页岩气开采中的井底压力并行计算

Parallel computing for bottom-hole pressure in shale gas reservoirs

根据页岩气流动特点建立了考虑混合气体高压物性参数、渗透率与孔隙度随压力变化的页岩气流动方程,通过定义拟压力函数将页岩气流动的偏微分方程线性化。针对页岩气开发采用水平井多段压裂技术,采用Newman乘积原理得到地层拟压力流动方程的解析解表达式。依据解析解的特征将解析解分解成适合并行计算的无限求和及积分形式,提出了一套基于CUDA的页岩气地层压力算法,将地层拟压力函数解析解划分为多个并行度较高的步骤,利用GPU的并行计算能力,设计每个步骤的CUDA核函数,在英特尔i3 540CPU(3.07GHz主频,4GB内存)和NVIDIA的GTX 550显卡上,计算了页岩气的井底压力,分析了井底压力特征。实验结果表明,页岩吸附影响曲线变化剧烈程度,而扩散主要影响曲线发生变化的时间,在GPU上的页岩气压力计算可达近40倍的加速比。

Considering the varying permeability and porosity of shale with pressure and of Mixed Gas＇ s high pressure characteristics,flow equations of shale gas were derived and then linearized introducing the pseudo-pressure.Theoretical solutions to the Multiple Hydraulically Fractured Horizontal Well（MHFHW）were presented applying the Newman Product Principle.Finding that the theoretical solution was composed of integral and infinite sum that are highly parallel,an algorithm was proposed basing on GPUbased CUDA computation.Implementation of this algorithm on the platform with Intel i3 540CPU and NVIDIA GTX 550Ti GPU shows almost 40Xspeedup,in which way fulfilling the real-time calculation of the bottom-hole pressure of MHFHW.Further,parametric investigation on the obtained results shows that absorption decides the amplitude while diffusion exerts delay on the pressure and derivative curve.