Modeling of spiral wound membranes for gas separations. Part I: An iterative 2D permeation model

Membranes are excellent alternatives for gas separations due to their low installation and maintenance costs. In industrial environment, membranes are usually organized in modules with spiral-wound or hollow fiber geometries. Because of their wide range of applications, the development of reliable mathematical models for industrial membrane operations is encouraged. In the present work, a mathematical model is proposed to describe gas separations in spiral-wound membranes, based on a phenomenological approach. The proposed model was validated in four case studies of common separations: (i) ammonia; (ii) hydrogen; (iii) CO2 from natural gas and (iv) CO2 from flue gas. It is shown that the proposed model is able to represent the analyzed phenomena accurately. The robustness and good performance of the model for several operation conditions were evaluated through sensitivity analyses. In addition, a novel numerical approach is proposed to solve the analyzed mathematical model. The proposed procedure presents good efficiency and accuracy and is faster and more efficient than the well-known shooting method, largely employed to perform membrane simulations, allowing the use of the model in real time applications.