The Improvement Of The Porous Media Seepage Equation

Groundwater Darcy flow equation and non-Darcy flow equations are the two basic porous media seepage equations, which are the basis of all other groundwater dynamics equations. Combined with the two basic equations are often used in the actual production. So, there is great theoretical and practical significance in the studying of two basic porous media seepage equations.After the advent of Darcy’s law in1856. It was confirmed by a large number of laboratory experiments and actual flows. With the deepening of research and practice, groundwater non-Darcy flow phenomena become more prominent. As the complexity of non-Darcy flow, the research of non-Darcy flow is not enough in-depth and extensive, is far less than the Darcy flow. Traditional non-Darcy flow equation do not comply with the flow mechanism in time and space, it can not portray the entire dynamic process of seepage, and it can not reflect the kinetics of dynamic chang of viscous force and inertia force in the entire seepage process. Therefore, in response to these problems and deficiencies, improving the traditional porous media seepage equation to make it be more in line with flow mechanism and kinetics and improve its portray accuracy, which has important theoretical significance.The research method, which combined with theoretical analysis and model experiments, is used in this article. Selecting equal-diameter pellets cube arrangement porous media hydraulics model as the studying object. Developed four kinds of porous media model, whose standard diameters are3mm,5mm,8mm and10mm. Using this model to carry on pressure drop experiment under different flow conditions. By measuring the flow rate and hydraulic gradient, to accurately receive the change of pressure drop in the entire seepage process, in order to study the resistance variation of the typical porous media. And on the basis of pressure drop experimental data, analysing on the characteristics, problems and describe precision of traditional basic porous media equation. Improving the Forchheimer equation(Ergun equation), proposing the improved Ergun formula expression. At last, Testing and research the improved equation on flow mechanism, kinetics and portrayed precision.Through above-mentioned experiments and research, the understanding and conclusions as follows:(1) Through the pressure drop experiment, the resistance variation of the typical porous media as follows:Darcy flow area is a small part of entire seepage process. So quadratic equation can well describe the entire porous media seepage process, in other words, covering the entire flow pattern of seepage equation is closer to the form of quadratic equation.the particle size is one of the main factors affecting the porous media seepage law. Under the same condition of the seepage velocity, as the particle size increases, carrying water capacity of the porous medium is gradually increased, the frictional resistance gradually decreases, the seepage head loss gradually decreases.(2) On the basis of pressure drop experimental data, analysing on the characteristics、 problems and fitting accuracy of traditional basic porous media equation. The conclusions as follows:Darcy formula’s fitting degree of four model experimental results in the Darcy flow are0.943,0.935,0.947,0.952. The formula calculation is generally lower than experimental value. Darcy formula has a higher accuracy in the Darcy flow. But with the increase of the seepage velocity, flow gradually generally becomes deviate from the linear law, the relative error between formula calculation and experimental values will gradually increase. In the Non-Darcy flow, Darcy formula is no longer applicable.Izbash equation’s fitting degree of four model experimental results are0.725,0.773,0.747,0.685. Izbash equation calculation is generally larger than experimental value in the low flow rate; while is generally lower in the high flow rate, and the relative error is gradually increases with the increase of velocity. In a word, Izbash equation applies only to portray the variation of the seepage hydraulic gradient in the low flow rate.Forchheimer equation(Ergun equation)’s fitting degree of four model experimental results are0.941,0.928,0.943,0.937. The equation calculation generally greater than experimental value. The relative error between equation calculation and experimental value is lagerer in the Darcy flow. After entering the non-Darcy flow, the equation has a higher accuracy, but as the velocity increases, the relative error between equation calculation and experimental value has a gradually increasing trend.(3) Improving the Forchheimer equation(Ergun equation), the understanding and conclusions as follows:The linear coefficient a of Ergun formula is derived by Darcy formula and Kozeny-Carman(KC) formula. The derivation process and physical concepts are clear.The quadratic coefficient b of Ergun formula not only related with the porous media parameters, but also related to the flow state. It will increase with the increase of seepage Reynolds number Re, they are basic polynomial function.Therefore, selecting the Ergun formula for the research base, improving it:retaining the linear coefficient expression of the Ergun formula, introducing Reynolds number Re into the expression of the quadratic coefficient b. Through porous media model seepage experimental data, fitting the relevant parameters and getting the improvd Ergun formula.(4) Testing and research the improved equation on flow mechanism, kinetics and portrayed precision. The conclusions as follows:The improved Ergun formula considers the characteristics of the nonlinear coefficient b change with the flow pattern, through the introduction of the Reynolds number, in order to well characterize the seepage hydraulic gradient variation of the cube arrangement porous media hydraulics model.The improved Ergun formula is more in line with the flow mechanism than traditional quadratic. It can portray the entire dynamic process of seepage and reflect the kinetics of dynamic chang of viscous force and inertia force in the entire seepage process. The improved Ergun formula can portray the entire dynamic process of seepage.The improved Ergun formula’s fitting degree of four model experimental results are0.955,0.947,0.949,0.958.The improved Ergun formula improves the fitting accuracy of the traditional quadratic equations in the Darcy flow region and overcomes the accuracy defects of the traditional Ergun formula. The improved Ergun formula can be used to predict the porous media seepage pressure drop under the different conditions of porosity, particle diameter and seepage velocity.At last, this article also proposed some improvements and in-depth research direction, such as exploring the seepage law of natural porous media, taking visualization experiments, testing the applicability of the improved Ergun formula, improving the experimental head pressure and so on.