Membrane based heat pumps systems have attracted the attention of many research groups as a potentially more environmentally friendly alternative to vapor compression systems that are being used for space cooling in 90\% of the buildings in the United States. Several prototypes systems have been developed, with reported claims of Energy Efficiency Ratio (EER) of 26. However, no detailed analysis are publicly available which demonstrates the capability of these systems in different climate zones. In this work, a full thermodynamic cycle model of a representative membrane heat pump system is developed and heat and mass transfer components were sized to provide 3 tons of cooling at nominal rating conditions. The main results were that the membrane heat pump system had an EER of 16-20 which is lower than some literature reported values. However, these systems had higher performance results than the conventional vapor compression system and performed well in the 6 different climate zones investigated resulting in energy savings.