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Ind. E n g . C h e m . Res. 1996,34, 4266-4276
MovingBed Reactor Model for the Direct Reduction of Hematite. Parametric Study Enrique D. Negri, Orlando M. Alfano, and Mario G. Chiovetta* INTEC, Instituto de Desarrollo Tecnolbgico para la Industria Quimica, Universidad Nacional del Litoral-CONICET, Giiemes 3450, 3000 Santa Fe, Argentina
The behavior of a direct-reduction, moving-bed reactor for the production of sponge iron from hematite is analyzed through the parametric study of the predictions obtained from a mathematical model previously presented by the same authors. The pellet-scale model is based on a three-moving-front scheme for the reduction of the various iron oxides, and it includes the water gas shift reaction (WGSR) in equilibrium in the sponge-iron layer. The reactor is modeled through a one-dimensional, heterogeneous, adiabatic, steady-state model. The numerical solution of the system of equations representing the problem is obtained by means of a novel solution scheme, since the conventional “shooting“ method presented stability problems. Results from the models with and without inclusion of the WGSR are compared. The results obtained with the complete model t h a t includes the WGSR introduce a significant advantage with regard to those brought about by simpler models. The complete model permits a n accurate representation of pilot-plant reactors, including the ability to detect regions of optimal operating conditions.
1. Introduction The majority of the mathematical models for iron oxides, direct-reduction, moving-bed reactors, in the literature use a heterogeneous, one-dimensional scheme to represent the process (Negri et al., 1985). Some of the models include the possible side reactions related to the gaseous species involved. For the typical operating conditions in an industrial reducing shaft furnace using a mixture of H2 and COz, the water gas shift reaction (WGSR), catalyzed by iron and its oxides, is the most important side reaction. Some of the models in the literature (Hara et al., 1976a)b;Hughes and Kam, 1982; Kaneko et al., 1982; Takenaka et al., 1986; Negri et al., 1991) include the WGSR. In these works, the approach to dealing with this side reaction follows various paths. Hara et al. (1976a,b), Kaneko et al. (1982), and Takenaka et al. (1986) consider the WGSR included, as a homogenous reaction, in the material balances for the gaseous phase (the source term being used in the equation is not related to the calculations at the pellet scale, or t o the reduced solid phase). Another alternative approach found in the literature, for a pellet with a single, moving reaction front, considers the reaction as taking place inside the reduced-iron layer (Hughes and Kam, 1982). The most recently published mathematical scheme models the WGSR in equilibrium inside the reduced-iron layer formed on a pellet represented by three moving reaction fronts (Negri et al., 1991). This pellet scheme was used in a one-dimensional, nonisothermal, steady-state, heterogeneous reactor model for the simulation of a directreduction shaft furnace for iron oxides. The simulations performed with this model, and with a simplified version that does not include the WGSR effects, were compared with the experimental results obtained by Takenaka et al. (1986) for a pilot-plant setup. From the comparison, it was concluded that the results from the model including the WGSR simulates more adequately the behavior of a moving-bed reactor for the range of operating conditions typical of an industrial reactor. In this work, the predictions obtained using the threemoving-front model of Negri et al. (19911, with and
* To whom correspondence should be addressed.
without the inclusion of the WGSR in equilibrium within the layer of sponge iron formed, are discussed and analyzed via a parametric study. The model including the WGSR was solved using a modified “shooting” method, via the partitioning of the reactor in modules for sequential resolution. On the basis of these simulations, typical profiles for solid conversion and for reducing gas utilization (both individual and total) are analyzed. The degree of approximation of the WGSR to the equilibrium condition is discussed for different compositions at the reactor inlet. Then, the effects of water content, temperature, and ratio of hydrogen to carbon monoxide compositions in the gas entering the reactor upon the parameters in the gaseous mixture exiting the reactor are studied. 2. System Modeling
2.1. Pellet Model. The pellet is modeled using a heterogeneousscheme with three moving reaction fronts thus allowing the simultaneous existence of three intermediate iron oxides (wustite, magnetite, and hematite) and reduced iron, as schematically shown in Figure l a . The reaction rates for the model without the WGSR (Negri et al., 1987, 1988) are
where subindex “A”indicates any of the reducing species (hydrogen or carbon monoxide) and “B” any of the oxidant species (water o r carbon dioxide). The matrix expression is composed of an effectiveness “factor” and an array of driving forces calculated on the basis of the compositions in the bulk gas phase. This “factor” for the matrix effectiveness includes all of the kinetic and transport resistances considered in the model. It is a well-known fact that the WGSR is catalyzed by iron and, although to a lesser extent, by its oxides. The reaction scheme is not that of a homogeneous reaction (the usual way of representing the WGSR when 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4267 3
3
(a) lron oxide
Solid outlet
Gos outlet
Reducing gos
(b) Figure 1. Schematic representation of (a) the three-interface pellet model and (b) the direct-reduction shaR furnace.
modeling direct-reduction reactors). Assuming that the reaction takes place in the reduced-iron layer, and that it is in equilibrium, the expression for the reduction rates in each of the three reaction fronts can be synthesized as follows (Negri et al., 1991):
In this particular case, explicit forms cannot be derived for the reduction rates in the various reaction fronts. This is so because the WGSR introduces a nonlinearity in the equations derived from the mass balances. The numerical solution of the system requires an iteration process, with eqs 2 and 4-7, for the calculation of the concentrations of the reducing species in the iron layer. Then, with these values, the reduction rates in all fronts can be computed using eq 2. The dimensionless expression for the reaction rate for a front j is
where O I can ~ be calculated using either eq 2 or 1,if a model with or without WGSR is considered, respectively. 2.2. Reactor Model. A heterogeneous, one-dimensional model is used to describe the behavior of the hematite reduction furnace (Figure lb). The scheme includes independent energy balances for each phase, and solid pellet particles as described by any of the models described in section 2.1 above. The origin for the coordinate system is located at the bottom of the reactor (gas inlet point). The following are assumed: (a) plug flow for both the solid and the gaseous phases, (b) uniform solid bed, and (c) constant physical properties for the system. The dimensionless expressions for the mass and energy balances in both the solid and gaseous phases for the two models considered results in the following system of ordinary differential equations:
The matrix expression thus obtained for the reduction rate in each front results similar conceptually to that in the model without WGSR. This matrix is built on the basis of a matrix consisting of the kinetic and transport resistances inside the pellet and o f a drivingforce vector. Here, the driving forces for each reaction are based on the concentrations at the wustite-iron moving front. These concentrations are calculated solving the nonlinear, algebraic, system of four equations with four unknowns:
(10)
3
The form of the derived expressions for each of the concentrations is
where N , is the molar flux due to the WGSR, given by
4268 Ind. Eng. Chem. Res., Vol. 34,No. 12, 1995
SECTION 1
When the WGSR is not included, the molar flux in eq 13 is null. This fact introduces a significant simplification into the complexity of the system. The dimensionless boundary conditions required to complete the description of the physical problem considered are
SECTION J
The reactor model presented above consists of a set of seven ordinary, first-order, nonlinear differential equations with “split” boundary conditions. Two dimensionless numbers, typical of this type of reactors, are worth noting: the gas to solid feed ratio (a)and the gas-to-solid heat capacity ratio (PI.
I
SECT’oN
I
3. Numerical Solution for the Reactor Model The nonlinear system of ordinary differential equations (ODE’S)described in section 2 is solved numerically, employing a particular solution scheme for each of the cases presented. The model without WGSR used a “shooting“technique to solve the boundary-value problem posed. The equations are integrated starting a t the upper extreme of the reactor and toward the lower end, afker compositions and temperature in the’gas are assumed a t the upper extreme (Negri et al., 1988). Once these values are assumed initially, and with the inlet solid-phase conditions known at the upper end of the furnace, the initialvalue problem thus resulting is solved using a marching method. The results obtained for the bottom of the reactor applying the numerical scheme are compared with the inlet gas-phase data. The calculation sequence is considered converged when the difference between this pair of values is lower than a prespecified error. If this requirement is not satisfied after completing any given calculation step, a new set of values is adopted for the gas outlet temperature and compositions, and the integration procedure is repeated until the convergence criterion is met. A Newton-Raphson method is employed to accelerate the convergence rate of the numerical scheme. The model with WGSR could not be solved using the approach described above (conventional “shooting”), because of an extremely high sensitivity of the scheme resulting for the solution of the ODE’S to the assumed values for gas concentration and temperature a t the outlet point. With the idea of using the numerical scheme developed already, the reactor was considered divided into artificial, mathematical sections which were solved using an iteration scheme (Negri, 1987). Each section or module (Figure 2) presents the problem of an ODE system with “split” boundary conditions. They are solved independently using a “shooting“ technique applied to eqs 9-13, with the boundary conditions given by the inlet solid and gaseous streams to each of the modules. The partitioning of the overall reactor in sections introduces pseudostreams between the modules. It is necessary to assume values for the concentrations and temperature to start the calculations.
Figure 2. Moving-bed reactor divided into N imaginary sections.
The procedure employed can be synthesized as follows: (i)A set of concentration and temperature values is assumed for the gas pseudostreams between every pair of sections in the reactor. Values for the concentration and temperature of the gas stream at the reactor outlet are also assumed: gas streams become completely identified if the reducing agent compositions and yco and the temperature 8, are known. (ii) The equations for the reactor are solved, as applied to each section, following the 1to N sequence, according to Figure 2. A whole set of new values is obtained after this calculation step. (iii)If all of the calculated values for the variables in the gas streams joining the artificial sections, and at the reactor outlet, differ in less than a prespecified tolerance when compared with those obtained in a previous calculation step, the procedure is considered converged and, thus, ended. Otherwise, step iv is performed. (iv) The equations for the reactor are solved, as applied t o each section, but now in a sense opposite to that in step ii, Le., following now the N to 1sequence, according to Figure 2. (v) If all of the most recently calculated values for the variables in the gas streams joining the artificial sections, and at the reactor outlet, differ in less than a prespecified tolerance when compared with those obtained in a previous calculation step, the procedure is considered converged and, thus, ended. Otherwise, step ii is performed again. In order t o accelerate the convergence rate of the iteration process in the procedure presented above, an alternating calculation sequence is employed. In an odd-number iteration, the information is transmitted from one section to another through the variables in the solid phase, with the gas phase concentration and temperature profiles either assumed or taken from the previous calculation round. After the end of this iteration, a new set of concentration and temperature values for the gas phase has been computed. This set will be used in the next calculation round. During an evennumber iteration, the information is transmitted by means of the gas phase, using the profiles in the solid phase from the previous calculation step. With this
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4269 Table 1. Parameter Values for the Model type of parameter operating conditions
heat and mass transfer parameters
values
T," = 1073 K Sa = 1kg/(m2 s) X H ~ ' = 0.19-0.80 XCO' = 0.19-0.80 moxa = 0.29 L=lm Cp,g= 33.5 J/(mol K) de.^. = 1.02 cm2/s
parameters for Hz reduction
references
T," = 1123-1273 K G: = 53.5 moY(m2 a) = 0-0.067 = 0-0.067 rp = 0.006 m E = 0.4 c ~=,840 ~ J/(kg K) De,c0 = 0.44 cm2/s kg,co= 0.61 m / ~
XH~OO
XCO~O
Perry and Chilton (1973) Reid et al. (1977) Sen Gupta and Thodos (1962)
E H ~=J 92 100 J/mol EH~ = ,71 ~ 200 J/mol EH~ = ,63 ~ 600 J/mol A H H ~=, ~-3010 J/mol AHH~,z = 71 400 J/mol A"H2,3 = 17 200 J/mol Ec0,I = 113 900 J/mol E c o , ~= 73 700 J/mol EC0,3 = 69 500 J/mol AHco,~= -48 500 J/mol AHc0,z = 24 900 J/mol M C 0 , 3 = -12 900 J/mol AHw= -32 900 J/mol
parameters for CO reduction
WGSR
method, the newly calculated temperatures transmit the information inhntaneously to the reactor section immediately above, because a modified set of variables is fed to this layer via the gas stream entering the section. This scheme proved faster than a simpler, one-way calculation sequence with no alternation in the computation steps. The convergence procedure in the scheme above is further accelerated applying the Wegstein algorithms (Wegstein, 1958) to each one of the involved variables (temperatures, and hydrogen and carbon monoxide compositions in every gas pseudostream), or at least t o some of them.
Tsay et al. (1976) Weast (1976) Tsay et al. (1976) Weast (1976) Weast (1976)
variable. The selection of this parameter to complete the input characterization is useful for the modeling and at the same time realistic in terms of the operational variables considered. For the analysis of the predictions obtained with the model, three main variables are studied in the results presented below: (i) the degree of reduction, (ii) the overall reducing-gas utilization, and (iii)the individual reducing-gas utilization. These variables are defined as follows: 3
j=1
4. Results and Discussion
A full parametric study of a direct-reduction shaft furnace fed with a mixture of reducing and oxidizing gases, and able to follow various reaction paths, requires the complete characterization of the gas-feed mixture. This knowledge is necessary to establish a proper comparison among predictions obtained with different pairs of parameter sets. In order to meet the characterization requirement, a couple of dimensionless numbers are particularly useful (Kaneko et al., 1982): (1) the ratio between reducing and oxidizing gas feed, defined as 6, and (2) the hydrogen to carbon monoxide feed ratio, defined as p . The definition of this parameters, in terms of the problem variables, is given by the following expressions: (16)
It should be noted that, based on the definition in eq 20, and because of the interconvertibility between Hz and CO caused by the WGSR, the individual utilization for each reducing gas can become either zero or negative at given positions within the reactor. Additionally, from an overall mass balance in the reactor, it is possible to obtain a relationship linking the exit-gas overall utilization and the overall degree of conversion at the solid output as follows:
(17)
(21)
For a system containing only the four species in eqs 16 and 17, another relationship can be considered, using the mass balance expressed as the summation of all four molar fractions equated to 1. Once the parameters 6 and p are fixed, the system now has only one degree of freedom. To completely characterize the input stream, it is sufficient to select the water mole fraction. In an industrial reactor, there exists a humidity control system operating on the gas feed. Hence, a certain degree of restraint can be applied on this operation
In Table 1, the system parameters are listed. They include (i) the operating conditions, (ii) the system dimensions, (iii)the physical and chemical properties, (iv) the heat and mass transfer constants, and (v) the kinetic parameters related to the chemical reactions taking place in the system. The set of constants in Table 1is similar to that used by Negri et al. (1988) in previous simulations. 4.1. Typical Conversion and Utilization Profiles. Figures 3a and 4a show the axial profiles for R , the degree of reduction, and for 7, the overall gas
p = YHzO/YCOO
4270 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 1.o
R 7)
05
0.0
0.5
0.0
5
0.0
1.0
0.5
5
(a)
(0)
0.4I
7,;
7):
0.2
0.2
0.0
0.0
0.0
A
0.5
5
1.0
0.0
0.5
5
1.0
Figure 3. Reactor axial profiles for YH~O' = 0: (a) degree of reduction and gas utilization and (b) hydrogen and carbon monoxide utilization. (-) Model with WGSR and ( - - - ) model without WGSR.
(b) Figure 4. Reactor axial profiles for ~ H ~ O=' (YH~O'),,,~: (a) degree of reduction and gas utilization and (b) hydrogen and carbon monoxide utilization. (-1 Model with WGSR and ( - - - I model without WGSR.
utilization, for two different values of the water concentration at the inlet. Figures 3b and 4b display the corresponding axial profiles for vi*, the individual utilization of both hydrogen and carbon monoxide. In order to show the effect of the WGSR upon the system, Figures 3 and 4 also display the profiles for the same variables predicted by the model when no waterconversion reaction is considered. The parameters used correspond t o operating conditions typical of a commercial reactor: the ratio between gas and solid flows entering the reactor a = 2.6; the reducing-agent to oxidizing-agent ratio 6 = 14; and the hydrogen to carbon monoxide ratio p = 1.4. The values chosen for the water mole fraction at the feed are those corresponding to the maximum and minimum possible humidity: Y H ~ O ' = 0 ~ ~ 4). (Figure 3) and Y H ~ O O = ( Y H ~ O O ) (Figure From the comparison of the predictions performed using the model with the water conversion reaction with those obtained without its inclusion, it follows that the degree of reduction is higher for the case in which the WGSR is taken into account (Figure 3a). The predicted overall gas utilization, when the WGSR is included, is lower for most part of the reactor, but it reverts for positions in the reactor closer to the gas exit. As shown in eq 21, the overall utilization is proportional to the degree of reduction of the whole reactor. Thus, as expected, the predictions for the overall utilization at the reactor outlet in Figure 3 are higher for the case including the WGSR.
Figure 3b shows significant variations for vi* in the vicinity of the gas inlet predicted by the model with the WGSR. In this zone of the reactor, a large increase in hydrogen utilization as well as an important decrease in carbon monoxide utilization can be observed. The latter, after going through a local minimum, starts increasing in a monotonous fashion. The presence of the WGSR explains the observed behavior: because there is no water at the reactor entrance, the equilibrium condition is rapidly approached, with the reaction of hydrogen and carbon dioxide to produce water and carbon monoxide. This effect leads to a sharp increase in hydrogen consumption and, due to simultaneous production of carbon monoxide, to a drop in the utilization of CO to negative values. The plots for hydrogen and carbon monoxide utilization contrast with those obtained without the WGSR inclusion. The major differences are related to the following facts: (i)for the feed-gas mixture analyzed, with no water contents, the driving force for the reduction reaction with hydrogen is maximal, while that for carbon monoxide is minimal; (ii) the reaction rate for hydrogen reduction is much faster than that for carbon monoxide. Additional predictions can be observed in Figure 4 for both the degree of reduction and gas utilization when the water concentration in the gas feed is set equal t o its maximum feed value. No significant changes are observed for the degree of reduction and the overall utilization (Figure 4a) when compared with those obtained when no water was fed to the reactor (Figure
(b)
Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 4271 3a). However, more significant changes can be observed from the plots for the individual utilization (Figure 4b). An increase is observed now in the carbon monoxide utilization, while a decrease is shown for the hydrogen utilization, including negative values. This behavior is opposite t o that detected by the model using the WGSR but with no feed-gas water content. In the case in Figure 4b, when no carbon dioxide is fed to the reactor, the feed-gas mixture is far away from the WGSR equilibrium point and rapidly moves toward it. Thus, the system reaches a situation where carbon dioxide is generated, with simultaneous CO consumption (a higher apparent Utilization) and hydrogen production (a lower, even negative, Utilization). When no WGSR is included, as in the case with no water in the gas feed, hydrogen utilization may become higher than carbon monoxide’s (i.e., for a = 3.4). Additionally, if the plots in Figures 3b and 4b for the model without the WGSR are compared, the separation between the hydrogen and carbon monoxide curves are less dramatic in Figure 4. This is so because the influence of the higher reduction rate for hydrogen is partially compensated by a carbon monoxide reaction rate operating at the highest possible driving force (null carbon dioxide contents in the gas feed). The overall comparison of Figures 3 and 4 indicates that the highest conversions are predicted by both models (with and without the WGSR) for the case with maximum-humidity gas feed. The reason is mainly a higher thermal level for the whole process: under this feed-gas condition, the exothermic, carbon monoxide reduction is favored, while the endothermic, hydrogen reduction is not. Moreover, there is an additional energy supply coming from the very WGSR, in the process of moving toward equilibrium as the carbon dioxide generation takes place. Another important factor in the predictions including the WGSR is that related t o higher CO utilization, which is observed even for the less favorable case in terms of CO consumption (Figure 3b). Conversely, hydrogen consumption is only slightly higher in the WGSR model, for the most favorable case (Figure 3b), and becomes lower for the least favorable situation (Figure 4b). The WGSR is responsible for this higher CO utilization: when operating close to the equilibrium point, this reaction replenishes part of the hydrogen already consumed, thus increasing the CO utilization. Under certain operating conditions (Figure 4), the model including the WGSR predicts higher utilization for carbon monoxide. For these conditions, because of the reduction rate differences between both reducing agents, the model without the WGSR does not predict the actual behavior which shows a higher carbon monoxide utilization. It is an experimentally proven fact (Hara et al., 1976a; Kaneko et al., 1982) that CO utilization is higher than hydrogen’s for the reported conditions. Hence, this fact is a major element in favor of the credibility of the model including the WGSR used in this paper (Negri et al., 1991). Given the relevance of the inclusion of the WGSR in a reliable simulation model, and in order to compare the behavior of the reaction system for various feedgas compositions, Figure 5 displays the results in the analysis of the axial profiles of the ratio Qw/Kw. This ratio represents the departure form the equilibrium condition. K, is the equilibrium constant for the WGSR in terms of mole fractions and a t system temperature, and Qwis the ratio of concentrations defined as
5.0
4.0
(Q, K, 1 3.0
2.0
1 .o
0.0 0 .o
0.1
5
1.0
Figure 5. Axial profiles of the WGSR concentration quotientequilibrium constant ratio (Qw/Kw) for different gas-feed compositions.
(22) (formally, the same ratio as in the equilibrium expression, but with the current values for the bulk-phase concentrations in it). Although the WGSR takes place mostly at the sponge-iron layer within the pellet, the analysis of the ratio Qw/Kwgives an idea of the degree of proximity of the gas mixture to the WGSR equilibrium condition. When the ratio is below 1, the WGSR will move toward the production of hydrogen at carbon monoxide expense. Conversely, values of the ratio higher than 1 will indicate the displacement of the reversible reaction toward carbon monoxide production and hydrogen consumption. Figure 5 shows that, in spite of a broad range of initial (feed-gas) conditions, the ratio reaches values close to unity in relatively short reaction lengths, usually shorter than 10% of the total reactor height. It can also be seen that, within a wide range of feed compositions, the sharp changes a t the reactor bottom, observed in the plots in Figures 3b and 4b, are only obtained for two limiting cases: (QW/Kw)O and (Qw/Kw)O 0, respectively. For all of the simulations shown, the solid inlet temperature is 1073 K. For this temperature, no deviation from the equilibrium condition a t the gas outlet could be observed in Figure 5. The reasons for this behavior are (a) temperature profiles are smooth, with no sudden variations that may produce a sharp increase in K, and a consequent decrease in Qw/Kw;and (b) the thermal contents of the incoming solids are very high, thus allowing the rapid formation of an iron layer, and the existence of the WGSR equilibrium from the very top of the reactor. The analysis in Figure 5 justifies the larger complexity of the model including the WGSR, as presented in this work, when compared with other modeling attempts found in the literature (Hara et al., 1976a; Hughes and Kam, 1982; Takenaka et al., 1986). Part of this degree of complexity is related to considering the WGSR as being catalyzed by iron, as is the case, instead of assuming a homogeneous reaction in the gas phase, a simpler but less accurate proposition. Additional complexity arises from the relaxation of the usual assumption of considering the WGSR in equilibrium in the bulk
-
OQ,
-
4272 Ind. Eng. Chem. Res., Vol. 34, No. 12, 1995 Table 2. Hydrogen and Carbon Monoxide Utilization
“O
7
H2
co
0.29 0.29
utilization model with WGSR 0.43 0.35 0.34
H2
0.30
0.27
gas-solid feed ratio
(a)
species
2.5
co
3.4
model without WGSR 0.37
(vi*) experimental dataa 0.49 0.36 0.37 0.26
After Takenaka et al. (1986). 0.8
0.7 I 0.0
1
I
0.5
1.o
(a)
0.4
1
I
0.2
0.o
0.5
!.O
YH020~(YH0z0)rnox
(b) Figure 6. Effect of relative feed humidity on (a) degree of reduction a t the outlet, and (b) hydrogen and carbon monoxide utilization at the outlet. (-1 Model with WGSR, and (- - -1 model without WGSR.
of the gas phase along the full reactor height. When no such assumption is made, the results show a significant deviation from the equilibrium condition at least in one reactor end, as shown in Figure 5. For different sets of operating conditions for industrial reactors, the deviation of the real behavior with regard to the equilibrium assumption in the bulk of the gas phase may become even more apparent. 4.2. Model Predictions for Various Parameter Sets. The effects of the feed-gas humidity on the reactor behavior can be observed in Figure 6. The degree of reduction a t the reactor outlet (Figure 6a) and the individual utilization for both reducing agents (Figure 6b) are shown as functions of the ratio feed-gas humiditylmaximum admissible humidity for the selected conditions ( p = 1.4, 6 = 14, a = 2.8). For both models, the variation of both R(I;=O) and q,*(
