孔隙度数值反演计算

Numerical Inversion of Porosity

由渗流微分方程定解问题和Peaceman方程给出了网格压力、井底压力对网格孔隙度的导数,利用三维渗流方程压强数值解计算井底压力对网格孔隙度的导数;采用共轭梯度法实现孔隙度均匀(或分块均匀)分布油藏模型的反演计算.算例表明,经过8～10次迭代后反演结果与真值的最大相对误差在0.03%以内,反演收敛于真值.

Derivatives of well-bore and grid-block pressure to grid porosity are derived from initial boundary value problems of fluid equations in porous media and inner boundary condition.The derivatives are computed with numerical solution of 3D fluid equation in porous media.A inverse iterative equation is constructed by conjugate method.Numerical inversion of porosity distribution are realized for uniform or block uniform distribution reservoirs.It shows that the relative error of inverse porosity is less than three ten thousandths for a homogenous porosity reservoir with about 8-10 iterations.Relative error of inverse porosity is less than one thousandth for a block homogenous porosity reservoir.Computed porosity automatically approachs to the real value in a few iterations.