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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

A Study on the Wilkins and Forchheimer Equations used in Coarse Granular Media Flow

Banerjee A., Pasupuleti S., Singh M. K., Kumar G. N. P.

Acta Geophysica

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2018

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Vol. 66, no. 1

81--91

EN

Complexity of the pore geometry and the random nature of flow velocity make it difficult to predict and represent post laminar flow through porous media. Present study experimentally investigates the applicability of Forchheimer and Wilkins equations for post laminar flow where Darcy’s law is invalid due to predominant inertial effect. It is observed that both porosity and media size have significant influence over the coefficients of the Forchheimer coefficients. To incorporate the effect of porosity and media size, behaviour of Forchheimer coefficients are investigated with hydraulic radius as characteristic length. An inversely proportional variation trend is found for all the present and earlier reported data. A new empirical relation between Forchheimer coefficients and hydraulic radius is obtained which can be universally applicable for all media size and porosity. Coefficients of the Wilkins equation are found to be non-deviating for different hydraulic radius in the present study and in the reported literature validating its applicability in predicting the non laminar flow through porous media. Further the Wilkins equation is modified after incorporating the correction factors for better applicability on the field.

4

Model przepływu powietrza w ośrodku porowatym z uwzględnieniem wewnętrznych źródeł ciepła

Skotniczy P.

Prace Instytutu Mechaniki Górotworu PAN

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2008

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Vol. 10, no. 1-4

103--113

PL

W artykule przedstawiono eksperymentalną metodę wyznaczania współczynnika przepuszczalności K oraz jej numeryczną weryfikację. Pomiary wykonano na specjalnie przygotowanym do tego celu stanowisku pomiarowym, ośrodek porowaty stanowiło złoże uformowane z kulek szklanych (ballotyna) o rozmiarze 5 mm. Do wyznaczenia wartości współczynnika K oraz współczynnika oporu kwadratowego zastosowano równanie Forchheimera. Przedstawione wyniki pomiarów mają posłużyć za podstawę do przeprowadzenia szeroko zakrojonej serii eksperymentów mających na celu określenie wpływu obecności źródła temperatury wewnątrz złoża porowatego na sposób wymiany masy w układzie materiał porowaty-powietrze.

EN

Presented paper discuses, an experimental method in prediction of K coefficient as well as its numerical verification. The measurements has been taken using specialized test bed, where porous bed was configured with 5 mm diameter glass balls. For determination of K coefficient as well as quadratic drag coefficient the Forchheimer equation has been used. Presented data are base for the further experiments concerning mass and heat exchange in porous bed – air complex.