Membrane-based gas separation continues to be an area of interest that is being explored for various applications and efforts are being made to enable large-scale implementation and commercialisation. Works on techno-economic studies in areas such as carbon capture, natural gas sweetening, and biogas upgrading has been reported. Various simulation studies have reported the effect of the membrane flow pattern on permeate recovery and purity. The simulation studies in this area have been limited to single-stage and two-stage membrane processes, while many of these studies considered polymer membranes, facilitated transport has barely been investigated. In addition, optimisation studies that compared different flow patterns in the membrane module have been few. The facilitation of gas permeation decreases as pressure is increased due to carrier saturation. However, an increased pressure increases the driving force, and a trade-off should be achieved. The different membrane flow patterns also have inherent driving force potential. In this work, a superstructure-based model that also embeds a fixed site carrier permeation membrane has been developed for CO2 capture from a coal-fired power plant and three scenarios based on the different flow patterns, i.e., co-current, counter-current and crossflow, were analysed to determine the effect of the flow pattern in the membrane module. The main objective of the optimisation was to minimise the cost of capture. The counter-current flow pattern resulted in the lowest cost of capture as it resulted in the most energy-efficient process system. The co-current flow-based optimisation results in configuration result in an 18 % increase in cost compared to the counter-current flow pattern optimisation run due to a 29 % increase in energy consumption. The crossflow pattern optimisation results in a 9 % increase in the annualised cost of capture compared to the counter-current flow.