Description of fluid flow around a wellbore with stress-dependent porosity and permeability

Abstract

Stress-dependent porosity and permeability effects have been widely studied at the laboratory scale, as they can significantly affect reserve estimates, well production rate and profitability. Based on current experimental data and theories, a general analytical method of calculating stress-dependent porosity and permeability is developed and applied to a wellbore producing oil from unconsolidated or weakly consolidated sand, with the aid of a coupled geomechanical model by which stress distributions around the wellbore can be specified. For clean weak sand, nonlinear elastic theory is appropriate for calculations of stress-dependent rock properties such as compressibility, porosity and permeability. When evaluated in terms of pore pressure variations, the stress-dependent aspect of porosity and permeability may be negligible as far as stress analysis concerned. With input of different stress-compressibility relationships, the model can be used to help screen those reservoirs for which the effect of stress on permeability should be considered during geomechanical analysis (sand production prediction, reservoir stress arching and shear, plasticity onset, etc.). Also, it can be used for analyzing formation compaction that results from the decrease of stress-dependent porosity. The model limitations have been discussed and it is believed that a microscopic approach based on particulate mechanics may be valuable for future research. Different boundary conditions commonly used in current geomechanics models have been compared and discussed in the development of the poro-inelastic geomechanics model, and boundary restraint is demonstrated to be a critical factor to stress solutions.