Modeling of Spiral Wound Membranes for CO<sub>2</sub> Removal from Natural Gas

Abstract

The proposed research aims to develop an effective model and design technique for gas separation systems based on spiral-wound. Object-Oriented Programming (OOP) paradigm was applied to create a simulator of the entire membrane module used to separate CO₂ from natural gas. The simulator's architecture is represented in a Unified Modelling Language (UML) diagram, and Python was used to create it. The model was built using forward finite difference techniques in both one and two dimensions. A two-stage membrane separation machine was used to test our mathematical model. There are six banks in the primary membrane separation unit, each with seven tubes; these tubes each contain twelve membrane elements. The initial stage of a gas separation process involves introducing the gas stream, which then splits into the retentate and permeate streams. The retentate stream is discharged out as a gaseous byproduct, while the permeate stream goes via a permeate compressor to raise its pressure before entering the second stage of the membrane unit. There are ten membrane elements in each of the tubes that make up the second-stage membrane unit's membrane banks. At this point, the goal is to waste as little hydrocarbon as possible. The second-stage retentate stream is reused as feed for the first-stage reactor, while the second-stage permeate stream is directed to the flare. This two-stage membrane separation device provides an empirical test of our mathematical concept. Several tweaks have been made to our model to improve precision and computational speed. There is a new dimensionless parameter, the selectivity and permeate flow rate equations have been simplified, and faster techniques for computing key variables have been implemented. Additionally, membrane package data can be imported into the new model for a deeper dive into sensitivity analysis. Using our proposed model, we determined how changes in factors including flow velocity, pressure ratio, carbon dioxide composition, membrane active area, and membrane thickness affected product purity and CO₂selectivity. There was an adverse relationship between product purity and feed rate, pressure ratio, CO₂mole fraction, and membrane thickness, but a positive correlation between product purity and membrane area. The mole fraction of CO₂also determines the selectivity for CO₂. Data collected in the field was used to verify the accuracy of the model. The validation data demonstrated that the model's predictions of MSU's performance were accurate within a margin of error of 3%.