(522e) Multiscale Perturbation Analysis of Mass Transfer and Reaction in a Microchannel with Porous Catalytic Coating

Microreactor technologies have been extensively studied in the context of process intensification, as a new strategy for reducing mass/heat transfer resistance[1]. Applications of these microsystems range from production of fine chemicals, pharmaceuticals and energy (e.g. synthesis gas and hydrogen for fuel cells) to catalyst screening and analytical measuring devices[2]. Although different designs and configurations have been considered, all explore the small characteristic dimensions for transverse diffusion and conduction (large surface-to-volume ratio). The incorporation of a catalytic porous coating in the wall of the microchannel provides a large total solid surface area, where heterogeneous reactions can take place. Reactants are transported in a fully developed laminar channel flow by convection and axial diffusion and diffuse radially towards the washcoat. Inside the catalyst layer, further diffusion through the porous media occurs, together with reaction at the active sites. Often the thickness of the catalyst layer is small enough for no internal mass transfer resistance to be considered. However, several situations have been observed in which diffusional limitations inside the washcoat are not negligible and criteria for diffusional-controlled regimes has to be provided[3]. In this case, the interaction between transport in the channel and reaction-diffusion processes in the porous layer determines the performance of the microchannel reactor. This configuration involves two domains (bulk channel and washcoat), which are coupled through continuity equations at the microreactor wall surface. The problem can become quite complex and challenging in terms of modelling, as concentration profiles at both catalyst and bulk fluid phases have to be determined. Numerical simulations can be too expensive and time consuming, especially if only design evaluation and preliminary optimization is required. Computational approaches can also require excessive resources when performing extensive parametric studies or when simulation of devices with a large number of channels is desired. In these cases, reduced order models can be very useful and provide important physical insight. Efficient modelling techniques have already been developed for surface wall catalysed reactions with no internal mass transfer resistance[4].

In this contribution, we use scaling and perturbation analysis[5,6] to obtain approximate concentration profiles in the channel and in the washcoat (where a first-order reaction is taking place), for a wide range of parameter sets. The dimensionless parameters describe the competition between the characteristic times for transport mechanisms and/or heterogeneous reaction and depend on flow properties, geometrical relations (e.g. aspect ratio, washcoat thickness) and reaction kinetics. This multi-scale analysis will contribute for the selection of suitable models for simulation in specific parameter ranges, since operating regimes are mapped and analytical solutions available for the relevant ones. In addition, some common approximations are critically evaluated (e.g. reduction to one-dimensional models by means of transfer coefficients) and criteria for simplifications derived (e.g. negligible radial concentration gradients; negligible mass transfer effects). Also, the range of validity of such approximations is provided.

The performance of the microreactor channel is also evaluated. The internal diffusion inside the washcoat can be measured by the effectiveness factor. The reactor should be operated so that the effectiveness factor is as high as possible (changing operating conditions or design). These conditions will be made clear by explicit effectiveness factor approximations in regimes of interest. In this case, internal and external mass transfer resistances can be compared as well.

Finally, design rules for microreactor channels are derived and optimum parameter regimes pointed out. Therefore, concentration and residence time can be easily controlled to allow higher conversion. The analytical approach employed results in a shortcut method for design and preliminary optimization of microreaction units, which can be competitive with high time consuming numerical procedures (CFD). On the other hand, simplification of the numerical procedure may be achieved by introduction of approximate analytical solutions in the regimes of interest.

References

[1] Mills PL, Quiram DJ, Ryley JF. Microreactor technology and process miniaturization for catalytic reactions--A perspective on recent developments and emerging technologies. Chemical Engineering Science. 2007;62(24):6992-7010.

[2] Ehrfeld W, Hessel V, Haverkamp V. Microreactors. Ullmann's Encyclopedia of Industrial Chemistry: Wiley; 2005; DOI: 10.1002/14356007.b16_b37

[3] Walter S, Malmberg S, Schmidt B, Liauw MA. Mass transfer limitations in microchannel reactors. Catalysis Today. 2005;110(1-2):15-25.

[4] Gervais T, Jensen KF. Mass transport and surface reactions in microfluidic systems. Chemical Engineering Science. 2006;61(4):1102-1121.

[5] Lin CC, Segel LA. Mathematics Applied to Deterministic Problems in the Natural Sciences: SIAM; 1988.

[6] Bender CM, Orszag SA. Advanced Mathematical Methods for Scientists and Engineers. New York: Springer-Verlag; 1999.