分支水平井不稳定压力和产量的计算

Calculation of transient pressure and production of multi-branch horizontal wells

给出了均质各向异性油藏中任意分支水平井的三维不定常渗流数学模型,用汇源积分方法导出了平面上均匀分布的任意分支水平井的压力分布通式.利用Duhamel褶积及Laplace数值正、反变换方法获得分支水平井产量和累积产量弹性特征曲线,分析了数学模型中主要控制参数对分支水平井的产量和累计产量的影响.结果表明:N分支水平井的压力曲线簇在中后期的变化趋势反映该地层中发生了平面径向流,而对应的压力导数曲线簇在相应处提升的程度趋近于N/2,无量纲井长主要影响曲线簇水平位置和对应各个流态特征曲线的出现与消失;N分支水平井的单个分支井段弹性产量递减受分支数影响明显,分支数越多,产量递减越快.

A mathematical model is first presented to describe fluid transient flow in a 3D homogeneous reservoir with multi-branch horizontal wells. Solutions to the model are developed using the integral of element solutions of instantaneous sinks. The solutions depict the pressure transient distribution of the multi-branch horizontal wells in the reservoir. Both pressure behavior and production decline curves of the multi-branch horizontal well are obtained numerically by employing Duhamel integral and Laplace Transformation. Characteristics of the curves influenced by key parameters in the model, including dimensionless well length, branch number, etc, are analyzed through concrete calculations. The results indicate that family of pressure curves of N-branch horizontal wells are plane radial flow at middle and later period of production, and curves of pressure derivative dp/dL of corresponding the pressure trend to N/2. The dimensionless length of horizontal hole LD mainly affects the position of the curves and appearance of the characteristic curves of flow pattern. The elastic production decline of a single horizontal hole is affected with branch number of horizontal holes, and the larger the branch number of horizontal holes, the faster production declines.