基于孔边应力集中的页岩渗透率模型及应力敏感性评价

Shale permeability evolution model and stress sensitivity analysis base on stress concentration

页岩储层油气主要储集于基质孔隙,考虑不同应力状态下孔隙周边的应力集中,采用复变函数与保角变换计算孔隙变形,建立基于孔边应力集中的渗透率模型,基于实验结果验证渗透率模型可靠性,分析页岩渗透率的应力敏感性。结果表明:基于孔边应力集中的渗透率模型可合理表征有效应力和孔隙压力对页岩渗透率的影响,孔隙压力增大能减弱页岩渗透率对有效应力变化的敏感性;不同方向的有效应力对页岩渗透率的影响具有显著差异,椭圆孔隙短轴方向应力对渗透率的影响较椭圆孔隙长轴方向应力高30%;常规模型(CB模型)未考虑椭圆孔隙的孔边应力集中,显著低估孔隙压力和水平有效应力变化对页岩渗透率的影响;在单轴应变的条件下,常规模型显著高估椭圆孔隙短轴方向应力和上覆岩层应力对页岩渗透率的影响,低估页岩渗透率达32%。该结果为分析压裂应力方向变化较大的储层渗透率提供依据。

Oil and gas are mainly stored in matrix pores shale reservoir.Considering the stress concentration around pores under different stress states,a permeability model based on the stress concentration at the edge of pores is established by using complex function and conformal transformation.The reliability of the permeability model is verified by experimental results,and the stress sensitivity of shale permeability is analyzed.The results show that the permeability model based on pore stress concentration can reasonably characterize the effects of effective stress and pore pressure on shale permeability,and the increase of pore pressure weakens the sensitivity of shale permeability to the change of effective stress.The effect of the effective stress in different directions on the permeability of shale is significantly different.The effect of the stress in the short axis direction of elliptic pores on the permeability is 30%higher than that in the long axis direction of elliptic pores.The conventional model(CB model)does not consider the stress concentration at the edge of elliptic pores,which significantly underestimates the effect of pore pressure and horizontal effective stress on shale permeability.Under the condition of uniaxial strain,the conventional model significantly overestimates the influence of elliptic pore stress and overburden stress on shale permeability,and underestimates shale permeability by 32%.The results can provide a theoretical basis for the effective analysis of reservoir permeability prediction with large changes in stress direction after fracturing and have guiding significance for oil and gas exploitation.