Effective Stress Law And Stress Dependent Mechanism For The Permeability Of Shale

Permeability sensitively dependent on stress state has important impact on productivity of oil and gas wells.To date,there are three limitations in stress-dependent permeability research.Firstly,the concept of effective stress law for the permeability is widely misunderstood.The experiment results are not comparable due to the different stress path and range.Secondly,the criterions in evaluating stress sensitive are no unified.Thirdly,there is no report of the impact of pore geometry on stress dependent permeability of tight rocks.Therefore,it is necessary to perform investigate on the mechanism of stress dependent permeability of shale reservoir.By combining mineralogy analysis,organic geochemistry analysis,pore structure analysis and rock mechanical properties analysis,to expanding understanding of petrophysical and mechanical properties of shale rocks,and provides the practical reference for investigating the mechanism of stress dependent permeability in shale gas reservoirs.Here we derived the expressions of the effective stress coefficients for the dual-porosity model and gas slippage effect model of shale rocks.We conducted the measurements using two different stress paths to measure the effective stress coefficients and verified the theoretical models.The results indicated that the effective stress coefficients of shale were less than 1,which also less than theoretical boundary of the foregone models due to the fracture in matrix.This result illustrates the permeability of shale is more sensitive to confining pressure than to pore pressure.Finally,we aimed to provide modified effective stress using effective stress coefficient for calculating the permeability at any combination of confining pressure and pore pressure.Permeability-porosity integrated tests,with increasing effective stress,were conducted to measure the stress dependent permeability and porosity of shale.By using an elliptical pore and a dual porosity model,we derived the fundamental expressions of the porosity sensitivity exponent.The results indicate that the porosity sensitivity exponent of elliptical pore media depends on the aspect ratio of the elliptical pore.The exponent increased from 2 to 3 with the aspect ratio decreased from 1 to 0.The porosity sensitivity exponent of the dual-porosity media depends on the width of the fracture,the ratio of the matrix porosity and the fracture porosity ?.When fracture width and matrix pore aperture are on an equal scale,the porosity sensitivity exponent increased from 2 to 3 with the ratio of the matrix porosity and the fracture porosity ? decreasing.In this scenario,the dual-porosity media can also be treated as an elliptical pore model.When the porosity sensitivity exponent is considerably larger than 3,the fracture width is much larger than the matrix pore scale,the porosity sensitivity exponent increased as ? increased.The results of the permeability-porosity integrated tests showed that the porosity sensitivity exponents of shale were generally lower than those of sandstones.The stress sensitive coefficients of shale were higher than sandstones because of the high pore compressibility of the shale samples.For some shale cores,the porosity sensitivity exponent ranged from 2 to 3 due to the abundance of matrix pores,including elliptical pores,and slot pores in equal scale.If no macro-scale fractures existed in these shale cores,then the matrix pores can be treated as elliptical pores with various aspect ratios.For other shale core samples,the porosity sensitivity exponents were larger than 3 as the fracture width was much larger than the matrix pores,and the matrix permeability contribution can be neglected.This extrapolation was verified by Walsh's model fitting with the measurement data of our samples,and the fitting result also show that the permeability of the sample with a small fracture aperture is more sensitive to the effective stress than a sample with a large fracture aperture.This paper improves the basic theory of effective stress law in unconventional reservoir,and takes a deep insight in the mechanism of stress-dependent permeability of shale.The results have an important academic value and practical applications in shale gas reservoir development.