Three-dimensional CFD Model of a Multitube Pd/Au Membrane Module for Hydrogen Purification
Rui Ma, Bernardo Castro-Dominguez, Anthony G. Dixon, Yi Hua Ma
Department of Chemical Engineering, Worcester Polytechnic Institute, 100 Institute Road, 01609 Worcester, MA, USA.
Hydrogen is an important chemical product due to its broad use in the generation of ammonia and methanol as well as a clean energy carrier. The U.S Energy Information Administration estimated that in the U.S., energy demand grows 0.4% per year. Coal gasification is a potential method to solve this problem since it generates electricity and H2 simultaneously. Nevertheless, this method also produces syngas, which is composed of methane, carbon dioxide, carbon monoxide and other impurities. Consequently, a separation process is required for the purification of H2. Compared to traditional separation methods, palladium (Pd) membrane separation technology has the advantage of high H2 selectivity, continuous operation and economic manufacturing costs. The objective of this work is to model accurately the performance of a multitube Pd membrane module and gain insight on the effects of different operating conditions.
A seven-tube membrane module has been designed and manufactured as shown in Fig. 1, capable of separating pure H2 from syngas mixtures. In this module, H2 enriched coal-derived syngas is introduced into the system as the feed; H2 permeates across the membrane and is collected at the inner tube side, while the unwanted gases are washed-out at the retentate side. Due to the broad variety of operating conditions, the membrane performance is hard to predict; thus, a computational fluid dynamics (CFD) simulation is used to optimize the operating conditions of this process. Compared to previously reported simulations, the module in this work takes heat transfer into consideration, making this framework more realistic since the temperature influences considerably the permeability and stability of the membranes. The performance of the multitube membrane module is accurately simulated, by generating a 3D model using COMSOL Multiphysics 5.0 solving simultaneously the continuity and Navier-Stokes equations as well as conservation of energy. Sieverts' law was used to define the permeation rate of H2 across each membrane, as shown in equation 1.
(1)
Where 
is H2 flux across the membrane, Q is the permeability
and 
is the thickness of membrane. 
and 
are the H2 partial pressures at retentate
side and permeate side, respectively. Equation 1 represents the
solution-diffusion mechanism for H2 transport; the permeability (Q) is
highly dependent on temperature. The overall effect of temperature on permeability
is introduced using the Arrhenius correlation as shown in equation 2.
(2)
Where Q0 is permeability constant and Ep is activation energy. Higher temperatures lead to higher permeabilities and thus higher H2 diffusion rates through the membrane.
The simulation was carried out under different Reynolds numbers (Re) within the laminar regime and various feed temperatures (523K-723K); the influences on the Péclet number and mass transfer resistances are clearly described under these circumstances. The depletion of H2 in the proximity of the membrane surface induces the formation of a gas boundary layer often called concentration polarization. The H2 partial pressure adjacent to the surface of the membranes is reduced due to the mass transfer resistance generated by concentration polarization. Furthermore, the simulation shows this phenomenon accurately by depicting a cross-sectional concentration profile of the shell side, as shown in Fig. 2. The results show that higher Re reduces concentration polarization by reducing the mass transfer boundary layer.
The performance of the system is analyzed based on the total H2 recovered on the tube side from the feed under the different operation conditions. Axial H2 concentration profiles (Fig. 3) show the H2 distribution, implying better H2 recovery at low Re. On the other hand, operating at high Re number or high Péclet numbers minimizes the effect of diffusion by markedly enhancing the convective forces. Although low feed flow rates lead to a high H2 recovery, they diminish the usage of the membrane. This is caused by early H2 depletion at the beginning of the membrane and a noteworthy axial H2 partial pressure gradient.
Furthermore, temperature distribution profiles show the influence of convective heat transfer of the gases to the membranes. Permeability distribution profiles along the membranes display the influence of temperature on H2 permeance. Operating at higher feed temperatures, close to the membrane temperature, increases the H2 recovery of the module; nevertheless lower temperatures display lower efficiencies due to the reduction of temperature at the surface of the membranes.
Based on the results obtained, the optimum operating conditions maximize H2 recovery; typically enhanced by low-moderate feed rates and high feed temperatures. This heat and mass transfer model is validated by comparing the results obtained in this study with previously reported experimental results of a single tube membrane module. The evaluation of the actual industrial model will be performed afterwards at the National Carbon Capture Center in Alabama.
Fig. 1. Membrane module set-up
Fig. 2. Cross-section concentration profile
Fig. 3. Hydrogen concentration profile across the retentate side of the multitube membrane module
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