Homogenization of immiscible compressible two-phase flow in highly heterogeneous porous media with discontinuous capillary pressures

2014 ◽  
Vol 24 (07) ◽  
pp. 1421-1451 ◽  
Author(s):  
Brahim Amaziane ◽  
Leonid Pankratov ◽  
Andrey Piatnitski
Keyword(s):  
Porous Media ◽  
Water Saturation ◽  
Initial Conditions ◽  
Coupled System ◽  
Heterogeneous Porous Media ◽  
Gas Pressure ◽  
Absolute Permeability ◽  
Two Phase ◽  
Effective Coefficients ◽  
Nonlinear Degenerate

This paper presents a study of immiscible compressible two-phase, such as water and gas, flow through highly heterogeneous porous media with periodic microstructure. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. We will consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. Consequently, the model involves highly oscillatory characteristics and internal nonlinear interface conditions. The microscopic model is written in terms of the phase formulation, i.e. where the wetting (water) saturation phase and the non-wetting (gas) pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the water saturation, subject to appropriate transmission, boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Moreover, the transmission conditions are nonlinear and the saturation is discontinuous at interfaces separating different media. Under some realistic assumptions on the data, we obtain a nonlinear homogenized coupled system with effective coefficients which are computed via a cell problem and give a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence.

Imaging and Resistivity Studies of Saturation Gradients in Two-Phase Flow in 3-D Porous Media

1996 ◽  
Vol 464 ◽  
Author(s):  
E. H. Kawamoto ◽  
Po-Zen Wong
Keyword(s):  
Computed Tomography ◽  
Porous Media ◽  
Two Phase Flow ◽  
Water Saturation ◽  
Glass Beads ◽  
Water Phase ◽  
Phase Flow ◽  
Two Phase ◽  
Vertical Column ◽  
X Ray

ABSTRACTWe have carried out x-ray radiography and computed tomography (CT) to study two-phase flow in 3-D porous media. Air-brine displacement was imaged for drainage and imbibition experiments in a vertical column of glass beads. By correlating water saturation Sw with resistance R, we find that there is a threshold saturation S* ≈ 0.2, above which R(SW) ∼ Sw−2, in agreement with the empirical Archie relation. This holds true for both drainage and imbibition with littlehysteresis, provided that Sw remains above S*. Should Sw drop below S* during drainage, R(Sw) rises above the Archie prediction, exhibiting strong hysteresis upon reimbibition. This behavior suggests a transition in the connectivity of the water phase near S*, possibly due to percolation effects.

Distribution of the Oil Phase Obtained Upon Imbibition of Water

1964 ◽  
Vol 4 (01) ◽  
pp. 49-55 ◽  
Author(s):  
Pietro Raimondi ◽  
Michael A. Torcaso
Keyword(s):  
Primary Production ◽  
Relative Permeability ◽  
Water Saturation ◽  
Initial Conditions ◽  
Flow Behavior ◽  
Phase System ◽  
Residual Oil ◽  
Two Phase ◽  
Connate Water ◽  
Phase Water

Abstract The distribution of the oil phase in Berea sandstone resulting from increasing and decreasing the water saturation by imbibition was investigated Three types of distribution were recognized: trapped, normal and lagging. The amount of oil in each of these distributions was determined as a function of saturation by carrying out a miscible displacement in the oil phase under steady-state conditions of saturation. These conditions were maintained by flowing water and oil simultaneously in given ratios and by using a displacing solvent having essentially the same density and viscosity as the oil.A correlation shows the amount of trapped oil at any saturation to be directly proportional to the conventional residual oil saturation Sir The factor of proportionality is related to the fractional permeability to the water phase. Part of the oil which was not trapped was displaced in a piston- like manner (normal part) and part was eluted gradually (lagging part). The observed phenomena are more than of mere academic importance. Oil which is trapped may well provide the fuel essential for forward combustion and thus be beneficial. On the contrary, in tertiary recovery operations, it is this trapped oil which seems to make current techniques uneconomic. Introduction A typical oilfield may initially contain connate water and oil. After a period of primary production water often enters the field either from surrounding aquifers or from surface injection. During primary production evolution and establishment of a free gas saturation usually occurs. The effect and importance of this third phase is fully recognized. However, this investigation is limited to a two- phase system, one wetting phase (water) and one non-wetting phase (oil). The increase in water content of a water-wet system is termed imbibition. In a relative permeability-saturation diagram such as the one shown in Fig. 1, the initial conditions of the field would he represented by a point below a water saturation of about 35 per cent, i.e., where the imbibition and the drainage curves to the non-wetting phase nearly coincide. When water enters the field the relative permeability to oil decreases along the imbibition curve. At watered-out conditions the relative permeability to the oil becomes zero. At this point a considerable amount of oil, called residual oil, (about 35 per cent in Fig. 1) remains unrecovered. Any attempt to produce this oil will require that its saturation be increased. In Fig. 1 this would mean retracing the imbibition curve upwards. In addition, processes like alcohol and fire flooding, which can be employed at any stage of production, involve the complete displacement of connate water and an increase, or imbibition, of water saturation ahead of the displacing front. Thus, in several types of oil production it is the imbibition-relative permeability curve which rules the flow behavior. For this reason a knowledge of the distribution of the non-wetting phase, as obtained through imbibition, whether "coming down" or "going up" on the imbibition curve, is important. SPEJ P. 49^

scholarly journals Numerical Simulation of Two-Phase Flows in Heterogeneous Porous Media

2020 ◽  
Vol 21 (2) ◽  
pp. 339
Author(s):  
I. Carneiro ◽  
M. Borges ◽  
S. Malta
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Water Injection ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
High Porosity ◽  
Two Phase ◽  
Recovery Method ◽  
Porosity And Permeability

In this work,we present three-dimensional numerical simulations of water-oil flow in porous media in order to analyze the influence of the heterogeneities in the porosity and permeability fields and, mainly, their relationships upon the phenomenon known in the literature as viscous fingering. For this, typical scenarios of heterogeneous reservoirs submitted to water injection (secondary recovery method) are considered. The results show that the porosity heterogeneities have a markable influence in the flow behavior when the permeability is closely related with porosity, for example, by the Kozeny-Carman (KC) relation.This kind of positive relation leads to a larger oil recovery, as the areas of high permeability(higher flow velocities) are associated with areas of high porosity (higher volume of pores), causing a delay in the breakthrough time. On the other hand, when both fields (porosity and permeability) are heterogeneous but independent of each other the influence of the porosity heterogeneities is smaller and may be negligible.

Fundamentals of Transport Equation Formulation for Two-Phase Flow in Homogeneous and Heterogeneous Porous Media

1999 ◽  
Author(s):  
Michel Quintard ◽  
Stephen Whitaker
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Practical Importance ◽  
Volume Averaging ◽  
Heterogeneous Porous Media ◽  
Homogenization Theory ◽  
Length Scale ◽  
Two Phase ◽  
The Hierarchical Structure ◽  
Method Of Volume Averaging

Most porous media of practical importance are hierarchical in nature; that is, they are characterized by more than one length-scale. When these length-scales are disparate, the hierarchical structure can be analyzed by the method of volume averaging (Anderson and Jackson, 1967; Marie, 1967; Slattery, 1967; Whitaker, 1967). In this approach, macroscopic quantities at a given length-scale are defined in terms of a boundary value problem that describes the phenomena at a smaller length-scale, and information is filtered from one scale to another by a series of volume and area integrals. Other methods, such as ensemble averaging (Matheron, 1965; Dagan, 1989) or homogenization theory (Bensoussan et al, 1978; Sanchez-Palencia, 1980), have been used to study hierarchical systems, and developments specific to the problems under consideration in this chapter can be found in Bourgeat (1984), Auriault (1987), Amaziane and Bourgeat (1988), and Sáez et al. (1989). The transformation from the Darcy scale to the large scale is a recurrent problem in reservoir and aquifer engineering. A detailed description of reservoir properties is available through geostatistical analysis (Journel, 1996) on a fine grid with a length-scale much smaller than the scale of the blocks in the reservoir simulator. “Effective” or “pseudo” properties are assigned to the coarse grid blocks, while the forms of the large-scale equations are required to be the same as those used at the Darcy scale (Coats et al., 1967; Hearn, 1971; Jacks et al., 1972; Kyte and Berry, 1975; Dake, 1978; Killough and Foster, 1979; Yokoyama and Lake, 1981; Kortekaas, 1983; Thomas, 1983; Kossack et al., 1990). A detailed discussion of the comparison between the several approaches is beyond the scope of this chapter; however, one can read Bourgeat et al. (1988) for an introductory comparison between the method of volume averaging and the homogenization theory, and Ahmadi et al. (1993) for a discussion of the various classes of pseudofunction theories.

scholarly journals Acoustic wave propagation in two-phase heterogeneous porous media

2013 ◽  
Vol 21 (3) ◽  
pp. 238-244
Author(s):  
J. I. Osypik ◽  
N. I. Pushkina ◽  
Ya. M. Zhileikin
Keyword(s):  
Porous Media ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Heterogeneous Porous Media ◽  
Acoustic Wave Propagation ◽  
Two Phase
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