Permeability Evolution And Slippage Effect Of Shale Under True Triaxial Stress States

The internal pore-fracture structure and pore size distribution(PSD)of shale as well as gas transport mechanisms in shale reservoirs are critical issues for the development of shale gas.Taking the Longmaxi shale(drilled from the national shale gas demonstration area in the Sichuan Basin,southwestern China)as the research object,the purpose of this study,on the basis of the multi-functional true triaxial geophysical(TTG)set-up,is to investigate the gas slippage effect and permeability evolution of shale under true triaxial stress states,by means of experimental testing,theoretical derivation,analytical analysis,and numerical simulation.In the present study,firstly,we used low-temperature gas(N2)adsorption(LTGA),mercury intrusion porosimetry(MIP),nuclear magnetic resonance(NMR),field emission scanning electron microscopy(FE-SEM),and X-ray computed tomography(CT)scanning to study the multiscale characteristics of shale's internal structure and PSD and,as a result,proposed a new pore size classification of shale in terms of gas transport mechanisms;secondly,we performed fluid-solid coupling experiments of shale under true triaxial stress states to investigate the permeability evolution of shale and proposed a new equation to calculate effective stress when predicting the permeability of shale;thirdly,we conducted permeability measurements of shale under true triaxial stress states to study the gas slippage effect and derived a permeability model considering the gas slippage effect;fourthly,based upon the traditional Klinkenberg equation,we developed a second-order correlation of Klinkenberg-corrected permeability and performed permeability measurements to experimentally verify the second-order approach;fifthly,we performed an analytical analysis to investigate the real gas effect on gas slippage phenomenon in shale and determined the specific range of pressure and pore size for the gas slippage phenomenon in shale reservoirs;and finally,we performed a numerical simulation to study the influence of gas slippage effect on shale gas production under the condition of multi-stage fractures.This study gives rise to the following conclusions:(1)NMR is able to reveal the full-scale PSD characteristics of shale.The full-scale PSD of shale exhibits apparent bimodal characteristics,corresponding to its dual system:nanopores and pore-microfractures.The shale nanopore system contributes much more to the total volume than the pore-microfracture system.A new pore size classification of shale considering gas transport mechanisms was proposed:adsorption pores(pore size<10 nm),slippage pores(10 nm<pore size<1000 nm),and seepage pores or fracture-pores(pore size>1000 nm).(2)Change in shale permeability was more pronounced in response to normal stress(?n is perpendicular to the bedding plane)but some effects of the horizontal stresses were also observed.A theoretical model was derived to describe permeability change with effective stress under in-situ stress conditions.The model was empirically matched with the experimental results.The assessment of relative contributions of normal and horizontal stresses(?t1 and?t2)was quantified,and the results showed the dominant effect of normal stress?n(80%).An almost 20-percent contribution of horizontal stress loading to permeability response indicates a need for improvement in computing effective stress in permeability predictions of shale.Thus,a more precise method was suggested to determine effective stress when predicting the permeability evolution of shale.(3)The apparent permeability and intrinsic permeability of shale both decreased with increasing effective stress.Due to the gas slippage effect,shale permeability is likely to be more sensitive to pore pressure instead of stress in relatively low pore pressures.Shale permeability decreased with increasing stress anisotropy.The slippage factor b increased with increasing effective stress,demonstrating that the gas slippage effect became more significant as effective stress increased.Also,we introduced a new correlation between slippage factor and intrinsic permeability,especially for gas shale.The slippage factor first increased slightly and then significantly with decreasing intrinsic permeability.By combining the stress and gas slippage effects,we introduced a theoretical model to describe the permeability evolution of shale employed at in-situ stress conditions.(4)Based upon the long circular micro-tube flow model and Navier-Stokes equation,a second-order correlation of Klinkenberg-corrected permeability was developed.The second-order model results in a lower Klinkenberg-corrected permeability compared with that from the traditional Klinkenberg equation and yields a better match with the experimental data.It is recommended that when the shale permeability is below 10^-18m²,the second-order approach should be taken into account.(5)The real gas effect suppresses the gas slippage phenomenon(by almost 13%)at low pressures,while enhancing it(by almost 25%)at high pressures.Darcy's law starts deviating when Kn>0.01 and becomes invalid at high Knudsen numbers(Kn>1).Slip flow(gas slippage phenomenon)dominates in the various gas transport mechanisms given the typical range of pressure and pore size in shale reservoirs.Gas transport in shale is predominantly controlled by the slippage effect that mostly occurs in nanopores(pore size:10 to 200 nm).(6)With the continuous production of shale gas,the reservoir pressure drop mainly occurs near the production well region,and the pressure drop&range in the direction of the main fracture of hydraulic fracturing is greater than that in the direction of the horizontal well.In comparison to Darcy's law,considering the gas slip flow would estimate a higher total shale gas production(by approximately 10%).This effect is more significant in the middle and late stages of gas production life time.