OPTIMIZATION OF A PD-BASED MEMBRANE REACTOR FOR HYDROGEN PRODUCTION FROM METHANE STEAM REFORMING A. J. ASSIS (1) C. E. HORI (2) L. C. SILVA (3) V. V. MURATA (4) (1,2,3,4)
School of Chemical Engineering – Federal University of Uberlandia – Uberlandia, MG, Brazil.
RESUMO Neste trabalho, propõe-se um modelo fenomenológico no estado estacionário para descrever o desempenho de um reator com membrana na produção de hidrogênio a partir da reforma a vapor do metano e realiza-se a otimização das condições operacionais. O modelo é composto por equações diferenciais ordinárias advindas dos balanços de massa, energia e quantidade de movimento e equações constitutivas. Usaram-se duas cinéticas intrínsecas disponíveis na literatura para descrever as reações da reforma a vapor do metano. Os resultados previstos pelo modelo foram validados com dados experimentais. Na otimização, foram avaliados os efeitos de cinco parâmetros importantes do processo, pressão de entrada do reator (PR0), vazão molar de alimentação de metano (FCH40), vazão molar de gás de arraste (FI), temperatura externa do reator (TW) e razão molar de alimentação entre vapor d’água e metano (M), simultaneamente na conversão do metano (XCH4) e na recuperação do hidrogênio (YH2). As melhores condições operacionais foram obtidas por otimização paramétrica simples e por um método baseado no gradiente, que por sua vez faz uso do código computacional DIRCOL em FORTRAN. Altas conversões de metano (96%) e recuperações de hidrogênio (91%) foram atingidas, nas condições ótimas.
ABSTRACT In this work, it is proposed a phenomenological model in steady state to describe the performance of a membrane reactor for hydrogen production through methane steam reform as well as it is performed an optimization of operating conditions. The model is composed by a set of ordinary differential equations from mass, energy and momentum balances and constitutive relations. They were used two different intrinsic kinetic expressions from literature. The results predicted by the model were validated using experimental data. They were investigated the effect of five important process parameters, inlet reactor pressure (PR0), methane feed flow rate (FCH40), sweep gas flow rate (FI), external reactor temperature (TW) and steam to methane feed flow ratio (M), both on methane conversion (XCH4 ) and hydrogen recovery (YH2 ). The best operating conditions were obtained through simple parametric optimization and by a method based on gradient, which uses the computer code DIRCOL in FORTRAN. It is shown that high methane conversion (96%) as well as hydrogen recovery (91%) can be obtained, using the optimized conditions.
PALAVRAS-CHAVE Modelagem e simulação, análise de sensibilidade, reações de reforma, hidrogênio, DIRCOL.
KEYWORDS Modeling and simulation, sensivity analysis, reforming reactions, hydrogen, DIRCOL. 1
Correspondence should be sent to A. J. Assis: Tel.: +55(34) 3239-4292; e-mail:
[email protected]
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1. INTRODUCTION Nowadays, methane steam reforming is the main route for hydrogen production. Methane steam reforming reactions are endothermic and reversible, which implies on the conventional technology, in high operating temperatures to reach satisfactory conversions [1]. Since the maximum conversion that could be achieved is the equilibrium conversion, the membrane technology is an alternative process that can overcome this limitation. Membrane reactors are generally constituted by concentric tubes in which one of them is the membrane. The membrane is usually made of Palladium or an alloy of Palladium-Silver that is only permeable by hydrogen. Therefore, in a membrane reactor, hydrogen is continuously removed from the reaction zone, displacing the chemical equilibrium and enabling operation at moderate temperatures. Satisfactory conversions are dependent on many factors such as the operating parameters [2]. Several studies [3-7] have studied the influence of the factors such as operating pressure, methane feed flow rate, operating temperature, sweep gas flow rate, area of permeation, etc., on the methane conversions. In this work a combination of a parametric optimization and a gradient-based optimization is made to provide an insight about the choice of some parameters that maximize the hydrogen recovery and the methane conversion for a small-scale reactor.
2. OBJECTIVES The objectives of this work are to carry out the mathematical modeling of a membrane reactor, in laboratory scale, for the methane steam reforming, to validate the model with experimental data, to verify the influence of important process variables and to find the best operating conditions that optimize the hydrogen recovery and the methane conversion.
3. MATHEMATICAL MODELING In accordance with [8] the reactions among methane, water, monoxide of carbon, carbon dioxide and hydrogen that present greater probability to occur during methane steam reforming are: (0.1) CH 4 + H 2O Ç CO + 3 H 2 − ∆H 298 K = −206.1 kJ / mol
CO + H 2O Ç CO2 + H 2 CH 4 + 2 H 2O Ç CO2 + 4 H 2
− ∆H 298 K = 41.15 kJ / mol − ∆H 298 K = −165.0 kJ / mol
(0.2) (0.3)
The reactor modeled is schematically represented in Figure. 1. The inner tube is the Pdbased membrane and the outer one is the shell. The catalyst is packed in the annular region. The inert or sweep gas passes into the inner tube in co-current flow mode.
Figure 1: Membrane reactor scheme considered in this work. The balance equations are: • Mass balance in the reaction chamber: For i= CH4, CO, CO2, H2O: 2
3 dFi = W ∑ν ij rj dZ j =1
(0.4)
3 dFi = W ∑ν ij rj − J H 2 Am dZ j =1
(0.5)
For i= H2
Where JH is given by: 2
J H2 = •
A0 e
E RTm
δ
(( p
0.5
(
− pH 2 p )0.5
))
= J H 2 Am
p
dZ
(0.6)
(0.7)
Energy balance in the reaction chamber:
ρ r Cv vr · r
•
)
Mass balance in the permeate side:
dFH 2 •
H2
3 ∂P d vr 1 dTR = TR + (Q1 − Q2 + W ∑ ( −∆H j )rj − H H2 J H2 Am ) ∂T V dZ Van dZ j =1
(0.8)
Energy balance in the permeate side:
ρ p Cv v p · p
dTp dZ
= Tp
∂P d v p 1 + (Q2 + H H2 J H2 Am ) ∂T V dZ V pe
(0.9)
Q1 is the heat exchanged between the reactor wall and the reaction chamber, and Q2 is the heat exchanged between the reaction chamber and the permeate:
Q1 = U1 A1 (Tw − TR )
(0.10)
Q2 = U 2 A2 (TR − TP )
(0.11)
The overall heat transfer coefficients were taken from [7]. • The catalytic bed pressure drop:
ρ u2 dPR =−f r s dZ dp
(0.12)
Where f is calculated by the Ergun's equation:
f =
1− ε b(1 − ε ) a+ 3 Re ε
(0.13)
The mathematical model considered real gases for thermodynamic properties calculations. Additional hypotheses adopted in the model development were: nonisothermal/nonisobaric, pseudo-homogeneous model, steady-state operation, plug-flow behavior was adopted for the permeate and reaction zone, nonexistence of boundary layer on the membrane and hydrogen diffusion in the membrane is the rate determining step for hydrogen permeation. The reactor dimensions used in this work were taken from [5]. All thermodynamic mixture properties were calculated using the Virial equation of state, with van der Waals mixing rules. The gases and the gaseous mixture viscosities were calculated by Chung’s method [10]. The values of constants a and b of Ergun’s equation are 150 and 1.75 respectively [11]. Other catalyst properties used were taken from [8]. Methane conversion and hydrogen recovery were defined as:
X CH 4 =
0 FCH − FCH 4 4 0 FCH 4
(0.14)
3
YH 2 =
FH 2 p FH 2 p + FH 2
(0.15)
4. RESULTS AND DISCUSSION 4.1 . Model Validation Two different intrinsic kinetics available for the reactions of methane steam reforming were used. The first one is reported by [8] and it is the oldest and widely used. The second one, by [12] is more recent and there is no reference about its use in a reactor model. The basic difference between them is that the first one was developed for catalysts of Ni/MgAl2O4 and only one of the products, the hydrogen, adsorbs on the surface. The second one was developed for catalysts of Ni/Al2O3 in which two products, hydrogen and carbon monoxide, adsorb on the surface. These two kinetics were evaluated during the validation of the model, in this work. The validation of each model was carried out using given experimental data of a Pd-based membrane reactor reported by [5] with the same design and operating conditions. Methane conversions obtained by the model were compared with the experimental ones reported by [5]. Methane conversions were evaluated for different steam to methane feed flow ratio, different operating temperatures and different operating pressures, and in this paper only a sample of the results are presented (Fig. 2).
Figure 2: Methane conversion versus reactor temperature.
Figure 3: Methane conversion profiles along the reactor.
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The agreement between the simulated results and the experimental ones was good as it can be seen in the Fig. 2. Moreover, the two available kinetics leads to similar results. The difference between them resides on their behavior along the reactor. As it can be seen in the Fig. 3, methane conversion has an abrupt rise at the reactor beginning. This behavior is somewhat different when Hou’s kinetics [12] was used, and this difference increases as the methane feed flow rate increases. In other words, Froment’s kinetics [8] predicts an abrupt change for the composition at the reactor beginning, whereas the Hou’s kinetics foresees a less sudden change. As it will be discussed further, molar methane feed flow rate less then 1x10-4 mol/s cause dramatic changes the compositions at the reactor beginning, and as a result, the optimization using the gradient based -4 optimization could not be performed for values smaller than 1x10 mol/s of methane feed.
4.2 .Parametric and gradient based optimization At first, Froment’s kinetics was chosen due to two mainly reasons. This kinetics is widely known and used, and also because it implies in less mathematical problems. Both kinetics demand products feed, the Froment’s kinetics requires hydrogen feed and Hou’s kinetics requires hydrogen and carbon monoxide feed. These problems are caused by the presence equations. Therefore, low -4 values were used (1.0·10 ) as initial conditions for these products. However, during the optimization using a gradient based method, the use of the Froment’s kinetics cause failure of the algorithm. In this case, the lower admissible value for methane feed flow rate was 1.0·10-4 mol/s and using the Hou’s kinetics only. To perform the optimization, a standard or reference operational condition for membrane reactors in methane steam reforming were taken according to [5]: PR0 = 136000 Pa, TW = 773.15 K, M = 3, FI = 2.75·10-5 mol/s and FCH40 = 2.75·10-5 mol/s.
4.3 .Parametric optimization In order to try to maximize methane conversion and hydrogen recovery, defined by Eqs. 1.14 and 1.15, different values around the standard parameters reported by [5] were adopted. The lower and upper bounds were chosen based on operating characteristics of the membrane reactors and on the Shu’s work [5]. The upper and lower bounds are shown in Table 1. As it is shown in Fig. 4 A and B, an increase in pressure, temperature and sweep gas flow cause an increase in methane conversion and hydrogen recovery. Conversely, an increase in methane conversion and hydrogen recovery is caused by a decrease in methane inlet flow. Particularly, an increase in steam to methane feed flow ratio (M) has an opposite effect on the methane conversion and hydrogen recovery. However, an increase in M causes an increase in the sum (XCH4 + YH2 ). Therefore, it can concluded that the use of the upper values of pressure, temperature and sweep gas and the lower methane feed value leads to the maximal methane conversion and hydrogen recovery, regardless of the interactions among the parameters. On the other hand, analyzing methane conversion and hydrogen recovery sum (Fig. 5 A), it can be noticed that the highest value for this parameter leads to the maximal methane conversion + hydrogen recovery. Indeed, the gain obtained in methane conversion, keeping the others parameters in the considered best conditions, is less than the setback obtained in the hydrogen recovery. Therefore, depending on the values of the other parameters, the trend of this effect change from an increase to a decrease in the objective (methane conversion plus hydrogen recovery). In other words, the interactions between the parameters are important in the optimization. Even so, high conversions (from 99.92 to 99.99%) and high recoveries (from 96.82 to 99.28%) could be achieved varying the steam to methane feed ratio and keeping the pressure, temperature and sweep gas at the highest values and the methane feed at the lowest value.
4.4.Optimization by a gradient based method (DIRCOL) Having in mind the importance of the interaction between the parameters, it is imperative to perform the optimization taking into account these interactions. In order to carry out this task a gradient based algorithm of optimization (DIRCOL) was used [13]. The optimization was performed directly from the differential equation by discretization. Therefore, the optimization problem was posed as: 5
Maximize: XCH4 + YH2 , Subject to: • Model equations (Equations 1.4 to 1.13); • Parameters bounds from Table 1; • Bounds of the state variables (for all state variables, the range is between 0 and 1 due to a normalization). Due to a numerical instability in the optimizer’s code the methane feed was kept in 1·10-4 mol/s, and the others parameters (PR0, TW, M and FI) were taken as variable decision. The optimization was carried out using the following input information supplied by the user: optimal tolerance and nonlinear feasibility tolerance equal 1.0·10-3, iscale equal 0, initial grid points equal 15, with equidistant grid points, initial estimates for the parameters equal PR0 = 506625.0 Pa, FI = 1.375·10-4 mol/s, TW = 873.15K e M = 2.5. The initial estimates for the state variables were based on a non linear fit on the integrated model. To avoid reaching local maxima, other initial estimates for the parameters were used, but all converged to the same values. The best parameters values are shown in Table 1. These parameters lead to a methane conversion of 96.27% and a hydrogen recovery of 91.26%, that are higher than 41.57% and 11.90% obtained in the adopted standard conditions changing methane feed -5 -4 -4 from 2.75·10 to 1.0·10 mol/s. It is important to emphasize that values lower than 1.0·10 mol/s cause numerical instability, probably because the dramatic change in composition in the reactor beginning achieved for low values of methane feed, as can be seen in Fig. 5 B. This figure also shows the profiles of methane conversion along the reactor. It is also import to cite that this optimization could be carried out only with the Hou’s kinetics, probably due to the fact that the Froment’s kinetics lead to a more dramatic change in composition than the Hou’s kinetics.
a)
b)
Figure 4: Parametric optimization: a) Effect of the pressure and temperature. b) Effect of the sweep gas flow rate and methane feed flow rate.
a)
b)
Figure 5: a) Effect of steam to methane feed flow ratio. b) Profiles along the reactor obtained by parametric optimization and optimization with DIRCOL.
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Table 1: Lower, upper bounds and best values of the parameters. Parametric optimization Optimization with DIRCOL lower Upper Best lower Upper best Parameters bound bound value bound bound value Pressure (Pa) 101325 506625 506625 101325 506625 506625 Temperature (K) 573.15 873.15 873.15 573.15 873.15 873.15 Sweep gas (mol/s) 2.75x10-5 1.375x10-4 1.375x10-4 2.75x10-5 1.375x10-4 1.375x10-4 Steam to 2.5 to 6 methane ratio 2.5 6 (not conclusive) 2.5 6 2.779 Methane feed (mol/s) 5x10-6 1x10-4 5x10-6 Fixed=1x10-4
5. CONCLUSIONS Comparing methane conversion obtained by the developed model using two available kinetics for methane steam reforming, it can be concluded that both characterize a good representation of the real reactor. However, the conversion profile obtained using Hou’s kinetics describes smoother concentration profiles along the reactor. By parametric optimization, it was possible to obtain high conversions and recoveries (more than 99 and 96 %) but, the best value could not be evaluated with assurance. The use of the DIRCOL to perform the optimization could only be possible with the use of Hou’s kinetics in the model, even so for a value of methane feed of 1·10-4mol/s. This value is about three times the standard value. A methane conversion of 96.27% and hydrogen recovery of 91.26% were obtained for the best parameters choice.
6. ACKNOWLEDGEMENT This work has been supported by Brazilian funding agency CNPq (Grant n. 475934/2006-7).
7. LIST OF SYMBOLS a - Ergun's equation constant, [-]; 2 0.5 A0 - Pre-exponential factor of the permeability, [mol/(m s Pa )]; A1 - Area of heat exchange between the reaction chamber and the external reactor temperature, [m2]; 2 A2 - Area of heat exchange between the reaction chamber and the permeate side, [m ]; 2 Am - Surface area of membrane permeance, [m ]; b - Ergun's equation constant, [-]; Cvp - The permeate mixture specific heat at constant volume, [J/(mol K)]; Cvr - The reaction mixture specific heat at constant volume, [J/(mol K)]; E - Activation energy, [J/mol]; f - Friction factor, [-]; fH2p - Hydrogen dimensionless flow rate in the permeate side, [-]; fi - Dimensionless flow rate of the i component in the reaction side, [-]; FCH40 - Methane feed flow rate, [mol/s]; FH2p - Hydrogen flow rate in the permeate, [mol/s]; Fi - Molar flow rate of component i in the reaction side, [mol/s]; FI - Molar flow rate of inert or sweep gas, [mol/s]; HH2 - Hydrogen enthalpy, [J/mol]; JH2 - Hydrogen permeation flux, [mol/m2s]; L - Reactor length, [m]; M - Steam to methane feed flow ratio, [-]; PR0 - The inlet reactor pressure, [Pa]; PR - Reaction pressure, [Pa]; Pr - Dimensionless reaction pressure, [-]; Pp - Permeate pressure. [Pa]; pH2 - Hydrogen partial pressure in the reaction side, [Pa]; pH2p - Hydrogen partial pressure in the permeate side, [Pa]; 7
Q1 - Heat exchanged between the reaction side and external environment, [J/s]; Q2 - Heat exchanged between the reaction side and the permeate side, [J/s]; rj - Rate of the reaction j, [Kmol/(Kg s)]; R - Gas constant, [J/(mol K)]; Re - Reynolds' number, [-]; Tm - Membrane temperature, [K]; Tp - Dimensionless permeate temperature, [-]; Tr - Dimensionless temperature of the reaction, [-]; TR- Temperature of the reaction side, [K]; Tw - The external temperature, [K]; us - Gaseous velocity of the reaction chamber, [m/s]; U1 - Overall heat transfer coefficient (reaction side and external side), [W/(m2K)]; 2 U2 - Overall heat transfer coefficient (reaction and permeation zone), [W/(m K)]; vp - Mean velocity of the gaseous mixture in the permeate, [m/s]; vr - Mean velocity of the gaseous mixture in the reaction chamber, [m/s]; Van - Annular volume, [m3]; 3 Vpe - Permeate volume, [m ]; XCH4 - Methane conversion, [-]; W - Catalyst mass, [Kg]; YH2 - Hydrogen recovery, [-]; z - Dimensionless axial position, [-]; Z - Axial position, [-]; • Greek letters δ - Membrane thickness, [m]; ∆Hj - Heat of the reaction j, [J/mol]; ε - Void fraction, [-]; µij - Stoichiometric coefficient of the component i in the reaction j, [-]; ρp - Permeate density, [Kg/m3]; 3 ρr - Reaction density, [Kg/m ]. • Subscripts i = CH4, CO, H2, H2O, CO2. j = 1, 2, 3 (reactions 1.1, 1.2, 1.3). k = CH4, CO, H2, H2O. p = permeate side. r = reaction side.
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