Abstract
A two-dimensional non-isothermal stationary mathematical model of the catalytic membrane reactor for the process of methanol dehydrogenation is described. Copper supported on the carbonaceous support was considered as a catalyst. The reaction of methanol dehydrogenation was thermodynamically conjugated with a reaction of hydrogen oxidation taking place in a shell side of the membrane reactor. The effects of various parameters on the methanol conversion and the methyl formate yield have been calculated with the developed model and discussed. Two different types of heating the gas flow were considered and compared. In the case of conjugated dehydrogenation process, the methyl formate yield reaches 77%, when the reactor outer wall was heated up to 150 °C. When the inlet gas flows in the tube and shell sides were heated up to 100 and 83 °C, correspondingly, the yield was 72%.
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Abbreviations
- A m :
-
Area of membrane, m2
- \(C_{i}^{\text{t,s,c}}\) :
-
Concentrations, kmol m−3
- c p :
-
Heat capacity coefficient, kJ g−1 K−1
- \(D_{{{\text{e}}i}}^{\text{t,c}}\) :
-
Effective coefficient of radial diffusion of component i, m2 s−1
- D ij :
-
Molecular diffusivity for component i in a binary mixture of i and j, m2 s−1
- \(D_{\text{m}}^{\text{t,c}}\) :
-
Coefficient of molecular diffusion, m2 s−1
- D kn :
-
Knudsen diffusion coefficient, m2 s−1
- d e :
-
Equivalent pore channel diameter, m
- d e1, d e2 :
-
Equivalent diameter, m
- d k :
-
Diameter of catalyst, m
- d r :
-
Diameter of membrane reactor, cm
- G t,s :
-
Gas flow rate, ml min−1
- − ∆H j :
-
Heat effect of reaction j, kJ mol−1
- l :
-
Length of reactor, m
- M i :
-
Molecular weight of ith compound, g mol−1
- N t,s :
-
Number of components in reaction mix
- N R :
-
Number of reactions within the tube side of reactor
- Perm:
-
Permeability
- P w :
-
Perimeter of wall, m
- \(P_{{{\text{H}}_{ 2} }}^{\text{t,s,c}}\) :
-
Partial pressure of H2, atm
- P 0 :
-
Pressure at normal conditions, atm
- Q 0 :
-
Permeability constant, kmol m−1 s−1 atm−1/2, defined in Gobina and Hughes (1994): \(Q_{0} {\kern 1pt} = \;1.0061 \times 10^{ - 12} \exp \,( - \,767.38/T)\)
- \(Q_{{{\text{H}}_{ 2} }}\) :
-
Hydrogen permeation rate through the membrane, kmol s−1
- r 1,2 :
-
Radial coordinate into the fixed bed catalyst, in the ceramic support, m
- R :
-
Universal gas constant, J mol−1 K−1
- S cr.s. :
-
Cross-sectional area of shell side, m2
- S sp1,sp2 :
-
Specific surface area, m−1
- T t,s,c,w :
-
Temperature, K
- T cr :
-
Critical temperature of substance, K
- T 0 :
-
Temperature at normal conditions, K
- \(u_{\text{l}}^{{{\text{t}},{\text{s}}}}\) :
-
Axial velocity, m s−1
- V cr :
-
Critical volume of substance, cm3 mol−1
- w j :
-
Rate of reaction, kmol kg −1cat s−1
- w s = η s \({\text{R}}_{{{\text{O}}_{x} ,{\text{H}}_{ 2} }}\) :
-
Rate of the hydrogen oxidation reaction, kmol kg −1cat s−1
- y i :
-
Mole fraction of ith component
- Re e :
-
Reynolds number, \(\text{Re}_{\text{e}} = v_{\text{e}} d_{\text{e}} \rho_{\text{g}} /\mu\)
- Sc:
-
Schmidt number (diffusion Prandtl’s criterion), \({\text{Sc}} = \mu /(\rho_{\text{g}} D_{\text{m}} )\)
- Pr:
-
Prandtl number, \({ \Pr } = \mu c_{\text{p}} /\lambda_{\text{g}}\)
- Nu:
-
Nusselt number
- α w :
-
Coefficient of heat transfer at wall, kJ m−2 s−1 K−1, \(\alpha_{\text{w}} = {\text{Nu}}_{\text{we}} \lambda_{\text{g}} /d_{\text{e}}\)
- α 1,2 :
-
Coefficient of heat transfer between the membrane/exterior wall and fixed bed catalyst (shell side), kJ m−2 s−1 K−1
- δ :
-
Membrane thickness, m
- δ c :
-
Ceramic support thickness, m
- ε t,s,c :
-
Porosity of catalyst layer (tube, shell side), ceramic support
- γ ij :
-
Stoichiometric coefficient for i-component into j-reaction
- \(\lambda_{\text{ef}}^{\text{t}}\) :
-
Effective coefficient of radial thermal conductivity, J m−1 s−1 K−1
- λ c :
-
Thermal conductivity of the ceramic support, J m−1 s−1 K−1
- λ g :
-
Thermal conductivity of argon gas, reference value, J m−1 s−1 K−1
- μ :
-
Dynamic viscosity of a gas mix, kg m−1 s−1
- \(\rho_{\text{G}}^{{{\text{t}},{\text{s}}}}\) :
-
Gas density, kg m−3
- \(\rho_{\text{k}}^{{{\text{t}},{\text{s}}}}\) :
-
Density of catalyst, kg m−3
- c:
-
Ceramic support
- in:
-
Inlet
- s:
-
Shell side
- surf:
-
Surface
- t:
-
Tube side
- W:
-
Wall of reactor
- m.f.:
-
Mole fraction
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Acknowledgements
This work was supported by Russian Academy of Sciences and Federal Agency of Scientific Organizations (state-guaranteed order for BIC, Project number 0303-2016-0014). The numerical calculations were carried out at Tomsk Polytechnic University within the framework of Tomsk Polytechnic University Competitiveness Enhancement Program (Grant VIU-TOVPM-316/2017).
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Shelepova, E.V., Ilina, L.Y. & Vedyagin, A.A. Energy-efficient dehydrogenation of methanol in a membrane reactor: a mathematical modeling. Chem. Pap. 72, 2617–2629 (2018). https://doi.org/10.1007/s11696-018-0491-x
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DOI: https://doi.org/10.1007/s11696-018-0491-x