页岩气藏体积压裂水平井产能有限元数值模拟

Finite element numerical simulation of shale gas production of hydraulically fractured horizontal well with stimulated reservoir volume

 何易东¹ 任岚¹ 赵金洲¹ 李志强¹ 邓鹏²

西南石油大学油气藏地质及开发工程国家重点实验室，四川 成都 610500 中国石油塔里木油田分公司塔中油气开发部，新疆 库尔勒 841000）

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China Tazhong Oil and Gas Development Department, Tarim Oilfield Company, PetroChina, Korla 841000, China)

 考虑到压裂过程中的多重复合作用，将压后页岩储层分为支撑主裂缝、缝网波及区与未压裂区。考虑基岩纳米孔隙中气体吸附与解吸、Knudsen扩散、滑脱流、黏性流，以及水压诱导裂缝应力敏感效应，建立了页岩气藏体积压裂生产动态模拟的物理模型和渗流数学模型。结合Galerkin有限元方法，对基质和裂缝渗流方程进行空间上的离散，推导了三角形单元有限元数值模型，给出了压裂水平井二维渗流场内、外边界条件和水力裂缝处理方法，对时间域采用向后差分，最后顺序求解裂缝和基质压力方程，模拟了页岩气藏体积压裂水平井生产动态和压力场分布。该研究为页岩气储层体积压裂产能评价提供了理论模型，对于有限元法模拟双重介质渗流场和产能预测具有现实意义。

 Affecting by multiple composite effects, shale gas reservoirs with complex fracture-network were divided into propped primary-fracture, stimulated area and unstimulated area. Considering adsorption and desorption of shale gas in matrix porosity, Knudsen diffusion, slippage effect, viscous flow, stress sensitivity of natural fractures, corresponding physical model for production simulation of volume fracturing and mathematical model of shale gas flow after hydraulic fracturing were established. Galerkin finite element has been used to discretize seepage equations for natural fracture and matrix with only taking two-dimensional flow into consideration. Finite element equation based on triangular element was derived, we also give the method for handling the boundary condition with considering two-dimensional seepage field for fractured horizontal well and main hydraulic fracture; backward difference was employed for time domain discretization, and pressure equation of matrix and fracture systems were solved sequentially to model pressure field and production of shale horizontal well with stimulated reservoir volume. This study provides a theoretical model for the evaluation of the volume fracturing of shale gas reservoirs, which has important theoretical and practical significance for the finite element method to simulate the flow field of the double porosity reservoir.

10.6056/dkyqt201704025