Ind. Eng. Chem. Process Des. Dev. 1885, 24, 286-294
286
indebted to W. Smith for her NMR analysis work.
Weltkamp, A. W.; Gutberlet, L. C. Ind. Eng. Chem. Process Des. Dev. 1970, 9, 386. William, R. B. Symposium on Composition on Petroleum Oils, Determination and Evaluation, ASTM Spec. Tech. Pub!. 1958, 224, 168. Yang, H. S.; Sohn, . Y. Ind. Eng. Chem. Process Des. Dev. 1985, Part 2 of the companion articles in this Issue.
Literature Cited Allred, V. D. Colo. Sch. Mines Q. 1964, 59, 47. Bae, J. H. Soc. Pet. Eng. J. 1969, 9, 287. Brown, J. K.; Ladner, W. R. Fuel 1960, 39, 87. Burnham, A. K.; Singleton, M. F., Lawrence Livermore National Laboratory, Rept. UCRL-88127, 1982. Hill, G. R.; Johnson, D. J.; Miller, L.; Dougan, J. L. Ind. Eng. Chem. Process Des. Dev. 1967, 6, 52. McKay, J. F.; Latham, D. R. Anal. Chem. 1980, 52, 1618. Reich, H. J.; Jantelat, M.; Messe, . T.; Wigert, F. J.; Roberts, J. D. J. Am. Chem. Soc. 1969, 91, 7445. Shape, C. E.; Ladner, W. R. Anal. Chem. 1979, 51, 2189. Sohn, . Y.; Yang, H. S. Ind. Eng. Chem. Process Des. Dev. 1985, Part 1 of the companion articles in this issue.
Received for review November 7, 1983 Revised manuscript received April 19, 1984 Accepted May 21, 1984
This work was supported in part by a Research Grant from the University of Utah Research Committee and the University of Utah College of Mines and Mineral Industries Mineral Leasing Fund.
Steam-Methane Reformer Kinetic Computer Model with Heat Transfer and Geometry Options Alexander P. Murray* and Thomas S. Snyder Westinghouse R&D Center, Pittsburgh, Pennsylvania
15235
A kinetic computer model of a steam/methane reformer has been developed as a design and analytical tool for cell system’s fuel conditioner. This model has reaction, geometry, flow arrangement, and heat transfer options. Model predictions have been compared to previous experimental data, and close agreement was obtained. Initially, the Leva-type, packed-bed, heat transfer correlations were used. However, calculations based upon the reacting, reformer gases indicate a considerably higher heat transfer coefficient for this reformer design. Data analysis from similar designs in the literature also shows this phenomenon. This is thought to be a reaction-induced effect, brought about by the changing of gas composition, the increased gas velocity, the lower catalyst temperature during reaction, and the higher thermal and reaction gradients involved in compact fuel cell reformer designs. Future experimental work is planned to verify the model’s predictions further. a fuel
has the options of: (1) inclusion/deletion of the water gas shift reaction, (2) flat slab or tubular geometry, (3) cocurrent, countercurrent, or double countercurrent flow arrangement, (4) different heat transfer coefficients, (5) specified exterior reformer tube temperature profile, and (6) CALCOMP plotting routines. Model predictions have been compared to simple reformer tube data and were found to agree within 15% of the exit conversions and within ~7% of the temperature profile, by use of an error
Introduction A joint program has been conducted by Westinghouse
and Energy Research Corporation (ERC) to develop an integrated phosphoric acid fuel cell system. A key component in the fuel cell system is the fuel conditioner, which catalytically reforms methane by reaction with excess steam to produce the hydrogen-rich feed gas for the fuel cells. As a design and analytical tool, a computer model of the methane reformer was required. This model would also assist in the design and interpretation of pilot plant scale reformer data, and in the development of heat transfer correlations. Steam reforming of methane is a key operation in many refinery and petrochemical processes, and, as such, it has been the subject of previous models by Oblad (1967), Grover (1970), Hyman (1968), Singh and Saraf (1979), and Olesen and Sederquist (1979); the details were not available for use in the fuel cell program. Fuel cell system reformers are different from standard industrial units: they are more compact (~60% as large), have higher reaction and thermal gradients, require a large dynamic operating range (25-125% of design), and can be small (~10 kW) or large (~10 MW). Typically, around
norm
indicate that a heat transfer coefficient some two times greater than Leva packed bed correlations actually exists, in agreement with other fuel cell reformer data. This is apparently a reaction-induced effect. This work demonstrates the utility and applicability of unidimensional, kinetic modeling to complex reacting media, and how simplifying assumptions render an incalculable problem solvable. The good model agreement with experimental data is indicative of a causal modeling basis and has validated the model for similar designs and scale-up. Heat transfer effects profoundly influence reformer operation, and, consequently, these must be included in the design; for example, a flat slab geometry for low-pressure situations or the double countercurrent flow arrangement for internal regenerative heat transfer. These designs have practical applications in other packed bed reactors operating on endothermic reaction systems.
0.75 lb-mol of hydrogen/h is required for each 10 kW of electric power in a phosphoric aqid fuel cell system. Therefore, fuel cell systems pose special design constraints, and a specific reformer model has been developed.
The Westinghouse model allows the demethanation reaction to be kinetically controlled, rather than invoking the equilibrium assumption, and a great deal of flexibility has been incorporated into the programming. This model
0196-4305/85/1124-0286$01.50/0
analysis. Model calculations on the reacting reformer
gases
Previous Kinetic Modeling Work Oblad (1967) and, later, Grover (1970) discussed a steam methane reformer computer model that includes heat ©
1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 Product Gas
287
Table I. Reformer Model Assumptions 1. Reforming and combustion gases flow with complete radial but axial mixing (i.e., plug flow). Only axial temperature changes are allowed, and radial temperature profiles are neglected. 3. A uniform temperature exists throughout each catalyst particle, and it is the same as the gas temperature in that section of the catalytic bed. 4. Distributor and manifold entrance effects are negligible. 5. The reaction kinetics are adequately described by a pseudo-first-order rate equation. 6. The kinetic expression represents a “global” or overall rate and hence includes reactivity differences found within the catalyst particles. 7. All gases behave ideally in all sections of the reformer. 8. Bed pressure drops are neglected. 9. Heat transfer is primarily by forced convection. Specific radiant heat transfer terms are neglected, as are heat losses to the environment. No heat transfer occurs between the product and reforming gases. 10. A single reformer tube is analzyed. Thus, all the tubes in the reformer behave independently of one another. 11. Equations 4 and 2 represent the reformer reactions. Reaction 1 is kinetically controlled, while Reaction 2 is equilibrium controlled. No carbon deposition is allowed in the reformer. no
2.
Figure
1.
Double countercurrent flow (DCCF) reformer tube.
transfer and reaction kinetics in the analysis. This model is based upon the following reaction choices CH4 + H20
=
CO + 3H2
(1)
CO + H20
=
C02 + H2
(2)
Carbon formation by reactions such as eq 3 is usually very small and can be neglected under normal industrial operating conditions. 2CO
=
C02 + C
(3)
This model assumes unidimensional (plug) flow of gases in the reformer tube and considers the kinetic rate equation to be first order in the methane partial pressure. The reaction rate is also included to account for reverse equilibrium effects. Good agreement was obtained with pilot plant reformer studies. Hyman (1968) developed a similar model. However, it differs in several important areas. The demethanation reaction choice becomes CH4 + 2H20
=
C02 + 4H2
(4)
instead of eq 1, and, with the water gas shift reaction (eq 2), it forms the basis for the model. The rate equation uses an expression derived from the law of mass action, instead of the first-order rate equation. Plug flow of the reformer gases is also assumed, and an exterior tube wall temperature profile is used in place of furnace gas flow rates. High hydrocarbon reforming can also be accommodated. Again, the model closely agrees with reformer plant data. Singh and Saraf (1979) have developed a model for side-fired steam-hydrocarbon reformers. Both methane and naphtha feedstocks are accommodated in the model algorithm. Equations 1 and 2 represent the reaction basis, and kinetic expressions are developed for both reactions. A pseudo-first-order rate expression describes the kinetics of eq 1. Extensive attention is given to radiative heat transfer from the burner gases to the reformer tube surface. A unidimensional model is developed and solved using numerical techniques. Close agreement is obtained between the model and operating reformer plants at different sites. Olesen and Sederquist (1979) consider a double countercurrent flow (DCCF) tubular geometry reformer (Figure 1). This design is also described by Smith and Santangelo
(1980). In this design, existing reformer gases transfer heat directly back into the catalyst bed, thus minimizing overall heat duty. Carbon formation effects are included. Their model analyzes a fuel cell system reformer and includes radial and axial mixing terms. Good agreement with actual reformer data is obtained, although, for all the model’s complexity, the agreement appears to be no better than for the previous plug flow models. Harth et al. (1978) introduce a novel application for reformer technology. This is the combination of a steammethane reformer with a high-temperature, gas-cooled nuclear reactor (HTGR), which provides an excellent means for long distance transport of thermal energy. At the consuming site, the reforming reactions can be reversed (methanation) and the energy released. An interesting facet of this work is the use of a DCCF reformer design. Calculations are based upon overall balances and catalyst data and, as such, do not involve explicit modeling. These literature models have all been developed for specific, existing, reformer designs, and therefore they are limited in their flexibility. For analysis, experimental, and general design purposes, a more flexible reformer model was desired, as optimum performance of an integrated fuel cell system does not necessarily imply optimum reformer performance, and, hence, multiple reformer designs might evolve. This reformer model is described herein.
Equation Development Table I outlines the basic assumptions of the model. Figures 2, 3, and 4 display the tubular geometry and variables involved, while Figure 5 shows the corresponding flat slab situation. The reforming gases flow up through the catalytic bed and react, producing hydrogen. The exit reforming gases leave via a manifold arrangement at the top, or, as a tubular geometry option, they can leave through the center tube depicted in Figure 2. Heat is supplied by the combustion gases flowing through the outermost duct (this is normally a section of the furnace around the reformer). The combustion gas flow arrangement can be countercurrent (Figures 2 and 3), cocurrent,
DCCF (Figure 4). The model assumes the following reactions as the basis for the mass balance (Akers and Camp, 1955; Allen et al., 1975; RostrupNielsen, 1975) (4) CH4 + 2H20 C02 + 4H2 = CO + H20 (2) C02 + H2 or
=
288
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Reactant
FlcwR-·-
Combustion Gas
—
Flow^
Figure 2. Heat transfer surfaces (major heat flux denoted by arrow Q). 1=1 Combustion
Combustion
Gases
Gases
Figure 4. Double countercurrent flow, tubular geometry reformer model (regenerative gases flow
Figure 3. Single-tube kinetic reformer model (countercurrent flow).
Reaction 4, the demethanation reaction, is considered to be kinetically controlled, while eq 2, the water gas shift reaction, is assumed to be equilibrium controlled. Equation 2 represents an equilibrium redistribution of the products of reaction 4 and goes in reverse as eq 2 is written. Hence, in this model, the water gas shift conversion is always negative. Carbon formation by reactions such as eq 3 is neglected, as normal fuel cell reformer operating conditions include a sizable steam excess (3:1 steam/carbon molar ratio). Thus, carbon deposition is precluded by reactions such as eq 4. 2CO
=
C + H20
C + C02 =
CO + H2
(3) (4)
Table II summarizes some of the previous kinetic equations used in the literature for the demethanation reaction, along with experimentally determined parameter values. Several of the rate equations include a term to account for equilibrium effects. These have been found to influence industrial reformers strongly. Therefore, an
on
the inside).
5. Dimensions and variables for the flat slab reformer (countercurrent flow).
Figure
equilibrium term was included in the model. Also, because of the large steam excess, a pseudo-first-order rate equation was used for the computer model (eq 5). -rCH4 =
=
(5)
k0e~EA/RTAP
Pch4
~
(6)
Pch4,e
represents the difference between the actual and equilibrium methane partial pressure. The two parameters, the frequency factor (k0) and the activation energy (EA), can be varied to represent catalysts of any reactivity. The methane partial pressure is written in terms of the methane molar flow rate, the total molar flow rate, the total pressure, and the reaction conversion. Denoting XI as the methane conversion by reaction 1 and XE as the equilibrium conversion, then the rate equation takes on the form
F 1(1 XI) F + 2XIF1 -
_rCH4
=
Pk0e-EA/RT
Fl(l
-
XE)
"I
F + 2XEF1 J
(7)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table
289
Summary of Kinetic Equations and Parameters Found in the Literature
11.°
workers
value
expression
Akers and Camp
-rCH4
=
k0
k0e~EA/RTpC}ii
(1955)
EA
Bodrov et al. (1964,
~r ch4
=
127
=
8778 (commercial cat.)
=
for nickel foil
k0e~EA/RTPch4
1967) k0
=
EA k0
Allen et al. (1975)
-rCH4
Rostrup-Nielsen
-rCH4
=
k0
k0e~EA/RTPch4
=
k0e~EA/RT[Pch4
(1
-
(Qr/Kp))]
k0
6.1 X 106
19400
=
1.04 X 104
=
EA -
31000 for commercial cat.
=
EA
X 106
1 =
20000 (assumed)
=
2.19 X 107
=
(1975)
EA EA Grover (1970)
~rau
Hyman (1968)
-rCH4
this work
-rCH4
=
k0e~EA/RT[PCH4
=
-
(PcoPh27Ph2oFe2)] k0
k0e-EA/RT(KE1PCHlPK2O*
=
-
k0e~EA/"RT(PCh4
=
PH2o4P0o2)
or k0
4.43 X 105
=
not reported
=
EA
-
26000 20000
=
8778
=
KE2
=
equilibrium constant of the reaction, CH4 + H20
KEi
=
equilibrium constant of reaction 4
=
CO + 3H2
100-1 X 105 10000-26000 PCh4,e is the methane partial pressure at equilibrium k0
Pch4,e)
=
EA
=
“Units: K0[lb-mol/(h lb of cat, atm]; EA [cal/mol].
Molar Flow/Rates
Table III.
Function of Reaction Conversions (Basis: 1-h Flows)
as a
mol in feed FI F2
component
ch4 CO C02
mol produced by reaction
F3
h2 n2
F4 F5 F6
totals
F
h2o
1
mol produced by reaction 2 0
FI
0
X1F1 -2X1F1 4X1F1
-X2 (F3 + X1F1) X2 (F3 + X1F1) -X2 (F3 + X1F1) X2 (F3 + X1F1)
0
0
F2 F3 F4 F4 F6
2X1F1
0
F + 2X1F1
This is then combined with the plug flow design equation (eq 8), and the definition of conversion in a flow system of uniform cross section (eq 9), to yield the reactor material
Kl
u0C0
XI
(8)
("rcHi)PB
~
-
uC (9)
=
dz
PBPk0e-EA/RT I
u0C0
J
[
Fl(l- XE)
F+2X1F1
F + 2XEFI
1 J
GO)
The model describes the reformer using six-component material balances. Five components are involved in the two-reaction scheme (methane, carbon monoxide, carbon dioxide, water (steam), and hydrogen). The capability of adding a diluent (nitrogen) requires the sixth component balance. Denoting the water gas shift conversion as X2 (based upon carbon dioxide), then, as has been done previously (Grover, 1970), all molar flows in the reformer can be represented in terms of the two conversions and the initial molar flow rates (Table III).
-
Wh24
PCH tPH202
^ch4^h2o2
(ID
P2
(12)
^CO^HjO
For both equilibria, the mole fractions can be expressed in terms of component molar flow rates, the total molar flow rate, the equilibrium constants, and the conversions for each reaction. Therefore, at specified temperature (fixed equilibrium constants) and boundary conditions (feed rates), eq 11 and 12 reduce to only two unknown variables (the conversions, XI and X2). Furthermore, eq 12 can be rearranged to yield a quadratic equation in X2 as a function of XI, providing a convenient iterative calculational sequence (eq 13-16). AX22 + BX
A B
=
=
(K2
-
2
+ C
=
0
(13)
1) (F3 + XLF1)2
(F3 + X1F1) (2X1F1K2
-
K2F2 -X2F4 5X1F1 F3 -
Equilibrium Calculations The equilibrium conversion required in the rate expression (eq 10) necessitates the solution of the combined equilibrium expressions for the two reactions (eq 1 and 2).
-
P CO ¡P h24
PCOPh2o
Fl(l-Xl)
-
The water gas shift reaction equilibrium is P CO 2P h2 Wh2
u0CQ
dXl
X1F1 X2 (F3 + X1F1) + X1F1 + X2 (F3 + X1F1) 2X1F1 X2 (F3 + X1F7 + 4X1F1 + X2 (F3 + X1F1
-
Assuming ideal gas behavior (fugacity coefficients of unity), the demethanation reaction equilibrium becomes
balance (eq 10).
d(-uC) ~~dT~
mol present
-X1F1
C
(14) -
-
F5) (15)
=
K2F2F4
-
2K2F2X1F1
-
(F3 + X1F1) (F5 + 4X1F1) (16)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
290
These equations complete the reformer’s material balance
description.
Energy Balances Neglecting heat transfer from the product gases, two energy balances can be written for the reformer. Thus, for countercurrent flow
reforming gas energy balance L1KTH TC)„(rD2) dZ + + (F3 + X1F1)(-AHR2) dX2 (17) dXl Fl(-AHRl)
(FACPA) dTC
=
-
combustion gas energy balance
(.MH)CH dTH
=
UI(TH
TC)JivD2) dZ
-
(18)
A cocurrent flow arrangement changes the sign of the left-hand side of eq 18. Alternatively, the combustion gas energy balance can be replaced by an exterior tube wall temperature profile of the form TW(Z) = A + B(Z) + C(Z2) + D(Z3) (19) a
The DCCF models (Figure 4) require the inclusion of product gas energy balance (.MR)CR dTR = UO' (TR TQJvDl) dZ (20) -
.1
.2
.3
ill
Figure
6.
.4
.5 .6 .7 Fractional Height
.8
.9
1.0
Cocurrent flow, 5-kW reformer tube profiles.
Chang, 1973). These are accurate to within 2% over the temperature range (425-1315 °C). This accuracy is within the error band of the original measurements.
Solution Algorithm
Also, equation (17) has to be modified to
Similar heat transfer area changes would have to be made in the other two energy balances, eq 17 and 20. For this work, the arithmetic mean temperature difference is used in eq 17, 17a, 18, 20, and 21. That is
The co- and countercurrent reformer models consist of system of five basic equations (eq 10,11,12,17, and 18) containing five independent variables (XI, XE, X2, TH, and TC), and, hence, are completely defined. The DCCF models add one equation and one variable and are also completely defined. Therefore, a unique solution can be obtained for each set of input data. The solution is generated by a finite difference/incremental approach. All differentials in the equations are expressed as finite difThe ferences across a small height increment ( ). equations are then rearranged and solved for all exit variables in terms of the input variables to that increment. This requires iteration loops on XE and the reformer gas temperature, TC (i + 1). This is repeated sequentially for all height increments in the reformer. End values are checked against actual input values and boundary conditions, and differences are quickly converged using secant methods. This solution algorithm has been programmed onto a Univac 1100 series computer.
(TH
Model Results
Z(FACPA) dTC UI(TH TC)JttD2) dZ + Fl(-AHRl)dXl + (F3 + XlFl)(-AHR2) dX2 + UO'(TR TC)JirDl) dZ =
-
-
(17a)
The latter term accounts for product gas heat transfer to the catalytic bed. In actual operation, this can amount to as much as 25% of the reformer’s heavy duty, thus substantially boosting the unit’s efficiency. A flat slab geometry design necessitates adjustments to the heat transfer area term. For example, using the dimensions displayed in Figure 5, eq 18 becomes (MH)(CH) dTH = UI(TH TC)av(2)(ASLAB + BSLAB) dZ (21) -
(TR
-
-
TC)av
=
(l/2)(Tffi+1
TC)av
=
(l/2)(Tfli+1
-
-
TCi+1 + TH, + TCi+1 + TR¡
-
TC) (22) TC)
(23)
where subscripts i and i + 1 refer to the bottom and top of the reformer section as shown in Figure 3. Hence, for co- or countercurrent flow arrangements, the energy balances represent two equations in two unknown variables (TCi+1 and THl+l), provided all the other terms have been assigned values from the material balances. These two equations can be solved explicitly for TC,+1 and THi+1 after conversion to finite difference forms. The DCCF models add an extra variable (TRi+l) and an extra equation (no. 21). Hence, the solution is also defined but the energy balances require an iterative solution.
Physical Property and Heat-Transfer
Calculations The heat-transfer calculations require correlations and physical property data. Three correlations are available within the program from standard references (Smith, 1970; and Perry and Chilton, 1973), and more can be added as necessary. Physical property and equilibrium data are included in the program as fitted correlations of published data (Perry and Chilton, 1973; Touloukian et al., 1970;
a
The computer model has been tested over a wide range of input variables and model choices. Figures 6, 7, and 8 display results obtained on conventional 5-kW reformer tube analyses (no central plug, Dl = 0 in Figure 2). As expected, the cocurrent flow profiles (Figure 6) show continually decreasing driving forces for temperature and conversion as the gases proceed through the reformer, with thermal and reaction equilibrium achieved at the exit. On the other hand, the countercurrent flow profiles (Figure 7) display nearly constant driving forces over the reformer’s height, achieving a higher exit temperature and conversion, as shown by comparing Figures 6 and 7. A higher activity catalyst will increase the conversion further. Thus, as intuition suggests, the countercurrent flow arrangement is more efficient. However, the cocurrent flow arrangement keeps the metal surfaces ~200 °F cooler, providing milder
conditions for the reformer’s structure and extending reformer tube life. These two points have to be considered in reformer design. Flow rate changes and fluctuations have practical significance for reformers. This is particularly true of small volume reformers in fuel cell systems, where the off-peak flow rate is 25% of the design flow rate. Figure 8 displays
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Figure
7.
291
Countercurrent flow, 5-kW reformer tube profiles.
9. Conversion dependence ment (60-kW flat slab reformer).
Figure
on
flow rate and flow arrange-
Flow Rate, kW
Figure 8. Conversion dependence on flow rate
(10 kW
=
295
SCF/h
H2).
predicted conversion dependence on flow rate for the two flow arrangements in a 5-kW tube. As Figure 8 shows, while the countercurrent flow arrangement provides a consistently higher conversion, and hence, hydrogen production rate, it also displays greater flow rate dependence.
Hence, under off-peak circumstances, too much hydrogen may be produced, presenting a control problem. Flat slab geometry reformers have been suggested as possible alternatives to tubular designs for low-pressure systems (
