Quasi-static imbibition was simulated using random and correlated stochastic network models. Using the snap-off pore-scale displacement observed by Lernormand et al. (1983) the effects of many parameters on relative permeabilities and residual saturation reported in the literature were reproduced and explained. Increased relative permeabilities and decreased residual non-wetting phase saturation were the results of an increased contact angle (Li and Wardlaw, 1986b;Gauglitz and Radke, 1990;Blunt et al., 1992; Mogensen and Stenby, 1998) a decreased pore-throat aspect ratio, the presence of long-range pore-pore size correlations (Iaonnidis and Chatzis, 1993;Blunt, 1997a), or local pore-throat correlations (Jerauld and Salter, 1990; Iaonnidis and Chatzis, 1993). By modifying the level of snap-off, or its spatial distribution, these parameters varied the efficiency of the displacement patterns and ultimately affect relative permeabilities and residual saturations. Mani and Mohanty (1999) performed simulations on networks with infinite-ranged fractional Brownian motion (fBm) correlations and reported trends of relative permeabilities and residual saturations that were opposite to others' results (Ioannidis and Chatzis, 1993;Blunt, 1997a). Applying a cut-off length to the fBm correlations reversed Mani and Mohanty's trends to conform with the common observations.
NomenclatureA input parameters, m g hydraulic conductance, m 3 s −1 Pa −1 k permeability, m 2 N number of vertices of polygon assumed as shape of pores and throats P pressure, Pa q flow rate, m 3 s −1 r inscribed-circle radius, m R capillary radius for cooperative pore-filling, m S saturation, fraction x random number in [0,1]
In a previous study Arns et al. (2004, Transport Porous Media 55, 21-46) we considered the role of topology on drainage relative permeability curves computed using network models derived from a suite of tomographic images of Fontainebleau sandstone. The present study extends the analysis to more complex imbibition displacements where the non-wetting fluid can be disconnected by snap-off as a result of swelling of wetting films in the corners of pores and throats. In contrast to the findings for drainage displacements which showed that relative permeabilities are significantly affected by network topology, the present study shows that the effect of topology on imbibition relative permeabilities depends on the level of snap-off. For strongly wetting conditions where snap-off dominates the displacement the effect of network topology is significantly smaller than for weakly wet conditions where snap-off is suppressed. For contact angles sufficiently large to completely suppress snap-off, the effect of topology on imbibition relative permeabilities is similar to that for drainage displacements. The findings are valid for random networks and for networks displaying short-range pore-throat and longer range spatial correlations.
The modern hydraulic fracturing technique was implemented in the oil and gas industry in the 1940s. Since then, it has been used extensively as a method of stimulation in unconventional reservoirs in order to enhance hydrocarbon recovery. Advances in directional drilling technology in shale reservoirs allowed hydraulic fracturing to become an extensively common practice worldwide. Fracturing technology can be classified according to the type of the fracturing fluid with respect to the well orientation into vertical, inclined, or horizontal well fracturing. Depth, natural fractures, well completion technology, capacity, and formation sensitivity of a shale reservoir all play a role in the selection of fracturing fluid and fracturing orientation. At present, the most commonly used technologies are multi-section fracturing, hydra-jet fracturing, fracture network fracturing, re-fracturing, simultaneous fracturing, and CO 2 and N 2 fracturing. This chapter briefly reviews the technologies used in shale reservoir fracturing.
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