Paul Papatzacos

Lattice Boltzmann simulations of contact line motion in a liquid-gas system

We use a lattice Boltzmann algorithm for liquid-gas coexistence to investigate the steady-state interface profile of a droplet held between two shearing walls. The algorithm solves the hydrodynamic equations of motion for the system. Partial wetting at the walls is implemented to agree with Cahn theory. This allows us to investigate the processes which lead to the motion of the three-phase contact line. We confirm that the profiles are a function of the capillary number and a finite-size analysis shows the emergence of a dynamic contact angle, which can be defined in a region where the interfacial curvature tends to zero.

Macroscopic Two-phase Flow in Porous Media Assuming the Diffuse-interface Model at Pore Level

The paper presents a model for two-phase flow, where liquid and gas are treated as one fluid with variable density. A one-component fluid and the diffuse-interface model for two-phase flow are assumed at pore level. The wetting properties of the fluid are described by the Cahn theory. Macroscopic equations are deduced in the framework of the Marle formalism. It is shown that two-phase flow in porous media can be described by the Cahn–Hilliard equation for the mass density. The concept of relative permeability is not needed. For non-neutral wetting, it is shown that a capillary pressure exists but that it is not a function of state. Two numerical illustrations are presented, one of them showing that the model is, at least in a simple steady-state situation, compatible with the generalized two-continuum model.

Numerical investigations of the steady state relative permeability of a simplified porous medium

The purpose of this paper is to investigate, by flow simulations in a uniform pore-space geometry, how the co and countercurrent steady state relative permeabilities depend on the following parameters: phase saturation, wettability, driving force and viscosity ratio. The main results are as follows: (i) with few exceptions, relative permeabilities are convex functions of saturation; (ii) the cocurrent relative permeabilities increase while the countercurrent ones decrease with the driving force; (iii) with one exception, phase 2 relative permeabilities decrease and phase 1 relative permeabilities increase with the viscosity ratio M = μ1/μ2; (iv) the countercurrent relative permeabilities are always less than the cocurrent ones, the difference being partly due to the opposing effect of the viscous coupling, and partly to different levels of capillary forces; (v) the pore-level saturation distribution, and hence the size of the viscous coupling, can be very different between the cocurrent and the countercurrent cases so that it is in general incorrect to estimate the full mobility tensor from cocurrent and countercurrent steady state experiments, as suggested by Bentsen and Manai (1993).

Approximate Partial-Penetration Pseudoskin for Infinite- Conductivity Wells

This paper presents a simple formula for the pseudoskin factor of a well with restricted flow entry where infinite conductivity is taken into account analytically. Comparisons with previously published result are shown graphically and in tabulated form. Topics considered in this paper include oil wells, natural gas wells, hydraulic conductivity, formation damage, graphs, and data analysis.

Relative Permeability From Capillary Pressure

A new theory is reviewed for single-component, two-phase flow in porous media. It includes wettability and capillary pressure as integral parts of the thermodynamic description and does not make use of the relative permeability concept. However, by providing a capillary pressure correlation, we are able to extract relative permeabilities and to show good consistency between rock property correlations.

Exact Solutions for Infinite-Conductivity Wells

In pressure transient testing, the infinite-conductivity condition translates mathematically into a uniform-pressure (or uniform-potential) condition at the well. This means the flux at different points of the well should be determined in such a way that potential remains uniform at the well. The integral equation for accomplishing this is solved analytically to yield the Laplace-transformed potential. For fractured-well problems, this leads to a relatively fast algorithm for drawing type curves directly on a computer screen. For limited-flow-entry problems, the analytical pressure expression can be used with the method of images to treat problems in reservoirs of finite thickness and/or areal extent.

Mixed-Wet Drainage and Imbibition Relative Permeabilities From the Diffuse Interface Theory

The Diffuse-Interface model for two-phase flow in porous media is applied to the invesigation of relative permeabilities in unsteady-state flows. It is shown that relative permeabilities have a transient regime where they can be significantly larger than 1. It is also shown that, when normalized by their endpoint values, relative permeabilities can be calculated from formulas involving thermodynamical and capillary pressure functions. The end-point relative permeabilities are linearly related to the fluid velocity, but the coefficients seem to be flow dependent.