scholarly journals Fluid flow in porous media using image-based modelling to parametrize Richards' equation

2017 ◽  
Vol 473 (2207) ◽  
pp. 20170178 ◽  
Author(s):  
L. J. Cooper ◽  
K. R. Daly ◽  
P. D. Hallett ◽  
M. Naveed ◽  
N. Koebernick ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Pore Structure ◽  
Soil Water ◽  
Stokes Equations ◽  
Contact Angles ◽  
Flow In Porous Media ◽  
Richards Equation ◽  
Water Retention Curve ◽  
Image Stack

The parameters in Richards' equation are usually calculated from experimentally measured values of the soil–water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A three-dimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 μm has been used to create a computational mesh. The Cahn–Hilliard–Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL Multiphysics. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil–water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation.

scholarly journals Homogenization of two fluid flow in porous media

2015 ◽  
Vol 471 (2176) ◽  
pp. 20140564 ◽  
Author(s):  
K. R. Daly ◽  
T. Roose
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Stokes Equations ◽  
Flow In Porous Media ◽  
Richards Equation ◽  
Water Release ◽  
Fluid Saturation ◽  
Starting Point ◽  
Release Curve ◽  
First Time

The macroscopic behaviour of air and water in porous media is often approximated using Richards' equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e. constant gas pressure, this model is shown to reduce to the simpler form of Richards' equation. The starting point for this derivation is the Cahn–Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media with the underlying geometrical and material properties.

Influence of stress sensitivity on microscopic pore structure and fluid flow in porous media

2016 ◽  
Vol 36 ◽  
pp. 20-31 ◽  
Author(s):  
Yongfei Yang ◽  
Wenjie Zhang ◽  
Ying Gao ◽  
Yujin Wan ◽  
Yunhe Su ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Pore Structure ◽  
Stress Sensitivity ◽  
Flow In Porous Media

scholarly journals Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 511
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Porous Media ◽  
Soil Water ◽  
Water Flow ◽  
Water Movement ◽  
Least Square ◽  
Flow In Porous Media ◽  
Fickian Diffusion ◽  
Richards Equation ◽  
Governing Equations ◽  
Soil Water Flow

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.

SECOND-GRADE MAGNETOHYDRODYNAMIC FLUID FLOW IN POROUS MEDIA

2010 ◽  
Vol 13 (11) ◽  
pp. 1033-1037
Author(s):  
Muhammad R. Mohyuddin ◽  
S. Islam ◽  
A. Hussain ◽  
A. M. Siddiqui
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Flow In Porous Media ◽  
Second Grade ◽  
Magnetohydrodynamic Fluid

scholarly journals Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

2019 ◽  
Vol 55 (11) ◽  
pp. 9592-9603
Author(s):  
Chul Moon ◽  
Scott A. Mitchell ◽  
Jason E. Heath ◽  
Matthew Andrew
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Statistical Inference ◽  
Persistent Homology ◽  
Flow In Porous Media

Experimental Study of Natural Ions and Rock Interactions for Seawater Breakthrough Percentage Monitoring during Offshore Seawater Flooding

SPE Journal ◽  
2021 ◽  
pp. 1-21
Author(s):  
Yanqing Wang ◽  
Xiang Li ◽  
Jun Lu
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Barium Sulfate ◽  
Large Deviation ◽  
Exchange Process ◽  
Reaction Model ◽  
Sodium Content ◽  
Flow In Porous Media ◽  
Formation Water ◽  
The Impact

Summary Seawater breakthrough percentage monitoring is critical for offshore oil reservoirs because seawater fraction is an important parameter for estimating the severity of many flow assurance issues caused by seawater injection and further developing effective strategies to mitigate the impact of those issues on production. The validation of using natural ions as a tracer to calculate the seawater fraction was investigated systematically by studying the natural chemical composition evolution in porous media using coreflood tests and static bottle tests. The applicable range of ions was discussed based on the interaction between ion and rock. The barium sulfate reactive model was improved by integrating interaction between ions and rock as well as fluid flow effect. The results indicate that chloride and sodium interact with rock, but the influence of the interaction can be minimized to a negligible level because of the high concentrations of chloride and sodium. Thus, chloride and sodium can be used as conservative tracers during the seawater flooding process. However, adsorption/desorption may have a large influence on chloride and sodium concentrations under the scenario that both injection water and formation water have low chloride and sodium content. Bromide shows negligible interaction with rock even at low concentrations and can be regarded as being conservative. The application of a barium and sulfate reaction model in coreflood tests does not work as well as in bottle tests because fluid flow in porous media and ion interaction with rock is not taken into account. Although sulfate and barium adsorption on clay is small, it should not be neglected. The barium sulfate reaction model was improved based on the simulation of ion transport in porous media. Cations (magnesium, calcium, and potassium) are involved in the complicated cation-exchange process, which causes large deviation. Therefore, magnesium, calcium, and potassium are not recommended to calculate seawater fraction. Boron, which exists as anions in formation water and is used as a conservative tracer, has significant interactions with core matrix, and using boron in an ion tracking method directly can significantly underestimate the seawater fraction. The results give guidelines on selecting suitable ions as tracers to determine seawater breakthrough percentages under different production scenarios.

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