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SUMMARY:Examination of Capillary Pressure-Saturation-Interfacial Area Rela
tion under Dynamic Conditions using Volume-Of-Fluid (VOF) Method
DTSTART;VALUE=DATE-TIME:20180517T171100Z
DTEND;VALUE=DATE-TIME:20180517T171300Z
DTSTAMP;VALUE=DATE-TIME:20200808T150652Z
UID:indico-contribution-780@events.interpore.org
DESCRIPTION:Speakers: Santosh Konangi (University of Cincinnati)\nConventi
onal two-phase flow equations (Richards Equation) for porous media at the
macroscale require capillary pressure (Pc) and relative permeability (Kr)
measured as a function of saturation (S). However\, these equations lack
solid theoretical foundation\, and there is still a considerable gap betwe
en the theory and experiments. In typical experiments\, an “average”
macroscopic capillary pressure is measured as the difference between the p
ressures of the non-wetting-phase reservoir at the inlet and wetting-phase
reservoir at the outlet of a porous medium. Traditionally\, this macrosc
opic phase pressure difference is assumed to be equal to the pore-scale ca
pillary pressure arising due to the curvature of the menisci at the fluid-
fluid invasion front. Many theoretical and experimental studies have show
n that the macroscopic definition is valid only at equilibrium (i.e. stati
c conditions) and if the phases are connected (Ferrari et al.\, 2013). Un
der non-equilibrium (dynamic) conditions\, when the fluids are moving\, th
e dynamic capillary pressure measured in experiments is a combination of c
apillary pressure at the invasion front and the pressure head caused by vi
scous effects (Lovoll et al.\, 2011). \nThe Pc-S relationship is non-uniq
ue\, and is flow process dependent\; different Pc-S curves are defined for
drainage and imbibition experiments\, resulting in “hysteresis” (Joek
ar-Niasar and Hassanizadeh\, 2012). Gray and Hassanizadeh (1991\, 1993) d
eveloped a theoretical framework for unsaturated capillary flows which pro
posed that the inclusion of specific fluid-fluid interfacial area will exp
licitly define the state of the system\, resulting in a unique relation be
tween capillary pressure\, saturation and interfacial area (Pc–Sw–awn)
. In this study\, we investigate the capillary pressure–saturation rela
tion under equilibrium and non-equilibrium conditions using pore-scale dir
ect numerical simulations (DNS). Direct numerical simulations (DNS) allow
for high resolution description of the geometry and time evolution of int
erfaces\, thereby permitting us to investigate the uniqueness of transient
Pc–Sw–awn surfaces. \nThe porous medium is represented by a quasi-tw
o-dimensional flow network of cylindrical obstructions. Hex-dominant comp
utational grids are generated to accurately resolve the inter-cylinder por
e space. The Navier–Stokes (NS) equations are solved in the pore space
on an Eulerian mesh using the open-source finite-volume computational flui
d dynamics (CFD) code\, OpenFOAM. The Volume-of-Fluid (VOF) method is emp
loyed to track the evolution of the fluid–fluid interface\; a static con
tact angle is used to account for wall adhesion. Simulations of drainage
and imbibition are performed for different capillary numbers by controllin
g the flow rate of the non-wetting (polydimenthlysiloxane oil) and wetting
(water) fluids. From these micro-scale simulations\, the pore-scale capi
llary pressure is directly determined at the fluid-fluid invasion front\;
this capillary pressure depends on the pore morphology and interfacial ene
rgy at the fluid-fluid interface\, without accounting for the viscous diss
ipation which is dependent on system size and invasion speed. The pore-sc
ale capillary pressure is upscaled using the fluid-fluid interfacial area
to estimate the macroscopic equilibrium (quasi-static) and non-equilibrium
(dynamic) Pc-Sw curves\; the Pc–S–awn surface is constructed to deter
mine whether the data points from drainage and imbibition processes fall o
n a unique surface under transient conditions.\n\nhttps://events.interpore
.org/event/2/contributions/780/
LOCATION:New Orleans
URL:https://events.interpore.org/event/2/contributions/780/
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