steam-methane reformer kinetic computer model with heat

288 Ind. Eng. Chem. Process Des. Dev. 1985, 24, 286-294

indebted to W. Smith for her NMR analysis work. Weltkamp, A. W.; Gutberiet, L. C. Ind. Eng. Chem. Process Des. Dev. 1970. 9 . 386.

Literature Cited Aiired, V. D. Cob. Sch. Mines 0. 1984, 59, 47. Bae, J. H. SOC. Pet. Eng. J. 1989, 9 , 287. Brown. J. K.: Ladner. W. R. Fuel 1980. 39. 87.

William, 'R. 6 . Symposium on Composltlon on Petroleum Oils. Determination

Yang, H. S.; Sohn. H. Y. Ind. Eng. Chem. Process Des. Dev. 1985, Part 2 and Evaluation, ASTM Spec. Tech. Publ. 1958, 224, 168.

of the companion articles in this issue.

Received for review November 7, 1983 Revised manuscript received April 19, 1984

Accepted May 21, 1984

University of Utah Research Committee and the University of Utah College of Mines and Mineral Industries Mineral Leasing Fund.

Burnham. A.' K.; Singleton, M. F., Lawrence Llvermore National Laboratory,

Hill, G. R.; Johnson, D. J.; MIHer, L.; Dougan, J. L. Ind. Eng. Chem. Process

McKay, J. F.; Latham, D. R. Anal. Chem. 1980, 52, 1618.

Shape, C. E.; Ladner, W. R. Anal. Chem. 1979, 51, 2189. Sohn, H. Y.; Yang, H. S. Ind. Eng. Chem. Process Des. Dev. 1985, part 1

Rept. UCRL-88127, 1982.

Des. Dev. 1987. 8 , 52.

Chem. Soc. 1989, 91, 7445.

of the companion articles in this issue.

Reich, H. J.; Jantelat, M.; Messe, M. 1.; Wigert, F. J.; Roberts, J. D. J. Am. This work was supported in part by a Research Grant from the

Steam-Methane Reformer Kinetic Computer Model with Heat Transfer and Geometry Options

Alexander P. Murray* and Thomas S. Snyder

Westinghouse RbD Center, Pittsburgh, Pennsylvania 15235

A kinetic computer model of a steamlmethane reformer has been developed as a design and analytical tool for a fuel cell system's fuel conditioner. Thls model has reaction, geometry, flow arrangement, and heat transfer options. Model predictions have been compared to prevbus 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 indlcate a conslderably 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.

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 Sard (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 (25125% of design), and can be small (- 10 kW) or large (- 10 MW). Typically, around 0.75 lb-mol of hydrogenlh is required for each 10 kW of electric power in a phosphoric acid 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

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 norm analysis. Model calculations on the reacting reformer gases 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 in- calculable 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 intemal regenerative heat transfer. These designs have practical applications in other packed bed reactors operating on endothermic reaction systems.

Previous Kinetic Modeling Work Oblad (1967) and, later, Grover (1970) discussed a steam

methane reformer computer model that includes heat

0196-4305/85/1124-0286$01.50/0 0 1985 American Chemical Society

Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 287

Product Gas Table I. Reformer Model Assumptions Insulating Cap

.-Annular Catalyst Bed

Burner Cavitv

Exhaust I Gas Gas Reiormer Gases Reformer

Gases

Figure 1. Double countercurrent flow (DCCF) reformer tube.

transfer and reaction kinetics in the analysis. This model is based upon the following reaction choices

(1)

(2) Carbon formation by reactions such as eq 3 is usually very small and can be neglected under normal industrial operating conditions.

(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 reverse reaction rate is also included to account for 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

(4) instead of eq 1, and, with the water gas shift reaction (eq 2), it form 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

CH4 + HzO = CO + 3H2 CO + H2O = COP + H2

2co = c02 + c

CHI + 2H20 = C02 + 4H2

1. Reforming and combustion gases flow with complete radial but

2. Only axial temperature changes are allowed, and radial

3. A uniform temperature exists throughout each catalyst

no axial mixing (i.e., plug flow).

temperature profiles are neglected.

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.

(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 steam- methane 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 a t 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 31, cocurrent, or 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) (2)

CH4 + 2Hz0 = COz + 4Hz CO + HzO = COZ + Hz

288 Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985

- 5 - i Center Line @ Z = Z , Know THZ, MH

I I + 1

Square Duct for Combustion Gas Fiw

I_

Primary Heat Flw - Q

Reactant FlwR - Combustion Gas Flowc -

Figure 2. Heat transfer surfaces (major heat flux denoted by arrow Q).

Combustion Gases

2 = z 'Hz' MH

Combustlon Gases

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. Equa- tion 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.

(3) (4)

Table I1 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

2co = c + c02 C + HzO = CO + H2

k D 3

@Z=O K n w T C O . PCo. I F i I , XEZ0

Figure 4. Double countercurrent flow, tubular geometry reformer model (regenerative gases flow on the inside).

Figure 5. Dimensions and variables for the flat slab reformer (countercurrent flow).

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 = kOe-EA/RTAP (5)

AP = PCHl - PCH4,E (6)

AP represents the difference between the actual and equilibrium methane partial pressure. The two parameters, the frequency factor (k,) 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 X 1 as the methane conversion by reaction 1 and X E as the equilibrium conversion, then the rate equation takes on the form

] ( 7 ) F l ( 1 - X 1 ) F + 2 X l F 1

F l ( 1 - X E ) F + 2 X E F l

- -rCH4 = Pkoe-EA/RT


Table 11." Summary of Kinetic Equations and Parameters Found in the Literature workers expression value

Akers and Camp (1955)

Bodrov et al. (1964, 1967)

Allen et al. (1975)

Rostrup-Nielsen (1975)

Grover (1970)

Hyman (1968)

this work

-rCH4 = k e-EAIRT PCH4 0

"Units Ko[lb-mol/(h lb of cat, atm]; E A [cal/mol].

-rCH4 = kOe-EA/RTP CH4

k o = 127

E A = 8778 (commercial cat.)

for nickel foil

ko = 1 X IO6 EA = 31 000 for commercial cat.

EA = 19400

ko = 1.04 X IO4 EA = 20000 (assumed)

ko = 2.19 X 10'

E A = 26000 or ko = 4.43 X lo6 E A = 20000

ko = not reported E A = 8778 KE2 = equilibrium constant of the reaction, CH4 + HzO = CO + 3Hz

KE1 = equilibrium constant of reaction 4

ko = 100-1 X IO5 EA = 10000-26000 PcH4,E is the methane partial pressure at equilibrium

k o = 6.1 X IO6

Table 111. Molar Flow/Rates as a Function of Reaction Conversions (Basis: 1-h Flows)

component mol in feed mol produced by reaction 1 reaction 2 mol present mol produced by

CH, F1 -XlFI 0 F1- XlFl F2 0 F3 XlFl F4 -2XlF1 F5 4XlF1 F6 0

totals F 2XlF1

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 balance (eq 10).

1 dX1 pBPkOe-EA'RT Fl(1-Xl) Fl(1- XE) - dz = [ uoCo ] [ F+2XlFl - F + 2XEFl

(10)

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 111).

Equilibrium Calculations The equilibrium conversion required in the rate ex-

pression (eq 10) necessitates the solution of the combined equilibrium expressions for the two reactions (eq 1 and 2).

-X2 (F3 + XlF1)

-X2 (F3 + XlF1)

F2 - X2 (F3 + XlF1)

F4 - 2XlF1- X2 (F3 + XlFI X2 (F3 + XlF1)

X2 (F3 + XlFI) 0 F6

0 F + 2XlF1

F3 + XlFl + X2 (F3 + XlF1)

F4 + 4X1F1+ X2 (F3 + XlFl

Assuming ideal gas behavior (fugacity coefficients of unity), the demethanation reaction equilibrium becomes

PCOzPH: - yCOzyH:

PCH~PH~O YCH4YH~02 K 1 = 2 - P2 (11)

The water gas shift reaction equilibrium is

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, a t specified temperature (fixed equilibrium constants) and boundary conditions (feed rates), eq 11 and 12 reduce to only two unknown variables (the conversions, X1 and X2). Furthermore, eq 12 can be rearranged to yield a quadratic equation in X2 as a function of X1, providing a convenient iterative cal- culational sequence (eq 13-16).

AX22 + BX2 + C = 0 (13)

A = (K2 - 1) (F3 + XlF1)' (14)

B = (F3 + XlF1) (2XlFlK2 - K2F2 -K2F4 -

C = 5XlF1 - F3 - F5) (15)

K2F2F4 - 2K2F2XlFl- (F3 + XlF1) (F5 + 4XlF1) (16)


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

C(FACPA) dTC = UI(TH - TC),,(aD2) dZ + Fl(-AHRJ dX1 + (F3 + XlFl)(-AHEJ dX2 (17)

combustion gas energy balance

(MH)CH dTH = UI(TH - TC),,(rD2) 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 ( P ) + ~ ( 2 3 ) (19) The DCCF models (Figure 4) require the inclusion of

a product gas energy balance (MR)CR dTR = UO’ (TR - TC),,(aDl) dZ (20)

Also, equation (17) has to be modified to C(FACPA) dTC =

UI(TH - TC),,(TD~) dZ + Fl(-AHRi)dXl + (F3 + XlFl)(-AHR*) dX2 + UO’(TR - TC),(TDl) dZ

(174

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 sub- stantially 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 =

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

UI(TH - TC),,(2)(ASLAB + BSLAB) dZ (21)

(TH - TC),, = (1/2)(TH,+1 - TC,+1 + TH, + TC,)

(TR - TC),, = (1/2)(TR1+1 - TC,+, + TR, - TC,) (22)

(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 (TC,,, and TH,,,), provided all the other terms have been assigned values from the material balances. These two equations can be solved explicitly for TC,+l and TH,+, after conversion to finite difference forms. The DCCF models add an extra variable 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;

Reformer Gas Temperature

I 1 0 Equilibrium

I Conversion i 1

Conversion

M Actual ( k i net I C )

Conversion

I 2 3 4 5 6 7 8 0 1 0 t / Z Fractional Height

Figure 6. 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 The co- and countercurrent reformer models consist of

a system of five basic equations (eq 10, 11,12,17, and 18) containing five independent variables (Xl, 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 gen- erated by a finite difference/incremental approach. All differentials in the equations are expressed as finite differences across a small height increment (a). The 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.

Model Results 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, D1 = 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 O 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 sig- nificance 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


Reformer Gas Temperature

Equi l ibr ium - Conversion

L

. % s V

Actual (k inet ic) Conversion

. I , 2 , 3 , 4 . 5 , 6 , 7 .8 , 9 1.0 L I Z Fractional Height

Figure 7. Countercurrent flow, 5-kW reformer tube profiles.

1.01 I I I I 1 I

Counter-current Flw

. 9

. 7 i ' I I I I 2 4 6 8 1 0

Flw 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 (<75 psig), primarily due to their superior heat- transfer characteristics. The model predicts conversion and temperature profiles for the flat slab reformers to be similar to the tubular profiles presented in Figures 6 and 7. However, the flat slab reformer exit conversion is some 5% higher, when calculated at similar conditions (e.g., space velocity, temperatures, etc.). This is due to the better heat transfer. Figure 9 shows the predicted flow rate sensitivities of both flow arrangements for a 60-kW slab reformer design. These curves are similar to those of the tubular design (Figure €9, except the conversion crossover point occurs within the range of study at the design length (2 = 4 ft). Decreasing the space velocity pushes this crossover point to a higher flow rate (curves at Z = 6 in Figure 91, but does not change the basic shape of the curves.

Model parametric studies on DCCF designs show similar flow rate trends as Figure 8, although the DCCF model

. 9

.7 t Counter-Current Flow

.6 I I I 1 1

kW Flow Rates

Figure 9. Conversion dependence on flow rate and flow arrangement (60-kW flat slab reformer).

20 40 60 m 100 120

L l i ! , , h l

7 w 1 I I I , I , , , i, 4w 0.00 0. 20 0.40 0.60 0. m 1. w

Fractional Height

Figure 10. Double countercurrent flow, tubular geometry temperature profiles (arrangement of Figure 4).

predicts a conversion slightly higher (5% maximum) than the countercurrent flow case. This effect is due to the heat transfer/recovery from the product gases. Figure 10 displays sample DCCF temperature profiles, showing the product gas effect.

Heat transfer strongly affects reformer design and performance (Hyman, 1968; Golebiowski and Wasala, 1973). Standard correlations (Smith, 1970; Perry and Chilton, 1973; Golebiowski and Wasala, 1973) give predicted local heat-transfer coefficients that vary by several hundred percent (Golebiowski and Wasala, 1973), and these should be experimentally determined for the reformer design of interest. However, the correlations in the model predict overall heat transfer coefficients in the range 2-5 Btu/h ft2 OF, using two Leva packed bed correlations from Smith (1970)

Nu = 3.5(ReJ0.' exp (24)


D P / D Ratio 0.062 0.123 0.185 0.246 0.308 0.369

I , I I I

2 4 6 8 1 0 1 2 Catatyst Particle Size ( mml

Figure 11. Catalyst particle size effects on heat transfer (10-kW design).

DP/D Ratio 0.062 0.123 0.185 0.246 O.M8 0.369

I I , 1 I , I

Table IV. Phillips Petroleum Reformer Data (from Hyman, 1968)

given (from input the article) used in the model

height, f t 40 2 = 40 tube i.d., in. 5 0 2 = 5 in. tube wall thickness, in. 17/32 used 0 3 = 6 in. (wall

thickness = in.) catalyst particle size, in.

mass flow rate, lb/ (h ft2) (superficial)

steam/methane ratio gas mix inlet

temperature, O F

tube wall temperature

inlet pressure, atm abs outlet pressure, atm ab output

gas mix outlet temperature, O F (cat. bed) feed carbon converted, % tube wall outlet temperature, O F

inlet particle Reynolds number

5 1 ; x 5 / s x (rings)

5476

7:l 687

TW = 1300 + (first, 3 ft unheadted, Z in f t )

172 - 0.2p

14.3 12.1

1460

91.7

1700

5000

, " 'Iz (spheres)

same, using 7:l steam/methane ratio, corresponds to FO = f42/08 lb-mol/h, F1 = 5.26, F4 = 36.82

7:l 687

same, entire tube heated

P = 13 atm throughout

1514 (calcd)

86.1 (calcd)

1660 (calcd)

4270 (calcd)

I

Table V. Westinghouse/ERC Reformer Tube Dataa distance from gas gas bed,

inlet, cm measured temp, OF, predicted

2 4 6 8 I O 1 2 Catalyst Particle Sire ( m m l

Figure 12. Catalyst particle size effecta upon hydrogen production rate (10-kW design).

(Leva correlation for cooling, used for the combustion gas side film coefficient)

Nu - 0.813 (Re,)0.9 exp - (25) [E] (Leva correlation for heating used for the reforming gas/catalytic bed side film coefficient).

These correlations, derived from flowing air experiments, indicate an almost linear flow dependence and a very strong particle size dependence. For example, using the wall temperature profile model (Le., eq 25 only), the predicted heat transfer coefficient sharply declines on either side of the maximum (Figure 11). This, of course, affects the conversion and hydrogen production rate (Figure 12), amply demonstrating the strong heat transfer effects on compact reformer design, such as would be required for fuel cell systems. Doubling the heat transfer coefficient increases the predicted exit conversion by around 10%.

0 5 10 15 20 25 30 25 40 45 41.5

653 770 851 914 954 995 1040 1103 1175 1274 1328

653 738 809 873 935 995 1052 1109 1168 1238 1327

[I Measured kinetic conversion = 98.4%; predicted kinetic conversion = 88.2%.

Limited internal Westinghouse data predicts an overall heat transfer coefficient in the range 5-10 Btu/h ft2 OF for the fuel cell reformer system, i.e., double that predicted by eq 25. This is supported by analyses of small reformer experimental data in the next section.

Comparison of the Model Predictions with the Available Data

No data is presently available for a flat slab reformer design as a means of evaluating the model's accuracy. Only limited data are available on DCCF designs, and these are insufficient for running the model. Fortunately, open literature data exist for evaluation of the tubular geometry models, using the wall temperature profile approach. Table IV compares the program predictions with data on a conventional reformer tube in the hydrogen plant of the Phillips Avon Refinery in California (Hyman, 1968) using catalyst data derived from the literature (Allen et al., 1975). As Table IV shows, the agreement is remarkable: within 6% on conversion and 60 OF on the exit temperature.


Table VI. Comparison of Model Predictions with the Experimental Data” conversions

temperature error norms measured predicted run cat. bed wall x1 X E x1 X E

~~ ~

1 6.5% <1% 0.876 0.851 0.644 0.759 2 7.8% <1% 0.883 0.869 0.695 0.818 3 9.6% <1% 0.821 0.851 0.730 0.859 4 8.6% <1% 0.822 0.891 0.706 0.859 5 7.8% <1% 0.759 0.834 0.612 0.751

“From the data of Christner (1979).

Unfortunately, insufficient data were presented for conversion and temperature profile comparisons.

Westinghouse/ERC data have been produced by an electrically heated, experimental reformer tube (-0.2 kW design capacity) and reported by Christner (1979). This has been analyzed using the wall temperature model. Table V shows a sample experiment vs. prediction comparison, and Table VI provides a summary. Good agreement is obtained between the measured and predicted temperature values, although the predicted conversion is - 15 ’3% too low. This may be due to uncertainties in the catalyst parameters or the heat transfer. These model calculations used a heat transfer coefficient double that of eq 25, as suggested by the analyses of Hoover et al. (1980). Given the close agreement of the temperature profiles, the heat-transfer coefficients appear to be in the right range. Discussion

Analysis and validation of the model’s fit of the experimental data fall into three areas: the heat transfer doubling factor, the model calculations, and experimental data variations/errors. As indicated before, the increased reformer heat transfer and its magnitude have been previously reported in the literature. Presumably, this dramatic (i.e., doubling) heat transfer improvement is a reaction related effect, such as the following.

1. The endothermic reformer reaction cools the catalyst particles, resulting in a greater temperature driving force than expected, and, hence, better than expected heat transfer.

2. As the reaction proceeds, hydrogen is produced, and, with ita better transport properties, heat transfer increases. This would be particularly true near the hot tube wall where the reaction rate and hydrogen concentration are greater.

3. The reaction produces a net mole increase, which increases the gas velocity, and in turn, the heat transfer. Again, this effect is greatest near the hot tube wall.

4. The compact, DCCF reformer design has larger thermal and reaction gradients as compared to conventional reformers, and hence, cannot be analyzed by a unidimensional model.

A unidimensional model would tend to obscure all these effects and combine them into a larger, apparent heat transfer coefficient. However, the sheer magnitude of the anomaly, and the previous literature reports, suggest that the anomaly is real. Currently, no plans exist to develop a two-dimensional model.

Radiative heat transfer effects are not included in the model. Hoover et al. (1980) analyzed both convective and radiative heat transfer to a fuel cell reformer tube under otherwise identical conditions and concluded there was little difference between the two cases (<20 O F difference in wall temperature). Additionally, the compact spacing of fuel cell reformer tubes and the high flow rates of rel- atively “low” temperature (2000-2500 O F ) gas past the tubes would minimize any radiation effects present. Ad-

ditional data from Hoover (1982) support this approach and also indicate a similar, reaction-induced heat transfer improvement over nonreacting gas heat transfer, using the same experimental unit.

The model kinetic, equilibrium, and physical property calculations have been thoroughly checked and validated. The model’s kinetic equation is a simplification but should be representative of the experimental conditions because of the excess steam. Measured catalyst activity parameters are used. However, these were determined for a slightly different version of the catalyst, and there is also experimental evidence of an activation energy change in the higher temperature end of the reformer (-1100 OF). This marks the beginning of a transition from a surface reaction-controlled rate to external gas film, diffusion resist- ance control. However, there is little catalyst data above this temperature to fully document the transition. In- traparticle diffusion should not be significant in this system, due to the highly endothermic nature of reformer reactions, which result in lower intraparticle temperatures and reaction rates. Diffusion effects are not explicitly included in the model, because these effects can usually be included by an appropriate, global rate expression (e.g., see Smith, 1970).

Finally, experimental variations include temperature and concentration errors and heat losses to the environment. Thermocouple reading and location errors probably con- tribute about 3%, and chromatograph and concentration measurement errors probably add another 3%. Heat losses are not included in the model, but may be significant for small systems. However, electrical heating should minimize this effect. Hence, the temperature and equilibrium conversion errors are approximately equal to the experimental uncertainty range, while the kinetic conversion errors are approximately double. Therefore, it seems reasonable to assume that a combination of low catalyst activity and experimental errors is responsible for the model deviations. Acknowledgment

The work described in this paper was performed under NASA Contract DEN3-161, funded by DOE and admin- istered by the Lewis Research Center; Project Manager: Robert B. King. The authors also wish to express their appreciation to Dr. William E. Young of Westinghouse for his assistance and guidance during this program, and to Dr. Larry G. Christner of ERC for the small reformer experimental results. Nomenclature AASLAB, ASLAB = flat slab reformer length dimensions

(Figure 5), m BBSLAB, BSLAB = flat slab reformer width dimensions

(Figure 5 ) , m c = methane molar concentration, kmol/m3 co = initial methane molar concentration, kmol/m3 CH = combustion gas molar heat capacity, J/mol K CR = product gas molar heat capacity, J/mol K

294 Ind. Eng. Chem. Process Des. Dev. 1985, 24, 294-296

D = diameter, m DE = equivalent (hydraulic) diameter, m DELTA = flat slab reformer wall thickness, m DP = particle diameter, m D1 = inner tube's 0.d. (Figure 2), m 0 2 = outer tube's i.d. (Figure 2 ) , m D3,D4 ,D5 = other reformer tube dimensions, m E A = Arrhenius activation energy, cal/mol F = total feed molar flow rate, kmol/h F1 = CHI feed molar flow rate, kmol/h F2 = CO feed molar flow rate, kmol/h F3 = C02 feed molar flow rate, kmol/h F4 = H20 feed molar flow rate, kmol/h F5 = H2 feed molar flow rate, kmol/h F6 = N2 (diluent) feed molar flow rate, kmol/h ko = Arrhenius frequency factor, kmol/(h kg of cat. atm) K1 = demethanation reaction equilibrium constant, atm2 K2 = water gas shift equilibrium constant M H = combustion gas molar flow rate, kmol/h MR = product gas molar flow rate, kmol/h Nu = Nusselt

P = total pressure, atm hp = difference between the actual and equilibrium methane

partial pressure, atm P C H 4 , Pco, Pco1, P H ~ o , P H ~ = component partial pressure, atm PCH4,F = equilibrium methane partial pressure, atm R = ideal gas constant, 1.99 cal/mol K (-rCH4) = demethanation reaction rate, kmol/(h kg of cat.) Re, = particle Reynolds number T = absolute temperature, K TC = reformer gas temperature, K TH = combustion gas temperature, K TR = product gas temperature, K (TH - TC),, = average temperature difference between TH

(TR - TC),, = average temperature difference between TR

TW = combustion tube wall temperature, K u = reformer gas velocity, m/h uo = initial reformer gas velocity, m/ h UI = overall heat transfer coefficient between the combustion

and reforming gases, kJ/(h m2 K) UO' = overall heat transfer coefficient between the product

and reforming gases, kJ/(h m2 K) X 1 = kinetic deme-

number

and TC, K

and TC, K

thanation reaction conversion XE = equilibrium demethanation reaction conversion X 2 , X E 2 = water gas shift reaction conversion YCH4, Yco, Y C O , = component mole fractions YHzo, YHz = component mole fractions 2 = reformer height, m AHR, = demethanation reaction enthalpy, kJ/mol of CH4 A H R 2 = water gas shift reaction enthalpy, kJ/mol of C 0 2 pB = catalyst bed density, kG of cat./m3 of reformer C(FACPA) = heat capacity of the reformer feed gas, J /h K

Literature Cited Akers, W. W.; Camp, D. P. AIChE J. 1955, 4, 471. Allen, D. W.; Gerhard, E. R.; Likens, M. R., Jr. Id. Eng. Chem. Process

Bodrov, N. M.; Apel'baum, L. 0.; Temkin, M. I. Klnet. Katal. 1964, 5(4), 696. Bodrov, N. M.; Apel'baum, L. 0.; Temkin, M. 1. Kinet. Katal. 1967, 8(4), 821. Chang, H. Y. Chem. Eng. 1973, 80(8). 122. Christner, L. G. "Technology Development for Phosphorlc Acid Fuel Cell Pow-

5th Quarterly Report"; DOEINASAINASA CR-

Goiebiowski, A.; Wasala, T. Int. Chem. Eng. 1973, 13(1), 133. Grover, S. S . Hydrocarbon Process. 1970. 49(4). 109. Harth, R.; Kugeler, K.; Nlessen, H. F.; Bottendahl, V.; Theis, K. A. Nucl.

Techno/. 1978, 38, 252. Hoover, D. Q., et al. "Cell Module and Fuel Conditioner Development: Quar-

terly Report No. 1, October-December 1979," NASA Contract DEN3-181, 1980.

Hoover, D. 0. "Cell Module and Fuel Conditioner Development: Final Report: October 1979January 1982," NASA CR-165193, Feb 1982.

Hyman, M. H. Hydrocarbon Process. 1968, 47(7), 131. Oblad, A. G. OilGas J. 1967, 54(16), 164. Olesen. 0. L.; Sederquist, R. A. "The UTC Stream Reformer," United Tech-

nologies Corporation, Windsor, CT; paper presented in Santa Barbara,

Perry, R. H.; Chilton, C. H. "Chemical Engineers Handbook," 5th ed., McGraw-Hill, Inc.: New York, 1973; pp 10-12 to 10-17.

Rostrup-Nielson, J. R. "Steam Reforming Catalysts," Danish Technical Press, Inc.: Copenhagen, 1975; pp 85-105.

Singh, C. P. P.; Saraf, D. N. Id . Eng. Chem. Process Des. Dev. 1979, 18, 1.

Smith, J. M. "Chemical Engineering Kinetics," 2nd ed., McGraw-Hlll: New York, 1970; pp 493-547.

Smith, W. N.; Santangelo, J. G. ACS Symp. Ser. 1980, No. 116, 147-178. Touloukian, Y. S. Liley, P. E.: Saxena, S. C. "TPRC Data Series"; Plenum:

New York, 1970: Vol. 3.

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Des. Dev. 1975, 14, 256.

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CA, OCt 23-25, 1979.

Received for review February 22, 1982 Revised manuscript received April 9, 1984

Accepted May 7, 1984

Cotretations for Estimating Critical Constants, Acentric Factor, and Dipole Moment for Undefined Coal-Fluid Fractions

Suphat Watanaslrl; Victor H. Owens,+ and Kenneth E. Starllng School of Chemical Englneering and Materials Science, Universify of Oklahoma, Norman, Oklahoma 730 19

Correlations have been developed to estimate critical constants, acentric factor, and dipole moment of model coal compounds and other hydrocarbons and thek derivatives. The correlations express the characterization parameters as functions of normal boiling polnt, specific gravity, and molecular weight, which are the inspection data normally obtained for undefined petroleum and coal flulds. Currently available correlations are applicable only to petroleum and nonpolar coal-fluid fractions. The present correlations extend the range of application to polar and associating fluids.

Introduction For undefined petroleum and coal fluids (or boiling-cut

fractions), it is a common practice that only inspection data, namely, normal boiling point ( Tb), specific gravity

t Morgantown Energy Technology Center, Morgantown, WV

(SG), and molecular weight (MW) are experimentally measured. However, in order to predict thermophysical properties of these fluids using corresponding-states correlations, values of the critical constants, acentric factor, and other characterization parameters for the fluids (or fractions) are necessary. Therefore, correlations for estimating these characterization parameters as functions of 26505.

0196-4305/05/1124-0294$01.50/0 0 1985 American Chemical Society

steam-methane reformer kinetic computer model with heat

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