!MODELING AND EVALUATION OF GRANULAR LIMESTONE DRY SCRUBBING PROCESSESi
A Thesis Presented to
The Faculty of the College of Engineering and Technology
Ohio University
In Partial Fulfillment
,.! ' of the Requirements for the Degree 1 w :, '?. :I 1 Master of Science
by
Sandip Chattopadhyay. -- August, 1992 This thesis has been approved for the Department of Chemical Engineering and the College of Engineering and Technology
f l I Assistant Profesddr of CHemical Engineering
&7 Dean of the Colleqe of Engineering and ~echnolo~~ ACKNOWLEDGEMENT
I realize my inadequacy in expressing myself when I make an attempt to show the depth of my gratitude to my teachers, well-wishers and my family who helped me in some way or the other in course of this work. This is just a token of my gratitude. I would like to take this opportunity to express my gratitude to my advisor Dr. K. J. Sampson for his valuable advice and guidance during the course of this study. Without his constant advise, this work would not have been completed. I express my deep gratitude to Dr. M. E. Prudich for offering valuable suggestions and for getting me totally involved in this area of study. I would like to acknowledge the partial financial support given by Ohio Coal Development Office (OCDO) for this work. I dedicate this thesis to my grandfather, who is a very special person in my life. I would like to express my sincere gratitude to my parents for their love, inspiration and understanding. I owe a special debt of gratitude to my wife, Mita, for her patience and constant encouragement. TABLE OF CONTENTS LISTOFFIGURES ...... ii LISTOFTABLES ...... iv 1.0 INTRODUCTION ...... 1 2.0 LITERATURE REVIEW ...... 10 2.1 Process simulation ...... 11 2.2 Equipment design parameters and economics .....14 3.0 MODEL DEVELOPMENT ...... 18 3.1Reactormodel ...... 18 3.1.1 Fixed bed configuration .....20 3.1.2 Cross flow moving bed configuration ...... 25 3.1.3 Mathematical solution technique ....27 3.2 Process design and cost model ...... 31 3.2.1Processdesign ...... 33 3.2.2 Cost model ...... 37 3.2.2.1 Cost variable identification ...... 37 3.2.2.2 Consumption of utilities ...41 3.2.2.3 Cost correlations ...... 43 3.2.2.4 Annual system cost ...... 46 4.0 RESULTS AND DISCUSSIONS ...... 48 4.1 Reactor bed performance ...... 49 4.1.1 Drying of the limestone bed ...... 49 4.1.2 Sulfur dioxide concentration ...55 4.1.3 Controlling rate of SO, removal ...... 55 4.1.4 Average SO2 removal ...... 60 4.2 Economic evaluation ...... 63 4.2.1 Effect of approach to saturation ...65 4.2.2 Effect of bed depth in the direction of gas flow ...... 68 4.2.3 Effect of sorbent particle size ...... 76 4.2.4 Effect of superficial gas velocity . 81 4.2.5 Effect of moving bed sorbent velocity ....86 4.2.6 Effect of coal sulfur content ...89 4.2.7 Effect of percentage removal of SO, .....90 5.0 CONCLUSIONS AND RECOMMENDATIONS ...... 91 NOMENCLATURE ...... 94 REFERENCES ...... 103 APPENDICES APPENDIX-A: COMPUTER PROGRAM LISTINGS ...... 107 APPENDIX-B: TRANSPORT AND PHYSICAL PROPERTY CORRELATION ...... 177 APPENDIX-C: MATERIAL AND ENERGY BALANCES ..... 197 LIST OF FIGURES
Figure 1-1 : Categorization of sulfur dioxide removal processes solely based on the initial SO2 removal step...... 3 Figure 1-2 : Fixed bed configuration...... 7 Figure 1-3 : Crossflow moving bed configuration. .... 8 Figure 3-1 : Schematic representation of the desulfurization plant ...... 35 Figure 4-1 : Gas phase water concentration as a function of vertical position for a fixed bed reactor. The third parameter is elapsed time. . 51 Figure 4-2 : Gas phase water concentration as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed...... 52 Figure 4-3 : Bed temperature as a function of vertical position for a fixed bed reactor. The third parameter is elapsed time...... 53 Figure 4-4 : Bed temperature as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed...... 54 Figure 4-5 : Gas phase SO? concentration as a function of vertical posltion for a fixed bed reactor. The third parameter is elapsed time. . 56 Figure 4-6 : Gas phase SO2 concentration as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed...... 57 Figure 4-7 : Controlling resistances at different times and positions for a fixed bed reactor. . 58 Figure 4-8 : Controlling resistances at different positions in a moving bed reactor...... 59 Figure 4-9 : Sulfur dioxide removal as a function of time in a fixed bed reactor...... 61 Figure 4-10: Sulfur dioxide removal as a function of vertical distance in a moving bed reactor. . 62 Figure 4-11: Number of reactor units and bed exhaustion time as function of approach to saturation for a fixed bed reactor configuration. . 66 Figure 4-12: Annual cost as a function of approach to saturation for a fixed bed reactor configuration...... 67 Figure 4-13: Bed height and number of reactor units as a function of approach to saturation for a moving bed reactor configuration. . 69 Figure 4-14: Annual cost as a function of approach to saturation for a moving bed reactor configuration...... 70 Figure Number of reactors, total cost of reactors and bed exhaustion time as a function of bed height for a fixed bed reactor configuration...... Figure Annual cost as a function of bed height for fixed bed reactor configuration...... Figure Number of reactors, total cost of reactor units and bed height as a function of bed length for a moving bed reactor configuration...... Figure Annual cost as function of bed length for a moving bed reactor configuration...... Figure Pressure drop, bed exhaustion time and number of reactor units as a function of sorbent particle size for a fixed bed reactor configuration...... Figure Annual cost as function of sorbent particle size for a fixed bed reactor configuration. Figure Pressure drop, number of reactor units and bed height as a function of sorbent particle size for a moving bed reactor configuration. Figure Annual cost as a function of sorbent particle size for a moving bed reactor configuration...... Figure Number of reactor units, pressure drop and bed exhaustion time as a function of superficial gas velocity for a fixed bed configuration...... Figure Annual cost as a function of superficial gas velocity for a fixed bed reactor configuration...... Figure Number of reactor units, pressure drop and bed height as a function of superficial gas velocity for a moving bed reactor configuration...... Figure Annual cost as a function of superficial gas velocity for moving bed reactor configuration...... Figure Reactor bed height and number of reactor units as a function of sorbent bed velocity for a moving bed reactor configuration. .. Figure Annual cost as a function of sorbent bed velocity for moving bed reactor configuration...... LIST OF TABLES
Table 3-1 : Characteristics of low sulfur coal used in the simulation...... 32 Table 3-2 : Characteristics of high sulfur coal used in the simulation...... 33 Table 3-3 : Identification number and description of different equipment...... 36 Table 4-1 : Baseline simulation conditions for fixed bed and moving bed configurations...... 48 Table 4-2 : Operating and cost parameters for base conditions...... 64 Table 4-3 : Effect of coal sulfur content on cost. ... 89 Table 4-4 : Effect of change in average SO2 removal percentage...... 90 Table 5-1 : Optimum operating parameters (3.5 wt% sulfur content coal and 90% SO2 removal) ...... 91 1
1.0 INTRODUCTION Air pollution is not a new problem, but the need for both immediate and long term solutions has recently accelerated. The need for "clean airt1has become more public in these recent years prompted by the Clean Air Act Amendments of 1990, which became law in November 1990. Controlling sulfur dioxide emissions from fossil fuel fired boilers is no longer a matter of choice for industrial plants. The bill requires that sulfur dioxide emissions be cut 10 million tons below the 1980 levels by the year 2000 A.D. (McIlvaine, 1991). The quantity of sulfur content in fuels varies widely -- ranging from less than 0.5% to more than 5%. High sulfur content coal reserves, mostly located in mid-eastern or mid- western states, are the main source of fuel for present day utility power plants. Because the limits on emissions continue to be decreased while the necessity to burn high sulfur content coal has increased, low-cost sulfur dioxide control technologies have become a necessity. Flue gas desulfurization (FGD) technology has been divided into two main groups, the non-regenerable processes (throwaway system) and the regenerable processes (recovery system). This breakdown is dependent on the disposition of the spent sorbent. Besides the above method of categorization, FGD processes can be sub-divided into different groups based on their initial SO2 removal step. This is shown in Figure 1-1. However, the present study 2 considers a system categorization based on sorbent disposition. The regenerable system, though often expensive and complex, reclaims a reusable or marketable byproduct such as sulfuric acid or elemental sulfur. In the non-regenerable system, which is more popular, the final product is thrown away. In this system a sodium or calcium-based additive such as soda-ash, lime or limestone is used. However, because relatively fewer regenerable systems are commercially operated, the main focus of this study will be on the non- regenerable processes (throwaway systems). The non- regenerable system can be classified into three major groups,
( i)wet/wet system, (ii)dry/dry system, and (iii)wet/dry system. In the wet/wet system the sorbent is in the form of slurry and/or solution and makes contact with the flue gas in a packed, tray or spray tower absorber. Sulfur dioxide is absorbed in the slurry and the desulfurized flue gas is released from the absorber via a mist eliminator. The waste stream is continuously withdrawn for disposal. It has been found that the removal efficiency of this process is greater than 90% even when high sulfur content coals are used (Prudich et al., 1988). However the main disadvantage of this process is its high cost which can be attributed to additional steps and equipment. It should also be noted that dry scrubbing processes tend to use more expensive sorbents than those used S~UI~ Calcium sulfate Alkaline Alkaline Ply Ash Earths slurry Sludge
Absorption Sulfu~dioxide in sodium hy&oxide/ Liquids carbonate/sulfite sodim sulfite Alkali or sulfate sodium citrate/ Metals phosghate/acetate Calcium sulfite or Sulfur
Commds sulfite Ammonium sulfate
Calcium salts SUlfuI dioxide Praceeses Sorption H2S or Sulfur 1 Solids I
caxbon Sulfur dioxide/ Sulfuric acid Adsorption
Non reactive / sulfur dioxide
Oxidation ~xygen Gas phase SSulfuric acid conversion Carbon I Sulfur Reduction
4/ Reducing ga# Sulfur
General Categories SO2 removal agent Final product
Figure 1-1. Categorization of sulfur dioxide removal processes solely based on the initial SO2 removal step (Torstrick et al., 1977) . 4 in wet scrubbers (usually ground or slurried limestone). The second group, the dry/dry system, involves direct injection of dry sorbent into the flue gas. No water is present in the liquid phase of the system, but the flue gas stream must be near saturation. Studies of the performance of dry-injection systems indicate that dry sorbent injection does not achieve high-sulfur removal from high-sulfur flue gases. The third group, the wet/dry system, involves the use of a humidified scrubber in the presence of a liquid water phase within the scrubber. Even though a liquid water phase exists within the scrubber, all products leaving the scrubber are dry. A bulk water phase dominates the behavior of the wet/dry system, in contrast to the umonolayeru water phase that is dominant in the dry/dry system. The dry scrubbing techniques generally can be divided into three categories: (1) in-furnace and over-furnace injection, (2) convective zone injection and (3) post-furnace (after the air heater) humidified in-duct injection. Post- furnace, where the temperature of the flue gas is below 350°F, is the prime focus of the present research. The wet/dry scrubbing technique requires the liquid phase water to be in direct contact with the sorbent particle in order to mediate SO, capture and produce reasonable capture rate. Humidified in-duct injection and in-duct spray drying are examples of wet/dry sorption system.
A novel wet/dry desulfurization post furnace process 5 (Limestone Emission Control process) was developed by Prudich et al. (1988) . The Limestone Emission Control (LEC) system is a wet/dry scrubbing process which uses a fixed or moving bed of limestone granules. A slip-stream of 400 ACFM flue gas from the 70,000 lb/hr stoker boiler, providing steam to Ohio University, was withdrawn and fed into the fixed bed LEC pilot plant unit. The flue gas first entered a spray chamber where it was conditioned to the desired temperature and humidity. The conditioned gas then entered the LEC reactor, passing downward through a fixed bed of limestone. The limestone bed depth (the bed dimension in the direction of the flue gas flow) was varied from 0 to 24 inches. The effects of varying limestone bed depth (6" to 1811),superficial flue gas velocity (1 to 2 ft/sec), flue gas humidity, flue gas SO2 concentration (500 to 3500 ppm) , and flue gas temperature were studied. Out of the 100 experimental runs conducted, 90% SO2 removal was obtained in all the cases and many of them showed removal of about 99%. In 1991, the fixed bed was replaced by a continuous moving bed with a capacity of capacity 5000 ACFM. The limestone bed has dimensions of 1411 X 36" X 128". The depth of the bed in the direction of flue gas flow is 14 inches. The superficial velocity of the flue gas through the reactor can be varied from 0.5 to 1.6 ft/sec. The results obtained from 30 experimental runs demonstrated SO2 removal of more than 90% and often up to 99%. 6 This thesis represents the development of second generation models of the fixed bed and cross flow moving bed dry scrubbing process on which cost comparisons are done. One way to gain an understanding of the basic chemical and physical processes involved in a fixed bed and cross flow moving bed is by developing and analyzing a mathematical model. The philosophy of the study is to generate designs based on mathematical models employing the best available data, and then to optimize the design relative to predicted capital and operating costs. For the purpose of this mathematical modeling, process alternatives were restricted to those involving the contact of flue gas with a wet, densely packed bed of limestone gravel. The two process alternatives considered were a fixed sorbent bed with continuous flow of flue gas in the downward direction and a cross flow bed with sorbent moving downward and flue gas moving horizontally. These two process configurations are represented schematically in Figures 1-2 and 1-3. The shaded portion of the cross flow bed indicates the wet portion. As the sorbent moves down the bed, the flue gas flowing across it dries out a progressively larger fraction of the bed. The horizontal shaded arrows indicate the relative SOz removal efficiency. The best SO2 removal performance occurs at the top of the bed. FLUE GASES
DESULFURIZED FLUE GASES FIXED BED SYSTEM.
TOP
BED DEPTH
TTOM
I TIME - QUALITATIVE BEHAVIOR OF mXED BED.
Figure 1-2. Fixed bed configuration. SO REMOVAL 2
DESULFURI'L FLUE GASES FLUE GASE:
DRY LIMESTONE
CROSSFLOW MOVING BED SYSTEM
Figure 1-3. Crossflow moving bed configuration. 9 Mathematical models were used to predict the performance of each design of the two configurations. The modeling elements include detailed material and energy balances, convective flow, mass transfer, heat transfer and chemical reaction occurring in the sorbent bed. A connection between the mathematical models for the two configurations and the process system cost was developed using a preliminary plant design. The mechanical details of the reactor beds, the material handling system of the sorbent, the fresh and recycled of sorbent flow, the pressure drop across the bed, equipment sizes and costs, and operating costs of a complete desulfurization plant were considered. The scope of the design and cost estimate included the humidification of entering flue gas into the reactor, desulfurization reactors, sorbent conveying and storage equipment, and an I.D. fan to compensate the pressure drop across the bed. Finally the outputs of the simulation were determined. The results of the two configurations were compared to evaluate the two processes for tentative optimized conditions. 10
2.0 LITERATURE REVIEW The problem of sulfur dioxide removal from stack gases has probably been the subject of more research than any other gas purification operation. This research had very little commercial impact until the 1970's when there was an explosive growth in the number of flue gas desulfurization (FGD) units installed in the United States and Japan. Unfortunately, this rapid growth is attributable more to regulatory pressures than to research breakthroughs. The FGD systems, in general, continue to be costly adjuncts to industrial operations which would otherwise release excessive amounts of sulfur dioxide into the atmosphere. Their success is measured in terms of minimizing cost and operating problems rather than making a profit from recovered sulfur values. The first known instance of sulfur dioxide removal by water scrubbing of the flue gas was at the Battersea Station of the London Power Company in 1929 (Hewson, Pearce, Pollitt, Rees, 1933). However, high cost and operating difficulties led to the abandonment of the system. Although a number of processes have been proposed for removal of sulfur dioxide, relatively few have attained commercial status. Evaluation of the technical merits, economics and commercial readiness of available FGD processes is usually done with computer modeling which falls into two categories: process simulation, and equipment design parameters and economics. 2.1 Process simulation Process simulation has been studied by several investigators. Early process simulations were performed on venturi scrubbers. An early effort in modeling the chemistry of the process was limited to gas/liquid/solid equilibria (Lowell, Ottmers, Schwitzgebel, Strange, Deberry, 1970). This model contained the data base information to determine activity coefficients and equilibrium constants for FGD species. Bechtel fitted scrubber data to this model in order to monitor gypsum saturation at the scrubber outlet (Epstein, Leivo, Rowland, 1972). A model based on fluid dynamics which involved the use of empirical correlations for a venturi scrubber was developed by Wen and Uchida (1972). The correlations were integrated gas and liquid velocities, SO2 concentration, water evaporation, and temperature across the length of the scrubber. This research treated absorption of SO2 into alkali solutions as a physical mechanism only. Dissolution of solid sorbent in the scrubber was neglected. In 1979, it was reported that SO2 removal efficiencies of greater than 90% for extended periods of time were possible, and that the limestone granules were easily regenerated with mild agitation (Shale and Stewart). Klingspor, Karlsson, Bjerle (1983) reported the first fundamental work on dry/dry capture of SO2 by limestone particles. Using a single limestone sample, they varied limestone particle size, 12 temperature, SO, concentration, and relative humidity to gain a better understanding of dry/dry sorption process. The study reveals that the rate of SO, removal was strongly dependent on the relative humidity. Jorgensen, Chang and Brna (1987) extended the study indicating that when using a lime as a sorbent, 60% to 90% of the lime was unreacted after SO, capture reaction had terminated. Another attempt of SO2 capture was made to model the wet/dry sorption system by assuming that both the rate of SO, removal and H20 evaporation are controlled by gas film mass transfer (Jozewicz and Rochelle, 1984). The reaction of ionized SO2 with ionized lime in the water film was considered to be instantaneous. Jozewicz also assumed an infinite rate of Ca(OH), dissolution. This research did not account for accumulation of sulfite/sulfate in the water film. The study was further extended by Harriot and Kinzey (1986), who considered both gas and liquid phase mass-transfer resistances in their modeling of wet/dry sorption system. This study assumed that there was no resistance to the dissolution of Ca(OH),. Moreover they did not account for the accumulation of sulfite/sulfate in the water film. In a mathematical model, Damle (1986) considered gas phase transport, liquid phase diffusion and solid phase dissolution. He reported the liquid phase diffusion resistance to be negligible. However, in 1987, Maibodi, Pearson, Counce and Davis considered all three resistances in 13 their simulation study of spray dryer absorber, but determined the predominate resistance to be the solid phase dissolution. A tentative modeling of a wet/dry sorption system done by
Karlsson and Klingspor (1987) predicted the performance of a
0.5 MW pilot plant. An anomalous change in the observed reaction rate constant was found to occur with changes in
slurry concentration. With an excess of lime, the SO, absorption was limited by gas phase diffusion while with a shortage of lime, the rate limiting step was the dissolution rate of the lime.
A model was developed by Gage and Rochelle (1989) to predict limestone reactivity based on the particle size distribution and solution effects. The study assessed scrubber performance as a function of limestone type and grind.
A fixed-bed limestone emission control (LEC) system was modeled by Appell in 1989. This model considered both the evaporation and condensation of water. The controlling mechanism was assumed to be the diffusional resistance of SO, in the gas phase. This model was further developed by
Visneski (1991) using a resistance-in-series kinetic model. In his study, the mechanism and effect of controlling resistance on the SOz removal was reported and also compared with experimental results from the LEC fixed bed, where the bed height was 12".
Reddy (1991) has done a mathematical simulation study on 14 the moving bed LEC process in which three-phase resistances were considered and studies were performed which considered the flow of liquid water relative to the sorbent bed. The model does not consider the effect of precipitate on the limestone surface.
2.2 Equipment design parameters and economics Several attempts have been made to compare the economics of the various processes. The results are strongly affected by the assumed bases, including the scope of items included in capital costs, unit costs assumed for calculating operating costs, and the time frame of the estimate. A study was made by the U.S. Environmental Protection Agency (EPA) to estimate the capital costs and annualized operating costs for five FGD systems (Ponder, Yerino, Katari,
Shah, Devitt, 1976). This study identified most of the items that affect the capital and annualized operating costs of FGD systems. The report also specified a "nomograph procedureww and a Itrapid equation proceduren to calculate different equipment sizing costs. The cost of lime/limestone systems and the major design parameters were calculated by the TVA/Bechtel Lime/Limestone Scrubbing Computer Model (Henzel, Laeske, Smith, Swenson, 1982) . Output from the model included equipment sizes and costs based on the PEDCO model (PEDCo Environmental, Inc.). This program maintains design and performance information on 15 operating FGD systems. Another study (Keeth, Ireland, and Radcliffe, 1991) was conducted during the period 1982-86 to evaluate the cost of 28 flue gas desulfurization processes for the purpose of providing a basis for screening these alternative processes. The design criteria considered for a 300 MW plant using coal are a sulfur content of 2.6%, a heating value of 13,100 Btu/lb, a 90% SO2 removal for wet process and a 50 to 80% removal for dry processes. The cost evaluations have been updated to 1990 costs and from the evaluation, it can be
concluded that of these 28 processes the costs, in terms of $/ton of SO2 removed, are very close. While the dry injection technologies have much lower capital costs, the total levelized cost might be higher due to the larger quantities and higher cost of the reagent required. In order to improve the accuracy of engineering cost estimates used in evaluating the economic effects of SOz and NO, controls on existing coal fired utility plants in Ohio, Kentucky, and the Tennessee Valley Authority (TVA) system, a study was made by Emmel, Piccot and Laseke (1989) under the National Acid Assessment Program (NAPAP). Most of the processes evaluated in their study were not developed commercially at the time of study. No comparison was made regarding the best option among 11 control technologies studied for specific boilers at each plant. A model to discriminate between the use of control 16 technologies and coal switching was developed and operated by IT-Air Quality Services (Laseke, Levy, 1991) . A market analysis was conducted with the aid of an integrated micro- computer based software system consisting of a unit level database, a cost and performance engineering model and a market forecast model. The model can accept in its system any combination of the technology modules, which are pre, in-situ, and post-combustion emission control. Interactions are reflected in a material balance tabulation at the exit of each module. Alterations in the material balance are used to account for integrated performance and cost effects. The output from the model reports reduction in SO,, NO, and particulate matter emissions; associated capital and annual costs and associated cost effectiveness values. An economic evaluation of a spray-dryer absorber (SDA)
for flue gas desulfurization of a 400 MW plant, operating on
2%, 2.5% and 3% sulfur content fuels was developed by Joy/Niro (Felsvang, Brown, Horn, 1991). The capital cost calculation for the SDA is based on proprietary estimating programs. The process design and equipment selection data are program output. The capital costs for SDA system are influenced by the gas flow rate and the gas temperature leaving the air heater, particulate and sulfur dioxide loadings, and sulfur dioxide removal. Higher sulfur dioxide loading and/or removal increases the size of lime slaking and ash handling equipment and decreases the size of recycle equipment. Operating cost 17 is influenced by lime consumption; as the SOz loading/removal increases, lime consumption increases exponentially. Along with increased lime consumption, a higher SO2 load increases the disposal rate. Power consumption is influenced mostly by the gas flow and the temperature.
An economic comparison of the LEC process and the conventional lime scrubbing process on an equatable basis was made by Prudich, Appell and Reddy in 1991 for a 500 MW coal- fired power plant. The equipment list for the LEC process was obtained by conceptually scaling up the existing LEC moving bed pilot plant at Ohio University. The cost for the wet limestone scrubber process was obtained from an EPRI technical report. The comparison shows that the LEC process has a distinct advantage in both the capital and operating cost.
The lower capital cost of the LEC process is due to its simpler mechanical design. The material handling associated with the LEC requires less electricity than the slurry handling system required by the wet limestone scrubber. The lower operating cost of the LEC process is a direct result of its lower water consumption due to the absence of slurries.
The benefits of the LEC process over the conventional lime scrubbing process were established but there has been no evaluation of the different LEC process configurations.
Therefore the objective of this work has been to model two LEC process configurations and evaluate their performance with respect to SO2 removal efficiency and cost of the plant. 18
3.0 MODEL DEVELOPMENT The process model for each configuration was developed in two steps. The first step was to study the performance of the sorbent bed using a first principles type mathematical model which reflects the underlying transport and chemical reactions involved in the desulfurization process. The overall performance of the bed was then incorporated into a process design and cost model for economic evaluation. This model calculates the capacity, dimension and cost of individual pieces of equipment and an annual cost for the plant.
3.1 Reactor Model Governing partial differential equations describing the performance of the desulfurization reactors were derived from component material balances for sulfur dioxide, water, and noncondensable components in the gas phase; overall material balances for the gas phase and the liquid phase; component material balances for carbonates and sulfates in the solid phase; and energy balances for the gas phase and combined liquid/solid phase. These equations were simplified into a workable form using four assumptions. During the beginning stages of model development it was assumed that the controlling resistance for the interphase transport of SO2 lies entirely in the gas phase boundary layer. There is considerable doubt concerning the accuracy of this assumption under the process conditions of interest. So, 19 in order to predict realistic overall reaction rates, the mass transfer coefficient, k,, was increased to an artificially high value during the preliminary set of runs. Thereafter, an improvement was made by considering a more realistic resistance-in-series kinetic model to calculate the SO, reaction rate. The modified assumption was that the reaction of SO2 with limestone is controlled by a combination of three resistances: transport of SO, across the gas film, diffusion of SO, through the liquid layer, and dissolution of solid calcium ions. Resistance due to diffusion across the precipitate layer was not considered in this study. The next assumption in simplifying the equations, was that the molar densities of CaC03 and CaS03 (or CaSO,) are considered to be the same, thus eliminating the solid phase material balance. In mathematical terms - PC = Pp - Ps (3-1) where the subscripts refer to unreacted carbonate, reacted precipitate, and total solid phase, respectively. Even though the actual mass densities of CaC03 and CaSO, (or CaSO,) are approximately the same, the increase in molecular weight associated with converting the sulfite (or sulfate) species implies that the overall molar densities must be different. However, the constant molar density assumption was used because it represents a convenient starting point for the mathematical development and because it enables approximate predictions of operating trends. 20 Although liquid density is a function of temperature, it is not a very strong function. In this third assumption, the modeling equations were simplified considerably by assuming that the liquid density is constant. The final simplifying assumption was that liquid and solid phase temperatures are equal.
T, = T, (3-2) This assumption may lead to some minor inaccuracies at the feed point in the bed or for the initial time period in unsteady-state problems.
3.1.1 Fixed bed configuration Using these simplifications, the governing equations for the fixed bed configuration are indicated below. The material and enthalpy balances are detailed in Appendix-C. The general label for the independent variable z, as specified in Appendix-C, is replaced by the specific direction variable y and the superficial solid velocity is set to zero. The gas phase volume fraction can be obtained from Equation (C-102).
where e, is the fraction of bed occupied by the gas, g, is the rate of transport of water from the gas phase to the solid phase, p, is the density of the liquid phase and t is the elapsed time. The concentration of water in the gas phase is given by substituting Equation (3-3) in Equation (C-111) .
where Cwg is the concentration of water in the gas phase and Ug is the superficial velocity of the gas phase. When the liquid volume fraction exceeds the amount that can be held as a static layer on the bed, then the liquid phase material balance can be written as
which follows from Equation (C-62). In Equation (3-5), el is the fraction of bed occupied by liquid, U1 is the superficial velocity of the liquid phase and 9 is an empirical function relating el and the trickling water velocity. The derivative of p with respect to vl-vs is specified as p/. Specchia and Baldi (1977) reported a correlation for the dynamic liquid hold in a packed bed as
where N,,, and NGa are Reynolds number and Galileo number for the liquid phase, respectively and g is the acceleration due to gravity. The value of cp/ in Equation (3-5) can be calculated by differentiating Equation (3-6) .
where
In Equation (3-lo), Fp is the packing factor of the bed, Dp is the sorbent particle diameter and p, is the viscosity of the liquid phase. When the liquid phase adheres to the solid phase, the liquid phase volume fraction can be calculated from Equation (C-21) .
The temperature of the liquid phase can be obtained from the liquid/solid phase material balance in Appendix-C. Equation (C-103) can be re-written as
where Cw, and Cw, are heat capacities of the sorbent and liquid water respectively. The rate of heat transfer from the gas phase to the liquid phase is indicated as gg and 23 enthalpies of water in the liquid and vapor phase are
specified as HUl and Hug, respectively. The temperature of the gas phase can be obtained from Equation (C-108).
where C is the heat capacity of the water vapor. The concentration of noncondensables can be calculated as
Gg = pg - CWg (3-14)
The superficial velocity in the gas phase can be obtained from the gas phase overall mass balance as detailed in Appendix-C.
Substituting Equation (3-3) in Equation (C-log), the superficial gas velocity can be written as
The concentration of SO, in the gas phase is given by Equation (C-110).
The primary dependent variables are the gas phase volume fraction, E,: the liquid phase superficial velocity, UL; the liquid temperature, T,; the gas phase temperature, T,; the gas phase superficial velocity, Ug: the gas phase sulfur dioxide concentration, Csg; and the gas phase water concentration, Cug. The independent variables are time, t, and vertical position,
Y In order to initialize the iterative solution procedure, boundary and initial conditions were developed for the governing equations. For this configuration the boundary conditions corresponded to the gas feed conditions.
Tg = Tg~ (3-17)
For the gas volume fraction and the liquid temperature, the initial conditions were obtained from specified bed conditions.
Eg = 1 - EL0 - E,
TI = TLO The other required initial conditions were derived from a modified form of the governing equations by setting the time derivatives equal to zero and solving the resulting set of ordinary differential equations. Using Equations (3-ll), (3-13), (3-14) and (3-4) gives Since the short term transients which occurred immediately after the start of the process are of little practical interest, an initial condition which minimized the short term transients was chosen; thereby, making possible the use of a larger numerical time step.
3.1.2 Cross flow moving bed configuration A different set of equations, which has been developed in Appendix-C, is needed for the cross flow configuration. In the following equations the dependent variable E, is replaced by the superficial liquid velocity, Ul, and the independent variable t is replaced by the horizontal position, x. The superficial liquid velocity can be obtained from Equation (C-
62).
From the liquid/solid phase material balance in Appendix-C, Equation (C-103) can be written as
The temperature of the gas phase can be obtained from Equation (C-108).
where
%g = Pg - %g (3-30)
The superficial velocity in the gas phase can be derived from Equation (C-109)
The concentration of SOz and water in the gas phase are given by Equations (C-110) and (C-111) as
and
The boundary conditions are indicated in the following equations. At y=O:
Ul = u10
Tl = T10 The governing equations for both configurations were derived from the same set of general balances by applying the appropriate geometric considerations. There is no horizontal position dependence for the fixed bed configuration and no time dependence for the cross flow configuration. Although in some cases the governing equations are ordinary differential equations, the collective set is equivalent to a set of partial differential equations which require a simultaneous solution. In the numerical procedure, all seven dependent variables are calculated at each point (y,t) for the fixed bed configuration and all six dependent variables are calculated at each point (x,y) for the moving bed conf iguration before proceeding to the next iteration.
3.1.3 Mathematical solution technique An analogue to Eulerfs method for solution of first order, nonlinear, ordinary differential equations was developed for the partial differential equations present in this research. The first step in developing the method was to recognize that all of the model equations can be represented 28 by the general form a a Azq + B-cp = E (3-40) ay where cp represents any of the dependent variables and A, B, and E may be functions of any of the system variables or constants. In some cases either A or B is equal to zero. The modified Eulerls method used here proposes the iteration formula
(P (YI~)= 'Po + (A'P~+A(P~>/~ (3-41) In this equation cpo represents the dependent variable evaluated at the base point in the interval, Acp, is an increment based upon the derivative evaluated at the base point, and Acp2 is an increment based upon the derivative evaluated at the new point. The implicit nature of this formula is derived from the dependence of Acp2 on the new point cp(y,t). The specific choice of independent variables y and t is used in this discussion only as a matter of convenience. The formula was used for solving the model equations for both of the process configurations. The value of cp(y,t) at the end of the numerical interval is calculated based upon the starting points cp(y-Ay,t) and cp(y,t-At). This is done using the predictor equation:
(P(YI~)= 'Po + A(P, (3-42) The value of cpo is taken to be a weighted average of the two base points. (Po = A(yrt-At) AY) o(y, t-At) + B(y-Ayy.t)At(P(y-Ay,t) (3-43) A(Y,t-At)AY + B(y-Ay,t)At
Similarly, Aq, is a weighted average of the right hand side of the governing differential equation multiplied by an appropriate step size.
At Ay ~[n(y,t-At) Ay + c(y-Ay,t) At]
Lapidus and Pinder (1982) found the predictor formula to be stable for the corresponding homogeneous partial differential equation. The remaining increment needed for the corrector equation, Aq,, is evaluated at the new point.
At Ay = E(yf t, A(Y, t-At)Ay + ~(y-Ay,t) At]
The modified Eulerfs iteration formula represents a nonlinear algebra problem due to the fact that the right hand side of the formula is a function of the solution point dependent variable values. Since this type of nonlinear algebra problem is normally expected to be well behaved, a successive substitution method is generally used to solve it. This method initializes the solution of the algebra problem with a first guess for the dependent variables at the new point generated using, the normal Eulerfs formula (predictor equation). In this case that formula is (P(~ft)= (Po + 41 (3-46)
The values for the set of variables cp (y,t) is substituted back into the right hand side of the modified Euler's formula to calculate values of E(y, t) and the modified Euler's formula (corrector equation) is used repeatedly until the dependent variable estimates converge. The successive substitution method described above can be improved using a Wegstein search to direct subsequent guesses for the dependent variables. The successive substitution method uses the iteration formula
whereas the Wegstein formula seeks a new estimate for cp by finding the intersection between the line
and the line formed by connecting the points (qi, f (qi)) and
(cpil,(qil)) (Perry, 1987). This procedure is applied to each of the variables for both the process configurations, assuming that there is no interaction between the variables. The intersection point is found from the formula
- -1 S (Pi - -fs-1 ((Pi-l) + -(Pi-1s-1 where 31
The Wegstein formula is used repeatedly until the average of the scaled differences between cp and f (cp) decreases to some small value.
3.2 Process design and cost model Desiqn basis An economic comparison between the two process configurations was developed for four different design cases. The cases are differentiated by two levels of sulfur content,
1.5 and 3.5 wt% sulfur coals, and two levels of removal efficiency, 90 and 98% sulfur dioxide removal. In each case a 500 MW power plant was considered. Two representative coals were identified. Their characteristics are summarized in
Tables 3-1 and 3-2. Flue gas generated by burning these two representative coals was considered in this study. The flue gas characteristics were calculated based upon an assumed 20% excess air rate, feed air at 80°F and 60% relative humidity, and complete combustion of the coal. For both the configurations, it was assumed that the sorbent was introduced in the reactor at 77 OF. A thirty year life and 70% operating capacity of the plant was assumed for economic evaluation. An overview of the parametric sensitivity of both configurations with 3.5 wt% sulfur coal and 90 wt% sulfur dioxide removal was done. The parameters which were varied around baseline Table 3-1. Characteristics of low sulfur coal used in the simulation. Source: Pennsylvania, Butler County, Upper Freeport Reference: Coal conversion system technical data book, HPC/T2286-01/4, Section IA.50.1., March 1982 Power plant output: 500 MW Power plant heat rate: 9,000 Btu/KWh Coal heating value: 9,000 Btu/hr Coal consumption rate: 500,000 lb/hr Ultimate analysis: (wt%, dry basis) Carbon 69.20 Hydrogen 4.46 Sulfur 1.50 Nitrogen 1.30 Oxygen 7.74 Ash 15.80 Total 100.00 Moisture Content: 2.6 wt% Flue Gas Rate: 1,216,000 scfm (wet basis) Flue Gas Composition: (mole%, wet basis) (3'2 (3'2 14.2 02 3.3 N2 74.6 7.8 SO 0.115 ~ogal 100.0 conditions were flue gas temperature and relative humidity (specified in terms of approach to saturation) , superficial gas velocity, sorbent particle size and sorbent bed depth. In addition to the above parameters, the effect of changing sorbent bed velocity was studied for the moving bed configuration. Table 3-2. Characteristics of high sulfur coal used in the simulation
Source: Ohio, Harrison County, Pittsburgh No. 8 Reference: Coal conversion systems technical data book, HCP/T2286-01/4, Section IA.50.1., March 1982 Power plant output: 500 MW Power plant heat rate: 9,000 Btu/KWh Coal heating value: 12,000 Btu/lb Coal consumption rate: 375,000 lb/hr Ultimate analysis: (wt%, dry basis) Carbon 71.30 Hydrogen 5.03 Sulfur 3.50 Nitrogen 1.34 Oxygen 9.23 Ash 9.60 Total 100.00 Moisture Content: 2.8 wt% Flue Gas Rate: 951,000 scfm (wet basis) Flue Gas Composition: (mole%, wet basis) C02 14.0 02 3.3 N2 74.8 Hz0 7.6 SO, 0.258 Total 100.0
3.2.1 Process design Most of the equipment in the process design was considered to be the same for both of the configurations. 1t is assumed that the flue gas from the electrostatic precipitator (ESP) of the power plant leaves the air-heater at 300 OF. When the hot gas passes over the sorbent bed, it tends to dry out. In order to minimize this effect, the gas is first humidified adiabatically by contacting it with water in a humidification chamber. The humidified flue gas then enters the reactors at a lower temperature. An induced draft 34 (1.) fan is used to discharge the desulfurized gas to the stack. Limestone is added as sorbent to the reactor bed by a bucket elevator and belt conveyor. A feed hopper is used to accept fresh limestone from a truck or front-end loader and to supply limestone to the bucket elevator by means of a screw feeder. The purpose of this hopper is to make up the limestone lost due to its reaction with SO2. After the reaction, the limestone coming out of the reactors is regenerated by means of a vibrating screen (one operating and one standby) and the regenerated limestone is recycled to the reactor units. The operation is in batch mode for the fixed bed configuration and is continuous for the moving bed configuration. The reaction products, which can not be regenerated, are disposed to an intermediate storage pile. The flow rate of sorbent around the recycle loop in each configuration is specified by assuming that all of the reacted sorbent and none of the unreacted sorbent is removed from the loop by the regeneration unit. Since the conversion of sorbent from CaC03 to CaS04 is not included in the model, the amount of reacted sorbent is calculated by considering the amount of SO, removed from the gas stream. For the fixed bed configuration it is assumed that the bed can be re-wetted ten times before the removal efficiency drops and the sorbent has to be regenerated. The estimate for this assumption is based upon operating experience with a fixed-bed pilot-scale unit (Prudich, 1988). Equipment included in the cost estimates is shown in Figure 3-1. This figure is applicable to either of the reactor configurations. Identifying numbers in Figure
3-1 correspond to the descriptions given in Table 3-3.
......
16
Spent Limestone
1 I Figure 3-1. Schematic representation of the desulfurization plant. Table 3-3. Identification number and description of different equipment. I I Identifier Description 1 A feed hopper which accepts fresh limestone from trucks or a front-end loader. A 10 ton capacity is assumed. 2 A screw feeder discharging the feed hopper. 3 A conveyor belt which transports the fresh limestone from the screw feeder to the bucket elevator. 4 A bucket elevator which lifts the fresh feed and recycled sorbent to another conveyor belt. 5 A conveyor belt which transports sorbent from the bucket elevator to the sorbent day tank. 6 A sorbent storage tank capable of holding one hour supply of feed. 7 A screw feeder discharging the day tank. 8 A conveyor belt which delivers limestone to the desulfurization reactors. 9 Multiple reactors arranged in parallel. 10 A conveyor belt which collects the spent sorbent from the reactors and delivers it to a holding bin. 11 A holding bin which feeds the regeneration unit, designed for 10 minutes holdup. 12 A screw feeder discharging the holding bin. 13 Regeneration units which separate sorbent by-product from the unreacted limestone by means of vibrating screen. A spare unit is included. 14 A conveyor belt which transports fines from the regeneration unit to an intermediate storage pile. 15 A conveyor belt which transports recycle material from the regeneration unit to the bucket elevator. 16 An I.D. fan which compensates for the pressure drop across the sorbent bed. 17 A two-fluid atomizer unit which humidifies the incoming flue gas.
The three intermediate storage units are designated as tanks plus separate screw feeders for the sake of costing only. The estimate does not include any cost for flue gas 37 ducting; however, the ducting cost should not vary between the different configurations. The intention for the cost estimation is to compare between these configurations only. An absolute cost estimate was not generated since equipment items which are common to each configuration are not included in the calculation.
3.2.2 Cost model
3.2.2.1 Cost variable identification Cost formulae for the different process units are dependent on capacities and dimensions of the units. These formulae are in turn, generated based upon the conditions specified for the particular reactor configuration. The formulation is started by identifying the relevant nomenclature with subscripts referring to the unit identifiers shown in Table 3-3 and Figure 3-1. Ni is the number of parallel units. Vi is the vessel volume. (ft3) Wi is the vessel width. (ft) Li is the vessel length. (ft) Hi is the vessel height. (ft) Mi is the mass of limestone contained in each unit. (lb) Gi is the limestone mass flow rate through each unit. (lblsec) ri is the holdup time. (sec) Ei is the inflation escalator. Ii is the installed cost factor. Ci is the installed cost for process unit(s) i for November 19 90. The sorbent mass flow rate through the reactor units and the number of parallel units for the fixed bed configuration can be expressed as 38
G9 = M9/79 (3-51) and
N9 = QgO/ (Ug0W9h) (3-52) where Qgo is the total volumetric flow rate of flue gas at the inlet of reactor units, in ft3/sec. The sorbent mass flow rate through the moving bed reactor units and the number of parallel units can be expressed as
'9 '9 = U,oW9bpd',o (3-53) and
N9 = Qgo/(Ug0W9H9) (3-54) The number of parallel reactor units is determined by dividing the total volumetric flow rate of the flue gas by the volumetric flow rate through an individual reactor. Values for h (for the fixed bed configuration), W, (for both of the configurations) , and H, (for the moving bed configuration) were chosen arbitrarily based upon perceived practical limits for the reactor dimensions. The values for H9 (for the fixed bed configuration) and (for the moving bed configuration) are set indirectly by pressure drop demands. After the mass flow rate and the number of reactors are determined, the rest of the flows can be obtained. All reactor outflows are combined in conveyor unit # 10.
(310 = N9G9 (3-55) This flow rate was continued to the regenerator. G13 = G12 (3-58) It is assumed that 20 percent of the sorbent is removed as
byproduct and 80 percent is recycled.
G14 = 0. 2G13 (3-59)
G15 = 0. 8G13 (3-60)
Assuming that the feed hopper only operates for 10 percent of the time gives
Gl = 10G14 (3-61) This flow is continued to the bucket elevator, so
G2 = G1 (3-62)
G3 = G2 (3-63) In the bucket elevator, the recycle stream is combined with the fresh feed.
G4 = G3 + G15 (3-64) Conveyor # 5 must be operated at the same maximum rate as the bucket elevator, so
G5 = G4 (3-65) The flow through the day tank is not periodic, so it has the same value as the outflow from the reactors.
G6 = Gl~ (3-66) This rate continues up to the reactor feed points.
G7 = G6 (3-67)
G8 = G, (3-68) The calculation proceeds by specifying the residence time,
sect for tanks # 6 and # 11
r6 = 1*6oe60 = 10.60 and the maximum mass in tank # 1
M1 = 10*2000 (3-71) where 76 and rll have units of sec and MI has units of lbs.
Then the mass in tanks # 6 and # 11 can be calculated as
M6 = G6~6 (3-72) and
M11 = G11711 and the volume for all three tanks as
V, = Ml/Pb (3-74)
V6 = M6/~b (3-75)
Vll = Mll/pb (3-76) In addition to the volume parameters, lengths are specified for the conveyors and a height is specified for the bucket elevator. The cost figures of screw feeders are calculated based on those for screw conveyors with lengths derived from the volume of the associated tanks. Rough estimates are used for the other lengths.
L~ = vl1I3
L3 = 200
H4 = 100
L, = 200
L7 = ~~113
L8 = 2N9L9
L1~= L8
L,, = vll1I3 41
L,, = 200 (3-85)
L15 = 100 (3-86) The length has units in ft and volume is in ft3. There was a need to develop a correlation for the pressure drop across the bed which is assumed to be the same as the pressure increase across the I .D. fan. The Ergun equation (McCabe and Smith, 1976) can be used for this purpose.
where the sphericity, 6, is taken to be 0.5; the values for
Ego, Ugo,and pgO are taken to be the same as those at the gas feed point to the bed; and AZ is the distance between the gas entry and the exit points in the bed.
3.2.2.2 Consumption of utilities Three utilities: water, compressed air, and power, are considered in estimating the operating cost. Humidification of the flue gas was achieved by dispersing water using two- fluid spray nozzles. The amount of water required is calculated as
The ratio of liquid flow rate to gas flow rates is considered as 0.2. The ratio has been calculated from the correlation given by Kim and Marshall (1971) where Dm is Sauter mean diameter, vrel is the relative velocity, o is the surface tension, L is the liquid flow rate and G is the gas flow rate. The ratio L/G has been calculated by assuming Dm to be 90 pm, the relative velocity to be 50 ft/sec and o to be 58.91 dynes/cm.
QA = 0.2(18.8/28.9)Qv (3-90) The same value of the L/G ratio was also used by Butz et al. (1991) in designing the humidification nozzle. The amount of limestone required for SO, sorption is calculated based on the amount of waste limestone generated.
Qs = G(14) (3-91) The power consumption of the various process units was also considered. The power requirement for the bucket elevator is given (Keeth et al., 1991) by
P4 = 0.002*0.746(G4*60*60/2000)H4 (3-92) where H4 is in ft, G,,has units of lb/sec, and P4 is in KW. The power requirement for 24 inch belt conveyors with a running angle of repose of 38' considered for limestone (Stanley, 1988) is formulated as
Pi = 8.64*10-~~~+ 7.2010-~~~~~ (3-93) for i = 3, 5, 8, 10, 14, and 15 where Gi has units of lb/sec, Li has units in ft and Pi has units in KW. No cost escalation has been included in this power estimate. Power for the screw feeders is estimated using the same formula as for the belt conveyors with a multiplier of 3 to account for the additional friction.
Pi = 3.0(8.64*10-3~i+ 7.2*10-~~,~~) (3-94)
for i = 2, 7, and 12 The fan power requirement (Perry et al., 1987) can be expressed as
Plb = 1.5*10-~~~Ap (3-95) where AP has units of lb,/ft2, Q, has units of ft3/sec and P,, has units of KW. Power for the humidification unit is estimated based upon that for an air compressor (Stanley, 1988), which is given by
PI, = 6.9277*10-3*0.0283*359*360~~A (3-96) where QA is volumetric flow rate of compressed air expressed in m3/day basis and PI, is is KW.
3.2.2.3 Cost correlations In this section, estimated installed capital costs are presented in the general form
Ci = Ii Ei ci* (C-97) where ci* is the referenced cost formula for unit i, Ei is the inflation escalator needed to compute the cost in November 1990 cost basis and I, is the installed cost factor needed to be converted from a purchased cost estimate.
Peters and Timmerhaus (1991) reported costs, in $, for a 44
24 inch wide belt conveyor which handles up to 300 tons/hr as
Ci = IiEi(7525 + 365Li) (3-98) with
Ii = 1.4 (3-99)
Ei = 1.0 (3-100)
and i = 3, 5, 8, 10, 14, 15
Reported costs (Stanley, 1988) for screw conveyors between 7
and 100 ft are given by:
Ci = I~E~( 700~~~"~) (3-101) with
Ii = 1.4 (3-102)
Ei = 372.5/325.0 (3-103) and i = 2, 7, 12
Using a reference cost of $99,300 in 1986 for a 5650 ft3
carbon steel tank (Keeth et al., 1991) and assuming a 0.7 capacity exponent, the tank cost formula is
Ci = IiEi(99, 300(~~/5650)~.~) (3-104) with
I, = 2.3 (3-105)
Ei = 372.5/318.0 (3-106) and i = 1, 6, 11 The cost estimate for the regeneration unit is based on a reported value for a vibrating screen (Stanley, 1988). The resulting formula is
C13 = 2.0*2059.O*Nl3Il3El3 (3-107 ) with 45
II3= 1.3 (3-108)
El, = 372.5/325 (3-109)
NI3 = 2 (3-110) The factor of 2.0 is used in order to include an estimate of the cost of the accompanying classification equipment. A costing formula for bucket elevators has been reported (Woods, 1982) as a function of capacity and lift.
C4 = 14E4(1.3~2000[H4(G4*60~60/2000)/1000] ) (3-111) with
I4 = 1.4 (3-112)
E4 = 372.5/300.0 (3-113)
In Equation (3-110) G4 has units of lb/sec and H4 has units of ft. The factor of 1.3 has been added to reflect the cost of motors and drives. The cost of the reactors is based on their weights. The total surface area, ft2, of the rectangular reactors is calculated by
A, = 2 ( W9L9+W9H9+L9H9) (3-114) Using a bulk density of 483 lb/ft3 for iron, a & inch wall thickness, and a multiplier of 2.0 to account for associated plenums, the weight of the reactor vessel, is given by
Mg = 2.0e483*(1/4)a(1/12)A, = 20.1% (3-115) where A, is in ft2 and M, is in lbs. This is then used in a cost formula for vertical vessels (Stanley, 1988) with
I9 = 1.5 (3-117)
E9 = 372.5/325.0 (3-118) A material factor of 1.7 for 304 stainless steel is included in Equation (3-116). For pressure drops of less than 18 inches water, the cost of a fan and motor (Ponder et al., 1976) is correlated as
C16 = I16E16[0.226627Qg + 86 (1.3415~~~)~'~~] (3-119) with 116= 1.4 (3-120) and E16 = 372.5/182.0 (3-121) where PI6 is the power, in KW, required by the I.D. fan. The cost of the humidification system, considering an air compressor and motor, is reported by Stanley (1988) as
C17 = 1~~~~~[5960(1.3415~~~)~~~~+ 86(1.3415~~~)~'~~] (3-122) where P17is the power, in KW, required by the compressor.
3.2.2.4 Annual system cost A calculation method for an annual system cost using a shortcut method is proposed in an EPA document by Ponder
(1976) . The cost of power is calculated based on $0.03 per KWh of electricity. 47 The limestone cost is based on a value of $0.01 per lb of limestone, which includes $lO/ton cost of purchase and $lO/ton for cost of disposal.
Cs = 0.01*3600*Qs (3-124) where Qs is in lb/sec. The cost of water is calculated based on a value of $1.50 per 1000 gallons of water
Cw = 7.4805~1.5*3600*Q~/(3.417*1000) where Qw is given in ft3/sec. The total operating cost can be calculated as
Co = Cp + CS + CW (3-126) The annual system cost includes the operating costs and a multiple of total fixed cost. The total fixed cost is calculated by summing all the installed costs for the process equipment.
The annual system cost can be calculated from Equations (3-126) and (3-127) as
CA = 365.0.7C0 + 0.17CF (3-128) A plant operating factor of 0.7 is assumed. The conversion factor of 0.17 annual dollars per capital dollar includes estimated costs for depreciation (straight line method), interim replacement (@0.35% of the capital cost), taxes ((34% of the capital cost), insurance ((30.3% of the capital cost), and the price of capital ((39% of the capital cost). 4.0 RESULTS AND DISCUSSIONS The results of the computer simulation of a desulfurization plant were analyzed for the fixed bed and the cross flow moving bed reactor configurations to evaluate the bed performance and plant cost. A number of simulations were done to study parametric sensitivity. Baseline conditions were chosen on the basis of a series of preliminary runs and operating data obtained from the pilot scale unit at the Ohio University campus. The baseline conditions are listed in Table 4-1.
Table 4-1. Baseline simulation conditions for fixed bed and moving bed configurations. I I Approach to saturation = 10°F Sorbent particle size = 0.01 ft Superficial gas velocity at the gas inlet point to the bed = 1.5 ft/sec Sorbent bed velocity (for the case of a moving bed) = 20 ft/hr Distance across the bed in the direction of flue gas flow = 1.5 ft Coal sulfur content = 3.5 wt% Sulfur removal = 90%
The study assumes that both the length and the width of a fixed bed reactor perpendicular to the direction of gas flow are 20 ft. For the case of a moving bed reactor, the width, perpendicular to the direction of gas flow and sorbent flow, is also considered to be 20 ft. 4.1 Reactor bed performance The results of primary interest are the reactor bed drying pattern and the average SO, removal.
4.1.1 Drying of the limestone bed The concentration of water in the gas phase at different vertical positions of the fixed bed reactor unit is plotted as a function of time in Figure 4-1. Figure 4-2 shows the concentration of water in the gas phase at different horizontal positions of the moving bed reactor unit. Bed temperature as a function of vertical positions for the fixed bed reactor is shown in Figure 4-3. Figure 4-4 shows the bed temperature of moving bed reactor ar different horizontal positions. The development and movement of the drying front is revealed indirectly from these figures. The fixed bed is initially at room temperature, so the moisture in the flue gas initially condenses on the bed, drying out the gas. After the gas flow begins, the bed temperature quickly increases to the wet bulb temperature. Although not revealed directly by Figure 4-1, the transient associated with the heating of the bed occurs in about 6 minutes. The vertical jumps in Figures 4-1 and 4-2 correspond to the points where the dry feed gas meets the wet portion of the bed and becomes saturated. In all cases the shapes of the curves at different times are identical, while the length of the straight horizontal portion 50 to the left of the jump increases as the bed dries out. In the dry portion of the bed the incoming gas heats the limestone to the feed gas temperature. When the drying front is reached the gas temperature decreases as water is evaporated. The bed temperature remains at the wet bulb temperature until all the water has been evaporated from the bed. In the drying zone the concentration of water in the flue gas increases until it becomes saturated, at which point evaporation ceases.
Similar behavior is observed in Figure 4-2 as the sorbent bed moves down the reactor unit. In this case cold sorbent is fed at the top of the bed. So, the moisture in the flue gas initially condenses on the bed, drying out the gas. As the bed moves down, the bed temperature increases to the wet bulb temperature. The gas temperature decreases to its wet bulb temperature as it flows across the bed. Although not revealed directly by Figure 4-2, the transient associated with heating the bed occurs in a vertical distance of about 14 inches. The vertical jumps correspond to the points where the dry feed gas, flowing across the bed, meets the wet portion of the bed and becomes saturated. In this case, the drying front position moves steadily across the bed as the point of reference moves down the bed. The horizontal length of the wet portion of the bed is directly related to the bed effectiveness because SO, removal is assumed to depend on the existence of liquid water on the surface of the sorbent. 0 Ln rC)
62 rnin 103 min 145 min 186 min 228 min 250 min 0 -0 n-4-J r~) f f f f 5- nE 0 WN* 0 - 0 1 r - 0- of Superficial gas velocity = 1.5 ft/sec. EN- Sorbent particle size = 0.01 ft. -o : ..+-' - Approach to saturation = 10°F. F 1 :a_ Coal sulfur content = 3.5 wtw. ;2: Sulfur removal = 90%. 0 - 0 -I b01 % o= 0 rnin 3-1- e, - V) - 0 I t Xi - V) - 0 - C3 -: - 0 IIIiI IIII~lIIl[IIIl~lIll~llll~IIII~IIII~IIII 0 2 4 6 8 10 12 14 16 18 Vertical Position (inch)
Figure 4-1. Gas phase water concentration as a function of vertical position for a fixed bed reactor. The third parameter is elapsed time. *- r)-- - 175 inch 355 inch 535 inch 715 inch 840 inch 0- -0- r f f f "Y M7
Sorbent bed velocity = 20 Superficial gas velocity = Sorbent particle size = 0.01 ft. Approach to saturation = 10°F. Coal sulfur content = 3.5 wb. Sulfur removal = 90%.
o~ll,lllllllllllIllllIllllIlllllllllIllllIllll 0 2 4 6 8 10 12 14 16 1 Horizontal Position (inch)
Figure 4-2. Gas phase water concentration as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed. L Superficial gas velocity = 1.5 ft/sec. a, Sorbent particle size = 0.01 ft. Approach to saturation = 10°F. Q Coal sulfur content = 3.5 we. Sulfur removal = 90%.
0 min
Vertical Position (inch)
Figure 4-3. Bed temperature as a function of vertical position for a fixed bed reactor. The third parameter is elapsed time. cr "0: - a - L - 3 - 4-J - 0 em-z Sotbent bed velocity = 20 ft/hr, al - Superficial ys velocity = 1.5 ft/sec. a, 1 Sorbent par icle size = 0.01 ft. - Approach to saturation = 10°F. - Coal sulfur content = 3.5 wk. E - Sulfur removal = 90%. 0 I- I- 01 Tt- w*: 0 inch a - m - - - 0 - ol IIIIl~lllll~lllll~lllll~lll'l~lllll *O 3 6 9 12 15 1 Horizontal Position (inch) Figure 4-4. Bed temperature as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed. 55
4.1.2 Sulfur dioxide concentration
The gas phase SO, concentration profiles for fixed bed and moving bed configurations are shown in Figures 4-5 and
4-6. In both the cases, the concentration of SO, in the gas phase increases sharply near the sorbent inlet and then gradually drops down. The initial spike in concentration is caused by the fact that the gas is rapidly cooled as it enters the bed in the areas where the sorbent is cool causing the overall gas density to rise. As the gas flows through the bed, the concentration of SO, remains constant till it reaches the wet part of the bed. After the initial transient disappears, the plots in Figures 4-5 and 4-6 show linear decays from the point where the bed first becomes wet. The straight portions of these curves indicate that the SO, removal rate is controlled by the dissolution of limestone. At lower concentrations, the decays become exponential. This is consistent with the fact that the transport rate is a first order process as the transport becomes liquid phase and eventually gas phase controlled.
4.1.3 Controlling rate of SO, removal
The controlling rate for the SO, removal reaction for the base conditions is shown in Figures 4-7 and 4-8 as a function of time and position, for the fixed bed and the moving bed reactors, respectively. The location of the reaction plane, as calculated in Appendix-B, determines the controlling Figure 4-5. Gas phase SO2 concentration as a function of vertical posltion for a fixed bed reactor. The third parameter is elapsed time, - - - -
Sulfur removal = 90~.
w-
C
C - Q) - c0 - 0 e, -
v, - - Q) VJ - 0 - c - a - 0) 0 - (3 - 0 IIIII~IIIII)I1III~11111~11111~11111~ 0 3 6 9 12 15 18 Horizontal Position (inch)
Figure 4-6. Gas phase SO2 concentration as a function of horizontal position for a moving bed reactor. The third parameter is vertical position in the bed. Liquid phase control
Figure 4-7. Controlling resistances at different times and positions in a fixed bed reactor. - - * 800------n - II - 0 - .C- 600-- w - - - a, - 0 -
- -C, - .CI]- - - -
.-
Horizontal Distance (inch)
Figure 4-8. Controlling resistances at different positions in a moving bed reactor. 60 mechanism of the reaction. From these figures, it can be observed that the rate of reaction is controlled by the dissolution of limestone when the gas reaches the wet part of the bed. As the SO, concentration decreases, the reaction becomes liquid phase controlled. At a very low concentration of SO,, the gas phase resistance controls the removal process. No reaction occurs in the dry portion of the bed.
4.1.4 Average SO, removal
The removal of SO, at any particular point in the bed for fixed bed and moving bed reactors is shown in Figure 4-9 and 4-10, respectively. Both the figures consider baseline simulation conditions. The percentage of SO, removed, at any particular time, in the case of a fixed bed reactor, or at any vertical position, in the case of a moving bed reactor, is represented as the instantaneous SO, removal. For the case of a fixed bed, the cumulative average of the instantaneous SO, removal from time zero to the referenced time is termed the average SO, removal at that particular time. For the case of a moving bed, the cumulative average of the instantaneous SO, removal from the top of the bed to a particular vertical position in the bed is termed as the average SO, removal at that particular position.
The average SO, removal was calculated for fixed bed and moving bed reactors at different times or at different vertical positions, until the targeted average SO, removal was Figure 4-9. Sulfur dioxide removal as a function of time in a fixed bed reactor. Moving Bed
Sorbent bed velocity = 20 ft hr Superficial gos velocity = I .dftjsec. Particle size = 0.01 ft. Approach to saturation = 10°F. Bed length = 1.5 ft. Coal sulfur content = 3.5 wtw.
Vertical Distance (inch)
Figure 4-10. Sulfur dioxide removal as a function of vertical distance in a moving bed reactor. 63 reached. Figure 4-9 shows that the average SO2 removal at the outlet of the fixed bed reactor unit reaches 90% after 250 minutes of run time. The instantaneous removal at that time is about 75%. Figure 4-10 shows that the average removal reaches 90% at a vertical distance of 840 inches from the top of the moving bed reactor while the instantaneous SO2 removal at that position is about 70%.
4.2 Economic evaluation A summary of the operating parameters and installed capital costs for the base conditions for fixed bed and moving bed configurations is given in Table 4-2. The system cost of the moving bed configuration is about 400 K$/year less than that for a fixed bed configuration with the same capacity. The cost of the reactor units represents the malor difference in the system cost. The number of reactor units for a fixed bed system is more than that for the moving bed system due to the assumption that the cross sectional area perpendicular to gas flow for the fixed bed system is preset to a value which turns out to be smaller than that for the moving bed configuration. The variations in the fixed cost of bucket elevator # 4, belt conveyor # 10, storage tank # 6 and holding bin # 11 are mainly due to the variation in sorbent load. The description of the different process units are shown in Figure
3-1 and Table 3-3. The operating costs for power vary due to the basic assumption that the fixed bed system operates in a Table 4-2. Operating and cost parameters for base conditions. I I Description Fixed Bed Moving Bed Reactor dimension (ft): I Length (x-direction) 20.0 1.5 Height (y-direction) 1.5 70.0 Width (z-direction) 20.0 20.0 Number of reactor units: 35 11 Power requirements (KW): Screw Feeder # 2 1.2 Belt Conveyor # 3 1.1 Bucket Elevator # 4 14.5 Belt Conveyor # 5 1.2 Screw Feeder # 7 0.3 Belt Conveyor # 8 1.4 Belt Conveyor # 10 1.4 Screw Feeder # 12 0.3 Belt Conveyor # 14 0.1 Belt Conveyor # 15 0.1 I.D. Fan # 16 88.5 Humidification System # 17 196.8
Operating Costs (K$/year): Cost of Power 56.3 76.7 Cost of Water 432.8 432.8 Cost of Sorbent 1008.7 1008.7
Fixed Cost (K$): Feed Hopper # 1 17.8 Screw Feeder # 2 1.1 Belt Conveyor # 3 112.7 Bucket Elevator # 4 43.8 Belt Conveyor # 5 112.7 Storage Tank # 6 32.0 Screw Feeder # 7 1.1 Belt Conveyor # 8 725.9 Reactor Units # 9 4744.1 Belt Conveyor # 10 725.9 Holding Bin # 11 9.1 Screw Feeder # 12 1.1 Regenerator Units # 13 12.3 Belt Conveyor # 14 112.7 Belt Conveyor # 15 61.6 I.D. Fan # 16 32.0 Humidification System # 17 442.1
I System Cost (K$/year) 2719.8 2324.5 I 65 batch mode and the moving bed system operates in a continuous mode.
4.2.1 Effect of approach to saturation The effects of variation in the feed gas humidity on the performance of the fixed bed configuration are shown in
Figures 4-11 and 4-12. As the feed flue gas approaches the saturation point, the sorbent bed dries out more slowly and the reactor bed can be used for a longer period of time before the average SO2 removal efficiency drops below the target value. At a constant superficial velocity, the number of reactor units is proportional to the reactor inlet flue gas flow rate. As the approach to saturation is decreased, the flue gas temperature decreases and thus the inlet flue gas volumetric flow rate decreases. This results in a fewer number of reactor units. As the humidity in the flue gas decreases, the reactor bed dries more rapidly, resulting in a decrease in the exhaustion time.
Figure 4-12 shows the annual system cost as a function of approach to saturation for the case of a fixed bed reactor configuration. The simulation result indicates that as the approach to saturation increases, the fixed cost increases due to the increase in number of reactor units. As the approach to saturation increases, the bed exhaustion time decreases. It has been assumed that the volume of sorbent storage is proportional to the bed exhaustion time. This leads to a - - - Superficial gas velocity = 1.5 ft/sec. - - o - - Bed height = 1.5 ft. 10 0: Particle size = 0.01 ft. ro LO- Coal sulfur content = 3.5 wb. v- - Sulfur removal = 9055. - - - - - n - - L 10 1: 0: -CO V-- Number of reactor units 4 - - - .. - - - a, - 6------.-E 0: -a-0 4 m-- - - - C - - 0 - - .- - - + - - II) a-0: - - - - L - - X - - - - a, 0: Bed exhaustion time 7 - 8 -0 - - 0 - - - 4 - m ------0 IlIIlIIII~I11111111~111111111~1IIIIIIII~IIII0 0 20 40 60 80 Approach to Saturation (OF)
Figure 4-11. Number of reactor units and bed exhaustion time as a function of approach to saturation for a fixed bed reactor configuration. System Cost
< i # - Superficial gas velocity = 1,5 ft/sec. Bed height = 1.5 ft. 0: Particle size = 0.01 ft. 0- - 0, Coal sulfur content = 3,5 wb. 90%, 4 w-- Sulfur removal = I(> - 0 - 0 - Operating Cost *I * I
- 0 - 0 0 """"'"""""'"'"'"'~'~""'""""""1 - 0 20 40 60 80 100 Approach to Saturation (OF) Figure 4-12. Annual cost as a function of approach to saturation for a fixed bed reactor configuration. 68 reduction in the operating cost of the downstream sorbent handling equipment. The system cost shows a minimum between a 5OF and 20°F approach to saturation. The effects of changing the approach to saturation for a moving bed system are shown in Figures 4-13 and 4-14. They reveal that as the flue gas approaches saturation, the sorbent dries out more slowly and the flue gas travels farther down the bed before the average SO, removal efficiency drops below the targeted value. For a constant superficial gas velocity, the bed height is inversely proportional to the number of reactor units. It appears from Figure 4-14 that as the number of reactor units increases there is an increase in the annual fixed cost and system cost. The minimum cost is obtained near the flue gas saturation point. The humidification cost doesn't show an appreciable impact on the operating cost.
4.2.2 Effect of bed depth in the direction of gas flow The number of reactor units, total cost of reactors and bed exhaustion time is plotted in Figure 4-15 as a function of fixed bed height. The other operating parameters are considered to be the same as in the base conditions. As the reactor bed height increases, the time required to dry the bed increases and the bed exhaustion time increases. However, the number of reactor units is independent of bed height. The number of reactor units is calculated based only on the cross sectional area perpendicular to the gas flow and the Approach to Saturation (OF)
Figure 4-13. Bed height and number of reactor units as a function of approach to saturation for a moving bed reactor configuration. Sorbent bed velocity = 20 ft hr. 0 Superficial gas velocity = I.Jft/sec. O1 Bed length = 1.5 ft. 8, Particle size = 0.01 ft. - Coal Sulfur content = 3.5 wb. System Cost - Sulfur removal = 90%. 8 0- 0: 2:- 0 -
6% 1 Operating Cost * 7A - d
o~lllllllllllllllllI1IIII1IIIII~IIIIIlIIl~1II~~~l~~~l~~~~1~~~~~l1~~~~~~~~~~~~~~~~I~~~~~~~~~l 0 10 20 30 40 50 6 0 70 80 90 Approach to Saturation (OF) Figure 4-14. Annual cost as a function of approach to saturation for a moving bed reactor configuration. Number of reactor units I 0
Superficial gas velocity = 1.5 ft/sec. Approoch to saturation = 10°F. Particle size = 0,01 ft, Coal sulfur content = 3,5 wb, Sulfur removal = 9M,
Bed Height (ft) Figure 4-15. Number of reactors, total cost of reactors and bed exhaustion time as a function of bed height for a fixed bed reactor configuration. 72 superficialvelocity. As the bed height increases the reactor size increases and the total cost of the reactors increases. In Figure 4-16, fixed cost, operating cost and system cost are plotted at different bed heights. At a bed height of 0.8 ft, the sorbent storage and handling costs are higher than that in a 1.5 ft bed height due to a significantly lower bed exhaustion time than the 1.5 it bed case. Thereafter, with an increase in bed height, the fixed cost increases due to the increase in reactor costs. As bed height increases, pressure drop also increases. The increase in pressure drop causes an increase in the cost of power and in the operating cost. It appears that the optimum cost may be obtained using a fixed bed reactor height between 0.8 it and 2.0 ft. For a moving bed system, the number of reactor units, total reactor cost and bed height are plotted at different bed lengths in Figure 4-17. The bed length, in the case of a moving bed, is defined as the horizontal distance of the bed in the direction of gas flow. With an increase in bed length, the bed height increases because drying occurs at a greater depth. It is also evident from the Figure 4-17, that the bed height increases with increasing bed length. Due to the increase in bed height, the number of reactor units decreases. The number reduces rapidly as the bed length increases from 0.75 ft to 1.5 it. It appears that the total reactor cost reaches a minimum at a bed length of around 1.5 ft. In Figure 4-18, where the annual costs are plotted against bed length, Operating cost
7 & Fixed cost
Superficial 90s velocity = 1.5 ft/sec, Approach to saturation = ~QOF* Particle size = 0.01 ft, Cool sulfur content = 3.5 w&, Sulfur removal = ga,
0.5 1.5 2.5 3.5 Bed Height (ft) gure 4-16. Annual cost as a function of bed height for a fixed bed reactor configuration. 0 0
Sorbent bed velocity = 20 ft/hr. Superficial gas velocity = 1.5 ft/sec. Approoch to saturation = 10°FF, Particle size = 0.01 ft. Coal Sulfur content = 3.5 wk. Sulfur removal = 9h,
Bed Length (ft)
Figure 4-17. Number of reactors, total cost of reactor units and bed height as a function of bed length for a moving bed reactor configuration, Operating Cost
Bed length (ft) - Figure 4-18. Annual cost as a function of bed length for a moving bed reactor configuration. a minimum cost is obtained at a bed length between 1.0 ft and
2.0 ft.
4.2.3 Effect of sorbent particle size Three different sizes of limestone particle as a sorbent have been studied. The pressure drop, bed exhaustion time and number of reactor units are shown in Figure 4-19 as a function of sorbent particle size. The sorbent particle sizes correspond to the mean particle diameter of fresh limestone which is fed to the reactor. The figure complies with Ergun's law as observed by the fact that the pressure drop across the bed decreases as the sorbent particle size increases. The cost of the power consumption of the I.D. fan decreases as the pressure drop across the bed decreases. However, the number of reactor units remains the same because the number of reactors is assumed to be independent of the particle size. Because the size and number of the reactors remain constant, the reduction in cost shown in Figure 4-20 is primarily due to the change in pressure drop. The optimum particle size appears to be between 0.008 ft to 0.015 ft. The pressure drop across a moving bed reactor, reactor bed height and number of reactor units are shown in Figure
4-21 as a function of the sorbent particle size. The cost is plotted in Figure 4-22 as a function of sorbent particle size. At a larger particle size the pressure drop across the bed decreases. The specfic surface area of the sorbent particle J - - - - - n - - 0a{ Cd -:g'Z' 1 I - I w - - x 1 - a) O r I ca, F"a,- E wra - : + - - - s - 0 Number of reactor units :$- *j 3 brOD- 1u X -is w Superficial gas velocity = 1.5 ft/sec. - Approach to saturation = 10DF. I u Bed height = 2.0 ft, - a) Coal sulfur content = 3.5 wb, Sulfur removal = 90sa4 -I m 1111 IIIII Illl~lllll'l"I 0
Sorbent Particle Size (ft) Figure 4-19. Pressure drop, bed exhaustion time and number of a reactor units as a function of sorbent particle size for a fixed bed reactor configuration, Superficial gas velocity = 1.5 ft/sec. 0 Approach to saturation = 10°F. Bed height = 2.0 ft. Coal sulfur content = 3.5 wb. Sulfur removal = 9%.
Operating Cost * Total Fixed Cost 4
Sorbent Particle Size (ft)
Figure 4-20. Annual cost as a function of sorbent particle size for a fixed bed reactor configuration. 0.004 0.006 0.008 0,010 0.012 0.014 0.01 6 Sorbent particle Size (ft)
Figure 4-21. Pressure drop, number of reactor units and bed height as a function of sorbent particle size for a moving bed reactor configuration. Sorbent bed velocity = 20 ft/hr. Superficial gas velocity = 1.5 ft/sec. Bed length = 1.5 ft. Approach to saturation = 10°F. Coal Sulfur content = 3,5 wt%. Sulfur removal = 90%.
System -
- 0: Operating Cost a 0: - - en- .-,- - 03 01 01 .--- - or 0: 0-- - - 0~lllIl~llll~llll~~I 0.004 0.007 0.010 0.013 0.01 6 Sorbent Particle Size (ft) Figure 4-22. Annual cost as a function of sorbent particle size for a moving bed reactor configuration. 81 decreases with an increase in the particle size. Due to the decrease in surface area the bed dries faster. This leads to a lower bed height at a larger particle size. It is apparent from Figure 4-21that there is a significant reduction in bed height as the particle size increases from 0.01 ft to 0.015 ft. With a constant bed width, the number of reactor units required for SO, removal increases as the bed height decreases. The increase in number of reactors for a change in particle size from 0.01 ft to 0.015 ft causes an increase in the fixed cost and system cost. The optimum particle size appears to be between 0.008 ft to 0.015 ft.
4.2.4 Effect of superficial gas velocity The effects of changing the superficial flue gas velocity through the fixed bed and moving bed reactor units are plotted in Figure 4-23 and 4-25, respectively. The annual costs for the fixed bed and the moving bed reactor configurations are plotted in Figure 4-24 and 4-26, respectively. For the fixed bed reactor system, as the superficial gas velocity increases, the pressure drop increases and the bed exhaustion time decreases. The number of reactors required decreases as the superficial gas velocity increases. This results in a decrease in the system costs as the superficial gas velocity reaches 2.5 ft/sec. With a further increase in the superficial gas velocity, 90% SO, removal can not be attained. Figure 4-23 shows zero bed exhaustion time at a Superficial Gas Velocity (ft/sec.)
Figure 4-23. Number of reactor units, pressure drop and bed exhaustion time as a function of super£ icial gas velocity for a fixed bed configuration. Approach to saturation = 10°F. Bed height = 1.5 ft. Particle size = 0.01 ft. Coal sulfur content = 3.5 wb. Sulfur removal = 90%.
\ Operating cost .a.
Superficial gas velocity (ft/sec) Figure 4-24. Annual cost as a function of superficial gas velocity for a fixed bed reactor configuration. a -? 0 e 1 I 0 - -S$ 3 :' m V] VI- E -0 - - - -0
Superficial Gas Velocity (ft/sec.)
Figure 4-25. Number of reactor units, pressure drop and bed height as a function of superficial gas velocity for a moving.bed reactor configuration. Sorbent bed velocity = 20 ft/hr. Particle size = 0.01 ft. Bed length = 1.5 ft. Approach to saturation = 10°F. Coal Sulfur content = 3.5 wt%. Sulfur removal = 9M.
Operating Cost + *
Superficial Gas Velocity (ft/sec)
Figure 4-26. Annual cost as a function of superficial gas velocity for a moving bed reactor configuration. 86 superficial gas velocity of 3.0 ft/sec and thereafter. The minimum system cost is obtained as the bed exhaustion time tends to zero; however this is an artifact of the assumption that only two reactors are charging or discharging at any given time. In practice, the number of idle reactor will increase dramatically as the bed exhaustion time approaches zero. So, the superficial gas velocity should be selected based on a suitable ratio of bed exhaustion time and reactor down time. In the case of a moving bed system, the increase in superficial gas velocity results in a decrease in bed height. As the bed height decreases, the cross-sectional area perpendicular to the gas flow decreases and this results in an increase in the number of reactor units. The pressure drop across the bed increases, as expected, with the increase in superficial gas velocity. The annual cost curves in Figure 4-26 shows that an optimum cost to be within a range of 1.25 - 2.5 ft/sec.
4.2.5 Effect of moving bed sorbent velocity The effect of changing the sorbent bed velocity in a moving bed reactor unit is shown in Figures 4-27 and 4-28. For a given bed length and an average SO, removal efficiency, the bed height increases as the sorbent velocity through the bed increases. The reactor height is inversely proportional to the number of reactor units required to remove SO, from a Sorbent bed velocity (ft/hr)
Figure 4-27. Reactor bed height and number of reactor units as a function of sorbent bed velocity for a moving bed reactor configuration. Superficial gas velocity = 20 ft/hr. Particle size = 0,01 ft. Bed lenath = 1 .Wt, Approoc to soturation = 10'~. Coal Sulfur content = 3.5 wb. Sulfur removal = 90%. System Cost -
Operating Cost
\ Fixed Cost
Sorbent bed velocity (ftlhr). Figure 4-28. Annual cost as a function of sorbent bed velocity for a moving bed reactor configuration. 89 given amount of flue gas.
The cost curves in Figure 4-28 shows that the fixed cost and the system cost decreases gradually for a change in sorbent bed velocity from 5 ft/hr to 20 ft/hr. However, as the sorbent velocity increases from 20 ft/hr to 30 ft/hr, the cost trend changes as the change in bed height dominates over the change in number of reactor units. It appears that the optimum sorbent velocity lies within a range of 10-30 ft/hr.
4.2.6 Effect of coal sulfur content A comparison between the two levels of sulfur content for the base conditions is shown in Table 4-3.
Table 4-3. Effect of coal sulfur content on cost.
Design Case Reactor No. of Operating Fixed System Dimension Reactors Cost Cost Cost (ftxftxft) (MS/Y~) (MS) (MS/yr)
1.5 wt% Sulfur Fixed Bed 2x20~20 45 3.5 1.6 5.1 Moving Bed 2x47~20 2 0 3.6 1.2 4.8
3.5 wt% Sulfur Fixed Bed 2x20~20 3 5 1.5 1.3 2.8 Moving Bed 2x112~20 8 1.5 0.8 2.3
In each case the fixed cost is higher for the fixed bed configuration. This is due to the fact that more reactor units are required for the fixed bed configuration. The design assumptions force the cross sectional area perpendicular to the flow for the fixed bed configuration to be smaller than that of the cross flow moving bed configuration. The system cost for a fixed bed configuration is also higher than for a moving bed configuration. In both configurations, the cost figures are higher for the low sulfur coal due to its assumed lower heating value.
4.2.7 Effect of percentage removal of SO,
Two different levels of average SO, removal are compared in Table 4-4 for the base conditions.
Table 4-4. Effect of change in average SO, removal percentage. I Design Case Operating Fixed System cost Cost Cost (MS/yr) (MS (MS/yr) 90% Removal Fixed Bed 1.5 Moving Bed 1.5 98% Removal Fixed Bed 1.6 Moving Bed 1.6
In both cases, the fixed cost for fixed bed configuration is higher than for the moving bed configuration. As the SO, removal efficiency increases, there is an increase in the operating cost and the fixed cost for both the configurations. Increased consumption in sorbent and power causes an increase in operating cost. The fixed cost increases due to an increase in total bed size. The trend obtained with the change in removal percentage is as expected. 5.0 CONCLUSIONS AND RECOMMENDATIONS 5.1 Optimum operating Parameter A mathematical process model has been used to simulate the fixed bed and moving bed configurations. The model includes a first principles analysis of the chemical and physical processes in the reactor as well as an overall material balance for the sorbent handling system. The parametric sensitivity has been studied at different saturation levels of the feed flue gas, reactor bed depths, sorbent particle sizes, superficial gas velocities, coal sulfur contents and average SO2 removal levels for both configurations. In addition to the above parameters, the effect of sorbent bed velocity has also been studied for the case of a moving bed configuration. Fixed and operating costs are estimated for different operating conditions and the optimum parameters are evaluated from the annual system cost. Within the selected simulation runs, the optimum range of operating parameters are summarized in Table 5-1.
Table 5-1. Optimum Operating Parameters (3.5 wt% sulfur content coal and 90% SO2 removal). I I Operating Parameters Fixed Bed Moving Bed Approach to saturation : 5O - 20°F 5'F Bed depth : 0.8 - 2.0 ft 1.0 - 2.0 ft Sorbent particle size : 0.008 - 0.015 ft 0.008 - 0.015 ft Superficial gas velocity : 2.5 ft/sec 1.25 - 2.5 ft/sec Sorbent bed velocity - 10 - 30 ft/hr 92 The model behaves in a consistent and rational manner. The general trends with respect to the parametric variation give expected results. From the simulation output it appears that the cost of the moving bed system may be lower than that of the fixed bed system. The simulation results are affected by several assumptions which are considered in the development of the model. A basic assumption of the modeling work presented in this thesis is that there is no precipitate layer accumulating on the limestone surface. However, the residence time of the limestone particles in the reactor is large enough for the precipitate layer to affect SO2 removal by increasing the resistance to calcium dissolution. In future models the inclusion of the effects of the precipitate layer may provide better insights into the kinetics of the process. The computer simulation results have not been compared to plant operation data. In order to put the model to practical application, the operating parameters need to be compared with plant operating results. Some of the cost correlations need to be reviewed and revised to render more accurate cost estimates. In the present model the cost of humidification appears to be relatively insensitive to flue gas humidity. There is room to improve the case sensitive cost correlations for sorbent storage and sorbent handling systems. The computational time involved in simulation has been 93 reduced to a large extent in comparison with the preceding models. Using a VAX/VMS V5.4-2 system, the computer time to simulate the present model varied from 45 minutes to 8 hours depending on flue gas humidity and average SO2 removal required. Modifying the program to run on a supercomputer would further reduce the computer run time. NOMENCLATURE The first column represents identification variables used in the computer program code and the second column represents identification variables used in the text.
A a Geometric surface area of the sorbent. (ft2/ft3 of reactor) AHG ahg The heat transfer area for transfer between the gas and liquid phases. (ft2/ft3 of reactor) AHL a,, The heat transfer area for transfer between the liquid and solid phases. (ft2/ft3 of reactor)
AMG The mass transfer area in the gas phase boundary layer. (ft2/ft3 of reactor)
AML am, The mass transfer area in the liquid layer. (ft2/ft3 of reactor)
AMP amp The mass transfer area in the precipitate layer. (ft2/ft3 of reactor)
AMS a,n, The mass transfer area at the unreacted sorbent surface. (ft2/ft3 of reactor)
AR A r Surface area of reactor bed. (ft2) C(1) Ci Installed cost for unit(s) i. ($) CA C, Annual system cost for the desulfurization plant. ( S/Y~) CCL CCL The concentration of ~a++in the liquid. (lbmole/ft3 of liquid) CCLE C,,, The concentration of ~a"in the liquid which is in equilibrium with the calcium in the unreacted limestone. The same as the solubility of the limestone. (lbmole/ft3 of liquid) CCLP CcLp The concentration of ~a"in the liquid at the outer surface of the precipitate layer. (lbmole/ft3 of liquid) CCLS C,,, The concentration of ~a"in the liquid at the surface of the unreacted limestone. (lbmole/ft3 of liquid) Operating cost for the desulfurization plant. (S/hr)
CP P The total cost of power. ($/hr) CPCS CPC, Heat capacity of sorbent. Includes sulfates, sulfites, and carbonates. (Btu/lbmole calcium ion/ " R) CPNG C,,, Heat capacity of noncondensables. Includes SO,, C02, N,, and 02. (Btu/lbmole/ OR) CPWG CpUg Heat capacity of water vapor. (Btu/lbmole/"R) CPWL Cw, Heat capacity of liquid water. (Btu/lbmole/"R) CSG Csg The concentration of SO2 in the gas. (lbmole/ft3 of gas CSGI Csgi The concentration of SO2 in the gas at the gas/liquid interface. (lbmole/ft3 of gas) CSLI Cs,i The concentration of SO3--(or SO4--)in the liquid at the gas/liquid interface. (lbmole/ft3 of liquid) CSLS CSI, The concentration of SO3--(or SO4--)in the liquid at the precipitate/unreacted sorbent interface. (lbmole/ft3 of liquid)
CSS Css The concentration of sulfate or sulfite in the solid. (lbmole/ft3 of solid) CW cw The total cost of water. ($/hr) CWG Cwg The concentration of water in the gas. (lbmole/ft3 of gas). CWGB CWgb The concentration of water in the gas in the bulk. (lbmole/ft3 of gas). CWGI Cwgi The concentration of water in the gas at the gas/liquid interface. (lbmole/ft3 of gas) CWL C,, The concentration of water in the liquid. Same as p, (lbmole/ft3 of liquid) DCL D,, Diffusivity of ~a++in the liquid layer. (ft2/sec) DELL 6, Thickness of water layer. (ft)
DELP 6, Thickness of precipitate layer. (ft) DELR 6r Thickness of SO3'- (SO4-') diffusion zone. Distance between gas/liquid interface and reaction front. ( ft)
DELTAP AP Pressure drop across the bed. (atm) DG Dg Diffusivity of binary gas system. (ft2/sec)
DL DL Diffusivity of an ion at infinite dilution. (ft2/sec). DP D, Sorbent particle diameter. (ft) DSG D,, Diffusivity of SO2 in the gas phase. (ft2/sec) DSL D,, Diffusivity of SO,-- (SO4--)in the liquid phase. ( ft2/sec) DSM D,, Sauter mean diameter. (micron) DWG Dug Diffusivity of water in the gas phase. (ft2/sec) E(1) Ei Inflation escalator for process unit i. (dimensionless)
EPSD E, Fraction of bed occupied by liquid after free draining. (dimensionless)
EPSG 6, Fraction of bed occupied by gas. (dimensionless)
EPSL E, Fraction of bed occupied by liquid. (dimensionless)
EPSS E, Fraction of bed occupied by solid. (dimensionless) FA Fa The Faraday number. (dimensionless) FC f, Interphase flux of ~a". (lbmole/ft2/sec) FCS fcs Flux of calcium ions in the solid phase in the direction of sorbent flow. Includes sulfates, sulfites, and carbonates. (lbmole/sec/ft2 of reactor) FP F, Packing factor of the reactor bed. (dimensionless) FG f, Flux of gas in the direction of gas flow. Includes noncondensables and water vapor. (lbmole/sec/ft2 of reactor) FNG f,, Flux of noncondensables in the gas phase in the direction of gas flow. Includes SO2, C02, N2, and 02. (lbmole/sec/ft2 of reactor) FS f, Interphase flux of SO3--(SO). (lbmole/ft2/sec) FSG f,, Flux of sulfur dioxide in the gas phase in the direction of gas flow. (lbmole/sec/ft2 of reactor) FSS f,, Flux of sulfate or sulfite groups in the solid phase in the direction of sorbent flow. (lbmole/sec/ft2 of reactor) FW f, Interphase flux of water. (lbmole/ft2/sec)
FWG f,, Flux of water in the gas hase in the direction of gas flow. (lbmole/sec/ftP of reactor)
FWL f,[ Flux of water in the liquid phase in the direction of liquid flow. (lbmole/sec/ft2 of reactor) G Gas flow rate. (lbs/min) Gi Sorbent mass flowrate through process unit i. (lb/sec)
gc Conversion factor. (32 ft*lb,,/lbf/sec2) g, Rate of heat transfer from the gas phase to the liquid phase. (Btu/sec/ft3 of reactor)
g, Rate of heat transfer from the liquid phase to the solid phase. (Btu/sec/ft3 of reactor) g, Rate of transport of sulfur (dioxide) from the gas phase to the solid phase. (lbmole/sec/ft3 of reactor) g, Rate of transport of water from the gas phase to the liquid phase. (lbmole/sec/ft3 of reactor)
H(I) Hi Height of process unit i. (ft) HCS H,, Enthalpy of sorbent. Includes sulfates, sulfites, and carbonates. (Btu/lbmole calcium ion)
h, Overall heat transfer coefficient between the gas and liquid phases. (Btu/sec/ft2/ OR) h, Overall heat transfer coefficient between the liquid and sorbent phases. (Btu/sec/ft2/ " R) HNG H,, Enthalpy of the noncondensables. Includes SO,, CO,, N,, and 02. (Btu/lbmole) HS H, Henry's law constant for SO2. Based on concentration of SO3-- (SO,-') In liquid phase. Evaluated at sorbent temperature. (atm.ft3/lbmole) HWG H,, Enthalpy of water vapor. (Btu/lbmole) HWL H,, Enthalpy of liquid water. (Btu/lbmole) I(1) Ii Installed cost factor for process unit i. (dimensionless) JG J, Factor for heat or mass transfer for gas phase. (dimensionless)
JL J, Factor for heat or mass transfer for liquid phase. (dimensionless)
KMC k, The pseudo mass transfer coefficient for ~a"in the dissolution zone. Based on liquid phase concentrations. (ft/sec) KMS k,, The mass transfer coefficient for SO2 in flue gas for transport of SO2 to the surface of the water layer. Based on gas phase concentrations. (ft/sec)
KMW k,, The mass transfer coefficient for water in flue gas for transport of water to or from the surface of the water layer. Based on gas phase concentrations. (ft/sec) KTG kt, Thermal conductivity of the gas phase. (Btu/sec/ft/ OR) KTGN kt,,, Thermal conductivity of the noncondensables. (Btu/sec/ft/ OR) KTGW kt,, Thermal conductivity of water vapor. (Btu/sec/ft/ " R) KTL kt, Thermal conductivity of the liquid phase. (Btu/sec/ ft/ " R) KTS kts Thermal conductivity of the solid phase. (Btu/sec/ft/ OR) L L Liquid flow rate. (lbs/min)
L(1) Li Length of process unit i. (it) Conductivity of an ion. LAM Latent heat of vaporization of water. Evaluated at T,. (Btu/lbmole) Length of bed in x direction. (ft) Length of bed in y direction. (ft) Mass of sorbent in process unit i. (lb)
Average number of calls to subroutine DEQTERMS per grid point. (dimensionless) Average molecular weight in the gas phase. (lb/lbmole) Average molecular weight in the liquid phase. (lb/lbmole) MN Molecular weight of noncondensables. (lb/lbmole) MR Mass of reactor vessel. (lb) MUG Viscosity of the gas phase. (lbmole/ft/sec) MUGB Viscosity of the in the bulk. MUG1 Viscosity of the gas at the gas/liquid interface. (lbmole/ft/sec) MUGN Viscosity of the noncondensables. (lbmole/ft/sec) MUGW Viscosity of water vapor. (lbmole/ft/sec) MUL Viscosity of the liquid phase. (lbmole/ft/sec)
MW Molecular weight of water. (lb/lbmole) N Charge on an ion. (coulombs)
N(I) Number of parallel units of type i. (dimensionless) NCS Concentration of calcium ions in the solid. Includes sulfates, sulfites, and carbonates. (lbmole/ft3 of reactor) NBIS Biot number for solid phase. (dimensionless)
NF Number of calls to subroutine DEQTERMS. NG Concentration of gas. Includes noncondensables and water vapor. (lbmole/ft3 of reactor) NFOS N,,, Fourier number for the solid phase. Also a dimensionless time. (dimensionless) NGA N,, Galileo number for the liquid phase. (dimensionless) NNG N,, Concentration of noncondensables in the reactor. (lbmole/ft3 of reactor) NPRG N,,, Prandtl number for the gas phase. (dimensionless) NPRL NPrl Prandtl number forthe liquid phase. (dimensionless) NREG N,,, Reynolds number for the gas phase. (dimensionless) NREL NReI Reynolds number for the liquid phase. (dimensionless) NSCS N,,, Schmidt number for sulfur dioxide in the gas phase. (dimensionless) NSCW Nscw Schmidt number for water in the gas phase. (dimensionless) NSG NSg Concentration of sulfur dioxide in the reactor. (lbmole/ft3 of reactor) NSS NSs Concentration of sulfate or sulfite groups in the reactor. (lbmole/ft3 of reactor) NWG Nu, Concentration of water vapor in the reactor. (lbmole/ft3 of reactor) NWL Nu, Concentration of liquid water in the reactor. (lbmole/ft3 of reactor) P P Total system pressure. (atm)
P(1) Pi Power consumption for unit i. (KW)
PHI @ Sphericity of sorbent. (dimensionless)
PHINW @,, Interaction parameter for the gas phase viscosity correlation. (dimensionless)
PHIWN @,, Interaction parameter for the gas phase viscosity correlation. (dimensionless) PS P, Partial pressure of SO2. (atm) PW P, Vapor pressure of water evaluated at sorbent temperature. (atm) Heat transfer flux. (~tu/sec/ft~) The amount of compressed air required for humidification system. (lbmole/sec) Total volumetric flowrate of flue gas in all parallel units. (ft3/sec) The amount of sorbent required for SO2 removal. (lb/sec) The amount of water required for humidification system. (lbmole/sec) R R Ideal gas constant. (ft3atm/lbmo1e/OR)
RHOC p, The density of the unreacted limestone layer. (lbmole calcium/ft3 of limestone)
RHOG p, The density of the gas phase. (lbmole/ft3 of gas) RHOL p, The density of the liquid phase. Same as Cwl. (lbmole/ft3 of liquid) RHOP p, The density of the precipitate layer. (lbmole calcium/ft3 of precipitate)
RHOS ps The density of the solid phase. Same as Ccs. (lbmole calcium/ft3 of solid) SIGMA a Surface tension. (dynes/cm) T t Time (sec)
TAU(1) ri Holdup time for unit i. (sec) TCW T,, Critical temperature of water. (OR) Temperature of the gas phase. (OR) Temperature of the liquid phase. (OR) Temperature of the solid phase. (OR) Superficial velocity of the gas phase. (ft3 gas/ft2 reactor/sec) Superficial velocity of the liquid phase. (ft3 gas/ft2 reactor sec) Superficial velocity of the solid phase. (ft3 gas/ft2 reactor/sec) V(I) Volume process unit VG v, Velocity of the gas phase. (ft/sec) VL vl Velocity of the liquid phase. (ft/sec)
VREL Vre~ Relative velocity. (ft/sec) VS v, Velocity of the solid phase. (ft/sec)
W(I) Wi Width of process unit i. (ft) X x Horizontal direction. The value is zero at the point where the flue gas enters the bed. Needed only for the case of cross flow reactors. (ft) y Vertical direction. The value is zero at the point where the sorbent phase enters the bed. Note that there may be cocurrent or counter-current flow of flue gas. (ft) YA Y, Absolute humidity. (lbmole water/ft3 dry gas) YAB Y,, Absolute humidity in the bulk. (lbmole water/ft3 dry gas) YAI Yai Absolute humidity at the gas/liquid interface. (lbmole water/ft3 dry gas)
y,, Mole fraction of noncondensables in the gas phase. (dimensionless) YGW y,, Mole fraction of water vapor in the gas phase. (dimensionless) YR Y, Relative humidity.
YRB Y,, Relative humidity in the bulk. YRI Yri Relative humidity at the gas/liquid interface. YS Y, Saturation humidity. YSB Y,, Saturation humidity in the bulk at T,. (lbmole water/ft3 dry gas)
YSI YSi Saturation humidity at the gas/liquid interface at T,. (lbmole water/ft3 dry gas) References Appell, K. W., "A Mathematical Simulation of ETS' Limestone Emission Control Process Using the Method of Characteristics: Fixed Bed Configuration/~as- Phase Mass Transfer Control, It M. S . Thesis, Ohio University, (1989) . Butz, R. J., J. A. Armstrong and T. G. Ebner, "Characterization of the Linear VGA Nozzle for Flue Gas Humidification, Proceedings : Acid Rain Retrofit Seminar: the Effective Use of Lime, pp. 33-50, Philadelphia, PA, (1991). Chan, P. K. and G. T. Rochelle, "Limestone Dissolution - Effects of pH, C02, and Buffers Modeled by Mass Transfer," ACS Symposium Series 188, (1982). Damle, A. S. , "Modeling of SO2 Removal in Spray-Dryer Flue Gas Desulfurization System, Project Summary, EPA/60O/S7-85/038, (1986). Dwivedi, P. N. and S. N. Upadhyay, "Particle - Fluid Mass Transfer in Fixed and Fluidized Beds," Ind. Eng. Chem. Process. Des. Dev., 16, p. 164, (1977). Emmel, T. E., S. D. Piccot and B. A. Laeske, "Ohio / Kentucky / TVA Coal-fired Utility SO2 and NO, Retrofit Study, Project Summary, EPA/600/S7-88/014, (1989). Epstein, M., C. C. Leivo and C. H. Rowland, ttMathematical Models for Pressure Drop, Particulate Removal in Venturi, TCA, and Hydro-fil ter Scrubbers, Proceedings: 2nd International Lime/Limestone Wet Scrubbing Symposium, EPA-APTD-1161 45-114, (1972). Felsvang, K. , B. Brown and R. Horn, ##Dry Scrubbing Experience with Spray Dryer Absorbers in Medium to High Sulfur Service, It Proceedings: Acid Rain Retrofit Seminar: the Effective Use of Lime, Philadelphia, PA, (1991). Foust, A. S., L. A. Wenzel, C. W. Clump, L. Maus and L. B. Andersen, Principles of Unit Operations, znd ed., Wiley, New York, (1980). Gage, C. L. and G. T. Rochelle, "Modeling of SO2 Removal in Slurry Scrubbing as a Function of Limestone Type and Grind," EPRI GS-6307 (1) , (1989). Gullett, B. K. and K. R. Bruce, "Identification of CaS04 Formed by Reaction of CaO and SO2, If Project Summary, EPA/600/S-7-88/024, (1989).
Harriot, P. and M. Kinzey, I1Modeling the Gas and Liquid Phase Resistances in the Dry Scrubbing Process for SO2 Removal, ' 3rd Pittsburgh coal conference, Pittsburgh, PA, pp. 220-236, (1986).
Henzel, D. S., B. A. Laeske, E. 0. Smith and D. 0. Swenson, Handbook for Flue Gas Desulfurization Scrubbing with Limestone, Noyes Data Corp., Park Ridge, CAI (1982).
Hewson, G. W., S. L. Pearce, A. Pollitt and R. L. Rees, If Sulf ur Dioxide Removal from Power Plants, If Soc . Chem. Ind. (London), Chem. Eng. Group, Proc., 15, p. 67, (1933).
Himmelblau, D. M. , I1Basic Principles and Calculations in Chemical Engineering, If sth ed., Prentice-Hall, Englewood Cliffs, NJ, (1989).
Johnson, H. J., llConsideration of Traditional Compliance Options Under the Clean Air Act Amendments of 1990, If Proceedings : Acid Rain Retrofit Seminar: The Effective Use of Lime, Philadelphia, PA, (1991).
Jorgensen, C., J. C. S. Chang and T. G. Brna, "Evaluation of Sorbents and Additives for Dry SOz Remo~al,~l Environ. Prog., 6(2), p. 26, (1987) .
Karlsson, H. T. and J. Klingspor, I1Tentative Modelling of Spray-dry Scrubbing of SO2, If Chemical Eng . Techno1 ., I, 10(2) , p. 104, (1987) .
Keeth, R. J., P. A. Ireland and P. T. Radcliffe, llEconomic Evaluation of 28 FGD Processe~,~~ Proceedings: Acid Rain Retrofit Seminar: the Effective Use of Lime, pp. 33-50, Philadelphia, PA, (1991).
Kim, K. Y. and W. R. Marshall, "Drop-size Distributions from Pneumatic Atomizers," AICHE Journal, vol. 17, (3), p. 575, (1971).
Klingspor, J., H. T. Karlsson and I. Bjerle, "A Kinetic Study of the Dry SO2-Limestone Reaction at Low Temperature, If Chem. Eng. Commun., 22, p. 88, (1983) .
Laeske, B. A. and M. A. Levy, ##MarketShare Estimation of Flue Gas Cleanup and Coal Supply Options," Proceedings : Acid Rain Retrofit Seminar: the Effective Use of Lime, Philadelphia, PA, (1991). Lapidus, L. and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, New York, (1982). Lowell, P. S., D. M. Ottmers Jr., T. I. Strange, K. Schwitzgebel and D. W. DeBerry, "A Theoretical Description of the Limestone Injection Wet Scrubbing Process, PB-193 029, NTIS, Springfield, VA, (1970). Maibodi, M. M., T. L. Pearson, R. M. Counce and W. T. Davis, llSimulation of Spray Dryer Absorber for Removal of SO2 from the Flue Gases, Proceedings: loth Symposium on FGD, EPRI CS-5167 (I), (1987). Maurin, P. G. ,llControlling SO2 Emissions, Plant Engineering, 52, (1985). McCabe, W. L. and J. C. Smith Unit Operations of Chemical Engineering, grd ed., McGraw-Hill, (1976). McIlvaine, R. W., "The 1991 Global Air Pollution Control and Its Relationship to The Solid Waste Industry,,, Journal of the Air & Waste Management Association, 42 (3), (1992). Ozisik, M. N., Heat Transfer, A Basic Approach, McGraw- Hill, New York, (1985).
Perry, R. H., D. W. Green and J. 0. Maloney, Perry's Chemical Engineers , Handbook, 6thed ., McGraw-Hill , New York, (1987). Peters, M. S. and K. D. Timerhaus, Plant Design and Economics for Chemical Engineers, 4th ed ., McGraw- Hill, (1991). Ponder Jr., T. C., L. V. Yerino, V. Katari, Y. Shah and T. W. Devitt , ',Simplified Procedures for Estimating Flue Gas Desul furization System Costs," Environmental Protection Technology Series, EPA- 600/2-76-150, (1976). Prudich, M. E., K. W. Appell, M. J. Visneski, J. D. McKenna, D. A. Furlong, J. C. Mycock, J. F. Szalay and J. E. Wright, "Small Pilot Plant Demonstration of ETS' Limestone Emission Control System," Final Report OCDO Grant no. CDO/R-86-24, (1988). Prudich, M. E., S. N. Reddy and K. W. Appell, "A Pilot Plant Demonstration of the Moving-Bed Limestone Emission Control (LEC) Process, " Proceedings: Acid Rain Retrofit Seminar: the Effective Use of Lime, Philadelphia, PA, (1991). Reddy, S. N., NA Mathematical Simulation of ETS' Limestone Emission Control (LEC) Process using a Moving Bed Configuration, M .S . Thesis, Ohio University, (1991). Reid, R. C. and T. K. Sherwood, The Properties of Gases and Liquids - Their Estimation and Correlation, McGraw-Hill, New York, (1958). Reid, R. C., J. M. Prausnitz and B. E. Poling, The Properties of Gases and Liquids, 5th ed., McGraw- Hill, NY, (1987).
Shale, C. C. and G. W. Stewart, llA New Technique for Dry Removal of SO2,l, znd Symposium on the Transfer and Utilization of Particulate Control Technology, " Denver, CO, (1979). Smith, J. M. and H. C. Van Ness, Introduction to Chemical Engineering Thermodynamics, 3rd* ed ., McGraw-Hill , New York, (1989). Stanley, W. M. , Chemical Process Equipment Selection and Design, Butterworths Series in Chemical Engineering, (1988). Torstrick, R. L., L.J. Henson and S.V. Tomlinson, llEconomic Evaluation Techniques, Results and Computer Modeling for Flue Gas Desul furization, EPA Symposium on Flue Gas Desulfurization, Hollywood, FL, (1977). Tseng, P. C. and G. T. Rochelle, "Dissolution Rate of Calcium Sulfite Hemihydrate in Flue Gas Desulf urization Processes, Environmental Progress, 5, p. 34, (1986). Visneski, M. J., nModeling of the Low Temperature Reaction of Sulfur Dioxide and Limestone Using a Three Resistance Film Theory Instantaneous Reaction Model,,,Ph.D. Dissertation, Ohio University, (1991). Wen, C. Y. and S. Uchida, llSimulationof SO2 Absorption in a Venturi Scrubber by Alkaline Solutionsn, Proceedings : znd International Lime/Limestone Wet Scrubbing Symposium, APTD-1161, (1972).
C************************************************************ C MAIN PROGRAM * C * C ROUTINE NAME : FIX. FOR * C LANGUAGE : FORTRAN 77 * C COMPILER : VAX LANGUAGE SENSITIVE EDITOR * C (VAXLSE), V5.4-2 * C COMPUTER : VAX 6000, MODEL 440 * C FINAL MODIFICATION DATE : APRIL 16, 1992 * C * c************************************************************ C This program simulates the operation of a fixed bed @ configuration, ......
REAL AMG, AHG, CSGO, CWGO REAL DEQA, DEQB, DEQE REAL DP, DT, DT1, DT2, DY REAL EPSS, EPSGO REAL GSGO, GSG, FS, FSA REAL LY, MG, MUG0 INTEGER IT1, IT2, IT3, IV, IY, NF, NT1, NT2, NT3 INTEGER NY, NY1, NY2, NY3 REAL PHI, QGO, REG, RHOS, RHOL REAL SCALE, T, TGO, TLO, UGO, ULO COMMON/COMCONSTANTS/AHGIAMGIDPPEPSS,FSAT,GC~MG~RHOBl $ RHOL,RHOS,SP COMMON /COMINPUT/ NTltNT2,NT3,DT,DTl,DT2, $ NY1,NY2,NY3,DYlNY,SCALE(7) COMMON /COMDEQTERMS/DEQA(7112000)IDEQB(7,12000), $ DEQE(7,12000), NF COMMON /COMMAIN/ PHI(7,12000),RG(12000) COMMON /COMPARA/ EPSGO,TLO,TGO,UGO,CSGO,CWGO,MUGO,RHOGO
C Input the output control paramaters and initial and C boundary values. CALL INPUT(EPSGO,ULO,TLOITGOIUGO,CSGO,CWGO,QGO) C Set counter for number of calls to subroutine DEQTERMS to C zero.
Initialize integral fraction of SO2 removed and time.
FSI = 0.0 T = 0.0 C Set corner point values for dependent variables. PHI (1,l) = EPSGO PHI(2,l) = ULO PHI(3,l) = TLO PHI(4,l) = TGO PHI (5,l) = UGO PHI (6,l) = CSGO PHI (7,l) = CWGO EPSLO = 1 - EPSGO - EPSS c Calculate the transport rate of SO2 per unit cross-section C of the bed at the reactor inlet.
GSGO = CSGO * UGO C Calculate viscosity and density of gas phase at the top of C the bed. CALL MUGFUNC(MUGO,TGO,CWGO) CALL RHOGFUNC (RHOGO,TGO) C Calculate terms in the partial differential equations for C the corner point,
CALL DEQTERMS ( 1)
@ Calculate initial values for dependent variables at each C point down the bed. Calculate terms in the partial C differential equations for each point down the bed.
DO 200 IY = 2,NY DO 80 IV = 1,3 80 PHI (IV,IY) = PHI (IV,IY-1) 200 CALL STEP(4,7,IY) C Output results for the initial condition. CALL OUTl(O,NT2,0.) CALL OUT2(0,0.)
@ Complete numerical solution for all time steps.
C Change the time step size after T is greater than DT1. C This can be done after the point where the feed sorbent has C heated up.
C Update boundary values at y=O for the next time interval. C Then calculate the terms in the DEQfs at the new point, CALL STEP(1,3,f) C Update interior values of the dependent variables down the C bed. Then calculate the terms in the DEQs at the new C point.
DO 500 IY = 2,NY 500 CALL STEP(l,7,IY) C Calculate the fraction of SO2 removed at different C time.
GSG = PHI(5,NY) * PHI(6,NY) FS = (GSGO - GSG) / GSGO C Update the integral of the fraction of SO2 removed and C time,
FSI = FSI + FS * DT T = T + DT C Calculate the average fraction of SO2 removed.
FSA = FSI / T C Stop if the desired average SO2 removal has been reached. C Otherwise go on to the next time step. IF (FSA .LE. FSAT) GO TO 1000 600 CONTINUE
@ Output selected results at the end of each secondary output e time interval. CALL
C Output complete results at the end of each primary output C time interval. CALL C Output results at the end of the simulation. 1000 CALL OUTl(ITl,IT2,T) CALL OUT2 (IT1, T) C Calculate the plant system cost. CALL COSTl(QGO,T,FSA,CA) STOP END e c*********************************************************** C SUBROUTINE STEP C C This subroutine generates new values of the dependent C variables at a single point c***********************************************************
SUBROUTINE STEP(IA,IB,IY,REG) REAL AT, BY, DDD, DEQA, DEQB, DEQE, DPHIO REAL DT, DT1, DT2, DY, EPSL, ET, EY, F1, F2 INTEGER IA, IB, IV, IY, LOOP, MUL, NF INTEGER NT1, NT2, NT3, NY, NY1, NY2, NY3 REAL PHI, PHIT, PHIY, PHIO, PHI1, PHI2, Q REAL REG, SLOPE, TEST, TL, UL
DIMENSION PHI1 (7), PHI2 (7), Fl(7) F2 (7) COMMON /COMCONSTANTS/ AHG,AMG,DP,EPSS,FSAT,GC,MG,RHOB, $ RHOL,RHOS,SP COMMON /COMINPUT/ NT1,NT2,NT3,DTrDT1,DT2, $ NYftNY2,NY3,DY,NY,SCALE(7) COMMON/COMDEQTERMS/DEQA(7,12000),DEQB(7,12000), $ DEQE(7,12000), NF COMMON /COMMAIN/ PHI (7,12000),RG(12000) COMMON /COMSTEP/ PHI0(7),DPHI0(7) COMMON /COMGX/ TEST C Assign dummy variables and calculate intermediate C quantities needed for the predictor step (EulerfsMethod). C Complete the predictor step by calculating the first guess @ for the new point, PHI1.
DO 100 IV = IA,IB AT = DEQA(IV,IY) ET = DEQE(IV,IY) PHIT = PHI(IV,IY) IF( IY .EQ. 1 ) THEN BY = 0 EY = 0 PHIY = 0 ELSE BY = DEQB(IV,IY-1) EY = DEQE(IV,IY-1) PHIY = PHI(IV,IY-1) ENDIF IF( (IV .EQ. 2) .AND. ((ABS(AT*DY+BY*DT) .LT. 1.OE-20) $ .OR. (ABS( (AT+BY)*DT*DY) .LT. 1.OE-20) ) ) THEN PHIO(2) = 0.0 DPHIO(2) = 0.0 ELSE PHIO(1V) = (AT*DY*PHIT+BY*DT*PHIY)/(AT*DY+BY*DT) DPHIO(1V) = (AT*ET+BY*EY)/(AT+BY)*DT*DY/(AT*DY+BY*DT) ENDIF PHII(1V) = PHIO(1V) + DPHIO(1V) 100 CONTINUE
C Set the dependent variables equal to the first guess values C so that the appropriate values will be passed in common.
C Complete a corrector step using the first guess. CALL FPHI(PHI1,F1,IAtIB,IY,REG) IF( TEST .GT. 1. ) GOT0 250
@ If the returned values are close to the first guess, set C the dependent variables equal to the returned values and C return to the main program.
DO 220 IV = IA,IB 220 PHI (IV,IY) = Fl(1V) IF( (PHI(2,IY)) .GT. 0.0 ) THEN UL = PHI(2,IY) TL = PHI(3,IY) CALL EPSLFUNC(EPSL,TL,UL) PHI(1,IY) = 1.0 - EPSL - EPSS ELSE PHI(2,IY) = 0.0 ENDIF IF( (PHI(6,IY)) .LEO 0.0 ) THEN PHI(6,IY) = 0.0 ENDIF RETURN
C If the returned values are not close enough to the first C guess, set the second guess equal to the first returned C values and proceed to the Wegstein search.
C Initialize the loop counter and begin the Westein search.
LOOP = 0 400 LOOP = LOOP + 1 C Set the dependent variables equal to the second guess C values so that the appropriate values will be passed in C common.
C Return to the main program if the maximum number of C Wegstein steps has been exceeded.
IF( LOOP .GT. 20 ) THEN IF( (PHI(2,IY)) .GT. 0.0 ) THEN UL = PHI (2,IY) TL = PHI(3,IY) CALL EPSLFUNC(EPSL,TL,UL) PHI(1,IY) = 1.0 - EPSL - EPSS ELSE PHI(2,IY) = 0.0 ENDIF IF( (PHI(6,IY)) .LT. 0.0 ) THEN PHI(6,IY) = 0.0 ENDIF RETURN ENDIF C Complete a corrector step using the second guess. CALL FPHI(PHI2,F2,IA,IB,IY,REG) IF( TEST .GT. 1. ) GOT0 450 C If the returned values are close to the second guess, C set the dependent variables equal to the returned values C and return to the main program.
DO 420 IV = IA,IB 420 BHI(IV,IY) = F2(IV) IF( (PHI(2,IY)) .GT. 0.0 ) THEN UL = PHI(2,IY) TL = PHI(3,IY) CALL EPSLFUNC(EPSL,TL,UL) PHI(1,IY) = 1.0 - EPSL - EPSS ELSE PHI(2,IY) = 0.0 ENDIF IF( (PHI(6,IY)) .LT. 0.0 ) THEN PHI(6,IY) = 0.0 ENDIF RETURN C If the returned values are not close enough to the second C guess, apply the Wegstein formula to the first and second C guesses and return values to get a new guess. Set the C first guess equal to the previous second guess and the C second guess equal to the new guess. 450 DO 500 IV = IA,IB DDD = PHI2 (IV)-PHI1 (IV) IF( ABS(PHI2 (IV)) .LT. 1.0E-20 ) THEN SLOPE = 0.0 ELSE IF ( ABS (DDD/PHI2(IV) ) .LT. 1. E-4 ) THEN SLOPE = 5.16. ELSE SLOPE = (F2 (IV)-F1 (IV)) /DDD ENDIF IF( SLOPE .GT. 5.16. ) SLOPE = 5.16. IF( SLOPE .LT. -1. ) SLOPE = -1. Q = SLOPE/(SLOPE-1) PHIl(1V) = PHI2(IV) F1 (IV) = F2 (IV) 500 PHI2(IV) = Q*PHI2(IV) + (1-Q)*F2(IV)
C Return to the beginning of the Wegstein loop.
END C c*********************************************************** C SUBROUTINE FPHI C C This subroutine generates and evaluates trial values for C new grid points. c***********************************************************
SUBROUTINE FPHI(PHI,F,IA,IB,IY,REG) REAL DEQA, DEQB, DEQE, DPHI, DPHIO REAL DT, DT1, DT2, DY, ER, F INTEGER IA, IB, IV, IY, NF, NT1, NT2, NT3 INTEGER NY, NY1, NY2, NY3 REAL PHI, PHIO, SCALE, TEST DIMENSION PHI (7),F(7) ,ER(7) COMMON /COMINPUT/ NT1,NT2,NT3,DTfDT1,DT2, $ NY1,NY2,NY3,DYfNY,SCALE(7) C0MM0N/C0MDEQTERMS/DEQA(7,12000),DEQB(7,12000~ $ DEQE(7,12000), NF COMMON /COMSTEP/ PHI0(7),DPHI0(7) COMMON /COMGX/ TEST
C Calculate the terms in the governing partial differential C equations for the current point. CALL DEQTERMS (IY,REG) C Generate a new guess for the dependent variables using the C corrector formula. DO 100 IV = IA,IB IF( (IV .EQ. 2) .AND. (ABS(DEQA(2,IY)*DY+ $ DEQB(2,IY) *DT) .EQ. f.OE-20) ) THEN DPHI = 0.0 ELSE DPHI = DEQE (IV,IY) *DT*DY/ (DEQA(IV,IY) *DY+DEQB (IVr IY)*DT) ENDIF
C Calculate the normalized average change of the dependent C variables for this corrector step.
TEST = 0. DO 200 IV = IA,IB ER(1V) = (PHI(IV) -F (IV)) *SCALE (IV) 200 TEST = TEST + ABS(ER(1V)) TEST = TEST/(IB-IA+l.) C Return to subroutine STEP RETURN END c c*********************************************************** C SUBROUTINE DEQTERMS C C This subroutine calculates the terms in the governing C partial differential equations. @*********************************************************
SUBROUTINE DEQTERMS (IY)
REAL AAA, AHG, AMG, CNG, CPCS, CPG, CPNG, CPWG, CPWL REAL CSG, CWG, CWGI, DEQA, DEQB, DEQE, DP, DSG, DWG REAL EPSG, EPSL, EPSLS, EPSS, GG, GS, GW, HDEL, HG REAL JG, KMC, KMS, KMW, KTG, LAM, MG, MUG, MUL REAL NPRG, NREG, NSCS, NSCW, PHI, PW REAL REG, RHOG, RHOL, RHOS REAL TG, TL, UG, UL INTEGER NF COMMON/COMCONSTANTS/AHG,AMG~DPIEPSS~FSAT~GC~MG~RHOB, $ RHOL,RHOS,SP C0MM0N/C0MDEQTE~S/DEQA(7,12000),DEQB(7~12000), $ DEQE(7,12000), NF COMMON /COMMAIN/ PHI(7,12000),RG(12000) COMMON /COMTRICK/ FP, CCLE, KMC, EPSLS C Translate dependent variables from general to specific C nomenclature. EPSG = PHI (1,IY) UL = PHI(2,IY) TL = PHI(3,IY) TG = PHI(4!IY) UG = PHI(5,IY) CSG = PHI (6,IY) CWG = PHI(7,IY) C Calculate the dependent variables with respect to bed C saturation condition.
IF( (PHI(2,IY)) .GT. 0.0 ) THEN CALL EPSLFUNC(EPSL,TL,UL) EPSG = 1.0 - EPSL - EPSS PHI (1,IY) = EPSG ELSE PHI(2,IY) = 0.0 EPSL = 1.0 - EPSG - EPSS ENDIF
C Calculate physical properties and transport rates. CALL MUGFUNC (MUG,TG ,CWG) CALL RHOGFUNC (RHOG, TG) CALL NREGFUNC(NREG,DP,RHOG,UG,MUG,EPSG) CALL JGFUNC(JG,NREG,EPSG) CALL DSGFUNC(DSG,TG,TL) CALL NSCSFUNC(NSCS,MUG,RHOG,DSG) CALL KMSFUNC(KMS,JG,UG,NSCS) CALL DELLFUNC(DELL,EPSL) CALL HSFUNC (HS, TL) CALL DSLFUNC (DSL,TL) CALL DCLFUNC(DCL,TL) CALLGSFUNC(GSfREG,CSGICWGIDCL,DELLIDSLdEPSLIHSdKMSlTG) CALL DWGFUNC(DWG,TG,TL) CALL NSCWFUNC(NSCW,MUG,RH0GIDWG) CALL KMWFUNC(KMW,JG,UG,NSCW) CALL PWFUNC(PW,TL) CALL CWGIFUNC(CWGI,PW,RHOG) CALL GWFUNC(GW,KMW,AMG,CWGtCWGIIEPSL) CALL CPNGFUNC(CPNG,TG) CALL CPWGFUNC (CPWG, TG) CALL CPGFUNC(CPG,CWG,TG,CPNG,CPWG) CALL KTGFUNC (KTG, TG, CWG) CALL NPRGFUNC(NPRG,MUG,CPG,KTG) CALL HGFUNC(HG,JG,CPG,RHOGdUGINPRG) CALL GGFUNC(GG,HG,AHG,TG,TL) CALL CPCSFUNC(CPCS,TL) CALL CPWLFUNC(CPWL,TL) CALL LAMFUNC (LAM,TL) CALL HDELFUNC(HDEL,LAM,TG,TL) Calculate noncondensables concentration. CNG = RHOG - CWG AAA = CNG*CPNG + CWG*CPWG Calculate the coefficient of the differential equation.
BBB = (0*625*FP*(DP**(-0.715))*(MUL**Oe295)) Calculate terms in the partial differential equations.
DEQA(1,IY) = 1.0 IF( PHI(2,IY) .LE. 0.0000 ) THEN DEQA(2,IY) = 0.0 ELSE DEQA(2, IY) = 1.1978*BBB*EPSL/ (EPSL*UL**(0.455) + $ 1.1978*BBB*UL) ENDIF DEQA(3,IY) = EPSS*RHOS*CPCS + EPSL*RHOL*CPWL DEQA(4,IY) = EPSG*AAA DEQA(5,IY) = 0.0 DEQA(6,IY) = EPSG DEQA(7, IY) = EPSG
DEQB(1,IY) = 0.0 DEQB(2,IY) = 1.0 DEQB(3,IY) = 0.0 DEQB (4,IY) = UG*AAA DEQB(5,IY) = 1.0 DEQB(6,IY) = UG DEQB(7,IY) = UG
DEQE (1,IY) = -GW/RHOL DEQE(2,IY) = GW/RHOL DEQE(3,IY) = GG + GW*HDEL DEQE(4, IY) = -GG DEQE(5,IY) = -GW*(l/RHOG-l/RHOL) - GG/TG/AAA DEQE(6,IY) = -CSG*DEQE(S,IY) - GS + CSG*GW/RHOL DEQE(7,IY) = -CWG*DEQE(S,IY) - GW + CWG*GW/RHOL Note controlling resistance of SO2 removal.
RG(1Y) = REG Increment the counter for the number of calls to this subroutine.
Return to either the main program or the subroutine FPHI. RETURN END e c*********************************************************** C SUBROUTINE INPUT C C his subroutine inputs the step size and convergence C control paramters. It also sets the boundary and initial
C values for dependent variables and constant physical- - C property parameters. c***********************************************************
SUBROUTINE INPUT(EPSGO,ULO,TLO,TGO,UGO~CSGO~CWGOIQGO) REALA, AHG, AMG, CSGO, CWGO REAL DP, DT, DT1, DT2, DY, EPSGO, EPSLO, EPSLS REAL EPSS, FNG, FSAT, FSGO, FWGO, FWGA REAL KMC, LR, MG INTEGER NT1, NT2, NT3, NY, NY1, NY2, NY3 REAL QGO, RHOL, RHOS, SCALE, TGO, TLO REAL UGO, ULO, WR, YR COMMON/COMCONSTANTS/AHG,AMGdDP,EPSS,FSATfGC,MG,RHOB, $ RHOL,RHOS,SP COMMON /COMDIMENS/ LR, WR COMMON /COMINPUT/ NT1,NT2,NT3,DT,DTlfDT2, $ NYl,NY2,NY3,DY,NY,SCALE(7) COMMON /COMCSG/ CSGORI, YR COMMON /COMTRICK/ FP, CCLE, KMC, EPSLS
C Input the flue gas flow rate, relative humidity at the e reactor inlet, average perventage of SO2 removal required, C sorbent particle ize, inlet flue gas temperature and inlet C superficial gas velocity. However, the inlet flue gas C temperature needs to be calculated from the psychrometric C chart following adiabatic cooling line at the selected C approach to saturation. WRITE(*,*) 'INPUT QGO, YR, FSAT, DP, TGO, UGO' READ(*,*) QGO, YR, FSAT, DP, TGO, UGO C Input the gas volume fraction, the inlet liquid superficial C velocity and the temperature of the liquid phase. WRITE(*,*) 'INPUT EPSGO, ULO, TLO' READ(*, *) EPSGO, ULO, TLO C Input the mole fraction of water and SO2 in the flue gas C before humudif ication and length and width of each reactor. WRITE(*,*) 'INPUT XW, XS, LR, WR' READ(*,*) XW, XS, LR, WR Calculate molar flow rate of noncondensables, water and SO2 in the gas phase before addition of water. The factor of 359 converts from SCF to lbmoles. FNG = (1.0 - XW - XS) * QGO / 359. FWGO = XW * QGO / 359. FSGO = XS * QGO / 359. Calculate concentration of water in the gas phase at the reactor inlet.
CALL PWFUNC(PW,TGO) CWGO = YR * PW / (73.02 * TGO) Calculate molar flow rate of water added in the flue gas. FWGA = (FWGO * (1. / (0.7302 * TGO * CWGO) - 1.) - $ FSGO - FNG) / (1. - 1. / (0.7302 * TGO * CWGO)) Calculate total molar flow rate of water in the gas at the reactor inlet.
FWGO = FWGO + FWGA Calculate total molar flow rate of gas at the reactor f nlet.
FGO = FNG + FWGO + FSGO Calculate concentration of SO2 in the gas phase at the reactor inlet.
CSGO = FSGO / FGO / (0.7302*TGO) Calculate total volumetric flowrate of flue gas in actual ft3/sec.
QGO = FGO*0.7302*TGO
Calculate concentration of SO2 in ppm at reactor inlet.
CSGORI = FSGO / FGO*l.E06 Input numerical step size control parameters.
WRITE(*,*) 'INPUT NT1,NT2,NT3,DT,DT1,DT2,NY1,NY2,NY3,DY' READ(*,*) NT1,NT2,NT3,DT,DT1,DT21NY1,NY21NY3,DY Calculate total number of numerical position steps. C Input scaling parameters in logarithmic form.
C Convert scaling parameters to decimal form.
C Open required output files.
C Calculate constant physical properties. CALL RHOSFUNC(RH0S) CALL RHOLFUNC (RHOL) CALL EPSSFUNC(EPSS) CALL AFUNC(A) CALL AMGFTJNC (AMG,A) CALL AHGFUNC(AHG,A) CALL GCFUNC (GC) CALL MGFUNC (MG) CALL RHOBFUNC (RHOB) CALL SPFUNC ( SP) CALL FPFUNC (FP) CALL CCLEFUNC(CCLE) CALL KMCFUNC (KMC) CALL EPSLSFUNC(EPSLS) C Return to main program. RETURN END e c*********************************************************** C SUBROUTINE OUT1 c! 6 This subroutine outputs results showing trends in the t C direction. C***********************************************************
SUBROUTINE OUT1(ITl1IT2,T) REAL DT, DT1, DT2, DY INTEGER IT1, IT2, IV, IY, NT1, NT2, NT3, NY, NY1, NY2, $ NY3 REAL PHI, SCALE, TI Y COMMON /COMINPUT/ NT1,NT2,NT3,DTfDT1,DT2, $ NYlfNY2,NY3,DY,NY,SCALE(7) COMMON /COMMAIN/ PHI(7,12000),RG(12000) a3 Output results for primary position intervals. Report time C in minutes and position in inches. DO 100 IY= ffNY,NY2*NY3 Y = (IY-l)*DY 100 WRITE(1,200) T/60fY*12,(PHI (IV,IY) I IV=lI5), $ PHI(6,IY)*l.OE6,PHI(7,IY)*1.OE6,RG(IY) 200 FORMAT(5X,F8.4,F6.2,F7.4fElO.3,2F8.3,2F7.4fF9.4fF4.l) C Insert a blank line in the output file.
C Return to main program. RETURN END c c*********************************************************** C SUBROUTINE OUT2 C C This subroutine outputs results showing trends in the y C direction along with a set of abbreviated results. c*********************************************************** SUBROUTINE OUT2(ITl,T) REAL DEQA, DEQB, DEQE, DT, DT1, DT2, DY INTEGER IT1, IV, IY, NF, NT1, NT2, NT3, NY, NY1, NY2, $ NY3 REAL PHI, SCALE, T, Y COMMON /COMINPUT/ NTlfNT2,NT3,DT,DT1,DT2, $ NY1,NY2,NY3,DYfNY,SCALE(7) C0MM0N/C0MDEQTEFU4S/DEQA(7,12000),DEQB(7,12000), $ DEQE(7,12000) ,NF COMMON /COMMAIN/ PHI(7,12000),RG(12000)
@ Output results for secondary position intervals. Report C time in minutes and position in inches.
DO 100 IY = lfNYfNY3 Y = (IY-l)*DY 100 WRITE(2,200) T/60,Y*12, (PHI(IV,IY) I IV=l, 5), $ PHI(6,IY)*l.OE6, PHI(7,IY)*l.OE6,RG(IY) 200 FORMAT(5X,F8.4,F6.2,F7.4,ElO.3,2F8.3,2F7.4~F9.4,F4.1) C Insert a blank line in the output file. C Output results for primary position intervals. Report time C in minutes and position in inches.
C Output total number of calls to subroutine DEQTERMS.
@ Return to main program. RETURN END C c********************************************************* e SUBROUTINE COST~(QGO,T,FSA,CA) C C This subroutine calculates the annual fixed bed system C cost. The annual fixed cost has been calculated C considering Depreciation, Interim Replacement, Taxes, @ Insurance and Capital charges. Annual system cost is C summation of total annual fixed cost and operating cost. c***********************************************************
SUBROUTINE COSTl(QGO,T,FSA,CA) REAL AR, C(17), CA, CO, DELTAP, DP REAL EPSGO, EPSS, FE(17), FI(17), G(16), GC, H(16) REAL LR, L(16), M(16), MG, MR, MUG0 REAL N(16), P(17), QA, QGO, QW REAL RHOGO, RHOB REAL SIGMAP, SIGMAC, SP, T, TAU(16) REAL UGO, V(16), W(16), WR INTEGER NR COMMON/COMCONSTmTS/AHGIAMGIDP,EPSS,FSATIGCIMG,RHoBl $ RHOL,RHOS,SP COMMON /COMDIMENS/ LR, WR COMMON /COMINPUT/ NTPfNT2,NT3,DT,DT1,DT2, $ NYl,NY2,NY3,DY,NY,SCALE(7] COMMON /COMMAIN/ PHI (7,12000),RG(12000) COMMON /COMPARA/ EPSGO,TLO,TGO,UGO,CSGO,CWGO,MUGO,RHOGO COMMON /COMCSG/CSGORI, YR
C Assign the values of the dimension of the reactors. Calculate the bed height.
Calculate the pressure drop across the reactor.
DELTAP = UGO/(GC*SP*DP)*(l.O-EPSGO)/EPSGO**3* $ (150.0*(1.0-EPSGO)*MUGO/(SP*DP)+ $ 1.75*RHOGO*MG*UGO) *H(9) *12.0/62.43 Calculate the amount of water required, including water of combustion.
Calculate the amount of compressed air required, by two-fluid atomizer to humidify the flue gas before entering into the reactor units.
Calculate the number of reactor units required, including operating stand-by, to clean the flue gas generated.
Calculate of reactor bed exhaustion time considering that it has been re-wetted 10 times.
Calculate mass flow rate of limestone through the reactor unit.
Calculate limestone transport rate through the conveyor belt which collects the spent sorbent from the reactors and delivers it to a holding bin.
Calculate limestone mass flow rate through the holding bin, screw feeder and regeneration unit. Considering the amount of calcium sulfate formed by reaction of sulfur dioxide with limestone, calculate limestone mass flow rate through the regenerator downstream conveyor belts.
Considering the feed hopper operates 10% of the time, calculate limestone mass flow rate through the feed hopper, downstream screw feeder and conveyor belt.
Calculate of limestone transport rate through the bucket elevator.
Considering the conveyor belt, which transports sorbent from the bucket elevator to the sorbent day tank, operates at the same maximum rate as the bucket elevator, calculate transport rate of limestone through this conveyor.
Considering the flow through the sorbent storage (day) tank is equal to the outflow of the reactors, calculate limestone flow rate through the sorbent storage tank and its downstream units.
Calculate the hold-up time of sorbent storage tank and holding bin.
Calculate the amount of limestone contained in feed hopper.
Calculate the amount of limestone contained in the sorbent storage tank and holding bin. C Calculate the volume of the above mentioned three holding C tanks.
C Estimate length or height of material handling equipment.
C*********************************************************** C *** COST CORRELATIONS *** c***********************************************************
C Calculate cost of belt conveyors.
C Calculate cost of screw conveyors. Calculate cost of tanks.
Calculate cost of regeneration units.
Calculate cost of bucket elevator.
Calculate cost of the reactor units. Calculate total surface area of each of the reactor units.
Calculate mass of each of the reactor units.
Calculate cost of all the reactor units. C Calculate cost of the fan.
c Calculate cost of humidification system.
C************************************************************** e A.** COST OF POWER *** e...... C Calculate power consumption. C Calculate power requirement for the bucket elevator,
C Calculate power requirement for belt conveyors.
C Calculate power requirement of screw feeders.
C Calculation of power requirement for fan.
C Calculate power requirement of the humidification system. C Calculate total power required by different drives.
SIGMAP = ~(2)+~(3)+P(4)+P(5)+P(7)+P(8)+P(lO)+p(12)+ $ P(14) +P(15) +P(16) +P(17)
C Calculate the operating cost, comprised of power, water and C sorbent,
C Output the summary of the run.
WRITE(3, *) SUMMARY OF THE RUN
WRITE (3,*) WRITE(3, *) WRITE(3,ll)DT 11 FORMAT(lXtfTime step. (sec)',T45,E10.2) WRITE (3,12)DY 12 FORMAT(1XIfLength step. (ft)f,T45fE10.2) WRITE(3,13) FSA 13 FORMAT(lXttPercentageof SO2 removed. (%)1tT45fF10.2) WRITE (3,14)IFIX (CSGORI) 14 FORMAT(1XtfS02Conc. at reactor inlet, (ppm)t,T45,110) WRITE (3,101)YR 101 FORMAT(lXtrRelativehumidity at inlet, (%)1,T45,F10.2) WRITE (3,102)TGO 102 FORMAT(lXRfInPetgas temperature. (R)f,T45,F10.2) WRITE(3,103)UGO 103 FORMAT(lX,tInlet superficial gas velocity. (ftls)', $ T45,F10.2) WRITE (3,104)DP 104 FORMAT(lXttSorbentparticle diameter. (ft)f,T45,F10.5) WRITE(3,*) WRITE(3,15)T/60.0 15 FORMAT(lXfrTimeat which bed dried. (min)f,T45RF10.4) WRITE(3,16) (T160.0)*10.O 16 FORMAT(1XPfTimeat which bed exhausted, gmin)f, $ T45,F10.4) WRITE(3,*) WRITE(3,17)E(9) 17 FORMAT (lXt Reactor Length (X-direction). (ft)', $ T47,FlO. 4) WRITE(3,18)H(9) 18 FORMAT(lXtfReactor Depth (Y-direction). (ftlP, $ T47,F10.4) WRITE (3,19)W (9) 19 FORMAT (lX,'Reactor Width (Z-direction). (ft) , $ T47,F10.4) WRITE (3,20)IFIX (QGO) 20 FORMAT(1XIfInput flue gas flow rate. (a~flsec)~, $ T45,IlO) WRITE (3,50)DELTAP 50 FORMAT(1XIfPress. drop. (inch. H20 ~olumn)~,T45,F10.2) WRITE (3,*) WRITE(3,70) 70 FORMAT(1XIfLimestone mass flow rates:') WRITE(3,21)G(l) 21 FORMAT(1XIfFlowratethru Feed Hopper # l.(lb/sec)', $ T45,F10.2) WRITE(3,23)G(4) 23 FORMAT(lX,fFlowrate thru Elevator # 4. (lbl~ec)~, $ T45,F10.2) WRITE(3,25)G(6) 25 FORMAT(1XIfFlowratethru Storage Tank # 6.(lb/sec)', $ T45,F10.2) WRITE(3,26)G(8) 26 FORMAT(lX,'Flowrate thru Belt Conveyor # 8. (lb/sec)', $ T45,F10.2) WRITE(3,27)G(9) 27 FORMAT(1XIfFlowratethru each Reactor # 9. (lbl~ec)~, $ T45,F10.2) WRITE (3,28)N(9) 28 FORMAT(1XIfNumber of Reactor ~nits.~T45,F10.2) WRITE(3,29)G(lO) 29 FORMAT (lX,' Flowrate thru Belt Conveyor # 10. (lblsec) , $ T45,F10e2) WRITE(3,32)G(14) 32 FORMAT(lX, 'Flowrate thru Belt Conveyor # 14. (lblsec)I, $ T45,F10.2) WRITE(3,33)G(15) 33 FORMAT (lX,' Flowrate thru Belt Conveyor # 15. (lblsec)' , $ T45,F10.2) WRITE(3,*) WRITE(3,22) 22 FORMAT(1XIfMassof Sorbent:') WRITE(3,24)M(1) 24 FORMAT(1XIfSorbentinFeedHopper # 1. (lb)',T45,FlO.2) WRITE(3,30)M(6) 30 FORMAT(1XIfSorbent in Storage Tank # 6. (1bIf, $ T45,F10.2) WRITE(3,31)M(9) 31 FORMAT(1XIfSorbent in each Reactor # 9. (lb)'! $ T45,F10.2) WRITE(3,72)M(ll) 72 FORMAT (lX,' Sorbent in Holding Bin # 11. (lb)' , $ T45,F10.2) WRITE (3,*) WRITE(3,34) 34 FORMAT(1XIfPowerRequirements:') WRITE(3,35)P(2) 35 FORMAT(lXffScrewFeeder # 2. (KW)',T44,F10.1) WRITE (3,36)P (3) 36 FORMAT(1XfUBeltConveyor # 3. (KW)f,T44,F10.1) WRITE(3,37)P(4) 37 FORMAT(1XIfBucket Elevator # 4. (KW)f,T44,F10.1) WRITE(3,38) P(5) 38 FORMAT(1XIfBeltConveyor # 5. (KW)f,T44,F10.1) WRITE(3,39) P(7) 39 FORMAT(lXflScrewFeeder # 7. (KW)',T44,F10.1) WRITE(3,40)P(8) 40 FORMAT(1XI1Belt Conveyor # 8. (KW)',T44,F10.1) WRITE(3,41)P(10) 41 FORMAT(1XI1Belt Conveyor # 10. (KW)',T44,F10.1) WRITE(3,42)P(12) 42 FORMAT(lX,fScrew Feeder # 12. (KW)rfT44,F10.1) WRITE(3,44)P(14) 44 FORMAT(1XIfBeltConveyor # 14. (KW)f,T44,F10.1) WRITE(3,45) P(15) 45 FORMAT(1Xf1BeltConveyor # 15. (KW)ffT44,F10.1) WRITE(3,46) P(16) 46 FORMAT(lXffI.D. Fan # 16. (KW)f,T44,Ff0.1) WRITE(3,73)P(17) 73 FORMAT (lX,PHurnidif ication system # 17. (KW) ,T44, F1O.l) WRITE (3,*) WRITE(3,47) SIGMAP 47 FORMAT(1XIfTotaP Power requirement. (KWh)f,T44,F10.1) WRITE (3,*) WRITE(3,48)O.03*SIGMAP*24.0*365.0*O.7/1OOO.O 48 FORMAT(lXflTotal Cost of Power. (K$/Year)',T44,FlO.l) WRITE(3,43)7.4805*1.5*3600.0*24.0*365.0*0.7*QW/3417000.O 43 FORMAT(1XIfTotal cost of Water. (K$/Year)f,T44,F10.1) WRITE(3,49)0.01*G(14)*3600.0*24.0*365.0*0.7/1000.O 49 FORMAT (lX,'Total Cost of Sorbent. (K$/Year) ,T44,F10.1) WRITE (3,*) WR1TE(3,51)C0*24.0*365.0*0.7/1000.0 51 FORMAT (lX, Total Operating Cost. (K$/Year)I, T44, F1O.l) WRITE (3,*) C Calculate total fixed cost.
SIGMAC = 0.0 DO 99 I = 1,17 99 SIGMAC = SIGMAC+C(I) C Output the cost of different equipment. WRITE(3,52)C(l) /1000.O 52 FORMAT(lXffCostof Feed Hopper # 1. (K$)f,T44,F10.1) WRITE(3,53)C(2)/1000.0 53 FORMAT(lXflCost of Screw Feeder # 2. (K$)f,T44,F10.1) WRITE(3,54)C(3)/1000.0 54 FORMAT(lX, 'Cost of Belt Conveyor # 3. (K$) ,T44 ,F10.1) WRITE(3,55)C(4) /1000.O 55 FORMAT(lX, 'Cost of Bucket Elevator # 4. (K$)',T44,F10.1) WRITE(3,56) C(5) /1000.O 56 FORMAT(lX,fCost of Belt Conveyor # 5. (K$)f,T44,F10.1) WRITE(3,57)C(6) /1000.O 57 FORMAT(lXtfCost of Storage Tank # 6. (K$)~,T44,F10.1) WRITE(3,58)C(7) /1000.O 58 FORMAT(lX,'Cost of Screw Feeder # 7. (K$)r,T44,F10.1) WRITE(3,59)C(8)/1000.O 59 FORMAT(lX, 'Cost of Belt Conveyor # 8. (K$) ,T44,F1O.l) WRITE(3,60)C(9) /1000.O 60 FORMAT (lX,'Cost of Reactor Units # 9. (K$)', T44, F1O.l) WRITE(3,61)C(fO) /1000.O 61 FORMAT (lXf'Cost of Belt Conveyor # 10. (K$)' ,T44, F1O.l) WRITE(3,62)C(11)/1000.0 62 FORMAT(1XI1Cost of Holding Bin # 11. (K$)',T44,F10.1) WRITE(3,63)C(12)/1000.O 63 FORMAT(lX,*Cost of Screw Feeder # 12. (K$)f,T44,F10.1) WRITE(3,64)C(13)/1000.0 64 FORMAT (lX,'Cost of Regenerator Units # 13. (K$)I, $ T44,FlO.l) WRITE(3,65)C(14) /1000.O 65 FORMAT(lX, 'Cost of Belt Conveyor # 14. (K$) ,T44,F10.1) WRITE(3,66)C(15) /1000.O 66 FORMAT(lX, 'Cost of Belt Conveyor # 15. (K$) ,T44,F1O.l) WRITE(3,67)C(16)/1000.0 67 FORMAT(lXtfCostof I.D. Fan # 16. (K$)f,T44,F10.1) WRITE(3,74)C(17) /1000.O 74 FORMAT(lX,'Cost of humidification system # 17. (kS)', $ T44,FlO.l) WRITE(3, *) WRITE(3,68)SIGMAC/1000.O 68 FORMAT(lX, 'Total Fixed Cost. (K$) ,~44,F10.1)
C Calculate of annual system cost, K$, which includes C operating cost and annual fixed cost.
C Output system cost of the plant.
WRITE (3,*) WRITE(3,69) CA 69 FORMAT(lX,'SYSTEM COST. (K$/Year)',T44,F10.1)
RETURN END C c*********************************************************** C MAIN PROGRAM * C * C ROUTINE NAME : MOV. FOR * C LANGUAGE : FORTRAN 77 * C COMPILER : VAX LANGUAGE SENSITIVE EDITOR* C (VAXLSE), V5.4-2 * C COMPUTER : VAX 6000, MODEL 440 * C FINAL MODIFICATION DATE : APRIL 17, 1992 * e * c*********************************************************** C This program simulates the operation of a cross flow C moving bed configuration. c***********************************************************
REAL AHG, AMG, CSGO, CWGO REAL DEQA, DEQB, DEQE REAL DP, DX, DY, DY1, DY2 REAL EPSGO, EPSS, FS, FSA, FSAT REAL FSI, GSGO, GSG REAL LX, LY, MUG0 REAL PHI, QGO, RHOL, RHOS, RHOGO REAL SCALE, TGO, TLO, UGO, ULO, VS INTEGER IY1, IY2, IY3, IV, IX, NF, NX, NX1, NX2, NX3 INTEGER NY1, NY2, NY3 COMMON/COMCONSTANTS/ RHOS,RHOL,EPSS,DP,AMG,AHG,VS,FSAT COMMON /COMINPUT/ NX1,NX2,NX3,DX,NY1,NY2dNY31 $ DYfDY1,DY2,NX,SCALE(6) C0MM0N/C0MDEQTERMS/DEQA(6,25000),DEQB(6,25000] , $ DEQE(6,25000),NF COMMON /COMMAIN/ PHI(6,25000),RG(25000) COMMON /COMPARA/ TLO,TGO,UGO,CSGO,CWGO,MUGO,RHOGO C Input output control paramaters and boundary values. CALL INPUT (ULO,TLO,TGO,UGO,CSGOfCWGOIQGO]
C Set counter for number of calls to subroutine DEQTERMS to C zeroo
C Initialize integral fraction of SO2 removed and length in C the y direction.
FSI = 0.0 LY = 0.0 C Set corner point values for dependent variables.
PHI(1,l) = ULO PHI(2,l) = TLO PHI(3,l) = TGO PHI (4,l) = UGO PHI (5,l) = CSGO PHI(6,l) = CWGO EPSGO = 1.0 - PHI(l,l)/VS - 0.543 C Calculate the transport rate of SO2 per unit cross-section C of the bed at the reactor inlet,
GSGO = CSGO * UGO
C Calculate viscosity and density of gas phase at the top of @ the bed, CALL MUGFUNC(MUGO,TGO,CWGO) CALL RHOGFUNC (RHOGO,TGO) C Calculate terms in the partial differential equations for @ the corner point. CALL DEQTERMS (1) e Calculate initial values for dependent variables at each C point across the bed. Calculate terms in differential C equations for each point across the bed.
DO 200 IX = 2,NX DO 80 IV = 1,2 $0 PHI(IV,IX) = PHI(IV,IX-1) 200 CALL STEP(3,6,1XtREG) Output results for the boundary condition. CALL 0UT1(OtNY2,0.) CALL OUT2(0,0.) C Complete numerical solution for all y direction steps.
C Change the length step size after LY is greater than DY1. C This can be done after the point where the feed sorbent has C heated up. C Update boundary values at x=O for the next y direction C interval. Then calculate the terms in the DEQs at the new C point. CALL STEP(1,2,1)
C Update interior values of the dependent variables across C the bed. Then calculate terms in the DEQs at the new C point,
DO 500 IX = 2,NX 500 CALL STEP(1,6,IX) C Calculate the fraction of SO2 removed at different point C inside the bed.
GSG = PHI (4,NX) *PHI (5,NX) FS = (GSGO-GSG)/GSGO C Update the integral of the fraction of SO2 removed and @ length.
FSI = FSI+FS*DY LY = LY+DY C Calculate the average fraction of SO2 removed.
FSA = AAA/LY
C Stop if the desired average SO2 removal has been reached. C Otherwise go on to the next step down the bed. IF (FSA .LE. FSAT) GO TO 1000 600 CONTINUE C Output selected results at the end of each secondary y - C direction output interval. 700 CALL 0UT1(IYltIY2,LY)
C Ouput complete results at the end of each primary y - C direction output interval. 800 CALL OUT2 (IYf,LY) C Output results at the end of the simulation. 1000 CALL OUTl(IYl,IY2,LY) CALL OUT2(IYltLY) @ Calculate the plant system cost. CALL COST2(QGO,EPSGOfLY,FSA,CA) STOP END e c*********************************************************** C SUBROUTINE STEP C 12 his subroutine generates new values of the dependent c variables at a single point. c*********************************************************** SUBROUTINE STEP(IA,IB,IX,REG) REAL AX, BY, DDD, DEQA, DEQB, DEQE, DPHIO REALDX, DY, DY1, DY2, EX, EY, F1, F2 INTEGER IA, IB, IV, IX, LOOP INTEGER NF, NX, NX1, NX2, NX3, NY1, NY2, NY3 REAL PHI, PHIX, PHIY, PHIO, PHI1, PHI2, Q REAL SCALE, SLOPE, TEST DIMENSION PHI1 (6), PHI2 (6), Fl(6) 32(6) COMMON /COMINPUT/ NX1,NX2,NX3,DXfNY1,NY2,NY3, $ DY,DY1,DY2,NX1SCALE(6) COMMON/COMDEQTERMS/DEQA(6,25000),DEQB(6,25OOO), $ DEQE(6,25000),NF COMMON /COMMAIN/ PHI(6,25000),RG(25000) COMMON /COMSTEP/ PHI0(6),DPHI0(6) COMMON /COMFPHI/ TEST
C Assign dummy variables and calculate intermediate C quantities needed for the predictor step (Euler's Method). C Complete the predictor step by calculating the first guess C for the new point, PHI1.
DO 100 IV = IA,IB BY = DEQB(IV, IX) EY = DEQE(IV, IX) PHIY = PHI(IV,IX) IF( IX .EQ. 1 ) THEN AX = 0 EX = 0 PHIX = 0 ELSE AX = DEQA(IV,IX-1) EX = DEQE(IV, IX-1) PHIX = PHI(IV,IX-1) ENDIF PHIO(1V) = (AX*DY*PHIX+BY*DX*PHIY)/(AX*DY+BY*DX) DPHIO (IV) = (AX*EX+BY*EY)/ (=+BY) *DX*DY/ (AX*DY+BY*DX) PHI1 (IV) = PHI0 (IV) + DPHIO (IV) IF (PHIl(1).LT.O.O) PHIl(1) = 0.0 100 CONTINUE
@ Set the dependent variables equal to the first guess values C so that the appropriate values will be passed in common.
C Complete a corrector step using the first guess. CALL FPHI(PHI1,F1,IA,IBfIXfREG) IF( TEST .GT. 1. ) GOT0 250 C If the returned values are close to the first guess, set C the dependent variables equal to the returned values and C return to the main program.
DO 220 IV = IA,IB 220 PHI(IV,IX) = Fl(1V) RETURN C If the returned values are not close enough to the first C guess, set the second guess equal to the first returned C values and proceed to the Wegstein search.
250 DO 300 IV = IA,IB 300 PHI2 (IV) = Fl(IV1 C Initialize the loop counter and begin the Wegstein search.
LOOP = 0 400 LOOP = LOOP + f C Set the dependent variables equal to the second guess C values so that the appropriate values will be passed in C common.
DO 410 IV = IA,IB 410 PHI (IV,IX) = PHI2 (IV) C Return to the main program if the maximum number of C Wegstein steps has been exceeded,
IF ( LOOP .GT. 20 ) RETURN C Complete a corrector step using the second guess. CALL FPHI PHI2,F2, IA,IB, IX, REG) IF ( TEST GT. 1. ) GOT0 450 C If the returned values are close to the second guess, set C the dependent variables equal to the returned values and C return to the main program.
DO 420 IV = IA,IB 420 PHI(IV,IX) = F2(IV) RETURN
C If the returned values are not close enough to the second C guess, apply the Wegstein formula to the first and second C guesses and return values to get a new guess. Set the C first guess equal to the previous second guess and the @ second guess equal to the new guess.
450 DO 500 IV = IA,IB DDD = PHI2 (IV)-PHI1 (IV) IF( ABS(PHI2 (IV) ) .LT. 1.OE-10 ) THEN SLOPE = 0.0 ELSEIF ( ABS (DDDIPHI2 (IV) ) .LT. 1. E-4 ) THEN SLOPE = 5.16. ELSE SLOPE = (F2 (IV)-F1 (IV) ) /DDD ENDIF IF( SLOPE .GT. 5.16. ) SLOPE = 5.16. IF( SLOPE .LT. -1. ) SLOPE = -1. Q = SLOPE/(SLOPE-1) PHIl(1V) = PHI2 (IV) F1 (IV) = F2 (IV) PHI2 (IV) = Q*PHI2 (IV) + (1-Q)*F2 (IV) 500 IF(PHI2 (1) .LT.O.O) PHI2 (1) = 0.0
C Return to the beginning of the Wegstein loop.
END c c*********************************************************** C SUBROUTINE FPHI e- C This subroutine generates and evaluates trial values for C new grid points. c*********************************************************** SUBROUTINE FPHI(PHI,F,IA,IB,IX,REG) REAL DEQA, DEQB, DEQE, DPHI, DPHIO, DX, DY, DY1, DY2 REAL ER, F INTEGER IA, IB, IV, IX INTEGER NF, NX1, NX2, NX, NY1, NY2, NY3 REAL PHI, PHIO, SCALE, TEST DIMENSION PHI(6),F(6),ER(6) COMMON /COMINPUT/ NXl,NX2,NX3,DX,NYl,NY2,NY3, $ DYfDY1,DY2,NX,SCALE(6) COMMON/COMDEQTERMS/DEQA(6,25OOO),DEQB(6,25OOO), $ DEQE(6,25000),NF COMMON /COMSTEP/ PHI0(6),DPHI0(6) COMMON /COMFPHI/ TEST C Calculate the terms in the governing partial differential C equations for the current point. CALL DEQTERMS (IX,REG)
C Generate a new guess for the dependent variables using the C corrector formula.
DO 100 IV = IA,IB DPHI = DEQE (IV,IX) *DX*DY/ (DEQA(IV,IX)*DY+DEQB (IV,IX) *DX) F(1V) = PHIO(1V) + (DPHIO(IV)+DPHI)*0.5 I00 IF (F(l).LT.O.O) F(1) = 0.0
C Calculate the normalized average change of the dependent C variables for this corrector step.
TEST = 0, DO 200 IV = IA,IB ER (IV) = (PHI(IV) -F (IV)) *SCALE (IV) 200 TEST = TEST + ABS(ER(1V)) TEST = TEST/(IB-IA+l.) C Return to subroutine STEP. RETURN END e c*********************************************************** C SUBROUTINE DEQTERMS C C This subroutine calculates the terms in the governing @ partial differential equations. c*********************************************************** SUBROUTINE DEQTERMS(IX,REG)
REAL AAA, AHG, AMG, CNG, CPCS, CPG, CPNG, CPWG, CPWL REAL CSG, CWG, CWGI, DEQA, DEQB, DEQE, DP, DSG, DWG REAL EPSG, EPSL, EPSS, FSAT, GG, GS, GW, HDEL, HG REAL JG, KMS, KMW, KTG, LAM, MUG INTEGER NF REAL NPRG, NREG, NSCS, NSCW, PHI, PW, RHOG, RHOL, RHOS REAL TG, TL, UG, UL, US, VS COMMON /COMCONSTANTS/ RHOS,RHOL,EPSS,DP,AMG,AHG,VS,FSAT COMMON/COMDEQTERMS/DEQA(6,25000)IDEQB(6,25000)l $ DEQE(6,25000) ,NF COMMON /COMMAIN/ PHI (6,25000),RG(25000) C Translate dependent variables from general to specific C nomenclature. UL =PHI(l,IX) IF (UL.LT.O.0) UL = 0.0 TL = PHI (2,IX) TG = PHI (3,IX) UG = PHI (4,IX) CSG = PHI (5,IX) CWG = PHI (6,IX)
C Calculate the liquid and gas volume fractions. CALL EPSLFUNC(EPSL,DELL,TL,UL) EPSG = 1 - EPSL - EPSS
@ Calculate superficial velocity of the bed.
C Calculate physical properties and transport rates. CALL MUGFUNC(MUG,TG,CWG) CALL RHOGFUNC (RHOG,TG) CALL NREGFUNC(NREG,DP,RHOGIUGIMUG,EPSG) CALL JGFUNC (JG, NREG ,EPSG) CALL DSGFUNC(DSG,TG,TL) CALL NSCSFUNC(NSCS,MUG,RHOG,DSG) CALL KMSFUNC(KMS,JG,UG,NSCS) CALL GSFUNC(GS,REG,KMS,AMGICSGdEPSLIDELLITGICWG,TL) CALL DWGFUNC(DWG,TG,TL) CALL NSCWFUNC(NSCW,MUG,RHOG,DWG] CALL KMWFUNC(KMW,JG,UG,NSCW) CALL PWFUNC(PW,TL) CALL CWGIFUNC(CWGI,PW,RHOG) CALL GWFUNC(GW,KMW,AMG,CWGICWGI,EPSL) CALL CPNGFUNC(CPNG,TG) CALL CPWGFUNC (CPWG, TG) CALL CPGFUNC(CPG,CWG,TG,CPNG,CPWG) CALL KTGFUNC(KTG,TG,CWG) CALL NPRGFUNC(NPRG,MUG,CPG,KTG) CALL HGFUNC(HG,JG,CPG,RHOG,UGINPRG) CALL GGFUNC(GG,HG,AHG,TG,TL) CALL CPCSFUNC(CPCS,TL) CALL CPWLFUNC(CPWL) CALL LAMFUNC (LAM,TL) CALL HDELFUNC(HDEL,LAM,TG,TL) C Calculate noncondensables concentration.
CNG = RHOG - me AAA = CNG*CPNG + CWG*CPWG C Calculate terms in the partial differential equations.
DEQA(1,IX) = 0.0 BEQA(2,IX) = 0.0 DEQA(3, IX) = UG*AAA DEQA(4,IX) = 1.0 DEQA (5,IX) = UG DEQA (6,IX) = UG
DEQE(1, IX) = GW/RHOL DEQE(2,IX) = GG + GW*HDEL DEQE(3, IX) = -GG DEQE(4,IX) = -GW/RHOG - GG/TG/AAA DEQE(5, IX) = -CSG*DEQE(4, IX) - GS DEQE(6, IX) = -CWG*DEQE(4, IX) - GW C Note controlling resistance of SO2 removal.
RG(1X) = REG C Increment the counter for the number of calls to this C subroutine.
C Return to either the main program or the subroutine FPHI. RETURN END c c*********************************************************** C SUBROUTINE INPUT c C This subroutine inputs the step size and convergence C control paramters. It also sets the boundary and initial C values for dependent variables......
SUBROUTINE INPUT(ULO,TLO,TGO,UGO~CSGO,CWGO~QGO) REAL AHG, AMG, CSGO, CWGO, CSGORI REAL DP, DX, DY, DY1, DY2 REAL EPSS, FNG, FWGO, FWGA, FSAT, FSGO, GC, MG INTEGER NX1, NX2, NX3, NX, NY1, NY2, NY3 REAL QGO, RHOB, RHOL, RHOS, SCALE REAL TGO, TLO, UGO, ULO, VS, WR, YR COMMON /COMCONSTANTS/ RHOS,RHOL,EPSS,DP,AMG,AHG,VS,FSAT COMMON /COMINPUT/ NX1,NX2,NX3,DX,NY1,NY2tNY31 $ DY,DY1,DY2,NXtSCALE(6) COMMON /COMCOST/ GC,MG,RHOB,SP COMMON /COMCSG/ CSGOR1,YR COMMON /COMDIMENS/ WR Input the flue gas flow rate, relative humudity at the reactor inlet, average percentage of SO2 removal required, sorbent particle size, inlet flue gas temperature and inlet superficial gas velocity. However the inlet flue gas temperature needs to be calculated from the psychrometric chart following adiabatic cooling line at the selected approach to saturation. WRITE(*,*) 'INPUT QGO, YR, FSAT, DP, TGO, UGO' READ(*,*) QGO, YR, FSAT, DP, TGO, UGO Input the bed velocity, the liquid volume fraction, the inlet superficial velocity and the temperature of the liquid phase. WRITE(*,*) 'INPUT VS, ULO, TLOf READ(*,*) VS, ULO, TLO Input the mole fraction of water and SO2 in the flue gas before humidification and width of each reactor, WRITE(*,*) 'INPUT XW, XS, WR' READ(*,*) XW, XS, WR Calculate molar flow rate of noncondensables, water and SO2 in the gas phase before addition of water. The factor of 359 converts from SCF to lbmoles. FNG = (1.0 - XW - XS)*QG0/359. FWGO = XW*QG0/359. FSGO = XS*QG0/359. Calculate concentration of water in the gas phase at the reactor inlet. CALL PWFUNC(PW,TGO) CWGO = YR*PW/ (73.02*TGO) C Calculate molar flow rate of water added in the flue gas. FWGA = (FWGO*(1./ (0.7302*TGO*CWGO) - 1.) - $ FSGO - FNG)/ (1. - f ./ (0.7302*TGO*CWGO) ) C Calculate total molar flow rate of water in the gas at the C reactor inlet.
FWGO = FWGO + FWGA C Calculate total molar flow rate of gas at the reactor C inlet.
FGO = FNG + FWGO + FSGO C Calculate concentration of SO2 in the gas phase at the C reactor inlet.
CSGO = (FSGO/FGO/(0.7302*TGO) )
C Calculate total volumetric flowrate of flue gas in C actual ft3/sec.
QGO = FGO*0.7302*TGO C Calculation of SO2 concentraion in ppm at reactor inlet.
CSGORI = FSGO /FGO*l.E06
C Input numerical step size control parameters. WRITE(*,*) 'INPUT NX1,NX2,NX3,DX,NY1,NY2,NY3,DY,DY1,DY2' READ(*,*) NXl,NX2,NX3,DX,NYl,NY2,NY3,DY,DYl,DY2 C Calculate total number of numerical position steps.
Input scaling parameters in logarithmic form.
WRITE(*, *) ' INPUT SCALE(1) , I = 1'6' READ(*! *) (SCALE(1),I=l, 6)
C Convert scaling parameters to decimal form. C Open required output files.
C Calculate constant physical properties. CALL AFUNC (A) CALL AHGFUNC (AHG, A) CALL AMGFUNC ( AMG ,A) CALL EPSSFUNC (EPSS) CALL GCFUNC (GC) CALL MGFUNC (MG) CALL RHOBFUNC (RHOB) CALL RHOLFUNC (RHOL) CALL RHOSFUNC (RHOS) CALL SPFUNC (SP)
C Return to main program. RETURN END e c*********************************************************** C SUBROUTINE OUT1 C C This subroutine outputs results showing trends in the y C direction. C***********************************************************
SUBROUTINE 0UT1(IYlfIY2,Y) REAL DX, DYfDY1,DY2 INTEGER IYf, IY2, IV, IX, NY1, NY2, NY3 INTEGER NX, NX1, NX2, NX3 REAL PHI, X, Y, LY COMMON /COMINPUT/ NX1,NX2,NX3,DX,NY1,NY21NY3f $ DYfDY1,DY2,NX,SCALE(6) COMMON /COMMAIN/ PHI(6,25000),RG(25000) C Output results for primary position intervals. Report C position in inches. 10 DO 100 IX= l,NX,NX2*NX3 X = (IX-l)*DX 100 WRITE(1,200) X*12 ,Y*12, (PHI(IV, IX) ,IV=l, 4) , $ PHI(5,IX)*l.OE6, PH1(6,IX)*l.OE6,RG(IX) 200 FORMAT(5X,2F8.2,El0.3,2F8.3,3F9.4,F4.1) C Insert a blank line in the output file. C Return to main program. RETURN END C c*********************************************************** C SUBROUTINE OUT2 e C This subroutine outputs results showing trends in the x C direction along with a set of abbreviated results. c*********************************************************** SUBROUTINE OUT2 (IY1, Y) REAL DEQA, DEQB, DEQE, DX, DY, DY1, DY2 REAL PHI, X, Y, ALP, LY INTEGER IY1, IV, IX, NF, NY1, NY2, NY3 INTEGER NXf NX1, NX2, NX3 COMMON /COMINPUT/ NX1,NX2,NX3,DX,NY1,NY2fNY3d $ DY,DYftDY2,NX,SCALE(6) C0MM0N/C0MDEQTERMS/DEQA(6,25000),DEQB(6,25000), $ DEQE(6,25000),NF COMMON /COMMAIN/ PHI(6,25000),RG(25000)
@ Output results for secondary position intervals. Report c position in inches.
10 DO 100 IX = 1,NXtNX3 X = (IX-l)*DX 100 WRITE(2,200) X*12,Y*12, (PHI(IV,IX) , IV=1,4), $ PHI(5~IX)*l~OE6~PHI(6~IX)*1eOE6~RG(IX) 200 FORMAT(5X,2F8.2,E10.3,2F8.313F9.4fF4.1) C Insert a blank line in the output file.
C Output results for primary position intervals. Report C position in inches.
C Output total number of calls to subroutine DEQTERMS. C Return to main program. RETURN END C c*********************************************************** C SUBROUTINE COST2 C C This suroutine calculates the annual moving bed system C cost. The annual fixed cost has been calculated C considering Depreciation, Interim Replacement, Taxes, C Insurance and Capital charges. Annual system cost is C summation of total annual fixed cost and operating cost. C c*************************************************************
SUBROUTINE COST2(QGO,EPSGOILY,FSA,CA) REAL AR, C (17), CA, CO, CSGORI, DELTAP REAL EPSS, FE(16), FI(16), FSAT, G(16), GC, H(16) REAL L(16), LX, LY,M(16), MG, MR, MUG0 REAL N(16), P(17), QA, QW, QGO, RHOB, RHOG REAL SP, SIGMAP, SIGMAC, TAU(16), UGO REAL V(16) ,VS,W(16), WR INTEGER NR COMMON /COMCONSTANTS/ RHOS,RHOL,EPSS,DP,MG,AHG,VS,FSAT COMMON /COMINPUT/ NX1,NX2,NX3,DXfNY1,NY2,NY3, $ DY,DYf,DY2,NX,SCALE(6) COMMON /COMPARA/ TLO,TGO,UGO,CSGO,CWGOfMUGOfRHOGO COMMON /COMCSG/ CSGOR1,YR COMMON /COMCOST/ GC,MG,RHOB,SP COMMON /COMDIMENS/ WR C Assign the values of the dimension of the reactor.
C Calculate length of reactor.
@ Calculation of pressure drop across the reactor.
DELTAP = UGO/(GC*SP*DP)*(l.O-EPSGO)/EPSGO**3*(150.0* $ (I.0-EPSGO) *MUGO/ (SP*DP)+l. 75*RHOGO*MG*UGO) * $ L(9) *12.0/62.43 Calculate amount of water required, including water of combustion.
Calculate the amount of compressed air required, by two fluid atomizer to humidify the flue gas before entering into the reactor units.
Calculate the number of reactor units required, including operating stand-by, to clean the flue gas generated.
NR = (QGOf( (UGO)*W (9)*H (9)) ) +2.0 N(9) = NR Calculate mass flow rate of limestone through the reactor unit.
Calculate limestone transport rate through the conveyor belt which collects the spent sorbent from the reactors and delivers it to a holding bin.
Calculate limestone mass flow rate through the holding bin, screw feeder and regeneration unit.
Considering the amount of calcium sulfate formed by reaction of sulfur dioxide with limestone, calculate limestone mass flow rate through the regenerator downstream conveyor belts.
Considering the feed hopper operates 10% of the time, calculate limestone mass flow rate through the feed hopper, downstream screw feeder, and conveyor belt. C Calculate limestone transport rate through the bucket C elevator.
C Considering the conveyor belt, which transports sorbent C from the bucket elevator to the sorbent day tank, operates C at the same maximum rate as the bucket elevator, calculate C transport rate of limestone through this conveyor.
C Considering the flow through the sorbent storage (day) tank C is equal to the outflow of the reactors, calculate C limestone flow rate through the sorbent storage tank and C its downstream units.
C Calculate the hold-up time of sorbent storage tank and C holding bin.
C Calculate the amount of limestone contained in feed hopper.
C Calculate amount of limestone contained in the sorbent C storage tank and holding bin.
C Calculate the volume of the above mentioned three holding C tanks.
C Estimate length or height of material handling equipment. C*********************************************************** C *** COST CORRELATIONS *** c***********************************************************
C Calculate cost of belt conveyors.
e Calculate cost of screw conveyors.
C Calculate cost of tanks. Calculate cost of regeneration units.
Calculate cost of bucket elevator.
Calculate cost of the reactor units. Calculate total surface area of each.of the reactor units.
Calculate mass of each of the reactor units.
Calculate cost of all the reactor units.
Calculate cost of the fan.
Calculate cost of humidification system. c*********************************************************** C *** COST OF POWER *** c*********************************************************** C Calculate power consumption. C Calculate power requirement for the bucket elevator.
C Calculate power requirement for belt conveyors.
C Calculate power requirement of screw feeders.
C Calculate power requirement for fan.
C Calculate power requirement of the humidification system.
C Calculate total power required by different drives.
C Calculate the operating cost, comprised of power, water and C sorbent,
WRITE(3,*) SUMMARY OF THE RUN I
WRITE(3, *) WRITE (3,*) WRITE(3,ll)DX 11 FORMAT(lX, 'X step. (ft) ,T45,E10.2) WRITE(3,12)DY 12 FORMAT(lX, 'Y step. (ft)',T45,E10.2) WRITE (3'13) FSA 13 FORMAT(lXtfPercentage of SO2 removed. (%)R,T45,F10.2) WRITE (3,14)IFIX (CSGORI) 14 FORMAT(IX, donc. at reactor inlet. (ppm) ,T45,110) WRITE(3,lOl) YR 101 FORMAT (lX,'Relative humidity at inlet. (%)' ,T45,F10.2) WRITE (3,102)TGO 102 FORMAT(lXtfInlet gas temperature. (R)',T45,F10.2) WRITE(3,103)UGO 103 FORMAT(lXtfInlet superficial gas velocity. $ (ftls)',T45,F10.2) WRITE(3,104)VS 104 FORMAT(lXtfSorbentbed velocity. (ft/sec)',T45,E10.2) WRITE(3,105)DP I05 FORMAT (lX,' Sorbent particle diameter. (ft)P, T45, F10.5) WRITE (3,*) WRITE (3,17)L (9) 17 FORMAT(lX,'Reactor Length (X-direction). $ (ft)',T47,F10.4) WRITE(3,18)H(9) 18 FORMAT (lX,' Reactor Depth (Y-direction) . $ (ft)#,T47,F10.4) WRITE(3,19)W(9) 19 FORMAT(lXffReactorWidth (2-direction). $ (ft)' ,T47,F10.4) WRITE(3,20) IFIX(QG0) 20 FORMAT(lX,'Input flue gas flow rate. $ (scf/sec) ,T45,110) WRITE(3,50)DELTAP 50 FORMAT(lXtfPress. drop. (inch. H20 ~olumn)~,T45,F10.2) WRITE (3,*) WRITE(3,YO) 70 FORMAT(lXtfLimestone mass flow rates:') WRITE(3,21) G(l) 21 FORMAT(lXffFlowratethru Feed Hopper # 1. $ (lb/~ec)~~T45,F10.2) WRITE(3,23)G(4) 23 FORMAT(lXtfFlowratethru Elevator # 4. $ (lb/sec)' ,T45,F10.2) WRITE (3'25) G (6) 25 FORMAT(lX,PFlowrate thru Storage Tank # 6. $ (lblsec) ,T45,F10.2) WRITE(3,26)G(8) 26 FORMAT(lX,'Flowrate thru Belt Conveyor # 8. $ (lb/sec)',T45,F10e2) WRITE(3,27)G(9) 27 FORMAT(lXtfFlowratethru each Reactor # 9. $ (lblsec) ,T45,F10.2) WRITE (3,28)N (9) 28 FORMAT(lXttNumberof Reactor ~nits.~T45,F10.2) WRITE(3,29)G(lO] 29 FORMAT(lXttFlowratethru Belt Conveyor # 10. $ (lb/sec) ,T45,F10.2) WRITE(3,32)G(14) 32 FORMAT(lX,tFlowrate thru Belt Conveyor # 14. $ (lb/sec) ,T45,F10.2) WRITE(3,33)G(15) 33 FORMAT(lX,tFlowrate thru Belt Conveyor # 15. $ (lb/~ec)~,T45,F10.2) WRITE (3,*) WRITE (3,22) 22 FORMAT(lXtrMassof Sorbent:') WRITE(3,24)M(l) 24 FORMAT(lXttSorbentin Feed Hopper # 1. (lb)ttT45,F10.2) WRITE(3,30)M(6) 30 FORMAT(lXttSorbentin Storage Tank # 6. $ (lb) ,T45,F10.2) WRITE(3,72)M(11) 72 FORMAT(lX,'Sorbent in Holding Bin # 11. $ (lb)' ,T45,F10.2) WRITE (3,*) WRITE(3,34) 34 FORMAT(lX,fPower Requirements:/) WRITE(3,35) P(2) 35 FORMAT(lX,tScrew Feeder # 2. (KW)f,T44,F10.1) WRITE (3,36)P (3) 36 FORMAT (lXt Belt Conveyor # 3. (KW) ,T44,F1O.l) WRITE(3,37) P(4) 37 FORMAT(lX,fBucket Elevator # 4. (KW)u,T44tF10.1) WRITE (3,38)P (5) 38 FORMAT(lXtfBeltConveyor # 5. (KW)f,T44,F10.1) WRITE (3,39)P (7) 39 FORMAT(lXttScrew Feeder # 7. (KW)ftT44tF10.1) WRITE(3,40)P(8) 40 FORMAT(lXftBelt Conveyor # 8. (KW)t,T44tF10.1) WRITE(3,41)P(10) 41 FORMAT(lX,tBelt Conveyor # 10. (KW)ttT44tF10.1) WRITE(3,42)P(12) 42 FORMAT(lX,tScrew Feeder # 12. (KW)ttT44,F10.1) WRITE(3,44) P(14) 44 FORMAT(lX,tBelt Conveyor # 14. (KW)P,T44,F10.1) WRITE(3,45)P(15) 45 FORMAT(lX,tBelt Conveyor # 15. (KW)f,T44tF10.1) WRITE(3,46) P(16) 46 FORMAT(lX,fI.D. Fan # 16. (KW)t,T44,F10.1) WRITE(3,73) P(17) 73 ~~RMAT(l~,~Humidificationsystem # 17. (KW)',T44,FlO.l) WRITE (3, *) WRITE (3,47)S1GMA.P 47 FORMAT(lX,tTotal Power requirement. (KWh)r,T44tF10.1) WRITE (3,*) WRITE(3,48)O.03*SIGMAP*24.0*365.0*0.7/1OOO.O 48 FORMAT(lXtlTotalCost of Power. (K$/Year)1,T44,F10.1) WRITE(3,43)7.4805*1.5*3600.0*24.0*365.0*0.7*QW/3417000.O 43 FORMAT(lX,'Total Cost of Water. (K$/Year)',T44,FlO.l) WRITE(3,49)O.Ol*G(14)*3600.0*24.0*365.O*O.7/1000.O 49 FORMAT(lX,'Total Cost of Sorbent. (~$/Year)~,T44,F10.1) WRITE (3,*) WRITE(3,51)CO*24.0*365.0*0.7/1OOO.O 51 FORMAT(lXtlTotalOperating Cost. (~$/Year)',T44,FlO.l) WRITE (3,*)
C Calculation of total Fixed Cost.
SIGMAC = 0.0 DO 99 I = 1,17 99 SIGMAC = SIGMAC+C(I)
C Output the cost of different equipment.
WRITE(3,52)C(1)/1000.O 52 FORMAT(lX, 'Cost of Feed Hopper # 1. (K$) ,T44,F10.1) WRITE(3,53)C(2)/1000.O 53 FORMAT(1Xr1Costof Screw Feeder # 2. (K$)',T44,F10.1) WRITE(3,54)C(3)/1000.O 54 FORMAT(lXtlCostof Belt Conveyor # 3. (K$)',T44,F10.1) WRITE (3'55) C (4)/1000.O 55 FORMAT(lX,lCost of Bucket Elevator # 4. (K$)', $ T44, F1O.l) WRITE(3,56)C(5)/1000.0 56 FORMAT (lX,'Cost of Belt Conveyor # 5. (K$)I, T44, F1O.l) WRITE (3,57)C (6)/1000.O 57 FORMAT(lX,tCost of Storage Tank # 6. (K$)r,T44,F10.1) WRITE(3,58)C(7)/1000.O 58 FORMAT(lXrlCost of Screw Feeder # 7. (K$)lfT44,F1O.1) WRITE(3,59)C(8)/1000.O 59 FORMAT (lX,'Cost of Belt Conveyor # 8. (K$) ,T44,F1O.l) WRITE(3,60)C(9)/1OOO.O 60 FORMAT (lX,'Cost of Reactor Units # 9. (K$)I, T44, F1O.l) WRITE (3'61) C (10)/lOOO. 0 61 FORMAT(lX, 'Cost of Belt Conveyor # 10. (K$) ,T44 ,F10.1) WRITE(3,62)C(ll) /1000.O 62 FORMAT(lXtlCost of Holding Bin # 11. (K$)',T44,F10.1) WRITE(3,63)C(12)/1000.0 63 FORMAT(1Xt1Cost of Screw Feeder # 12. (K$)',T44,FlO.l) WRITE(3,64) C(13) /1000.O 64 FORMAT(lXtlCostof Regenerator Units # 13. (K$)', $ T44, F1O.l) WRITE(3,65)C(14) f1000.O 65 FORMAT(lX, 'Cost of Belt Conveyor # 14. (K$) ,T44,F10.1) WRITE(3,66)C(15) /1000.O 66 FORMAT (lX,'Cost of Belt Conveyor # 15. (K$) ,T44, F1O.l) WRITE(3,67) C(16) /1000.O 67 FORMAT(lX, 'Cost of I.D. Fan # 16. (K$) ,T44,F10.1) WRITE(3,74)C(17) /1000.O 74 FORMAT(lX,fCost of humidification system # 17, $ (K$)',T44,F1Oe1) WRITE (3,*) WR1TE(3,68)S1GMAC/1000.0 68 FORMAT(lX, 'Total Fixed Cost. (K$) ,T44,F10.1) C Calculate annual system cost, K$, which includes operating C cost and annual fixed cost.
WRITE(3, *) WRITE(3,69)CA 69 FORMAT(lXlfSYSTEMCOST. (~$/Year)~,T44,FfO.l) RETURN END c! SUBROUTINES C SUBROUTINES * C***********************************************************
C SUBROUTINE AFUNC C C This subroutine calculates the geometric surface area. C***********************************************************
SUBROUTINE AFUNC (A) REAL A COMMON /cOMCONSTANTS/ RHOS,RHOL, EPSS, DP, AMG, AHG, VSl FSAT
RETURN END C C*********************************************************** C SUBROUTINE AHGFUNC C C This subroutine calculates the gas/liquid heat transfer C area. C***********************************************************
SUBROUTINE AHGFUNC (AHG,A) REAL A, AHG
AHG = A RETURN END C C*********************************************************** C SUBROUTINE AHLFUNC C C This subroutine calculates the liquid/solid heat transfer C area. C***********************************************************
SUBROUTINE AHLFUNC (AHL,A) REAL A, AHL AHL = A RETURN END e c************************************************************* C SUBROUTINE AMGFUNC e C This subroutine calculates the gas phase mass transfer @ area. c***********************************************************
SUBROUTINE AMGFUNC(AMG,A) REAL A, AMG
RETURN END e c*********************************************************** C SUBROUTINE AMLFUNC C e This subroutine calculates the liquid phase mass transfer @ area. c************************************************************ SUBROUTINE AMLFUNC (AML,A)
AML = A RETURN END
C SUBROUTINE AMPFUNC e C This subroutine calculates the precipitate layer mass C transfer area. C***A***************f*********************************f****
SUBROUTINE AMPFUNC(AMP,A) REAL A, AMP AMP = A RETURN END C c*********************************************************** C SUBROUTINE AMSFUNC C C This subroutine calculates the unreacted sorbent surface C mass transfer area. c***********************************************************
SUBROUTINE AMSFUNC (AMS,A) REAL A, AMS
AMS = A RETURN END c c************************************************************* C SUBROUTINE CCLEFUNC e C This subroutine calculates the equilibrium concentration C of limestone in water......
SUBROUTINE CCLEFUNC(CCLE) REAL CCLE
CCLE = 3.744E-06 RETURN END e c********************************************************* e SUBROUTINE CPCSFUNC C C This subroutine calculates the heat capacity of sorbent......
SUBROUTINE CPCSFUNC(CPCS,TL) REAL CPCS, TL CPCS = 0.024749*TL+6.314764 RETURN END C c*********************************************************** C SUBROUTINE CPG C C This subroutine calculates the heat capacity of the gas C phase......
SUBROUTINE CPGFUNC(CPG,CWG,TG,CPNG,CPWG) REAL CPG, CPNG, CPWG, CWG, TG, YGW
RETURN END e c*********************************************************** C SUBROUTINE CPNGFUNC C C This subroutine calculates the heat capacity of C noncondensables. c***********************************************************
SUBROUTINE CPNGFUNC(CPNG,TG) REAL CPNG, TG
CPNG = 6.713+2.609E-04*TG+3.54E-07*TG**2-8.052E-ll*TG**3 RETURN END C c*********************************************************** C SUBROUTINE CPWGFUNC c C This subroutine calculates the heat capacity of water C vapor. c*********************************************************** SUBROUTINE CPWGFUNC(CPWG,TG) REAL CPWG
CPWG = 7.3 + 1.3667E-03*TG RETURN END e ...... C SUBROUTINE CPWLFUNC C C This subroutine calculates the heat capacity of liquid C water. c***********************************************************
SUBROUTINE CPWLFUNC(CPWL) REAL CPWL
CPWL = 18.0 RETURN END C c*********************************************************** C SUBROUTINE CWGIFUNC C C This subroutine calculates the concentration of water at C the gaslliquid interface. c***********************************************************
SUBROUTINE CWGIFUNC(CWGI,PW,RHOG) REAL CWGI, PW, RHOG
RETURN END C C SUBROUTINE DCLFUNC C c This subroutine calculates the diffusivity of calcium ions C in the liquid phase. c*********************************************************** SUBROUTINE DCLFUNC(DCL,TL) REAL DCL, TL
DCL = 1.5851976E-ll*TL RETURN END C c*********************************************************** C SUBROUTINE DELLFUNC e @ This subroutine calculates water layer thickness. c***********************************************************
SUBROUTINE DELLFUNC(DELL,EPSL) REAL AHG, DELL, EPSL, MG
DELL = EPSL/AHG RETURN END c! C*********************************************************** C SUBROUTINE DSGFUNC C C This subroutine calculates the diffusivity of SO2 in the C gas phase. c******************************************************
SUBROUTINE DSGFUNC(DSG,TG,TL) REAL DSG, TG, TL DSG = 2.24678E-07*(TG+TL)-9.2172E-05 RETURN END 6 ...... C SUBROUTINE DSLFUNC C C This subroutine calculates the diffusivity of SO2 in the C Piquid phase. c***********************************************************
SUBROUTINE DSLFUNC(DSL,TL) REAL DSL, TL
DSL = 3.411633E-ll*TL RETURN END c c************************************************************ C SUBROUTINE DWGFUNC e C This subroutine calculates the diffusivity of H20 in the C gas phase. c***********************************************************
SUBROUTINE DWGFUNC(DWG,TG,TL) REAL DWG, TG, TL
DWG = 4.18957E-7*(TG+TL)-1.71873E-4 RETURN END C c*********************************************************** C SUBROUTINE EPSLFUNC C C This subroutine calculates the liquid phase volume C fraction. c***********************************************************
SUBROUTINE EPSLFUNC(EPSL,DELL,TL,UL) REAL EPSL, EPSLS, DELUL,DP REAL MUL, NREL, RHOL, TL EPSLS = 0.0632 ULMX = EPSLS*VS
C Calculate the liquid phase Reynolds number if the water in C the bed is more than the saturation amount.
IF( UL. GT. ULMX ) THEN DELUL = UL - ULMX C Calculate liquid phase viscosity.
C Calculate liquid phase Reynolds number.
NREL = DP*DELUL*RHOL/MUL
@ Calculate the packing factor of the reactor bed unit.
C Calculate the total hold up of the bed which is the sum C of the static hold up and the dynamic hold up of the bed.
EPSL = EPSLS+0.32*FP*DP**(-1.26)*(0.0830079*NREL**7 $ -0.875204*NREL**6+3.71383*NREL**5-8.11901* $ NREL**4+9.74891*NREL**3-6.46261*NREL**2+ $ 2.85311*NREL+0.058944)*(4.57136E-5*MUL+ $ 2.065213-5) ELSE C If the amount of water in the bed is less than that needed C to saturate the bed then the hold up is calculated by C equating the actual velocity of the bed to the actual C velocity of the water.
EPSL = UL/VS ENDIF
C Calculate water layer thickness.
DELL = EPSL/AMG RETURN END C C*********************************************************** C SUBROUTINE EPSLS c C This subroutine calculates the static hold up of the bed. c***********************************************************
SUBROUTINE EPSLSFUNC(EPSLS) REAL EPSLS
EPSLS = 0.0632 RETURN END e c************************************************************ C SUBROUTINE EPSSFUNC C C This subroutine calculates the solid phase volume fraction. c*************************************************************
SUBROUTINE EPSSFUNC(EPSS) REAL EPSS C EPSS is the fraction of the bed occupied by solid. @ (dimensionless)
EPSS = 0.543 RETURN END C c*********************************************************** @ SUBROUTINE FPFUNC e C This subroutine calculates the packing factor of the bed. c***********************************************************
SUBROUTINE FPFUNC(FP)
REAL AHG, AMG, DP, EPSLS, EPSS, FP, FSAT REAL GC, MG, RHOB, RHOL, RHOS, SP RETURN END C c*********************************************************** C SUBROUTINE GCFUNC C C This subroutine calculates the acceleration due to gravity. c**********************************************************,*
SUBROUTINE GC FUNC(GC)
REAL GC
RETURN END e c*********************************************************** C SUBROUTINE GGFUNC e C This subroutine calculates the gaslliquid heat transport C rate. c***********************************************************
SUBROUTINE GGFUNC(GG,HG,AHG,TG,TL) REAL AHG, GG, HG, TG, TL
GG = HG * AHG * (TG - TL) RETURN END c c************************************************************* C SUBROUTINE GLFUNC e C This subroutine calculates the liquid/solid heat transport C rate. c*********************************************************** SUBROUTINE GLFUNC(GL,HL,AHL,TL,TS) REAL AHL, GL, HL, TL, TS GL = HL * AHL * (TL - TS) RETURN END c c************************************************************* C SUBROUTINE GSFUNC C C This subroutine calculates the sulfur dioxide transport C rate.
REAL AMG, CCLE, CSG, CWG REAL DCL, DSL, DELL, DELR REAL EPSL, HS, KMC, KMS REAL R, TG, TL, YGW
C Calculate the location of the reaction front.
R = 0.7302 YGW = R*CWG*TG IF( EPSL .LE. 0.0 .OR. CSG .LE. 0.0 ) THEN GS = 0.0 REG = 0.0 RETURN ELSE KMC = f.6256E-03 CCLE = 3.7443-6 HS = 0.00238961*TL**2-2.39879*TL+610.467 CALL DCLFUNC(DCL,TL) CALL DSLFUNC(DSL,TL)
DELR = (DELL+DCL/KMC-CCLE*DCL/CSG/KMS/ $ (1.0-YGW))/(l.O+CCLE*DCL*HS/CSG/ $ (1.0-YGW) /R/TG/DSL) C If DELR is less than zero, then the reaction is gas phase C diffusion controlled.
IF( DELR .LE. 0.0 ) THEN GS = KMS*AMG*CSG REG = 1.0 RETURN C If DELR is greater than or equal to the water layer C thickness then the reaction is solid dissolution rate C controlled. ELSE IF ( DELR .GE. DELL ) THEN GS = KMC*CCLE*AMG REG = 2.0 RETURN C If DELR is greater than zero and less than the water layer C thickness then the reaction is controlled by the both C rates. ELSE GS = (( CSG*R*TG/HS+CCLE*DCL/DSL)/(R*TG/KMS/ $ HS+DELL/DSL+DCL/KMC/DSL))*AMG REG = 3.0 RETURN ENDIF ENDIF END C c*********************************************************** e SUBROUTINE GWFUNC C e This subroutine calculates the water transport rate. c****+******************************************************
SUBROUTINE GWFUNC(GW,KMWfAMG,CWGICWGI,EPSL) REAL AMG, CWG, CWGI, EPSL, GW, KMW
GW = KMW * AMG * (CWG - CWGI) IF( EPSL .LE. 0.0 .AND. GW .LT. 0. ) GW = 0.0 RETURN END c ...... C SUBROUTINE HDELFUNC C C This subroutine calculates the enthalpy difference between C liquid water at the liquid temperature and water vapor at the gas temperature. c***********************************************************
SUBROUTINE HDELFUNC(HDEL,LAM,TG,TL) REAL HDEL, LAM, TG, TL HDEL= LAM+8.202022* (TG-TL) RETURN END C c*********************************************************** e SUBROUTINE HGFUNC C C This subroutine calculates the gaslliquid heat transfer e coefficient. C***********************************************************
SUBROUTINE HGFUNC(HG,JG,CPG,RHOG,UG,NPRG) REAL CPG, HG, JG, NPRG, UG
RETURN END e c*********************************************************** C SUBROUTINE HSFUNC c C This subroutine calculates the Henry's law constant for C sulfur dioxide. c*********************************************************** SUBROUTINE HSFUNC(HS,TL) REAL HS, TL
RETURN END c c*********************************************************** C SUBROUTINE JGFUNC C C This subroutine calculates the coulburn j-factor for heat C and mass transfer in the gas phase. c*********************************************************** SUBROUTINE JGFUNC(JG,NREG,EPSG) REAL EPSG, JG, NREG RETURN END C c*********************************************************** C SUBROUTINE KMCFUNC c C This subroutine calculates the pseudo mass transfer C coefficient for Ca - ions in the dissolution zone. C***********************************************************
SUBROUTINE KMCFUNC (KMC) REAL KMC
KMC = 1.62563-03 RETURN END C C*********************************************************** C SUBROUTINE KMSFUNC e C This subroutine calculates the sulfur dioxide mass transfer C coefficient. c*********************************************************** SUBROUTINE KMSFUNC(KMS,JG,UG,NSCS) REAL JG, KMS, NSCS, UG
KMS = JG*UG/(O.603776*NSCS+O.404978) RETURN END C c************************************************************* C SUBROUTINE KMWFUNC C C! This subroutine calculates the water vapor mass transfer C coefficient. c*********************************************************** SUBROUTINE KMWFUNC(KMW,JG,UG,NSCW)
REAL JG, KMW, NSCW, UG
RETURN END C C*********************************************************** e SUBROUTINE KTGFUNC 6 C This subroutine calculates the gas phase thermal C conductivity. C***********************************************************
SUBROUTINE KTGFUNC (KTG, TG ,CWG) REAL ANW, AWN, CWG, KTG, KTGN, KTGW, TG, YGN, YGW
KTGN = 6.2407E-07+6.6358E-09*TG KTGW = 1.4702E-06+4.4643E-09*TG AWN = 1.009553 ANW = 1.107273 YGW = 0.7302*CWG*TG YGN = 1.0-YGW KTG = YGW*KTGW/(YGW+YGN*AWN)+(YGN*KTGN)/(YGN+YGW*ANW) RETURN END e c*********************************************************** C SUBROUTINE LAMFUNC e C This subroutine calculates the latent heat of vaporization C of water. c***********************************************************
SUBROUTINE LAMFUNC(LAM,TL) REAL LAM, TL
LAM = -12.2565*TL+25602.8 RETURN END e ...... C SUBROUTINE MGFUNC e C Thsi subroutine calculates molecular weight of the gas. C***********************************************************
SUBROUTINE MGFUNC (MG) REAL MG
RETURN END e ...... C SUBROUTINE MUGFUNC e e Thfs subroutine calculates the gas phase viscosity......
SUBROUTINE MUGFUNC(MUG,TG,CWG) REAL CWG, MUG, MUGN, MUGW, PHINW, PHIWN, TG, YGN, YGW
YGW = 0.7302*CWG*TG YGN = 1.0-YGW MUGW = 8.0649E-10*TG-7.85993-8 MUGN = 5.1777E-10*TG+le53943E-7 PHIWN = 4.73325E-4*TG+0.883549 PHINW = -3.05792E-4*TG+1.0178 MUG=MUGW/(l.O+YGN/YGW*PHIWN)+MUGN/(l.O+YGW/YGN*PHINW) RETURN END C c*********************************************************** C SUBROUTINE MULFUNC e C Thfs subroutine calculates the liquid phase viscosity. c***********************************************************
SUBROUTINE MULFUNC(MUL,TL)
REAL MUL, TL MUL = -1.0346I.E-l1*TL**3+f098974E-8*TL**2- $ 1.28379E-5*TL+0.00279162 RETURN END C c*********************************************************** C SUBROUTINE NPRGFUNC e C This subroutine calculates the gas phase Prandtl number. C***********************************************************
SUBROUTINE NPRGFUNC(NPRG,MUG,CPe,KTG) REAL CPG, KTG, MUG, NPRG
NPRG = (MUG*CPG)/KTG RETURN END C c*********************************************************** C SUBROUTINE NREGFUNC e C This subroutine calculates the gas phase Reynolds number. c***********************************************************
SUBROUTINE NREGFUNC(NREG,DP,RHOG,UGtMUGIEPSG)
RETURN END e c*********************************************************** C SUBROUTINE NSCSFUNC eR C This subroutine calculates the Schmidt number for sulfur e dioxide. c***********************************************************
SUBROUTINE NSCSFUNC(NSCS,MUG,RHOG,DSG) REAL DSG, MUG, NSCS, RHOG NSCS = MUG/ (RHOG*DSG) RETURN END C c*********************************************************** C SUBROUTINE NSCWFUNC C C This subroutine calculates the Schmidt number for water C vapor. c***********************************************************
SUBROUTINE NSCWFUNC(NSCW,MUG,RHOGIDWG)
REAL DWG, MUG, NSCW, RHOG
NSCW = MUG/ (RHOG*DWG) RETURN END e C*********************************************************** C SUBROUTINE PWFUNC c C This subroutine calculates the water vapor pressure. C***********************************************************
SUBROUTINE PWFUNC(PW,TL) REAL PW, TL
RETURN END C c***********************************+*********************** e SUBROUTINE RHOBFUNC C C This subroutine calculates bulk density of the sorbent. C***********************************************************
SUBROUTINE RHOBFUNC(RH0B) REAL RHOB RHOB = 169.3 RETURN END C c*********************************************************** C SUBROUTINE RHOCFUNC C C This subroutine calculates the density of the unreacted C limestone layer. c***********************************************************
SUBROUTINE RHOCFUNC (RHOC) REAL RHOC
RHOC = 4.23 RETURN END C c*********************************************************** C SUBROUTINE RHOGFUNC e C This subroutine calculates the density of the gas phase. c***********************************************************
SUBROUTINE RHOGFUNC(RHOG,TG) REAL RHOG, TG
RHOG = 1.3697/TG RETURN END c c************************************************************* C SUBROUTINE RHOLFUNC m C; C This subroutine calculates the density of the liquid phase. c*************************************************************
SUBROUTINE RHOLFUNC (RHOL) REAL RHOL RHOL = 3.417 RETURN END e c*********************************************************** C SUBROUTINE RHOPFUNC C C his subroutine calculates the density of the precipitate @***********************************************************C layer. SUBROUTINE RHOPFUNC(RH0P) REAL RHOP
RHOP = 4.647 RETURN END
C SUBROUTINE RHOSFUNC C C This subroutine calculates the density of the solid phase. c***********************************************************
SUBROUTINE RHOSFUNC (RHOS) REAL RHOS c***********************************************************
RHOS = 4.6 RETURN END e c*********************************************************** C SUBROUTINE SPFUNC(SP) C C This subroutine calculates the sphericity of the sorbent C particles......
SUBROUTINE SPFUNC (SP) REAL SP RETURN END C
TRANSPORT AND PHYSICAL PROPERTY CORRELATIONS
TRANSPORT RATE EXPRESSIONS
Sulfur f Dioxide) Trans~ortRate (9,) A resistance in series model is being used to estimate the reaction rate or equivalently the sulfur (dioxide) transport rate. The chemical reaction is assumed to occur instantaneously at the reaction front. Possible resistances include diffusion across the gas phase boundary layer, through the liquid layer, and the dissolution of solid calcium ions. The dissolution process is modeled using a mass transfer coefficient, hc. In order to determine the transport rate we must first assume a location for the reaction front, 6,, within either the liquid layer or precipitate layer and then calculate the position of the reaction front from a solution of the appropriate set of algebraic equations shown below. If the assumed position proves to be incorrect then the location may have to recalculated assuming that the other layer controls. For example if the reaction front is assumed to be in the liquid layer and the calculated position is deeper than the liquid layer thickness then the position must be recalculated assuming the reaction front is within the precipitate layer. This is caused by the fact that there are two possible controlling resistance positions deeper than the liquid layer. Once the position of the reaction front is known the transport rate can be back-calculated from the equations below. For the case of gas layer diffusion control or the transport rate is calculated from
For the case of liquid layer diffusion control or
For the case of dissolution control or 6i+Jp < 6, we have
Water Transport Rate (gw) A mass transfer coefficient based upon the gas side driving force is used to correlate the water mass transfer rate.
9, = %w%g ( Cwg-Cwgi ) GasILi~uidHeat Transport Rate (gg) Newton's law of cooling is used to correlate the heat transfer rate between the liquid and gas phases.
Eiauid/Solid Heat Transport Rate (gl) Newton's law of cooling is used to correlate the heat transfer rate between the liquid and solid phases.
TRANSPORT COEFFICIENTS GasILiauid Heat Transfer Coefficient (hg) The vapor phase heat transfer coefficient is obtained using Colburn j-factor (Dwivedi and Upadhyay, 1977) as follows :
The computational requirements for this correlation can be simplified by replacing N~~~~/~.
The accuracy of this approximation has been checked for the values of Npr between 0.7 and 1.15. This range corresponds to a temperazure range of 520 to 620 OR. The simplified correlation is then Calcium Pseudo-Mass Transfer Coefficient: (hC) The mass transfer coefficient for limestone dissolution has been considered to be constant (Visneski, 1991). The assumed value is given as
Sulfur Dioxide Mass Transfer coefficient (hS) The following form is reported (Foust et al., 1980)
The computational requirements for this correlation can be simplified by replacing N~~~~/~.
The accuracy of this approximation has been determined for values of Nscs between 1.125 and 1.6. This range corresponds to a temperature range of 520 to 670 OR. The simplified correlation is then
kms " Jg"g 0.603776Nscs + 0.404978
Water VaDor Mass Transfer Coefficient (hw) The following form is reported (Foust et a1.,1980).
The computational requirements for this correlation can be simplified by replacing N~~~~/~~
The accuracy of this approximation has been tested for values of Nscw between 0.60 and 0.85. This range corresponds to a temperature range of 520 to 670 OR. The simplified correlation is then
kmw " Jg"g 0.743154Nscw + 0.267317 TRANSPORT ANALOGY PARAMETERB Colburn i Factor for Heat and Mass Transfer in the Gas Phase ( Jg) The following correlation is valid over the range
Dwivedi and Upadhyay (1977) studied particle-fluid mass transfer in fixed beds and fluidized beds for different gases and liquids. They concluded after an iterative least-square study that the mass transfer factor is inversely proportional to the bed voidage and that gas and liquid phase data can be best presented as
The computational requirements for this correlation can be simplified by replacing the numerator in the expression with a polynomial.
The accuracy of this approximation for values of NReg between 150 and 290 which corresponds to a temperature range of 520 to 770 OR.
DIMENSIONLESS TRANSPORT GROUPS
Gas Phase Prandtl Number (Nprg) By definition Gas Phase Revnolds Number (NReg) McCune and Wilhelm (1988) introducedthe following equation to correlate packed bed data
Liauid Phase Revnolds Number (NRel) By definition
Schmidt Number for Sulfur Dioxide (Nscs) By definition
Schmidt Number for Water Va~or(NScW) By definition
Diffusivitv of Calcium Ions in the Liauid Phase (Dcl) At infinite dilution, ionic diffusivities are calculated as (Dwivedi and Upadhyay, 1977)
where 1, and n are the equivalent ionic conductivity and charge on the ion respectively, and Fa is the Faraday number. Liquid diffusivities at a particular temperature can be estimated using the Stokes-Einstein (Dwivedi et al., 1977) relationship
Using a value of 85.035 ft2/sec for the diffusivity of ~a++at 298OK (Foust et al., 1980) in the Stokes-Einstein relationship gives
Diffusivitv of Sulfur Dioxide in the Gas Phase (Dsg) Gilliland (Reid and Sherwood, 1953) adopted the concept of rigid spherical molecules undergoing elastic collisions and empirically correlated the diffusion coefficient of a binary gas system at low pressure as
where Dg is the diffusivity of binary gas system, M1 and M2 are molecular weights, and Vbl and Vb2 are atomic volumes of the two species under consideration. Considering the pressure of the system to be constant, the equation can be written as
The diffusivity of a binary system evaluated at a particular temperature can be expressed, relative to a reference temperature and reference diffusion coefficient, as
In this correlation flue gas is modeled as air. Considering a diffusion coefficient for an S02/air system at 273 OK and 1.0 atmosphere of 0.122 cm2 /sec. (Foust et al., 1980), the diffusivity for the S02/gas system is
The simplified correlation is then Diffusivitv of Sulfur Dioxide in the Liauid Phase (Dsl) Following the method used for Dcl and using a value of 114.097 ft2/sec at 298OK (Dwivedi and Upadhyay, 1977) in the Stokes- Einstein relationship gives
Diffusivitv of Water Vapor (Dwg)
The same method as used for DSg is used here. Considering a diffusion coefficient for a waterlair system at 298OK and 1.0 atmosphere of 0.260 cm2/sec (Reid et al., 1958), the diffusivity for the water/gas system is
The simplified correlation is then
DENSITIES Densitv of the Unreacted Limestone Laver (p,) Chan and Rochelle (1982) calculated the molar density of calcite to be 0.0217 gmrnole/cm3 (2.712 g/cm3) . This is equivalent to
p, = 4.230 lbmole of calcium ion/ft3 (B-35) Densitv of the Gas Phase (pg) Assuming ideal gas behavior we can write
At atmospheric pressure this correlation is
Densitv of the Liauid Phase (pl) The following correlation is valid of the range 492OR < T < 670°R The density of water is being used to estimate the density of liquid phase. The following specific form was found by regression analysis.
The model fit is demonstrated below. Temperature Density Density (OR) (lbmole/ft3) (lbmole/ft3) ( Actua 1) (Predicted)
The average value of
is wfthin 2% of the maximum and minimum values in the table above. Density of the Preci~itateLaver (pp) The molar volume of CaS04 can be expressed in terms of its density. Gullet and Bruce (1989) analyzed and indicated the CaS04 molar volume to be 45.64 cm3/gmmole (2.98 g/cm3). This is equivalent to
p, = 4.647 lbmole of calcium ion/ft3 (B-40) VISCOSITIES Gas Phase Viscositv (pg) The viscosity of a binary gas mixtures (air/noncondensables), at Pow pressure is given by Wilke's equation as (Chan and Rochelle, 1982)
where @mand @NW are interaction parameters and given by
P~Nand are the pure component viscosities, and noncondensa'%" les (N) and water (W) are the two components in the binary mixture. Replacing Mw and MN with numerical values, we have the following expressions for and @Nw.
and
The pure component viscosities of water vapor and noncondensables are (Gullet and Bruce, 1989) and (Reid et al., 1958)
and
Here we have modeled the noncondensables component as air. Considering that air and water vapor behave ideally at atmospheric pressure, the mole fractions of water and noncondensables can be written as and
Within the operating temperature range of 520° R to 620° R the values of and em are as follows
Over this range the interaction parameters can be approximated as constants. Actual values vary from the average values given below by no more than 2 percent.
WN" 4.73325*10-~2~+ 0.883549 and em WN" -3.05792 *10-~2~+ 1.0178 In addition the pure component viscosities can be represented as linear functions of Tg. * 8.0649 10-lO*~g - 7.85994 lom8 (B-52) and Pgw WN" 5.1777*10-~~*~~+ 1.53943 lo-' (B-53) '%N The accuracy of these approximations are demonstrated in Figures 6 and 7 for values of Tg between 520 and 620 OR. PEASE EQUILIBRIUM PARAMETERS Solubility of Limestone (Ccle) The equilibrium concentration of limestone in water reported by Visneski (1991) as
HenrvPs Law Constant for Sulfur Dioxide (Hs) The Henry's law constant for SO2 in air (atm ft3/lbmol) is given by Rabe and Harris (1963) as
The simplified correlation applicable for the temperature range 520 to 660°R is
Water VaDor Pressure (Pw) The following correlation is valid over the range
The Clapeyron equation for the calculation of the latent heat of vaporization is (Foust et al., 1980) where A and B are constants. This equation is useful for many purposes, but it is not sufficiently precise to provide accurate values over a wide range of temperatures. The Antoine equation has the form where A, B and C are constants. This equation is more satisfactory and more widely used. Most vapor pressure estimation and equations stem from an integration of Clausius- Clapeyron (Foust et al., 1980) equation where mvaP is the enthalpy of vaporization and Bvvap is the volume change due to vaporization. The options one has in this integration are limited. However, results available in the literature vary widely as each researcher normally introduces correction terms to obtain more accuracy. One particular form that is commonly used (Foust et al., 1980) is B In (Pw) = A - + DT + In (T) - T+C where A, B, C, D and E are constants. This form is referred to here as a modified Antoine equation. The following specific form was found by regression.
(B-61) The following table demonstrates the model fit: Temperature Vapor Pressure Vapor Pressure (OR) (atm) (atm) (Actual) (Predicted) The vapor pressure correlation can be approximated with
The accuracy of this approximation is valid for values of T1 between 530 and 672OR.
GEOMETRIC PARAMETERS Geometric Surface Area (a)
Analysis of a limestone sample (Vanport AASHTO #9, sample number LS870616A) gave the following particle size distribution.
U.S. Standard Size Range Representative wt% Screen Sizes (mm) Size (mm)
Using a value of the shape factor of 0.5 (which is a typical value for non uniform solids (Smith and Van Ness, 1975) ), a value for eB of 0.543, and calculating areas for each particle size based on the representative size shown above, the following value for the specific area is found
The geometric surface area for different size distribution can be calculated as a function of sorbent particle size as GaslLiauid Heat Transfer Area (ahg)
ahg = a
~iouid/SolidHeat Transfer Area (ahl)
ahl = a
Gas Phase Mass Transfer Area (%g)
amg = a
Liauid Phase Mass Transfer Area (aml)
%l = a Precipitate Laver Mass Transfer Area (sP)
%p = a Sorbent Surface Mass Transfer Area (%,)
%s = a Liauid Laver Thickness (J1) The dynamic holdup for a packed bed with trickling water has been correlated by Specchia and Baldi (1977) as
where NRpl is the Reynolds number for the liquid phase, NGa is the Galileo number, , is the mass transfer area at the unreacted sorbent surface, dp is the particle diameter and E, is the solid phase volume fraction given in Equation (B-76). The total liquid holdup, E, is the sum of dynamic holdup, and the static liquid holdup, el,. The liquid phase Reynolds number is defined as
The Galileo number is defined as Substituting the above equations and on simplification the total liquid holdup becomes
The liquid water thickness can be calculated as
61 = €/aml Solid Phase Volume Fraction (E,) A I1tapnbulk density analysis of a limestone sample (Vanport AASHTO #9, sample number LS 870520A) indicates a bulk density of 1.4723 lb/ft3 for dry limestone. Dividing this by a value for of 2.712 implies that the solid phase volume fraction is
Note that a value of ~,=0.5 has been reported elsewhere (Yu and Sotirchos, 1987) for limestone.
HEAT CAPACITIES Heat Capacity of Sorbent (CpCs) The following correlation is valid over the range 536.4OR < T < 2160°R (for CaC03) The following form is reported (Smith and Van Ness, 1975)
Heat Ca~acitvof Noncondensables (CpNg) The following correlation is valid over the range
The following form is reported (Himmelblau, 1989) for air. The heat capacity of air is being used to estimate the heat capacity of noncondensables present in the flue gas. Heat Ca~acitvof Water Vapor (CW) The following correlation is valid over the range
491.4"R < T < 3240.0°R The following form is reported by Smith and Van Ness (1975):
Cpus = 7.3 + 1.3667*10-~~ Heat Capacity of Liuuid Water (Cwg) The following correlation is valid over the range
The following form is reported by Himmelblau (1989)
Over the temperature range of interest, a constant value can be used.
C,, 18.0 (B-81)
ENTHALPY DIFFERENCE PARAMETERS Enthalpv Difference for Water (Hwg-HwL) By definition
Latent Heat of Va~orizationof Water (A) The following correlation is valid over the range
The Watson correlation (Smith and Van Ness, 1975) estimates the latent heat of vaporization of a pure liquid at a partfcular temperature using a known value of the latent heat of vaporization at a reference temperature. The correlation has the form
Using a value for the latent heat of vaporization of water at 590°R of 18351 Btu/lbmole (Himmelblau, 1989) and a value for the critical temperature of water of 1164.78OR, the above equation becomes
The model fit is shown below. Temperature 1 (Actual) 1 (Predicted) ( OR) (Btu/lbmole) (Btu/lbmole)
A simple linear relationship can be used over the temperature range of interest. THERMAb CONDUCTIVITIEB Gas Phase Thermal Conductivity (&g) An empirical relation proposed by Wassiljewa (Reid, Prausnitz and Poling, 1987) for thermal conductivity of gas mixtures is
where ktgi is the thermal conductivity of species i, interaction parameter for species i and j, and ygi is t e mole fraction of species i in the gas phase. For a water/ noncondensables binary mixture the relation is
Considering that gas behaves ideally at atmospheric pressure we have
Ygw = CwgRT/P = 0.7302CwgT (B-88) and
The thermal conductivities of water and noncondensables (Appell, 1989) are
ktgw = 1.4702*10-~+ 4.4643-10-'T and ktgN = 6.2407*10-' + 6.6358*10-'T Here we have modeled the noncondensables component as air. Mason and Saxena (Reid et al., 1987) suggested that Aij can be expressed as Considering a value of Ak of 1.065 as proposed by Mason and Saxsena, the values of Aij for the system under consideration are
Over the range of interest, constant values for A, and A, can be assumed
MOLECULAR WEIGHTS Molecular weiaht of Noncondensables (MN) Since the noncondensables are being modeled as air, the molecular weight is taken as
MN = 28.95 Molecular weisht of Water (%)
% = 18.0
MATERIAL AND ENTEALPY BALANCE8
GENERAL MATERIAL AND ENTEALPY BALANCES The following equations represent the most general equation set, Equations for specific process configurations and kinetic models are derived from these equations by applyiny appropriate simplifications. The direction z is general and can stand for x or y depending on the direction of the flow. The more general unsteady-state case is analyzed. Simple material balances are constructed as follows:
-zfcea = Na at ca and a a -~fw1+ gw = pw1
The interphase transport rate for noncondensables and calcium is assumed to be zero. The interphase transport of SO2 to the sorbent is assumed to be balanced by the interphase transport of COz from the sorbent. The loss of O2 from the gas phase due to adsorption (and reaction to convert sulfite to sulfate) is neglected. Material balances for the gas and solid phase sulfur and for the gas and liquid phase water are identified as I1keyw equations since these are the primary dependent variables of interest in the material balances. The gas phase and solid/liquid phase enthalpy balances are a a -x( f .&qg+f wgHwgl - gg - gwHwg = (NN~HN~+NW~HW~)(C-8) and a a - ( f +fwlw1 1 + gg + gwHwg = (NceHcs+NwlHwl) (C-9) The heat effects associated with interphase transport of SO2, C02 and O2 are ignored. Noncondensables and sorbent species have averaged or representative enthalpies. Note in particular that H,, is the enthalpy of all sorbent species per lbmole of calcium. The liquid and solid phases are assumed to be at the same temperature. The latent heat of vaporization of water is assumed to be released to the liquid phase as condensation occurs. his corresponds to the assumption that the heat transfer resistance is in the gas boundary layer outside the liquid.
A critical assumption inherent in these equations is that the temperature in the solid phase is uniform across the particles. A rough estimate for the Biot number for this system gives a value of
where required values for the calculation are
This means that if one waits 1.0 minute following a step change in the gas temperature, the temperature in the center of a spherical solid pellet will fall (or rise) to within approximately 20 percent of the equilibrium value (Ozisik, 1985). For this result the following values are also required.
p, = 150 lb/ft2 C~s= 0.21 Btu/lb/OF N,,, N,,, = 3.3 Since the bed residence time of sorbent particles is much
longer than one minute, . the assumption of a uniform temperature distribution in the solid phase seems to be adequate. However it is also true that inaccurate results will be generated near the solid feed point and for short times in unsteady-state applications. DETAILED MATERIAL BALANCES Before solving the four material balances they must be expressed in a set of four dependent variables. At the outset, we expect these to be the four concentrations Ceg, Csg. Cyst and Cwle (It turns out that Cwl is replaced by U1 In thls 11st. )
Gas Phase Material Balances: The key gas phase material balances are and
On the 1.h.s. of these equations we can substitute and
Differentiating these expressions gives and
This in turn requires an explicit expression for Us and aU laze These quantities can be found from the general material balance for the total gas stream. The equation is repeated here,
Using the ideal gas law we can substitute
fg = UgPg = UgP/ (RTg) (C-17) and into the general material balance. Note that the pressure is assumed to be constant. The result of the substitution is Taking the derivative of the products in this equation and rearranging the result gives
au =-gw- a a T +-Us. a. xis o,mEg+TpEg Tgxig
At any point in the bed, derivatives on the r.h.s. of this equation can be calculated from other material balance equations yet to be derived. The value of dUg/dz can then be calculated from this equation. Values for Ug can only be found by integrating this equation from the gas feed point (z=0) to a particular point in the bed. Note that the time derivative of Us does not appear in the equation. Expressions for dTg/dt and dTg/dz will come from the relevant enthalpy balances. For deg/dt if we use Eg = 1 - El - E, then
A form for ae,/at and d~,/at will be found later. For the derivatives on the r.h.s. of the key gas phase material balances we can use
WRen the appropriate derivatives for these variables are taken we find and
Using these relationships plus the previously shown relationships and 202 in the key gas phase material balances gives a a a a -UgzCsg - C~gzUg- 9s = egzc~g + C~gZEg (3-29) and a -ua a a -"g~% - Cwga~s - gw = eg~Cwg+ %gzeg (c-30) ~f the form for aUg/dz is substituted into these equations the last term on the r.h.s. cancels out leaving
and
Solid Phase Material Balances: For the solid phase we need to consider the key material balance
For the 1.h.s. of this equation we can use
1 fss/Pp + (fcs-fss)/Pc 1 - - - -+-- - P s f c, PC '"'[fcs Pp - :c1
The expression for l/p, is a simple weighted average of the individual component molar volumes. Note that pp and pq are constants. In order to use the above expression for Us it is necessary to assume that fC, is constant. This assumption replaces the less restrictive general material balance for calcium given at the outset and repeated here. The assumption is equivalent to assuming that as the sorbent expands due to conversion from calcium carbonate to calcium sulfate (or sulfite) that it does not expand in the direction of the sorbent flow. An explicit form for ps can be found after substituting
fss = UsCss and fcs = U,Ccs into the equation for l/ps and recognizing that
This gives
which simplifies to
Ps = PC ' css(~c/~p-l) (C-42) Using this form the expression for fss can be written
Differentiating this gives (after simplification)
For the r.h.s. of the key material balance for solid phase sulfur we can use
Nss = EsCss and E, = E,o(P~o/P~)
This expression for E, also stems from the assumption that fcs is constant. An explicit expression for Nss is then 204 Differentiating this gives
Using these results, the key material balance then becomes
The derivative of E, w.r.t. t is also required for the evaluation of Ug. It can be found in a fashion similar to that for the derivatives of fs, and Ns, w.r.t. z to be
Liaufd Phase Material Balances: It turns out that for the liquid phase material balance
the most convenient dependent variable to use is U1. The relevant starting equations are
where is a functional correlation and vl-v, is the independent variable for this correlation. The correlation is obtained from Specchia and Baldifs (1977) equation as where - - 0.625~D -0.715 0.295 kl - P P p1 Note that in equations (C-52) and (C-53) Cwl is constant since the concentration of dissolved species is neglected. ~ifferentiating these equations w.r.t. the appropriate variable gives where pt is the derivative of p w.r.t. vl-v,. The velocity of the sorbent phase is constant so the time derivative is zero. For the other derivative on the r.h.s. we can use and find after some rearrangement that
Note that the derivative of w.r.t. t is also required for the evaluation of Up. Using these results the key material balance for the liquid water now can be written
where qf can be obtained from Specchia and Baldits (1977) correlation as
and the packing factor, Fp can be written as
This form of the key material balance is only used when the liquid volume fraction exceeds the amount which is held as a static layer on the bed. This condition can be expressed as
If the condition is not met then there are two alternatives. If the sorbent bed is moving we know that Since v, is constant we can write
In this case the key material balance becomes
If the sorbent bed is not moving then we can go back to the general form of the liquid phase material balance and substitute
fWl = 0 and a a a pw1= PlZEl + (€1/~1)~~1 and end up with 2 07 DETAILED ENTHALPY BALANCE8 The gas phase and solid/liquid phase enthalpy balances are
a a -z(fcsHcs+fw1%1) + gg + 4wHwg = z(NcsHc.+Nw1Hw1 ) (C-73)
~xpandingthese equations gives
- a a a a (c-74) - NN&~N~ + H~gzN~g+ NwgzHwg + HwgxNwg and a a a a -fcszHcs - Hcs~fcs- ~W~ZHW~- Hwlzfw1 + gg + ~wHw~
The material balances (in their basic form) can be used to eliminate many of the terms from these equations. This leaves
- a a - NN~ZHN~+ NwgzHwg and a a -fcszHcs - fw1zHw1 + gg + gw(Hwg-Hw1)
Using the general principal in these equations gives and (C-80) The only other simplification needed is to substitute for the fluxes and concentrations. In terms of the explicit variables in the material balance we can use
f,, = ugc,,
fwg = UgCwg
fcs = USPS
fw1 = UICwl = UIPl
NN~= E,C,g
Nwg = €lCwg
N~S= 'BPS
Nw~= ElCwl = ElPl We can als~use - 'N~ 'N~ - Pg-'wg Eg = 1-El-€, if necessary. The following auxiliary equations are also required by the key equations:
and where the equation for corresponds to the case of
and applies only for the case of a moving sorbent bed. since the SO2 transport rate is assumed to be independent of the solid phase composition and since
the equation for Css is not required. After imposing the simplifying assumptions on the material balances as discussed in model development and rearranging both the material and enthalpy balances into a form and order corresponding to a natural order of calculation in the required numerical algorithm we have
The above three equations (Eq. (C-99) to C (100) ) can be replaced by
for the case of stationary bed. The equations (C-100) and (C-101) are interchangeable forms. a a ( ~s~s=~c.+"1~1C~wl),T1+ ~~s~sc,cs+~l~lcpwl)3-$1 a a - a a ~,mcs,+u,~csg - -CsgzUg-gs -csgaf €9 (C-110) and a a - a a Egx Cwg+Ugz Cwz - -cwg -9, -cwg Eg (C-111)