Numerical modelling of pressure-dependent permeability in Bentheim sandstone

A method for the numerical determination of pressure-dependent permeability in sandstones is developed. The proposed method is restricted to a hydrostatic pressure load that is below the pore collapse pressure.

Our modelling approach is generally based on the idea of digital rock physics. Starting from a µCt-scan, the pore space of a given rock sample is detected and transferred into a numerical model. Subsequently, the stationary Stokes equations are solved, and the permeability is determined from the simulated pressure and velocity fields.

To model the pressure dependence, it is assumed that the deformation of the rock's micro-structure due to pore throat closing has a significant influence on the change in permeability. In our workflow, the respective pore throats between the individual grains of the original CT image are reconstructed using the watershed algorithm and combined in a separate phase of the numerical model. During several simulations, a steadily increasing artificial flow resistance is assigned to the pore throat phase and the respective permeability of the whole sample is determined. Finally, the pressure-dependent permeability curve can be reconstructed via a correlation between flow resistance and pressure load.

The proposed workflow is validated with externally published data of a Bentheim sandstone sample. It is observed that the model is generally able to reproduce the characteristics of a experimentally determined pressure-dependent permeability curve.