In practical sweeping gas membrane distillation (SGMD) with hollow fiber membrane tube banks (HFMTB), the tubes are often populated in a randomly distributed configuration. The brine and the sweeping gas counter-currently flow inside and between the tubes, whereby heat and moisture exchange. Water vapor transferred through the membranes from the hot brine side to the cold gas side is taken out of the HFMTB by the sweeping gas. Conjugate heat and mass transfer in the tube bank is investigated. Three square modules consisting of 20 fibers, the brine stream inside the fibers, and the sweeping gas stream between the fibers with various randomly populated features are selected as the computational domains. The equations governing the momentum and heat mass transports in the tube side, membrane side, and shell side are established and solved based on the conjugate heat and mass transfer boundary conditions. The friction factors, local and mean Nusselt and Sherwood numbers in the modules are obtained and validated. Effects of the tube distributions, packing fractions, and moisture diffusivities in membranes on heat and mass transfer are studied. The HFMTB is recommended to be the regularly distributed one. The automatic processing of the regularly distributed HFMTB should be realized in future.