non-Darcy Flow Model Research Articles

A Potential Formulation of Non-Linear Models of Flow through Anisotropic Porous Media

A theoretical analysis, based on the search for a normal dissipation potential, is performed in order to generalize the empirical non-Darcy one-dimensional flow models to 3-D flows through anisotropic porous media. In an abstract framework, it is proven that a large number of heuristic non-linear equations governing the multidimensional flow through isotropic porous media can be derived starting from a potential strictly related to the mechanical power dissipated by the fluid. Such a formulation allows to define, for the tensor permeability case, a wide class of filtration models according to the Onsager's generalized theory of dissipative mechanical systems. A consistent generalization to anisotropic permeability case of polynomial flow models is proposed. Both primal and dual mixed variational formulations associated to the proposed quadratic and incomplete cubic flow models are introduced and discussed.

Numerical well model for non-Darcy flow through isotropic porous media[*]This work was supported in part by the EPA under grant # R 825207-01-1, by the State of Texas under ARP/ATP grant # 010366-168 and by a gift grant from Mobil Oil Corp.

Numerical simulation of fluid flow in a hydrocarbon reservoir has to account for the presence of wells. The pressure of a grid cell containing a well is different from the average pressure in that cell and different from the bottom-hole pressure for the well [17]. This paper presents a study of grid pressures obtained from the simulation of single phase flow through an isotropic porous medium using different numerical methods. Well equations are proposed for Darcy flow with Galerkin finite elements and mixed finite elements. Furthermore, high velocity (non-Darcy) flow well equations are developed for cell-centered finite difference, Galerkin finite element and mixed finite element techniques.

Unsteady free convection flow over a vertical flat plate immersed in a porous medium

Using the Laplace transformation technique, the problem of unsteady free convection flow over a vertical flat plate imbedded in a porous medium is solved analytically for two different kinds of thermal boundary conditions. In the analysis, a non-Darcy flow model with negligible inertial effects is adopted. In terms of the obtained solutions for the temperature and velocity parameters, expressions for the fully developed Nusselt number are derived. The obtained analytical solutions may be used to verify the validity of obtained numerical solutions for more complicated similar transient free convection problems in the fully developed limiting case.

Effect of porosity on natural convective heat transfer in a fluid saturated porous medium

Abstract The effect of porosity on natural convective flow and heat transfer in a fluid saturated porous medium has been investigated using Galerkin's finite element method. A generalised non-Darcy flow model with porosity as a separate parameter is used. Results indicate that the non-Darcy regime is highly sensitive to porosity changes. A variation of the order of 40% in the average Nusselt number is possible with change in the porosity, for the Rayleigh and Darcy number ranges considered.

Network modeling of non-Darcy flow through porous media

Darcy's law is inadequate for describing high-velocity gas flow in porous media, which occurs in the near well-bore region of high capacity gas and condensate reservoirs. This study is directed at understanding the non-Darcy flow behavior. A pore-level network model has been developed to describe high velocity flow. The inputs to the model are pore size distributions and network coordination numbers. The outputs are permeability, non-Darcy coefficient, tortuousity and porosity. The additional pressure gradient term is found to be proportional to the square of the velocity in accordance with the Forchheimer's equation. The correlation between the non-Darcy coefficient and other flow properties (the permeability, the porosity and the tortuousity) is found to depend on the morphological parameters being changed. General correlations are derived between these flow properties.

Drain pipe performance determined using a non-Darcy finite element model

The saturated flow towards drain pipes wrapped with voluminous envelope was investigated by means of a two-dimensional finite element model for non-Darcy flow. special attention was given to the flow in the immediate vicinity of the drain pipe which may cause the movement of soil particles and, as a result, clogging of the envelope. Non-linear elements were used for a better representation of the geometry around the drain and for more accurate prediction of hydraulic heads owing to nonlinear interpolation. Results showed the influence of non-Darcy flow on the head losses near the drain and on the water table heights for variable envelope permeability.

Forchheimer and Brinkman extended Darcy flow model on natural convection in a vertical cylindrical porous annulus

In the present numerical work, the Forchheimer and Brinkman extended Darcy flow model is used for studying the natural convection heat transfer in a vertical cylindrical porous annulus. Forchheimer inertial and Brinkman viscous terms have been characterized by two non-dimensional numbers. The present description renders the formulation suitable for vertical annuli as well as for rectangular cavity. Numerical results obtained by SAR scheme indicate, that Brinkman viscous terms lead to a higher decrease in the average Nusselt number compared to the Forchheimer inertial terms. Numerical results obtained with the present non-Darcy flow model are in good agreement with the available experimental results of a high permeability porous medium for which results obtained with the Darcy flow model show considerable deviation.

Conjugate free convection heat transfer analysis of a vertical plate fin embedded in non-Darcian porous media

The influence of non-Darcian flow phenomena on the natural convection heat transfer from a vertical plate fin embedded in a porous medium was studied. With the thin-fin approximation for the plate fin and the non-Darcy flow model for the convective fluid, numerical solutions were generated to demonstrate the importance of non-Darcian effects on conjugate natural convection flow adjacent to the fin. These effects, which are often involved in convective transport of fluid through porous media, include high-flow-rate inertial force, solid-boundary viscous resistance, nonuniform porosity distribution, and thermal dispersion. The present work aims to investigate these effects on the fin heat-transfer characteristics such as fin temperature distributions, the local heat transfer coefficient, the local heat flux, and the overall rate of heat transfer.

Combined boundary and inertia effects for fully developed mixed convection in a vertical channel embedded in porous media

The fully developed laminar mixed convection in a vertical channel embedded in porous media has been solved by using non-Darcy flow model. Through proper manipulation of nondimensional variables and parameters, the governing equations are derived and the thermal boundary conditions on the left and right walls can be prescribed as isothermal-isothermal, isothermal-isoflux, or isoflux-isothermal, respectively. Including the Darcian force, buoyancy force and boundary effect, the exact solutions for temperature and velocity profiles are obtained. Meanwhile, parametric zones for the occurrence of flow reversal based on the analytical solutions are presented. Finally, the numerical solution is also provided to investigate their further influence due to the existence of inertia effect.

A Capillary Model for Non-Darcy Flow through Porous Media

A parallel capillary porous flow model is constructed from capillaries with “wall forces.” The model exhibits critical pressure gradients and nonlinear discharge velocity at low pressure gradients, while for high gradients the discharge velocity is linear.