212
Ind. Eng. Chem. Process Des. Dev. 1089, 22, 212-217
Dynamfc Behavior of Moving-Bed Coal Gasiflers Myung Kim and Babu Joseph’ Chemkal Englne8rIng Department, WasMngton Un/vers& In St. LOUIS, St. Lo&, Mlssourl 63730
A matt”tical model is devekped to predict the dynamic behavior of movingbed coal gasification reactors. The model Is limited to dry& product gasbauOn reactors and incorporates the long-term transient effects associated with the coal bed. Short-term transients are approximated using the steady-state version of the equations. The model is used to study the transient response of the gasifier to changes in coal feed rate, oxygen flow rate, and steam flow rate. The effects of step changes In these varlables on the product gas composition and temperature profiles within the reactor are given. The controllability of the gasifier when subject to typlcel disturbances is also examined.
Introduction The production of clean fuels from coal by gasification is an important step toward meeting the energy needs of this nation. Although there are many different techniques for gasifying coal, the moving-bed (Lurgi-type) processes are the oldest and the best known. A moving-bed gasifier is a vertical countercurrent reactor in which coal reacts with airsteam or oxygen-steam gas mixtures. Coal is added at the top of the reactor and moves downward by gravity while ash (dry powder, clinker, or molten slag) is removed from the bottom to maintain the level of the coal bed. Gas mixture is fed to the bottom of the reactor and flows upward. The term fixed-bed is sometimes used to describe the moving-bed since normally the top of the coal bed is maintained a t a fairly constant level. There are several advantages to a pressurized movingbed process over the entrained flow and fluidized bed type gasifiers. Because of countercurrent flow, the sensible heat of the ash is recovered by the cold incoming gas stream and, a t the top of the bed, the sensible heat of the gas is utilized to heat the coal feed. Generally high conversion of coal is obtained because of the long residence time. The primary disadvantage of the moving-bed reactor is the difficulty in processing highly agglomerating coals without pretreatment. Fines of coal, which tend to block the passage of gas through the bed, also cannot be used. Some typical coals which could be used in the Lurgi gasifier are Wyoming, Illinois No. 6, Pittsburgh No. 8, and New Mexico coals. Recently METC (Morgantown Energy Technology Center) has demonstrated that highly agglomerating coals such as Arkwright bituminous coal and Western Kentucky coal can be gasified if a stirrer is provided in the Lurgi type gasifier. Attempts to model the gasifier date back several years. Qualitative models have been reported by Elgin et al. (1974), Hoogendorn (1973),Rudolph (19721, and Hebden (1975). In a detailed study, Arri and Amundson (1978) developed a rigorous mathematical model for the reaction taking place around a char particle. The model was used in studying the gasification of char in a countercurrent reactor. The resulting multipoint boundary value problem was solved numerically. Although the authors did not make any comparisons with plant data, several parametric studies were reported. More recently, Yoon et al. (1978a) reported a comprehensive model of the moving-bed gasification reactor. Unlike Arri and Amundson (1978), who divided the reador into distinct combustion and gasification zones, these authors allowed all the reactions to occur throughout the reactor. Different (ash segregated and shell progressive) 0196-4305/83/1122-0212$01.50/0
models were studied and they concluded (based on comparison with plant data) that the shell progressive model gave more accurate predictions. The homogeneous model proposed by Yoon et al. was extended by Cho and Joseph (1981), who presented a heterogeneous model. Again this study was limited to steady-state effects only. Dynamic studies of coal gasification processes are scarce. Yoon et al. (197813) used their steady-state model to predict approximate dynamic behavior of the gasifier. They assumed that the behavior of the solid and gas are in plug flow with a narrow intensive reaction zone in which most of the carbon is consumed by combustion and gasification reactions. Based on this assumption, they approximated the dynamic behavior through a series of steady-state models in which the reaction zone moved slowly. More recently, Daniel (1980) published a transient model for moving-bed gasifier using a different approach. In this model short-term transients were approximated as instantaneous and long-term transients were treated as constant. Transients of an intermediate time scale are modeled in detail. The combustion is treated as taking place instantaneously. The gasification zone is modeled using the steady-state material balance equations and the unsteady-state heat balance. These two transient models have helped to identify the major transient effects in the gasifier. However, the simplifying assumptions involved limit the range of applicability of the model in the evaluation of the stability of operation and controllability of the reactor. The objective of this work is to develop a transient model that is capable of predicting the internal and external transient behavior of the gasifier when it is subject to typical input disturbances and under typical control loops. Development of the Dynamic Model The dynamic model development closely parallels the heterogeneous steady-state model of Cho and Joseph (1981). Since the model is discussed in detail in this earlier paper, only a brief outline is given here. Figure 1 shows the schematic of the gasifier and the major reactions taking place. In the top part of the reactor, the coal is dried and devolatilized by the hot gases exiting from the reactor. The temperature of the coal is increased and approaches that of the gas stream. These two events are quite rapid and take place within a short distance of the reactor. Since the time taken is of the order of seconds, these events were approximated as instantaneous in the dynamic model. The products of devolatilization were predicted using the Gregory and Littlejohn (1965) corre0 1983 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 213 Coal
With the assumptions stated above, the mass and energy balance equations become char:
Product Gas
Drying Devolatilization
W E T COAL ' DRY COAL DRY COAL 'CH,OH.
+
H20
ac, = aF, + (r3+ r4 + r5 + re) at az
YP**
(1)
steam: Gasification
hydrogen: aCH, at = - -aFH2az
Combustion
+ ( 1 - 0 + 4)r3 +
(E- p)r4 + 2p)
(4 - a Aih
2
Steam B'Oxygen (or Air)
Figure 1. Typical zone8 and reactions in a moving-bed
r5 + r8 (3)
carbon monoxide: gasifier.
lation. It is further assumed that the N2 in the coal is converted to NH3 and sulfur is converted to H2S in this zone. The remaining char is represented by the formula CH,O, where a and /3 are determined by material balances. In the gasification zone, the char reacts with steam, carbon dioxide, and hydrogen. The remaining char is burned in the combustion zone consuming the oxygen and leaving an ash residue. In the development of the dynamic model the axial and radial dispersions of mass and energy are neglected. The dominant transport mechanism in the gasifier is turbulent mixing due to the high axial flux of the gaseous stream and the high temperature. Among the reactions, the water formation reaction is the fastest and is assumed to go to completion. Char-oxygen and char-steam reaction is moderate and controlled by diffusion resistances. A shrinking core model is used to describe the kinetics of these reactions. Although charcarbon dioxide and char-hydrogen reactions are also heterogeneous, they are assumed to be controlled by the slow intrinsic reaction kinetics. Because of the complex physical and chemical events taking place in the gasifier, it is necessary to introduce some assumptions for developing a model that is mathematically and computationally tractable but at the same time retains the major characteristics of the process. The dynamic model of the process is obtained by writing the unsteady-state mass, energy, and momentum balances. However, certain simplifying assumptions can be introduced without destroying the accuracy of the model. As mentioned earlier, the axial and radial dispersions of mass and energy were neglected. The velocity of the solid mass through the gasifier is assumed to be constant (fixed by the rate of removal of ash through the rotating grates at the bottom of the gasifier). This is a reasonable assumption for the shell progressive type model which assumes that the char particle retains an ash layer surrounding the unreacted core. The residence time of the gases in the reactor is of the order of a few minutes whereas the residence time of the solid phase is of the order of hours. Thus the dominant time constants of the process will arise from the accumulation terms in the solid mass balance and one could effectively consider the gas phase to be in steady state with respect to changes taking place in the solid phase. The momentum balance can be used to predict variations in the pressure. However, the pressure drop across the reactor is fairly small, and the effect of pressure on the reactor performance is small. Hence, the pressure is assumed to be constant along the reactor.
acto
dFC0
at
az
-e--
+r3+2r4+ (4)
carbon dioxide:
acto, =-- d F C 0 , -r4+ at az methane:
-= - -a F C H , aCCH,
az + r5
at
oxygen:
total gas:
2 at = -5+ (4+ 1)r3 + (4 + 1)r4 + aZ
(4-
l)r5 +
(4
-y
+ l)r6
(8)
solid energy balance:
gas energy balance:
I
N
C r i C ( b , j H 8 j- aijHgj)- UA(T, - T,) i=3 j = 1
+ hSe(T,- T,)
(10) The solution of the above set of equations is greatly simplified for the case of low operating pressures where the gas phase accumulation term can be neglected. Further, it was shown in the earlier work (Cho and Joseph, 1981) that the thermal capacity of the solid is small in comparison with the energy being released by the chemical reactions that the solid temperature can be assumed to be at a pseudo steady state with respect to the gas. This allows the derivative terms in the solid energy balance to be set to zero, reducing it to an algebraic equation. This leaves only the accumulation term in the solid mass balance to be integrated with respect to time. The flux of char, F,, and the concentration, C,, can be related to each
214
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983
other using the velocity of solid mass through the reactors as follows F, = VC, (11) where V is the velocity of the solid stream. In the above equations we have neglected the effect of radial and axial dispersion of mass and energy. These dispersions could cause some secondary effects on the dynamics of the gasifier. Solution Procedure The integration of the solid mass balance equation with respect to time is carried out as follows
parameter reactor length reactor diameter particle size coal feed rate oxygen feed rate steam feed rate temperature of feed gas operating pressure
a Data (Illinois) based on Westfield pilot plant operation. Coal feed rate based on Westfield plant operation is 13 040 kg/h.
-x)
where C, is an arbitrary reference concentration of x is a conversion variable, the equations can be reduced to form At axe+1 xnI - ax@+l rqn rgn ren) 1-1 1+1 = xi” + - ( r a n
+
c,
+
data
3.048 m 3.658 m 0.01 m 13 350 kg/h for Illinois coal 29 000 kg/h for Wyoming coal 183 kmol/h for both coals 1757 kmol/h for Illinois coal 1244 kmol/h for Wyoming coal 644 K 25 atm
Table 11. Product Gas Distribution (Volume Percent) for Illinois Coala
Noting that Fc = VC, and representing
c, = C,(1
Table I. Operating Parameters Used for Simulationa
+
+
(13)
where a = V(At/BAz). The semiimplicit form has the advantage of yielding a linear set of equations to solve at every time step. A set of linear tridiagonal equations is solved readily using the Thomas algorithm. The boundary conditions used are x = 1.0 at z = L. Note that setting the accumulation terms to zero in the gas phase mass and energy balance yield equations identical with those obtained for the steady state. Hence exactly the same procedure can be used to integrate this set of equations in the spatial direction a t every time step. Details of the procedures used are given in Cho’s thesis (1980). It is interesting to note that the solution of the steadystate equations which includes the steady-state mass balance for the char requires an iterative procedure due to the split boundary conditions. In the dynamic case, the char concentration throughout the reactor is known at any time step during the integration in time domain, and as a result, the remaining gas phase equations are easier to integrate in the spatial direction (no iterative procedure required). This formulation has the added advantage of the ability to predict the ash layer depth in the gasifier accurately. With the steady-state model, prediction of the ash layer depth proved difficult in instances where the char conversion was complete because the ash layer in the gasifier represented a zone in which essentially no changes took place in the gas or solid stream. The equations are solved in the following order. An initial profile of temperatures and compositions is either assumed or taken from the steady-state program. The solid mass balance equation is integrated to determine the solid composition profile at the next time step. The gasphase mass balances and the energy balances are integrated next by the Runge-Kutta fourth-order method. Step sizes used varied from l/looto 1/2w of the reactor length. Results and Discussion The dynamic model was used to study the response of the gasifier to a variety of feed disturbances. The data used in the simulation are shown in Table I. (Testa were conducted using the highly reactive Wyoming coal as well as the less reactive Illinois coal.) The steady-state results
a
component
plant data
dynamic model
hydrogen carbon monoxide carbon dioxide methane others
39.1 17.3 31.2 9.4 3.0
44.6 19.2 27.5 6.7 2.1
Operating conditions of Table I.
DISTANCE
Elgin e t al. (1974).
(Z/L)
Figure 2. Temperature and coal conversion profile following a 10% step increase in coal feed rate for the Illinois coal.
predicted by the model compared well with the earlier results of Cho and Joseph (1981) as well as those of Yoon et al. (1978). Table I1 compares the steady-state results obtained using thismodel with some published experimental results on the Westfield pilot plant gasifier. The data agree reasonably well, with the largest error in the prediction of COP Since no experimental dynamic studies have been reported in the literature it is not possible to validate the dynamic model fully at this time. Figures 2 and 3 compare the response of the gasifier to step changes in coal feed rate. An increase in coal feed rate increases the downward velocity of the coal. The ash layer depth decreases and the position of maximum temperature moves downward; 99% of the change is achieved in about 2 h of operating time. There is almost no change in the maximum solid temperature. A decrease in coal feed rate has the reverse effect as shown in Figure 3. The response is rapid in the beginning, reaching almost 80% of the change in the first half hour. The ash layer depth
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 215
6001
a - 10%
"'1
440
z
p
,w.
08-
v)
K
06-
02Hr.
z
8-I a 8
Final
04-
