A Comprehensive Model for Catalytic Membrane

I NTERNATIONAL J OURNAL OF C HEMICAL R EACTOR E NGINEERING Volume 4

2006

Article A5

A Comprehensive Model for Catalytic Membrane Reactor Shashi Kumar∗

Sukrit Shankar†

Pushan R. Shah‡

Surendra Kumar∗∗

∗

Indian Institute of Technology Roorkee, Roorkee, U.A., India, [email protected] Jaypee Institute of InformationTechnology Noida (Deemed University) U.P., India, [email protected] ‡ Indian Institute of Technology Roorkee, Roorkee, U.A., India, pushan [email protected] ∗∗ Indian Institute of Technology Roorkee, Roorkee, U.A., India, [email protected] ISSN 1542-6580 †

Brought to you by | Indian Institute of Technology Roorkee Authenticated | 59.163.196.43 Download Date | 12/13/13 3:06 PM

A Comprehensive Model for Catalytic Membrane Reactor Shashi Kumar, Sukrit Shankar, Pushan R. Shah, and Surendra Kumar

Abstract Catalytic membrane reactors are multifunctional reactors, which provide improved performance over conventional reactors. These are used mainly for conducting hydrogenation/ dehydrogenation reactions, and synthesis of oxyorganic compounds by using inorganic membranes. In this paper, comprehensive model has been developed for a tubular membrane reactor, which is applicable to Pd or Pd alloys membrane, porous inorganic membranes. The model accounts for the reaction on either side, tube or shell, isothermal and adiabatic conditions, reactive and non reactive sweep gas, multicomponent diffusion through gas films on both sides of membrane, and pressure variations. Equations governing the diffusion of gaseous components through stagnant gas film, and membranes have been identified and described. The model has been validated with the experimental results available in literature. By using the developed model catalytic dehydrogenation of ethylbenzene to produce styrene in a tubular membrane reactor have been simulated. Four catalysts available for this reaction have been evaluated for their performance. It is our view that the model may be used to develop general purpose software for the analysis and design of tubular catalytic membrane reactors through numerical simulation. KEYWORDS: catalytic membrane reactor, dehydrogenation reaction, reactor modeling, permeation, porous inorganic membrane


Kumar et al.: Model for Catalytic Membrane Reactor

1.

INTRODUCTION

In the last two decades, the demand for higher conversion, and better yield and selectivities of the desired reaction products with energy saving considerations has led to new, ingenious configuration and design of chemical reactors. In this regard, multifunctional reactors where reactions combined with separation, have received much attention in both academic and industrial research. Membrane reactors are such type of multifunctional reactors and these are currently being applied to many chemical reactions worldwide. The most widely used perspective of membrane reactor is the removal of a product to change the existing thermodynamic limits on the yield of desired product and thereby to drive the equilibrium limited reactions towards completion. Besides, other potential advantages of membrane reactors are: fewer side reactions, expanded allowable range of temperature and pressure for a reaction (Armor, 1989), increased residence time for a given volume of the reactor (Armor, 1995) and more efficient purification. The applications of membrane reactor are mainly focused on the reaction systems containing hydrogen (e.g. dehydrogenation /hydrogenation reactions) or oxygen (e.g. Synthesis of oxyorganic compounds) using inorganic membranes. Membrane as defined by Coronas and Santamaria (1999) is a “semi permeable barrier, which is selective only to certain molecules and imposes resistance on the permeation flux for the rest”. The most important characteristics of the membrane are, thus, permeability and selectivity. Both are dependent on the membrane layer configuration and its porous structure (pore size, porosity, and tortuosity), temperature, molecular weight and in addition on different transport mechanisms. Inorganic membranes may be either porous materials or non porous impervious films. Dense impervious films include Pd-Pd alloy membrane which are semipermeable to hydrogen, and solid oxide electrolyte dense membranes such as modified zirconias and perovskites which are highly selective for oxygen at high temperatures. Since Pd-Pd alloy membranes offer high permeability only for specific gases mainly hydrogen, these have been in use for dehydrogenation and hydrogenation reactions. However, on commercial scale their applications are limited due to their high cost and low permeability due to high wall thickness of 100-150 µm (Hermann et al., 1997), difficulty in fabrication, sensitivity to poisoning by sulfur species, and embrittlement upon aging (Julbe et al., 2001). In order to overcome these drawbacks and to search suitable and cheaper membranes having sufficient thermal, mechanical and chemical stability, various valuable efforts have been made. Inorganic porous membranes are found to have promising future for industrial applications in catalytic reactor and thereby currently are in great use. Coronas and Santamaria (1999) and Dixon (2003) reviewed and illustrated more precisely the applications of porous inorganic membranes in catalytic reactions. The porous inorganic membranes can be divided into three types depending upon the pore sizes, namely macroporous (dp>50 nm), mesoporous (50>dp>2 nm ) and microporous (dp < 2 nm), (Dixon, 2003). Macroporous membranes provide no separation and are used as support layers of small pore size to form composite membranes. These are also applied some times where a well controlled reactive interface is required. α -alumina membranes are of macroporous type. Mesoporous membranes have generally pore sizes in the range of 4-5 nm. The examples of mesoporous membranes are Vycor glass, and composite membrane of γ alumina supported on macroporous α -alumina support. Mesoporous membranes have low selectivity but high permeability. Microporous membranes being of very small pore sizes, provide high potential for molecular sieving effects with very high separation factors. Carbon molecular sieves, porous silica and zeolite membranes are few examples of microporous membranes (Dixon, 2003). These membranes are stable at high temperature and resist chemical attack. Currently the supported thin film of microporous materials on alumina or on porous stainless steel is most active area of membrane applications (Coronas and Santamaria, 1999). Commercial ceramic membranes are available comparatively at low cost. These membranes have an asymmetric structure consisting of two layers namely support layer and separation layer. The support layer is composed of generally α alumina and has large pores with a low-pressure drop. The separation layer is prepared from different materials such as γ alumina, zirconia, silica etc. and controls the permeation flux. Ceramic membrane exhibits high permeability but relatively low selectivity and, therefore, low separation factor since available pore size (≅ 4 nm) is sufficient for molecular sieving. The separation of gaseous components through ceramic membrane is governed by Knudsen diffusion. The effective Knudsen permeability is inversely proportional to the square root of molecular weight of separating gas component. This implies that in dehydrogenation reactions, the hydrogen gas as product, being low in molecular weight, may be permeated easily through the membrane as compared to the other gases of high molecular weight. This fact leads to the conclusion that one of the methods to improve the separation factor of product and to reduce the permeability of reactant through membrane is to choose a reactant, which has a high molecular weight such as ethyl benzene (Yang et al., 1995). In this regard for instance, the H2/N2 separation factor lies in the range of 2.8 –3.2


1

International Journal of Chemical Reactor Engineering

2

Vol. 4 [2006], Article A5

(Yang et al., 1995) whereas the H2/EB separation factor is 7.3 (Wu and Liu, 1992), which is comparatively very much high. A large number of modelling studies on membrane reactors have been carried out using various chemical reactions specially dehydrogenation and hydrogenation reactions. These models are specific under certain limited conditions of the system studied. Wu and Liu (1992) developed pseudohomogeneous model for isothermal operation using ceramic membrane with reaction in tube. Gobina et al. (1995b) developed the model for isothermal condition considering radial concentration gradient, reaction in tube and microporous membrane system. Abdalla and Elnashaie (1995) gave pseudohomogeneous model for fluidized bed reactor with or without Pd membrane. Hermann et al. (1997) presented the model with reaction in tube, which takes into account the mass transport mechanism prevailing in the various layers of membrane. The model by Koukou et al. (1997) takes into account the various heat exchanges occuring inside the reactor. Elnashaie et al. (2001) developed pseudohomogeneous model with reaction in tube using Pd membranes. Gobina et al. (1995a), Elnashaie et al. (2000), and Moustafa and Elnashaie (2000) considered reactive sweep gas and Pd membrane to develop pseudohomogeneous model. Assabumrungrat et al. (2002) developed model for non isothermal condition with reaction in shell using Pd membranes. In view of the above, a comprehensive model has been developed in the present work, which takes into account isothermal / non-isothermal conditions, reactive / non-reactive sweep gas, multicomponent diffusion in the stagnant gas films on both sides of the membrane, effective multicomponents diffusion through membrane, permeation through various types of porous and Pd composite membranes, multicomponent mass transport through catalyst particles, pressure drop variations in reaction and permeate sides. This model has been reduced to pseudohomogeneous model and based upon this a case study for the production of styrene has been numerically simulated. Four catalysts, viz. Catalyst I, Catalyst A, Catalyst B, and Catalyst C have been studied in terms of yield and selectivity of styrene using ceramic membrane. The best catalyst thus found, has been considered for further studies. The model has been solved at various temperature conditions, purge gas to feed conditions. Optimum value of temperature and purge to feed ratio have been estimated. The yield and selectivity results are compared with Pd membranes.

2.

DEVELOPMENT OF THE COMPREHENSIVE MODEL

The catalytic membrane reactor is a cylindrical reactor equipped with a membrane. This membrane is inert with respect to chemical reaction and tubular in shape. The tubular membrane divides the reactor in two zones, viz. zone 1 and zone 2, as shown in figure 1. Zone 1 is reaction zone, which is packed with catalyst particles. The reaction feed is introduced into this zone. The zone 2 is permeate zone where the purge gas or sweep gas is introduced counter currently or cocurrently with respect to the feed to carry away the permeated gasses from the permeate zone. Either of the zones may be the reaction zone. Obviously, other zone will be the permeate zone. The purge gas may be reactive or nonreactive. If purge gas is reactive and the corresponding reaction is catalytic, the permeate zone is also packed with appropriate catalyst. As far as the permeation through membrane is concerned, the permeation of gaseous component through membrane takes place from higher partial pressure side to lower partial pressure side for that component. Thus, permeation may be from either side of the membrane depending upon the partial pressures. Keeping above facts in view the comprehensive model equations are developed for catalytic tubular membrane reactor as shown in fig. 1. The model supports different process options such as the use of inert sweep gas or the reactive sweep on permeate side, isothermal or non-isothermal operation, porous membrane or Pd alloy composite membrane with porous support. The permeance of species through porous membrane and permeance of hydrogen through Pd-Pd alloy membrane have been discussed in detail in the section 3.

2.1

Assumptions

The model equations are developed on the basis of following assumptions. (i) The reaction and permeate sides of the reactor are operated under steady state conditions. (ii) In both sides the behaviour of bulk gas is assumed to be ideal. (iii) The plug flow of bulk gas is assumed. Axial diffusion of mass and heat and radial concentration gradients on both sides are considered to be negligible. (iv) The stagnant gas films on both sides of membrane are considered, while radial temperature gradients across the membrane are neglected.



3

membrane

Shell side ( Permeate zone)

Purge gas Purge gas + permeated gas R1

Reaction feed

R2

R3 products

Purge gas + permeated gas

Purge gas L

Tube side filled with catalyst (Reaction zone)

Figure 1 Schematic diagram of membrane reactor

2.2

Mass balance equations

This section comprises of the mass balance equations for transport through tube, for transport through shell, for transport in catalyst particles, and for transport though membrane. In the tube and shell side mass balance equations “+” sign with rj is used for the component which is produced by the reaction j, and “-” sign with rj is used for the component which is consumed by the reaction j.

2.2.1

Mass balance equations for tube side

The reaction feed is introduced into the tube which is packed with catalyst particles. Let n1 be the total number of reactions occurring in tube which includes main reactions and all side reactions as well. Let n 2 be the total number of components present in gaseous mixture flowing through packed tube. This includes all gaseous reactants, products and inerts (if any). Set of the component mass balance equations has been developed by taking mass balances around control volume in the tube as follows. “+” sign with Ji indicates the permeation of component i from tube to shell and “-” sign indicates the permeation of component i from shell to tube through membrane. These equations can be written for all n2 components accordingly as follows. In terms of molar flux it is given below. n1 dN ti 2J − ρ B1 ∑ η j (± s ij r j ) ± i = 0 dz R1 j=1

i = 1 to n2

(1)

This equation can be written for molar flow rate of ith component as follows:

dFti dz

− πR12ρ B1

n1

∑ η ( ±s j =1

j

ij

rj ) ± 2π R1 J i = 0

i = 1 to n2

(2)

For plug flow , the variation of fractional conversion of ith reactant in jth reaction is given by

dxtij dz

=

π R12 ρ B1 η j rj sij Ftio

(3)

If n3 represents the number of reactions where component i is the reactant , then over all conversion of ith component will be n3

= ∑ x tij

(4)

j=1



4


The value of n3 may be different for different components. Mole fraction yti of ith component is computed by the following equation.

Fti

yti =

=

n2

∑F

ti

i =1

2.2.2

N ti

(5)

n2

∑N i =1

ti

Mass balance equation for shell side

The sweep gas may be reactive or inert. If it is reactive, reactions will also occur in the permeate side, i.e. in the shell. Let n4 be the number of reactions occurring in shell and n5 be the total number of components. The component material balances give the following equations.

( −1)

n4

dN si − β1ρ B 2 dz

m

∑ η (± j =1

j

sij rj ) ± β2

(R

2 R2 J i

3

2

− R22

)

= 0 ; i = 1 to n5

(6)

Where, m = 2 for co-current flow of sweep gas in shell and reactants in tube, m = 1 for counter current flow of sweep gas in shell and reactants in tube, and β1 = 1, if sweep gas is reactive and reactions occur in shell side. β1= 0, if sweep gas is inert and no reaction occurs in shell. β2= 0, if component i is not permeated through membrane β2= 1, if component i is permeated through membrane “+” sign with β2 indicates the permeation of component i from the shell to tube and “-” sign indicates the permeation of component i from the tube to shell. In porous membranes, the permeation of component may occur in either direction depending upon the partial pressure of the component in shell and tube. In terms of molar flow rate, equation (6) can be written as follows:

( −1)

dFsi − β1ρ B 2 π R32 − R22 dz

(

m

n4

) ∑ η .( ± s r ) ± β j =1

j

ij j

2

2πR2 J i = 0

;

(7)

i =1 to n5 If membrane is very thin in comparison to the tube diameter, then R 2 can be taken equal to R1. If reactions occur in shell side, then we can use equation (3) for the variation of fractional conversion of ith reactant in jth reaction in the shell with small modifications as under.

dxsij dz

(

π R32 − R22

=

)

ρ B 2 η j .rj sij β1

Fsio

(8)

Here, Fsio is molar flow rate of reactant i in the feed in shell. It will include the molar flow rate of reactant i with sweep gas and molar flow rate of reactant i permeated through membrane from tube side. If n6 represents the number of reactions where component i is the reactant, then over all conversion of reactant i will be

=

n6

∑x j =1

(9)

sij

The mole fraction of ith component in the shell side gaseous mixture is given by the following equation.

ysi =

Fsi n5

∑F i =1

si

=

N si

(10)

n5

∑N i =1

si



5

In above mass balance equations for tube side and shell side, the effectiveness factor is used. The value of this factor is generally available in the literature for a particular catalyst and reaction. If it is not available then it may estimated as follows. The effectiveness factor is a measure of how far the reactant diffuses into the catalyst particle before reacting. It is defined as the ratio of the actual reaction rate to the rate of reaction that would result if entire interior surface were exposed to the external particle surface conditions, i.e. rate of reaction at bulk conditions of concentration and temperature (Fogler, 2001). Thus the effectiveness factor ηj, for jth reaction is computed by the following equation.

ηj =

3 rp

3

(r ) ∫ j

rp 0

r 2 rj .dr

(11)

b

Here (rj)b is the reaction rate at bulk conditions of concentration and temperature. For tube side reaction rp is used for the tube side catalyst; likewise for the shell side reaction (if any) rp is used for the shell side catalyst. In order to estimate bulk concentration of reactant component i in gas contained within the pores, following equation may be used. “r” is the radial coordinate representing the radius of a spherical catalyst particle.

sij rj ρ B

d 2Ci 2 dCi + = 2 dr r dr

(12)

( Di )e

The boundary conditions are: At r = 0, Ci is finite, i.e. dCi/dr = 0. At r = rp ; Ci = Cis.

2.2.3

Mass balance equations for diffusion through membrane

The membrane is surrounded by stagnant thin gas film on the tube side as well as on the shell side. The temperature and pressure are considered to be constant within the gas film. The multicomponent diffusion through membrane in radial direction involves the diffusion through gas film and through porous membrane. The diffusion of component i in multicomponent ideal gas mixture (having n7 components) at low density through stagnant gas film is described by Stefan-Maxwell’s equation (Bird et al., 2002) as follows.

dyi = dr

n7

∑C j =1

T

1

Dij

(y J i

j

− y j Ji

)

(13)

For tube side gas film the above equation is

dyi R Tt = dr PtT

n7

1

∑ (D ) ( y J j =1

i

j

− y j Ji

)

(14)

ij t

and for the shell side gas film, it assumes the following form.

dyi R Ts = dr PsT

n7

1

∑ (D ) ( y J j =1

i

j

− y j Ji

)

(15)

ij s

In equations (14) and (15), (Dij)t and (Dij)s are binary diffusion coefficients of the pair i-j in multicomponent mixture at temperature and pressure conditions of tube and shell sides respectively. These diffusivities are independent of concentration. “r” is radial coordinate which represents the thickness of the gas film. Thickness of gas film may be computed by various methods as suggested by Bird et al. (2002). The multicomponent diffusion through the porous membrane is described by dusty gas model, which takes into account the Knudson diffusion and viscous flow of gas through the membrane. By using dusty gas model (Hermann et al., 1997; and Seader and Henley, 1998), one obtains.



6

dyi R T ⎛ n7 ( yi J j − y j J i ⎜∑ = dr P ⎜ j =1 ε / τ ( Dij ) t ⎝ 2 ε dp where Bo = τ 32 dCi and J i = − ( Dik )e dr

)

−

⎞ Ji ⎟ − yi ( Dik )e ⎟⎠

⎡1 + ⎢ µd ⎢⎣ P


Bo ( Dik )e

dP ⎤ ⎥ dr ⎥⎦

(16)

(17) (18)

(Dik)e is evaluated by using equation (40) described later. P and T are pressure and temperature respectively at the side from where the component is getting permeated through membrane. “r” is radial coordinate which represents the thickness of membrane.

2.3

Energy balance equations

The temperature gradient dT/dz in tube and shell side under isothermal conditions is zero. Under adiabatic conditions , the energy balance differential equation is derived by assuming that the membrane offers no resistance to heat transfer, and external heat transfer resistances between bulk gas and catalyst particle are negligible due to high conductivity of catalyst particle (Elnashaie et al., 2001; Hermann et al., 1997; and Moustafa and Elnashaie, 2000). Therefore, Tt and Ts are assumed to be identical and equal to T. The energy balance gives the equation for overall temperature gradient as follows.

FT C p

n1 ⎡ dT = − ⎢ πR12ρ B1 ∑ ( ±∆H j ) η j .rj + β1π R32 − R22 ρ B 2 dz j =1 ⎣

(

)

⎤

n4

∑ ( ±∆H ) η .r ⎥ j

j =1

j

j

⎦

(19)

‘+’ sign with ∆Hj is used for endothermic reaction and ‘-‘ sign with ∆Hj is used for exothermic reaction. FT is total flowrate of gases which includes the flowrate in shell as well as in tube . CP is average heat capacity of this gaseous mixture.

2.4

Momentum balance equation

The Ergun equation is used to calculate the pressure drop across solid bed packed with catalyst particle in the tube side (Bird et al., 2002) as follows.

µt vtz

dPtT = − 150 x 10−5 dz

( 2r )

2

p

(1 − εb )

2

ε3b

− 1.75 x 10−5

ρ g vtz2 ⎡1 − εb ⎤ ⎢ ⎥ 2rp ⎣ εb3 ⎦

(20)

Where vtz is superficial velocity of gas in tube in z direction. The ideal behaviour of gases gives

Tt vtz = 0.0224 273

n2

∑N i =1

ti

= Go/ρg

(21)

if “a” is total particle surface area/ volume of bed, then

rp =

3 (1 − ε )

(22)

a

Modified Hagen – Poiseuille law (Bird et al., 2002) is used to compute pressure drop in shell side. If there is no packing, this law yields,



dPsT = dz

−8µ s vsz ln

7

R2 R3

⎡R ⎤ ln ⎢ 2 ⎥ ⎡⎣ R32 + R22 ⎤⎦ + ⎣ R3 ⎦

(R

2 3

− R

2 2

)

(23)

For ideal gas behaviour , vsz reads

Ts 273

vsz = 0.0224

n5

∑N i =1

si

(24)

The partial pressure of ith component in tube and shell can be expressed by the following equations.

Pti =

N ti

x PtT

∑N i =1

Psi =

N si

ti

x PsT

(26)

n5

∑N i =1

3.

(25)

n2

si

PERMEATION RATE OF GASES THROUGH MEMBRANE

As discussed in the introduction, inorganic membranes include dense membranes and porous membranes. Dense membranes are exclusively permselective to either H2 or O2 and so are largely and successfully used in reactions consuming or generating H2 or O2. In these membranes transport process involves the desolution of the gas in the membrane material. H2 permselective dense membranes include Pd and Pd alloy membranes. The synthesis and permeation rate of hydrogen through Pd-Pd alloy membranes have been discussed by Collins and Way (1993), and Shu et al. (1991). The transport mechanism in porous membranes include viscous flow Knudsen diffusion, surface diffusion, capillary condensation and molecular sieving. These membranes have higher value of permeability and lower value of selectivity. A notable exception are zeolite membranes with a promising future for applications to catalytic reactors (Coronas and Santamaria, 1999). Zeolite membranes are a type of microporous membranes. The gas transport through mesoporous membrane is governed mainly by Knudsen diffusion. In case of microporous membrane, the permeation of gases is governed by adsorption and diffusion of molecules for which Stefan-Maxwell flux equations supplemented by configurational Monte Carlo Simulation of adsorption equilibria may be used. Non equilibrium dynamic simulations are also being used to understand phenomena at the molecular level (Dixon, 2003). There are a number of research papers addressing progresses on microporous membranes regarding their synthesis and permeability characteristics. A few studies on microporous membranes are reviewed and summarized by Coronas and Santamaria (1999), Julbe et al. (2001) and Zaman and Chakma (1994). Caro et al. (2000) focused their studies on zeolite and Sol-get based microporous membranes. Coronas et al. (1997) discussed the characterization and permeance properties of ZSM-5 tubular membranes and revealed that the permeance bahaviour may be the result of permeation through non zeolite pores in parallel to zeolite pores. They prepared the membrane by in-situ synthesis. Meizner and Dyer (1993) studied the transport properties of microporous inorganic membranes and discussed theoretical basis for describing gas transport through both monolithic and multilayer porous systems. Bhandarkar et al. (1992) and Shelekhin et al. (1992) studied gas permeability properties of various gases in microporous silica membranes mathematically as well as theoretically in terms of selectivity factors by considering diffusion as well as adsorption. Jeong et al. (2003 a & b) reported the synthesis of a FAU type zeolite membrane on a porous α-Al2O3 support tube using a hydrothermal process. They studied the permeation and separation properties of this membrane for mixture of benzene and saturated C4-C7 hydrocarbons. The transport mechanism of gases through molecular sieve carbon membrane has been studied by Sznejer and Sheintuch (2004), Itoh and Haraya (2000), and Sznejer et al. (2004). The aforementioned literature portrays a brief review regarding the permeation of gases through microporous membranes. A delineate analysis and formulation of the permeation rate of hydrogen through Pd-Pd alloy membranes and permeation rate of gases through porous ceramic membranes in hydrogenation / dehydrogenation membrane reactor is carried out in the following subsections. Since, we intend to confine our



8


studies to the systems where only porous ceramic and Pd-Pd alloy membranes are applied, a detailed mathematical formulation of permeance through microporous membranes is kept out of the scope of this paper.

3.1

Permeation rate of gases through Pd and Pd alloy composite membranes

Pd and its alloys have very high permeabilities for hydrogen as compared to other gases. Commercially available Pd/Pd alloys membranes are either thick films or thick walled tubes. However, the high cost of Pd metal leads the prospects for the improvement of the preparation techniques of membranes with very thin Pd or Pd-alloy films to make the processes economically more feasible. In this regard the composite Pd microporous ceramic membranes are prepared by plating a thin film of Pd or its alloys on the selective layer of commercially available ceramic membrane tubes. H2 gas permeates through the ceramic support as well as through Pd alloy film. (Collins and Way, 1993) has mentioned that the H2 fluxes for a 4 nm Membralox membrane at transmembrane pressure difference from 100 to 2000 kpa are 23-44 times higher than the fluxes measured for the composite Pd ceramic membrane. This leads to the conclusion that mass transfer resistance of the ceramic support is minimal. Therefore, hydrogen permeabilities through composite membranes are essentially considered to be the permeabilities of the Pd film. Hence for Pd membranes as well as for Pd alloys composite microporous ceramic membranes the permeation rate Q i for all components except H2 is zero. This gives Ji = 0; i represents all gaseous components except H2. The diffusion of gas in Pd-Pd alloy film does not depend on the actual structure of the membrane film. The diffusion occurs when the gas is dissolved in the film to form more or less homogeneous solution. This type of diffusion can be considered to follow Fick’s Law (Geankoplis, 2001). The membrane film is treated as a uniform homogeneous like material. In many cases, the experimental data for diffusion of gases in membranes are not given as diffusivities and solubilities but as permeabilities. The permeability coefficient pmi is generally defined as mole of gas i diffusing per second per m2 cross sectional area through a membrane 1 m thick under a pressure difference of 1 atm pressure. Thus, using Fick’s law, the permeation flux of hydrogen though Pd-Pd alloy composite membrane in terms of permeability coefficient can be written as follows (Collins and Way, 1993; Moustafa and Elnashaie, 2000; and Uemiya el al., 1991).

pmH 2

J H2 =

δ

⎡⎣ PtH 2 n − PSH 2 n ⎤⎦

(27)

Here hydrogen permeability coefficient pmH 2 is in mole. m/m2 sec (atm)n . Consequently the permeation rate of hydrogen at any radial distance r in the membrane is given by

dQH 2 dz

= 2π r J H 2

(28)

Thus the permeation rate of H2 through the membrane to the permeate side is

dQH 2 dz

= 2π R2

J H2

(29)

and by equation (27), it is

dQH 2 dz

= 2π R2

pmH 2 δ

⎡⎣ PtH 2 n − PSH 2 n ⎤⎦

(30)

A number of Pd membrane tubes embedded into catalyst bed are also in use (Abdalla and Elnashaie, 1995). The cross sectional area of all membrane tubes is assumed to be equal to that of the single tube passing through the center. The sweep gas flow rate is equally divided through the membrane tubes. In this case, equation (27) for H2 permeation rate is expressed as

dQH 2 dz

=

2π n8 R2 δ

pmH 2

⎡⎣ PtH 2 n − PSH 2 n ⎤⎦

Where n8 represents the number of membrane tubes. For single tube n8 = 1.


(31)


9

The value of n in above equation (31) is influenced by the solubility of H2 in metal, rates of surface processes and bulk diffusion. All these factors depend on temperature. Therefore, n and permeability coefficient vary with temperature. The dependence of permeability coefficient on temperature (Collins and Way, 1993) is as follows: ; T is in K (32) p mH 2 = pmH 2 ,0 exp [-E/RT] When H2 atoms form an ideal solution in Pd or Pd - alloy metal, Sievert’s half power pressure law is followed (Abdalla and Elnashaie, 1994; Collins and Way, 1993; Shu et al.,1991). In this case n is equal to 0.5 . Hence equation (27) and (30) are reduced to as given below.

J H2 = dQH 2 dz

pmH 2 δ

⎡ PtH 2 ⎣

= 2 π R2

−

pmH 2 δ

PSH 2 ⎤⎦ ⎡ PtH 2 ⎣

(33)

−

PSH 2 ⎤⎦

(34)

H2 permeation flux and rate, for instance, through a composite membrane consisting of a 6 µm thick Pd –Ag alloy on 0.11 cm Vycor glass support are expressed by equations (33) and (34) respectively, where permeability coefficient p mH 2 is determined as a function of temperature according to following equation (Gobina et al., 1995b).

⎡ 77.75 ⎤ pmH 2 = 0.32 x10−6 exp ⎢ − , mole.m / m 2 sec atm0.5 ; T is in K ⎥ T ⎦ ⎣ For non-ideal solution n may be different from 0.5. The values of n and p mH 2 at specific temperature for composite Pd alloy ceramic membranes with different configurations are given in the Table 1 (Collins and Way, 1993; and Dittmeyer et al., 1999). Table 1 The values of n and hydrogen permeabilities at specific temperatures for composite Palladium – Ceramic membranes Membrane Description T(K) n p mH 2

20-µm palladium film on ceramic membrane with 10 –nm pore layer 17-µm palladium film on ceramic membrane with 200 –nm pore layer

823

(mol.m/(m2.s.Pan)) 1.43x10-8

723 773 823

2.34 x10-9 4.04 x10-9 6.82 x10-9

0.622 0.595 0.568

11.4-µm palladium film on ceramic membrane with 200-nm pore layer

873 823 873

9.96 x10-9 3.23 x10-9 5.84 x10-9

0.552 0.602 0.566

0.526

From Table 1, the H2 permeation data for composite Pd ceramic membrane with 17 µm, and 11.4 µm Pd film are combined for all temperatures mentioned in the table, and the calculated parameters of equations (30) and (32) are as follows: (i)

For 17 µm Pd film pmH 2 ,0 = 5.29 x 10-8 mol.m/m2.s Pa0.573 E = 14450 J/mol n = 0.573

(ii)

For 11.4 µm Pd film pmH 2 ,0 = 1.62 x 10-8 mol.m/m2.s Pa0.580



10


E = 8880 J/mol n = 0.580 Moreover, the permeability of H2 depends on the equilibrium solubility of H2 and its diffusivity in Palladium. Therefore, in equations (33) and (34), the term

p mH 2 δ

at any radial distance r , may be defined in terms

of diffusion and concentration of H2 in pure Pd as follows (Abdalla and Elnashaie, 1994; Elnashaie et al., 2000; Elnashaie el al., 2001; and Hermann et al., 1997 ).

pmH 2 δ

DH

=

Co

r Po ln

(35)

R2 R1

Where DH is Fick’s diffusion coefficient of hydrogen dissolved in Pd and Co is the solubility or standard concentration of dissolved H2 in Pd. Both are determined as a function of temperature according to following equations.

⎡ 2610 ⎤ DH = 2.3 x 10−7 exp ⎢ , m 2 / s ; T is in K ⎥ ⎣ T ⎦ Co = 3.03 x 105 T –1.0358 , mole/m3

Po is standard pressure at permeate side in atm. Thus, the molar flux of H2 through membrane is,

J H2 =

DH Co

⎡ P R2 ⎣ tH 2 r Po ln R1

−

PSH 2 ⎤⎦

(36)

Consequently, the permeation rate of H2 from equation (28) reads

dQH 2 dz

=

2π DH Co ⎡ P R2 ⎣ tH 2 Po ln R1

−

PSH 2 ⎤⎦

(37)

Table 2 gives the configuration of few membranes where equations (36) and (37) are applicable. Table 2 Configuration of Membranes Configuration of membrane 10 µm thick Pd layer on 2 mm thick porous support with pore size of 0.2 µm and porosity of 0.5 5 x 10-4 mm thick Pd layer on porous ceramic support tube with a diameter of 6.87 cm Metal membrane developed by Bend Research Inc. (1996) , are composed of base metal support layer carrying an intermediate layer of silica or alumina above which there is a coating of metal layer of Pd alloy. Porous ceramic membrane tube with a 5 x 10-4 mm thick Pd film deposited on the surface.

Reference Hermann et al., 1997 Elnashaie et al., 2001 Elnashaie et al., 2000 Abdalla and Elnashaie, 1995

Table 3 provides the summary of hydrogen fluxes based on feed pressure of pure hydrogen equal to 790610 Pa and a permeate pressure of 101325 Pa for different membranes (Collins and Way, 1993). Composite Pd micorporous membranes have the highest hydrogen fluxes with the exception of the ceramic membrane which has highest H2 fluxes due to Knudsen diffusivity.



11

Table 3 Hydrogen Fluxes for Inorganic Membranes Membrane Description

T (K)

Composite palladium –ceramic membrane (11.4-µm palladium film) Composite Palladium – porous glass membrane 13 -µm palladium film Composite metal membrane (25-µm palladium film on 30 - µm vanadium with 1 - µm intermetallic diffusion barrier between palladium and vanadium) Composite metal membrane (1-2-µm palladium film on 0.25 mm thick niobium tube) Metal oxide membrane (SiO2 deposited in pores of 4-nm Vycor glass membrane) Ceramic membrane (asymmetric membrane with 4 –nm pore top layer)

823

Hydrogen flux (mol/m2.s) 0.71

773

0.56

973

0.30

698

0.40

723

0.015

3.2

811

23

Permeation rate of gases through porous ceramic membranes

The diffusion of gases through porous membrane depends on actual structure of the membrane and inter connected voids, i.e. pores in the membrane. The gas diffuses in the void volume and takes a tortuous path which is greater than the membrane thickness δ by a factor τ called tortuosity. Diffusion does not occur in the inert solid of the membrane. If the pore diameter of the membrane is large compared to the molecular diameters of the gaseous components and pressure difference exists across the membrane, bulk or convective flow through the pores occurs. Such a flow is not perm selective and therefore, no separation between gaseous components occurs. However, if partial pressure differences for various components exist across the membrane keeping total pressure same on both sides of the membrane, perm selective diffusion of the components through the pores by Fickian type diffusion will take place, resulting in the effective separation. If the pores are of the order of molecular size of few components in the gaseous mixture, the diffusion of molecules of these components and the molecules of size greater than the pore will be restricted, resulting in an enhanced separation. This situation is highly desirable. Another special situation exists for gas diffusion where the mean free path of the molecules is greater than the pore diameter and / or the total pressure is low. This type of diffusion is called Knudsen diffusion and generally occurs in porous membranes. It is dependent on molecular weight. The collisions occur primarily between gas molecules and the pore wall rather than between gas molecules. Thus, the permeation flux of gaseous component i through membrane can be written as (Geankoplis, 2001; and Seader and Henley, 1998 ).

Ji = Where

( Di )e ( Pti

− Psi )

(38)

RT δ

(Di )e

is the effective diffusivity of component i. In the absence of a bulk flow effect, the effective

diffusivity can be written as

( Di )e

ε ⎡1 1 ⎤ = + ⎢ ⎥ τ ⎣ Di Dik ⎦

−1

(39)

In ceramic porous membrane, Knudsen diffusion controls the permeation flux of the various gaseous components through membrane. Hence effective diffusivity by equation (39) is modified as



12

( Di )e

=

ε Dik = ( Dik )e τ


(40)

If the kinetic theory of gases is applied to a straight cylindrical pore, the Knudsen diffusivity is given by the following equation (Seader and Henley, 1998) 1/ 2

Dik

d ⎡ 8 RT ⎤ = p ⎢ ⎥ 3 ⎣ πM i ⎦

1/ 2

= 48.50 d p

⎡T ⎤ ⎢ ⎥ ⎣ Mi ⎦

(41)

Hence, permeation flux of gaseous component i through porous ceramic membrane by equations (38), (40), and (41), can be written as

Ji =

ε Dik τ RT δ

( Pti

− Psi )

(42)

In terms of permeability, Ji can be expressed as

Ji =

pmi δ

( Pti − Psi )

(43)

By equation (42), thus the permeability of component i is

pmi =

ε Dik τ RT

(44)

The permeation rate of component i at any radial distance r in the membrane is

dQi = 2π r J i dz

(45)

and permeation rate of component i through membrane to permeate side (eg from tube to shell side) of reactor will be as given below.

dQi = 2π R2 dz 4.

Ji

(46)

CASE STUDY

In the case study the dehydrogenation of ethylbenzene (EB) has been studied in a commercial ceramic membrane reactor. The catalytic dehydrogenation of ethyl benzene to produce styrene, is an example of commercially important dehydrogenation reactions. This reaction is reversible and endothermic in nature. It is therefore, limited by thermodynamic equilibrium. This reaction has been widely studied in various types of membrane reactors. Wu et al. (1990) studied experimentally the dehydrogenation of ethyl benzene in an alumina membrane with 4 nm pore size using industrial catalyst and achieved 15 % high conversion of ethyl benzene as compared to the conversion in packed bed. Wu and Liu (1992) carried out simulation studies on a hybrid system, i.e. a conventional packed bed reactor followed by porous ceramic membrane reactor. They observed an increase in ST yield by more than 5 % over the thermodynamic limit. Becker et al. (1993) also investigated the conversion of ethyl benzene to ST in alumina membrane reactor and observed again 10 to 15% higher conversion in membrane reactor. Abdalla and Elnashaie (1994) have studied two fluidized bed configurations with and without selective metallic membranes by comparing it with equivalent industrial fixed bed unit. A considerable increase in the ST production has been achieved over that of the industrial fixed bed unit. Quicker et al. (2000) also observed an increase in ST yield by 14% in a Pd composite membrane, compared to conventional packed bed reactor. Moustafa and Elnashaie (2000) and Elnashaie et al. (2000) studied simultaneous production of ST and cyclohexane in an integrated membrane reactor using Pd membranes and found considerable increase in selectivity and ST yield over the industrial value.



13

Besides, simulation results on the use of Pd composite membranes have been reported in several studies (Abdalla and Elnashaie, 1994; Gobina et al., 1995b; She et al, 2001). In this case study, the mixture of EB and steam is fed into the reaction zone to perform the reaction. In the permeation zone, steam as sweep gas or purge gas is introduced to carry away the permeated gases from the reactor. The developed comprehensive model in section 2, is reduced to a pseudo homogeneous one dimensional mathematical model considering one main dehydrogenation reaction and five other side reactions under isothermal conditions. In first step, the model equations are solved for an industrial catalyst. It is known that the kinetic properties of the catalyst and the balance between the amount of gases produced and amount of gases permeated play a key role for the utilization of membrane effect besides membrane permeability (Dittmeyer et al., 1999). Therefore, three catalysts available in literature, have also been employed in the reactor and their performances along with industrial catalyst in terms of yields of products are compared. The best catalyst, thus found, is considered for further simulation studies. The operating conditions that will lead to maximum ST yield are evaluated. Commercial ceramic membrane results are compared with Pd-alloy composite membrane.

4.1

Kinetic model

The dehydrogenation of ethylbenzene (EB) to styrene (ST) can be represented by one main reaction (i.e. ethylbenzene to styrene) along with five side reactions (Clough and Ramirez, 1976; Elnashaie et al., 2000; Sheppard and Maier, 1986; and Wu and Liu, 1992). These six reactions are reversible. However, all side reactions are much slower in comparison to the main reaction (Sheppard and Maier, 1986) and are far from equilibrium at finite time where the main reaction may get completed. In view of this fact, all side reactions are considered irreversible and their reverse rates are excluded from the kinetic model. The reactions along with respective rate expressions are as follows: (1)

C6H5C2H5 ⇔ C6H5C2H3 +H2

⎛ r1 = k1 ⎜ PEB ⎝

PST PH 2 ⎞ ⎟ = k1 ⎡⎣ PEB − PEB ,eq ⎤⎦ K EB ⎠

−

(47)

PST ,eq PH 2 ,eq ⎛ −∆F 0 ⎞ , atm K EB = exp ⎜ ⎟ = PEB ,eq ⎝ RT ⎠ ∆F0 = a + bT + cT2 J/mole where a = 122725.16 (J/mol), b = -126.27 (J/mol.K) and c = -2.19 x 10-3 (J/mol K2) (2)

C6H5C2H5 + H2Æ C6H5C2H5 + CH4

(

r2 = k2 PEB PH 2 (3) (4) (5)

(48)

C6H5C2H5 Æ C6H6 +C2H4 r3 = k3 PEB 1/2C2H4 +H2O Æ CO + 2H2

(49)

r4 = k4 PH 2O PC2 H 4 0.5

(50)

(

)

CH4 + H2O Æ CO + 3H2

(

r5 = k5 PH 2O PC2 H 4 (6)

)

)

CO + H2O Æ CO2 + H2

(

r6 = k6 ( PT / T 3 ) PH 2O PCO

(51)

)

(52)

Four catalysts are considered for the present study. The rate constant for jth reaction is represented by kj = 1000 exp ( Aj – Ej/RT)


(53)


14


Here Aj is the dimensionless pre-exponential factor and Ej is activation energy in J/mole. The kinetic parameters for all six reactions corresponding to each catalyst are given in Table 4 (Elnashaie et al., 2001). The compositions of four catalysts are as follows (Elnashaie et al., 2001; Wu and Liu, 1992). Industrial Catalyst (Catalyst I): 62 % Fe2O3-36% K2CO3-2% Cr2O3 Catalyst A: 80% Fe2O3 - 20% K2O Catalyst B: 75% Fe2O3- 20% K2O-5% CeO2 Catalyst C: 70% Fe2O3 - 20 % K2O - 5% CeO2 - 5% Cr2O3 Table 4 Values of Kinetic Parameters for Four Catalysts Reaction Number 1 2 3 4 5 6

4.2

Kinetic Parameters A1 E1 A2 E2 A3 E3 A4 E4 A5 E5 A6 E6

Catalyst I

Catalyst A

Catalyst B

Catalyst C

0.851 90891 0.56 91515 14.00 207989 0.12 103996 -3.21 65723 21.24 73628

0.30 87820 -0.38 102668 13.25 193515 0.12 103996 -3.21 65723 21.24 73628

0.43 86565 0.81 97334 13.35 187992 0.12 103996 -3.21 65723 21.24 73628

0.75 83357 0.77 100555 12.19 188630 0.12 103996 -3.21 65723 21.24 73628

Pseudohomogeneous model

The comprehensive mathematical model is reduced to pseudohomogeneous model by setting following conditions. (i) Commercial tubular ceramic membrane is considered. Therefore permeation flux Ji in balance equations has been considered according to section 3.2. (ii) The reactions are considered to occur in tube. Therefore, catalyst is packed in tube, i.e. inside the commercial ceramic membrane tube. There are six reactions as mentioned in section 4.1. The components are ethylbenzene (EB), styrene (ST), hydrogen (H2), steam (H2O), toluene (TOL), benzene (BEN), methane (CH4), ethylene (C2H4), carbon monooxide (CO), and carbon dioxide (CO2). Thus, in tube side, for mass balance n1 = 6, and n2 =10. (iii) Purge gas is non reactive. Thus no reaction is considered to occur in the shell side. Therefore, β1 = 0 , n4 = 0 in shell side balances. (iv) Steam is used as purge gas, which is also a reactant in tube. Since commercial membrane is selective for all components. Therefore, the permeation is from tube to shell. Thus • n5 = n7 = 10, viz. (EB), (ST), (H2), (H2O), (TOL),(BEN), (CH4), (C2H4), (CO), (CO2). • β2 = 1 with ‘-‘ sign and PtT > PsT in shell side mass balance. • Ji with ‘+’ sign in tube side mass balance equations. (v) The purge gas in shell and tube are assumed to flow in cocurrent mode since this represents optimum conditions for the use of porous membranes (Gobina et al., 1995b). Therefore m = 2 in shell side balance equations. (vi) The catalyst pellet equations are discarded because concentration gradients in catalyst pellets are neglected due to small pellet size (Gobina et al., 1995b). (vii) Isothermal condition is considered. Therefore dT/dz = 0. (viii) All the effectiveness factors with reaction rates are taken to be equal to unity.



(ix)

Since the effect of pressure drop on the performance of reactor is negligible (Wu and Liu, 1992), isobaric conditions are assumed to prevail in tube side as well as in shell side. Therefore PtT and PsT are constant. Radial species gradients through membrane are neglected. Since ethylbenzene and steam are two reactants in feed, equation (3) can be written for ethylbenzene and steam as follows.

(x) (xi) dxtEBj dz

15

=

π R12 ρ B1

rj

FtEBO

= 0 ; j = 1, 2, 3

(54)

and

dxtH 2Oj dz

=

π R12 ρ B1

rj

FtH 2OO

= 0 ; j = 4, 5, 6

(55)

According to equation (4), for the overall conversion of EB and H2O are 3

∑ xtEBj

and

j =1

5

∑x j =4

tH 2Oj

respectively

(56)

The performance of porous membrane reactor has been compared in terms of yields and selectivities of product and byproducts, and conversion of ethyl benzene. The mechanism of reaction (3) clearly shows that the reactions (1) and (3) are two parallel reactions. Therefore, benzene is also a primary product. Reaction (2) shows the consumption of ethyl benzene to form toluene. Thus, it is decided to estimate the yield and selectivities of only three products, viz styrene, benzene and toluene. Percent selectivity and percent yield of product, percent conversion of ethyl benzene can be expressed by the following formulae [PI = styrene , benzene, toluene] % yield of PI =

PI (Pr oduced ) x 100 Ethylbenzene (Feed)

% selectivity of PI = PI (Pr oduced) x 100 ∑ PI (produced) PI

where PI (produced) = PI (retented) + PI (permeated) % conversion of EB =

EB (Feed) − EB (outlet) x 100 EB (Feed)

where, PI (produced) = PI (retented) + PI (permeated) and EB (outlet) = EB at outlet of permeate side + EB at outlet of retented side.

5.

MODEL VALIDATION

In order to validate the model, experimental results obtained by Yang et al. (1995) on the dehydrogenation of EB to ST in a laboratory tubular porous alumina membrane reactor, were considered. The permeation properties of the membrane were: permeation area = 0.8 x 2.7 x 10-3 m2; H2/N2 separation factor = 2.8 - 3.2; H2 flux = 7 x 10-7 mol/m2sec-1Pa-1. On this basis the flux through membrane for other gaseous species can be calculated by using equations (41) and (42). The catalyst used was similar to industrial catalyst and it was packed in tubes. Its properties are: specific area = 3-4m2/g; packed density = 1.2-1.4 x 103 kg/m3 ; particle size = 20 - 30 mesh. The other operating conditions were: catalyst loading = 10 ml; bed height = 37 mm; LHSV =1.0 hr-1; H2/EB (volume ratio) =1.3-1.6; reaction temperature = 893 K.



16


The percent increase in EB conversion was investigated as a function of purge gas flow rate, and reaction temperature. Here, the percent increase in EB conversion is defined as

Percent increase in EBConversion =

( Conversion

membrane

− Conversion fixed bed

Conversion fixed bed

) x100

The pseudohomogeneous model is solved for the operating conditions of this laboratory reactor to verify the model predictions. Table 5 provides the comparison of the model predictions with the experimental data. It is clear from the table that all model predictions are in good agreement with the experimental data. Thus model simulates the laboratory reactor very well. Table 5 Percent increase in ethyl benzene conversion Percent increase in ethyl benzene conversion Experimental Calculated % error

6.

Purge gas flow rate in ml/min 100 1.0 0.975 2.56

200 4.0 3.878 3.15

300 3.0 2.946 1.83

400 2.0 2.016 -0.79

500 1.5 1.469 2.11

Operating temperature at purge gas flow rate = 200 ml/min 863 K 893 K 2.5 4.0 2.440 3.881 2.46 3.07

RESULTS AND DISCUSSION OF SIMULATION

The standard operating conditions and physical parameters for the membrane reactor selected in this study for simulation are listed in table 6. The model equations constitute initial value problem. The computer program in MATLAB using its ordinary differential equation solver, “ ode 45” is used to solve these model equations. An exhaustive numerical simulation have been carried out to obtain the following results. Table 6 Operating conditions and physical parameters of reactor Parameters Length Density of Industrial Catalyst Density of Catalyst A Density of Catalyst B Density of Catalyst C Radius of Industrial Catalyst Pore radius of Industrial catalyst Pore radius of catalyst A Pore radius of catalyst B Pore radius of catalyst C Temperature Total pressure in reaction side Total pressure separation side Steam to Ethylbenzene Ratio (Dilution Ratio) Membrane Pore diameter Membrane Thickness Membrane Porosity Membrane Tortuosity

Value 0.20 m 2146 kg/m3 4541 kg/m3 4920 kg/m3 4939 kg/m3 2 x 10-3 m 240 x 10-9 m 20.7 x 10-9 m 15.5 x 10-9 m 12.3 x 10-9 m 913 K 1.2 bar 1.0 bar 6.0 mol/mol 40 x 10-10 m 5 x 10-6 m 0.5 2.95



6.1

17

Comparative performance of four catalysts

For valid comparison amongst four catalysts, namely catalyst I, catalyst A, catalyst B, and catalyst C, mathematical model is solved for all four catalysts for similar design and operating conditions as mentioned in table 6. Table 7 shows the values of yields and selectivities of styrene (ST), benzene (BEN), and Toluene (TOL) and conversion of ethyl benzene (EB) for all four catalysts in porous ceramic membrane reactor. Table 7 Comparative Performance Studies of Different Catalysts in Membrane Reactor S.No. 1 2 3 4 5 6 7

Catalyst Parameter Yield of ST (%) Yield of BEN(%) Yield of TOL (%) Conversion of EB (%) Selectivity of ST (%) Selectivity of BEN(%) Selectivity of TOL(%)

I

A

B

C

56.14 7.58 1.91 65.63 85.55 11.54 2.91

50.16 10.95 0.28 61.40 81.70 17.84 0.46

46.51 39.52 0.75 86.78 53.59 45.54 0.87

71.67 9.80 0.66 82.13 87.27 11.94 0.80

Following conclusions may be drawn. The conversion of EB is highest with catalyst B and lowest with catalyst A. This implies that catalyst B is most active and catalyst A is least active catalyst. The highest conversion of EB with catalyst B is at the expense of large production of undesired product benzene. This gives the highest benzene yield with catalyst B, which is 421.67 % higher than catalyst I and 303.16 % higher than catalyst C. Additionally, the yield and selectivity of styrene is lowest with catalyst B. These results prove unsuitability of catalyst B for production of desired product styrene. Amongst catalyst I, catalyst A and catalyst C, the yield of styrene with catalyst C is 42.87 % higher than catalyst A and 27.65 % higher than catalyst I. Although, the yield of benzene is higher with catalyst C than catalyst I and lower than with catalyst A, selectivity of styrene is higher in case of catalyst C as compared to catalyst I and catalyst A. The above facts leads to the conclusion that the catalyst C is the best catalyst for the production of styrene in porous membrane reactor. Among catalyst I, A, and B, catalyst I is best. Although the activity of catalyst A is poor, it gives better quality of products than catalyst B. For further studies , the effect of various parameters on the performance of ceramic membrane reactors have been studied by using catalyst C. The results are discussed in the following sections.

6.2

Effect of operating temperature

Operating temperature has significant effect on the membrane reactor performance. The suitable operating temperature range is 850 to 950 K. Table 8 clearly shows that yields of ST, BEN, TOL increase with temperature due to endothermic nature of reactions. Percent increase in yield of ST, BEN, TOL decreases with increase in temperature. At 950 K yield of ST is only 3 % higher than at 925 K. At 950 K the increase in BEN and TOL yields is 46.3% and 12.4% respectively. Selectivity of ST decreases with temperature and percent decrease in selectivity of ST is high at temperature 950 K. Thus, it can be concluded that the operating temperature must lie between 900 K to 950 K to obtain significant yield of ST. Therefore, a temperature of 925 K has been chosen for further studies.



18


Table 8 Effect of operating temperature S.No. 1 2 3 4 5

Temperature, K Parameter Yield of ST (%) % increase Yield of BEN(%) % increase Yield of TOL (%) % increase Conversion of EB (%) % increase Selectivity of ST (%) % decrease

850

875

900

925

950

49.98

59.07 18.19 3.69 82.56 0.39 51.24 63.15 20.84 93.53 2.20

66.61 12.76 6.25 69.08 0.53 36.48 73.38 16.20 90.76 2.96

71.67 7.60 9.80 56.94 0.66 23.43 82.13 11.91 87.27 3.86

73.75 2.90 14.35 46.34 0.74 12.36 88.83 8.16 83.02 4.86

2.02 0.26 52.26 95.64

Fig 2 shows that if the length of reactor is increased, beyond 0.3 m, the increase in yield of ST is insignificant. Thus at prevailing operating conditions 0.3 m length is appropriate length for porous ceramic membrane reactor.

80

950 925

70

% Styrene Yield

60

900

50

875

40

850

30 20 10 0 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

z (m)

Figure 2: Styrene yield at varying temperature

6.3

Effect of steam to ethyl benzene ratio

Table 9 shows the effect of H2O/EB ratio on yields and selectivities of ST, BEN and TOL and on conversion of EB. This ratio is changed by keeping total amount of feed constant. The yield and selectivity of ST increase while yield and selectivity of BEN and TOL decrease with increase in H2O/EB ratio. So from table 9 it is evident that high H2O/EB ratio shows better results than low H2O/EB ratio. At high ratios, e.g. 5 and 6, there is no significant increase in the yield of styrene. This fact supports the consideration of 6 as H2O/EB ratio in most of the membrane reactor performance studies.



19

Table 9 Effect of Steam to Ethyl Benzene Ratio S.No. 1 2 3 4 5 6 7

H2O/EB Parameter Yield of ST (%) Yield of BEN(%) Yield of TOL (%) Conversion of EB (%) Selectivity of ST (%) Selectivity of BEN(%) Selectivity of TOL(%)

6

5

4

3

71.67 9.80 0.66 82.13 87.27 11.94 0.80

71.06 10.59 0.84 82.49 86.14 12.84 1.02

69.60 11.72 1.13 82.45 84.41 14.21 1.38

66.95 13.46 1.63 82.03 81.61 96.41 1.99

6.4

Effect of purge gas flow rate

The inert purge gas is introduced in the shell to transport permeated gases easily through the shell. Easy removal of permeated gases enhances the permeation rate of gases. Since porous ceramic membrane possesses high permeability and low selectivity, reactants and products both get permeated with increased rate. The permeation of products increases the conversion whereas permeation of reactant decreases the conversion. Therefore, there will be an optimum value of purge gas flow rate at which yield will be higher. From table 10 it is evident that the overall conversion, yields of BEN, and TOL decrease and the selectivity of ST increases with the increase in purge gas flow rate. The highest yield of ST is achieved at a purge gas flow rate of 210 ml/min. Table 10 S.No.

Effect of Purge Gas Flow Rate Parameter 70 72.77 9.78 0.67 83.21 87.45

Purge Gas Flow Rate, ml/min 140 210 350 72.78 72.79 72.77 9.71 9.66 9.54 0.66 0.64 0.61 83.15 83.08 82.92 87.53 87.61 87.76

1 2 3 4 5

Yield of ST (%) Yield of BEN(%) Yield of TOL (%) Conversion of EB (%) Selectivity of ST (%)

6.5

Comparison with Pd composite membrane

560 72.66 9.38 0.58 82.61 87.96

As discussed in section 3.1, Pd membranes are selective only for H2. Accordingly the model equations are modified by putting permeation rate of all components other than H2 equal to zero . The model is solved for same operating conditions mentioned in table 6 using catalyst C. The configuration of Pd membrane has been chosen from table 2 which is 10 µ m thick Pd layer on 2 mm thick porous support with pore size of 0.2 µm and porosity of 0.5. For this configuration, the permeation flux of H2 through membrane is described by equation (36). Table 11 shows following results. Since H2 being one of the products in ST production, is permeated , the forward reaction rate increases which in turn increases the ST yield. On the other hand in ceramic membrane, the reactant EB also gets permeated with product H2, therefore, ST yield is higher in case of Pd membrane than ceramic membrane. According to equation (48), in the production of TOL, H2 is a reactant. The loss of reactant H2 due to permeation through membrane decreases the yield of TOL. The yield of BEN also decreases due to enhanced rate of ST production as EB is reactant in both ST and BEN productions (Eq. 47 and 49). From these results it is evident that by using Pd composite membrane we can get good quality product with high yield. Table 11 Simulation Results by using Pd Composite Membrane S.No. 1 2 3 4 5 6 7

Parameter Yield of ST (%) Yield of BEN(%) Yield of TOL (%) Conversion of EB (%) Selectivity of ST (%) Selectivity of BEN(%) Selectivity of TOL(%)

Pd. Composite Membrane reactor 80.24 8.33 0.60 89.16 89.99 9.34 0.67



20

6.6


Partial pressure profiles

Figs. 3 and 4 show the partial pressure of the reactants and products using catalyst C. It is evident from the curves that the partial pressures of the side products from reactions 4, 5, 6 (Eqs. 50, 51, 52) are very very low as compared to the side products from reactions 1,2,and 3 (Eqs. 47, 48, 49). Similar behaviour has been observed with other three catalysts, namely catalyst I, catalyst A, catalyst B. When the model is solved with the similar conditions using catalyst C and ceramic membrane as mentioned in table 6, excluding reaction 4, 5, and 6 from the kinetic model, the results are found to be very close to the results of original model. This leads to the conclusion that reactions 4, 5, and 6 can be excluded from the kinetic model, without any significant changes in numerical values of interest.

0.18 0.16

Partial Pressure (atm)

0.14

PST

0.12 0.1

PH2

0.08 0.06 0.04

PEB

0.02 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

z (m)

Figure 3: Partial pressure profile in tube side of membrane reactor

6.7

Tube side pressure profile

In the previous computations, effect of pressure drop on the reactor performance has been neglected. In order to study its effect, the momentum balance equation in section 2.4 is also solved along with model equations to obtain total pressure profile along the reactor length in tube side. Pressure at the exit of reactor is found to be 1.18 atm, which is approximately 1.67 % less than the entrance pressure of 1.2 atm. Thus, according to simulation results pressure profile is flat along the length of reactor and its effect therefore, on the product yield is found to be negligible. These results are in accordance with the results given by Elnashaie et al., (2001) and Wu and Liu, (1992).

6.8

Effect of Damkohler number

The Damkohler (Da) number is a dimensionless group, defined as k1PtTL/NtEB. It represents the contact time determined by flow rate or reactor length. Thus percent ST yield increases with the increase of Da number upto a maximum value at which the rate of ethyl benzene to ST is equal to its reverse rate.



21

0.018 0.016

PBEN

Partial Pressure (atm)

0.014

PC2H4

0.012 0.01 0.008 0.006 0.004

PCO

PCH4

PCO2

PTOL

0.002 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

z (m)

Figure 4: Partial pressure profiles in tube side of membrane reactor

6.9

Effect of reactive purge gas

The pseudohomogeneous model is further extended to study the effect of reactive purge gas by considering the hydrogenation of benzene to produce cyclohexane on shell side along with the dehydrogenation of EB on tube side. For the hydrogenation reaction, supported nickel catalyst is used. The reaction is C6H6 + 3H2 Æ C6H6 The rate expression and catalyst properties are taken from Elnashaie et al. (2000). For this, a Pd composite membrane is used, which is 10 µm Pd layer on 2mm thick porous support with pore size of 0.2 µm and porosity of 0.5. Therefore, H2 gets only permeated through the membrane from tube side to shell side and reacts there with benzene to produce cyclohexane. The flow rate of reactive purge gas is 70 ml/s. The percent EB conversion is found to be 94.5% which is approximately 6% higher than inert purge gas case as mentioned in table 11. The yield of ST is also found to be higher by only 1.78%.

6.10

Nonisothermal operation

The model equations are also solved along with energy balance equation (19) for nonisothermal operation with inert purge gas. Other operating conditions are same as given in table 6. The heat of reactions are used as given by Harmann et al. (1997). Figure 5 provides the temperature profile along the length of reactor during nonisothermal operation. For isothermal conditions the temperature profile is horizontal at feed temperature, whereas for nonisothermal conditions, the temperature drops at the beginning of the reactor up to a length approximately equal to 0.1 m. This is due to high consumption of heat of endothermic reaction. After this temperature starts increasing slowly. Therefore, for endothermic reactions, isothermal conditions significantly overestimates the conversion of EB



22


in the reactor. Since selectivity of ST decreases with the increase in operating temperature, the selectivity of ST is higher under nonisothermal conditions in comparison to the isothermal condition where operating temperature is high. However, the isothermal condition provides the highest value of the ST yield.

930 920

Temperaature (K)

910 900 890 880 870 860 850 0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

z (m)

Figure 5 Temperature Profile along the length of reactor during nonisothermal operation

7.

SUMMARY AND CONCLUSIONS

An attempt has been made to develop a comprehensive model of a catalytic tubular membrane reactor. Any type of membrane, viz. Pd, Pd alloy or porous, may be used. It considers steady state, isothermal and adiabatic operation. Reactions can be on either sides (tube or shell) of the reactor with the provisions of multicomponent diffusion through gas films. The model is quite general in its scope and application. Application of model is demonstrated by taking a case study of the production of styrene by catalytic dehydrogenation of ethylbenzene, an example which is widely studied. Performance of four catalysts were evaluated by using the model. Model equations are stiff in nature. Therefore, appropriate numerical methods may be used to solve the model equations. The developed model may be used to study a wide variety of catalytic reacting systems in membrane reactors, and also to develop software for this purpose.



ACKNOWLEDGEMENT Authors are grateful to the Chemical Engineering Department, Indian Institute of Technology Roorkee, and Jaypee Institute of Information Technology (Deemed University), Noida, for allowing cooperation in the field of numerical simulation and modelling of engineering systems between two institutions.

NOTATIONS (Di)e (Dik)e ∆Hj Ci Cis CP CT Di Dij Dik dp Fsi Fsio FT Fti Ftio Go Ji k1, k2 k3, k5 k4 k6 KEB L Mi n1 n2 n3 n4 n5 n6 n7 n8 Nri Nsi Nti Pi Pi,eq pmi Psi PsT PT Pti PtT Qi R r

Effective diffusivity of component i, m2/sec Effective Knudsen diffusivity of component i, m2/sec Heat of reaction j, J/mole Concentration of component i, mole/m3 Concentration of component i at surface of catalyst, mole/m3 Average heat capacity of gaseous mixture in reactor, J/mole.K Total concentration of gaseous mixture, mole/m3 Diffusivity of component i, m2/sec Binary diffusivity of the pair ij in multicomponent mixture, m2/sec Knudsen diffusivity of component i, m2/sec Diameter of membrane pore , m Molar flow rate of component i in shell, mole/sec Molar flow rate of component i in feed to shell side, mole/sec Total molar flow rate of gaseous mixture in reactor, mole/sec Molar flow rate of component i in tube, mole/sec Molar flow rate of component i in feed to tube side, mole/sec Mass velocity of gaseous mixture, kg/m2.sec Molar flux of component i through membrane, mole/sec.m2 Rate constant for reaction (1) and (2) respectively, mole/kg catalyst.sec.atm Rate constant for reaction (3) and (5) respectively, mole/kg catalyst.sec.atm2 Rate constant for reaction (4), mole/kg catalyst.sec.atm0.5 Rate constant for reaction (6), mole/kg catalyst.sec.atm3 Equilibrium constant for reaction (1), atm Length of reactor, m Molecular weight of component i, kg/kmole Number of reactions in tube, (-) Number of components in tube, (-) Number of reactions where i is reactant, (-) Number of reactions in shell, (-) Number of components in shell, (-) Number of reactions in shell where i is reactant, (-) Number of components in gas permeating through membrane, (-) Number of Pd membrane tubes, (-) Molar flux of component i through catalyst particle, mole/sec.m2 Molar flux of component i in axial direction of shell side, mole/sec.m2 Molar flux of component i in axial direction of tube side, mole/sec.m2 Partial pressure of component i , atm Partial pressure of component i at equilibrium , atm Permeability coefficient of component i, mole.m/m2. sec.atm Partial pressure of component i in shell, atm Shell side total pressure, atm Total pressure of gaseous mixture, atm Partial pressure of component i in tube, atm Tube side total pressure, atm Permeation rate of component i through membrane, mole/sec Gas constant = 8.314, J/mole.K Radial coordinate , m


23


24

R1 R2 R3 rj rp sij T Vsz vtz xsij xtij yi, yj ysi yti z

ID of tube, m OD of tube, m ID of shell, m Rate of reaction j, mole/sec.kg of catalyst Radius of catalyst particle, m Stoichiometric coefficient of component i in reaction j, (-) Temperature, K Superficial velocity of gas in shell in z direction, m/sec Superficial velocity of gas in tube in z direction, m/sec Fractional conversion of reactant i by reaction j in shell, (-) Fractional conversion of reactant i by reaction j in tube, (-) Mole fraction of component i and j respectively diffusing through membrane, (-) Mole fraction of component i in shell, (-) Mole fraction of component i in tube, (-) Spatial coordinate, m

Abbreviations BEN Benzene EB Ethylbenzene ST Styrene TOL Toluene Suffix C2H4 CO EB H2 H2O o s ST T t

Ethylene Carbon monoxide Ethylbenzene Hydrogen Steam Initial / feed Shell side Styrene Total Tube side

Greek Symbols β1 , β2 Conditional parameters used in shell balance equations, (-) ρB1 Density of catalyst in tube, kg/m3 of bed ρB2 Density of catalyst in shell, kg/m3 of bed ρB Density of catalyst, kg/m3 ρg Density of gaseous mixture, kg/m3 µd Dynamic viscosity, atm.sec µt Viscosity of gaseous mixture in tube, atm.sec µs Viscosity of gaseous mixture in shell, atm.sec ηj Effectiveness factor of reaction j, (-) ε Porosity of membrane, (-) εb Void fraction of packed catalyst bed in reactor, (-) τ Tortuosity of membrane, (-) δ Thickness of membrane, m




REFERENCES Abdalla, B.K., Elnashaie, S.S.E.H., “Catalytic dehydrogenation of ethylbenzene in membrane reactors”, AIChE J., Vol. 40, 2055-2059 (1994). Abdalla, B.K., Elnashaie, S.S.E.H., “Fluidized bed reactors without and with selective membranes for the catalytic dehydrogenation of ethylbenzene to styrene”, Journal of Membrane Science, Vol. 101, 31-42 (1995). Armor, J.N., "Catalysis with permselective inorganic membrane", Journal of Applied Catalysis, Vol. 49, 1-25 (1989). Armor , J.N., "Membrane Catalysis: Where is it now, what needs to be done", Catalysis Today, Vol. 25, 199-207 (1995). Assabumrungrat, S., Suksomboon, K., Praserthdam, P., Tagawa, T., Goto, S., "Simulation of a paladium membrane reactor for dehydrogenation of ethylbenzene", Journal of Chemical Engineering of Japan, Vol. 35, No. 3, 263-273 (2002). Becker, Y.L., Dixon, A.G., Ma, Y.H., Moser, W.R., “Modelling of ethylbenzene dehydrogenation in a catalytic membrane reactor”, Journal of Membrane Science, Vol. 77, 233-244 (1993). Bhandarkar, M., Shelekhin, A.B., Dixon, A.G., Ma, Y.H., "Adsorption, permeation, and diffusion of gases in microporous membranes. I. Adsorption of gases on microporous glass membranes", Journal of Membrane Science, Vol 75, 221-231 (1992). Bird, R.B., Stewart, W.E., Lightfoot, E.N., “Transport phenomena”, II edition, John Wiley and Sons, (2002). Caro, J., Noack, M., Kolsch, P., Schafer, R., "Zeolite membranes-state of their development and perspective", Microporous and Mesoporous Materials , Vol 38, 3-24 (2000). Clough, D.E., Ramirez, W.F., “Mathematical modeling and optimization of the dehydrogenation of ethylbenzene to form styrene”, AIChE J., Vol. 22 (6), 1097-1105 (1976). Collins, J.P., Way, J. D., “Preparation and characterization of a composite palladium ceramic membrane”, Ind. Eng. Chem. Res., Vol. 32, 3006-3013 (1993). Coronas, J., Falconer, J. L., Noble, Richard D., "Characterization and permeation properties of ZSM-5 tubular membranes", AICHE Journal, Vol 43, No. 7, 1797-1812 (1997). Coronas, J., Santamaria, J., “Catalytic reactors based on porous ceramic membranes”, Catalysis Today, Vol. 51, 377-389 (1999). Dittmeyer, R., Hollein, V., Quicker, P., Emig, G., Hausinger, G., Schmidt, F., “Factors controlling the performance of catalytic dehydrogenation of ethylbenzene in palladium composite membrane reactors”, Chemical Engineering Science, Vol. 54, 1431-1439 (1999). Dixon, A.G., "Recent research in catalytic inorganic membrane reactor", Internatiopnal Journal of Chemical Reactor Engineering, Vol 1, Review R6, 1-35 (2003). Elnashaie, S.S.F.H., Moustafa, T., Alsoudani, T., Elshishini, S.S., “Modelling and basic characteristics of novel integrated dehydrogenation-hydrogenation membrane catalytic reactors”, Computers and Chemical Engineering, Vol. 24, 1293-1300 (2000). Elnashaie, S.S.E.H, Abdallah, B.K., Elshishini, S.S., Alkhowaiter, S., Noureldeen, M.B., Alsoudani, T., “ On the link between intrinsic catalytic reactions kinetics and the development of catalytic processes-catalytic dehydrogenation of ethylbenzene to styrene”, Catalysis Today, Vol. 64, 151-162 (2001).


25

26



Fogler, H.S., “Elements of chemical reaction engineering”, II edition, Prentice Hall of India, (2001). Geankoplis, C.J, “Transport phenomena and unit operations”, III edition, Prentice Hall of India, (2001). Gobina, E., Hou, K., and Hughes, R., “ Ethane dehydrogenation in a catalytic membrane reactor coupled with a reactive sweep gas”, Chemical Engineering Science, Vol. 50, No. 14, 2311-2319 (1995a). Gobina, E., Hou, K., Hughes, R., “Mathematical analysis of ethylbenzene dehydrogenation: Comparison of microporous and dense membrane systems”, Journal of Membrane Science, Vol. 105, 163-176 (1995b). Hermann, Ch., Quicker, P., Dittmeyer, R., “Mathematical simulation of catalytic dehydrogenation of ethylbenzene to styrene in a composite palladium membrane reactor”, Journal of Membrane Science, Vol. 136, 161-172 (1997). Itoh, N., Haraya, K., " A carbon membrane reactor", Catalyst Today, Vol 56, 103-111 (2000). Jeong, B. H., Hasegawa, Y., Sotowa, K. I., Kusakabe, K., Morooka, S.,"Permeation of binary mixtures of benzene and saturated C4 - C7 hydrocarbons through an FAU - type zeolite membrane" , Journal of Membrane Science, Vol 213, 115-124 (2003a). Jeong, B.H., Sotowa, K.I., Kusakabe, K., "Catalytic dehydrogenation of cyclohexane in an FAU - type zeolite membrane reactor", Journal of Membrane Science, Vol. 224, 151-158 (2003 b). Julbe, Anne, Farrusseng, David, Guizard, Christian, “ Porous ceramic membranes for catalytic reactors - overview and new ideas”, Journal of Membrane Science, Vol. 181, 3-20 (2001). Koukou, M. K., Chaloulou, G., Papayannakos, N., Markatos. N. C., "Mathematical modelling of the performance of non-isothermal membrane reactors", Int. J. Heat Mass Transfer, Vol. 40, No. 10, 2407-2417 (1997). Meizner, D.L., Dyer, Paul N., "Characterization of the transport properties of microporous inorganic membranes", Journal of Membrane Science, Vol 140, 81-95 (1998). Moustafa, T.M., Elnashaie, S.S.E.H., “Simultaneous production of styrene and cyclohexane in an integrated membrane reactor”, Journal of Membrane Science, Vol. 178, 171-184 (2000). Quicker, P., Hollein V., Dittmeyer, R., “Catalytic dehydrogenation of hydrocarbons in composite palladium membrane reactors”, Catalysis Today, Vol 56, 21-34 (2000). Seader J.D., Henley E.J., "Separation process principles", John-Wiley and Sons, Inc. USA (1998). She, Y., Han, J., Ma, Y.H., “Palladium membrane reactor for the dehydrogenation of ethylbenzene to styrene", Catalysis Today, Vol. 67, 43-53 (2001). Shelekhin, A.B., Dixon, A. G., Ma, Y.H., "Adsorption, permeation, and diffusion of gases in microporous membranes. II. Permeation of gases in microporous glass membranes", Journal of Membrane Science, Vol 75, 233244 (1992). Sheppard, C.M., Maier, E. E., “Ethylbenzene dehydrogenation reactor model”, Ind. Eng. Chem. Process Design Dev., Vol. 25, 207-210 (1986). Shu, J., Grandjean, B.P.A., Neste, A. Van, Kaliaguine, S., “ Catalytic palladium based membrane reactors: A review" , The Canadian Journal of Chemical Engineering, Vol. 69, 1036-1060 (1991). Sznejer, G. A., Efremenko, I., Sheintuch, M., "Carbon membranes for high temperature gas separations: experiment and theory", AIChE J., Vol 50, No. 3, 596-610 (2004).



27

Sznejer, G., Sheintuch, M., "Application of a carbon membrane reactor for dehydrogenation reactions", Chemical Engineering Science, Vol. 59, 2013-2021 (2004). Uemiya, S., Sato, N., Ando, H., Kikuchi, E., “The water gas shift reaction assisted by a palladium membrane reactor”, Ind. Eng. Chem. Res., Vol. 30 (3), 585-589 (1991). Wu, J.C.S., Gerdes, T.E., Pszczolkowski, J. L., Bhave, R.R., Liu, P.K.T., “Dehydrogenation of ethylbenzene to styrene using commercial ceramic membrane reactors”, Sep. Sci. Technol., Vol. 25, 1489-1510 (1990). Wu, J. C. S., Liu, K.T. Paul, “Mathematical analysis on catalytic dehydrogenation of ethylbenzene using ceramic membranes”, Ind. Eng. Chem. Res.,Vol. 31, 322-327 (1992). Yang, Wei-Shen, Wu Ji Cheng, Lin Li Wu, "Application of membrane reactor for ethylbenzene", Catalysis Today, Vol. 25, 315-319 (1995).

dehydrogenation of

Zaman, J., Chakma, A, "Inorganic membrane reactors", Journal of Membrane Science, Vol 92, 1-28 (1994).
