MATHEMATICAL MODELLING OF METHANE STEAM REFORMING IN A MEMBRANE REACTOR: AN ISOTHERMIC MODEL

MATHEMATICAL MODELLING OF METHANE STEAM REFORMING IN A MEMBRANE REACTOR: AN ISOTHERMIC MODEL

E.M. ASSAF1,^*, C.D.F. JESUS² and J.M. ASSAF²

¹ Departamento de Físico-Química, Instituto de Química de São Carlos,

Universidade de São Paulo, Av. Dr. Carlos Botelho, 1465, Cx. Postal 780,

Phone: [phone], Fax: [phone], CEP:13560-970 - São Carlos, SP, Brazil

e-mail: [e-mail]

² Departamento de Engenharia Química, Universidade Federal de São Carlos,

Rod. Washington Luiz, km 235, Phone: [phone], Fax: [phone], CEP: 13565-905,

São Carlos, SP, Brazil e-mail: [e-mail]

(Received: November 5, 1997; Accepted: March 10, 1998)

Abstract - A mathematical modelling of one-dimensional, stationary and isothermic membrane reactor for methane steam reforming was developed to compare the maximum yield for methane conversion in this reactor with that in a conventional fixed-bed reactor. Fick's first law was used to describe the mechanism of hydrogen permeation. The variables studied include: reaction temperature, hydrogen feed flow rate and membrane thickness. The results show that the membrane reactor presents a higher methane conversion yield than the conventional fixed-bed reactor.

Keywords: Membrane reactor, steam reforming, mathematical model

INTRODUCTION

Methane steam reforming consists in the reaction of methane and steam on a supported nickel catalyst to produce a mixture of H₂, CO, CO₂ and CH₄. Currently, this process is the main route to obtain hydrogen and synthesis gas for ammonia and methanol.

Methane steam reforming in industry is carried out in a catalytic multitubular fixed-bed reactor. The reforming plant is composed of two units: the primary reformer, where the methane and water steam reaction occurs and the secondary reformer, where air is added to supply both the nitrogen necessary for ammonia synthesis and the oxygen to react with the non-converted methane to produce carbon monoxide and hydrogen.

Methane steam reforming involves two reversible reactions: reforming and the water-gas shift reaction. The first is endothermic and limited by thermodynamic equilibrium. Therefore, the development of a membrane-based separation process can open up the possibility of increasing the conversion of the reforming process. As hydrogen is selectively removed from the reactor, the chemical equilibrium of the reactions is shifted to the product, resulting in an increase in the conversion of methane to hydrogen and carbon dioxide. As an additional advantage, the membrane reactor offers the possibility of supplying hydrogen with the same conversion degree but higher purity, than that supplied by the conventional reactor, under less severe operational conditions. Methane steam reforming in a membrane reactor is not an equilibrium-limited reaction, but rather a mass transfer-limited reaction related with membrane porosity and diffusivity.

In this context, this work presents the mathematical modelling of a one-dimensional, stationary and isothermic membrane reactor in order to obtain hydrogen from the steam reforming of methane and compare the maximum conversions with those obtained from a conventional reactor.

METHANE STEAM REFORMING

The Process

In methane steam reforming, the catalytic fixed-bed reactor is fed with a gas mixture of CH₄ and H₂O in a molar ratio from 1:3 to 1:4. The commercial catalyst is composed of nickel supported on gamma-alumina. The industrial reactor is composed of vertical tubes (between 10 and 900) with internal diameters from 7 to 16 cm and lengths from 6 to 12 m, inserted in to a radiant furnace chamber. The entrance reactor temperature is 600^oC and pressures varies from 1.5 to 3.0 MPa (Rostrup-Nielsen, 1975). Exit temperature is limited by the metallurgical limitations of the tubes, since at higher temperatures the metal tube may creep under stress.

The main reactions involved in the steam reforming process are the hydrocarbon to carbon monoxide conversion and the water-gas shift (Xu and Froment, 1989a) :

CH₄ + H₂O ó CO + 3H₂ (R1)

CO + H₂O ó CO₂ + H₂ (R2)

Several other lateral reactions may occur in this process, but these reactions were not considered here. Steam reforming is an endothermic process, except for the water-gas shift, which is slightly exothermic.

Mathematical Model of the Fixed-bed Reactor

Mathematical modelling has been reported by Rostrup-Nielsen (1975), Singh and Saraf (1979), Xu and Froment (1989b) and Ziolkowski & Szustek (1991).

The one-dimensional, steady-state, pseudo-homogeneous approach and isothermic model used to simulate the conventional fixed-bed reactor can be represented by:

(1)

where F is the molar flow, X_i is conversion of component i, z is the length of the reactor, r _b is the apparent density of the catalytic bed, A is the reactor cross section area and R_i is the reaction rate. The ordinary differential equations were solved with a algorithm to integrate in the axial direction (an explicit Runge-Kutta method with a variable step).

The kinetic model used here was obtained in the work of Singh and Saraf (1979 ):

(2)

(3)

where R_j is rate of reaction j, k⁰ is the reaction rate coefficient, E_a is the activation energy, T is the temperature, R is the constant gas, P_i is the partial pressure of component i, P_TOT is the total pressure and K_{eq j} is the equilibrium constant of reaction j.

MODELLING THE MEMBRANE REACTOR

The Membrane Reactor

The membrane reactor have a number of different types of reactor configurations containing membranes inside. The membrane can provide a barrier to a number of components of the reaction effluents, while permiting permeation by others, or it may be used as a catalyst support by depositing a catalytically active component on it. The membrane reactor has been used to increase conversions in thermodynamically or kinetically-limited catalytic processes. This reactor is applied to obtain conversion levels up to the theoretical equilibrium value. These higher conversion levels can be obtained as a consequence of the shift in thermodynamic equilibrium of the reversible reactions in the direction of product formation, as a consequence of removal by a diffusion mechanism of a product desirable for the semipermeable membrane. Based on this concept, incorporation in reactors of a separation membrane, especially a selective membrane for hydrogen separation, has been proposed and studied (Uemiya et al., 1991, Kikuchi et al., 1991, Deng and Wu, 1994, Chai et al., 1994).

The use of membrane reactors in high temperature catalytic processes is increasing as a consequence of the development of good quality inorganic membranes and inorganic membranes composed of a thin metal film deposited on a ceramic support. The metallic membranes, especially pure palladium and silver-palladium alloys, are extremely sensitive in separating hydrogen from other gas components, although they are very expensive and have lower mechanic resistance when compared with the ceramic membranes. The metal/ceramic membrane presents higher hydrogen permeability than the normal palladium membrane, while high hydrogen selectivity remains constant.

Hydrocarbon steam reforming has been used on an industrial scale to produce hydrogen. As the reaction is highly endothermic, the high reaction temperatures are thermodynamically favorable to increasing hydrogen production. If hydrogen is selectively removed from the reaction system, high temperatures are no longer necessarily required from the thermodynamic point of view. In addition, the palladium membrane is only permeable to hydrogen, and the presence of carbon monoxide is avoided.

Reactor Model

The membrane reactor configuration is simple and consists of an external steel tube (shell) with entrance and exit places for the sweep gas (permeation zone). A ceramic, metallic or composite metal/ceramic porous tube is placed inside the shell and sealed at the edges (reaction zone). A methane and steam water mixture is continuously fed in to the catalytic zone. A sweep gas, usually nitrogen, is introduced on the permeation side to drag the permeated gas.

The membrane reactor modelling has been reported by Itoh (1990), Shu et al. (1994) and Itoh et al. (1994). The hypothesis adopted to solve the mathematical model used in this work was a one-dimensional, steady-state, isothermic and isobaric reaction. The ordinary-differential equations for the variations in flow of each component are shown in sequence. The reaction occurs on the reactional side along the length of the reactor resulting in a mixture of reagents and products. Each component of the mixture can pass over to the permeation side as a consequence of the type of membrane and of the corresponding permeation mechanism.

The permeation mechanism of the palladium membrane is configurational and diffusive. In this case, hydrogen permeation velocity (Q_H) is given by Fick's first law (Lewis, 1967) :

(4)

A_m= p d_mL (5)

where D_h is the hydrogen diffusion coefficient, A_m is the area of the membrane, t_m is the membrane thickness, C_r and C_s are the hydrogen concentrations dissolved in the membrane at the reaction and separation interfaces, d_m is the external diameter and L is the length of the reactor.

The hydrogen diffusion coefficient in the membrane was adjusted using previous data (Lewis, 1967) for several temperatures. The adjustment equation is:

(6)

with D_h in m²/h and T in ^oC.

A material balance of each component in a differential section of the reactor (dL) results in the following ordinary differential equations:

Reaction side:

(7)

Permeation side:

(8)

where u_i and v_i are flow velocity of each component on the reaction and permeation side; r_i is the reaction rate, given by the Singh and Saraf model (equations 2 and 3); Q_i is the permeation velocity of component i from the reaction to the permeation side and A is the cross-sectional reactor area.

The set of ordinary differential equations was numerically solved using the Runge-Kutta algorithm with a variable step.

RESULTS AND DISCUSSION

Standard conditions used to simulate the behavior of the methane steam reforming process in the conventional fixed-bed reactor and the membrane reactor can be seen in Table 1.

Solutions for the mathematical models of the fixed-bed reactor and the membrane reactor, equations 7 and 8, resulted in several plots for the conversion of methane. Comparisons of these results can be seen in the next figures. Some operational conditions were changed in order to verify their influence on the process.

Figure 1 shows that, with the membrane reactor, methane conversion is always higher than that obtained with the fixed-bed reactor. The yield of the process with the membrane reactor increases around 16% in comparison with the conventional reactor. It is also observed that the higher the reaction temperature, the higher the equilibrium conversion.

Figure 2 presents the effect of thickness of the palladium film. For thinner film, methane conversion increases, due to the smaller mass transfer resistance. On the other hand, mechanical limitations exist in the construction of continuous thin films of palladium supported on ceramic substrates presenting surfaces without flaws or cracks. These surface defects make the membrane less selective. Experimental work with membrane reactors shows a thickness of palladium films of around 5 x 10^-6 to 20 x 10^-6 m (Jemaa et al., 1996; Collins and Way, 1993).

Table 1:
Parameters and operational conditions used to simulate the reactors

Condition of operation/parameter	Value
Entrance temperature	973 K
Total pressure in the reaction zone	35.4 atm
Total pressure in the permeation zone	20 atm
Initial flows	CH4= 1202 kmol/h H20= 5000 kmol/h CO= 0 CO2= 200 kmol/h H2= 100 kmol/h N2= 0.10 * Ftotal of the reaction zone
Length of the tubes	12 m
Number of tubes	396
Thickness of palladium film	5 x 10-6 m

Figure 1:
Methane conversion vs. reactor length for several reaction temperatures.

Figure 2:
Methane conversion vs. reactor length for several thicknesses of the palladium film.

Figures 3 and 4 show the effect of pressure on the methane conversion throughout the reactor. In figure 3, the pressure in the permeation zone was kept constant and equal to 20 atm, while the pressure in the reaction zone was changed. It is observed that a lower pressure in the reaction zone favors reagent conversion, showing that for this reaction equilibrium displacement in the direction of the products is favored by a decrease in pressure. In figure 4, the pressure in the reactor zone was kept constant and equal to 35.4 atm, while that of the permeation zone was varied. In this case, the smaller the pressure in the permeation zone, the larger the pressure gradient between the permeation and reaction zones, favoring the diffusive flow of hydrogen through the membrane and, therefore, increasing the conversion of methane.

In figure 5, where the profiles of methane conversion along the length of the reactor are presented for several initial flows of hydrogen, it is possible to see that the larger the initial hydrogen flow is, the smaller is the methane conversion, as a function of spatial velocity.

Figure 3: Methane conversion vs. reactor length for several pressures in the reaction zone. P_permeation = 20 atm

Figure 4: Methane conversion vs. reactor length for several pressures in the permeation zone. P_reaction = 35.4 atm

Figure 5:
Methane conversion vs. reactor length for several initial flows of hydrogen.

CONCLUSIONS

The membrane reactor always presented higher methane conversions when compared to the conventional fixed-bed reactor, as a consequence of the displacement of thermodynamic equilibrium in the direction of the formation of hydrogen. With the continuous hydrogen permeation through the membrane, it is possible to obtain levels of methane conversion higher than those obtained in the fixed-bed reactor.

These results show the potential of the membrane reactor for use in the methane steam reforming reaction.

NOMENCLATURE

A Reactor cross-section area, m²

A_m Area of the membrane, m²

C Concentration of the hydrogen, kmol/m³

d_m External diameter of the reactor, m

D_H Diffusion coefficient of hydrogen, m²/h

E_a Energy of activation, kJ/kmol

F Molar flow, kmol/h

i Component

k⁰ Reaction rate coefficient, kmol/h/atm

K_eq Equilibrium constants, m³/kmol

L Reactor length, m

P Partial pressure, N/m²

P_TOT Total pressure, N/m²

Q_H Permeation velocity of the hydrogen, kmol/h

r Rate of reaction, kmol/m³/h

r Zone of reaction

RRate of reaction, kmol/kg_cat/h

R Gas constant, kJ/kmol/K

s Zone of separation

t_m Membrane thickness, m

T Temperature, K

u Flow velocity in the reaction zone, kmol/h

v Flow velocity in the permeation zone, kmol/h

X Fractional conversion

z Axial coordinate

r _b Apparent density of the catalytic bed, kg/m³

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*

To whom correspondence should be addressed.

Publication Dates

• Publication in this collection
  09 Oct 1998
• Date of issue
  June 1998

History

• Accepted
  10 Mar 1998
• Received
  05 Nov 1997