The Physics of Flow Through Porous Media (3rd Edition)

Appropriate relative permeability curves for two-phase flows through subsurface fractures remain unclear. We have conducted decane-water and nitrogen-water two-phase flow experiments and simulations on real variable-aperture fractures in rocks under confining stress. Experiments have been conducted on fractures for different combinations of rock type (granite or limestone), wettability (contact angle of water: 0 or 90 ), and intrinsic fracture permeability (10 211 m 2 or 10 210 m 2 ) using different combinations of shear displacement (0 or 1 mm) and effective confining stress (1 or 40 MPa). It has been demonstrated that nonwetting phase relative permeability depends on capillary pressure, except at either a higher contact angle or higher intrinsic permeability (i.e., bigger aperture), where no influence of capillarity is expected from the Young-Laplace equation. In the absence of an influence of capillarity, relations between wetting and nonwetting phase relative permeabilities agree with that of the X-type relative permeability curves. In order to determine the relative permeability curves under the influence of capillarity, the experimental results have been analyzed by two-phase flow simulations of the aperture distributions of the fractures. It has been revealed that nonwetting phase relative permeability becomes zero, even at a small wetting phase saturation of approximately 0.3, while wetting phase relative permeability exhibits Corey-type behavior, resulting in m-shaped relative permeability curves. Similar curves have been reported in the literature, but have not been demonstrated for real fractures. It has been revealed that the new m-type and traditional Xtype relative permeability curves are appropriate for describing two-phase flows through subsurface fractures.

“…Under the cubic law assumption, a unidirectional flow of phase i through a horizontal fracture may be described as follows:

Q_{i} = \frac{W \cdot a_{e f f, i}^{3} \cdot Δ P_{i}}{12 \cdot μ_{i} \cdot L},

Q_{i} = \frac{W \cdot a_{e f f, i}^{3}}{12 \cdot μ_{i} \cdot L} \cdot \frac{P_{i n, i}^{2} - P_{o u t, i}^{2}}{2 P_{o u t, i}},

k_{e f f, i} = \frac{a_{e f f, i}^{2}}{12},

k_{r, i} = \frac{k_{e f f, i}}{k},

where k eff,i , k r,i , and k are the effective and relative permeabilities of phase i and the intrinsic permeability, respectively.…”

Section: Experimental and Numerical Methodsmentioning

confidence: 99%

New ν‐type relative permeability curves for two‐phase flows through subsurface fractures

Watanabe

Sakurai

Ishibashi

et al. 2015

“…The commonly used equations to model steady state laminar two‐phase flow in a single fracture are the generalized Darcy equations. For the water phase, To take the compressibility effect of the gas into account, the gas phase equation must be written in the following form [ Scheidegger , 1974]: where subscripts l and g stand for liquid and gas, respectively, p i and p o are the pressures at the inlet and the outlet of the fracture, u is the superficial velocity or the Darcy velocity (flow rate per unit of cross‐section area), μ is the dynamic viscosity, L is the fracture length, k abs is the absolute permeability, and k rl and k rg are the relative permeabilities of the liquid and the gas, respectively.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of liquid‐gas flow structure effects on relative permeabilities in a fracture

Chen

Horne

Fourar

2004

[1] Two-phase flow through fractured media is important in geothermal, nuclear, and petroleum applications. In this research an experimental apparatus was built to capture the unstable nature of the two-phase flow in a smooth-walled fracture and display the flow structures under different flow configurations in real time. The air-water relative permeability was obtained from experiment and showed deviation from the X curve behavior suggested by earlier studies. Through this work the relationship between the phase channel morphology and relative permeability in fractures was determined. A physical tortuous channel approach was proposed to quantify the effects of the flow structure. This approach could replicate the experimental results with a good accuracy. Other relative permeability models (viscous coupling model, X curve model, and Corey curve model) were also compared. Except for the viscous coupling model, these models did not interpret the experimental relative permeabilities as well as the proposed tortuous channel model. Hence we concluded that the two-phase relative permeability in fractures depends not only on liquid type and fracture geometry but also on the structure of the two-phase flow.

“…Theoretically, tortuosity decreases a system's conductivity or diffusivity by a factor τ −2 . The square is required because both the distance traveled, and the distance over which the gradient applies, are increased by the tortuosity [e.g., Scheidegger , 1960; Bear , 1972; Dykhuizen and Casey , 1989; Epstein , 1989; Moldrup et al , 2001]. But when relating tortuosity to time rather than to effective diffusivity, the effect of tortuosity must be squared again, because in diffusive processes the mean passage time scales with the square of the (chemical) path length.…”

Section: Resultsmentioning

confidence: 99%

Scale dependence of intragranular porosity, tortuosity, and diffusivity

Ewing

Liu

2010

[1] Diffusive exchange of solutes between intragranular pores and flowing water is a recognized but poorly understood contributor to dispersion. Intragranular porosity may also contribute to the "slow sorption" phenomenon. Intragranular pores may be sparsely interconnected, raising the possibility that accessible porosity and diffusive exchange are limited by pore connectivity. We used a pore-scale network model to examine pore connectivity effects on accessible porosity, tortuosity, and diffusivity in spherical particles. The diffusive process simulated was release of a nonsorbing solute initially at equilibrium with the surrounding solution. High-connectivity results were essentially identical to Crank's analytical solution. Low-connectivity results were consistent with observations reported in the literature, with solute released at early times more quickly than indicated by the analytical solution, and more slowly at late times. Values of accessible porosity, tortuosity, and diffusivity scaled with connection probability, distance to the sphere's exterior, and/or the sphere's radius, as predicted by percolation theory. When integrated into a conventional finite difference model, the scaling relationships provide a consistent and physically sound way to incorporate such nonuniformities into models of intragranular diffusion.Citation: Ewing, R. P., Q. Hu, and C. Liu (2010), Scale dependence of intragranular porosity, tortuosity, and diffusivity, Water Resour. Res., 46, W06513,