Irreversible inelastic processes are responsible for mechanical and chemical compaction of sedimentary rocks at the time of burying. Our purpose is to describe the inelastic response of the rock at large time scales. In order to do this, we build a model that describes how porosity progressively decreases at depth. We use a previous geometrical model for the compaction process of a sandstone by grain interpenetration that is restricted to the case of mass conservation. In addition, we introduce a compaction equilibrium concept. Solid grains can support stresses up to a critical effective stress, σc, before plastic flow occurs. This critical stress depends on temperature and is derived from the pressure-solution deformation law. Pressure solution is the plastic deformation mechanism implemented during compaction. Our model predicts a porosity destruction at a depth of about 3 km. This model has the property to define a range of compaction curves. We investigate the sensitivity of the model to the main input parameters: liquid film thickness, grain size, temperature gradient, and activation energy.