Nonequilibrium consolidation model for pressured shale layers

A simplified mathematical model is developed for fluid migration as a separate phase in the consolidation process due to sedimentation. The consolidation mechanism is presented and the sedimentation ratio is related to the consolidation of shales. The model is composed of simple differential equations which relate the mass balance equation to the linear fluid flow law and pressure increment. In the derivation of equations the fluid and shale compressibilities are taken into consideration. In addition, the shale porosity decrease with depth is included in the consolidation equations. These equations are converted into dimensionless standard forms, which are universally valid for any fluid migration or shale consolidation calculations. The equations are solved numerically by the finite difference method, and the results are presented as graphs referred to as type curves. These type curves are simple tools for those who do not want to be concerned with the mathematical aspects but are interested particularly in quantitative answers concerning the fluid-migration and consolidation processes.