Research On Flow Resistance Of Porous Media Based On Tube-sphere Model

The porous media plays a vital role in daily life and industrial production,such as research on groundwater penetration,research and development of aviation materials,collection of oil and gas,at all.The research on porous media is of great significance,therefore,especially with the rise of artificial intelligence and capillary research,which has made the development of micro nano scale field.The porous media under micro nano scale has gradually become a new focus of discussion.In order to explore the flow mechanism of porous media,combined with the previous established tube flow model and flow around model and actual structure and flow characteristics of porous media,the tube-sphere model was established.The model considers the flow resistance of porous media as the superposition of tube flow viscous resistance,the resistance of flowing around a small ball and through the variable diameter of a channel.Therefore,a new pressure drop formula is derived by using the traditional fluid mechanics theory.According to the seven groups of experimental data collected in the literature,the derived formula is verified and compared with the classical Ergun equation and Carman equation.It is found that in six cases,the results of the derived formula have better adaptability than that of the Ergun equation,and are comparable to the calculated results of Carman's equation in the Darcy Regime.Then the derived pressure drop formula is dimensionless,and the above seven groups of data and the other 28 groups of data are also dimensionless.It is found that the calculated results are in good agreement with 34 groups of data(see Figure.3.8).At the same time,because the fractal theory can describe the complex and disordered material with mathematical language,the fourth chapter of this paper,based on the tube-sphere model,uses the fractal theory to deduce the pressure drop of porous media,and obtains the fractal formula of the pressure drop of porous media flow.By citing 8 groups of data for verification,and selecting the Ergun equation for comparison,it's found that the calculation results of 8 groups of data are consistent with the experimental data,and 7 groups of calculation errors are less than the Ergun equation,which shows that the fractal formula based on the tube-sphere model is reasonable.By comparing the traditional formula with the fractal formula,it is found that in the three groups of experimental data cited in the nonlinear regime,the calculation of the pressure drop by the fractal formula is smaller,and the difference between the experiment and the experiment is quite large.Combined with the analysis of the flow around in Section 3.4,it is considered that one of the reasons is that the fractal formula is too small for the calculation of the flow around,but the deep reason still needs to be further explored.According to the calculation results of traditional formula and fractal formula derived from tube-sphere model,it is found that the flow around pressure drop has a great influence on the whole pressure drop loss,and this influence will not disappear with the change of Reynolds number.At a small Reynolds number,the pressure drop of the flow around mainly contributes to the viscous pressure drop;at a large Reynolds number,the pressure drop of the flow around mainly contributes to the inertial pressure drop,increasing the calculation of the flow around pressure drop can reduce the calculation error(In section by 4.4.1-4.4.2).By using 36 sets of experimental data to verify the pressure drop formula of the pore throat model,it is found that the overall error is greater than that of the Ergan equation,and when the dimensionless Reynolds number is less than 100,the calculation results of the two formulas are smaller;when the dimensionless Reynolds number is greater than 100,the results of the two formulas are larger.Through the idea of tube flow plus flow around,this article establishes a tube-sphere model.The traditional and fractal formulas were tested by 35 and 8 groups of data,it is found that the error of the two formulas is small,which shows that the tube-sphere model has its rationality.It is hoped that this model can provide some ideas for the later research of porous media.However,because the structure of porous media is too complex,many internal flow problems are still unresolved,so the scope of application of tube-sphere model and its formula still needs further analysis of experimental data.The selected data parameters are: Particle size range: 0.0375-56.8 mm;Porosity range:0.32-0.882;Reynolds number range: 0.006-10730.