考虑压敏效应的低渗透油藏非线性流动特征

摘要

基于低渗透油藏非线性渗流速度函数导数的连续性,推导了实数域内低渗透油藏的非线性运动方程,确定了低渗透油藏视渗透率和视拟启动压力梯度的数学表达式,并论证了渗流速度函数导数连续与渗透率变化连续是相容的；建立了考虑压敏效应的低渗透油藏油井定产量生产时的非线性渗流数学模型；鉴于数学模型的强非线性,采用高效的有限差分Douglas-Jones预估校正法求得了其数值解,并与全隐式有限差分法所求数值解进行对比验证了解的正确性.结果分析表明;非线性运动方程和拟线性运动方程对应的瞬时无因次井底压力双对数曲线初期存在“拐点”,拟线性运动方程对应双对数曲线的“拐点”更为突出；渗透率模数主要影响曲线后半段,其值越大,压力下降越剧烈；低渗透油藏非线性渗流存在动边界；拟线性流动动边界的传播速度比非线性流动的要慢.%Based on the continuity of the derivative of the nonlinear seepage velocity function in low-permeability reservoirs,the nonlinear kinematic equation in the real number field for the low-permeability reservoirs was deduced.The mathematical formula of the apparent permeability and the apparent pseudo threshold pressure gradient were defined.It was demonstrated that the continuous derivative of the seepage velocity function was consistent with the continuous permeability change.The mathematical model of the nonlinear flow in low-permeability reservoirs with stress sensitive effect under the condition of constant well production rate was constructed.Owing to its strong nonlinearity,efficient Douglas-Jones predictor-corrector finite difference method was adopted to obtain its numerical solution.Moreover,its accuracy was verified by comparison with the numerical solution obtained by the fully implicit finite difference method.Result analysis shows:log log curves of dimensionless transient wellbore pressure corresponding to the nonlinear kinematic equation and pseudo-linear kinematic equation both have inflexions at the initial period.And the inflexion corresponding to the pseudo-linear one is more obvious; the permeability modulus has a major effect on the second half of these curves; the bigger its value,the sharper the pressure drop; there exists a moving boundary in the nonlinear flow in low-permeability reservoirs; the moving boundary of the pseudo-linear flow moves more slowly than that of the nonlinear flow.