The primary driver of operating costs in natural gas processes is the energy consumption of the compression system. Multistage compression configurations are commonly employed and hence play a vital role in optimization of natural gas processes. In this study, a generalized disjunctive programming model for multistage compression is formulated. The model is useful for both synthesis and optimization of multistage compression configurations. By using this approach, we further seek improvements in shaft work savings. The model relies on thermodynamic equations and is designed to minimize the consumption of shaft work. The model is handled by employing the logic-based branch and bound algorithm, eliminating the need for explicit conversion into a MINLP, which in turn leads to improved convergence and faster computational performance. The model solution yields optimal pressure levels, and hence stage shaft work consumptions. A case study of multistage compression for a prior optimized single mixed refrigerant (SMR) process obtained from literature is used to test the proposed model. The model�s outcomes are validated through simulation using the Aspen Hysys software. Savings in shaft work of atmost 0.0088, 0.4433, and 1.2321 are obtained for the two, three, and four stage compression systems respectively against the optimized base cases from literature. © The Authors, published by EDP Sciences.