Begell House Inc.
Journal of Porous Media
JPM
1091-028X
22
1
2019
HOMOGENIZE COUPLED STOKES–CAHN–HILLIARD SYSTEM TO DARCY'S LAW FOR TWO-PHASE FLUID FLOW IN POROUS MEDIUM BY VOLUME AVERAGING
1-19
10.1615/JPorMedia.2018028699
Jie
Chen
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China 710049
Shuyu
Sun
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China 710049; Computational Transport Phenomena Laboratory, Division of Physical Science and
Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900,
Kingdom of Saudi Arabia
Zhengkang
He
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China 710049
volume averaging
porous media
Stokes–Cahn–Hilliard equations
Darcy's law for twophase flow
A technique of local volume averaging is applied to obtain general equations that depict mass and momentum transport
of incompressible two-phase flow in porous media. Starting from coupled Stokes–Cahn–Hilliard equations for incompressible two-phase fluid flow, the averaging is performed without oversimplifying either the porous media or the fluid mechanical relations. The resulting equations are Darcy's law for two-phase flow with medium parameters which could be evaluated by experiment. The Richards equation of the mixed form can be deduced from the resulting equations. The differences between the resulting equations and the empirical two-phase fluid flow model adopted in oil industry are discussed using several numerical examples.
EFFECT OF A WAXY CRUDE OIL'S YIELD STRESS ON THE CONING PHENOMENON: A NUMERICAL STUDY
21-35
10.1615/JPorMedia.2018028707
Ali
Salehi-Shabestari
School of Mechanical Engineering, College of Engineering, University of Tehran, Center of
Excellence in Design and Optimization of Energy Systems (CEDOES), Tehran, Iran
Mehrdad
Raisee
School of Mechanical Engineering, College of Engineering, University of Tehran, Center of
Excellence in Design and Optimization of Energy Systems (CEDOES), Tehran, Iran
Kayvan
Sadeghy
School of Mechanical Engineering, College of Engineering, University of Tehran, Center of
Excellence in Design and Optimization of Energy Systems (CEDOES), Tehran, Iran
waxy crude oil
water coning phenomenon
Bingham model
modified Darcy's law
The effect of a waxy crude oil's yield stress is numerically investigated on the "water coning phenomenon" using
the Bingham rheological model. After modifying Darcy's law for purely viscous non-Newtonian fluids, it was used
to relate the flow rate to the pressure gradient. Having derived the governing equations for the axisymmetric case,
the implicit pressure explicit saturation (IMPES) method was used to numerically solve the governing equations. To
verify the code, a comparison was made with published data for the water coning of Newtonian/Newtonian pair. The
effect of yield stress and plastic viscosity on the critical rate, the breakthrough time, and the cone shape was obtained
numerically. It is shown that by an increase in the yield stress of the displaced oil, the time needed by the water to cone upward and break into the wellbore is decreased. That is to say, the yield stress of the displaced fluid has a negative effect on the water coning phenomenon. On the other hand, the yield stress induced in the displacing fluid by polymeric additives is predicted to delay the coning phenomenon.
ASSESSMENT OF CAPILLARY PRESSURE ESTIMATE BASED ON FLUID-FLUID INTERFACE CURVATURE
37-52
10.1615/JPorMedia.2018028698
Marzio
Piller
Department of Engineering and Architecture, University of Trieste, via A. Valerio 10, 34127
Trieste (TS), Italy
Gianni
Schena
Department of Engineering and Architecture, University of Trieste, via A. Valerio 10, 34127
Trieste (TS), Italy
Diego
Casagrande
Department of Geotechnology, Delft University of Technology, 2628 CN Delft, Netherlands
Pacelli L.J.
Zitha
Helmholz Zentrum fur Umweltforschung, Permoserstr. 15, 04318, Leipzig, Germany; Delft University of Technology, Department of Geotechnology, 2628 CN Delft, The Netherlands
capillary pressure
porous media
X-ray tomography
surface curvature
Young–Laplace
Highresolution X-ray tomography can be used to measure the local mean curvature of fluid–fluid interfaces within the
pores of opaque, permeable porous media. Thereof, the pore-scale capillary pressure can be estimated via the Young–Laplace equation. We critically review the aforementioned method by processing experimental data acquired with an
X-ray cone-beam laboratory station and compare capillary pressure estimates with results of pore-scale numerical
simulations. The method looks promising but is rather sensitive to the attainment of an equilibrium state for the fluid mixture and to the numerical calculation of curvature. Numerical simulation results provide evidence that dynamic
effects result in a larger discrepancy between values of the capillary pressure computed from first principles (i.e.,
pressure difference across the interface) and from geometric considerations (i.e., curvature estimation and Young–Laplace equation).
OIL RECOVERY BY THERMAL EXPANSION FROM A HOMOGENEOUS DEFORMABLE POROUS MEDIUM
53-71
10.1615/JPorMedia.2018029060
P. F.
Aguilar-Gastelum
Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, C.P. 07730, Del. Gustavo A.
Madero, Ciudad de México, México
Octavio
Cazarez-Candia
Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, C.P. 07730, Del. Gustavo A.
Madero, Ciudad de México, México
thermal expansion
oil recovery
geomechanics
deformable medium
In the oil industry, one of the main recovery mechanisms along the application of a thermal oil recovery method is
thermal expansion. Thus, it is imperative to know its role under different reservoir conditions, taking into account the deformation of the porous medium. In this work, two mathematical models for oil and oil-water recovery from cores by thermal expansion are presented. One model allows the simulation of a core saturated with oil and the other one a core saturated with oil-water. The models involve hydrodynamics, heat transfer, and geomechanical phenomena, as well as a deformable mesh model for their numerical solution, which was obtained using the finite element method. Oil and water recovery, pressure, porosity, permeability, and core deformation were predicted for a core saturated with either oil or oil-water. The predictions agree very well with the theoretical data reported in literature. The effect of core deformation, due to pressure and temperature, on predictions was studied. It was found that under the simulation conditions used in this work, taking into account the geomechanical phenomena reveals that (1) the cumulative oil production, by thermal expansion, is larger than by a load and (2) the cumulative oil production is largest when both a load and thermal expansion are applied. Thus, thermal expansion is a very important mechanism for oil recovery and should be incorporated into oil recovery numerical simulations, through a geomechanical model, to compute porosity changes in a more realistic fashion.
NUMERICAL STUDY ON NATURAL CONVECTION IN A POROUS CAVITY THAT IS PARTIALLY HEATED AND COOLED BY SINUSOIDAL TEMPERATURE AT VERTICAL WALLS
73-85
10.1615/JPorMedia.2019018275
Liamena
Hassinet
LESEI, Department of Mechanical Engineering, University of Batna 2, Algeria
Mohamed
Si-Ameur
LESEI Laboratory, Department of Mechanical Engineering, Technology Faculty, University of Batna 2, Algeria
natural convection
porous medium
partial heating
cooling
sinusoidal temperature profiles
We numerically study unsteady natural convection flow in a cavity filled with porous media in two dimensions using
a Brinkman–extended Darcy model. The cavity is heated at the lower half of the left vertical wall and cooled at the
upper half of the right vertical wall by sinusoidal varying-temperature profiles, with amplitudes for heating λH and
for cooling λC. Horizontal and remaining walls are insulated. We use the finite-control volume method to numerically solve governing conservative equations of mass, momentum, and energy. The problem is analyzed for different values of Rayleigh number Ra in the range 103 ≤ Ra ≤ 106, aspect ratio parameter Ar in the range 1 ≤ Ar ≤ 4, and sinusoidal temperature function in ranges 0.25 ≤ λH ≤ 1.0 and 0 ≤ λC ≤ 1.0. Numerical results show that heat transfer is mainly due to conduction at low Ra ≤ 104. The conduction heat-transfer regime is also indicated for low λH and λC ≤ 0.5. Conduction decreases with increasing λH and λC, and convection gradually becomes dominant with increasing Ra and decreasing Ar. Heat transfer increases with increasing Ra, λH, λC, and Ar = 2, when the convection regime is dominant.
APPLYING THE CONTINUOUS-TIME RANDOM WALK MODEL TO NON-FICKIAN DISPERSION IN MISCIBLE DISPLACEMENT THROUGH CARBONATE ROCK
87-105
10.1615/JPorMedia.2019020224
Yeison
Villamil
Faculty of Mechanical Engineering, Department of Petroleum Engineering, University of
Campinas, Cidade Universitaria Zeferino Vaz - Barão Geraldo, Campinas - São Paulo, Brazil,
13083-860
J. A.
Vidal Vargas
Faculty of Mechanical Engineering, Department of Petroleum Engineering, University of
Campinas, Cidade Universitaria Zeferino Vaz - Barão Geraldo, Campinas - São Paulo, Brazil,
13083-860
Osvair V.
Trevisan
Faculty of Mechanical Engineering, Department of Petroleum Engineering, University of
Campinas, Cidade Universitaria Zeferino Vaz - Barão Geraldo, Campinas - São Paulo, Brazil,
13083-860
miscible displacement
non-Fickian behavior
CTRW
dispersion coefficient
ADE
x-ray
computed tomography
In this article, we analyze mass transport in a miscible displacement process using a heterogeneous porous medium,
applying both continuous-time random walk (CTRW) and advection−dispersion equation (ADE) models. We include
a series of theoretical tests using the CTRW scheme against curves of the total concentration model (TCM), referred
to here as blind tests. CTRW is compared with ADE based on two experimental displacement tests that are carried
out through carbonate rock from a Brazilian outcrop. Experimental tests consist of (1) injecting fresh water into the rock sample that is saturated with a brine solution and (2) inverting the fluid injection sequence, with brine displacing fresh water. We obtain transport concentration curves using x-ray computed tomography (CT). This technique also provides in-situ concentration profiles at different positions along the sample. All experimental curves are analyzed using CTRW and ADE models. We calculate dispersion coefficients for ten different sections of carbonate rock and confirm variation of the dispersion coefficient. The CTRW model fits transport curves more closely than the classical ADE model. Mathematically, CTRW obtained an optimal result of the dispersion coefficient by an error of fitting. However, with the β parameter, CTRW was ineffective for characterizing local heterogeneity of the rock. In theoretical blind tests, the CTRW model does not effectively reproduce the Peclet number of the original flow, although concentration curves are a reasonable match at low mass-transfer regimes. We found that after increased mass transfer, neither of the curves matched well.
A NUMERICAL STUDY OF FERROFLUID (Fe3O4) IN THE PRESENCE OF A MAGNETIC DIPOLE INSPIRED BY SLIP AND VISCOUS DISSIPATION EFFECTS SUBMERGED IN A POROUS MEDIUM
107-117
10.1615/JPorMedia.2018029067
Zahid
Iqbal
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila 44700, Pakistan
Bilal
Ahmad
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila 44700, Pakistan
Ehnber Naheed
Maraj
Department of Mathematics, Faculty of Sciences, HITEC University, Taxila 44700, Pakistan
ferrofluid
magnetic dipole
slip flow
porous medium
thermal radiation
viscous dissipation
The present article is a theoretical attempt to investigate the stretching flow and heat transfer phenomena most encountered in the plastic films and sheet industry. This study is performed to analyze the behavior of slip flow of ferrofluid in a porous medium. Effects of viscous dissipation and thermal radiation are taken into account in the presence of a magnetic dipole. The developed nonlinear ordinary differential equations are tackled numerically using the Runge−Kutta−Fehlberg method coupled with a shooting scheme. Graphical results for velocity, temperature, and skin friction and heat flux are obtained and analyzed in a physical manner. Skin friction at the wall enhances with increasing ferromagnetic–hydrodynamic interaction parameter. Local heat flux is found to be an increasing function of thermal radiation and decreases with an increasing ferromagnetic parameter.
IMMISCIBLE VISCOUS FINGERING IN AN ANNULAR HELE-SHAW CELL WITH A SOURCE
119-130
10.1615/JPorMedia.2018028822
Oleg A.
Logvinov
Faculty of Mechanics and Mathematics, Moscow MV Lomonosov State University, Moscow
119992, Russia
Hele-Shaw cell
radial viscous fingering
surface tension
The displacement of a viscous fluid from an annular Hele-Shaw cell with a source of finite radius by a less viscous
one is studied. The fluids are considered immiscible, so that surface tension forces are acting on the interface. Linear analysis shows a stabilizing effect of surface tension and the presence of a critical interfacial mode with the highest rate of growth. The number of the critical mode is strongly dependent on the capillary number and is virtually independent of the viscosity ratio. The consistency with experimental data is acceptable for small capillary numbers. Numerical simulation of the displacement process is conducted using the continuum surface force (CSF) model. A stabilizing effect of surface tension clearly appears at the initial stage of displacement. The number of generated viscous fingers turns out to be in satisfactory agreement with linear theory and experimental data. However, the lateral surface of viscous fingers can lose stability at the subsequent (nonlinear) stage of displacement.