Foam Generation Hysteresis in Porous Media: Experiments and New Insights

Foam application in subsurface processes including environmental remediation, geological carbon-sequestration, and gas-injection enhanced oil recovery (EOR) has the potential to enhance contamination remediation, secure \(\hbox {CO}_{2}\) storage, and improve oil recovery, respectively. Nanoparticles are a promising alternative to surfactants in creating foam in harsh environments. We conducted \(\hbox {CO}_{2}\)-in-brine foam generation experiments in Boise sandstones with surface-treated silica nanoparticle in high-salinity conditions. All the experiments were conducted at the fixed \(\hbox {CO}_{2}\) volume fraction and fixed flow rate which changed in steps. The steady-state foam apparent viscosity was measured as a function of injection velocity. The foam flowing through the cores showed higher apparent viscosity as the flow rate increased from low to medium and high velocities. At very high velocities, once foam bubbles were finely textured, the foam apparent viscosity was governed by foam rheology rather than foam creation. A noticeable hysteresis occurred when the flow velocity was initially increased and then decreased, implying multiple (coarse and strong) foam states at the same superficial velocity. A normalized generation function was combined with CMG-STARS foam model to cover full spectrum of foam behavior in the experiments. The new model successfully captures foam generation and hysteresis trends in presented experiments in this study and data from the literature. The results indicate once foam is generated in porous media, it is possible to maintain strong foam at low injection rates. This makes foam more feasible in field applications where foam generation is limited by high injection rates that may only exist near the injection well.     

Scaling Immiscible Displacements in Porous Media with Horizontal Wells

Despite the increase in horizontal well applications, scaling fluid displacement in porous medium with horizontal wells is yet to be fully investigated. Determining the conditions under which horizontal wells may lead to better oil recovery is of great importance to the petroleum industry. In this paper, a numerical sensitivity study was performed for several well configurations. The study is performed in order to reveal the functional relationships between the scaling groups governing the displacement and the performance of immiscible displacements in homogeneous reservoirs produced by horizontal wells. These relationships can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. In addition, they provide the condition under which a horizontal well configuration may yield better recovery performance. These results have potential applications in modeling immiscible displacements and in the scaling of laboratory displacements to field conditions.     

Horizontal Redistribution of Two Fluid Phases in a Porous Medium: Experimental Investigations

Classical models for flow and transport processes in porous media employ the so-called extended Darcy’s Law. Originally, it was proposed empirically for one-dimensional isothermal flow of an incompressible fluid in a rigid, homogeneous, and isotropic porous medium. Nowadays, the extended Darcy’s Law is used for highly complex situations like non-isothermal, multi-phase and multi-component flow and transport, without introducing any additional driving forces. In this work, an alternative approach by Hassanizadeh and Gray identifying additional driving forces were tested in an experimental setup for horizontal redistribution of two fluid phases with an initial saturation discontinuity. Analytical and numerical solutions based on traditional models predict that the saturation discontinuity will persist, but a uniform saturation distribution will be established in each subdomain after an infinite amount of time. The pressure field, however, is predicted to be continuous throughout the domain at all times and is expected to become uniform when there is no flow. In our experiments, we also find that the saturation discontinuity persists. But, gradients in both saturation and pressure remain in both subdomains even when the flow of fluids stops. This indicates that the identified additional driving forces present in the truly extended Darcy’s Law are potentially significant.     

Nonsimilar Solutions for Mixed Convection in Non-Newtonian Fluids Along Horizontal Surfaces in Porous Media

A nonsimilar boundary layer analysis is presented for the problem of mixed convection in power-law type non-Newtonian fluids along horizontal surfaces with variable heat flux distribution. The mixed convection regime is divided into two regions, namely, the forced convection dominated regime and the free convection dominated regime. The two solutions are matched. Numerical results are presented for the details of the velocity and temperature fields. A discussion is provided for the effect of viscosity index on the surface heat transfer rate.     

A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media

It is well known that the relationship between capillary pressure and saturation, in two-phase flow problems demonstrates memory effects and, in particular, hysteresis. Explicit representation of full hysteresis with a myriad of scanning curves in models of multiphase flow has been a difficult problem. A second complication relates to the fact that P ^c–S relationships, determined under static conditions, are not necessarily valid in dynamics. There exist P ^c–S relationships which take into account dynamic effects. But the combination of hysteretic and dynamic effects in the capillary relationship has not been considered yet. In this paper, we have developed new models of capillary hysteresis which also include dynamic effects. In doing so, thermodynamic considerations are employed to ensure the admissibility of the new relationships. The simplest model is constructed around main imbibition and drainage curves and assumes that all scanning curves are vertical lines. The dynamic effect is taken into account by introducing a damping coefficient in P ^c–S equation. A second-order model of hysteresis with inclined scanning curves is also developed. The simplest version of proposed models is applied to two-phase incompressible flow and an example problem is solved.     

Transport in Porous Media

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Transport in Porous Media     

Transport in Porous Media

Table of Contents

Transport in Porous Media     

Electrohydrodynamics in Porous Media

In this work we develop the volume averaged form of the frequency-dependent governing equations for electrohydrodynamics in a saturated porous medium. The concept of local electrical equilibrium is identified, and when this condition is valid we obtain a one-equation model describing the coupled transport of momentum and electric charge. When local electrical equilibrium is not valid, separate forms of Maxwell's equations must be developed for both the fluid and solid phases.     

Transport in Porous Media

Table of Contents

Transport in Porous Media     

Arrhenius Activation Energy Effect on Free Convection About a Permeable Horizontal Cylinder in Porous Media

Transport in Porous Media - This study numerically analyzed the Arrhenius activation energy effect on free convection about a permeable horizontal cylinder in porous media. The surface of the...     

Convective Acceleration in Porous Media

Transport in Porous Media - Convective acceleration occurs in porous media flows due to the spatial variations of the nonuniform flow channel geometry of natural pores. This article demonstrates...     

Three Pressures in Porous Media

In a thermodynamic setting for a single phase (usually fluid), the thermodynamically defined pressure, involving the change in energy with respect to volume, is often assumed to be equal to the physically measurable pressure, related to the trace of the stress tensor. This assumption holds under certain conditions such as a small rate of deformation tensor for a fluid. For a two-phase porous medium, an additional thermodynamic pressure has been previously defined for each phase, relating the change in energy with respect to volume fraction. Within the framework of Hybrid Mixture Theory and hence the Coleman and Noll technique of exploiting the entropy inequality, we show how these three macroscopic pressures (the two thermodynamically defined pressures and the pressure relating to the trace of the stress tensor) are related and discuss the physical interpretation of each of them. In the process, we show how one can convert directly between different combinations of independent variables without re-exploiting the entropy inequality. The physical interpretation of these three pressures is investigated by examining four media: a single solid phase, a porous solid saturated with a fluid which has negligible physico-chemical interaction with the solid phase, a swelling porous medium with a non-interacting solid phase, such as well-layered clay, and a swelling porous medium with an interacting solid phase such as swelling polymers.     

Flow in Random Porous Media

Flow in a porous medium with a random hydraulic conductivity tensor K(x) is analyzed when the mean conductivity tensor (x) is a non-constant function of position x. The results are a non-local expression for the mean flux vector (x) in terms of the gradient of the mean hydraulic head (x), an integrodifferential equation for (x), and expressions for the two point covariance functions of q(x) and (x). When K(x) is a Gaussian random function, the joint probability distribution of the functions q(x) and (x) is determined.     

Foam Drainage in Porous Media

In this paper we present a simple analysis of liquid drainage in foams confined in porous media. First we derive the equation for the evolution of the liquid saturation using general mass and momentum conservation arguments and phenomenological relations between the transport parameters and liquid saturation. We find an unusual foam drainage equation in which the determinant terms express the competition between the external force field, represented here by the gravity field, and capillary pressure gradient. We present analytical solutions of the drainage equation in three cases: (a) gravity forces are dominant over capillary forces, (b) capillary forces are dominant over gravity forces, and (c) capillary and gravity forces are comparable in order of magnitude.     

Mixing-Limited Reactions in Porous Media

Transport in Porous Media - Acid mine drainage is generated when sulfide minerals are exposed to air and water through the porous subsurface, and it is significantly accelerated by the action of...     

A Note on Local Thermal Non-equilibrium in Porous Media and Heat Flux Bifurcation Phenomenon in Porous Media

This work address a number of fundamental issues and concepts related to local thermal non-equilibrium and the heat flux bifurcation phenomenon in porous media. Different types of heat flux bifurcation phenomenon are discussed in relation to previous works by the authors.     

Evaporation and Condensation Fronts in Porous Media

Flow of a fluid through a porous medium is considered with allowance for heat conduction. Both fronts at which the liquid is transformed into steam or a liquid-steam mixture and fronts with inverse transformations are studied. The evolutionarity conditions of these fronts are considered and a model of their structure is proposed.     

Dispersion and Chemical Reactions in Porous Media

The effect of chemical reactions on the process of admixture transport by a flow through a porous medium is considered. On the basis of a number of examples it is shown that the dispersion coefficient depends on the chemical reaction rate constant.