The rate of heat and mass transfer through distillation membranes is typically estimated using an over-simplified, straight-cylindrical-pore approach coupled with several empirical correction factors that are included to compensate for the simplicity of the approach. In the present work, we have calculated for the first time the rate of transport of heat and mass through three-dimensional virtual membranes from first principles without the need for any empirical correction factors. More specifically, molecular dynamic (MD) simulations are conducted in idealized 3-D geometries that resemble the microstructure of a nanofiber membrane. The SPC/E molecular model and coarse-grain Pea model are considered to simulate, respectively, water molecules and air. The fibers, on the other hand, are constructed as simple metal lattice, and their contact angle with water is controlled using a scaling factor from the Lorentz-Berthelot mixing parameters. A proof-of-concept study is presented to demonstrate the capabilities of the new modeling approach in predicting the effects of the membranes microstructural properties on the desalination performance. While the simulations are conducted at scales 3-4 orders of magnitudes smaller than an actual electrospun membrane, the conclusions can be applied membranes with more practical dimensions.