Summary
Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account.
In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs.
Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.
EFFECTS OF DIFFERENT BLOCK SIZE DISTRIBUTIONS IN PRESSURE TRANSIENT RESPONSE OF NATURALLY FRACTURED RESERVOIRS
