Modeling Fixed Bed Membrane Reactors for Hydrogen Production through Steam Reforming Reactions: A Critical Analysis

Membrane reactors for hydrogen production have been extensively studied in the past years due to the interest in developing systems that are adequate for the decentralized production of high-purity hydrogen. Research in this field has been both experimental and theoretical. The aim of this work is two-fold. On the one hand, modeling work on membrane reactors that has been carried out in the past is presented and discussed, along with the constitutive equations used to describe the different phenomena characterizing the behavior of the system. On the other hand, an attempt is made to shed some light on the meaning and usefulness of models developed with different degrees of complexity. The motivation has been that, given the different ways and degrees in which transport models can be simplified, the process is not always straightforward and, in some cases, leads to conceptual inconsistencies that are not easily identifiable or identified

Progress on modeling and design of membrane reactors for hydrogen production

This paper presents an overview of recent research carried out by the authors on the development and analysis of mathematical models describing hydrogen production in membrane reactors. The case considered is that of methane steam reforming (SR) in a reactor with the typical double pipe configuration, in which a hydrogen-permeable membrane is present on the outer wall of the innermost tube. The model developed accounts for the rate of reaction, convective and dispersive transport in the axial and radial directions, and hydrogen permeation across the membrane. Density variations with pressure and gas composition have been accounted for, leading to a full coupling of mass and momentum transport. Different geometric aspect ratios have also been studied to assess the influence of catalyst volume on the overall performance of the system. The presence of two distinct transport regimes, in which hydrogen permeation is limited either by transport within the packed bed or permeation across the membrane, has been identified, along with the operating conditions that determine their range of existence. This has allowed the development of a simplified model, valid under the hypothesis that the reaction is fast compared to transport. In the permeation-controlled regime, the permeate flow rate and recovery may be found by solving a set of two PDEs, whereas an analytical solution is available for the transport-controlled regime. The main steps and observations that have brought to the development of the simplified model are presented, along with a guide to its implementatio

A tunable microfluidic device toiInvestigate the influence of fluid-dynamics on polymer nanoprecipitation

Polymer drug-embedding nanocapsules are attracting increasing attention as effective tools for the targeted delivery of pharmaceutical molecules on specific biological tissues. Besides, it is well established that an effective selectivity of the delivery dictates that the size of the carrier particles be accurately controlled, thus maintaining the size dispersion of the particle population as low as possible. To this end, microfluidics-assisted precipitation provides a promising alternative to the traditional processes in that the structure of the flow - ultimately controlling the particle size distribution - can be reliably predicted from the solution of Navier-Stokes equations in the laminar regime. Notwithstanding the great potential provided by microfluidics techniques, much about the interaction between fluid-dynamics and polymer transport and precipitation is yet to be understood. In this work, we investigate polymer precipitation in a simple cross-junction inflow-outflow microchannel, which has proven a viable benchmark to gain insight into the physics of nanoprecipitation in that the particle size distribution is sensitively dependent on the flow operating conditions. Specifically, previous experimental work by some of these authors proved that average particle size can vary by an order of magnitude for operating conditions where the solvent flow rate varies by a factor of three, while keeping the non-solvent flow rate constant. The scope of this work is to show that such sensitive dependence on operating conditions finds direct correspondence in the kinematic structure of the flow, which undergoes abrupt qualitative changes in the same range of operating conditions, provided a fully three-dimensional solution of the incompressible Navier-Stokes equation (thus retaining the inertial term in momentum balance) is afforded

How does radial convection influence the performance of membrane module for gas separation processes?

A two-dimensional axial-symmetric isothermal model, based on full coupling between mass and momentum transport, has been developed to describe the separation of a binary gaseous mixture in a packed bed membrane module. Steady-state conditions have been studied. The gaseous mixture to be separated enters an annular gap between two co-axial cylinders. The inner wall of the outer cylinder is impermeable to both components, whereas a membrane, with infinite selectivity towards one of the components, is supported onto the outer wall of the inner cylinder. A radial flux of the permeating components is therefore present. The main focus was on the determination of the influence of radial convection on the performance of the separator, which has been analysed in terms of three dimensionless groups. Different transport regimes could be identified, corresponding to different values of the dimensionless groups. The impact of radial convection has been assessed by comparing model predictions with those of a fully uncoupled one-dimensional model. A discrepancy up to 20% of the recovery has been observed in industrially relevant ranges of the parameters

Separation of polydisperse particle mixtures by deterministic lateral displacement. the impact of particle diffusivity on separation efficiency

Deterministic lateral displacement (DLD) has been recently proposed as a simple and efficient method to separate a polydisperse mixture of particles based on particle size. The separation device consists of a shallow rectangular channel filled with a periodic lattice of micrometer-sized obstacles, whose principal direction forms an angle with the channel walls. Particles are dragged by a carrier flow stream through the device. Experiments have shown that particles larger than a critical size depart from the average direction of the carrier flow, as they are systematically deflected by the obstacles while being dragged downstream. Theoretical models based on the geometric structure of the Stokes flow through the obstacle lattice have been proposed to predict the average direction of particle current flux. Besides, little is known about the dispersion of diffusing particles about the average particle current. In this article, we show that the interaction between the deterministic and stochastic components of particle motion results in a large-scale, possibly anisotropic, convection-enhanced dispersion process, which may hinder separation far beyond what could be predicted from the value of the bare particle diffusivity. The prediction of dispersion regimes results therefore essential for an optimal design of DLD devices. Copyright © 2012 Curtin University of Technology and John Wiley & Sons, Ltd

Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials

Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D-perpendicular to along the direction orthogonal to the uniform drive in the limit where Pe -> infinity. A simple one-dimensional model is proposed, which predicts the anomalous scaling D-perpendicular to similar to 1/[A(1) + A(2) log(Pe)]

On the hyperbolic behavior of laminar chaotic flows

International centre for mechanical sciences CISM courses and lectures no. 51

One-sided invariant manifolds, recursive folding, and curvature singularity in area-preserving nonlinear maps with nonuniform hyperbolic behavior

Two-dimensional nonlinear models of conservative dynamics are typically nonuniformly hyperbolic in that there are nonhyperbolic trajectories that coexist with a "massive" hyperbolic region. We investigate the influence of nonhyperbolic points on the global geometric structure of a invariant manifolds associated with points of the hyperbolic region. As a case study, we consider a transformation of the Standard Map family and analyze the structure of invariant manifolds in the neighborhood of an isolated parabolic (fixed) point x(p). This analysis shows the existence of lobes enclosing the parabolic point, that is, of simply connected regions containing x(p) whose boundary is formed by two continuous arcs of stable and unstable manifolds that intersect only at two points. From the existence of such regions, we derive that (i) there are points of the hyperbolic region where the local curvature of invariant manifolds is arbitrarily large and (ii) manifolds possess the recursively folding property. Property (ii) means that given an invariant manifold W and established an orientation on it, in the neighborhood of any point of the chaotic region there are nearby arcs of W that are traveled in opposite directions. We propose an archetypal model for which the existence of lobes and the recursive folding property can be derived analytically. The impact of nonuniform hyperbolicity on the evolution of physical processes that occur along with phase space mixing is also addressed. (c) 2005 Elsevier Ltd. All rights reserved

Connecting the spatial structure of periodic orbits and invariant manifolds in hyperbolic area-preserving systems

This Letter discusses the equivalence between the Bowen measure associated with the set Per(n) of periodic points of period n of hyperbolic area-preserving maps of a smooth manifold, and the measure associated with the intersections between stable and unstable manifolds of hyperbolic points. In typical cases of physical interest (i.e., nonuniformly hyperbolic systems) these measures are found to be highly nonuniform (multifractal). (c) 2005 Elsevier B.V. All rights reserved

Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow

We study the steady-state characterization of an advecting-diffusing three-dimensional flow defined in the annular region between coaxial cylinders of finite length that can rotate independently. A phase transition occurs when the cylinder velocities vary, which controls the spectral properties of the dominant eigenvalue and eigenfunction of the advection-diffusion equation for high Péclet numbers. The localization abscissa of the dominant eigenfunction can be used as the order parameter of the transition, and is a continuous function of the wall velocity. Conversely, the exponent characterizing the scaling of the real part of the dominant eigenvalue displays a discontinuous behavior at the critical point. Theoretical arguments support the localization properties observed numerically and provide a simple explanation of this phenomenon. © 2008 The American Physical Society