 905.2 901.9 898.9 896.5 895.2 896.2  127.9 127.9 113.1 111.8 110.6 109.2 107.8 106.4 104.9 103.6 102.5 101.5 100.8 100.2 100.7 100.1 100.2 100.8 102.6 106.9 116.4  100.7 101.0 107.4 72.8 46.4 30.4 20.8 14.9 11.4 9.3 8.0 7.2 6.7 6.5 6.2 6.0 5.7 5.4 5.2 4.8 4.4  228.7 228.8 220.5 184.6 156.9 139.6 128.6 121.3 116.4 112.9 110.5 108.7 107.5 106.6 106.9 106.1 105.9 106.3 107.8 111.7 120.7  177 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh3 Superficial gas velocity = 5.99 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  178 page 2 of6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 812.3 C 12.750 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 340.730 kg/hr 2643.858 kg/hr 72.0 % 0.300 sec. 0.100 2.525 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  6.147 m/s 3.077 m/s 5.992 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  179 page 3 of 6  HEAT RELEASE DISTRIBUTION  (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.258625 0.006435 0.060164 0.000144 0.012962 0.000058 0.002760 0.000027 0.000635 0.000002 0.000137 0.000000 0.000031 0.000001 0.000013 0.000000 0.000003 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000  Height  TOTAL  0.385113  0.534937 0.025247 0.009468 0.014644 0.005495 0.009723 0.003660 0.006133 0.002588 0.004100 0.002051 0.002707 0.001709 0.002032 0.001462 0.001593 0.001332 0.001429 0.001263 0.001335 0.001217 0.001232 0.001170 0.001201 0.001126 0.001078 0.001083 0.001027 0.001080 0.000939 0.001031 0.000818 0.000989 0.000755 0.000988 0.000629 0.000936 0.000528 0.000868 0.000459 0.000893 0.005050 0.614887  180 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.070199 0.013500 0.057427 0.000000 0.049735 0.000000 0.045732 0.000000 0.043320 0.007485 0.041694 0.017631 0.040611 0.024464 0.039862 0.028172 0.039301 0.029309 0.038829 0.029512 0.038400 0.029735 0.038000 0.029642 0.037614 0.030066 0.037253 0.030170 0.036901 0.030455 0.036571 0.031002 0.036266 0.031235 0.035972 0.031846 0.035706 0.032373 0.035467 0.032682 0.035236  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0054 atm. 0.210000 atm. 0.03 5 atm. 0.034 atm.  181 page 5 of 6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  837.8 839.3 832.7 836.2 786.1 833.0 784.0 782.3 829.8 827.0 781.1 824.5 780.5 780.4 822.4 820.5 780.7 819.0 781.3 817.6 783.8 786.4 816.2 815.1 788.9 814,1 788.8 813.2 789.0 812.3 789.7 811.6 791.4 811.1 794.6 800.2 810.8 810.8 810.3 830.1 811.5  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  812.3 C 0.005 C 812.3 C 106.8 C  182 page 6 of 6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  331.166 246.560 156.579 102.403 69.743 50.044 38.157 30.984 26.657 24.045 22.460 21.317 20.224 19.101 17.948 16.760 15.542 14.292 13.013 11.707 10.373  837.8 839.3 836.2 833.0 829.8 827.0 824.5 822.4 820.5 819.0 817.6 816.2 815.1 814.1 813.2 812.3 811.6 811.1 810.8 810.8 811.5  98.3 97.9 87.9 87.4 87.1 86.8 86.7 86.7 86.7 86.8 87.0 88.2 88.4 88.4 88.4 88.6 89.0 89.6 90.8 93.0 97.3  100.4 100.8 106.7 106.8 74.5 53.4 40.6 32.9 28.2 25.4 23.6 22.2 21.0 19.8 18.6 17.3 16.0 14.6 13.2 11.7 10.1  198.7 198.7 194.6 194.2 161.5 140.2 127.3 119.6 114.9 112.2 110.6 110.4 109.4 108.2 107.0 105.9 105.0 104.3 104.0 104.7 107.4  183 page 1 of 6  CFB H E A T R E L E A S E AND H E A T TRANSFER M O D E L RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh4 Superficial gas velocity 5.99 m/s Solids reciculation rate 50 kg/m2s Highvale coal(mean dp 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION  PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  184 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 764.4 C 21.250 kg/s 50.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 334.951 kg/hr 2599.018 kg/hr 72.0 % 0.300 sec. 0.100 2.525 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  6.212 m/s 3.107 m/s 5.992 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  185 page 3 of 6  HEAT RELEASE DISTRIBUTION  (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.257134 0.000530 0.055538 0.001910 0.012797 0.000014 0.002853 0.000013 0.001002 0.000003 0.000353 0.000113 0.000254 0.000001 0.000081 0.000000 0.000065 0.000004 0.000021 0.000004 0.000031 0.000003 0.000014 0.000004 0.000008 0.000006 0.000007 0.000004 0.000018 0.000000 0.000005 0.000001 0.000002 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000001  Height  TOTAL  0.375245  0.527291 0.026825 0.010168 0.015019 0.005935 0.009405 0.004031 0.006096 0.003002 0.004286 0.002480 0.003105 0.002090 0.002637 0.001927 0.002335 0.001734 0.002037 0.001652 0.001967 0.001618 0.001808 0.001501 0.001710 0.001572 0.001558 0.001435 0.001604 0.001371 0.001320 0.001343 0.001180 0.001287 0.000960 0.001219 0.000857 0.001197 0.000659 0.001142 0.000511 0.001071 0.006260 0.624755  186 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.072593 0.031569 0.059943 0.016184 0.051720 0.008136 0.047600 0.006963 0.044969 0.011088 0.043167 0.016966 0.041880 0.021508 0.040922 0.023921 0.040157 0.025435 0.039510 0.025717 0.038910 0.026202 0.038355 0.026501 0.037807 0.027027 0.037303 0.026612 0.036807 0.027727 0.036352 0.028494 0.035931 0.029672 0.035555 0.030273 0.035201 0.031363 0.034886 0.032257 0.034608  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0042 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  187 page 5 of 6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  780.8 776.5 781.9 735.2 779.2 734.5 776.6 734.7 774.3 735.6 772.2 737.0 770.5 738.6 769.0 740.1 767.8 767.0 741.3 744.6 766.2 747.8 765.4 751.1 764.9 751.3 764.4 751.8 764.0 752.8 763.6 754.3 763.4 756.9 763.2 761.2 763.2 768.4 763.3 781.7 763.8  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  764.4 C 0.004 C 764.4 C 106.8 C  188 page 6 of 6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  401.087 306.273 198.719 134.022 95.034 71.518 57.334 48.776 43.612 40.494 38.535 36.836 34.966 33.027 31.010 28.918 26.748 24.498 22.173 19.766 17.282  780.8 781.9 779.2 776.6 774.3 772.2 770.5 769.0 767.8 767.0 766.2 765.4 764.9 764.4 764.0 763.6 763.4 763.2 763.2 763.3 763.8  86.4 85.9 77.7 77.6 77.6 77.8 78.0 78.4 78.6 78.9 79.2 81.0 80.8 80.8 80.9 81.1 81.4 81.9 82.8 84.2 86.9  100.3 100.7 106.2 106.2 100.7 75.5 60.3 51.1 45.5 42.1 39.9 37.6 35.7 33.7 31.6 29.4 27.1 24.7 22.2 19.6 16.8  186.6 186.5 183.9 183.8 178.3 153.3 138.3 129.4 124.1 121.0 119.1 118.6 116.5 114.5 112.5 110.5 108.5 106.7 105.0 103.8 103.8  189 page 1 of6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh5 Superficial gas velocity 5.99 m/s Solids reciculation rate 15 kg/m2s Highvale coal(mean dp 2.89 mm) . FUEL PHYSICAL PROPERTIES AND COMPOSITION  PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION nun 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  190 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 852.1 C 6.375 kg/s 15.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 347.226 kg/hr 2694.266 kg/hr 72.0 % 0.300 sec. 0.100 3.030 m  GAS VELOCrnES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  6.090 m/s 3.049 m/s 5.992 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  191 page 3 of 6  HEAT RELEASE DISTRIBUTION  (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.384113 0.000993 0.081644 0.001149 0.017436 0.000019 0.003700 0.000010 0.000954 0.000000 0.000240 0.000001 0.000103 0.000001 0.000047 0.000001 0.000034 0.000016 0.000018 0.000001 0.000027 0.000000 0.000006 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000  Height  TOTAL  0.553297  0.449719 0.011341 0.007597 0.003789 0.004170 0.002066 0.002620 0.001942 0.001758 0.001930 0.001303 0.001620 0.001022 0.001235 0.000863 0.000981 0.000724 0.000784 0.000671 0.000627 0.000617 0.000540 0.000561 0.000505 0.000598 0.000458 0.000566 0.000413 0.000559 0.000406 0.000549 0.000368 0.000557 0.000271 0.000510 0.000273 0.000511 0.000247 0.000504 0.000232 0.000507 0.002974 0.446703  192 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTPJBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.064817 0.032562 0.047682 0.033750 0.041712 0.038638 0.039566 0.037759 0.038501 0.033150 0.037794 0.030272 0.037249 0.030134 0.036829 0.030661 0.036503 0.031216 0.036236 0.031911 0.036014 0.032211 0.035826 0.032213 0.035642 0.032355 0.035472 0.032526 0.035309 0.032435 0.035150 0.032545 0.034995 0.033092 0.034863 0.032986 0.034731 0.033042 0.034605 0.033026 0.034481  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0031 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  193 page 5 of 6  TEMPERATURE DISTRIBUTION Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  905.0 907.5 898.8 845.8 903.7 899.4 841.3 836.7 895.1 831.9 891.0 827.0 887.1 822.2 883.3 879.6 817.7 876.0 813.5 872.4 809.9 806.7 869.2 807.4 865.9 808.0 862.6 808.7 859.8 807.9 857.0 808.4 854.5 811.2 852.3 850.6 818.2 849.8 833.5 868.0 850.9  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  852.1 C 0.003 C 852.1 C 106.8 C  194 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  255.628 185.093 114.618 72.151 46.542 31.091 21.771 16.146 12.750 10.701 9.465 8.721 8.264 7.896 7.504 7.106 6.708 6.304 5.902 5.495 5.090  905.0 907.5 903.7 899.4 895.1 891.0 887.1 883.3 879.6 876.0 872.4 869.2 865.9 862.6 859.8 857.0 854.5 852.3 850.6 849.8 850.9  113.6 113.5 100.9 99.9 98.8 97.7 96.6 95.6 94.6 93.7 92.9 92.2 91.8 93.2 92.6 92.5 92.6 93.2 94.7 98.1 106.0  100.7 214.4 101.0 214.5 107.3 208.2 177.5 77.6 149.0 50.2 33.6 131.3 23.6 120.2 17.5 113.1 13.9 108.4 11.6 105.3 10.3 103.2 9.5 101.7 9.0 100.8 8.5 101.7 8.0 100.7 7.6 100.1 7.1 99.7 99.8 . 6.7 6.2 100.9 5.6 103.7 111.0 5.0  195 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh2b Superficial gas velocity = 6.96 m/s Solids reciculation rate =15 kg/m2s Highvale coal (mean dp = 2.89 mm) # of particles in MC method = 400 FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  196 page 2 of 6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  400 70.0 % 898.9 C 6.375 kg/s 15.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 403.300 kg/hr 3129.367 kg/hr 72.0 % 0.300 sec. 0.100 3.283 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  7.064 m/s 3.536 m/s 6.958 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  197 page 3 of 6  HEAT RELEASE DISTRIBUTION Height (m) 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone TOTAL  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core 0.296334 0.000769 0.062872 0.000290 0.013703 0.000306 0.003105 0.000135 0.000735 0.000084 0.000309 0.000002 0.000141 0.000001 0.000063 0.000000 0.000032 0.000000 0.000020 0.000000 0.000012 0.000000 0.000006 0.000000 0.000002 0.000000 0.000003 0.000000 0.000001 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000001 0.427439  0.554419 0.014896 0.008152 0.004266 0.004592 0.002118 0.002852 0.001509 0.001890 0.001702 0.001367 0.001592 0.001048 0.001323 0.000854 0.001051 0.000751 0.000860 0.000674 0.000671 0.000635 0.000591 0.000620 0.000526 0.000599 0.000493 0.000588 0.000455 0.000580 0.000445 0.000571 0.000395 0.000555 0.000378 0.000557 0.000384 0.000554 0.000351 0.000538 0.000342 0.000537 0.003794 0.572561  198 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.062086 0.021621 0.047834 0.023283 0.042258 0.028653 0.039970 0.033086 0.038825 0.031379 0.038072 0.029099 0.037510 0.028511 0.037075 0.029260 0.036731 0.030054 0.036453 0.031068 0.036223 0.031391 0.036017 0.031620 0.035830 0.031655 0.035652 0.031780 0.035481 0.031715 0.035314 0.031962 0.035158 0.031970 0.035004 0.031778 0.034850 0.031890 0.034703 0.031827 0.034558  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0032 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  199 page 5 of6  TEMPERATURE DISTRIBUTION Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  962.0 955.2 964.3 898.1 960.2 893.0 955.7 887.6 951.1 946.7 882.0 876.2 942.4 870.3 938.3 934.1 864.3 929.9 858.8 853.8 925.7 921.6 849.5 848.1 917.7 913.7 846.5 845.0 909.9 843.6 906.3 843.6 903.0 846.7 900.0 854.7 897.6 872.5 896.4 897.4 911.5  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  898.9 C 0.003 C 898.9 C 106.8 C  200 page 6 of 6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  244.887 176.105 108.381 67.562 42.946 28.095 19.131 13.725 10.462 8.491 7.304 6.586 6.153 5.899 5.709 5.503 5.295 5.083 4.871 4.656 4.440  962 0 964 3 960 2 955 7 951 1 946 7 942 4 938 3 934 1 929 9 925 7 921 6 917 7 913 7 909 9 906 3 903 0 900 0 897 6 896 4 897 4  128 2 128 1 113 3 112 1 110 8 109 4 108 0 106 6 105 2 103 9 102 7 101 7 101 1 100 4 100 9 100 4 100 4 101 1 102 9 107 1 116 7  100.8 101.0 107.4 72.7 46.3 30.4 20.8 14.9 11.4 9.3 8.0 7.2 6.7 6.5 6.2 6.0 5.7 5.4 5.2 4.8 4.4  229.0 229.1 220.7 184.8 157.1 139.8 128.8 121.5 116.6 113.2 110.7 109.0 107.8 106.9 107.1 106.3 106.1 106.5 108.1 111.9 121.1  201 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh700 Superficial gas velocity = 6.96 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  202 page 2 of6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 859.9 C 12.750 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 395.687 kg/hr 3070.295 kg/hr 72.0 % 0.300 sec. 0.100 2.777 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  7.122 m/s 3.567 m/s 6.958 m/s  Bed temperature used in calculating heat transfer area and gas velocities  849.9 C  203 page 3 of6  HEAT RELEASE DISTRIBUTION Height (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.258362 0.000590 0.055214 0.001039 0.013448 0.000117 0.003640 0.000399 0.001683 0.000008 0.001767 0.000002 0.000499 0.000000 0.000221 0.000000 0.000084 0.000000 0.000145 0.000000 0.000053 0.000000 0.000051 0.000000 0.000017 0.000000 0.000123 0.000000 0.000044 0.000000 0.000016 0.000000 0.000005 0.000000 0.000011 0.000000 0.000003 0.000000 0.000011 0.000000 0.000003 0.000011  0.566111 0.020026 0.008767 0.007124 0.005038 0.004689 0.003222 0.003693 0.002311 0.003065 0.001771 0.002469 0.001498 0.002033 0.001218 0.001562 0.001138 0.001418 0.001078 0.001351 0.001023 0.001158 0.000974 0.001013 0.000953 0.000976 0.000931 0.000852 0.000892 0.000808 0.000893 0.000753 0.000877 0.000636 0.000840 0.000645 0.000834 0.000479 0.000784 0.000433 0.000759 0.005340  TOTAL  0.380679  0.619321  204 page 4 of6  OXYGEN PARTIAL PRESS SURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.066418 0.025838 0.053535 0.022029 0.046858 0.021824 0.043752 0.020122 0.041830 0.020567 0.040394 0.021998 0.039458 0.023719 0.038775 0.026167 0.038252 0.026929 0.037792 0.026905 0.037386 0.027740 0.037022 0.028582 0.036693 0.028730 0.036359 0.029381 0.036061 0.029570 0.035776 0.029772 0.035505 0.030455 0.035255 0.030271 0.035009 0.031314 0.034793 0.031600 0.034591  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0023 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  205 page 5 of6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  891.2 885.4 892.7 889.3 834.7 885.8 831.6 882.4 829.0 879.4 826.5 824.3 876.6 874.1 822.6 871.8 821.1 869.6 820.1 867.8 822.1 824.2 866.0 826.2 864.2 862.9 828.3 861.6 828.6 860.5 829.7 859.5 831.7 858.7 835.5 858.1 842.5 858.1 854.6 877.8 858.9  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  859.9 C 0.002 C 859.9 C 106.8 C  206 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  316.944 233.423 146.824 94.664 63.214 44.242 32.797 25.889 21.720 19.205 17.688 16.738 15.982 15.211 14.412 13.591 12.744 11.869 10.968 10.042 9.091  891.2 892.7 889.3 885.8 882.4 879.4 876.6 874.1 871.8 869.6 867.8 866.0 864.2 862.9 861.6 860.5 859.5 858.7 858.1 858.1 858.9  110.7 110.2 98.4 97.7 97.1 96.5 96.1 95.7 95.3 95.1 95.0 95.1 96.9 96.9 97.0 97.2 97.7 98.5 100.1 102.9 108.4  100.5 100.8 106.8 101.3 67.7 47.4 35.1 27.7 23.2 20.5 18.9 17.8 16.8 15.9 15.1 14.2 13.2 12.2 11.2 10.1 8.9  211.2 211.0 205.2 199.0 164.8 143.9 131.2 123.4 118.6 115.6 113.8 112.9 113.7 112.9 112.1 111.4 110.9 110.8 111.3 113.0 117.3  207 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case: sh900 Superficial gas velocity = 6.96 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION  PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  208 page 2 of6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 860.5 C 12.750 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 395.687 kg/hr 3070.295 kg/hr 72.0 % 0.300 sec. 0.100 2.777 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity Bed temperature used in calculating heat transfer area and gas velocities  7.122 m/s 3.567 m/s 6.958 m/s 849.9 C  209 page 3 of6  HEAT RELEASE DISTRIBUTION  (m)  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone  0.477220 0.342553 0.004300 0.074679 0.013539 0.000576 0.017038 0.004955 0.000289 0.003826 0.003514 0.000511 0.001003 0.003038 0.000150 0.000253 0.002745 0.000036 0.000126 0.002074 0.000030 0.000031 0.001647 0.000000 0.000007 0.001382 0.000000 0.000002 0^001109 0.000000 0.000000 0.001106 0.000000 0.000002 0.000942 0.000000 0.000000 0.000905 0.000000 0.000001 0.000822 0.000000 0.000000 0.000741 0.000000 0.000000 0.000717 0.000000 0.000000 0.000651 0.000000 0.000000 0.000567 0.000000 0.000000 0.000512 0.000000 0.000000 0.000466 0.000000 0.000000 0.000398 0.004768 0.000000  Height  TOTAL  0.501927  0.007436 0.004236 0.002766 0.001992 0.001493 0.001223 0.001082 0.000982 0.000928 0.000922 0.000848 0.000853 0.000836 0.000802 0.000775 0.000743 0.000729 0.000737 0.000692 0.000691  0.498073  210 page 4 of 6  OXYGEN PARTIAL PRESS SURE DISTRIBUTION Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.066846 0.031068 0.051215 0.033960 0.044474 0.035640 0.041798 0.032011 0.040337 0.027738 0.039364 0.026677 0.038644 0.027007 0.038093 0.027774 0.037651 0.028930 0.037286 0.028606 0.036946 0.029225 0.036646 0.029315 0.036355 0.029683 0.036079 0.030116 0.035821 0.030156 0.035573 0.030445 0.035339 0.030921 0.035121 0.031221 0.034910 0.031434 0.034714 0.031819 0.034529  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0010 atm. 0.210000 atm. 0.035 atm. 0.034 atm.  211 page 5 of 6  TEMPERATURE DISTRIBUTION Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  891.7 893.5 885.9 835.2 890.1 886.5 832.1 829.4 883.0 879.8 826.9 876.9 824.7 874.4 823.0 872.1 821.6 870.0 820.6 868.2 822.6 866.4 824.7 864.7 826.7 828.8 863.4 829.2 862.1 861.0 830.3 860.0 832.3 859.2 836.1 843.0 858.7 858.7 855.3 878.4 859.5  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  860.5 C 0.001 C 860.5 C 106.8 C  212 page 6 of 6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  316.944 233.423 146.824 94.664 63.214 44.242 32.797 25.889 21.720 19.205 17.688 16.738 15.982 15.211 14.412 13.591 12.744 11.869 10.968 10.042 9.091  891.7 893.5 890.1 886.5 883.0 879.8 876.9 874.4 872.1 870.0 868.2 866.4 864.7 863.4 862.1 861.0 860.0 859.2 858.7 858.7 859.5  110.8 110.4 98.5 97.8 97.2 96.6 96.1 95.7 95.5 95.2 95.1 95.2 97.0 97.0 97.1 97.4 97.8 98.7 100.2 103.1 108.5  100.5 100.8 106.9 101.4 67.7 47.4 35.1 27.7 23.2 20.5 18.9 17.8 16.8 15.9 15.1 14.2 13.2 12.2 11.2 10.1 8.9  211.3 211.2 205.4 199.1 164.9 144.0 131.3 123.5 118.7 115.7 113.9 113.0 113.8 113.0 112.2 111.5 111.0 110.9 111.4 113.2 117.4  213 page 1 of6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRITTEN BY: DALE W.C. JU COMBUSTOR: UBC COMBUSTOR CASE: RUN NO. 21, APRIL 21 1988 Case: uhO Superficial gas velocity = 7.03 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm)  FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 . Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  .  Wt%  9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  214 page 2 of6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 35.0 % 792.5 C 0.696 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 22.863 kg/hr 177.399 kg/hr 50.4 % 0.300 sec. 0.860 3.200 m  GAS VELOCrnES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  7.384 m/s 3.647 m/s 7.030 m/s  Bed temperature used in calculating heat transfer area and gas velocities  857.9 C  215 page 3 of6  HEAT RELEASE DISTRIBUTION  Height (m) 0.00 0.16 0.48 0.80 1.12 1.44 1.76 2.08 2.40 2.72 3.04 3.36 3.68 4.00 4.32 4.64 4.96 5.28 5.60 5.92 6.24 Cyclone TOTAL  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core 0.317052 0.005887 0.071983 0.000893 0.015944 0.000692 0.004155 0.000459 0.002142 0.000052 0.001592 0.000021 0.000909 0.000002 0.000222 0.000012 0.000200 0.000383 0.000344 0.000548 0.000692 0.000000 0.000007 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.477665  0.305613 0.029671 0.009973 0.017396 0.005973 0.013057 0.004362 0.009720 0.003486 0.008220 0.003020 0.007529 0.002748 0.006999 0.002584 0.006848 0.002449 0.006309 0.002425 0.006106 0.002373 0.006034 0.002349 0.006743 0.002428 0.006760 0.002529 0.007350 0.002600 0.007849 0.002783 0.008391 0.003011 0.008868 0.003295 0.009645 0.003666 0.010064 0.004114 0.010948 0.004818 0.004705 0.522335  216 page 4 of 6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION Height (m) 0.00 0.32 0.64 0.96 1.28 1.60 1.92 2.24 2.56 2.88 3.20 3.52 3.84 4.16 4.48 4.80 5.12 5.44 5.76 6.08 6.40  Partial Pressure of Oxygen (atm.) Streamer Core 0.101073 0.050014 0.082836 0.051504 0.073647 0.051164 0.068944 0.051587 0.065837 0.051353 0.063474 0.050136 0.061521 0.049017 0.059852 0.047547 0.058266 0.046136 0.056704 0.044455 0.055137 0.043668 0.053828 0.041194 0.052458 0.039494 0.051084 0.037074 0.049655 0.034576 0.048167 0.031930 0.046627 0.029271 0.045058 0.026194 0.043449 0.023381 0.041871 0.020259 0.040204  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0016 atm. 0.210000 atm. 0.037 atm. 0.037 atm.  217 page 5 of6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.16 0.48 0.80 1.12 1.44 1.76 2.08 2.40 2.72 3.04 3.36 3.68 4.00 4.32 4.64 4.96 5.28 5.60 5.92 6.24  879.1 883.4 881.2 828.0 867.1 823.6 855.7 847.1 821.5 820.6 840.6 820.0 835.7 831.8 819.4 819.6 828.9 825.8 820.6 815.8 822.6 819.5 811.0 806.2 816.3 804.3 813.3 802.3 810.6 800.4 808.0 805.4 798.0 795.0 802.5 791.4 799.4 786.9 795.6 781.8 791.2  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  792.5 C 0.002 C 792.5 C 106.8 C  218 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.16 0.48 0.80 1.12 1.44 1.76 2.08 2.40 2.72 3.04 3.36 3.68 4.00 4.32 4.64 4.96 5.28 5.60 5.92 6.24  394.263 171.130 111.608 80.285 63.788 55.069 50.507 48.088 46.797 46.122 46.005 47.861 51.859 57.031 63.672 72.284 83.593 98.506 118.322 144.943 180.706  879.1 881.2 867.1 855.7 847.1 840.6 835.7 831.8 828.9 825.8 822.6 819.5 816.3 813.3 810.6 808.0 805.4 802.5 799.4 795.6 791.2  109.9 109.7 96.9 95.9 95.4 95.2 95.1 95.0 95.0 95.2 95.2 90.9 92.1 91.7 91.3 90.8 90.3 89.7 88.9 88.0 87.0  99.4 99.8 105.0 83.7 66.0 56.6 51.6 48.9 47.4 46.5 46.3 49.1 52.6 57.7 64.4 73.0 84.4 99.5 101.1 101.1 101.2  209.2 209.5 201.9 179.6 161.4 151.8 146.7 143.9 142.4 141.7 141.5 „ 140.0 144.7 149.4 155.7 163.9 174.8 189.2 190.0 189.1 188.1  219 page 1 of 6  CFB HEAT RELEASE AND HEAT TRANSFER MODEL RUN RESULTS FROM HEAT TRANSFER ROUTINE HEAT.F, VERSION 8.1 WRTTTEN BY: DALE W.C. JU COMBUSTOR: Studsvik Prototype CASE: Sardinian Coal Case : low load test case, sh6 Wall disturbance factor changed from 310 to 470 Superficial gas velocity = 3.30 m/s Solids reciculation rate = 30 kg/m2s Highvale coal(mean dp = 2.89 mm) FUEL PHYSICAL PROPERTIES AND COMPOSITION PROXIMATE ANALYSIS Weight % 12.200 Ash 15.200 Moisture 0.170 Sulphur 3.050 Hydrogen 52.900 Carbon 0.680 Nitrogen 15.800 Oxygen PARTICLE SIZE DISTRIBUTION mm 7.925 5.613 3.962 2.794 1.981 1.397 0.991 0.701 0.495 0.351 0.246 0.175 0.124 0.088 0.053 0.045 0.038 0.000  wt% 9.250 10.920 13.180 12.110 11.090 8.730 7.750 5.480 4.750 3.740 3.410 3.990 1.290 0.000 0.000 0.000 0.000 0.000  220 page 2 of6  COMBUSTION CONDITIONS # of particles in Monte Carlo Method % of total wall area with membranes Solids return temp, equals cyclone temp. Solids recirculation rate Solids recirculation flux Gas cross-flow coefficient Combustion efficiency Excess air Volatile transfer fraction Number of fuel feed points Fuel feedrate Air feedrate % of total air that is primary Residence time of particles in cyclone Reflection coefficient Height at which developed zone begins  100 70.0 % 604.5 C 12.750 kg/s 30.000 kg/m2s 0.100 m/s 100.0 % 20.000 % 0.300 1 185.551 kg/hr 1439.763 kg/hr 67.8 % 0.300 sec. 0.100 2.020 m  GAS VELOCITIES Core insterstitial gas velocity Streamer interstitial gas velocity Superficial gas velocity  3.489 m/s 1.743 m/s 3.300 m/s  Bed temperature used in calculating heat transfer area and gas velocities  854.9 C  221 page 3 of6  HEAT RELEASE DISTRIBUTION  Height (m) 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92 Cyclone TOTAL  Fraction of Total Heat Release Char Volatiles Streamer Core Streamer Core 0.376003 0.002162 0.082293 0.000125 0.017668 0.000042 0.003817 0.000002 0.000833 0.000001 0.000188 0.000000 0.000045 0.000000 0.000014 0.000000 0.000004 0.000000 0.000002 0.000000 0.000001 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.545026  0.382288 0.019153 0.013069 0.011832 0.007722 0.007813 0.005338 0.005403 0.004024 0.004050 0.003246 0.003218 0.002861 0.003026 0.002561 0.002623 0.002407 0.002475 0.002234 0.002254 0.002118 0.002127 0.001936 0.001974 0.001744 0.001693 0.001697 0.001582 0.001542 0.001299 0.001354 0.001118 0.001241 0.000804 0.001071 0.000626 0.000980 0.000439 0.000843 0.000265 0.000757 0.001993 0.454974  222 page 4 of6  OXYGEN PARTIAL PRESSSURE DISTRIBUTION  Height (m) 0.00 0.26 0.51 0.76 1.00 1.26 1.51 1.76 2.01 2.27 2.52 2.77 3.02 3.29 3.54 3.79 4.04 4.29 4.54 4.79 5.04  Partial Pressure of Oxygen (atm.) Streamer Core 0.077348 0.048006 0.059016 0.045328 0.050294 0.041629 0.046541 0.038226 0.044397 0.035594 0.042924 0.033920 0.041784 0.032109 0.040819 0.031386 0.039957 0.030958 0.039141 0.030936 0.038368 0.030799 0.037649 0.030732 0.036987 0.031092 0.036373 0.031123 0.035810 0.031625 0.035319 0.031970 0.034881 0.032764 0.034519 0.033223 0.034208 0.033683 0.033951 0.034138 0.033739  Pressure convergence tolerance Partial pressure of oxygen entering Partial pressure of oxygen leaving riser Partial pressure of oxygen leaving cyclone  0.0011 atm. 0.210000 atm. 0.034 atm. 0.033 atm.  223 page 5 of6  TEMPERATURE DISTRIBUTION  Height (m)  Temperature (C) Streamer Core  0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  618.3 619.0 615.6 587.4 615.3 587.4 612.4 588.8 610.2 591.1 608.6 593.7 607.4 595.3 606.9 596.8 606.4 598.4 605.8 599.9 605.4 605.1 599.8 599.7 604.8 604.5 599.6 599.7 604.3 599.9 604.1 600.4 604.0 603.9 601.5 603.4 603.9 607.2 604.0 615.9 604.2  Solids return temperature Temperature convergence tolerance Cyclone temperature Wall temperature  604.5 C 0.001 C 604.5 C 106.8 C  224 page 6 of6  HEAT TRANSFER COEFFICIENTS Height Density Core Temp. Heat Transfer Coefficient (W/m2C) (m) (kg/m3) (C) Radiative Convective Overall 0.00 0.13 0.38 0.63 0.88 1.14 1.39 1.64 1.89 2.15 2.40 2.65 2.90 3.16 3.41 3.66 3.91 4.17 4.42 4.67 4.92  490.237 400.288 273.636 197.644 151.900 124.329 107.699 97.668 91.803 86.734 80.762 74.758 68.662 62.458 56.192 49.906 43.656 37.489 31.461 25.619 20.007  618.3 619.0 615.3 612.4 610.2 608.6 607.4 606.9 606.4 605.8 605.4 605.1 604.8 604.5 604.3 604.1 604.0 603.9 603.9 604.0 604.2  57.3 57.1 52.9 52.9 53.1 53.5 53.8 54.2 54.4 55.2 54.7 54.7 54.7 54.7 54.7 54.8 54.8 55.0 55.3 55.8 57.2  100.3 100.5 105.0 104.7 104.1 103.4 102.7 99.7 93.3 87.2 81.6 75.5 69.3 63.1 56.7 50.3 44.0 37.7 31.5 25.5 19.6  157.6 157.7 158.0 157.6 157.2 156.8 156.5 153.8 147.7 142.4 136.4 130.3 124.1 117.8 111.4 105.1 98.8 92.7 86.8 81.3 76.7  225 APPENDIX D LIST O F V A R I A B L E S  D.l  INPUT F I L E F R O M H Y D R O D Y N A M I C  MODEL  Variable  Description  Variable Name in Senior's Model  acell(i) acell(ncell) acell(ny+i) acfin acinit asfin asinit at riser dbavg denp devh emiss flux(i j)  cross-sectional area of core cells (m ) primary zone cross-sectional area (m ) cross-sectional area of annulus cells (m ) cross-sectional area of core at the top of theriser(m ) core cross-sectional area at height = 0 m (m ) cross-sectional area of annulus at the top of theriser(m ) annulus cross-sectional area at height = 0 m (m ) cross-sectional area (m ) average density of the bed (kg/m ) particle density (kg/m ) height of developing zone (m) particle radiation emissivity i = cell number j = 1 height of cell (m) = 2 radial flux out of the cell (kg/m s) = 3 axial flux out of the cell (kg/m s) = 4 cell density (kg/m ) solids recirculation rate (kg/m^s) thermal conductivity of gas number of cells along theriser,not including the primary zone fraction of the total combustion air that is primary air weight percentage of particles at sieve size siv(i) (%) perimeter ofriser(m) volume of primary zone (m ) reflection coefficient particle sieve sizing (mm) superficial gas velocity (m/s) temperature of the bed (°C) temperature of the heat transfer surface (°C) mean core gas velocity (m/s) 2  2  2  2  2  2  2  2  3  3  bed(4) dbav(3) PP(1>1) PP(4,4)  2  2  3  fluxr k ny pair pdist(i) per primev rc siv(i) sug tb twall uc  3  hydg(l) teg nzb  peri bed(l) hydz(5) ug(5) t ug(l)  226  ult(i)  D.2  ultimate analysis of fuel (%) i = 1 ash i = 2 moisture i = 3 sulphur i = 4 hydrogen i = 5 carbon i = 6 nitrogen i = 7 oxygen mean annulus gas velocity (m/s) fractional volatiles yield  PP(1>2) pp(l,10) PP(1,6) PP(M) PP(1,3) PP(1,9) PP(1,5) ug(2) PP(1,7)  U S E R INPUT FILE  Variable  Description  cl, c2 ceff const 1 cross eps eps2 eps3 exair nfeed npart perc rf rf2 rt tair tref tsp vtf  constants used in the devolatilization equation combustion efficiency constant in wall convective heat transfer coefficient calculation gas mass transfer crossflow coefficient tolerance of oxygen partial pressure calculation tolerance of bed temperature calculation tolerance of bed temperature within the energy balance subroutine "htrans fractional excess air number of equally spaced feed points at the bottom of the primary zone number of particles used in the Monte Carlo method fraction of particles that will leave a cell during time step relaxation factor in oxygen partial pressure calculation relaxation factor in temperature calculation residence time of the cyclone (s) combustion air inlet temperature (°C) reference temperature (°C) particle surface temperature (°C) volatile transfer fraction  D.3  PROGRAM VARIABLES  Variable afeed areaw(i j), areae(ij), arean(ij), areas(i,j) areat(i j)  Description air feedrate (kg/s) cell area on west, east, north and south face  total surface area of cell (m^)  227  eg cp denb(2) denb(i+2) deng distv(i) dpcut dt dx(i j), dy(i j) f fluxc(ij)  fuel heat (i) heatv(i) htarea ncell nx o2feed o2need pcyc pmatl(i), pmat2(i), pmatt(i) po2 presc(i) press(i) primeh rarea recirc sbc tcyc temp(i) tempo(i) tin tinit volp  gas heat capacity particle heat capacity primary zone bed density(kg/m ) bed density at a given height (kg/m ) gas density (kg/m ) volatiles heat release distribution cut-off particle diameter in the cyclone (m) time step dimensions of the cell (m) fraction of total wall area that is a heat transfer surface i = cell number j = 1 height of cell (m) = 2 radial flowrate out of the cell (kg/s) = 3 axialflorateout of the cell (kg/s) = 4 cell mass (kg) fuel feedrate (kg/s) heat release in cell heat release due to devolatilization heat transfer area (m ) number of cells number of cells in the radial direction oxygen feedrate (kg/s) oxygen feedrate needed per kg/s of fuel feedrate (kg/s) oxygen partial pressur in cyclone (atm) probability of how a particle will move in a cell 2  2  3  2  partial pressure of oxygen in the airfeed (atm) core cell partial pressure of oxygen (atm) annulus cell partial pressure of oxygen (atm) height of primary zone (m) " total wall area (m ) solids recirculation flowrate(kg/s) Stefan-Boltzmann constant (W/m2k4) cyclone temperature (°C) cell temperature (°C) cell temperature in previous iteration (°C) mixing temperature of fuel feed and combustion air (°C) initial guess of bed temperature (°C) particle volume (m ) 2  3  228  APPENDIX E ENTHALPY BALANCE SPREADSHEETS  229  case: H i earner tamo IX and C) 1140 876  1 22  g-conv tad 1239 cond  1127 853  21  20  heat heat total heat heat heat  9 IW) 918 oond  p-conv I -con v •ad 1424 cond  1114 841  19  1107 834  18  1104 830  17  1102 828  18  1100 827  15  1100 827  14  1100 827  13  1092 819  12  1091 818  11  1092 819  10  1093 820  0  1094 821  8  1096 823  7  1098 825  8  1101 828  6  1103 830  4  1107 833  3  1157 884  2  1159 886  }-COfW  g-conv lad 1731 cond p-oonv g-conv lad 1896 cond p-conv g-conv •ad 2170 oond p-conv g-oonv •ad 2082 oond p-oonv g-conv lad 2266 oond p-oonv g-oonv •ad 2206 cond p-oonv g-oonv lad 2391 cond p-conv g-conv lad 2614 oond p-oonv g-oonv tad 2744 oond p-conv g-conv •ad 3400 cond p-oonv g-conv •ad 4229 cond p-oonv g-oonv •ad 6268 cond p-oonv g-conv •ad 7636 oond p-conv g-oonv •ad 10993 cond p-oonv g-oonv •ad 16086 oond p-oonv g-conv •ad 31001 cond p-oonv g-conv •ad 48116 cond p-conv g-conv •ad 424343 oond p-conv g-conv •ad  generated fn stieamer generated In cote heat genetated ttenafened to cooling wait leaving top of risef entering bottom o l riser  <W> west east -3114 -6 0 246406 -433 0 -3617 -37937 1 -3436 246280 0 76 0 604 -34968 4 -3763 242908 0 0 369 •33441 2777 -4064 6 239286 0 627 0 4049 -32617 8 -4368 234997 0 633 0 4646 -32182 9 -4664 230276 0 0 702 -31928 6363 -4963 9 226408 0 764 0 6763 -31783 10 -6236 22O360 0 0 790 -31764 6047 10 -5511 216332 0 , 0 924 -31744 8309 13 -6782 0 202981 1048 0 7964 -30777 14 -6126 326019 0 1104 0 8398 -30707 14 -6667 0 626316 1133 0 8644 -30796 14 -7661 0 860443 0 1167 -30919 8887 14 -9037 0 1416677 1177 0 9074 -31077 -11482 16 2338468 0 0 1196 9280 -31277 -16639 16 0 3874176 0 1208 -31538 9428 15 -22277 0 6427881 1224 0 9623 -31829 16 -33466 0 10674766 1241 0 9844 -32147 16 -35436 0 17741971 1262 0 10017 -32617 2 -35765 0 29196541 0 173 -38963 1486 -228624 21 0 -76682666 869 0 6774 -250996  674839 1937081  total % d i l l , o l heat gen.  2611720 -1371007 -10041809 8903554 2457  51  shO OOI0  north 0 1017426 •1213 -6 0 1222069 -1494 9 0 1434562 -1776 6 0 1648716 -2066 4 0 1861821 -2329 2 0 2072030 -2698 1 0 2278671 -2860 1 0 2480706 -3116 0 0 2678639 -3368 0 0 2871612 -3671 8 0 3066389 -3837 1 0 3382024 -4229 -1 0 3870825 -4871 -1 0 4714676 -6936 -2 0 6114953 -7702 -3 0 8440036 -10637 -8 0 12304693 •15514 -10 0 16727945 -23618 -16 0 29406283 -37102 -30 -1 47177737 -62990 -826 0 76413186 -96247 -62  south 0 -1222067 1494 •9 0 -1434818 1776 -8 0 -1848749 2055 -4 0 -1861908 2329 -2 0 -2072113 2698 -1 0 -2278708 2860 -1 0 -2480731 3116 0 0 -2678609 3366 0 0 -2871501 3671 -8 0 -3066414 3837 -1 0 -3362060 4229 1 0 -3870826 4871 1 0 -4714643 6936 2 0 -6116182 7702 3 0 -8440266 10637 6 0 -12305316 16612 10 0 -18729276 23616 16 0 -29408147 37100 30 1 -47180374 62992 826 0 -76411429 96262 62 -1 0 0 -2501  temp IK and C) 1131 867  1130 867  1130 867  1130 867  1131 858  1132 869  1133 860  1136 861  1138 863  1137 864  1139 886  1141 8«8  1143 870  1146 873  1148 876  1161 878  1164 881  1168 884  1181 888  1165 891  1163 890  g  <*>  1820 cond  p-oonv j-conv •ad 1809 cond p-oonv g-conv •ad 1826 oond p-oonv g-conv •ad 1947 cond p-conv g-oonv •ad 2033 cond p-conv g-oonv •ad 2170 cond p-conv g-oonv •ad 2233 cond p-conv g-conv •ad 2180 oond p-oonv g-oonv •ad 2266 cond p-oonv g-conv •ad 2516 oond p-oonv g-conv •ad 2877 cond p-oonv g-oonv •ad 2801 oond p-oonv g-oonv •ad 3216 oond p-oonv g-conv •ad 3029 oond p-oonv g-oonv •ad 3738 oond p-oonv g-oonv •ad 4863 oond p-conv g-conv •ad 8166 cond p-conv g-conv •ad 18178 cond p-conv g-oonv •ad 55014 cond p-conv. g-conv •ad 215078 oond p-oonv g-oonv •ad 159B444 cond p-conv g-oonv •ad  west 6 -246406 433 3517 -1 -245280 -76 -604 -4 -242908 -359 -2777 -8 -239288 -627 -4049 -8 -234997 -833 -4848 -9 -230276 -702 -5383 -9 -226408 -764 -6763 -10 -220360 -790 -8047 -10 -215332 -824 -8309 -13 -202981 -1048 -7964 -14 -326019 -1104 -8398 -14 -628316 -1133 -8644 -14 -860443 -1167 -8887 -14 -1416677 -1177 -9074 -16 -2338468 -1196 -9260 -16 -3874178 -1208 •9428 -16 -8427881 -1224 -9823 -16 -10674766 -1241 -9844 -16 -17741971 -1252 -10017 -2 -29196641 -173 -I486 -21 78582666 -669 -6774  (W) east north 0 0 0 -10174472 0 -883660 0 -1 0 0 0 -10416858 0 -882121 0 88 0 0 0 -10860764 -881667 0 0 -6 0 0 0 -10906293 0 -881506 0 -62 0 0 0 -11147264 0 -881777 0 -98 0 0 0 -11386535 0 -882270 0 -118 0 0 0 -11619385 0 -882918 0 -136 0 0 0 -11848632 -883701 0 0 -149 0 0 0 -12073137 0 -884600 0 -160 0 0 0 -12292831 0 -885605 0 -171 0 0 0 -12501389 -887000 0 0 -224 0 0 0 -12832252 0 -888277 0 -241 0 0 0 -13386184 0 -889178 0 -269 0 0 0 -14232838 0 -880344 0 -279 0 0 0 •16868268 -888222 0 -304 0 0 0 0 -18006204 0 -884968 0 -343 0 0 0 -21862908 0 -877865 -386 0 0 0 0 -28338043 0 •864380 0 -417 0 0 0 -39031753 0 -839431 -419 0 0 0 0 •58773442 0 -796178 0 -373 0 0 0 -86807821 0 -727867 108 0  south 0 10416631 882102 -89 0 10660602 881536 6 0 10904993 881482 60 0 11146936 881752 96 0 11386213 882245 118 0 11619078 882896 134 0 11848309 883677 147 0 12072762 884673 169 0 12292363 886671 169 0 12600888 888964 222 0 12831774 888244 239 0 13364660 889143 267 0 14232286 889310 277 0 16656887 888199 302 0 18004696 884943 341 0 21892189 877935 384 0 28337072 864350 416 0 39030695 839408 418 0 58774287 796190 373 0 86824429 727798 -101 -4 8903667 0 -9887  230  •hi l « n > (K and Ci  1  a (WI  <W) aast  waat  oora tamo (K and O  aouth  north  1107 834  9 (WI 2 0 0 6 oond r-conv  22  1123 850  1 2 1 2 eond > cmw  -6046 0  -4 474162  0 1609963  0 -2048216  (con* 1100  1 4 0 1 cond p-CO"V  0 -34676 -5667  -366 -2780  21  -1877 -8 0  2652 -10 0  2048232 -2661 10  -2478666 3112  0  0  1107  2478703 -3112 7  -2888277 3663 -6  834  0  0  2888321 -3663 6  -3305440 4177  1107 834  2 2 6 2 cond p-oonv g-oonv 2 3 8 4 oond >-oonv )-OOnV  ad 836  0-eonv ad 1100  20  827  1096  18  822  1082 819  18  17  1090 817  16  108S 816  1 6 8 1 oond  1039 816  1038 816  13  12  1086 812  11  1084 811  10  1092  1076 802  -3 0  1107 834  0-conv rad 2 3 6 6 oond ^•oonv  0 -30860 -7901 0  34S 2620 6 404767  -4177 3 0 3688384  4681 -2 0 -4078814  1108 836  •ad 2 4 6 7 oond p-oonv  0-oonv  0 -30640  397  -4681 2  6168 -1  •ad 2 4 8 8 oond  tad 2 6 8 3 oond  3 1 2 4 cond p-oonv gconv lad . 3 1 8 7 cond  802  4  1076 903  3  1123 86C  1126 863  0  63 0  -11 0 17477684  -447784 -161  0 0  -17029877 -862319  -1112  0 0  12 0  16 0  0 0  -17477418 -861326  17811666 860666  -3 -433520 -260  861340  -1866 -4  0 0  -IE 0  -419131  0  -17811386  0 18331670  33  -345 -2520 -5 -404767  0 0 0 0  -880663 -33 0 -18331293  858862 46 0 18737320  -397 -2890  0 0  -858848 -46  858486 66  -6  0  0  0 18129036  g-oonv  1  -1  0 0  -869486 -56  0  1106  -6  0  0  0  0  461 3364  -4800069 8087  836  0 -30447  4446798 -6636  rad 2 7 6 0 OOnd p-oonv  -434 -3166  0  -376614 -461  0 0  -19128816 -859142  19506731 856806  -3364  -9373 0 0  6 382938 480  0 4800142 -8067  -30423 -9827  3498  0 0 -29961  601196 630  -11862 0  9 887487  0 -29661  714  4676  6169  1  -  5636  g-eonv •ad  0  0 20221336  -487  0  -868744  858875  -3662 -7  0 0  -76 0  80 0  -368964 -684  0 0  -4238 -8 -601186  20692279 868669 101 0  -630 -4676  0 0 0 0 0  -20221234 -868670 -80 0 -20692366 -868673 -101  21196072 856218 116  -8  0  0  0  -987467 -714 -6169  0 0  -21198316 -868227  22187326 856934  -6623 -1 0  6604  g-oonv  1112 839  rad 2 7 2 6 cond p-oonv gconv •ad 3 1 2 8 oond p-oonv g-oonv rad 3 6 0 8 ootid  0  -116  139  0 -22187646 -866947  23821202 854246  -6804 6 0 6814677 -7366 2  -8 0 -5914496 7366 -2 0 -6396518 8086 -6  •ad  1111 838  0  0  1113  8396688 4086  -7364759  840  p-oonv g-oonv  1114 841  3 6 3 2 oond p-conv  -10 -1627829  g-oonv  -801  0 0 0  -5789  0  6  9311 -6 0 -8978781  •ad  0  0  1118  p-oonv  0  2680647  8876831  -11654662  843  g-conv  0  886  -11366  14766  •ad 7 6 0 4 oond p-COOV  -28146  8388 12  6  0-conv  0 -28886  11366 -8  rad  -6  0  0  1118  4464832  846  11664718  -1610202C  863  -14766  20405  6  -28662  8966 13  0  -3 0  1120  0  847  7384849  18102071  -23487064  0  1033  -20406  28804  -28909  7488  3  2  13 12266909  0  0  23486843  -35768860  850  0  1084  -28807  45418  -28946  7807  -3  11  14  0  1  1126  20380694 1128  36762891 -46420  -56168856  852  8266  -11  860  3 33489481  -i  0  1126  75476  -140  0  173  -11  0  0  0  p-oonv  -2680647  0  -23821878  26520541  g-oonv  -886  0  -864263  848073  -8399  0  4 2 2 0 oond  -174  213  -12  0  0  -4454832  0  -26521066  0 30988106  -863  0  -849060  838541  -8968  0 0  -214  -13  0  256 0  p-conv  -7384848  0  -30988620  38390294  g-oonv  -1033  0  -839662  822401  rad  -7488  0  -258  -13  0  0  0  p-conv  -12265608  0  -38388876  60664348  g-conv  -1084  0  -822382  792211  rad  -7907  0  -288  -14  0  0  0  p-oonv  -20360694  0  g-oonv  -1126  0  -50660223 -782147  71030870 740036  rad  -8269  0  -288  •1  0  104391066 662403  •ad 5 2 2 4 cond p-conv g-oonv  1123  -290E4 34108  -349370  0 -19870682  2 8 0 6 cond p-oonv  6  0  868761 77  0 0  1110 837  11  0  -858896 -70  •«  0 -5466926  6789  -33778  0 19870335  0 6140387  0  g-oonv rad  0 -19606616  0  -18340  C  71  0 0 0  2 7 4 5 oond p-oonv gconv  -28380  -33738  -64  0  836  0  p-oonv  0  -6 -362838 -480 -3498  1110  7364877 -8311  0  65  0  10  -20970  869162  -6140377 6623 1  1627829 801  -13648 0  •ad 3  -883608  0  6 376614  0 -30076 -10943  p-oonv 0-conv  0  -2  3169  3662 7 368964 684 4238 8  3 2 9 8 6 cond  862332  38 281  -18737068  -30468 -10263 0  2 8 8 9 2 cond  863621 -62 0 17030137  0  lad 3 1 8 8 cond p-oonv 0-conv  p-oonv  0 0 -16569810  -390530  497  1 0 9 9 7 oond  -885327  0 0 0  o-oonv  0  6 4 2 6 cond  0  836  0  >ad 4 0 6 1 oond  385 2780 0 -461622  1108  p-oonv g-oonv  p-oonv g-conv  0 16570060  0  6 349370  lad 3 6 8 2 oond  0 -16069264  -4446774  0  p-oonv g-conv  g-oonv  aouth  0 0  0  380630 434  -30613 -8902  2 7 8 6 oond  •ad  north  4 -474162  4078871 -6168  0  lad 1076  2890 6  -8411  p-oonv  g-conv 6  ^conv •ad  -3698311  lad 6  p-oonv  0 3306487  4 5 4 4 oond p-conv  1076 803  ad 2 1 8 6 oond  1966 4  •ad  7  -7  419131  1079  804  3 433620 269  p-conv gconv  0  p-oonv g-oonv  1077  161 1112  ad 2 1 1 2 cond  -31201 -7371  0-conv 8  2 447784  l-oonv 1107 834  >-oonv  rad 2 0 6 1 cond  808  306  -8249  0 0  • ad 9  -38 -281  0 -31783 -6820  ad 1 8 3 8 cond >-conv j-coov  lad 1088 816  14  0 -32770 0  Haw p-conv  g-conv lad 16  0  0 461622  (WI aaat  waat  •ad 8 7 2 7 oond  2 0 6 4 3 oond  51626  300  288 0  66168063  -89727629  866  p-oonv  -33489481  0  0 -71021079  0-conv  C  131  g-eonv  -739832  104E  73  0  -283  -56  -218174 C  13 -8988667  C 89726047  -1 0  1126 866  •ad 1 4 4 1 3 6 1 cond p-conv  -131 -1046  0  -34476  -76476 -86C  114146  •ad 4 8 7 4 7 6 cond p-oonv  -13 89966671  0 0  C  3SE 3086  -11413!  C  -366  0  0 -104374346 -662297  -2 14249526 0  -7:  -1777  66  -5381  7 7 6 7 3 cond  C  p-oonv  g-oonv  -2226K  •ad  heat generated in streamer heet generated in core total heat generated heet transferred to cooling well -16356635  heat leaving top of near  14249626  heat entering bottom of riser % (iff. of heat gen.  Q  1 8 8 6 1 1 oond  288  g-oonv •ad  -3086  c  231  «h2 streamer tamo tK and C) 1 1183 22 810  21  1144 871  20  1127 863  10  1118 646  IB  9 (Wl 611 cond >-oonv ) COTIV lad 649 cond p-oonv j-conv •ad 607 oond p-oonv j-conv •ad 899 oond p-oonv g-oonv tad 920 cond  1116 843  17  1116 843  16  1118 846  16  1116 843  14  1119 846  13  1122 848  12  1126 863  11  1131 868  10  1136 863  8  1143 869  8  1149 876  7  1164 881  6  1160 887  6  1185 892  4  1170 897  3  1227 964  2  1226 954  p-conv g-oonv lad 963 cond p-conv g-oonv lad 1013 cond p-oonv g-oonv •ad 1035 cond p-conv g-oonv lad 1099 cond p-oonv g-conv lad 1239 cond p-oonv g-conv •ad I486 oond p-conv g-conv •ad 1811 oond p-conv g-conv •ad 2281 cond p-conv ' g-oonv •ad 3016 cond p-oonv g-oonv •ad 6708 oond p-conv g-conv lad 7416 cond p-conv g-conv •ad 5983 oond p-oonv g-oonv lad 3440 cond p-conv g-conv •ad 13269 oond p-conv g-conv •ad 38986 cond p-conv g-conv lad 344006 cond p-conv g-conv lad  heat generated In streamer heat generated In core total heat generated heat tianafened to cooling wall heat leaving top of riser heat entering bottom ot riset  (W) east  west -1600 -4 0 66734 0 -318 -42661 •2852 -1676 7 0 84027 0 648 -37278 4642 -1766 12 68242 0 0 987 8182 -34976 16 -1837 70634 0 0 1223 10071 -33990 17 -1921 71782 0 1367 0 -33634 11189 19 • -2006 0 72602 1437 0 11899 -33617 18 -2089 0 72802 1464 0 12218 -33910 20 -2188 0 72302 1699 0 13368 -33638 20 -2273 109181 0 1628 0 -33973 13732 -2446 20 170366 0 1653 0 -34348 14068 20 -2725 271786 0 1846 0 14198 -34888 -3184 20 440464 0 1632 0 14216 -36617 -3944 20 721361 0 1602 0 14126 -38229 19 -6169 1166116 0 1661 0 13944 -37014 -7282 19 0 1968228 1618 0 13739 -37822 18 -10744 3288188 0 1481 0 -38698 13584 •16499 18 0 6429628 1466 0 13608 -39366 18 -26067 9026303 0 1442 0 13530 -40071 17 -38725 0 15017203 0 1425 13648 -40806 -39044 3 0 24726604 0 211 -46443 2162 38 -246371 0 -63136147 1101 0 11210 -316664  438133 2128113  total % dill, ol heat gen.  2664246 -1506717 -5880891 4809782 -13679  I  =H  north 0 661326 -626 -2 0 681799 -689 9 0 694608 -726 4 0 637867 -787 2 0 686623 -852 1 0 738449 -920 0 0 791767 -989 -1 0 846216 -1050 1 0 900048 -1126 -1 0 961887 -1240 -1 0 1145117 -1434 -2 0 1399767 -1754 -2 0 1822882 -2286 -3 0 2528870 -3171 -6 0 3696948 -4642 -8 0 6662097 -7090 -11 0 8904695 -11166 -17 0 14321612 -17948 -26 0 23343402 -29267 -43 -1 39377731 -60936 -836 0 63119962 -78667 -6  south 0 -561739 669 -7 0 -694560 726 -4 0 -837804 787 -2 0 •686672 862 -1 0 -738431 920 0 0 -701766 989 1 0 -846188 1060 -1 0 -900036 1125 1 0 •991876 1240 1 0 -1146083 1434 2 0 -1399772 1764 2 0 -1622878 2286 3 0 -2526887 3171 6 0 -3698991 4842 8 0 -5662727 7090 11 0 -8904789 11166 17 0 -14322070 .17951 26 0 -23340099 29257 43 1 -38378208 60936 836 0 -63120969 78657 6 -1 0 0 -3966  cote temo IX and Cl 1169 896  1168 896  1170 898  1172 899  1176 902  1178 905  1182 909  1188 912  1190 918  1194 921  1198 925  1202 929  1208 933  1211 937  1216 942  1219 946  1223 950  1228 966  1233 969  1237 963  1236 962  g (Wl 1061 oond >-oonv j-conv tad 1131 cond p-oonv g-oonv lad 1102 oond p-conv g-conv tad 1115 oond  p-oonv g-conv •ad 1160 cond p-conv g-oonv led 1198 oond p-conv g-oonv •ad 1161 oond p-oonv g-oonv lad 1211 oond p-oonv g-oonv •ad 1241 oond p-oonv g-oonv •ad 1279 oond p-oonv g-oonv •ad 1369 oond p-oonv g-oonv •ad 1480 oond p-conv g-oonv •ad 1582 oond p-oonv g-oonv •ad 2186 oond p-oonv g-oonv •ad 3901 cond p-conv g-oonv •ad 4436 cond p-oonv g-oonv •ad 9023 cond p-conv g-conv •ad 16606 cond p-conv g-conv •ad 63614 oond p-conv g-conv •ad 218684 cond p-conv g-conv tad 1603696 oond p-oonv g-conv •ad  west 4 -66734 318 2862 -7 •64027 -648 -4642 -12 -68242 -687 -8182 -16 -70634 -1223 -10071 -17 -71782 -1367 -11189 -18 -72602 -1437 -11999 -18 -72602 -1464 -12218 -20 -72302 -1599 -13368 -20 -109181 -1628 -13732 -20 -170366 -1663 -14068 -20 -271785 -1649 -14198 -20 -440464 -1832 -14216 -20 -721361 •1602 -14125 -16 -1189116 -1681 -13944 -19 -1968228 -1516 -13739 -18 -3286188 -1481 -13684 -18 -6429628 -1456 -13508 -18 -9029303 -1442 -13630 -17 -16017203 -1426 -13648 -3 -24726604 -211 -2152 -38 83136147 -1101 -11210  (W| east 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  north 0 -6613208 -918387 0 0 -6565892 -917218 127 0 -6632428 -918380 -182 0 -6706157 -620761 -313 0 -6783748 -023769 -396 0 -5883476 -627166 -446 0 -6944464 -930766 -479 0 -6026852 -934480 -498 -1 -6107807 -638541 -648 -1 •6227031 -942618 -667 -1 -8407846 -946824 -685 -1 -8890419 -960390 -696 -1 -7142032 -953710 -602 -1 -7876194 -966296 -609 -1 -9076706 -967626 -813 -1 •11057221 •966810 -813 -1 -14338240 -962728 -639 -1 -16783471 -942983 -656 -1 -28832464 -623890 -851 0 -43862021 -887783 -663 0 -68422621 -830548 188  south 0 6585963 917229 -127 0 6632503 918363 163 0 6708201 620769 313 0 6783768 923771 398 0 6863489 027168 447 0 5944489 930770 479 0 6026887 634482 496 1 8107812 938642 548 1 8227027 942617 567 1 6407819 946620 685 1 6690392 960382 596 1 7141961 963699 601 1 7874984 966270 607 1 9076367 667688 611 1 11057136 960803 612 1 14338111 662720 636 1 19783466 942962 866 1 28830479 923627 646 0 43847089 887883 648 0 88419367 830603 -193 -6 4809790 0 -21766  232  case: streamer  9 (W) 096 Had p-conv J-oonv ad 1147 oond p-conv |-oonv ad 1367 Dond i-conv l-eonv ad 1640 oond p-oonv l-oonv •ad 1777 oond >conv J-oonv •ad 2041 oond 3-conv g-conv rad 2231 cond p-oonv g-oonv tad 2342 oond p-oonv 0-oonv tad 2610 oond p-oonv g-oonv tad 2676 oond p-oonv 0-oonv tad 2801 cond p-conv Q-oonv tad 3106 oond p-oonv 0-conv tad 3462 oond p-oonv 0-conv tad 4416 oond p-conv 0-oonv •ad 6883 oond p-oonv 0-oonv •ad 8814 oond p-oonv 0-conv rad 13386 oond p-conv 0-conv rad 21264 cond p-conv 0-oonv rad 3213E cond p-oonv Q-oonv rad 68847 cond p-oonv 0-oonv •ad 368886 cond p-oonv 0-conv rad  1 22  1103 630  21  1063 610  20  1073 BOO  IS  1066 786  IB  1066 781  17  1063 790  16  1062 789  16  1062 789  14  1062 789  13  1061 788  12  1066 762  11  1064 781  10  10S4 781  g  1084 780  8  10S4 780  7  1064 781  6  10S6 782  E  10S7 784  4  1068 766  3  1106 833  2  110E 834  heat generated In at ream©* heat generated In cote total heat generated heat ttansTonod to cooling wait heat leaving top of riser heat entering bottom of  IW) west -3336 0 0 -32123 -3781 0 0 -29860 -4180 0 0 -28733 -4693 0 0 •28126 -4998 0 0 -27789 -6396 0 0 -27611 -6784 0 0 -27631 -6163 0 0 -27612 -6634 0 0 -27624 -6897 0 0 -27387 -7278 0 0 -26813 -7807 0 0 -26726 -8676 0 0 -26672 -10108 0 0 -26640 -12481 0 0 -26646 -16417 0 0 -26716 -22661 0 0 -26839 -33006 0 0 -2701C -33076  0  C -27234 -33376 C C -3243" -213436 ( ( -20887;  661821 1610242  riser total % diff. of heat gen.  2162062 *1226111 -9374778 8443089 4262 I ol  north -6 316613 -426 -3061 0 316696 11 79 3 312616 242 1666 6 308380 378 2684 8 303422 484 3164 6 29797S 616 3623 7 292226 666 3772 7 286241 680 3948 7 280189 600 4091 8 276092 864 4468 10 307008 807 5469 11 496626 881 5840 11 816763 912 6194 12 1342478 962 6660 12 2217718 1010 6896 13 3673386 1060 7206 13 6092691 1087 7606 14 10114584 1120 7790 14 16808017 1146 8023 2 27648934 147 1127 16 -7339270C 606 4644  eh3 core temp (K and C)  0 0 961446 -1243726 1316 -688 -8 -6 0 0 -1630960 1243672 1638 -1316 -6 6 0 0 1630921 -1818308 1867 -1638 •3 6 0 0 1816308 -2103488 2271 T1967 -2 3 0 0 2103446 -2384684 2680 -2271 -1 2 0 0 2384697 -2661486 -2680 2882 -1 1 0 0 -2832944 2661454 3179 -2883 0 1 0 0 2832881 -3198636 3466 -3179 0 0 0 0 3198685 -3468726 3743 -3468 -1 0 0 0 3466626 -3714160 3998 -3743 -6 1 0 0 3714166 -4003634 4336 -3698 -1 6 0 0 4003673 •4485876 4880 -4336 -1 1 0 0 4486828 -6286252 6728 -4860 0 1 0 0 5266239 •6615438 7172 -5728 0 0 0 0 6616323 -8822338 9673 -7173 2 0 0 0 8822024 -12488134 13660 -8673 4 -2 0 0 12488383 -18681036 20186 -13662 8 -5 0 0 18578489 -28704706 31206 -20186 19 •6 1 0 -46639741 28702018 52391 -31207 683 -16 -1 0 46637746 -73244317 79670 •S2383 40 •664 C -1 C 73242436 C -7966" -1866 -46  812  1084 811  1084 811  1084 811  108S 812  1088 812  1086 813  1087 614  1088 815  1088 816  1080 817  1092 819  1064 821  1006 822  1088 825  1100 827  1103 830  1106 833  1109 836  1113 836  1113 836  9 (WI 1836 cond p-conv j-oonv ad 1887 oond i-conv l-oonv tad 2034 oond p-conv |-conv •ad 2147 oond >-oonv j-oonv rad 2160 oond p-conv 0-ccnv •ad 2240 oond p-oonv 0-oonv •ad 2347 oond p-conv Q-oonv rad 2363 oond p-oonv g-conv •ad 2448 oond p-oonv 0-oonv •ad 2643 cond p-oonv g-oonv •ad 2645 oond p-conv 0-oonv •ad 2748 cond p-oonv Q-oonv tad 2802 cond p-oonv g-oonv •ad 3204 oond p-conv Q-oonv lad 3780 oond p-conv Q-oonv •ad 4764 oond p-oonv Q-conv •ad 7003 oond p-conv g-oonv •ad 13852 oond p-conv g-oonv •ad 40110 cond p-conv Q-conv •ad 151312 cond p-oonv g-oonv tad 1355746 oond p-conv 0-oonv lad  west 6 -316613 42S 3051 0 -315686 -11 -78 -3 -312616 -242 -1666 -6 -308380 -378 -2584 -8 -303422 -464 -3164 -6 -287875 -518 -3523 -7 -282226 -666 -3772 -7 -286241 -680 -3848 -7 -280189 -600 -4091 -8 -276092 -654 -4458 -10 -307008 -807 •5468 -11 -488626 -881 -5840 -11 -816763 -912 •6184 -12 -1342478 -982 -6660 -12 -2217718 -1010 •6896 -13 -3673388 -1060 -7206 -13 -6092591 -1087 -7606 -14 •10114584 -1120 -7780 -14 -16808017 -1146 -8022 -2 -27646834 -147 -1127 -16 7338270C -606 -4644  (WI aouth north east 0 0 0 0 -8614676 9827332 0 -720668 718176 0 0 -76 0 0 0 0 •9927516 10242101 0 -719188 718433 0 76 -6 0 0 0 0 -10242282 10566128 0 •718448 718047 0 6 32 0 0 0 0 -10666290 10864631 0 -71 BOSS 717893 0 -33 57 0 0 0 0 -10864738 11169808 0 -717800 717906 0 -68 76 0 0 0 0 -11168724 11489366 0 -717812 718039 0 -76 67 0 0 0 0 -11468473 11783456 0 -718048 718269 0 -87 96 0 0 0 0 -11763483 12051606 0 -718271 718577 0 -96 104 0 0 0 0 -12061613 12333679 0 -718677 716662 0 -104 110 0 0 0 0 -12333622 12610794 0 -718949 718434 0 -110 124 0 0 0 0 -12610694 12920664 0 -719428 720088 0 -123 159 0 0 0 0 -12920642 13422699 0 -720082 720602 0 -159 177 0 0 0 0 -13422617 14242603 0 -720497 . 720368 0 -177 199 0 0 0 0 -14242864 16690666 -720371 718250 0 0 •199 226 0 0 0 0 -16680824 17815317 0 -718263 716388 0 -227 260 0 0 0 0 -17816308 21488066 0 -716387 710487 0 -260 298 0 0 0 0 -21497587 27603026 0 -710471 699226 0 -298 326 0 0 0 0 -27601214 37731283 0 -699180 679669 -326 331 0 0 0 0 -37726183 64639470 0 -878607 642497 0 •327 306 0 0 -646262360 820803440 0 •64236G 567567 0 -268 -67 c -3 c 0 c -82067212 8443002 -687600 0 c -7207 63 c  233  case: 1  streamer temD (K and C) 1065 22 782 21  1042 788  20  1034 781  19  1030 767  18  1028 764  17  1026 763  18  1026 752  15  1024 761  14  1024 761  13  1026 762  12  1018 743  11  1016 741  10  1013 740  9  1012 739  8  1010 737  7  1009 738  8  1008 736  5  1008 734  4  1006 736  3  1050 776  2  1052 778  cote (WI temp (K and C) north south west 1037 0 -6 0 -5182 764 660966 1478506 •2011261 0 2163 -1666 0 -409 •8 -28770 -2569 -7 0 1037 -1 0 -6622 783 547673 2011216 •2634494 0 2748 -2163 •116 0 -6 -710 8 -26422 0 1036 1 0 -6641 783 633138 2634426 -3045407 0 -2748 3314 45 0 6 -4 271 -24719 0 0 1036 2 -7337 518024 3045280 -3542316 763 0 143 -3314 3664 0 4 -3 866 -24306 3 0 0 1037 -8013 502670 3642183 -4026006 763 0 -3864 4366 207 0 3 -2 1247 -24066 3 0 0 1037 •8666 467196 4024822 •4402776 764 0 -4397 4912 246 0 1600 2 -1 -23905 3 0 0 1037 •9297 764 471824 4492646 -4945918 0 -4612 6410 278 0 1676 1 -1 -23817 4 0 0 1038 -9908 466686 4946571 -6383523 784 0 -6410 6891 0 301 1807 1 0 -23766 0 0 1038 4 -10467 766 441667 6383286 -5806924 0 -6892 6366 316 0 0 2 -23746 1902 0 1039 4 0 -11066 0 426756 5806674 -6214013 766 304 -6366 6718 0 -23844 1831 -2 -16 6 0 0 1039 -11582 786 342472 6213738 -6540842 0 -6719 7142 521 0 -23006 3101 16 -3 0 0 1040 7 -12186 557183 6540604 -7083084 767 0 683 -7142 7740 0 3466 3 •2 -22838 8 0 0 1041 -13142 0 911392 7082730 -7980964 768 636 -7741 8716 0 3776 2 -3 -22726 0 0 1042 -14722 6 789 0 1499147 7680616 -9468149 10341 697 -8718 0 -4 4146 3 -22688 9 0 0 1044 -17338 770 0 2476027 9467678 -11933743 -10342 13037 767 0 4 -6 4665 -22444 0 1046 10 0 -21668 772 0 4094073 11933184 -16023128 17618 -13038 0 838 4986 5 -4 -22317 0 0 1047 11 -28862 774 0 6782400 16022337 -22807497 -17617 24969 906 0 4 -1 5402 -22232 0 0 1060 -30416 , 12 777 0 11263336 22606304 -34073919 964 -24660 37338 0 6767 1 7 -22213 12 0 1 ' 1062 -30462 779 0 18692236 34072683 -62807089 -37336 81167 1007 0 6062 -7 646 -22278 -1 0 1066 1 -30766 782 0 30736466 62806101 -83602467 -61168 91818 122 0 -26238 792 -648 80 -1 106E 11 -196848 0 0 782 0 -83873650 83804228 -91816 0 386 0 2484 -60 -1214 -189497  0  IW) 1092 cond p-oonv I-conv ad 1408 oond p-conv 0-oonv lad 1832 oond p-oonv |-conv lad oond 2060 a-eonv 0-oonv lad 2623 oond p-oonv 0-oonv lad 2820 oond p-oonv 0-oonv lad 3436 oond p-oonv g-conv •ad 3340 oond p-conv g-conv •ad 3862 oond p-oonv g-oonv lad 3869 cond p-oonv 0-conv lad 4210 cond p-conv 0-conv lad 4360 cond p-conv 0-oonv isd 4988 oond p-oonv g-oonv lad 6837 cond p-oonv 0-oonv lad 6876 cond p-conv 0-conv lad 9162 Oond p-conv 0-conv •ad 13049 cond p-oonv 0-conv ted 20120 oond p-oonv 0-conv lad 36163 cond p-conv 0-conv tad 68434 bond p-oonv g-conv •od 439661 cond p-conv 0-conv •ad  hast generator! In streamer heat generated In core total heat generated heat ttanslened to coding watl heat leavtno top of deer heat entering bottom of itaet  628690 1494217  total % diff. of heat gen.  sh4  2122807 -1138038 -13691396 13017001 10377 I ol  g IW) cond l-oonv l-oonv rad 2440 cond p-conv g-oonv •ad 2669 cond p-conv j-oonv tad 2606 cond p-oonv g-oonv tad 2754 cond p-oonv g-oonv tad 2876 cond p-conv 0-conv tad 2968 cond p-conv 0-conv •ad 3081 oond p-conv 0-oonv •ad 3376 oond p-conv 0-oonv •ad 3236 cond p-oonv 0-oonv rad 3622 cond p-conv g-conv •ad 3574 cond p-oonv 0-oonv tad 3842 cond p-conv 0-oonv tad 4288 cond p-conv 0-oonv tad 6006 cond p-conv 0-conv tad 6062 cond p-conv g-conv tad 8663 oond p-conv 0-conv tad 14704 oond p-conv 0-conv tad 40018 oond p-conv g-conv tad 140369 oond p-conv 0-conv tad 1236114 oond p-cortv 0-oonv tad  (W) east north aouth 6 0 0 0 -680968 0 -14786568 16343007 408 0 -682778 681065 2568 0 -1 -44 1 0 0 0 -647673 0 -15343602 16889371 116 0 -681092 679696 710 0 43 -16 -1 0 0 0 -633136 0 •15890044 18422096 -46 0 -676726 878648 -271 0 16 2 -2 0 0 0 -618024 0 -16422640 16840262 -143 0 -676579 677670 -868 0 -3 15 -3 0 0 0 -602670 0 -16841086 17443336 -207 0 -677803 676723 -1247 0 -16 24 -3 0 0 0 -487186 0 -17444268 17831088 -248 0 •676769 675888 -1500 0 -26 31 -3 0 0 0 •471824 0 -17932076 18403668 -278 0 -676026 676348 -1876 0 -33 37 -4 0 0 0 -466688 0 •18404560 18860761 -301 0 -675384 874790 -1807 0 -38 41 -4 0 0 0 -441567 0 -18861737 18302675 -316 0 -674826 674288 -1902 0 •43 44 -4 0 0 0 -425766 0 -18303871 19726782 -304 0 -674334 673866 -1831 0 -46 44 -8 0 0 0 -342472 0 -19729713 20072370 -621 0 -673868 673760 -3101 0 -48 61 -7 0 0 0 -657183 0 -20073101 20631088 -683 0 -673804 673471 -3488 0 -82 96 -8 0 0 0 -911392 0 -20631689 21644649 -636 0 -673488 672497 -3776 0 -96 108 -9 0 0 0 -1499147 0 -21646126 23048976 -687 0 -672616 670381 -4146 0 -110 128 -9 0 0 0 -2476027 0 -23047229 26626718 -767 0 -670389 666213 -4666 0 -130 166 -10 0 0 0 -4084073 0 -26626188 28627882 -838 0 -666169 658561 -4886 0 -168 183 -11 0 0 0 -6762400 0 -29626252 36420108 •906 0 -868520 644832 -6402 0 -182 206 -12 0 0 0 -11253336 0 -36416910 47686242 -664 0 -644778 620836 -6787 0 -203 221 -12 0 0 0 -18692238 0 -47680171 66380836 -1007 0 -620766 679430 -6062 0 -217 214 -1 0 0 0 -30735465 0 -66371620 97029108 -122 0 -679346 516061 -792 0 -210 -24 -11 0 -2 0 83873860 0 -97027308 13017003 -386 0 -518042 0 -2484 0 28 -3602 west  234  case: streamer tamo (K and C) 1 1141 22 868  21  1107 833  20  1081 818  10  1084 811  IB  1082 808  17  1081 808  16  1082 80S  16  1084 811  14  1078 806  13  1080 807  12  1083 810  11  1067 813  10  1081 818  6  1096 822  8  1100 827  7  1105 832  6  1110 837  6  1114 841  4  1119 848  3  1172 896  2  1172 889  9 (W) 614 oond p-oonv l-conv ad 546 oond y-conv |-oonv lad 604 oond p-oonv g-oonv •ad 801 oond p-oonv g-oonv lad 816 cond p-oonv g-oonv tad 900 oond p-oonv g-oonv lad 914 cond p-oonv g-oonv lad 1014 oond p-oonv g-oonv tad 1118 oond p-oonv g-oonv •ad 1196 oond p-oonv g-conv •ad 1361 oond p-conv g-oonv •ad 1770 cond p-oonv g-conv •ad 2176 cond p-oonv g-conv •ad 2736 oond p-oonv g-oonv •ad 3690 oond p-oonv g-oonv •ad 4274 oond p-oonv g-conv •ad 4323 cond p-conv g-oonv •ad 4616 oond p-oonv g-conv •ad 10936 oond p-oonv g-oonv •ad 27313 oond p-conv. g-conv •sd 300376 oond p-oonv g-conv •ad  heat genetated In streamer heat genetated In core total heat generated heat transferred to cooling wall heat leaving top of riser heat entering bottom of riser  west -1728 0 0 -36831 -1863 0 0 -32630 -2003 0 0 -30737 -2144 0 0 -29947 -2288 0 0 -29840 •2432 0 0 -20682 -2676 0 0 -29662 -2722 0 0 -26968 •2860 0 0 •26236 •3031 0 0 -29461 -3306 0 0 -20797 -3764 0 0 -30209 -4464 0 0 -30680 -6718 0 0 -31203 -7746 0 0 -31764 -11112 0 0 -32332 -18710 0 0 -32905 -28018 0 0 -33470 -36164 0 0 -34025 •36498 0 0 -41033 -233166  -6 97632 -390 -3108 5 105330 374 2837 8 109278 743 6637 12 111546 943 6972 13 112866 1066 7811 14 113678 1126 8348 14 114148 1172 8725 14 113992 1174 8808 17 104273 1390 10382 17 182692 1424 10711 18 269062 1434 10861 16 419436 1432 10677 17 886238 1421 11004 17 1130383 1402 10874 17 1889911 1378 10911 17 3101988 1367 10869 16 6166308 1341 10884 16 8672321 1333 10922 16 14268138 1327 11006 2 23465396 201 1773 36 -80318187 1031 0 9096 -262996  a  371720 1836161  total % did. ol heat gen.  (W) east  2207881 -1326760 -6468746 4677129 -9498  north 0 624191 -613 -3 0 682110 -600 7 0 658783 -694 3 0 744429 -793 2 0 834786 -894 1 0 928016 -996 0 0 1022716 •1100 0 0 1118289 -1206 -1 0 1213816 -1293 2 0 1301880 -1402 -1 0 1448680 -1662 -1 0 1892183 -1826 -2 0 2098247 -2264 -3 0 2767382 -2690 -4 0 3883128 -4187 -6 0 5739482 -8203 -9 0 6628606 -6641 -14 0 13976703 -16099 -21 0 22544248 -24362 -34 -1 36811380 -42097 •690 0 60286926 -64798 -8  *h5  cote temp (K and C) 1124 0 861 -682107 800 -7 1123 0 860 -668756 694 -3 1124 0 -744397 851 793 -2 0 1126 862 -834706 894 -1 1128 0 -927964 866 696 0 0 1130 867 -1022871 1100 0 1133 0 660 •1116226 1206 1 1138 0 883 -1213543 1293 -2 1139 0 866 -1301838 1402 1 1142 0 889 -1448620 1662 1 1148 0 872 -1692094 1826 2 1149 0 -2096177 876 2264 3 1163 0 880 -2767306 2990 4 1166 0 883 -3883052 4167 6 1180 0 -5739346 887 6203 9 1164 0 -8826306 891 9642 14 1168 0 896 -13974796 16100 21 0 1173 896 -22642768 24362 34 1177 1 904 -36811427 42097 690 1181 0 908 -60266900 64794 9 1179 -1 906 0 0 -3031 south  g (Wl 1122 cond p-conv g-oonv •ad 1116 oond p-conv g-oonv rad 1132 oond p-oonv g-oonv rad 1130 cond p-conv g-oonv •sd 1234 cond p-conv g-conv rad 1216 oond p-oonv g-oonv •ad 1237 oond p-oonv g-conv rad 1253 oond p-oonv g-oonv •sd 1327 oond p-conv g-oonv •sd 1266 oond p-oonv g-conv •ad 1426 cond p-conv g-oonv •sd 1628 oond p-conv g-conv rad 1678 oond p-oonv g-oonv rad 2014 oond p-oonv g-oonv rad 2489 cond p-conv g-oonv •ad 3417 cond p-oonv g-conv •ad 6006 cond p-oonv g-oonv •sd 13998 oond p-oonv g-oonv rsd 47846 oond p-oonv g-oonv rsd 187622 oond p-conv g-oonv rsd 1646120 cond p-oonv g-conv rad  (Wl east 6 0 -97632 0 390 0 3106 0 -6 0 -105330 0 -374 0 -2837 0 -9 0 -109278 0 -743 0 -6637 0 -12 0 -111546 0 -943 0 -6972 0 -13 0 -112866 0 -1068 0 -7811 0 -14 0 •113676 0 -1126 0 -8348 0 -14 0 -114148 0 0 -1172 -8726 0 -14 0 -113992 0 -1174 0 -8808 0 -17 0 -104273 0 -1390 0 -10382 0 0 -17 -162692 0 -1424 0 -10711 0 -18 0 -269092 0 -1434 0 -10861 0 -18 0 -419438 0 -1432 0 -10977 0 0 -17 -686238 0 -1421 0 -11004 0 -17 0 -1130363 0 -1402 0 -10974 0 -17 0 -1889911 0 -1378 0 0 -10911 -17 0 -3191968 0 •1367 0 -10869 0 -16 0 -5156308 0 -1341 0 -10884 0 -16 0 -8672321 0 -1333 0 •10922 0 -18 0 -14266138 0 -1327 0 0 -11006 -2 0 -23466386 0 -201 0 -1773 0 -36 0 60318187 0 -1031 0 -9096 0 west  north 0 •5241813 -760614 0 0 -6336060 -749364 131 0 -6442686 -749848 -88 0 -6565385 -761186 -199 0 -6871633 -762087 -269 0 -5789800 -766046 -295 0 -6909262 -767278 -319 0 -8029468 -766831 -338 0 •8149688 -782016 -342 0 -6281184 -784882 -412 0 -6431825 -787766 •432 0 -6898796 -770474 -442 0 -7128684 -772864 -463 0 -7821854 -774890 -484 -1 -8961764 -776663 -476 -1 -10842209 -774812 -463 -1 •13966390 -771389 •516 -1 •19126316 -783442 -542 -1 -27714928 -747824 -535 0 -41970176 -718240 -456 0 -86297791 -671547 143  south 0 5338187 746384 -130 0 6442748 749870 91 0 6655549 761210 200 0 6671811 763011 281 0 6790016 766073 296 0 6909476 767307 321 0 0029678 759858 338 0 8149787 762039 344 0 6281368 764606 414 0 6431756 787780 433 0 8698888 770486 443 0 7128723 772868 463 0 7821844 774889 464 1 6961718 776660 476 1 10842198 774811 463 1 13966413 771391 516 1 19125842 763423 641 1 27712764 747566 532 0 41965070 718153 461 0 66287271 671439 -160 -7 4577136 0 -16376  235  1  streamer temp IK and C) 1183 22 810 21  1144 871  20  1127 863  19  1119 846  18  1116 843  17  1116 843  16  1118 846  16  1116 843  14  1119 846  13  1122 848  12  1128 863  11  1131 866  10  1136 863  8  1143 868  8  1149 878  7  1164 881  8  1160 887  6  1166 882  4  1170 897  3  1227 964  2  1228 964  9 IW) 611 oond >-conv l-oonv tad 849 cond p-conv g-oonv lad 607 oond p-oonv g-oonv tad 688 oond o-conv a-conv •ad 820 cond p-conv g-oonv lad 983 cond p-conv g-conv lad 1013 oond p-oonv g-conv lad 1036 oond p-oonv g-oonv •ad 1088 oond p-oonv g-conv lad 1238 cond p-oonv g-conv lad 1486 cond p-conv g-conv lad 1811 cond p-oonv g-oonv lad 2281 cond p-oonv g-conv lad 3018 oond p-conv g-conv tad 6708 cond p-conv g-conv lad 7418 cond p-conv g-conv lad 6983 cond p-conv g-conv lad 3440 cond p-conv g-conv tad 13269 cond p-conv g-oonv lad 38986 cond p-conv g-conv lad 344006 cond p-conv g-conv lad  heat generated In streamer heat generated in core total heat generated heat transferred to cooling wall heat reaving top of riser heat entering bottom of riser  436133 2128113  total % diff. of heat gen.  IW) west east north 0 -4 -1600 661329 0 66734 -316 -626 0 -2 -42661 -2862 0 7 -1676 681769 64027 0 -889 648 0 4842 8 -37276 0 12 -1766 694808 66242 0 -726 987 0 8162 4 -34976 16 0 -1837 637667 70634 0 1223 -787 0 -33990 10071 2 17 0 -1921 888623 71782 0 1367 -862 0 11189 1 -33634 18 0 -2006 72602 738448 6 1437 -820 0 11869 0 -33617 0 18 -2088 791767 72602 0 1464 -888 0 12218 -1 -33010 20 0 -2168 72302 846215 0 1699 -1060 0 13368 1 -33638 0 20 -2273 109181 900048 0 -1126 1628 0 13732 -1 -33973 0 20 -2446 0 170366 991887 -1240 1663 0 14068 -1 -34348 0 20 -2726 271786 1146117 0 1648 -1434 0 -2 -34888 14188 -3164 20 0 0 440464 1399767 1832 -1764 0 14216 -2 -36617 20 0 -3944 0 721361 1922862 1802 -2286 0 -38229 14126 -3 0 -6199 19 ' 0 1188115 2626870 -3171 1661 0 -37014 13844 -6 0 18 -7282 0 1868228 3898948 -4642 0 1516 13738 -8 -37822 18 0 -10744 0 3288166 5652097 -7090 1481 0 13584 -11 -38698 18 0 -16499 0 6428628 6904685 1456 -11166 0 13608 -17 -39366 0 -26067 18 0 8028303 14321812 1442 -17848 0 13530 -26 -40071 17 0 -38726 0 16017203 23343402 -26267 1426 0 13548 -43 -40806 -1 -38044 3 0 24726604 38377731 -60836 0 211 2162 -836 -49443 36 0 -249371 0 -63136147 63119962 -78657 0 1101 -E -316664 11210  2564246 -1506717 -5880891 4809782 -13679 [ ^  cote temp IK and C) 0 1169 -681736 898 669 -7 0 1168 -684660 896 726 -4 0 1170 -837804 696 787 -2 0 1172 -686572 698 662 -1 0 1176 -738431 802 820 0 0 1176 -781766 905 989 1 0 1182 •845188 909 1050 -1 0 1188 -900036 912 1126 1 0 1180 -991876 916 1240 1 0 1194 •1146083 921 1434 2 0 1198 -1398772 926 1754 2 0 1202 -1822876 929 2266 3 0 1206 -2626887 833 3171 5 0 1211 •3698991 937 4642 8 0 1215 -6862727 942 7090 11 0 1219 -8804789 846 11166 17 0 1223 -14322079 950 17961 26 0 1228 -23340088 966 28267 43 1 1233 -38378208 869 60836 836 0 1237 -63120986 963 78867 6 -1 1236 0 962 0 -3968 south  0 IW) 1061 oond >-conv i-conv tad 1131 cond p-conv j-conv tad 1102 cond p-conv g-conv tad 1116 oond p-oonv g-oonv tad 1160 cond p-conv g-conv tad 1166 oond p-oonv g-oonv tad 1161 oond p-oonv g-conv tad 1211 oond p-oonv g-oonv tad 1241 cond p-oonv g-oonv tad 1279 cond p-conv g-conv tad 1369 cond p-conv g-conv tad 1480 oond p-conv g-oonv •ad 1562 cond p-conv g-conv tad 2166 cond p-conv g-conv tad 3901 oond D-oonv g-conv lad 4436 cond p-conv g-conv tad 9023 cond p-conv g-oonv tad 16606 cond p-conv g-conv tad 63814 cond p-conv g-oonv lad 218664 cond p-oonv g-oonv tad 1803696 cond p-conv g-conv tad  IW) east 4 0 -55734 0 318 0 2862 0 -7 0 -64027 0 -648 0 •4842 0 -12 0 •88242 0 -887 0 -8182 0 -16 0 -70634 0 -1223 0 -10071 0 -17 0 -71782 0 -1367 0 -11188 0 -18 0 -72602 0 -1437 0 -11699 0 -18 0 -72602 0 -1484 0 -12218 0 -20 0 -72302 0 -1599 0 -13368 0 -20 0 -109181 0 -1628 0 -13732 0 -20 0 -170368 0 -1863 0 -14088 0 -20 0 -271786 0 -1849 0 -14198 0 -20 0 •440464 0 -1632 0 -14216 0 -20 0 -721361 0 -1602 0 -14126 0 -18 0 -1189116 0 -1561 0 -13944 0 -19 0 -1988226 0 -1516 0 -13738 0 -18 0 -3266168 0 -1481 0 -13584 0 -IB 0 •5429628 0 -1456 0 •13608 0 -18 0 -8029303 0 -1442 0 -13630 0 -17 0 -15017203 0 -1426 0 -13648 0 -3 0 -24726804 0 •211 0 -2162 0 •38 0 83136147 0 -1101 0 -11210 0 west  north 0 -6613208 -618387 0 0 •6686892 -817218 127 0 -6832426 -918380 -162 0 -6706167 -620761 -313 0 -6783748 -923766 -388 0 -5663475 -827166 -446 0 -6944464 -930786 -479 0 -6026862 -934480 -466 -1 -8107807 -938641 -648 -1 -8227031 -842618 -687 -1 -8407846 •846824 -685 -1 -6690419 -960390 -696 -1 -7142032 -953710 •602 -1 -7675194 -866298 -609 -1 -8076705 -967625 -613 -1 -11067221 -966810 -613 -1 -14338240 -862728 -638 -1 -19783471 -842883 -866 -1 •28832454 -823690 -651 0 -43662021 -887763 -663 0 -68422821 -830546 188  aouth 0 6686863 817228 -127 0 6632503 918393 163 0 5708201 620769 313 0 5783786 923771 396 0 6883488 827168 447 0 5844488 830770 478 0 6026887 834482 486 1 6107612 939642 648 1 6227027 942617 567 1 6407819 846620 586 1 6690362 950382 596 1 7141961 963699 601 1 7874984 866270 607 1 8078367 967688 611 1 11067136 956803 812 1 14338111 962720 639 1 19783456 942982 866 1 28830479 923627 649 0 43647088 867663 648 0 68418367 830503 -193 •8 4809790 0 -21765  236  ah700 g (W)  streamer 1  1082  1161 878  22  west jond >-conv conv  21  sand i conv j-conv  1128 866  1210  1116 842  1 8 2 7 Bond i-oonv  20  10  IB  -628 -4  2068 -4 0 -1864808  1132 866  1779 -6  0 0  1108 836  ad 1 6 0 6 oond >-conv  -33611 •4071 0  1106 832  g-oonv lad 1901 cond p-conv  0 -32770 -4376 0  236430  0 1861606 -2056 4 0 1684769  g-oonv lad 2 0 4 0 oond p-oonv g-conv lad  0 -32318 -4673 0  838 4883 6 230726  -2333 2 0 2076412  0 -32079  706 6409  -2602 1  2151 cond p-conv  -4963  9  0  0  1136  0  226830  0 -31960  -2484896 3122  862  g-conv  2262221 -2B64  1102  16  7 239742  828  lad 2 4 6 3 cond p-conv  1101  IB  828  g-conv 2 5 6 7 oond p-conv g-conv  1101 828  1083 820  2 6 2 2 cond p-conv g-oonv  12  1063 818  3408 cond p-conv g-conv  11  1063 820  •ad 3 6 7 7 cond p-conv g-conv •ad  10  3941 cond p-conv  1084 821  g-conv •ad 6  5 1 3 0 cond p-oonv  1096 823  •ad 8  1098 824  6 2 3 6 cond p-conv  1100  7 7 5 4 cond p-oonv g-conv  827  6  829  1106  noe  88" 1  -2876618 3577 -8  864  0 -3060643  1139  •6764  13  0  0 0  203346 1060  2878443 -3678  •30937 -6137 0 0  8001 14 325667 1106  8 0 3060732 ' -3844  0 -3388348 4237  -30872  8448  -8681 0 0  14 627308 1136  1 0 3368066  1 0 -3877806 4880 1  3844 -1 1141 668  1143 870  -30860  8701  -7576 0  14 662067  0 3877638  0  1145  -4723060  872  0  1180  •4880  6946  -31078 -9066  8834 14  2 0 -6128436  1418261  -1 0 4722778  0  1161  -6946  7716  -31243  9139  -2  3  0 8126690  0  1199  -7717  10666  9326 15  -4 0  6 0  -16671 0  3981478  8465634  -12327344  0  1212  -10666  16636  1153  p-conv  0  10690107  18760386  -28463883  0 -32302  1241 9881  -23664  37169 28  -37166 -2t -1  p-oonv  C  g-conv  C 391 fX  lad  heat genetated in streamer  581164  heat generated In core  1926667  total heat genetated  2610031  heat transfened to cooling wall  -1378776  heat leaving t o p of hser  -10069106 riser  6829996 total  dlff. of heat g e n .  4144 I  61  3083 cond.  p-oonv  1182 889  -76548400 98427  1444  -83S  64  4666(1  181457  883 -  -220777  89;  164411C  0  0  0  0 -11838780 -884469 0 0 -138  11888048  0  BS6223 160 0  0 -11869781  12093927  0  -794 -8092  0 0  -8B6278 -162  -10  0  0  -216729 -828 -8349 -13 -203346 -1060 -8001 -14  888124 169 0 12314140 887140  0 -12094860 -886177 0 0 -162  171  0  0 0 -12316000 8 8 7 2 0 2 0 -176 0  -8446 -14  0 0 0 -12624260 0 -886823 -226 0 0 0  -627308 -1136  0 -12856288 -888941 0  -326597 -1106  -8701 -14  0 13389482 890796 269 14269160  0 0  •282 0  -9139  0  -16  0 12866428 888882 244  -247  -1181  -2343019  888661 226  0 0 0 -13390207 -890843 0  0  0 •14269806 -891020 0  -1418261  0 12523387  0 890989 281 0 16666903 689903  -284  307  0 0 0 -15886688  18038419  0  0  -889942  0 0  -308 0  338  -16  p-oonv  -3881476  g-conv  -1212 -8496 -16  -878396  886702  -9869  0  -386  -16  0  0  0 39088293  g-conv  -1224  0  p-oonv  -10880107  g-oonv  -1241  0 -28376349 -885639 0  -9881 -15  0 0  -17765604  a  p-oonv g-conv  oond  -1252  0  -2  0  -29236811  g-conv  •187 •1444 -23  p-oonv  76728603  g-conv liad  -610:  -71E  -403  0  -36084462 -840664 0  •10046  p-oonv  cond  0 28361401  0  -6438281  •ad cond  0  0 -18038764 21828236 -886818 878422 0 388 •340 0 0 0 -21828606  p-oonv  •ad 116E  C  C  -767 -6806 -10  -8328  •ad 1166  -1  -261 f  -226830  119 0 11839172 884422 136  -1198  17316 cond  832  -8310:  -5409 -9  883758  -883267 -67 0 0 -11406266 0 -883769 0 -121  rad  1 0 0 8 0 oond  888  1  47262B6E  0 0 0  g-conv 6 8 2 8 oond  rad 1159  0  -638 -4883 -9 -230725 -708  888600  rad  -47248778 63103  262388U 16;  ( ZL C - 7 6 7 2 8 6 0 : 76648601) -9843 ! 711> <) -5<I sio: - 2 6 2 3 9 'I  -22909S  cond..  p-conv g-oonv  16  g-conv  2  rad 3 0 8 7 oond  876  0  1262  p-oonv g-conv  877  23666  10046  rad 2714 cond  rad  0  0  p-conv g-oonv  883256 95 0 11404711  5039 cond  -16640 -10  -36812  2 5 8 6 oond  11186860  0 -883019 0 -81 0 0 0 -11186471  1160  1E  -32886  p-oonv g-conv  89 6 0 0 0 -10878148 10623660 -883078 682983 0 58 0 -7 0 0 0 0 -10924011  -6934 -14  1224 9666  0  rad 2 4 4 8 oond  0 0  -631 -4089 -8 -235430  rad 3 6 3 3 oond p-conv g-conv  -33619  -ie  p-oonv g-conv  -2794 -7 -239742  1147 874  0 -31991  29454874  rad 2 6 6 6 cond  -243328 -359  -862087 -1180  g-conv  16  p-conv g-conv  -80  p-oonv g-conv  882  17766604  2 3 8 3 oond  rad  0 -8466264  -31449  0  p-oonv g-oonv  886  -4237 -1  -35488  p-oonv g-conv rad 2 2 9 3 oond  rad  1166  g-conv  *  0  10 0  p-conv  heat entering bottom of  2883026 -3372  -18760860  •ad 43646C  116  826 8348  1137  -6 0  •ad 88E  0  12326669  6202E cond  116E  0  9496 16  g-conv  a  3372 0  6438281  2O6O0 cond p-oonv  836  -3122 0  0  •ad 4  794  -22317  12127 cond  832  0  -31703  •ad C  0  863  p-conv  •ad 1 0 3 2 9 oond  1102  rad 2 2 2 7 oond  rad  1136  1  16 2343019  p-oonv j-conv  -1  0 0  0  •ad  1134 861  -2883138  -11607  g-conv 7  2602 -1 0 -2282266 2884  0  0  g-oonv  1133 660  -2076492  2484827  0 0  •ad  -2 0  10  8062 10 216729  rad 2148 cond  2333  220777  -31906  lad 13  757 5806  g-oonv  -6247  •31912 -5622  •ad 14  531 4089 8  -90 0 10678744 683044  rad cond >-oonv  ad  1 e o nv  1103 830  17  -1778 6  -1  0 0 0 -10433807 • 8 8 3 6 4 2 0  2111  p-conv l-conv  0 -1436869  358 2794  0  1131 868  -9  9 0 1436848  3635  0 -1661688  -6  826 4 243326  0 10433466 883613  -1 -245742  1018170 •1216  -36122 -3760  south  0 10191988 -886071  1131 868  -434 -3636  0 1224146 -1487  north  0 0 0  2 0 0 6 cond l-conv g-conv  0  1 246742 80  (Wl east  6 -245824 434  west  Bond  1823  -38131 -3443  0  g (Wl  1132 866  0 -1224188 1497  0 0  ad  t e m o (K and C)  north  -5 245824  -3120 0  ad  cote  (Wl east  -408  0  0 -68854S91 •796311 0 -37E  0 0 c c c  C -88009734 1 -72937( 5  406  840847 413 0 68868984 788376 379 0 86999148 728280 -62 -4 8829999 0 -9968  237  sh900 streamer temp (K and C) 1162 878  1 22  g rw) 1004 oond p-conv j-conv rad 1177 cond  1128 866  21  p-conv )-conv •ad 1291 cond  1116 843  20  10  p-conv g-oonv lad 1432 cond  1108 838  18  1106 832  17  1103 830  16  1102 828  16  1102 826  14  1102 828  13  1064 820  12  1063 820  11  1094 821  10  1096 822  0  1096 823  8  1088 826  7  1100 827  8  1103 829  6  1106 832  4  1108 836  3  1166 888  2  1161 888  p-conv g-conv  I  I  heat heat total heat heat heat  generated In streamer generated bi core heat genetated transferred to cooling wall leaving top of riser entering bottom of riser  •ad 1644 cond p-conv g-oonv lad 1809 cond p-oonv g-oonv •ad 1888 cond p-oonv g-oonv •ad 2076 oond p-«onv g-conv •ad 2284 cond p-oonv g-conv •ad 2376 oond p-conv g-conv •ad 2790 oond p-conv g-oonv •ad 2798 oond p-oonv g-oonv •ad 3486 oond p-conv g-conv •ad 4 2 3 2 oond p-conv g-oonv •ad 6326 cond p-conv g-oonv •ad 7304 oond p-oonv g-conv •ad 8968 oond p-oonv g-oonv •ad 9698 cond p-oonv g-conv •ad 13967 cond p-conv g-conv •ad 46018 cond p-conv g-conv •ad 433979 cond p-oonv g-conv •ad  (W) east  west -3123 -6 0 248006 0 -433 -38214 •3640 1 -3446 246889 0 78 0 623 -36201 4 -3763 0 243615 361 0 2810 -33674 6 -4074 239877 0 630 0 4091 -32840 -4370 a 236564 0 636 0 4881 -32381 8 -4876 230843 0 706 0 -32142 5413 -4668 8 226917 0 766 0 -32016 6802 -5260 10 220840 0 762 0 -31978 8086 •5526 10 216764 0 823 0 6340 -31970 -6798 13 203366 0 1046 0 -30889 8001 14 -6140 0 326864 0 1104 6438 -30825 -8684 14 527417 0 0 1133 -31011 8690 14 •7670 0 882288 0 1167 8814 -31136 -9069 14 1418668 0 0 1176 9126 -31260 -11611 15 2343731 0 1196 0 8320 -31494 -15678 16 0 3883011 1211 0 9496 -31762 15 -22333 8442735 0 0 1227 -32044 9698 -33660 16 0 10699684 0 1247 -32369 8932 15 -36628 0 17786266 1281 0 10124 -32726 -36853 2 0 29269667 176 0 -38237 1602 -229230 23 0 -76776729 0 705 -262641 6066  564410 1067090  total % diff. of heat gen.  2511499 -1378766 -10066260 8936120 2593  =3  north . 0 1018834 -1218 -6 0 1226042 -1468 9 0 1437938 -1780 6 0 1662595 -2069 4 0 1868130 -2334 2 0 2076811 -2604 1 0 2283780 -2866 1 0 2486677 -3124 0 0 2684860 -3374 0 0 2678388 -3580 8 0 3062628 •3848 1 0 3370076 -4239 -1 0 3878778 -4883 -1 0 4726676 -5949 -2 0 6128183 -7720 -3 0 8469810 -10662 -8 0 12333261 -16548 -10 0 18770868 -23669 -16 0 28472192 -37179 -29 -1 47280628 -63143 -834 0 76598188 -86490 -63  south 0 -1226032 1498 -8 0 -1437927 1780 -6 0 -1852632 2068 -4 0 -1886113 2334 -2 0 -2076803 2604 -1 0 -2283721 2866 -1 0 •2488603 3124 0 0 -2684824 3374 0 0 -2878396 3580 -8 0 -3062481 3846 -1 0 -3370100 4238 1 0 -3878708 4883 1 0 -4726720 6949 2 0 -6128281 7720 3 0 -8469996 10681 6 0 -12333662 15646 10 0 -18771288 23668 16 0 -29471673 37181 26 1 -47278028 83144 836 0 -76696361 96484 62 -1 0 0 -2620  cote temo (K and C) 1133 868  1132 868  1132 859  1132 868  1133 860  1134 861  1136 862  1137 663  1138 865  1136 886  1141 866  1143 870  1146 872  1148 874  1160 877  1153 880  1156 883  1180 688  1163 890  1167 884  1166 893  g IW) 1746 oond p-conv g-conv rad 1746 oond p-conv g-conv •ad 1860 cond p-conv g-oonv •ad 1841 oond p-conv g-oonv •ad 1876 oond p-conv g-oonv •ad 1967 oond p-oonv g-oonv •ad 2024 cond p-conv g-oonv •ad 2112 oond p-oonv g-oonv •ad 2165 cond p-conv g-conv •ad 2144 oond p-conv g-conv •sd 2328 oond p-oonv g-conv •ad 2348 oond p-oonv g-oonv •ad 2497 oond p-oonv g-conv •ad 2806 oond p-oonv g-oonv •ad 3404 cond p-conv g-oonv •ad 4406 cond p-conv g-oonv •ad 7668 cond p-conv g-oonv tad 18635 oond p-oonv g-oonv •ad 53687 cond p-conv g-conv •ad 207218 oond p-oonv g-conv •ad 1634746 cond p-conv g-conv •ad  west 5 -246006 433 3640 -1 -245899 -79 -623 -4 •243616 -361 -2810 -6 -239877 -630 -4091 -8 -236584 -836 •4891 -8 -230843 -706 -6413 -8 -226917 -768 -6802 -10 -220640 •702 -8086 •10 •215764 -823 -6340 -13 -203396 ^-1040 -8001 -14 -326864 -1104 -6438 -14 -627417 -1133 -8690 -14 -862268 -1167 -8914 -14 -1418668 -1178 -9129 -16 -2343731 -1196 -9320 -16 -3683011 -1211 -9495 -16 -6442736 -1227 •9698 -15 -10696884 -1247 -8832 -16 -17786268 -1261 -10124 -2 -29268667 -176 -1502 -23 76776728 -706 -6066  (W) east north 0 0 0 -10188276 0 -886704 0 0 0 0 0 -10441008 0 -884261 0 82 0 0 0 -10688262 0 -883685 0 -4 0 0 0 -10930978 0 -883683 0 -68 0 0 0 -11173220 0 -863831 -63 0 0 0 0 -11411828 0 -884308 0 •117 0 0 0 -11846088 0 -864848 0 -134 0 0 0 -11876692 0 -886718 0 -147 0 0 0 •12100379 0 -888688 0 -168 0 0 0 -12320148 0 •887672 0 -188 0 0 0 -12629014 0 -888860 0 -223 0 0 0 •12860688 0 -880239 0 -241 0 0 0 -13384846 0 -881138 0 -269 0 0 0 -14284426 0 -881318 0 -281 0 0 0 -16691888 0 -890243 0 -309 0 0 0 -18048320 0 -886988 0 -346 0 0 0 -21943227 0 -879983 0 -390 0 0 0 -28403787 0 -886386 0 -422 0 0 0 -38124766 0 -841431 0 -427 0 0 0 -66814882 0 -787169 0 -383 0 0 0 -86064177 -728746 0 0 68  south 0 10441083 884259 •91 0 10886348 883873 4 0 10931095 883682 69 0 11173348 883841 94 0 11411939 884316 117 0 11646174 864964 134 0 11675753 886723 148 0 12100415 886699 168 0 12320174 887676 168 0 12628016 888960 223 0 t2860608 880240 241 0 13364689 891134 269 0 14264307 861311 281 0 16861686 880230 309 0 18046977 886972 346 0 21942829 679969 389 0 28402626 866359 421 0 39123188 841387 425 0 66812066 797119 381 0 86046826 726686 -86 -4 8836124 0 -9982  238  uhO «tr earner temp IK and C) 1 1066 22 782  9 W) 1698 oond p-oonv l-oonv •ad 1467 oond p-oonv g-oonv rad 1406 oond p-oonv g-conv rad 1293 oond p-conv g-conv rad 1224 oond p-conv g-oonv •ad 1144 cond p-conv g-oonv •ad 1072 cond p-conv g-conv •ad 986 cond p-conv g-conv •ad 883 cond p-conv g-oonv •ad 880 cond p-oonv g-conv •ad 870 cond p-oonv g-conv •ad 876 oond p-oonv g-conv lad 1000 cond p-oonv g-conv •ad 1021 cond p-conv g-conv •ad 1101 cond p-conv g-conv •ad 1206 oond p-conv g-conv •ad 1484 cond p-conv g-oonv •ad 2006 cond p-conv g-oonv rad 2667 cond p-conv g-conv rad 6186 cond p-conv g-conv •ad 14260 cond p-conv g-conv lad  1060 767  21  20  1084 791  19  1068 796  18  1071 798  17  1074 800  18  1076 802  16  14  13  12  11  10  9  8  7  6  6  4  3  2  1077 804  1078 806  1074 801  1083 820  1094 821  1093 820  1083 819  1083 820  1084 821  1096 821  1097 824  1101 828  1167 883  1167 884  heat generated in streamer heat generated tn core total heat generated heat transferred to cooHng wall heat leaving top of rlaet heat entering bottom of  west -4860 0 0 -4006 -4693 0 0 -4084 -4720 0 0 -4164 -4872 0 0 -4212 -3982 0 0 -4261 -3468 0 0 -4299 -3066 0 0 -4331 -2748 0 0 -4363 -2609 0 0 •4394 -2326 0 0 -4306 -2266 0 0 -4633 -2266 0 0 -4837 -2306 0 0 -4620 -2377 0 0 -4617 -2610 0 0 -4828 -2756 0 0 -4838 -3217 0 0 -4863 -4094 0 0 -4889 -6169 0 0 -4787 •6286 0 0 -6816 -10043 0 0 -11101  43926 101196  riser total % diff. of heat gen.  |  145122 -1 BI 208 -468374 604417 -43 o[  (Wi east 3 -530624 64 420 3 -398807 60 384 3 -287123 66 366 3 -223387 62 361 3 -168884 61 346 3 -128487 62 366 3 -88112 67 393 3 -75264 62 432 4 -67782 69 484 7 -41346 129 886 2 5681 37 283 2 8989 44 322 3 15989 64 465 4 26446 86 817 6 51306 107 783 7 94553 137 1010 9 178887 176 1308 12 334726 220 1668 14 639413 268 2066 -1 1164486 -16 -128 0 -3085162 -73 -621  north 0 2616625 -3368 8 0 2082588 -2746 -3 0 1663160 -2216 -2 0 1383360 -1620 •2 0 1157200 -1621 -1 0 986371 -1284 -1 0 853976 -1121 -1 0 762937 -986 0 0 674718 -886 0 0 613996 -786 1 0 670219 -765 -4 0 672616 -760 0 0 676178 -756 0 0 591082 -774 0 0 816628 -808 0 0 666401 -872 0 0 767846 -993 0 0 933396 -1225 -1 0 1287661 -1669 -2 0 1908634 -2671 -37 0 3063693 -4013 •0  south 0 -2O02684 2746 3 0 -1663134 2218 2 0 -1383343 1820 2 0 -1157161 1521 1 0 -986370 1284 1 0 -863972 1121 1 0 -762931  core temp (K and C) 1064 761  1069 789  1072 799  636  1076 803  480  1079 806  439  1061 808  406  1084 811  379  see  0 0 -674714 885 0 0 -614002 788 -1 0 -670214 766 4 0 -672633 760 0 0 -678188 768 0 0 -691076 774 0 0 -616819 808 0 0 -665390 872 0 0 -767822 883 0 0 -833362 1226 1 0 -1267884 1869 2 0 -1908466 2671 37 0 -3063706 4013 0 0 0 0 -146  0 (W) 703 cond >-conv g-conv lad 600 cond  1086 813  1069 816  1093 820  1099 826  1100 827  1102 829  1106 832  1109 836  1114 841  1120 847  1128 868  1140 867  1164 661  1161 878  p-oonv ) con v •ad cond p-conv g-conv •ad cond p-oonv g-conv •ad oond p-oonv g-oonv •ad cond p-conv g-conv tad cond  p-conv g-conv lad 369 cond p-oonv g-conv •ad 364 cond. p-conv g-oonv •ad 344 cond p-oonv g-oonv tad 447 oond p-oonv g-conv tad 404 oond p-oonv g-conv •ad 386 oond p-oonv g-conv rad 409 oond p-oonv g-conv •ad 633 cond p-conv g-conv •ad 872 cond p-conv g-conv tad 820 cond p-conv g-conv tad 1242 cond p-conv g-conv tad 3196 cond p-conv g-conv tad 11860 cond p-conv g-conv tad 76529 cond p-conv g-conv rad  west -3 530624 -64 -420 -3 398807 -60 -384 -3 287123 -66 -366 -3 223387 -62 -361 -3 168884 -61 -346 -3 128487 -62 -369 -3" 98112 -67 -393 -3 76264 •82 -432 -4 67762 -69 -484 -7 41346 -129 -698 •2 -6881 -37 -283 -2 -8969 -44 -322 -3 -16989 -64 -466 -4 •28446 -86 •617 -6 -61306 -107 -783 -7 -84553 -137 -1010 -8 -176887 -176 -1308 -12 -334726 -220 -1668 -14 -639413 -288 -2066 1 -1154486 16 128 0 3066182 73 621  (W) east 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  north  south  0 -3041406 -36206 0 0 -2608037 -40784 -21 0 •2110781 -42108 -18 0 -1812613 -43112 -18 0 -1588264 -43896 -16 0 -1418608 -44618 -14 0 -1288615 -45024 -14 0 -1191146 -46469 -16 0 -1115646 -45644 -16 0 -1067730 -46199 -18 0 -1016630 -46664 -36 0 -1022100 -48780 -8 0 -1030872 -46874 -11 0 -1048882 -47004 -17 0 -1076671 -47160 -23 0 -1127068 -47316 -28 0 -1221888 -47439 -39 0 -1399423 -47466 -62 0 -1736106 -47176 -89 0 -2374818 -46179 -86 0 -3620186 -43316  1  17  0 2609066 40784 21 0 2110777 42106 18 0 1812523 43113 18 0 1588260 43886 16 0 1418810 44616 14 0 1288818 46024 14 0 1181140 45458 16 0 1115833 46844 16 6 1067710 46188 18 0 1016681 46662 35 0 1022077 48779 8 0 1030667 46674 11 0 1048974 47003 17 0 1076681 47160 23 0 1127076 47317 28 0 1221666 47442 36 0 1388430 47466 62 0 1736070 47176 86 0 2374849 46176 66 0 3620187 43318 -17 -1 504418 0 -759  239  case: stteamer t e m p (K a n d C )  1 22  west  314  889 616  oond p-conv g-conv •ad  21  880  619  607  p-conv g-oonv  877  741  603  876  600  673  -12626  -4976173  804  g-oonv  0  81  -2497  3052  -12360  289  1  -1  -11323  1  0  0  877  0  922010  4976209  -6887635  804  667  0  97  •3062  3814  358  1  0  1  0  0  877  p-oonv  0  924743  5887571  -6803027  604  g-oonv  0  106  -3614  4178  666  0  0  878  920407  6803049  -7714296  606  g-conv  0  112  •4178  4738 0  876  7714366  -8615024  606  g-conv  0  118  •4738  5281  •12306  426  0  0  -16691  2  0  0  878  p-conv  0  684237  8816088  -9600736  606  g-oonv  0  122  •6261  6836  -12311  460  0  0  -18367  2  0  0  879  -10376766  805  6410  0  686448  9500749  g-oonv  0  127  -6836  -12316  0  876  10378833  •11249662  606  g-oonv  0  61  -8410  6840  -12608  227  -8  •14  -20893  2  0  0  876  0  682071  11248702  -11634226  606  0  187  -8840  7313  -12173  721  14  -3  -22251  3  0  0  880  p-conv  0  1134890  11934334  -13062861  607  g-conv  0  240  -7313  7888 0  881  13062888  -14936013  607  g-conv  0  314  -7688  9131  -11662  1148  7  -9  -22848  6  0  0  882  p-conv  0  3114618  14938126  -18047854  608  g-conv  0  400  -9131  11038  •ad  -11814  8 3 8 7 oond  0  0  883  6172703  16047733  -23220807  610  g-conv  0  481  -11038  14224  -11882  1788  8  -7  -22862  7  0  0  888  p-oonv  0  8607830  23220868  -31634841  612  g-oonv  0  674  -14224  19660  •ad  -11602  0  1  888  14364094  31834581  -48204633  616  g-conv  0  841  -18650  29799  -11602  2361  0  300  -23341  1  -1  0  892  p-conv  0  23446076  46204478  •69676336  618  g-conv  0  77  -29800  42887  -13264  oond p-conv g-conv •ad  h e a t g e n e t a t e d In s t r e a m e r  339686  h e a t g e n e t a t e d In c o t e  841346  299  -300  22  8  0  0  882  0  -69836467  69674774  0  618  0  279  -42887  0  -66426  1066  -22  -602  heat translened to cooHng wad heat IMvirvg  , f >  P of  heat entering b o t t o m of  riser  •6744010  riser  % diff. o f  6372863 total heat gen.  I  822 0|  271  •6  0  13  0  0  0  0  p-oonv  -669669  0  -8767313  9668830  g-oonv  -11  0  -268966  297896  -42  0  0  0  0  0  •694292  0  -9666890  10661033  g-oonv  -56  0  -287691  296830  -205  0  0  -1  0  0  0  p-oonv  -611838  0  -10680911  11472713  g-oonv  -81  0  -298827  295774  -299  0  •4  -1  0  0  0  -922010  0  •11472596  12394492 294733  -87  0  -296771  -368  0  -7  4  7  10  -1  0  0  0  p-oonv  -924743  0  -12394388  13318824  g-conv  -108  0  -284730  293710  •ad  -391  0  -10  12  -1  0  0  0  p-oonv  -920407  0  -13318708  14239628  g-conv  -112  0  -293708  282712  -413  0  2 0 8 4 oond  -12  14  -1  0  0  0  p-conv  -909406  0  -14238608  16147353  g-conv  -116  0  -262710  281748  rad  -428  0  -14  -2  0  0  0  p-oonv  -884237  0  -16147283  16040707  g-conv  -122  0  -201746  290820  rad  -450  0  -16  18  -2  0  0  0  p-conv  -886448  0  -16040624  16926061  g-oonv  -127  0  -290818  286916  •469  0  2 2 6 2 oond  2 6 0 7 oond  2 6 4 6 oond p-oonv  -18  16  20  -1  0  0  0  -678519  0  -18625974  17804072 288993  -61  0  -289916  -227  0  -20  -2  0  0  0  p-oonv  -682071  0  •17803984  18484770  g-conv  -167  0  -288991  288318  •ad  -721  0  -8  -3  0  0  0  p-conv  -1134890  0  -18494676  18628766  g-oonv  -240  0  -288316  287282  -880  0  2863 cond  3 0 4 8 oond  3 4 3 8 oond  -34  8  34  44  -4  0  0  0  p-oonv  -1876566  0  -18628676  21607124  g-oonv  •314  0  -287261  286427  -1148  0  4 0 8 4 cond  -44  62  -6  0  0  0  p-conv  -3114618  0  -21607093  24622633  g-oonv  -400  0  -286427  282182  -1460  0  6747 cond  -62  85  -6  0  0  0  p-oonv  -6172703  0  -24622724  26797694  g-conv  -491  0  -282183  278628  1 0 8 3 3 oond  -1788  0  -86  113  -7  0  0  0  p-oonv  •8607830  0  -29798002  38407470  g-oonv  -674  0  -278630  286702  -2096  0  30046 cond  -113  144  -8  0  0  0  p-oonv  -14364064  0  -38406403  62762447  g-conv  -641  0  -266708  246685  -2361  0  112848 cond  -144  168  -1  0  0  0  p-conv  -23446076  0  -62763866  76113936  g-conv  -77  0  -248682  223488  -288  0  -8  0  0  -1  68836467  0  -76114367  6372664  -276  0  -223490  0  -1068  0  6  -1641  •ad 647736  6  -1  p-oonv  •ad  -149382  total heat generated  298969  tad  8  6  •ad 249601  617  -300049  2 0 0 8 oond  0  -23036  •sd  890  7  0  •ad  p-conv  26224 cond  816  2086  73  tad  6  0  14160 cond  g-conv  1826 cond  -8  -22888  •ad  587  9  8797442  •ad  p-conv  8 2 9 6 oond  687  1480  0  -7866367  •ad  0  1678666  -13  0  0  p-conv  -7  4  0  0  0  •ad  •ad  3  0  1 -838366  g-oonv  cond  880  1006  p-oonv  •ad  0  878618  •12100  300064  1802 oond  8  1  0  -22810  668  2  0  -18744  p-conv  3 8 0 8 cond p-conv  681  888  469  -301178  rad  0  909405  p-conv  0  1488 cond  0  1  0  •ad  3  0  -16697  p-conv  4 7 8 4 cond  861  413  266  1268 oond  0  1  0 -12303  g-oonv  •ad  -14181  •ad  4  0  7969498  g-conv  p-oonv  g-oonv 3581  391  -7158286  •ad  -12763  -12306  0  0  •ad  -12318  p-oonv  881  2497  4073262  •ad  6  -1962  811638  3 1 0 4 oond  862  66  0  •ad  6  0  877  2828 cond  884  604  0  603  7  877  -4073191  .  0  -802263  •ad  0  3189368  south  0  p-conv  1168 oond  -1  0  894292  -1  •ad  664  2  1  0  1  2 6 6 7 oond  867  42  -8603  north  3  tad  1962  (W) east  west oond  667 cond  -2  0  600  8  1422  1  600  889  -910  -1422  •ad  8  -73  11  2 6 1 7 cond  871  0  0  lad  10  604  g-oonv  2336 cond  878  877  -2330606  3  886  •ad  0  1604426  -271  9 (W)  -3  0  638366  206  600  11  -2  -1  0  877  2004 cond  873  •1006  -6812  604  •ad  12  010  -8803  600  873  -411  -12412  600  13  -266  0  1 8 7 2 oond  873  0  -3166266  •ad  14  604  0  p-oonv  873  -1504386  2330844  g-oonv  16  716840  0  1 6 3 7 oond  873  802283  1323 oond p-oonv  600  16  0  669669  •ad 17  877  0  p-oonv g-conv  674  0  -7138  lad 18  t e m p (K a n d C )  south 0  p-conv  862 cond  601  north -3  -12760  oond  tad 10  core  east  -4641  -13279  cond  lad 20  sh6  IW)  9 (W)  oond p-conv g-conv •ad  -170  -6  

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