738
I n d . Eng. Chem. Res. 1987,26, 738-745
Dynamic Modeling of a Pilot -Scale Fluidized-Bed Coal Gasification Reactor R. Russell Rhinehart,+Richard M. Felder,* and James K. Ferrell Department of Chemical Engineering, North Carolina State University, Raleigh, North Carolina 27695-7905
A dynamic mathematical model of a pressurized fluidized-bed coal gasification reactor has been developed and used to correlate data from a pilot-scale reactor. The model accounts for pyrolysis, oxidation, char gasification, and subsequent gas-phase reactions, fines elutriation and heat losses from t h e reactor, and simulates both transient and steady-state operation. If the values of three model parameters are adjusted to fit data obtained during a steady-state operating period, the model yields good predictions of 11reactor-state variables and the dynamic response to an upset in operating conditions, so provides an excellent basis for adaptive supervisory control of the reactor. Control of a chemical reactor is often hampered or prevented by multivariable coupling, dead time, and inability to measure key state properties. These difficulties can be overcome by using a dynamic simulation model to predict the effects of changes in operating conditions, provided that the model is capable of predicting the reactor response accurately in a time substantially less than the real-time response. Unfortunately, both model accuracy and speed are difficult to achieve for reactors with even moderately complex kinetics and hydrodynamics; moreover, these objectives are frequently incompatible, so that a compromise is required between full rigor and expedient approximation. Linear response models with empirically determined coefficients have often been used for process control. However, such models tend not to be useful for extrapolation to new process states, and the many coefficients usually required are difficult to determine with a reasonable level of confidence. A preferable approach is to use a phenomenological model with a few judiciously selected adjustable parameters (McGreavy, 1983; Ray, 1983; Sargent, 1983). Since chemical processes and their diagnostic instrumentation are generally subject to systematic errors and changes during the operating period, it is advisable to incorporate adaptive capability into the model, using process data feedback to adjust model parameter values. An adaptive dynamic model has been developed for the North Carolina State University pilot-scale fluidized-bed coal gasification reactor and has been used to correlate experimental data for the steamloxygen gasification of a New Mexico subbituminous coal. The reactor was operated over as wide an experimental range as possible to explore the effects of temperature (1050-1250 K), bed height (0.64-0.97 m), steam-to-carbon feed ratio (1.0-2.7 mol of steam/mol of C), and coal feed rate (15-30 kg/h). Background Transport phenomena in a fluidized bed are complex, involving bubble-to-emulsion mass and energy exchange, downflows in the emulsion, and interactions among bubbles (Botterill, 1975; Keairns, 1976). However, when bubbling is vigorous, backmixing can be extensive enough to make the fluidized bed behave approximately as a perfectly mixed reactor (Lee et al., 1970; Wen, 1979). A number of experimentally verified steady-state models have been proposed for fluidized-bed reactors, including those of Eklund and Svensson (1983) for the gasification
of black shale, Kossakowski (1981) for the atmospheric gasification of char, and Johnson (1974) for the steam/ hydrogen gasification of bituminous char. One particularly germane to the present study is the coal gasifier model developed by Purdy and co-workers (Purdy et al., 1981; 1984; Purdy, 1983), who found that a well-mixed reactor model was as effective a t simulating their reactor as was a version of the more complex bubble assemblage model of Kat0 and Wen (1969). There exist relatively few published attempts at dynamic modeling of fluidized-bed gasifiers. Notable are models of a biomass gasifier (Chang et al., 1984), a catalytic coal gasifier (Franklin et al., 1982), a pressurized coal gasifier (Goyal et ai., 1982), a catalytic butane hydrogenolysis reactor (McFarlane et al., 1983), an atmospheric coal/char gasifier (Weimer, 1980; Weimer and Clough, 1981),and an atmospheric char gasifier (Kutten, 1978). The model developed by Chang et al. (1984) simulates the dynamic behavior of an isothermal manure gasifier. Devolatization yields are predicted from laboratory data correlations. The two-phase treatment of the fluidized bed requires the simultaneous solution of 15 differential equations. Elutriation and spent ash removal are not treated, and only the first few minutes of startup are considered. The steady-state limit of the model has been qualitatively compared with experimental results, but the predicted dynamic reactor behavior has not been confirmed. The model of Franklin et al. (1982) is for a bottom-feed coal gasification reactor with no oxygen in the feed. Elutriation is not treated since the fines are presumed to be returned to the bed, and pyrolysis is not treated specifically but instead is included in an empirical gasification scheme. The model of Goyal et al. (1982) is for a moderate pressure agglomerating gasifier with in-bed coal feed and fines return. Additional reactive gases are injected into the bed for control of ash agglomeration and removal. These two models are proprietary and are only qualitatively described in the cited publications. The Weimer-Clough study (Weimer, 1980; Weimer and Clough, 1981) formulates a hydrodynamic model of a bubbling fluidized bed and applies the model to a coal gasifier. The model accounts for coal pyrolysis but does not allow for temperatve dependence of the devolatization yields. The Kutten (1978) model applies to an atmospheric air/fed char gasifier with a settled bed depth of 3-6 m. Neither of these models has been experimentally validated.
* To whom correspondence should be addressed. 'Current address: Department of Chemical Engineering,Texas Tech University, Lubbock, TX 79409.
Experimental Section Coal Gasification/Gas Cleaning Pilot Plant. The coal gasifier is part of a complete coal gasification and gas
0888-5885/87/2626-0738$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 739 cleaning pilot plant at North Carolina State University (NCSU). The plant was designed and constructed under the sponsorship of the US Environmental Protection Agency, with the object of studying the environmental impact of coal conversion processes. The reactor design was subcontracted to the Institute of Gas Technology; like the IGT Hygas reactor, the NCSU reactor uses top feed of coal. Completed in 1978, the plant is operated by the NCSU Department of Chemical Engineering (Felder et al., 1980; Ferrell et al., 1980). The major objectives of the pilot plant project are to characterize the rates of formation and the fates of potential pollutants in both the gasification and gas cleaning processes. To date, peat, lignite, subbituminous coal, and bituminous char have been gasified (Ferrell et al., 1982a-c; Purdy, 19831, and chilled methanol and hot potassium carbonate solutions have been used as acid gas removal solvents (Staton, 1983, 1985). Reactor effluent characterization has included measurement of trace metal evolution (Ferrell et al., 1982a; Felder et al., 1982; Rudisill, 1984), nitrogen gas evolution (Zand, 1984; Farzam et al., 1985), tar composition and generation rates (Ferrell et al., 1982b), and wastewater composition (Lee, 1985). Other important objectives of the project have included the steady-state modeling of the reactor and gas cleaning operations (Kelly, 1981; Purdy, 1983; Staton, 1985). Reactor. The reactor is a 15-cm-i.d. stainless steel pipe enclosed in several layers of Fiberfrax bulk ceramic insulation and contained in a 61-cm-i.d. carbon steel pipe. Ground coal is screw-conveyed continuously from a feed hopper into the top of the reactor and falls 2 m onto the fluidized bed. Steam and oxygen are preheated to 800 K, blended, and injected vertically at the bottom of the bed through three 2.5-cm-diameter nozzles. The entrance jet voids are estimated to penetrate 10 cm into the bed. The reactor pressure is controlled at 800 kPa (100 psig). The bed height is controlled by adjusting the spent ash/char removal rate and the midbed temperature by adjusting the oxygen feed rate. Thermocouples mounted in an axial thermowell, four in the bed and two in the freeboard, are used to obtain the temperature profile in the reactor. A coal feed particle requires 1/2-5 s to fall through the freeboard region above the fluidized bed. Very small particles can be entrained and leave the unit without reacting. Elutriated fines are trapped in an external cyclone and are not returned to the reactor. Coal particles heat, dry, and devolatilize in the freeboard region. Calculations indicate that drying and devolatization should be complete in the freeboard for all but the largest (fastest falling) particles. Representative coal, steam, and oxygen feed rates are 23, 25, and 6 kg/h, respectively. The corresponding dry make-gas flow rate is roughly 30 std m3/h. The average surface-area-weighted diameter of the in-bed solid particles is 0.2 mm. Under normal operating conditions, the fluidized bed is calculated to be in the slugging mode. About 5% of the feed carbon normally leaves the reactor in the spent ash/char waste, but under some conditions this figure has been as low as 1% . Calculations from literature correlations, as well as the uniformity of the measured in-bed temperatures, indicate that the bed is well-mixed except for the small jet entrance zone. A number of sensors are used during pilot plant operation, including thermocouples, orifice and laminar flow metering devices, and differential pressure cells. Each sensor has an individual amplifier/transmitter linked to a DEC PDP 11/23 minicomputer, which averages, stores, and processes the data. Sixteen plant control loops are
Table I. Analyses of New Mexico Subbituminous Coal ultimate wt % Droximate wt% C 53 moisture 8 H 5 volatile matter 36 0 18 ash 22 N 1.2 fixed carbon 34 S 0.8 ash 22 ~
regulated with a Honeywell TDC-2000 digital process control computer. Willis (1981) gives a detailed description of the data acquisition and control systems. Sampling and Analysis. Analyses of the coal feed and the gas, liquid, and solid reactor effluents are performed off-line. Multiple coal samples, taken as the coal is loaded into the feed hopper, are blended prior to analysis. The spent ash/char and the cyclone fines are sampled after the run. Gases are sampled and analyzed 3 times during the steady-state portion of a run. Hot gas (2’= 620 K) is continuously sampled isokinetically downstream of the cyclone, at a rate of about 0.8 SCMH. The tars and solids in the sampled gas are trapped in a steel wool filter; condensable and water-soluble species are removed in a cold water quench, and the “dry” 800-kPa gas is either metered and vented or drawn into 1-L coated stainless steel or glass bombs. The solids and tars are separated by a methylene chloride extraction. Additional gas samples are drawn from various positions in the fluidized bed through a three-port filter made of 1-pm sintered stainless steel felt, at a rate of about 0.4 SCMH. The sample treatment is similar to that used for the make-gas. Gas chromatographyis used to determine concentrations of fixed gases, sulfur gases, and light aliphatic and aromatic hydrocarbons. Analyses for selected element and ion concentrations and chemical oxygen demand are routinely performed on condensate samples, and more detailed compound characterization is occasionally carried out by using high-pressure liquid chromatography. Proximate, ultimate, and sieve analyses are routinely performed on the solid feed and effluent streams. Additional details about the sampling and analytical procedures are given by Lee (1985), Rhinehart (1985), and Zand (1984). Feedstock and Run Conditions. The New Mexico subbituminous coal used in this study was obtained from the Navaho mine of the Utah International Company, Fruitland, NM, and was shipped to the U S . Department of Energy Morgantown Technology Center, Morgantown, WV, where it was ground and sieved to 10 x 80 std US mesh. The coal was used as received at NCSU. Typical proximate and ultimate analyses are given in Table I. Following each gasification run, reactor material balances were constructed on total mass and on elemental carbon, hydrogen, oxygen, and nitrogen. A run was used for data correlation and modeling studies if it met the following criteria: (1)a good steady-state was achieved (minimal fluctuations and negligible drift in the values of key process variables); (2) the total mass balance closure was between 97.5% and 102.5%; (3) carbon, hydrogen, oxygen, and nitrogen balance closures were each between 90% and 110%; (4) the sum of the absolute errors (deviations from 100%) in the five balances was less than 25%. Fifteen of the 28 gasification runs met all of these criteria. The operating conditions of these runs are summarized in Table 11.
Simulation Model Only a summary of the principal model features will be given here. A detailed description of the model formula-
740 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 Table 11. Summary of Run Conditions run G068B GO74 GO76 GO78 GO79 G081B G081D GO84 GONM05 GONMO6 GONM07 GONM08 GONMO9 GONMll GONM14
bed temp, K 1248 1177 1206 1148 1226 1210 1162 1198 1227 1221 1221 1217 1227 1215 1210
coal feed, kg/h 28.9 30.5 23.1 18.6 19.1 23.5 22.4 21.7 20.4 18.1 13.1 15.7 19.2 15.5 17.7
molar steam/C
ratio 1.12 0.97 1.54 1.71 1.73 1.21 1.69 1.82 1.77 1.99 2.67 2.15 1.77 2.22 1.92
bed height, m 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.97 0.64 0.64 0.64 0.64 0.64 0.64 0.64
molar
H2/C0 ratio 1.55 2.36 1.83 2.28 1.81 1.68 2.24 2.11 1.98 1.96 2.18 1.99 1.84 2.25 1.95
tion is presented by Rhinehart (1985). Coal enters the top of the reactor and is assumed to dry completely in the freeboard. Some of the dried feed particles are elutriated and undergo no further reaction; the remaining feed particles devolatilize to an extent determined by the average reactor bed temperature. The devolatilized char enters the bed and is immediately dispersed. Oxidation of char to CO and C02 takes place instantaneously, and reaction-rate-limited char gasification then takes place uniformly throughout the bed. The water gas shift reaction is assumed to be in equilibrium, an assumption supported by analyses of in-bed gas samples. All gases behave ideally. The gas entrance jets are assumed to have a negligible effect on the reactor performance. Of the many gaseous species involved in coal gasification, seven-Oz, H20, H2,CO, COz,CHI, and Nz-that typically account for more than 99% by volume of the in-bed and pyrolysis gases are considered by the model. Feed Particle Elutriation. The predictions of published correlations for the elutriation rate (Bachovchin et al., 1981; McDonald, 1982; Wen and Chen, 1982) were found to be several orders of magnitude lower than measured rates. Further, the measured elutriate was found to contain 60 w t % ash, regardless of the reactor operating conditions and in-bed composition. These results imply that the dominant elutriation mechanism in the NCSU top-feed reador is direct entrainment of coal feed particles, the fines of which contain 60 wt % ash. The following expression for the elutriation rate was determined by multiple regression of measured rate data
E =O.~~U~'.~*F'~~~ (1) where E is expressed in kg/s, uo (m/s) is the superficial velocity at the freeboard exit, and F (kg/s) is the coal feed rate. Freeboard Reactions. Drying and pyrolysis of the feed coal take place in the freeboard region above the fluidized bed. A significant fraction of the reactor make-gas originates in this region, so that it is necessary to have an accurate representation of the phenomena occurring there. Drying is assumed to be complete in the freeboard region and so presents no particular problem. Expressions for the extent of pyrolysis and the composition of the products have been proposed in the literature (Suuberg et al., 1978; Solomon, 1979; Howard, 1981; Rutledge, 1984). However, since these expressions are all based on data obtained at process conditions that differ significantly from those in the freeboard section of the NCSU gasifier, there is no reason to expect them to provide a good correlation of the
gasifier data, and indeed they do not. It was accordingly necessary to obtain experimental correlations for the freeboard contribution to the make-gas. Doing so proved to be no small task, since the sampling and analysis of both in-bed gases and reactor make-gas introduced errors which compounded when the component flow rates in these two gases were subtracted. The method finally adopted, which is described in detail in the Results section of this paper, involved using water as a tracer. The results led to correlations for devolatization yields of Hz, CO, C02, and CHI of the form where Mi/Mdafis the mass of component i volatilized expressed as a fraction of the mass of dry ash-free feed coal, T is the devolatization temperature, and Ai and Biare regression coefficients. Since the final devolatization occurs near the bed surface, the temperature (7')is taken to be the average bed temperature. Char Oxidation. The char oxidation reaction can be represented as c + a02 (2 - 2a)CO (2a - 1)COz (3)
-
+
The value of a, the oxidation stoichiometric factor, depends on the coal and reaction conditions. At high temperatures and pressures, a value of 0.5 (signifying that carbon monoxide is the only reaction product) has often been reported (Arthur, 1951; Laurendeau, 1978; Wen, 1979). Modeling studies were performed both for a fixed value of a = 0.5 and treating a as an adjustable model parameter, in all cases assuming complete and instantaneous consumption of oxygen. Char Gasification. Char enters the bed at the average bed temperature. Both the gas and solid phases of the bed are assumed to be well mixed, so that the bed is isothermal, isobaric, and spatially uniform. The particle size distribution within the bed is assumed to be constant throughout the period of reactor operation, an assumption supported by experimental measurements. The char gasification reaction sequence and rate laws proposed by Johnson (1979) are used. This representation has been used successfully to describe the gasification of chars from bituminous coal (Wen and Dutta, 1979; Purdy, 1983), subbituminous coals (Schmal et al., 1982; Purdy, 1983), and a lignite (Rhinehart, 1985). According to Johnson, the gasification process can be represented stoichiometrically by C
+ H2O CO + H2 C + 2H2 + CH4
(4) (5)
and by a linear combination of the two 2C
+ H2O + H2 + CO + CH4
(6)
The rate equations for the Johnson kinetic scheme are complex and are presented and discussed in numerous publications, including Rhinehart (1985). The gasification rate depends on several parameters intrinsic to the coal (pore structure, imbedded mineral catalytic nature, etc.) and extrinsic to it (the maximum temperature experienced by the char during its devolatization). Johnson modeled the extrinsic contribution as an exponential dependence on devolatization temperature and lumped the intrinsic contributions into a rate multiplier (the "char reactivity") to be experimentally determined. In the NCSU reactor model, a value of 0.5 was used for the char reactivity, and the values of all other rate law coefficients were taken from Johnson (1979). The water gas shift reaction,
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 741 CO
+ H2O + COP + H2
(7)
is assumed to be at equilibrium in the bed. With the thermodynamic expression for the Gibb’s free energy of reaction lhearized about 1117 K, the equilibrium equation is
(PCO$’HJ/(PCO.PH~O) = exp(-3.699 + 4020/T)
(8)
Heat losses from the bed resulting from radiation to the freeboard, convective transfer to the reactor wall, and inbed drying and heating of particles are treated collectively in the energy balance. A calculated total heat loss rate of 1.5 kW was found to provide a reasonable correlation of data for the runs performed in this study, although improved correlations were obtained by treating the heat loss as an adjustable parameter. Model Algorithm. Rate laws for the three reactions of the Johnson kinetic model, balances on solid carbon and ash in the bed, and a transient energy balance constitute the principal fluidized bed model equations. These six coupled ordinary differential equations, which are given in detail by Rhinehart (1985), may be expressed in terms of six time-dependent state variables: T, Pco, PHp,PCH4, PHzp1and X , the fraction of fixed (nonvolatile) carbon gasified at a given time. The equations are discretized in the time-implicit Euler’s form and solved simultaneously with the nonlinear algebraic equations for the water gas shift equilibrium constraint (eq 8), elutriation rate (eq l), devolatization yields (eq 2), and bed carbon oxidation (eq 3). The solid and gas feed stream flow rates and temperatures and the proximate and ultimate coal analyses are read as input variables. From the proximate analysis, the moisture and ash feed rates are determined, and the oxidation reaction yield is then calculated from eq 3. Initial values of the six state variables are estimated, and the devolatization yields, char feed rate, superficial gas velocity, and elutriation rate are calculated. The in-bed reaction rates are calculated from the assumed state variable values and are used to solve the six discretized differential equations for the time step under consideration. The solutions along with the water gas shift equilibrium relation are used to recalculate the in-bed gas composition and hence to recalculate the state variables. Variable values assumed for the next iteration are determined by using a damped Wegstein algorithm (Felder and Rousseau, 1986): the values used are 0.6 of the way from the estimates for the current iteration to the Wegstein-calculated values. The procedure is terminated when the sum of the squares of the relative changes in the six state variables is less than 0.0001. After convergence is achieved, the in-bed gas production rates are added to the previously calculated freeboard production rates, and the procedure is repeated for the next time increment. Steady state is declared when the state variables change by less than 1% over a simulated 1-h period. A time increment of 30 s was found to be small enough to achieve a good balance between minimizing both discretization errors and computation time. Additional information about the convergence properties of the algorithm are presented in the Results section of this paper. Model Adaptation. Even when the intention is to reproduce conditions in a pilot-scale reactor, changes in uncontrolled variables such as ambient temperature, feed coal moisture content, and thermowell position lead to differences between runs. Adaptive control can be effectively used to compensate for these inevitable fluctuations. Three adjustable parameters provide the model with adaptive capability. The parameters are P I (=a), the ox-
idation stoichiometric factor of eq 3; P2,the reactor heat loss rate; and P3 (=Mco/Mdd),the fractional yield of CO from freeboard pyrolysis. Values of these parameters were estimated by fitting the model to steady-state values of three measured quantities: Yl,the make-gas flow rate; Y 2 (=T), the average fluidized-bed temperature; and Y3,the molar H2/C0 ratio in the make-gas. Although the latter quantity was measured off-line in the NCSU facility, it would not be difficult to institute on-line gas composition monitoring, so that all three of these variables could be used to provide real-time feedback for an adaptive control algorithm. A finite-difference approximation of the NewtonRaphson algorithm was used to determine the values of the model parameters that matched predicted and measured values of Yl, Y2,and Y3. If P is the vector of model parameters, Y the vector of measured variables, and Y ( P )the values of these variables predicted by the mode[ the object is to determine P such that
F = Y-Yp=O
(9)
If P, is the vector of parameter values at the nth iteration of the procedure, the Newton-Raphson algorithm determines successive parameter estimates from the relations
J,AP = -F, P,+l = P,
+ AP
(10) (11)
where J, is the Jacobian matrix of first derivatives, aFl/aPJ, evaluated at P = P,. The elements of the Jacobian are determined by perturbing the adjustable model parameters (one at a time) from their values at P,, simulating the reactor for the new parameter values, determining the new values of the components of F , and replacing aF,/aPJwith AFJAP,. The elements of AP are determined by solving eq 10 using Cramer’s rule, and P,+lis then calculated from eq 11. The procedure is terminated when (1)the elements of P each change by less than 0.01% from one iteration to the next and (2) the absolute values of the elements of F a r e less than 0.002 SCMH, 0.1 K, and 0.004 mol/mol, respectively. The execution time might have been decreased by reevaluating the Jacobian only after every third or fourth iteration; however, the more exact method was found to provide rapid enough convergence to make this approximation unnecessary. Results Correlations for Pyrolysis Yields. The experimental determination of the coefficients of eq 2 is outlined below in terms of the following variables, each of which has the units kg of water/h: C1 = steam flow into the bed; C2 = moisture content of the feed; C3 = pyrolytic water from the chemically bound H and 0 in the coal; C4 = water in the make-gas leaving the reactor; C5 = net consumption of water in the bed. From these definitions, c 5 = (Cl
+ c2 + C3) - c 4
(12)
The values of C1, C2, and C4 were measured, and the value of C3, the pyrolytic water contribution, was taken to be 2.7% by mass of the dry ash-free coal feed (Solomon and Colket, 1978). The net in-bed water consumption rate, C5, was calculated from eq 12. The production rate of CO in the oxidation stage of the process was next calculated from the measured O2feed rate by using eq 3, assuming complete oxygen consumption. The following iterative method was then used to determine pyrolysis yields. A fixed minor extent of the methanation
742 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 Table 111. Devolatilization Coefficients for Equation 2 component A , PIP B, g/(g.K) -7.23 X lo-' 7.06 x 10-5 H2 1.07 1.04 x 10-3 co 8.0 X lo-' 0.0 COP 2.50 x 10-4 CH, -2.16 X lo-' devol. yield a t 1200 temp dependence a t 1200 K, K, g/g P/(g.K) component eq 2 lit." eq 2 lit." 5.0-8.0 X H2 0.013 0.011-0.016 7.06 X 2.5-10.0 X 0.018 0.005-0.027 1.04 X co 0.0-0.05 0.080 0.007-0.260 0.0 C02 0.085 0.027-0.170 2.50 X IO-, 1.5-68.0 X lo-, CH, "Rutledge, 1984; Stangeby and Sears, 1981; Solomon, 1979; Solomon and Colket, 1978.
reaction (eq 5) was assumed and a value of the extent of the hydrogasification reaction (eq 4) was guessed. (The methanation reaction occurs to a very slight extent at the prevailing reaction conditions, so that a more rigorous treatment is not justified.) The bed gas composition was adjusted to satisfy the water gas shift equilibrium assumption, and the net water consumption in the bed (C5) was calculated and compared with the value obtained from eq 12. The calculation was repeated for different assumed extents of the hydrogasification reaction, until the calculated value of C5 agreed to within 0.01% with the experimentally deduced value. Once convergence was achieved, the flow rates of all of the reactive species leaving the fluidized bed were calculated from stoichiometric relations. The difference between the measured flow rate of a component a t the reactor exit (i.e., in the make-gas) and its calculated flow rate at the bed exit is Mi, the rate at which this component is produced in the freeboard region. Freeboard yields obtained in this manner were fitted with the expression of eq 2. The values of the regression coefficients Aiand Bifor the devolatization yields of hydrogen, carbon monoxide, carbon dioxide, and methane are given in Table 111. The yields determined in this manner are in qualitative agreement with pyrolysis yields reported by other investigators for subbituminous and bituminous coals, as shown in Table 111. Model Algorithm Performance. The model algorithm was implemented on a DEC VAX 11/750 computer. At or near a simulated steady state, one to three iterations were required to converge for a 30-s time step. Under these conditions, simulation and display of an hour of operating time required about 2 CPU s. To simulate the initial stages of a transient period (i.e., the period following an imposed change in operating conditions), up to 50 iterations were required per time step, but only about a second of CPU time was added for the full simulation. The simulated values of the reactor variables approached their asymptotic limits monotonically and smoothly. An order-of-magnitude reduction in the convergence criterion coupled with a 30% reduction in the integration step time did not change the model output. Steady-State Modeling. The model was tested using global values of the three adjustable model parameters: P1(=a) = 0.5, P2 = 1500 JJs, P3 = the value of Mco/Mdaf given by eq 2, with the coefficients of Table 111. Figure 1 plots predicted vs. measured steady-state values of the total make-gas flow, average reactor temperature, and H2/C0 mole ratio in the make-gas for the 15 acceptable runs. The data are seen to scatter about the 4 5 O line, indicating that the long-time asymptotic behavior predicted by the model provides a good representation of the steady-state reactor behavior. Plots for individual flow rates of Hz, HzO, CO, COz, N2,and CH, and of carbon in
1 0Make-Gas F l o w Rate A x i s Ranoe = 0.005 to A Reactor Temperature 0
0.013 scms
/
A x i s Range = 1100 t o 1250 K H /CO Mole Ratio APis Range = 1.0 t o 3.0
I
8/
40 W _I 3
a > 0 W
I-
o W 0
a LL
0
MEASURED VALUES
Figure 1. Predicted vs. measured process variables: global parameter values.
0 Global Parameter Values Local Parameter Values
CL
0
I
3001
0
+ W
/"
( 4 r
0
n
u
200
n w a CL
100
200
300
400
MEASURED C O RATE, MOL/HR
Figure 2. Predicted vs. measured CO production rate.
the spent ashJchar are similar in appearance (Rhinehart, 1985). Results for methane exhibit a greater degree of scatter, but statistical tests (x2,sign, rank sign, runs, regression) indicate that the model provides an acceptable correlation of the reactor output a t the 5 % level of significance for all 10 variables. As would be expected, when the three adjustable model parameters (Pl,Pz, and P3)were varied for each run to fit the values of the three measured process variables (Yl,Y2, and Y3)to obtain what will be termed "local parameter estimates", the predictions of the other seven variables improved considerably, as verified by a rank sign test at the 5% level of significance (Rhinehart, 1985). The improvements can be seen on the plots of predicted vs. measured H2 and CO output flow rates shown in Figures 2 and 3. Because the make-gas flow rate, the reactor temperature, and the H2/C0 mole ratio were used for local parameter determination, plots of predicted vs. measured
Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987 743 0
(A)
Global Parameter Values Local Parameter Values
z Y
13
-
Y) U
IW
Predicted
K
g
12
U J
lo
3
-”= W
4
11
-20
1750 U 3
1700
I
I
-10
0
10
TIME,
MINUTES
,
20
30
40
50
60
(E)
+Measured - Predicted
cpap
q
1
I
4
200
300 MEASURED
400
H2
RATE,
500
600
700
1650
MOL/HR
Figure 3. Predicted vs. measured H2production rate.
values of these variables would fall exactly on the 45’ line. Analysis of variance indicates that within-run variations did not have a statistically significant influence on the estimated parameter values, but between-run variations did (Rhinehart, 1985). Transient Modeling. Experiments were performed in which the oxygen controller was switched from cascade to direct control, simultaneous step changes were made in the feed rates of coal, steam, and oxygen to the reactor, and the transient responses of the make-gas flow rate and the average bed temperature were measured. Posttransient sampling yielded the new steady-state values for all of the other reactor variables, including the H2/C0 ratio in the make-gas. Values of the adjustable model parameters (P) were determined by fitting data obtained during the steady-state period preceding the step changes, and the model with the fitted parameters incorporated was then used to predict the transient responses. Figure 4 is a plot of the measured and predicted make-gas flow rates and average bed temperatures vs. time for one of these experiments. The rates of change and asymptotic limits of the state variables predicted by the model (smooth curves) and the measured responses (noisy curves) are seen to be in good agreement. The noise in the measured signals is due to a combination of cyclic responses of the reactor pressure and oxygen feed controllers, unevenness in the coal feed rate, and plant electrical disturbances. The transient responses of all measured process variables are similar to those shown in Figure 4, in that they follow roughly exponential decaying paths over a 1-2O-min period followed by a slow drift of up to 2 h. The model indicates that the initial response is due primarily to temperature changes in the fluidized bed; when there is little or no temperature change, the initial portion of the response is complete within about 1 min (the system pressure controller response time). The predicted slight long-term drift is due to changes in composition of the bed contents. In operation, after an apparent steady state was reached, the oxygen feed controller was returned to cascade mode, so that the drift was only observed as a long-term drift in the O2 feed rate. Figure 5 plots predicted vs. measured values of the percentage changes (pretransient to post-transient) in the steady-state values of the make-gas flow rate, bed tem-
-20
-10
0
10
TIME,
MINUTES
20
30
40
50
60
Figure 4. Predicted and measured reactor transient responses: (a) transient make-gas flow rate response; (b) transient temperature response.
0 h
0
Make-Gas Flow Rate Change A x i s Range = -30 t o +30% Reactor Temperature Change A x i s Range = -60 t o + l o 0 K H,/CO Mole R a t i o Change A x i s Range = -0.6 t o +0.6
MEASURED CHANGE
Figure 5. Predicted vs. measured asymptotic changes following a step change in reactor conditions.
perature, and H2/C0 mole ratio, and Figure 6 plots predicted vs. measured transient times (defined as the time required for the reactor temperature to traverse 95% of the distance between its pretransient and posttransient steady-state values). The plots show that the model has an excellent capability of predicting both the transient and asymptotic responses of the reactor for significant changes in operating conditions, a result confirmed by several statistical tests (x2,sign, rank sign, and regression tests at the 5% level of significance). The applicability of the model to process control, under conditions where disturbances are likely to be less severe than those introduced in these experiments, is thus indicated.
744 Ind. Eng. Chem. Res., Vol. 26, No. 4, 1987
to dramatic improvements in the organization and clarity of the paper.
Nomenclature a = oxidation stoichiometric factor, mol/mol Ai = linear regression coefficient, g/g B, = linear regression coefficient, g/(g.K) Cl-C5 = flow rates of water in various process streams, kg/h E = elutriation rate, kg/s F = coal feed rate, kg/s
Lo
w I-
-
3 z c
w
f
F = Y - Y, J = Jacobian matrix of F with respect to P M , = mass of component i volatilized, g Mdaf= dry ash-free mass of the feed coal, g p 1 = partial pressure of the ith component, kPa PI = a, mol/mol Pz = heat loss from the reactor, J / s p3 = MCO/Mddf,g/g P = model parameter vector P, = nth estimate of the parameter vector P T = average fluidized bed temperature, K
Lo W
z 0
p.
Lo
D: w
IO
0
20
30
40
uo =
superficial velocity at the freeboard exit, m/s
X = fraction of nonvolatile (base) carbon gasified from the MEASURED RESPONSE T I M E ,
MINUTES
Figure 6. Predicted vs. measured step response times.
Conclusions A dynamic simulation model for the North Carolina State University fluidized-bed coal gasification reactor has been developed and experimentally validated. Inputs to the model include reactor pressure, feed coal composition and flow rate, and input flow rates and temperatures of steam, oxygen, and nitrogen; outputs include transient and asymptotic (steady-state) values of the average bed temperature, carbon conversion, and make-gas flow rate and composition. The model accounts for pyrolysis, oxidation, and char gasification reactions, as well as fines elutriation and heat losses from the reactor. The model provides a good correlation of operating data over as broad a range of experimental conditions as it is possible to achieve in the reactor. The agreement lends credibility to the model assumptions of water gas shift equilibrium in the bed, a stationary particle size distribution, well-mixed reactor behavior, and instantaneous oxidation of carbon. The Johnson kinetic model provides a good basis for simulation of char gasification, but published correlations for fines elutriation and pyrolysis yields were inadequate, and correlations were instead developed from experimental reactor operating data. If the values of three model parameters are adjusted to fit data obtained during a steady-state operating period, the model yields good predictions of the subsequent dynamic response to an upset in operating conditions and so provides an excellent basis for adaptive supervisory control of the reactor. Acknowledgment We express appreciation to the US Environmental Protection Agency for their support of this project under Cooperative Agreement CR-809317 and the Phillips Petroleum Company for fellowship assistance provided to R.R.R. Thanks are also extended for assistance with reactor operation, sampling, analysis, and data acquisition and processing provided by Keith Carnes, Gary Folsom, S. Ganesan, David Hitch, Paula Jay, Barry King, Robert Ma, Mark Purdy, Chuck Ramsdell, Tracy Rudisill, Karen Rutledge, Steve Staton, and Bill Willis. Finally, we acknowledge with gratitude the thoughtful comments and corrections provided by Thomas O’Brien of the Morgantown Energy Technology Center, whose contributions led
char Yl = dry make-gas flow rate, SCMH Yz = T,K Y3 = molar H,-to-CO ratio in the make-gas, mol/mol Y = vector of measured reactor output variables Y , = vector of predicted reactor output variables 0 = null vector
Literature Cited Arthur, J. R. Trans. Faraday SOC.1951, 47, 164. Bachovchin, D. M.; Beer, J. M.; Sarofim, A. F. AIChE Symp. Ser. 1981,205, 76-85. Botterill, J. S . M. Fluid-Bed Heat Transfer; Academic: London, 1975. Chang, C. C.; Fan, L. T.; Walawender, W. P. AIChE Symp. Ser. 1984,80, 80-90. Eklund, H.; Svensson, 0. Ind. Eng. Chem. Process Des. Deu. 1983, 22, 396-401. Farzam, A. 2.; Felder, R. M.; Ferrell, J. K. Fuel Process. Technol. 1985,10, 249-259. Felder, R. M.; Kau, C.-C.; Ferrell, J. K.; Ganesan, S. EPA Project Summary Report EPA-600/S7-82-027, 1982; EPA, Washington, DC. Felder, R. M.; Kelly, R. M.; Ferrell, J. K.; Rousseau, R. W. Environ. Sci. Technol. 1980, 14, 658. Felder, R. M.; Rousseau, R. W. Elementary Principles of Chemical Processes, 2nd ed.; Wiley: New York, 1986; p 601. Ferrell, J. K.; Felder, R. M.; Rousseau, R. W.; Ganesan, S.; Kelly, R. M.; McCue, J. C.; Purdy, M. J. EPA Project Summary Report EPA-600/7-82-023, 1982a; EPA, Washington, DC. Ferrell, J. K.; Felder, R. M.; Rousseau, R. W.; Kelly, R. M.; Purdy, M. J.; Ganesan, S. EPA Project Summary Report EPA-600/S782-054, 1982b; EPA, Washington, DC. Ferrell, J. K.; Felder, R. M.; Rousseau, R. W.; McCue, J. C.; Kelly, R. M.; Willis, W. E. EPA Project Summary Report EPA-600/780-046, 1980; EPA, Washington, DC. Ferrell, J. K.; Felder, R. M.; Rousseau, R. W.; Purdy, M. J.; Ganesan, S.; Bradley, A. A. Energy and Environmental Research Laboratory Report NTIS NCEI-0043, 1982c; North Carolina State University, Raleigh. Franklin, H. D.; Parnas, R. S.; Kahn, C. D.; Gaitonde, N. Y. “Dynamic Simulation of Exxon’s Catalytic Coal Gasification Process”, Presented at the AIChE Annual Meeting, Los Angeles, Nov 1982. Goyal, A.; Rehmat, A.; Knowlton, T. M.; Leppin, T.; Waibel, R.; Patel, J. G. “Support Studies for the U-Gas Coal Gasification Process”, Presented at the AIChE Annual Meeting, Los Angeles, Nov 1982. Howard, J. B. In Chemistry of Coal Utilization, 2nd suppl ed.; Elliott, M. A., Ed.; Wiley-Interscience: New York, 1981. Johnson, J. L. Kinetics of Bituminous Coal Char Gasification with Gases Containing Steam and Hydrogen; Advances in Chemistry Series 131; American Chemical Society: Washington, DC, 1974. Johnson, J. L. Kinetics of Coal Gasification;Wiley: New York, 1979.
Ind. Eng. Chem. Res. 1987,26, 745-750 Kato, K.; Wen, C. Y. AZChE Symp. Ser. 1969, 66(105), 100-167. Keairns, D. L., Ed. Fluidization Technology; Hemisphere: Washington, DC, 1976; Vol. 1. Kelly, R. M. Ph.D. Dissertation, North Carolina State University, Raleigh, NC, 1981. Kossakowski, E. R. Ph.D. Dissertation, Trinity College, - . University of Cambridge, UK, 1981. Kutten. M. Ph.D. Dissertation.. Citv- Universitv of New York, New York, 1978. Laurendeau, N. M., Prog. Energy Combust. Sci. 1978,4, 221-270. Lee, M. K. A. M.S. Thesis, North Carolina State University, Raleigh, 1985. Lee, B. S.; Pyrcioch, E. J.; Schora, F. C. Chem. Eng. Prog. Symp. Ser. 1970, 66(105), 152-156. McDonald, F., Presented at the AIChE Annual Meeting, Los Angeles, CA, Nov 1982; Paper 80f. McFarlane, R. C.; Hoffman, T. W.; Taylor, P. A.; MacGregor, J. F. Znd. Eng. Chem. Process Des. Dev. 1983,22, 22-31. McGreavy, C. Comput. Chem. Eng. 1983, 7(4), 529-566. Purdy, M. J. Ph.D. Dissertation, North Carolina State University, Raleigh, 1983. Purdy, M. J.; Felder, R. M.; Ferrell, J. K. Znd. Eng. Chem. Process Des. Deu. 1981, 20, 675. Purdy, M. J.; Felder, R. M.; Ferrell, J. K. Znd. Eng. Chem. Process Des. Deu. 1984, 23, 287. Ray, W. H. Comput. Chem. Eng. 1983, 7(4), 367-394. Rhinehart, R. R. Ph.D. Dissertation, North Carolina State University, Raleigh, 1985. Rudisill, T. S. M.S. Thesis, North Carolina State University, Raleigh, 1984. Rutledge, K. L. M.S. Thesis, North Carolina State University, Raleigh, 1984.
745
Sargent, R. W. H. “New Challenges for Process Control”, Presented a t the AIChE Annual Meeting, Washington, DC, Oct 1983. Schmal, M.; Monteiro, J. L. F.; Castellan, J. L. Znd. Eng. Chem. Process Des. Dev. 1982, 21,256-266. Solomon, P. R. DOE Contract Report ET-78-(2-01-3167, 1979; United Technologies Research Center, East Hartford, CT. Solomon, P. R.; Colket, M. B. Presented at the 17th International Symposium on Combustion; Pittsburgh, PA, 1978; pp 131-143. Staton, J. S.M.S. Thesis, North Carolina State University, Raleigh, 1983. Staton, J. S. Ph.D. Dissertation, North Carolina State University, Raleigh, 1985. Suuberg, E. M.; Peters, W. A.; Howard, J. B. Znd. Eng. Chem. Process Des. Deu. 1978, 1701, 37-46. Weimer, A. W. Ph.D. Dissertation, University of Colorado, Boulder, 1980. Weimer, A. W.; Clough, D. E. AZChE Symp. Ser. 1981,205, 51-65. Wen, C. Y.In Proceedings of the NSF Workshop on Fluidization and Fluid-Particle Systems Research Needs and Priorities; Littman, H., Ed.; Rensselaer Polytechnic Institute: Troy, NY,Oct 1979; pp 317-395. Wen, C. Y.; Chen, L. H. AZChE J. 1982,28(1), 117-128. Wen, C. Y.; Dutta, S. Coal Conversion Technology; Wen, C. Y., Lee, B. S., Eds.; Addison-Wesley: Reading, MA, 1979; p 1. Willis, W. E.Ph.D. Dissertation, North Carolina State University, Raleigh, 1981. Zand, A. M.S. Thesis, North Carolina State University, Raleigh, 1984. Received for review February 3, 1986 Revised manuscript received September 30, 1986 Accepted December 6,1986
Improvements in Batch Distillation Startup Juan R. GonzBlez-Velasco,*Miguel A. Gutierrez-Ortiz, Jose M. Castresana-Pelayo, and Jose A. Gonziilez-Marcos Departamento de Qutmica Tgcnica, Universidad del Pats Vasco, 48080 Bilbao, Spain
Numerical simulations show that both the energy and time requirements in the start-up phase of batch distillation processes can be reduced by decreasing the backmix in the condenser holdup. Furthermore, computed results in the simulation show that filling the holdups with feed liquid is better than the usual way of filling the plates and condenser with condensed vapors. The increasing significance of fine chemistry, the need of recovering profitable materials from waste products, and the great development of computers in process control have renewed interest in batch distillation. The rigorous mathematical model of batch distillation is complex due to the presence of liquid holdup in the overhead equipment (condenser and reflux drum) and plates and consists of a stiff simultaneous differential equation system that is analytically intractable and numerically unstable (Robinson, 1970,1971; Sadotomo and Miyahara, 1983). This instability increases for small but nonnegligible liquid holdups in relation to the still pot holdup. The mathematical models reported in the literature allow determination of the time-varying compositions and temperatures during the product take-off period. In the models with appreciable holdups, the compositions of the holdups (included that of the reboiler) at the end of the start-up period without distillate withdrawal preceding the overhead take-off period are usually considered as the starting points for that period. The time consumed in starting up the unit with appreciable holdups can be an important fraction of the total distillation time (Goldman, 1970; Luyben, 1971; Sadotomo and Miyahara, 1983), particularly for close boiling sepaOS88-5885/87/2626-0745$01.50/0
rations and systems with large holdups. Consequently, to optimize the whole process, the start-up period may have to be considered as part of the complete batch distillation cycle (Robinson, 1971). However, the startup has not been considered by most authors, with the exception of Huber (1964), Converse and Huber (1965), Mayur and Jackson (1971))and Domenech et al. (1977a,b). This reduces the validity of many optimization studies to cases where the take-off period is dominant. Obviously, the start-up period has to achieve a very quick composition change in order to reach the prescribed condenser hold-up composition as soon as possible. Variations in the start-up procedure and/or the equipment characteristics may be used to minimize the duration of this period. The models of batch distillation units reported in the literature consider a backmixing flow behavior within the condenser holdup (Domenech et al., 1977a,b; Guy, 1983; Sadotomo and Miyahara, 1983), as this assumption generally matches the equipment supplied by the manufacturers. In this paper we propose the modification in the overhead equipment of the unit in order to more closely approach a plug-flow behavior within the condenser. We 0 1987 American Chemical Society
