  Pressure solution is an important process in sedimentary basins, and its
behaviour depends mainly on the sediment rheology and temperature distribution.
The compaction relation of pressure solution is typically assumed to be a
viscous one and is often written as a relationship between effective stress and
strain rate. A new derivation of viscous compaction relation is formulated
based on more realistic boundary conditions at grain contacts. A nonlinear
diffusion problem with a moving boundary is solved numerically and a simple
asymptotic solution is given to compare with numerical simulations. Pressure
solution is significantly influenced by the temperature gradient. Porosity
reduction due to pressure solution is enhanced in an environment with a higher
thermal gradient, while porosity decreases much slowly in the region where the
thermal gradient is small. Pressure solution tends to complete more quickly at
shallower depths and earlier time in higher temperature environment than that
in a low one. These features of pressure solution in porous sediments are
analysed using a perturbation method to get a solution for the steady state.
Comparison with real data shows a reasonably very good agreement.
