致密油储层基质渗透率极低，应力敏感性强，传统的基于拟稳态假设和定压力边界条件得到的常量形状因子模型无法准确表征致密储层基质-裂缝间的非稳态窜流规律。通过考虑致密储层基质应力敏感及裂缝压力衰竭的影响，建立了致密储层基质-裂缝不稳定窜流模型。利用Pedrosa代换和正则摄动法对模型进行了线性化处理，通过Laplace变换求得了在Laplace空间下的解析解，结合Duhamel原理得到了考虑裂缝压力变化的解。通过与Hassanzadeh模型计算结果以及精细网格有限元解的结果进行对比，验证了模型的正确性。利用新模型研究了基质应力敏感以及裂缝压力衰竭对基质-裂缝间窜流规律的影响。研究表明：考虑裂缝压力衰竭影响后，应力敏感对形状因子的影响更为显著；裂缝压力递减越快，初期形状因子的值越大，但是递减的越早且递减速度越快，导致平衡后形状因子值越小；裂缝压力递减速度很小时，窜流速度会先上升达到平衡然后再递减。
The tight formation has the characteristics of the extremely low permeability and the sensitivity of the permeability to the effective stress. The conventional constant shape factor model cannot accurately characterize the transient inter-porosity flow characteristics. In this paper, a new model is established by considering the effect of the stress sensitivity and the time-dependent fracture pressure boundary condition. The Pedrosa substitution and the perturbation method are applied to eliminate the nonlinearity of the model. The Laplace transformation method is used to obtain the analytical solution in the Laplace domain. Based on the Duhamel principle, the solution under the time-dependent fracture pressure boundary condition is obtained. The results obtained by the new model are compared with those obtained by the model of Hassanzadeh and the finite element analysis to validate the new model. Finally, the influences of the stresssensitivity and the decreasing velocity of the fracture pressure on the shape factor and the velocity of the inter-porosity flow are discussed. It is shown that the larger the stress sensitivity coefficient, the smaller the value of the shape factor and the smaller the velocity of interporosity flow will be. The fracture pressure depletion has a significant effect on the inter-porosity flow. The effects of the matrix stress sensitivity become more pronounced when the effects of the fracture pressure depletion are considered. Moreover, the shape factor and the velocity of inter-porosity flow are different in different stages as the fracture pressure depletion coefficient is not the same. The velocity of the inter-porosity flow will increase first to reach an equilibrium and then decrease when the decreasing rate of the fracture pressure is small, which is different from the results obtained under the constant fracture pressure boundary condition. The estimation of the velocity of the inter-porosity flow would be inaccurate if the effect of the fracture pressure depletion is not take into account. The new model provides a theoretical basis for the development of tight reservoirs and can be used in the study of the well test analysis and the numerical simulation of multi-fractured horizontal wells in a tight formation.
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