具有越流的双层定压边界油气藏井底压力的精确解及典型曲线

Exact Solution and Typical Curve for Two Layers Constant Pressure Boundary Reservoir with Crossflow

由于在钻井过程中泥浆的侵入、射孔以及井下作业 ,实际的油气井总有一定的表皮效应。对于双层油气藏来说 ,各层的表皮效应可能不同。本文采用最大有效井径的概念 ,在考虑表皮效应和井筒储存的影响的条件下 ,建立了一个新的具有层间越流的双层定压边界油气藏井底压力的动态模型。通过拉氏变换得到了拉氏空间下以Bessel函数表示的精确解。运用Crump数值反演方法 ,得到了实空间的解 ;分析了压力动态特征。该模型不但适合于表皮系数为正的情况 ,也适合于表皮系数为负的情形。最后指出了Bourdet模型的局限性。用新模型绘制的典型曲线进行拟合 。

The skin factor is usually caused by improper drilling, completion technology, acidization or stimulation. The skin factor of different layers is probably different for multilayered reservoir. The maximum effective hole diameter mathematical model describing flow of slightly compressible fluid through a two layer reservoir with crossflow is solved rigorously with consideration of wellbore storage and different skin factors. The exact solutions obtained for a well producing at a constant rate from a radial drainage area constant pressure outer boundary condition are expressed in terms of ordinary Bessel functions. The numerical computation of these solutions is made by the Crump numerical inversion method and the behavior of the systems is studied as a function of various reservoir parameters. The new model is numerically stable. The Bourdet model is numerically stable only when the skin is positive. Because the curves explicitly include skin factor and other reservoir parameters, the techniques is expected to be more accurate than the Bourdet technique.