Research of Reservoir Rock Properties in Violation of Darcy's Linear Law

Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory

“…From these conditions it follows that the functions 10 , 20 , 30 , 40 setting the initial conditions (5) must satisfy the equations Thus, we have found an infinite set of solutions to the original problem, depending on the values of the parameters , , = 1,2,3,4 the components of which are expressed by formulas (16) to (19). To find the parameters , , = 1,2,3,4 compare conditions (12) to (15) with conditions (6). From this comparison for the parameters we obtain the system…”

“…A lot of researches have been devoted to the study of fluid motion taking into account inertial effects in a porous medium. Among them, it is worth noting the works, where restrictions on the use of the linear Darcy's law are considered and the nonlinear laws of fluid motion are studied in the presence of a Reynolds number greater than [12][13][14]. The lower limit of the linear Darcy's law applicability is determined by the existing of non-Newtonian rheological properties of the liquid, its interaction with the solid skeleton of a porous medium at sufficiently low filtration rates.…”

“…The first generalization of Darcy's law to the case of large was founded by Dupuis, who formulated a two-term filtration law. Later, the Austrian researcher F. Forchheimer independently established two-term filtration law, which is still called F. Forchheimer equation, and its generalization with a nonstationary effect was proposed by the authors of papers [7,12,13,15,16]. A lot of scientific papers are devoted to the numerical solution of liquid flow problems [17,18].…”

One Class of Smooth Bounded Solutions to the Cauchy Problem for a Three-Dimensional Filtration Model With Darcy's Law

“…The theory of filtration is one of the main areas of scientific research due to its economic importance in connection with the extraction of oil and gas products, the development of subsoil, where the main extraction technologies are managed by the laws of filtration theory. The main law of the filtration theory, which describes the movement in a porous medium, is the linear Darcy law [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”