ISSN 1000-3665 CN 11-2202/P

    孔隙介质非达西渗流Forchheimer方程量化评价

    Quantitative evaluation of forchheimer equation for non-darcy flow in porous media

    • 摘要: Forchheimer方程作为非达西渗流中广泛应用的基本方程之一,方程中 A 、 B 系数的确定一直是孔隙介质渗流领域中的热点及难点,不同学者根据渗流试验结果提出了不同的Forchheimer方程 A 、 B 系数的经验公式,但对于均质以及混合粒径的非均质条件下评价各经验公式适用性的研究较少。因此在渗流阻力试验的基础上,采用归一化目标函数和线性回归法评价了Forchheimer方程经验公式的适用性,为不同孔隙介质条件下Forchheimer方程经验公式的选取提供参考。结果表明:对于均质孔隙介质,Sidiropoulou公式对水力梯度有着很好的预测效果;对于2种混合粒径孔隙介质,在使用平均粒径的基础上,还应考虑混合粒径的质量比和大小因素,Macdonald公式的预测效果受混合粒径的质量比和大小影响较小,Kadlec and Knight公式对于水力梯度的预测结果较为稳定;对于5种混合粒径孔隙介质,使用d60作为特征粒径进行预测的效果较好,Kadlec and Knight公式对于系数A的预测效果较好,Ergun公式对于系数B的预测效果较好。研究结果能够为工程中均质及非均质松散砂砾石孔隙介质渗流计算的Forchheimer方程的选取提供依据。

       

      Abstract: The Forchheimer equation is one of the basic equations widely used in non-Darcy seepage. The determination of coefficients A and B in the equation has always been a hotspot and difficulty in the field of porous media seepage. Different studies have proposed various empirical formulas for the coefficients A and B from seepage experiments. However, there are few studies evaluating the applicability of each empirical formula under homogeneous condition and heterogeneous with mixed particle size. In this study, to provide basic information for selecting the empirical formula of the Forchheimer equation under different porous media conditions, the normalized objective function (NOF) and linear regression method are used to evaluate the applicability of the empirical formula of the Forchheimer equation, on the basis of the seepage resistance experiment. The results show that: for homogeneous porous media, Sidiropoulou’s formula has a good prediction effect on hydraulic gradient. For the porous media mixed two kinds of particle size, the mass ratio and size factors of the mixed particle size should be considered based on the average particle size. The prediction effect of the Macdonald formula is slightly affected by the mass ratio and the mixed particle size; while the predicted hydraulic gradient from the Kadlecan and Knight formula is relatively stable. As to the porous media mixed five kinds of particle size, the predictive effect of using d60 as the characteristic particle size is fine.The Kadlecan and Knight formula is suitable to predict coefficient A, and the Ergun formula is effective to predict coefficient B. This study can provide a basis for selecting the Forchheimer equation for seepage of homogeneous and heterogeneous loose sand and gravel porous media in engineering.

       

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