Disclosed herein are methanol production processes that include a sweep-based membrane separation step using a membrane that is selective to carbon dioxide over hydrogen. Using the processes of the invention, the efficiency of methanol production from syngas is increased by reducing the compression requirements of the process and/or improving the methanol product yield. In certain embodiments, a hydrogen-rich stream is generated; this hydrogen-rich stream can be sent for other uses. An additional benefit is that the processes of the invention may debottleneck existing methanol plants if more syngas or carbon dioxide is available, allowing for feed of imported carbon dioxide into the synthesis loop. This is a way of sequestering carbon dioxide.