Mathematical Modeling of Natural Gas Separation Using Hollow Fiber Membrane Modules by Application of Finite Element Method through Statistical Analysis

Abstract

Abstract Hollow fiber membrane permeators used in the separation industry are proven as preferred modules representing various benefits and advantages to gas separation processes. In the present study, a mathematical model is proposed to predict the separation performance of natural gas using hollow fiber membrane modules. The model is used to perform sensitivity analysis to distinguish which process parameters influence the most and are necessary to be assessed appropriately. In this model, SRK equation was used to justify the nonideal behavior of gas mixtures and Joule-Thomson equation was employed to take into account the changes in the temperature due to permeation. Also, the changes in temperature along shell side was calculated via thermodynamic principles. In the proposed mathematical model, the temperature dependence of membrane permeance is justified by the Arrhenius-type equation. Furthermore, a surface mole fraction parameter is introduced to consider the effect of accumulation of less permeable component adjacent to the membrane surface in the feed side. The model is validated using experimental data. Central Composite Designs are used to gain response surface model. For this, fiber inner diameter, active fiber length, module diameter and number of fibers in the module are taken as the input variables related to the physical geometries. Results show that the number as well as the length of the fibers have the most influence on the membrane performance. The maximum mole fraction of CO2 in the permeate stream is observed for low number of fibers and fibers having smaller active lengths. Also results indicate that at constant active fiber length, increasing the number of fibers decreases the permeate mole fraction of CO2. The findings demonstrate the importance of considering appropriate physical geometries for designing hollow fiber membrane permeators for practical gas separation applications.