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

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.

Analysis of Influencing Factors on the Gas Separation Performance of Carbon Molecular Sieve Membrane Using Machine Learning Technique

“…In the fields of biomedicine, chemistry, materials, and the environment, the machine learning technique has been successfully applied to the analysis of the relationship between the characteristics and the performances of materials [15][16][17][18][19]. Specific to membrane-based gas separation, machine learning has been applied to the performance prediction and structural optimization of polymer membranes, zeolite membranes, metal-organic framework membranes, and composite membranes [20][21][22][23][24][25][26]. For CMS membrane, Behnia et al [27] predicted the gas permeability and selectivity through statistical analysis and modeling based on five influential factors, including the type of precursor, blend composition of precursors, final pyrolysis temperature, vacuum pressure during pyrolysis, and operating pressure.…”

Developing a fast and robust numerical method for the simulation of cocurrent hollow fiber gas separation membranes for process flowsheet synthesis

“…Kaldis et al [19] utilized the Brown's version of this method [20] based on the Pan's original problem formulation, for the cocurrent and counter-current modes of operation and obtained a high level of accuracy. Similarly, the finite element method that shares certain similarities with orthogonal collocation has been applied to membrane simulation independently [21][22][23] or with the aid of commercial software applications [24]. The main drawback of the orthogonal collocation and finite element methods are complex solution algorithms and massive computational burden in terms of both processing time and memory usage.…”

Process simulation and optimization of oxygen enriched combustion using thin polymeric membranes: effect of thickness and temperature dependent physical aging

“…20,[22][23][24][25][26][27][28][29][30][31][32][33][34] It is found that incorporation of the non-ideal effects in earlier works have been focused on departure of operating parameters from ideal conditions attributed to the fact that membrane gas separation is often operated at a wide range of operating temperature, pressure and feed composition, 26,35 such as (1) real gas behavior due to interaction between gas molecules, 22,24,[28][29][30][31][32][33] (2) Joule Thomson temperature drop due to cooling when gas permeates from high to low pressure end through the confined restriction of membrane pores under adiabatic expansion 22,25,[27][28][29][30][31][32][33] and (3) concentration polarization that refers to the phenomena of built-up of concentration gradient in the stagnant gas zone due to retention of less permeable gas component. 20,24,25,[28][29][30][31][32][33] Over recent years, published mathematical modeling works have been diverted to quantification of membrane gas transport property as a direct consequence of change in surrounding operating ...…”