It is long known that for high-velocity fluid flow in porous media, the relation between the pressure drop and the superficial velocity is not linear. Indeed, the classical Darcy law for shear stress dominated flow needs to be extended with a quadratic term, resulting in the empirical Darcy-Forchheimer model. Another approach is to simulate the foam numerically through the volume averaging tech...

The large amount of nanoscale pores in shale results in the inability to apply Darcy's law. Moreover, the gas adsorption of shale increases the complexity of pore size characterization and thus decreases the accuracy of flow regime estimation. In this study, an apparent permeability model, which describes the adsorptive gas flow behavior in shale by considering the effects of gas adsorption, st...

We propose and analyze a third-order in time numerical algorithm for the Stokes-Darcy system for flows in fluid saturated karst aquifers. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term while a third-order explicit Adams-Bashforth scheme is utilized for the time discretization of the interface term. The scheme is efficient in the sense that one ne...

Dissolution mechanisms in porous media may lead to unstable dissolution fronts (“wormholing”). It has been shown in the literature that Darcy-scale models may reproduce all the characteristics of such dissolution patterns. This paper considers the core-scale averaged behavior of these Darcy-scale dissolution models. The form of core-scale equations is discussed based on the volume averaging of ...

water alternating gas (wag) technique is used in the petroleum industry to inject carbon dioxide (co2) into underground formations either for sequestration or enhanced oil recovery (eor) processes. co2 injection causes reactions with formation brine or aquifer and produces carbonic acid, the acid dissolves calcite and changes flow behavior significantly. modeling and investigating effects of co...

Linear stability of double diffusive convection of Darcy-Maxwell fluid with Soret and Dufour effects is investigated. The effects of the Soret and Dufour numbers, Lewis number, relaxation time and solutal Darcy Rayleigh number on the stationary and oscillatory convection are presented graphically. The Dufour number enhances the stability of Darcy-Maxwell fluid for stationary convection while it...

Modeling the interaction between surface and subsurface flow is a challenging environmental problem. One such example is the simulation of transport of contaminants through rivers into the aquifers. Mathematically, this complex problem can be modeled by the coupled system of Stokes and Darcy equations. The aim of this paper is to formulate and analyze a discontinuous finite element method for t...

This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotic...

In this paper we investigate the accuracy of a Darcy-scale model for competitive adsorption in a porous medium through comparison with a smoothed particle hydrodynamics (SPH) pore-scale model. SPH is a Lagrangian, particle based modeling method which uses the particles as interpolation points to directly discretize the governing equations of the system. The models consider a binary system of co...

Ten years ago Hou, Lowengrub and Shelley [4] published a state-of-the-art boundary integral simulation of a classical viscous fingering problem, the Saffman–Taylor instability [12]. In terms of complexity and level of detail, those computations [4] are still among the most ramified and accurately computed interfacial instability patterns that have appeared in the literature. Since 1994, the com...