有限导流压裂定向井耦合流动模型

A Coupling Flow Model of Finite-conductivity Fractured Directional Well

考虑人工裂缝、斜井筒和地层中的耦合流动,将压裂定向井的流动分为地层向裂缝渗流、裂缝内流动和斜井筒变质量管流.采用镜像反映和势叠加原理,建立地层中势分布和渗流数学模型.应用边值理论,将人工裂缝面离散为裂缝网格,并与斜井筒变质量管流模型进行耦合,建立有限导流压裂定向井耦合流动数学模型,并形成相应的迭代算法.应用分析表明:该模型与Prats图版法相比,对于垂直缝吻合度较高;裂缝导流能力和井斜角对产量及裂缝面压力分布影响较大.

Considering artificial fracture,inclined wellbore and formation coupling flow,flow to directional well is divided into three parts： Flow from reservoir to fracture,flow in fracutre and variable mass flow in production pipe. Principles of potential superposition and mirror reflection as well as the concept of infinitesimal line congruence are used to model flow from reservoir to fracture and potential distribution in reservoir. By discreting fracuture to 2D grid,boundary theory is used to couple flow dynamics in fracture with variable mass flow in inclined pipe. A comprehensive coupling model for finite-conductivity fractured directional well is shown.Iteration method is used to solve the model. A practical case shows that for vertical fracutre result of coupling model agrees with that of Prats method. Fracture conductivity and inclined angle have great effects on productivity and pressure.