Abstarct: Due to the enormous wasted energy in natural gas pressure reduction stations, using of systems such as expansion engine which is a reciprocating engine without any ignition, to energy recovering for electricity generation, is very applicable. Expansion engine works in contrary with reciprocating compressors and instead of valves, ports are used to inlet and outlet the gas. For controlling these ports, five valve configurations have been modeled, cylinder, flange, uniflow, piston and slide valve. First three valves have been modeled for the first time in this these, but last two valves have been used in steam engines. In this study which its main purpose is the simulation and optimization optimum opening/closure timing of ports, firstly all geometrical parameters such as port dimensions, pistons’ diameter and course, connecting rod length, crank radius and so on, have been optimized for the single acting expansion engine in Matlab software, and then simulation has been done on double acting case. For this purpose, with assumption of methane as an ideal and a real gas, opening/closure timing of inlet and outlet ports has been optimized due to maximize the exergy efficiency which is the main goal of this thesis. Genetic Algorithm and AGA8 equation of state have been used for optimization and calculating natural gas properties, respectively. Then, the effect of gas compositions and inlet pressure on achieving optimum port timing have been studied. Results showed that according to maximum amount of power generation and exergy efficiency, engine with cylinder valve has the best performance. It has been achieved that if ports have been modeled time variable, engine will show better performance. Results indicated that in cylinder and flange valves, the greatest lost of exergy is the result of admission process, while exergy lost due to exhaust process has the main role in other valve configurations.