Abstract
The paper considers the development of algorithms for an adequate description of processes of different scales in porous media. The choice of a computational technique is determined by the reference size of the problem being solved. Models of porous medium flow under Darcy’s law, neglecting the medium microstructure, are used for the simulation at macro-scale. While at micro-scale, a direct description of fluid flow in porous channels with complex geometry by means of gas dynamic equations is used. In the first case the proposed model of non-isothermal multiphase multicomponent flow in a porous medium includes the mass balance and total energy conservation equations modified by analogy to the known quasi-gas dynamic equations. The model features are the introduction of minimal reference scales in space and in time and the change of the system type from parabolic to hyperbolic to increase the stability of explicit difference schemes applied for approximation. In the second case the dimensionless form of the quasi-gas dynamic system with pressure decomposition, developed by the authors earlier, is adapted to the simulation of flows in the pore space. The fictitious domain method is proposed to reproduce the core microstructure. The developed approaches have been verified by test predictions.
Highlights
The numerical simulation of fluid flows in porous media is one of urgent research topics all over the world. These studies are of great practical importance for the petroleum and metallurgical industries, since modeling the hydrocarbon recovery and minerals mining, calculations of groundwater dynamics, modeling operations in various technological units, for example, in catalytic reactors, as well as the digital analysis of small rock samples can reduce the number of expensive natural experiments
The choice of a model and computational technique should be determined by the reference size of the applied problem being solved
To simulate flows at micro-scale a direct description of fluid flow in the pore space of rocks by means of gas dynamic equations can be used [5, 6]. In the both cases the present research is based on further development of the known quasi-gas dynamic (QGD) system of equations [7]
Summary
The numerical simulation of fluid flows in porous media is one of urgent research topics all over the world. To simulate flows at micro-scale (e.g. investigation of core samples with reference sizes of the order of micrometers and less) a direct description of fluid flow in the pore space of rocks by means of gas dynamic equations can be used [5, 6]. In the both cases the present research is based on further development of the known quasi-gas dynamic (QGD) system of equations [7]. The developed approaches have been verified by a number of test predictions
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