Fluid Flow In Media Research Articles

Applications of critical path analysis to uniform grain packings with narrow conductance distributions: I. Single-phase permeability

Accurate estimation of single-phase permeability (k) has broad application in numerous areas, particularly modeling flow and transport in porous materials. Various techniques have been proposed in the literature to estimate k from other medium's properties, such as porosity, grain and/or pore size distribution, and pore connectivity. Among them critical path analysis (CPA) from statistical physics − first developed to model fluid flow in media with broad conductance distributions − has been successfully applied to heterogeneous soils and rocks. However, its application to uniform sphere and/or glass bead packs that represent homogeneous porous media with narrow conductance distributions needs to be investigated. In this study, we invoke concepts from CPA and estimate k from average grain diameter and formation factor in uniform sand and glass bead packings. By comparing theory with eight datasets including 105 packs from the literature, we demonstrate that CPA estimates permeability in homogeneous media accurately. We also compare our CPA-based model estimations with those from the Kozeny–Carman, Revil and Cathles, and RGPZ models. Results indicate that the CPA approach estimates k more precisely than other three models studied here.

Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions

The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous materials that contain multiple scales of pores cannot be adequately described by the classical Darcy equations. It is for this reason that mathematical models for fluid flow in media with multiple scales of pores have been proposed in the literature. However, these models are analytically intractable for realistic problems. In this paper, a stabilized mixed four-field finite element formulation is presented to study the flow of an incompressible fluid in porous media exhibiting double porosity/permeability. The stabilization terms and the stabilization parameters are derived in a mathematically consistent manner, and the computationally convenient equal-order interpolation of all the field variables is shown to be stable. A systematic error analysis is performed on the resulting stabilized weak formulation. Representative problems, patch tests and numerical convergence analyses are performed to illustrate the performance and convergence behavior of the proposed mixed formulation in the discrete setting. The accuracy of numerical solutions is assessed using the mathematical properties satisfied by the solutions of this double porosity/permeability model. Moreover, it is shown that the proposed framework can perform well under transient conditions and that it can capture well-known instabilities such as viscous fingering.

Study on fluid flow in nonlinear elastic porous media: Experimental and modeling approaches

A theoretical model for describing the changes in the porosity and permeability with fluid pressure in elastic deformed porous media was presented firstly. Secondly, the changes in porosity and permeability of sandstones were studied by experimental approach, and the exponential correlations between porosity, permeability and fluid pressure in porous media were obtained by regression based on these experimental data. Thirdly, based on the theory of nonlinear deformation of porous media and the continua theory on porous media and fluids, a fluid filtration mathematical model considering nonlinear elastic deformation of porous media was developed. To get insights into the performances of fluid flow in the media, exact analytical solutions of the nonlinear model were obtained by traveling-wave transmission. The main parameters were input to analyze the difference of the solutions and their effects on the characteristics of the fluid pressure distribution with space and time. It is found that the effect of nonlinear elastic deformation may lead to the nonlinear distribution of fluid pressure in porous media at one-dimensional case at a one-dimensional case. However, the distribution of fluid pressure in porous media is linear only when the pressure-dependent factors of pressure rock permeability, porosity, fluid density and viscosity satisfy a special correlation.

Design of Two-Phase Displacement Experiments

This paper presents and demonstrates a systematic approach to the selection of experimental designs leading to accurate estimates of relative permeability and capillary pressure functions for two-phase flow in porous media. The objective is to select the most appropriate experimental designs for determining the flow functions accurately within the saturation range covered by the experimental data. The work is based on a linearized covariance analysis. In this analysis we utilize analytical sensitivity coefficients to calculate confidence intervals for the flow functions. These confidence intervals are estimates of the accuracy with which the flow functions can be determined for a given experimental design. We validate the confidence interval estimates through a Monte Carlo study. A previously reported non-linearity measure seems not to be applicable for determining the utility of the linearized covariance analysis for the porous media fluid flow model.