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1

Quantitative characterization of seepage behavior in rough fracture considering hydromechanical coupling effect: an experimental study

Yu Xiang, Zhang Tong, Yang Ke, Yu Fei, Liu Yang, Tang Ming

Acta Geophysica

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2023

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Vol. 71, no. 5

2245--2264

EN

To study the effect of fracture morphology and in situ stress on the seepage behavior of rough fractures, hydraulic–mechanical experiments with different confining stresses, pore pressures and fracture geometry were carried out. The dimensionless parameter non-Darcy coefficient factor K and K-based critical Reynolds number model (KCRN) was proposed to characterize the behavior of rough-wall fracture and fluid seepage. The results show that the seepage flow of rough-wall fracture can be well described by Forchheimer equation. As the confining pressure increases from 1 to 31 MPa, the two walls of the rough fracture are compressed, and the fluid flow capacity is weakened, resulting in an increase of 2–3 orders of magnitude in Forchheimer viscosity coefficient A. Also affected by the increase in the confining pressure, the contact area between the two walls of the rough fracture increases, which makes the fluid channel become curved, increases the dissipation of water pressure in the inertial process and causes the inertial term coefficient B to increase by 2–3 orders of magnitude in general. In the whole range of test confining pressure (1 MPa–31 MPa), the flow state of rough fracture fluid is divided into zones based on the critical Reynolds number. The average hydraulic aperture decreases with the increase in the confining pressure, which can be perfectly fitted by hyperbolic function. The calculated critical Reynolds number of six rough fracture samples varies from 0.0196 to 1.0424. According to the experimental data, the K-based critical Reynolds number model (KCRN) is validated, and the validation results prove the accuracy and reliability of the model.

2

Alternative relationships to enhance the applicability of nonlinear filtration models in porous media

Banerjee Ashes, Jagupilla Sarath Chandra K., Pasupuleti Srinivas, Annavarapu Chandra Sekhara Rao

Acta Geophysica

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2023

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Vol. 71, no. 4

1787--1799

EN

Nonlinear filtration in porous packing has remained a research challenge till this day. There have been numerous attempts to model the flow characteristics under such conditions. However, as demonstrated in the present study, these models are applicable for only some specific conditions. The present study attempts to develop an empirical model which can be widely applicable. The Forchheimer-type models have been the most widely used in the literature for prediction of flow in porous media. The study identifies that the Ergun equation (the most popular form of the Forchheimer equation) with its original coefficients is unable to predict the flow properties over a wide range of data. Similar observation can be made for all other identical models. However, by optimising the coefficient values (A = 3705.79 and B = 6.17), the equation's performance can be significantly improved. The current study aims to create a working model that can be used to predict flow in porous media under a variety of packing, fluid, and flow conditions using multivariate polynomial regression and machine learning tools. It was observed that media size has far greater influence on the coefficients than any other parameter. Empirical models were created to predict Forchheimer coefficients, which represent R2 values greater than 0.9 for training, validation, and test data. These models were further tested on a separate dataset with velocity and hydraulic gradient data compiled from the literature. The models were found to have very reliable performance with R2 values above 0.90.

3

Cattaneo-christov heat flux on an MHD 3D free convection casson fluid flow over a stretching sheet

Shankar D. Gowri, Raju C.S.K., Kumar M.S. Jagadeesh, Makinde Oluwole Daniel

Engineering Transactions

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2020

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Vol. 68, iss. 3

223--238

EN

In this investigation, we analyze the magnetohydrodynamic (MHD) three-dimensional (3D) flow of Casson fluid over a stretching sheet using non-Darcy porous medium with heat source/sink. We also consider the Cattaneo-Christov heat flux and Joule effect. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable transformations and solved by using the shooting technique. The effects of the non-dimensional governing parameters on velocity and temperature profiles are discussed with the graphs. Also, the skin friction coefficient and Nusselt number are discussed through tables. We also validate our results with the ones already available in the literature. It is found that the obtained results are in excellent agreement with the existing studies under some special cases. Our analysis reveals that the thermal relaxation parameter reduces the temperature field for the Newtonian and non-Newtonian fluid cases. It is also found that the temperature profile is decreased in the Newtonian fluid case when compared with the non-Newtonian fluid case.

4

Non-Darcian mixed convection flow over a sphere embedded in a porous medium

Al-Harbi S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 2

321-335

EN

The mixed convection flow over a sphere embedded in a porous medium has been studied by boundary layer analysis. Solutions for the transformed equations are presented by the Keller-box numerical scheme. Results for the velocity and temperature fields as well as friction factor and Nusselt number are presented for aiding and opposing flow conditions.

5

Modelowanie przepływu w ośrodku porowatym z nieliniowym prawem filtracji

Sławomirski M. R.

Prace Instytutu Mechaniki Górotworu PAN

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2008

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Vol. 10, no. 1-4

193--204

PL

Tematem pracy jest analiza przepływu z nieliniowym dynamicznym prawem filtracji wiążącym prędkość filtracji U z jednostkowym spadkiem ciśnienia J w ośrodku porowatym. Rozpatrzono szczegółowo jedynie taką formułę dynamicznego prawa filtracji, która jest niezmiennicza względem odbicia lustrzanego oraz możliwa do bezpośredniego rozszerzenia na przepływy wielowymiarowe. Odrzucając znane z literatury formuły nie spełniające powyższych warunków (tj. traktowane jako niepoprawne fizykalnie) oraz stosując twierdzenie Weierstrassa o aproksymacji i wykorzystując wyniki uzyskane z teorii homogenizacji rozważono przepływy z dynamicznym prawem filtracji w postaci dwuparametrowego równania trzeciego rzędu (13) lub równoważnie (14). Przeanalizowano prostoliniowy przepływ jednowymiarowy, przepływ osiowo-symetryczny oraz sferyczno-symetryczny. Uzyskano formuły na rozkład ciśnienia w strefie drenażu oraz nieliniową zależność między produkcją studni (odwiertu) a wielkością depresji w strefie drenażu. Podobnie, uzyskano rozkład ciśnienia w przepływie sferyczno-symetrycznym, a także formuły na zależność między natężeniem przepływu a występującym w takim przepływie spadkiem ciśnienia. Sformułowano równanie różniczkowe transportu opisujące dwuwymiarowy nieliniowy przepływ w ośrodku porowatym. Ze względu na istniejące nieliniowości równanie to może być rozwiązane jedynie metodami numerycznymi.

EN

The paper concerns the analysis of the incompressible fluid motion through porous media described by a nonlinear dynamic relationship between the superficial flow velocity U and pressure drop per unit of distance J. It has been assumed that the dynamic relationship describing fluid motion must be valid for one- and multidimensional fluid motions, and moreover, it must be invariant with respect to the refl ection of the co-ordinate system. U vs. J relationships encountered in the literature and violating the requirements mentioned above have been rejected. On the other hand, applying the Weierstrass approximation theorem with respect to U vs. J relationsip, and taking into account the results obtined from the homogenisation theory the author has assumed the third order relationsip between U and J represented by Eqs. (13) and (14). One-dimensional staighforward, cylindrical and spherical flows have been analysed. For the well neighbouring zone the pressure distribution and the relationship between well production and and pressure difference have been determined. In a similar way, the pressure distribution and the relationship between pressure drop and flow rate have been determined for spherical flow. Moreover, the transport equation for non-linear two-dimensional flow in a porous layer has been obtained. Owing to non-linearities the transport eqution may only be solved by means of the numerical methods.