Numerical solution of a mathematical model for hollow-fiber membrane gas separation system

Abstract

A mathematical model has been developed for the separation of CO2 from natural gas (CH4) using hollow-fiber membrane module. Numerical solution technique using Runge-Kutta-Merson method, available from the NAG FORTRAN Library as the subroutine D02BBF, is used to solved the mathematical model. The model is used to predict the effects of the operating conditions, namely, feed pressure and feed composition on the performance of the separation of CO2 from natural gas (CH4). The solution strategy employs initial value problem estimate and the establishment of feed pressure profile and gas composition profile . The model developed was used to predict the performance of a commercial size membrane permeator with a diameter and length of 5.08 cm and 304.8 cm respectively. The membrane area utilized was 232877.97 cm2 with 7200 active fibers. The volumetric feed flow rate was 1.83 x 10 (6) cm3 (STP)/s. The ranges of pressure and feed composition used are 2068-5170 cm Hg and 5-50% respectively. The model predicted the carbon dioxide purity in the permeate stream 65.54% and retentate 0.146% respectively. The results obtained was based on feed pressure, feed composition and temperature of 5170 cm Hg, 5% carbon dioxide and 25C respectively. The model also found that the Mechanical Energy Balance equation (Bernoulli equation) which was incorporated in the mathematical model satisfactorily predict the feed pressure drop along the fiber length. The predicted feed pressure drop was found to significantly affect the performance of a single-stage hollow-fiber membrane permeator.