scholarly journals Porous media: The Muskat problem in three dimensions

2013 ◽  
Vol 6 (2) ◽  
pp. 447-497 ◽  
Author(s):  
Antonio Córdoba ◽  
Diego Córdoba ◽  
Francisco Gancedo
Keyword(s):  
Porous Media ◽  
Three Dimensions ◽  
Muskat Problem

Qualitative and Quantitative Analyses of the Three-Phase Distribution of Oil, Water, and Gas in Bentheimer Sandstone by Use of Micro-CT Imaging

2012 ◽  
Vol 15 (06) ◽  
pp. 706-711 ◽  
Author(s):  
M.. Feali ◽  
W.V.. V. Pinczewski ◽  
Y.. Cinar ◽  
C.H.. H. Arns ◽  
J.-Y.. -Y. Arns ◽  
...  
Keyword(s):  
Porous Media ◽  
Complex Geometry ◽  
Phase Distribution ◽  
Three Dimensions ◽  
Residual Oil ◽  
Oil Saturation ◽  
Spatial Continuity ◽  
Three Phase ◽  
Oil Water ◽  
Oil Films

Summary It is now widely acknowledged that continuous oil-spreading films observed in 2D glass-micromodel studies for strongly water-wet three-phase oil, water, and gas systems are also present in real porous media, and they result in lower tertiary-gasflood residual oil saturations than for corresponding negative spreading systems that do not display oil-spreading behavior. However, it has not yet been possible to directly confirm the presence of continuous spreading films in real porous media in three dimensions, and little is understood of the distribution of the phases within the complex geometry and topology of actual porous media for different spreading conditions. This paper describes a study with high-resolution X-ray microtomography to image the distribution of oil, water, and gas after tertiary gasflooding to recover waterflood residual oil for two sets of fluids, one positive spreading and the other negative spreading, in strongly water-wet Bentheimer sandstone. We show that, for the positive spreading system, oil-spreading films maintain the connectivity of the oil phase down to low oil saturation. At similar oil saturation, no oil films are observed for the negative spreading system, and the oil phase is disconnected. The spatial continuity of the oil-spreading films over the imaged volume is confirmed by the computed Euler characteristic for the oil phase.

Rock dissolution patterns and geochemical shutdown of –brine–carbonate reactions during convective mixing in porous media

2015 ◽  
Vol 764 ◽  
pp. 296-315 ◽  
Author(s):  
X. Fu ◽  
L. Cueto-Felgueroso ◽  
D. Bolster ◽  
R. Juanes
Keyword(s):  
Porous Media ◽  
Chemical Speciation ◽  
Hydrodynamic Instability ◽  
Three Dimensions ◽  
Chemical System ◽  
Scalar Dissipation ◽  
Convective Mixing ◽  
Geochemical Reactions ◽  
The Impact ◽  
Rayleigh Benard

AbstractMotivated by the process of $\text{CO}_{2}$ convective mixing in porous media, here we study the formation of rock-dissolution patterns that arise from geochemical reactions during Rayleigh–Bénard–Darcy convection. Under the assumption of instantaneous chemical equilibrium, we adopt a formulation of the local reaction rate as a function of scalar dissipation rate, a measure that depends solely on flow and transport, and chemical speciation, which is a measure that depends only on the equilibrium thermodynamics of the chemical system. We use high-resolution simulations to examine the interplay between the density-driven hydrodynamic instability and the rock dissolution reactions, and analyse the impact of geochemical reactions on the macroscopic mass exchange rate. We find that dissolution of carbonate rock initiates in regions of locally high mixing, but that the geochemical reaction shuts down significantly earlier than shutdown of convective mixing. This early shutdown feature reflects the important role that chemical speciation plays in this hydrodynamics–reaction coupled process. Finally, we extend our analysis to three dimensions and explore the morphology of dissolution patterns in three dimensions.

scholarly journals On the respect to the Hashin-Shtrikman bounds of some analytical methods applying to porous media for estimating elastic moduli

2021 ◽  
Vol 15 (2) ◽  
pp. 14-25
Author(s):  
N. Nguyen ◽  
N.Q Tran ◽  
B.A Tran ◽  
Q.H Do
Keyword(s):  
Porous Media ◽  
Elastic Moduli ◽  
Effective Properties ◽  
Minimum Energy ◽  
Three Dimensions ◽  
Effective Elastic Moduli ◽  
The Finite Element Method ◽  
Energy Principle ◽  
Minimum Energy Principle ◽  
Recent Method

In this work, some popular analytic formulas such as Maxwell (MA), Mori-Tanaka approximation (MTA), and a recent method, named the Polarization approximation (PA) will be applied to estimate the elastic moduli for some porous media. These approximations are simple and robust but can be lack reliability in many cases. The Hashin-Shtrikman (H-S) bounds do not supply an exact value but a range that has been admitted by researchers in material science. Meanwhile, the effective properties by unit cell method using the finite element method (FEM) are considered accurate. Different shapes of void inclusions in two or three dimensions are employed to investigate. Results generated by H-S bounds and FEM will be utilized as references. The comparison suggests that the method constructed from the minimum energy principle PA can give a better estimation in some cases. The discussion gives out some remarks which are helpful for the evaluation of effective elastic moduli. Keywords: Maxwell approximation; polarization approximation; Mori-Tanaka approximation; effective elastic moduli; porous medium.

scholarly journals Steady Flux Regime During Convective Mixing in Three-Dimensional Heterogeneous Porous Media

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 58 ◽  
Author(s):  
Christopher Green ◽  
Jonathan Ennis-King
Keyword(s):  
Porous Media ◽  
Three Dimensional ◽  
Heterogeneous Porous Media ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Anisotropic Porous Media ◽  
Initial Flow ◽  
Anisotropic Models ◽  
Convective Mixing ◽  
Heterogeneous Models

Density-driven convective mixing in porous media can be influenced by the spatial heterogeneity of the medium. Previous studies using two-dimensional models have shown that while the initial flow regimes are sensitive to local permeability variation, the later steady flux regime (where the dissolution flux is relatively constant) can be approximated with an equivalent anisotropic porous media, suggesting that it is the average properties of the porous media that affect this regime. This work extends the previous results for two-dimensional porous media to consider convection in three-dimensional porous media. Through the use of massively parallel numerical simulations, we verify that the steady dissolution rate in the models of heterogeneity considered also scales as k v k h in three dimensions, where k v and k h are the vertical and horizontal permeabilities, respectively, providing further evidence that convective mixing in heterogeneous models can be approximated with equivalent anisotropic models.

scholarly journals Growth in the Muskat problem

2020 ◽  
Vol 15 ◽  
pp. 7 ◽  
Author(s):  
Rafael Granero-Belinchón ◽  
Omar Lazar
Keyword(s):  
Porous Media ◽  
Initial Data ◽  
Multiphase Flow ◽  
Flow In Porous Media ◽  
Regularity Criteria ◽  
Critical Spaces ◽  
Muskat Problem

We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criteria in terms of some norms of the initial data in critical spaces (Ẇ1,∞ and Ḣ3∕2).

Sign in / Sign up

Export Citation Format

Share Document