Approximate Analytical Pressure Studies on Dual Porosity Reservoirs with Stress-sensitive Permeability

Abstract

Abstract Pressure transient analysis in porous media is commonly studied by assuming constant reservoir permeability over an entire range of formation pressure. Such assumption may not be applicable to natural fractured reservoirs where fracture permeability reduces during production. At present, there are still lacks of analytical pressure transient studies on dual porosity reservoirs with stress-sensitive permeability of the natural fractures. An approximate analytical model was proposed in this work to investigate the pressure transient in the naturally fractured reservoirs. It was assumed that only fracture permeability was stress-sensitive, which was a function of a permeability modulus and pressure differences. The permeability function was substituted into the cylindrical pressure diffusion equation to calculate pressure distribution in the reservoir. The obtained non-linear equations were linearized by a transformation equation, and then simplified by a zero-order perturbation technique. Finally, two inner boundary conditions and three outer boundary conditions were applied, and total 6 solutions in the Laplace space were presented. Calculated pressures from the models with and without stress-sensitive permeability were compared. It was found that the stress-sensitive solutions can be obtained by integrating the solutions from constant permeability models with the permeability modulus. For an infinite reservoir with constant flow rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottomhole from the model with fracture permeability sensitivity is 48% higher than that of the constant fracture permeability model at later production time. Such difference can be as high as 122% if permeability modulus increases to 0.15. For locations further away from the wellbore (e.g., 12.7 m), the required pressure difference for the two models are close to each other. Finally, the exchange flow rates from reservoir matrix to natural fractures were calculated to identify different flow regimes. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture permeability-sensitivity on reservoir pressure distribution, it can also be applied to buildup analysis of well test data from stress-sensitive formations.