Nonequilibrium Effects During Spontaneous Imbibition

Abstract

Accurate models of multiphase flow in porous media and predictions of oil recovery require a thorough understanding of the physics of fluid flow. Current simulators assume, generally, that local capillary equilibrium is reached instantaneously during any flow mode. Consequently, capillary pressure and relative permeability curves are functions solely of water saturation. In the case of imbibition, the assumption of instantaneous local capillary equilibrium allows the balance equations to be cast in the form of a self-similar, diffusion-like problem. Li et al. [J. Petrol. Sci. Eng. 39(3) (2003), 309-326] analyzed oil production data from spontaneous countercurrent imbibition experiments and inferred that they observed the self-similar behavior expected from the mathematical equations. Others (Barenblatt et al. [Soc. Petrol. Eng. J. 8(4) (2002), 409-416]; Silin and Patzek [Transport in Porous Media 54 (2004), 297-322]) assert that local equilibirum is not reached in porous media during spontaneous imbibition and nonequilibirium effects should be taken into account. Simulations and definitive experiments are conducted at core scale in this work to reveal unequivocally nonequilbirium effects. Experimental in-situ saturation data obtained with a computerized tomography scanner illustrate significant deviation from the numerical local-equilibrium based results. The data indicates: (i) capillary imbibition is an inherently nonequilibrium process and (ii) the traditional, multi-phase, reservoir simulation equations may not well represent the true physics of the process. NomenclatureA cross-sectional area (m 2 ) Bo Bond number, ratio of buoyancy to capillary forces (dimensionless) CT computerized tomography number (Hounsfields) D coefficient of diffusion (m 2 s −1 ) f mobility ratio function (dimensionless) g acceleration due to gravity (ms −2 ) J Leverett function (dimensionless) k absolute permeability (m 2 ) k r relative permeability (dimensionless) L length (m) M mobility ratio, dimensionless 128 S. S. LE GUEN AND A. R. KOVSCEK p pressure (Pa) P c capillary pressure (Pa) S saturation (dimensionless) t time (s) u velocity (ms −1 ) x coordinate along the core (m or dimensionless) Greek Symbols ∇ gradient φ porosity (dimensionless) λ mobility (m 2 force −1 s −1 ) µ viscosity (Pas) ρ density (kg m −3 ) σ interfacial tension (force m −1 ) τ relaxation time (s) ξ similarity variable (m s 1/2 ) Subscripts g gas nw nonwetting phase r residual w wetting phase

Fundamentals of Reservoir Surface Energy as Related to Surface Properties, Wettability, Capillary Action and Oil Recovery from Fractured Reservoirs by Spontaneous Imbibition

“…Added to this is the fact that, for pure countercurrent spontaneous imbibition, the flow of one phase through the slice is exactly equalled by the reverse flow of the other phase, and both these are over the same area. The concept of a single function representing capillary pressure has been recently challenged by Le Guen & Kovscek (2006) who suggest that non-equilibrium effects should be taken into account. If this behaviour obtains, it would add another variable.…”

An Analytic Solution for the Frontal Flow Period in 1D Counter-Current Spontaneous Imbibition into Fractured Porous Media Including Gravity and Wettability Effects

“…Some studies have, however, suggested that significant non-equilibrium effects exist during spontaneous imbibition implying that this phenomenon is essentially an unsteady-state process (Barentblatt 1971;Barenblatt and Vinnichenko 1980;Barenblatt and Gilman 1987;Barenblatt et al 2002;Barenblatt et al 2003;Silin and Patzek 2004;Guen and Kovscek 2006;Juanes 2009). The main feature of an unsteady-state process is that relative permeability and capillary pressure are time-dependent variables.…”

“…It is important to notice that all studies on non-equilibrium effects during spontaneous imbibition have considered this process at core-scale level where gravity effects usually are very small and therefore neglected. Spontaneous imbibition is therefore inherently a non-equilibrium process at core-scale (Guen and Kovscek 2006). Whether this non-equilibrium process is significant at field-scale is still an open question.…”

Ensemble phase averaged equations for multiphase flows in porous media. Part 1: The bundle-of-tubes model

“…In these systems, capillary action plays a crucial role in driving the motion of fluids within the porous media (Washburn, 1921;Richards, 1931;Scheidegger, 1974;Ianson and Hoff, 1986;Hall et al, 1984;Gray and Hassanizadeh, 1991;Liu, 1991;Hassanizadeh and Gray, 1993;Alava et al, 2004;Faybishenko, 2004). Extensive theoretical investigations and advanced experimental techniques, such as neutron radiography, have been applied to study the motion of the fluids (Gummerson et al, 1979;Hassanizadeh and Gray, 1993;Moseley and Dhir, 1996;Beliaev and Hassanizadeh, 2001;Gray et al, 2002;Lockington and Parlange, 2003;Tsakiroglou et al, 2003;Culligan et al, 2004;Shiozawa and Fujimaki, 2004;El Abd et al, 2005;Manthey et al, 2005;Le Guen and Kovscek, 2006;Hilfer, 2006;Czachor, 2007;Hall, 2007). Despite intensive interrogation, models for such flows are still largely empirical.…”

“…Later, experimental observations found that the pressure difference exhibits more complicated characters. The validity of both the diffusion approach and extensions of Darcy's law have been questioned (Gummerson et al, 1979;Hillel, 1980;Hassanizadeh and Gray, 1993;Prat, 1995;Lockington and Parlange, 2003;Tsakiroglou et al, 2003;Shiozawa and Fujimaki, 2004;Hilfer, 2006;Le Guen and Kovscek, 2006;Czachor, 2007;DiCarlo, 2007;Hall, 2007).…”