基于半解析方法的多分支水平井模型试井解释研究

Semi-Analytical Modeling for Pressure Transient Analysis of Multilateral Horizontal Well

摘要: 针对多分支水平井复杂结构渗流表征难题，本文提出一种基于线源离散与拉普拉斯变换的半解析试井模型。通过Newman乘积原理将任意构型的多分支井筒离散为有限线源段，结合拉普拉斯域叠加求解方法，建立了盒状储层中复杂分支结构的瞬态渗流数学模型。该模型突破传统点源方法的几何限制，能够实现对任意结构多分支水平井的建模求解。采用Starfest数值反演技术实现井底压力的高效求解，并以双分支井为例，识别出八个典型流动阶段。在此基础上，通过对储层基本参数和井筒基本参数的敏感性分析，总结了不同因素对流动阶段特征的影响规律。该模型为任意结构多分支井的试井解释与优化设计提供了普适性理论工具。

Abstract: The challenge of seepage characterization for complex structures of multi-branch horizontal wells is addressed in this paper through a semi-analytical well testing model based on line-source discretization and Laplace transform. Newman’s product principle enables the discretization of multi-branch wellbores with arbitrary configurations into finite line-source segments, which, combined with the superposition solution method in the Laplace domain, establishes a transient seepage mathematical model for complex branch structures in box-shaped reservoirs. This model overcomes the geometric limitations of traditional point-source methods, facilitating the modeling and solution of multi-branch horizontal wells with arbitrary configurations. The Stehfest numerical inversion technique ensures efficient calculation of bottom-hole pressure, and case studies on dual-branch wells identify eight typical flow stages. Sensitivity analyses of basic reservoir and wellbore parameters summarize the influence laws of different factors on flow stage characteristics. This model provides a universal theoretical tool for well testing interpretation and optimization design of multi-branch wells with arbitrary structures.