Two-phase Porous Media Research Articles

Two-phase porous media flows with dynamic capillary effects and hysteresis: Uniqueness of weak solutions

In this paper, we obtain the uniqueness of weak solutions for a two phase flow model in a porous medium. A particularity of the model is that the dynamic effects and hysteresis are included in the capillary pressure. To prove the uniqueness, we define an auxiliary elliptic system.

Parameter sampling capabilities of sequential and simultaneous data assimilation: II. Statistical analysis of numerical results

We assess and compare parameter sampling capabilities of one sequential and one simultaneous Bayesian, ensemble-based, joint state-parameter (JS) estimation method. In the companion paper, part I (Fossum and Mannseth 2014 Inverse Problems 30 114002), analytical investigations lead us to propose three claims, essentially stating that the sequential method can be expected to outperform the simultaneous method for weakly nonlinear forward models. Here, we assess the reliability and robustness of these claims through statistical analysis of results from a range of numerical experiments. Samples generated by the two approximate JS methods are compared to samples from the posterior distribution generated by a Markov chain Monte Carlo method, using four approximate measures of distance between probability distributions. Forward-model nonlinearity is assessed from a stochastic nonlinearity measure allowing for sufficiently large model dimensions. Both toy models (with low computational complexity, and where the nonlinearity is fairly easy to control) and two-phase porous-media flow models (corresponding to down-scaled versions of problems to which the JS methods have been frequently applied recently) are considered in the numerical experiments. Results from the statistical analysis show strong support of all three claims stated in part I.

Gelfand-type problem for two-phase porous media

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classical Gelfand problem the thermal explosion occurs exclusively owing to the absence of stationary temperature distribution. We also show that the presence of interphase heat exchange delays a thermal explosion. Moreover, we prove that in the limit of infinite heat exchange between phases the problem of thermal explosion in two-phase porous media reduces to the classical Gelfand problem with renormalized constants.

EOS7Rn—A new TOUGH2 module for simulating radon emanation and transport in the subsurface

A new fluid property module, EOS7Rn, was developed for TOUGH2 to simulate the transport of radon gas (222Rn) in saturated–unsaturated soils. It is an enhanced version of the EOS7R module for radionuclide transport, with a source term added in the transport equation to model radon generation by emanation from radioactive decay of the soil radium (226Ra) content. We implemented variable physical properties (diffusion coefficient, emanation factor, adsorption coefficient, and Henry's law coefficient) of this gas component in two-phase (liquid–gas) porous media as a function of soil moisture and/or soil temperature. Numerical trials have been carried out to ensure that temporal and spatial numerical discretization of this nonlinear source term are effective and have properly been implemented in TOUGH2. We performed comparative studies between EOS7Rn and an exact analytical solution at steady-state isothermal unsaturated conditions for many numerical experiments of one-dimensional (1D) radon transport in homogeneous and layered soil columns typical of Uranium Mill Tailings (UMT) landfill soils.We found that the radon activity concentration profiles and flux densities calculated by EOS7Rn were in good agreement with the analytical solution for all the studied numerical experiments. Relative errors in radon mass balance and flux densities were determined to be negligible. For the second verification of EOS7Rn for transient nonisothermal radon transport problems, two simulation examples are presented to demonstrating the importance of the radon emanation and thermal effects on radon transport in a geothermal reservoir. Like most other sister modules, EOS7Rn can simulate nonisothermal multiphase flow and fully coupled three-dimensional transport in fractured porous media. It will help in predicting the radon exhalation from highly radium-contaminated soils and underground cavities to outdoor and indoor environments.

Effective Thermal Conductivity Modelling for Closed-Cell Porous Media with Analytical Shape Factors

This paper presents a fully analytical model for the effective thermal conductivity of two-phase porous media with two-/three-dimensional closed cells, applicable to honeycombs and closed-cell foams. The present model combines an existing analytical expression derived based on the Laplace heat conduction equation with an analytical shape factor which corrects the deviation caused from a non-circular (or non-spherical) pore inclusion. Results demonstrate the validity of the present model capable of analytically estimating the effective thermal conductivity of closed-cell porous media. The simple yet accurate model provides the physical mechanisms of how effective thermal conductivity depends upon the shape of pores.

Seismic Response of Dam-Sediment-Water on Fluid-Solid Coupling

Studying the important effects of sediments on the seismic response of dams ,This paper established the calculation model based on regarding the water reservoir as compressible fluid ,the dam and the foundation as an elastic solid, the sediment as Liquid-Solid two-phase porous medium. The results showed that the sediment thickness and properties have important effects on the dam seismic. Increasing the thickness of sediment ,the seismic response of acceleration significantly decreased, the hydrodynamic pressure significantly reduced , which is benefited to the safety of the dam.

Acoustic wave propagation in two-phase heterogeneous porous media

The propagation of an acoustic wave through two-phase porous media with spatial variation in porosity is studied. The evolutionary wave equation is derived, and the propagation of an acoustic wave is numerically analyzed in application to marine sediments with various physical parameters.

Controllability and observability in two-phase porous media flow

Reservoir simulation models are frequently used to make decisions on well locations, recovery optimization strategies, etc. The success of these applications is, among other aspects, determined by the controllability and observability properties of the reservoir model. In this paper, it is shown how the controllability and observability of two-phase flow reservoir models can be analyzed and quantified with aid of generalized empirical Gramians. The empirical controllability Gramian can be interpreted as a spatial covariance of the states (pressures or saturations) in the reservoir resulting from input perturbations in the wells. The empirical observability Gramian can be interpreted as a spatial covariance of the measured bottom-hole pressures or well bore flow rates resulting from state perturbations. Based on examples in the form of simple homogeneous and heterogeneous reservoir models, we conclude that the position of the wells and of the front between reservoir fluids, and to a lesser extent the position and shape of permeability heterogeneities that impact the front, are the most important factors that determine the local controllability and observability properties of the reservoir.

Determination of hydraulic conductivity of a suspension

Abstract The process of sedimentation and subsequent gravity compression of kaolin and water suspensions was investigated experimentally. 45 batch tests were carried out and the time dependence of the height of the suspension column was measured. The one-dimensional equations of Darcian mechanics of two-phase porous media are applied to formulate the studied process mathematically. A very natural assumption makes it possible to find a solution of the forward problem for a starting period of the process. Analysis of the theoretical function and the experimental data gives hydraulic conductivity as a function of the suspension concentration. The obtained results are presented and discussed.

Global transmission and reflection coefficients of the ultrasonic component in porous media: A new approach

The purpose of this paper is to propose a new approach to determining the global ultrasonic transmission and reflection coefficients in a random porous medium. Boundary conditions at the interface of the medium were used to determine local transmission and reflection coefficients. A study of the behavior of different waves inside the medium was carried out to derive a new global formulation that takes interior phenomena into consideration. All the results were obtained independently of the geometrical and physical characteristics of the medium so that the method can be applied to any two-phase porous medium. This study is based on normal incidence ultrasonic wave propagation.

A simplistic model for the tortuosity in two-phase close-celled porous media

We present an analytical model capable of demonstrating the dependence of tortuosity of two-phase porous media upon two topological parameters: porosity and pore shape. Based on a generalized effective thermal conductivity model and a particular solution to the Laplace heat conduction equation for two-phase porous media having randomly distributed non-conducting circular pores, an analytical model of tortuosity is derived. For non-circular pores such as idealized polygonal pores, the circularity-based concept of pore shape factor is incorporated into the model, which is capable of analytically unifying existing models which are valid only for limited porosity ranges and circular pore shapes.

Thermal stretching in two-phase porous media: Physical basis for Maxwell model

An alternate yet general form of the classical effective thermal conductivity model (Maxwell model) for two-phase porous materials is presented, serving an explicit thermo-physical basis. It is demonstrated that the reduced effective thermal conductivity of the porous media due to non-conducting pore inclusions is caused by the mechanism of thermal stretching, which is a combination of reduced effective heat flow area and elongated heat transfer distance (thermal tortuosity).

Analysis and experimental verification of the relation between Scholte wave velocity and sediment containing two-phase fluid properties

Based on several ultrasonic suspension models, i.e. Urick, Urick-Ament, HT and Mcclements, the Scholte wave propagation characteristics are analyzed at the interface between sediment concentration two-phase fluid and porous medium solid. The interface wave propagation characteristic equation are found using the complex wave number equation given by the aforementioned four models. Relationships between Scholte velocity and the two-phase fluid properties, (e.g., dispersion, volume content, particle size) are discussed. Scholte wave propagation and signal are obtained by Comsol simulation. By using the time delay estimation method, it is found that the obtained Scholte wave velocity are in accord with that given in Urick-Ament and HT models.

Binary Level Set Methods for Dynamic Reservoir Characterization by Operator Splitting Scheme

AbstractIn this paper, operator splitting scheme for dynamic reservoir characterization by binary level set method is employed. For this problem, the absolute permeability of the two-phase porous medium flow can be simulated by the constrained augmented Lagrangian optimization method with well data and seismic time-lapse data. By transforming the constrained optimization problem in an unconstrained one, the saddle point problem can be solved by Uzawas algorithms with operator splitting scheme, which is based on the essence of binary level set method. Both the simple and complicated numerical examples demonstrate that the given algorithms are stable and efficient and the absolute permeability can be satisfactorily recovered.

Scientific Problems on Seismic Resistance of Bridge of Pile Foundation in Liquefiable Site

Aiming at the scientific goals of seismic resistance of bridge of pile foundation in liquefiable site, several scientific key problems were presented. Then, the following were analyzed in detail: Mechanism of large-scale table test on dynamic pile-soil-bridge interaction in liquefiable site; the Pyke’s modified dynamic constitutive model of soil; Kagawa’s p-y relation for analysis of piles lateral resistance behavior, and evaluation of degradation and velocity effect on piles vertical resistance. The results show that quasi-static and dynamic analysis need to be advanced for prediction of dynamic pile-soil-bridge interaction; the continuum media model based on Biot's dynamic coupled theory for two-phase porous media should be further developed; Kagawa’s p-y relation is the better choice for analysis of lateral resistance behavior of piles and should be improved, and liquefaction should be considered when analyzing the influences of degradation effect and velocity effect on the vertical resistance behavior of piles.

Numerical Simulation of Two-Phase Flow in a Rotating Packed Bed

According to the development of a new type of oil purifier——HIGEE rotating oil purifier, this paper has carried out related numerical simulations. The two-phase porous medium flow model in the rotating packed bed (RPB) was built, and by using CFD software, the distribution of the phases in the RPB which is on the condition of high gravity (HIGEE) field and the porous media has been simulated. The paper has developed the influencing rule of key technologies parameters which affect the separating efficiency of the rotating packed bed.

Equivalent formulations and numerical schemes for a class of pseudo-parabolic equations

This paper investigates three different formulations for a class of pseudo-parabolic equations. Such equations are encountered, for example, as a model for two-phase porous media flows when dynamic effects in the capillary pressure are included. We first show the equivalence of the three different formulations for the original equation. On the basis of this, we further investigate the corresponding discretization in time and give some numerical examples.

On the Influence of Permeability and Young's Modulus on the Dehydration of a Strongly Shrinkable Two-Phase Porous Medium: A Model Sensibility Analysis and the Development of a Contact Mechanics Measurement Setup

A model that describes the mass transfer in a two-phase shrinkable porous media by using a classic Darcy law for the fluid relative to solid transfer has been recently developed by Cáceres et al.[ 1-2 ] This model describes the coupling between the fluid pressure and the solid structure deformation tensor by using the Terzaghi stress tensor decomposition for the media and elastic constitutive law for the solid structure.[ 3 ] The aim of this article is to point out the sensitivity of this model relative to the two main physical parameters that govern the coupled mass transfer and stress level in a strongly shrinkable porous medium, namely, permeability and the Young's modulus. An experimental setup that makes possible the simultaneous measurement of those two parameters as well as the Poisson ratio is developed in agreement with the recent theoretical suggestions of Lin et al. The experimental evolution of these quantities versus the moisture content is discussed for an agar gel.

双水平集逼近油藏模型特征的数值模拟方法

In this paper, Uzawas algorithms by steepest gradient descent scheme and operator splitting scheme for dynamic reservoir characterization by a binary level set approach are explored. The permeability of two-phase porous media flow can be recovered by the augmented Lagrangian optimization method with well data and seismic time-lapse data. After adding the constraint functions to the augmented Lagrangian optimization functional, the saddle points can be found by steepest gradient descent scheme and operator splitting scheme, which is based on the essence of binary level set method with few difficulties. In the end, the numerical examples demonstrate that the given algorithms will be efficient, stable when the permeability is recovered.

Entropic Burgers’ equation via a minimizing movement scheme based on the Wasserstein metric

As noted by the second author in the context of unstable two-phase porous medium flow, entropy solutions of Burgers’ equation can be recovered from a minimizing movement scheme involving the Wasserstein metric in the limit of vanishing time step size (Otto, Commun Pure Appl Math, 1999). In this paper, we give a simpler proof by verifying that the anti-derivative is a viscosity solution of the associated Hamilton Jacobi equation.