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Study of relative permeability variation during unsteady flow in saturated reservoir
rock using Lattice Boltzmann method
Étude de la variation de la perméabilité relative au cours d’écoulement transitoire dans une roche
réservoir saturée en utilisant la méthode des réseaux de Boltzmann
Pak A., Sheikh B.
Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
ABSTRACT: The importance of relative permeability coefficient on the productivity of oil reservoirs is well-known in Petroleum
Geomechanics. Relative permeability is one of the main macroscopic parameters that heavily influence the two-phase flow regime in
saturated porous rock which governs the rate of oil extraction from the well. In this study the dominant mechanisms of the flow of two
immiscible fluids (water and oil) in porous media have been studied at the pore scale by using a developed simulator based on Lattice-
Boltzmann Method. The validity of the numerically-derived relative permeability values demonstrate the capability of Lattice
Boltzmann Method in modeling the complicated pore scale phenomena encountered in petroleum geomechanics.
RÉSUMÉ: L'importance du coefficient de perméabilité relative pour la productivité des réservoirs est bien connu en géomécanique
pétrolière. La perméabilité relative est l'un des principaux paramètres macroscopiques fortement influençant le régime d'écoulement
bi-phasique dans des roches poreuses saturées qui régit le l'extraction du pétrole. Dans cette étude, les mécanismes dominants de
l'écoulement de deux fluides non miscibles (eau et huile) dans les milieux poreux ont été étudiés à l'échelle des pores en utilisant un
simulateur développé sur la base des réseaux de Boltzmann. La validité des valeurs numériquement obtenues pour la perméabilité
relative démontre la capacité de la méthode des réseaux de Boltzmann pour la modélisation des phénomènes complexes rencontrés à
l'échelle des pores en géomécanique pétrolière
.
KEYWORDS:Relative Permeability, Lattice Boltzmann Method, Steady/Unsteady Flow, Petroleum Geomecahnics
1 INTRODUCTION
Relative permeability is an essential petro-physical property
required for description of multi-phase flow in petroleum
reservoirs. It is a direct measure of the ability of the porous
medium to produce one fluid when two or more fluids are
present. This flow property is the result of the composite effects
of porosity, pore geometry, wettability, saturation history,
reservoir temperature, reservoir pressure, overburden pressure,
and rock type. The relative permeability curves are very
important in the study of reservoir productivity. They are used
in predicting production rate and recovery from the reservoirs
during all recovery stages (primary, secondary, and tertiary).
Briefly, there are two basic approaches for determination of
relative permeability curves from laboratory core flow tests:
steady and unsteady state methods. In the steady-state method,
the fluids are injected simultaneously into core plugs. In the
unsteady-state method, a fluid is injected to displace another
fluid present in the core. Steady-state test data processing is
relatively simple, but the experiments are tedious and lengthy,
because attaining steady state fluid saturations within the core
requires long times, in the order of hours, following the
initiation of tests under certain fluid injection rates. In contrast,
unsteady-state laboratory tests can be performed rapidly and the
tests better represent the real physics of the phenomenon.
However, recording of a number of parameters are not possible
during the experiment and also data interpretation is a much
more difficult task. In both methods, data processing is further
complicated unless fluid displacement rates are sufficiently high
to minimize the core inlet and outlet capillary end-effects.
Details on each technique are covered in Keehm et al. (2004),
and Ramstad et al. (2011).
Recently, pore-scale numerical modeling has emerged for
simulation of fluid flow through porous media. The main
advantage of such models is incorporating the micro-scale
processes that control the large-scale phenomena. Fluid/fluid
and fluid/solid interactions are examples of such processes that
have significant effects on the flow regimes.
A recently developed computational fluid dynamic method
which is ideal for simulating fluid flows in complicated
geometries such as porous media at the pore scale is Lattice
Boltzmann Method (LBM) (Chen & Doolen, 1998). LBM is
suitable for modeling intricate fluid flow problems such as
multiphase flow in complex structures. LBM was applied to
flow through porous media soon after its emergence in 1989
(Succi, 1989). Considerable growth of its application in
modeling multiphase flow through porous media mainly origins
from its algorithm simplicity and accuracy in handling irregular
flow paths, modeling the behavior of fluid/fluid interfaces and
simulation of fluid/solid interactions (e.g. Chen & Doolen 1998;
Pan et al. 2004; Schaap et al. 2007).
In this study a 2D LBM-based numerical code is developed
which is capable of modeling steady-state and unsteady-state
flow of two immiscible fluids through porous media. After
validation of the code by some benchmark problems, a well-
documented experimental work was simulated by the developed
model.
2 LATTICE BOLTZMANN METHOD
The most popular LB model is the Bhatnagar–Gross–Krook
(BGK) model (Chen et al. 1992) with a standard bounce-back
(SBB) scheme for fluid–solid boundaries. However, some
problems have encountered difficulties with this popular
method. In BGK method the collision operator is approximated
by a single-relaxation-time (SRT) approximation, which has
some defects such as numerical instability and viscosity
dependence of boundary locations, especially in under-relaxed
situations (Qian et al. 1992). The viscosity dependent boundary
