低渗透煤层气水两相非线性渗流数学模型及计算分析

 在考虑煤层气的解吸和扩散效应及启动压力梯度的基础上,对低渗透煤层气藏流体输运特性进行分析,建立了低渗透煤层气水两相非线性渗流数学模型,推导出非线性渗流阶段气水两相的控制方程组。通过实例计算表明,液相拟启动压力梯度从0.001MPa/m增加至0.007MPa/m,煤层产气峰值下降约15%;不考虑启动压力梯度时的产气峰值量要比液相拟启动压力梯度为0.001MPa/m的产气峰值提升约7%。因此启动压力梯度的存在阻碍了裂隙中流体的流动,对煤层气开发影响较大。

A Mathematical Model for Gas-water Two-phase Nonlinear Flow in Low Permeability Coal Reservoirs and Calculation Analysis

The transport behavior of fluids in low permeability coalbed methane reservoirs is analyzed with considerations of the desorption and diffusion effects of the coalbed methane and the threshold pressure gradient. A mathematical model for gas-water two-phase nonlinear flow is established for low permeability coal reservoirs. The governing equations for the gas-water two-phase nonlinear flow are derived. The case study shows that, when the liquid phase threshold pressure gradient is increased from 0.001MPa/m to 0.007Mpa/m, the maximum gas production of coal reservoirs is reduced by nearly 15%; compared with the liquid phase threshold pressure gradient of 0.001MPa/m, the maximum gas production without the threshold pressure gradient is increased by nearly 7% and the cumulative gas production also has a certain extent of increase. Therefore the existence of the threshold pressure gradient makes the fluid in fractures more difficult to flow and leads to a low production rate. The case study shows that the mathematical model of the gas-water two-phase nonlinear flow could provide a theoretical basis for defining a reasonable gas-well deliverability of low permeability coal reservoirs.