scholarly journals On the consistency of scale among experiments, theory, and simulation

2017 ◽  
Vol 21 (2) ◽  
pp. 1063-1076 ◽  
Author(s):  
James E. McClure ◽  
Amanda L. Dye ◽  
Cass T. Miller ◽  
William G. Gray
Keyword(s):  
Capillary Pressure ◽  
Fluid Phase ◽  
Interfacial Area ◽  
Simulation Method ◽  
Flow In Porous Media ◽  
State Function ◽  
State Equations ◽  
Fluid Saturation ◽  
Phase Saturation ◽  
Two Fluid

Abstract. As a tool for addressing problems of scale, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. We consider the case of modeling of two-fluid-phase flow in porous media, and we focus on issues of scale as they relate to various measures of pressure, capillary pressure, and state equations needed to produce solvable models. We apply TCAT to perform physics-based data assimilation to understand how the internal behavior influences the macroscale state of two-fluid porous medium systems. A microfluidic experimental method and a lattice Boltzmann simulation method are used to examine a key deficiency associated with standard approaches. In a hydrologic process such as evaporation, the water content will ultimately be reduced below the irreducible wetting-phase saturation determined from experiments. This is problematic since the derived closure relationships cannot predict the associated capillary pressures for these states. We demonstrate that the irreducible wetting-phase saturation is an artifact of the experimental design, caused by the fact that the boundary pressure difference does not approximate the true capillary pressure. Using averaging methods, we compute the true capillary pressure for fluid configurations at and below the irreducible wetting-phase saturation. Results of our analysis include a state function for the capillary pressure expressed as a function of fluid saturation and interfacial area.

scholarly journals On the Consistency of Scale Among Experiments, Theory, and Simulation

2016 ◽  
Author(s):  
J. McClure ◽  
A. Dye ◽  
C. Miller ◽  
W. Gray
Keyword(s):  
Capillary Pressure ◽  
Fluid Phase ◽  
Theoretical Models ◽  
Simulation Method ◽  
Flow In Porous Media ◽  
State Function ◽  
Fluid Saturation ◽  
Wide Range ◽  
Phase Saturation ◽  
Two Fluid

Abstract. The career of Professor Eric F. Wood has focused on the resolution of problems of scale in hydrologic systems. Within this context, we consider an evolving approach known as the thermodynamically constrained averaging theory (TCAT), which has broad applicability to hydrology. Specifically, we consider the case of modeling of two-fluid-phase flow in porous media. Two-fluid flow processes in the subsurface are fundamentally important for a wide range of hydrologic processes, including the transport of water and air in the vadose zone and geological carbon sequestration. Mathematical models that describe these complex processes have long relied on empirical approaches that neglect important aspects of the system behavior. New data sources make it possible to access the true geometry of geologic materials and directly measure previously inaccessible quantities. This information can be exploited to support a new generation of theoretical models that are constructed based on rigorous multiscale principles for thermodynamics and continuum mechanics. The challenges to constructing a mature model are shown to involve issues of scale, consistency requirements, appropriate representation of operative physical mechanisms at the target scale of the model, and a robust structure to support model evaluation, validation, and refinement. We apply TCAT to perform physics-based data assimilation to understand how the internal behavior influences the macroscale state of two-fluid porous medium systems. Examples of a microfluidic experimental method and a lattice Boltzmann simulation method are used to examine a key deficiency associated with standard approaches. In a hydrologic process such as evaporation, the water content will ultimately be reduced below the irreducible wetting phase saturation determined from experiments. This is problematic since the derived closure relationships cannot predict the associated capillary pressures for these states. In this work, we demonstrate that the irreducible wetting-phase saturation is an artifact of the experimental design, caused by the fact that the boundary pressure difference does not approximate the true capillary pressure. Using averaging methods, we measure the true capillary pressure for fluid configurations at and below the irreducible wetting phase saturation. Results of our analysis include a state function for the capillary pressure expressed as a function of fluid saturation and interfacial area.

Modeling Two-Phase Flow in Porous Media Including Fluid-Fluid Interfacial Area

2008 ◽  
Author(s):  
Jennifer Niessner ◽  
S. Majid Hassanizadeh ◽  
Dustin Crandall
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Two Phase Flow ◽  
Interfacial Area ◽  
Flow In Porous Media ◽  
Extended Model ◽  
Phase Flow ◽  
Two Phase ◽  
Specific Interfacial Area ◽  
Macro Scale

We present a new numerical model for macro-scale two-phase flow in porous media which is based on a physically consistent theory of multi-phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy’s law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid–fluid interfaces. An alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We show how parameters can be obtained for the alternative model using experimental data from a new kind of flow cell and present results of a numerical modeling study.

scholarly journals Development of a numerical workflow based on <i>μ</i>-CT imaging for the determination of capillary pressure–saturation-specific interfacial area relationship in 2-phase flow pore-scale porous-media systems: a case study on Heletz sandstone

Solid Earth ◽  
2016 ◽  
Vol 7 (3) ◽  
pp. 727-739 ◽  
Author(s):  
Aaron Peche ◽  
Matthias Halisch ◽  
Alexandru Bogdan Tatomir ◽  
Martin Sauter
Keyword(s):  
High Resolution ◽  
Pore Size ◽  
Capillary Pressure ◽  
Interfacial Area ◽  
Scale Model ◽  
Phase Flow ◽  
Pore Scale ◽  
Pore Size Distributions ◽  
Phase Saturation

Abstract. In this case study, we present the implementation of a finite element method (FEM)-based numerical pore-scale model that is able to track and quantify the propagating fluid–fluid interfacial area on highly complex micro-computed tomography (μ-CT)-obtained geometries. Special focus is drawn to the relationship between reservoir-specific capillary pressure (pc), wetting phase saturation (Sw) and interfacial area (awn). The basis of this approach is high-resolution μ-CT images representing the geometrical characteristics of a georeservoir sample. The successfully validated 2-phase flow model is based on the Navier–Stokes equations, including the surface tension force, in order to consider capillary effects for the computation of flow and the phase-field method for the emulation of a sharp fluid–fluid interface. In combination with specialized software packages, a complex high-resolution modelling domain can be obtained. A numerical workflow based on representative elementary volume (REV)-scale pore-size distributions is introduced. This workflow aims at the successive modification of model and model set-up for simulating, such as a type of 2-phase problem on asymmetric μ-CT-based model domains. The geometrical complexity is gradually increased, starting from idealized pore geometries until complex μ-CT-based pore network domains, whereas all domains represent geostatistics of the REV-scale core sample pore-size distribution. Finally, the model can be applied to a complex μ-CT-based model domain and the pc–Sw–awn relationship can be computed.

Machine Learning for Capillary Pressure Estimation

2021 ◽  
pp. 1-20
Author(s):  
A. A. Kasha ◽  
A. Sakhaee-Pour ◽  
I. A. Hussein
Keyword(s):  
Machine Learning ◽  
Capillary Pressure ◽  
Rock Sample ◽  
Original Data ◽  
Measured Data ◽  
Flow In Porous Media ◽  
Rock Types ◽  
Mercury Injection ◽  
Phase Saturation ◽  
Pressure Estimation

Summary Capillary pressure plays an essential role in controlling multiphase flow in porous media and is often difficult to be estimated at subsurface conditions. The Leverett capillary pressure function J provides a convenient tool to address this shortcoming; however, its performance remains poor where there is a large scatter in the scaled data. Our aim, therefore, was to reduce the gaps between J curves and to develop a method that allows accurate scaling of capillary pressure. We developed two mathematical expressions based on permeability and porosity values of 214 rock samples taken from North America and the Middle East. Using the values as grouping features, we used pattern-recognition algorithms in machine learning to cluster the original data into different groups. In each wetting phase saturation, we were able to quantify the gaps between the J curves by determining the ratio of the maximum J to the minimum J. Graphical maps were developed to identify the corresponding group for a new rock sample after which the capillary pressure is estimated using the average J curve of the identified group and the permeability and porosity values of the rock sample. This method also provides better performance than the flow zone indicator (FZI) approach. The proposed technique was validated on six rock types and has successfully generated average capillary pressure curves that capture the trends and values of the experimentally measured data by mercury injection. Moreover, the proposed methodology in this study provides an advanced and a machine-learning-oriented approach for rock typing. In this paper, we provide a reliable and easy-to-use method for capillary pressure estimation in the absence of experimentally measured data by mercury injection.

scholarly journals Wettability Effects on Capillary Pressure, Relative Permeability, and Irredcucible Saturation Using Porous Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Olugbenga Falode ◽  
Edo Manuel
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Water Saturation ◽  
Porous Plate ◽  
Reservoir Rock ◽  
Flow In Porous Media ◽  
Wettability Alteration ◽  
Initial Water ◽  
Phase Saturation

An understanding of the mechanisms by which oil is displaced from porous media requires the knowledge of the role of wettability and capillary forces in the displacement process. The determination of representative capillary pressure (Pc) data and wettability index of a reservoir rock is needed for the prediction of the fluids distribution in the reservoir: the initial water saturation and the volume of reserves. This study shows how wettability alteration of an initially water-wet reservoir rock to oil-wet affects the properties that govern multiphase flow in porous media, that is, capillary pressure, relative permeability, and irreducible saturation. Initial water-wet reservoir core samples with porosities ranging from 23 to 33%, absolute air permeability of 50 to 233 md, and initial brine saturation of 63 to 87% were first tested as water-wet samples under air-brine system. This yielded irreducible wetting phase saturation of 19 to 21%. The samples were later tested after modifying their wettability to oil-wet using a surfactant obtained from glycerophtalic paint; and the results yielded irreducible wetting phase saturation of 25 to 34%. From the results of these experiments, changing the wettability of the samples to oil-wet improved the recovery of the wetting phase.

Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling

2010 ◽  
Vol 655 ◽  
pp. 38-71 ◽  
Author(s):  
V. JOEKAR-NIASAR ◽  
S. M. HASSANIZADEH ◽  
H. K. DAHLE
Keyword(s):  
Porous Media ◽  
Capillary Pressure ◽  
Two Phase Flow ◽  
Interfacial Area ◽  
Pore Network ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Specific Interfacial Area ◽  
Non Equilibrium

Current macroscopic theories of two-phase flow in porous media are based on the extended Darcy's law and an algebraic relationship between capillary pressure and saturation. Both of these equations have been challenged in recent years, primarily based on theoretical works using a thermodynamic approach, which have led to new governing equations for two-phase flow in porous media. In these equations, new terms appear related to the fluid–fluid interfacial area and non-equilibrium capillarity effects. Although there has been a growing number of experimental works aimed at investigating the new equations, a full study of their significance has been difficult as some quantities are hard to measure and experiments are costly and time-consuming. In this regard, pore-scale computational tools can play a valuable role. In this paper, we develop a new dynamic pore-network simulator for two-phase flow in porous media, called DYPOSIT. Using this tool, we investigate macroscopic relationships among average capillary pressure, average phase pressures, saturation and specific interfacial area. We provide evidence that at macroscale, average capillary pressure–saturation–interfacial area points fall on a single surface regardless of flow conditions and fluid properties. We demonstrate that the traditional capillary pressure–saturation relationship is not valid under dynamic conditions, as predicted by the theory. Instead, one has to employ the non-equilibrium capillary theory, according to which the fluids pressure difference is a function of the time rate of saturation change. We study the behaviour of non-equilibrium capillarity coefficient, specific interfacial area, and its production rate versus saturation and viscosity ratio.A major feature of our pore-network model is a new computational algorithm, which considers capillary diffusion. Pressure field is calculated for each fluid separately, and saturation is computed in a semi-implicit way. This provides more numerical stability, compared with previous models, especially for unfavourable viscosity ratios and small capillary number values.

scholarly journals Geometric state function for two-fluid flow in porous media

2018 ◽  
Vol 3 (8) ◽  
Author(s):  
James E. McClure ◽  
Ryan T. Armstrong ◽  
Mark A. Berrill ◽  
Steffen Schlüter ◽  
Steffen Berg ◽  
...  
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Flow In Porous Media ◽  
State Function ◽  
Two Fluid

scholarly journals On the dynamics and kinematics of two‐fluid‐phase flow in porous media

2015 ◽  
Vol 51 (7) ◽  
pp. 5365-5381 ◽  
Author(s):  
W. G. Gray ◽  
A. L. Dye ◽  
J. E. McClure ◽  
L. J. Pyrak‐Nolte ◽  
C. T. Miller
Keyword(s):  
Porous Media ◽  
Fluid Phase ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Fluid

scholarly journals Tracking interface and common curve dynamics for two-fluid flow in porous media

2016 ◽  
Vol 796 ◽  
pp. 211-232 ◽  
Author(s):  
J. E. McClure ◽  
M. A. Berrill ◽  
W. G. Gray ◽  
C. T. Miller
Keyword(s):  
Porous Media ◽  
Fluid Phase ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Flow In Porous Media ◽  
Fluid Interfaces ◽  
Phase Flow ◽  
The Common ◽  
Spurious Currents ◽  
Two Fluid

The movements of fluid–fluid interfaces and the common curve are an important aspect of two-fluid-phase flow through porous media. The focus of this work is to develop, apply and evaluate methods to simulate two-fluid-phase flow in porous medium systems at the microscale and to demonstrate how these results can be used to support evolving macroscale models. Of particular concern is the problem of spurious velocities that confound the accurate representation of interfacial dynamics in such systems. To circumvent this problem, a combined level-set and lattice-Boltzmann method is advanced to simulate and track the dynamics of the fluid–fluid interface and of the common curve during simulations of two-fluid-phase flow in porous media. We demonstrate that the interface and common curve velocities can be determined accurately, even when spurious currents are generated in the vicinity of interfaces. Static and dynamic contact angles are computed and shown to agree with existing slip models. A resolution study is presented for dynamic drainage and imbibition in a sphere pack, demonstrating the sensitivity of averaged quantities to resolution.

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