We study the effect of burial depth on thermodynamics and transport properties of fluids confined between mineral surfaces. The solvation curve and diffusion coefficients of fluid films confined between mineral surfaces have been obtained for different states of stress and temperature using Grand Canonical Monte Carlo and molecular dynamics simulations. Our results indicate that the mass transport coefficient (film thickness times diffusion coefficient) of the thin films of fluids trapped at grain contacts decrease by a factor 40 from 1 km to 3 km and 10 km. This effect has strong implications on the rates at which mechano-chemical processes of deformation (e.g. pressure solution) occur in the upper crust.