P. Cruz

Cyclic adsorption separation processes: analysis strategy and optimization procedure

Abstract An innovative analysis strategy and an optimization procedure have been developed with the purpose of design, evaluation and optimization of small- and large-scale units of cyclic adsorption processes using the classical Skarstroms cycle: pressure swing adsorption (PSA) and vacuum swing adsorption (VSA). The system of partial differential equations of the dynamic simulator model was solved using a recent numerical technique developed within our group, based on an adaptive multiresolution approach, thus ensuring stability and accuracy. The simulator provides models for the multiple phenomena involved in fixed-bed adsorption: pressure drop, mass transfer resistance and energy balance. An extended parametric analysis is presented for the particular case of oxygen production from air by PSA and VSA: influence of the normalized purge flow rate, the high and low pressure values, dimensionless pressurization time, dimensionless production time, pressure drop and temperature in the bed.

Using wavelets for solving PDEs : an adaptive collocation method

The purpose of the author in this communication is to introduce the chemical engineering community to the basic features of wavelet-based adaptive collocation methods for solving PDEs (partial derivative equations) and to give an illustration of its powerful capabilities.

Adaptive multiresolution approach for solution of hyperbolic PDEs

This paper establishes an innovative and efficient multiresolution adaptive approach combined with high-resolution methods, for the numerical solution of a single or a system of partial differential equations. The proposed methodology is unconditionally bounded (even for hyperbolic equations) and dynamically adapts the grid so that higher spatial resolution is automatically allocated to domain regions where strong gradients are observed, thus possessing the two desired properties of a numerical approach: stability and accuracy. Numerical results for five test problems are presented which clearly show the robustness and cost effectiveness of the proposed method. 2002 Elsevier Science B.V. All rights reserved.

Modeling a catalytic polymeric non-porous membrane reactor

Abstract A theoretical study on a catalytic polymeric non-porous membrane reactor is performed. The conversion enhancement over the thermodynamic equilibrium is studied when conducting an equilibrium gas-phase reaction of the type A+B⇔C+D. The model used considers perfectly mixed flow patterns and isothermal operation for the retentate and permeate. It is concluded that the conversion of a reversible reaction can be significantly enhanced when the reactants’ diffusion coefficients are lower and/or sorption coefficients are higher than the products’. This happens for Thiele modulus and contact time over certain threshold values. It was also observed that it is preferable to enhance conversion through an increase in the reactants’ sorption coefficients, since this leads to lower reactor dimensions. Since the performance of a non-porous membrane reactor depends on both the sorption and diffusion coefficients, a study of such system cannot be based exclusively on the permeabilities of the components. Favorable combinations of diffusion and sorption coefficients can provide a coupled effect over the reactor’s conversion.

A study on the performance of a dense polymeric catalytic membrane reactor

Abstract A theoretical study on a catalytic polymeric dense membrane reactor (CPDMR) is performed. The conversion enhancement over the thermodynamic equilibrium value is studied for an equilibrium gas-phase reaction of the type a A+ b B⇔ c C+ d D for three different conditions: Δ n >0, Δ n =0 and Δ n n =( c + d )−( a + b ). For each of these cases, it is studied the influence of the reaction product sorption and diffusion coefficients. The model used considers perfectly mixed flow patterns and isothermal operation in the retentate and permeate sides. It is concluded that the conversion of a reversible reaction can be significantly enhanced when the diffusion coefficients of the products are higher than the reactants’ and/or the sorption coefficients are lower. The extension of this enhancement depends on the reaction stoichiometry, global concentration inside the membrane, Thiele modulus and contact time values. It was also observed that it would be preferable to have a conversion enhancement based on higher product diffusion than on lower product sorption coefficients, since this leads to smaller reactor size. Since the performance of a dense membrane reactor depends on both the sorption and diffusion coefficients in a different way, a study of such a system cannot be based only on the permeabilities of the reaction components.

Modeling catalytic membrane reactors using an adaptive wavelet-based collocation method

Abstract For certain operating conditions and reaction schemes, catalytic membrane reactors (CMRs) may present sharp concentration profiles in the membrane. Using conventional fixed grid methods for solving the model equations in such conditions may lead to inaccurate predictions of the reactor’s performance. This is demonstrated for two reaction systems: A⇌B (for which a semi-analytical solution is available) and A⇌B+3C (which describes the cyclohexane dehydrogenation). Simulation results obtained with a fixed grid method using finite differences are compared to those from an adaptive method using an algorithm based on interpolating wavelets. Showing higher accuracy and computational efficiency, the latter proved to be a useful tool in dealing with this kind of problems.

Considerations on the performance of hollow-fiber modules with glassy polymeric membranes

Glassy polymeric membranes are widely used in the separation of gas mixtures. Typically, the permeability of these membranes has a pressure and composition dependence that is well described by the dual-mode transport model. Nevertheless, for simplicity, most of the hollow-fiber permeator models only consider constant permeability, which can lead to inaccurate results. A comparative theoretical study is performed on the influence of two different membrane mass transport models on gas separation hollow-fiber modules: the constant permeability and the dual-mode transport models. n nThe comparison is performed in terms of the recovery and purity of the faster gas, under different design and operation conditions. Simulations are performed for the He/CH4 separation in a polycarbonate membrane. It is shown that the differences in performance exhibited by the two models can go up to 10% for recovery and 5% for purity, particularly for high-permeate pressures. n nPressure drop on the retentate and permeate sides is analyzed. Two pressure drop models based on Hagen–Poiseuille equation are considered and compared: constant viscosity, evaluated for feed conditions, and composition-dependent viscosity. It is concluded that neglecting viscosity composition dependency can lead to errors up to 20% in pressure drop calculations, consequently affecting the hollow-fiber performance in terms of recovery and purity.