A novel optimization method, based on a mathematical modeling approach, for the design and operation of a hollow fiber membrane module is developed. The purpose of the membrane is to purify unconventional gases, such as coalbed methane gas, by removing carbon dioxide. For the design of the membrane module, the number of fibers within the module must be reasonably set as one of the design variables of the optimization problem. Therefore, a mixed integer nonlinear programming (MINLP) model including integer variables - i.e., the number of fibers in this study-is required to obtain optimal design conditions. However, if the integer variable is involved in the highly nonlinear model, the probability of success in the optimization calculation becomes very low because of the big computation load. Thus, this paper introduces: (1) a new optimization modeling technique which is able to solve the MINLP problem efficiently; (2) a successful scale up design optimization from laboratory (0.5 Nm(3)/h) to large commercial scale (500 Nm(3)/h); (3) design optimization results under different gas feed conditions, and (4) dynamic optimization results obtained by varying gas feed conditions.