Numerical study of gas separation using a membrane Nawaf Alkhamis a,b , Dennis E. Oztekin a , Ali E. Anqi a,c , Abdulmohsen Alsaiari a,b , Alparslan Oztekin a,⇑ a Lehigh University, Dept. of Mechanical Engineering & Mechanics, USA b King Abdulaziz University, Dept. of Mechanical Engineering, Saudi Arabia c King Khalid University, Dept. of Mechanical Engineering, Saudi Arabia article info Article history: Received 6 June 2014 Received in revised form 24 September 2014 Accepted 26 September 2014 Available online 17 October 2014 Keywords: Computational fluid dynamics Membrane modeling Gas separation Turbulent flow abstract Computational fluid dynamics simulations are conducted for multicomponent fluid flows in a channel containing spacers. A new and unique model has been presented for the treatment of the membrane boundaries in the separation CO 2 from CH 4 in a binary mixture. The equation governing the flux through the membrane is derived from first principles. The membrane is modeled as a functional surface, where the mass fluxes of each species will be determined based on the local partial pressures, the permeability, and the selectivity of the membrane. The approach introduced here is essential for simulating gas–gas separation. Baseline Reynolds stress, k–x BSL, and large eddy simulation, LES, turbulence models are employed to study spatial and temporal characteristics of the flow for Reynolds number up to 1000. It is shown here that the spacers have a strong effect on the membrane performance. The process of sep- arating CO 2 from CH 4 is improved by the presence of spacers in the membrane system. It is demonstrated that spacers should be an integral part of the membrane system design in the application of gas–gas separation. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Natural gas consumption has increased significantly in recent years. The impurities found in raw natural gas, extracted from underground, should be minimized to protect pipelines from corrosion. Membranes are used to separate these undesired gasses, thereby purifying the natural gas. In order to minimize capital and operation costs of the purification process, the membrane performance needs to be enhanced. In this study, flows of a binary mixture, CH 4 and CO 2 , in a channel bounded by two membranes are studied for a wide range of Reynolds numbers. Cases, with and without spacers of varying sizes and shapes, are considered. The steady flow, bounded by the membrane walls, is characterized by a simple laminar flow model in the case without any spacers, and by a k–x baseline Reynolds stress turbulent model in the case with spacers. A unique model is presented for the treatment of the membrane boundaries; with which CO 2 absorption and CH 4 losses through the membrane are calculated for both cases. The membrane flux model, derived from basic principles by the present authors, is necessary to accurately represents gas separation and is valid for the desalination process in the limit the concentration of the one of the component tends to zero. In the past, gas–gas separation using a membrane had been studied extensively by several investigators. Such studies include: improving the permeability and the selectivity of the membrane [1–5]; operating the membrane at the optimum temperature and pressure [6–8]; or improving the separation modules [9–11]. In this study, the focus is less on these aspects of separation and more on enhancing the membrane performance using momentum mix- ing. This is a well-known and studied alternative approach for improving membrane performance. There have been extensive studies which show that enhanced momentum mixing in an open channel improves membrane performance in water treatment. However, the effect of mixing on the membrane’s performance in gas–gas separation has not been studied. Several investigations study the effects of momentum mixing on the membrane performance without considering the mass transport. Karode and Kumar [12] and Saeed et al. [13] consider a steady 3D laminar flow model to study the effects of a cylindrical spacer on the pressure drop at low Reynolds number. Fimbres- Weihs et al. [14] and Ranade and Kumar [15] employed a direct numerical simulation (DNS) of the Navier–Stokes equation to study the effects of a cylindrical spacer on the pressure drop and the drag coefficient for a wide range of Reynolds numbers reaching above 1000. They have reported that the critical Reynolds number for the onset of transition from steady to unsteady flow occurs at around 300. Schwinge et al. [16] have studied how the staggered and the inline cylindrical spacers affect the flow field using direct http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.072 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: alo2@lehigh.edu (A. Oztekin). International Journal of Heat and Mass Transfer 80 (2015) 835–843 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt