分形渗流基本公式及分形油藏样板曲线

对具有双重分维(管径分维和迂曲分维)多孔介质中流体的流动,导出了渗流速度、渗透率及孔隙度的公式,证明了这些公式在不同的坐标系中都是成立的,并在不同的坐标系中建立了微可压缩流体的渗流偏微分方程,即分形渗流的压力扩散方程.给出了线源条件下压力降落解和压力恢复解.对于考虑井储及表皮的实际井筒也求得了相应的解,并绘制出无限大地层的样板曲线,给出试井解释的方法、步骤.结果表明,对所研究的双重分形介质,用传统的压降半对数直线段试井分析、压力恢复的豪纳(Horner)法以及GringartenBourdet图版的曲线拟合法会带来较大误差,特别是迂曲分维较大的情形,以上方法是不适用的.

Basic formulas of fractal seepage and type-curves of fractal reservoirs

The basic expressions for the flow in the porous media with dual fractal dimensions (surface fractal dimension and tortuosity fractal dimension) are derived,and they include seepage velocity formula,permeability formula and porosity formula.It is proved that these formulas are correct in any coordinate system.The partial differential equations for the seepage of slightly compressible fluid in the porous media,that is,pressure diffusion equations for the dual fractal porous media are established in various coordinate systems.And the solutions of these equations are obtained for line-source well and under considering wellbore storage and skin factor.The typical curves for infinite formation are drawn in log-log plots.The well-testing interpretation method and steps by type-curve fitting are given.The study indicates that for the dual fractal porous media the well testing analysis by Horner method and Gringarten-Bourdet curve fitting technique will brings greater errors,particularly for the media with greater tortuous fractal dimension.