Asymptotic Analysis of Binary Gas Mixture Separation by Nanometric Tubular Ceramic Membranes: Cocurrentand Countercurrent Flow Patterns

Analytical gas-permeation models for predicting the separation process across membranes (exit compositions and area requirement) constitutes an important and necessary step in understanding the overall performance of membrane modules. But, the exact (numerical) solution methods suffer from the complexity of the solution. Therefore, solutions of nonlinear ordinary differential equations that govern the performance of the membrane modules for gas separations by approximate and asymptotic methods are useful in the design and comparison of processes. In this work, the asymptotic methods were applied for predicting the performance of nanometric tubular ceramic membranes in the separation of binary gas mixtures with cocurrent and countercurrent flow patterns. Also, the exact (numerical) solutions of the governing equations using the fourth order Rung-Kutta technique were proposed. The comparison of the results showed a good agreement between the exact solution and asymptotic analysis methods over the whole range of selectivities (1 ≤ α ≤ ∞) . Because, the asymptotic curves into the former (α → 1) and latter (α → ∞ ) boundaries had a suitable overlap with each other to cover the whole range of selectivities. The accuracy of this method was verified by a comparison of the predicted results with different literature experimental data and mathematical models. This result suggests the use of the asymptotic analysis method to provide excellent shortcut, preliminary design information.