We developed a grain‐based pore‐scale model that tracks capillary‐stable positions of fluid–fluid interfaces (menisci) between grains of arbitrary wettability. The model explicitly calculates the stable menisci positions between two‐dimensional disks at particular capillary pressures. With changing capillary pressure, the menisci are tracked and conditions for menisci stability in a pore throat (Haines condition) or menisci merging in a pore body (Melrose condition) are elucidated. When a meniscus becomes unstable, a pore‐filling event occurs, and an invasion percolation routine is used to find the next stable position of the meniscus (or menisci). We tested the method on networks extracted from two‐dimensional porous media consisting of randomly distributed oil‐wet and water‐wet disks. The model is robust in that it handles both filling mechanisms simultaneously and seamlessly even across changes in capillary pressure from positive to negative values. We compared the results of the two‐dimensional model as a function of fractional wettability to experiments in fractionally wet packs. We found good qualitative agreement between the model and the experiments for a water–oil system on both imbibition and drainage.

We develop a grain based model for capillarity controlled displacement within 3D fractionally wet porous media. The model is based on a novel local calculation of the position of stable interfaces in contact with multiple grains. Each grain can have a different, arbitrary contact angle with the interface. The interface is assumed to be locally spherical for menisci separating the bulk non-wetting and wetting phases. The fluid/fluid interfaces between pairs of grains (surfaces of pendular rings) are assumed toroidal. Because the calculation of interface position is entirely local and grain-based, it provides a single, generalized, geometric basis for computing pore-filling events during drainage as well as imbibition. This generality is essential for modeling displacements in fractionally wet media. Pore filling occurs when an interface becomes unstable in a pore throat (analogous to Haines condition for drainage in a uniformly wet throat), when two or more interfaces come into contact and merge to form a single interface (analogous to the Melrose condition for imbibition in uniformly wet medium), or when a meniscus in a throat touches a nearby grain (a new stability criterion). The analytical solution for stable interface locations generalizes the Melrose and Haines criteria previously validated for pore-level imbibition and drainage events in uniformly wet media. The concept of tracking the fluid/fluid interface on each grain means that a traditional pore network is not used in the model. The calculation of phase saturation or other quantities that are conveniently computed in a network can be done with any approach for defining pore bodies and throats (e.g. Delaunay tessellation, Voronoi tessellation, and medial axis methods). The fluid/fluid interfaces are mapped from the grain-based model to the network as needed. In addition, the model is robust as there is no difference in the model between drainage and imbibition, as all criteria are accounted for both increasing and decreasing capillary pressure. To validate the model, we perform a series of drainage/imbibition experiments (oil/water) on fractionally wetted porous media prepared by mixing oil-wet grains with water-wet grains. In both experimental and simulation results, the drainage/imbibition curves shifts to lower capillary pressure with increasing fraction of oil-wet grains. Using the model, we delineate which pore filling criteria occur as a function of initial wetting phase and wettability of grains. The shape and position of the pressure-saturation curve is shown to be a function of the pore filling types, and hysteresis arises naturally from the model. Introduction A rock containing immiscible fluids is wetted by the fluid that has smaller surface energy of interaction with the rock (Dullien 1992). Consequently the wettability of reservoir rocks determines the distribution of fluids within the pore space of the rock (Anderson 1987a; Anderson 1987b). Fluid distribution at the pore scale is important because this affects the macroscopic rock/fluid properties such as capillary pressure curves and relative permeability curves. Many rock minerals have a tendency to be wetted by water, and thus reservoir rocks are typically water-wet before they are filled with oil. However, chemical species within the oil that are charged can change the wettability of the reservoir rocks to oil-wet during geological time (Salathiel 1973). Reservoirs can be partly oil-wet and partly water-wet due to wettability alteration, which occurs on the part of the reservoir rock that is exposed to the crude oil (Salathiel 1973). This altered state is referred to in the literature variously as heterogeneous wettability (Laroche et al. 1999), fractionally wettability (Tsakiroglou and Fleury 1999) and mixed wettability (Van Dijke et al. 2000; van Dijke and Sorbie 2003; Al-Futaisi and Patzek 2004; Valvatne and Blunt 2004).

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One of the most common field development plans in shale plays involves drilling lease/acreage retention wells in different areas followed by coming back and drilling infill wells. In majority of these shale plays, job sizes for hydraulic fracturing treatment are getting bigger over time in order to achieve more volume as well as value. However, due to depletion, there exists a pressure sink around the older existing producers and that significantly increases the possibility of older well getting "frac-hit" by new stimulation, and receiving large volume of frac fluid. Frac-hits can easily be seen using pressure gauges in older wells, and other surveillance techniques including chemical/RA tracers, microseismic, etc. One of the other "interference" effects that change the behaviour of parent well is refracturing. Operators are identifying candidates that were either poorly stimulated initially or have lost productivity over their life, and are refracturing those wells. In both frac-hits and refracs, there is a change in well productivity; and understanding and quantifying this loss/gain in production still remains challenging. In this paper, both analytical and numerical modeling techniques were used to explore the existing workflows and techniques in the literature to study frac-hits and refracs. Rate transient analysis (RTA) was used to complement the numerical reservoir simulation models. Flow regimes were identified on superposition time plots using RTA (linear flow regime, boundary-dominated regime), and numerous sensitivities were run on the frac-hit/refrac timing, reservoir matrix permeability. Frac-hit examples from Eagle Ford shale were examined. This paper studies the existing RTA techniques to model frac-hits/refracs and compares them with the new technique proposed herein. It was observed that RTA models needed to be re-initialized to model post frac-hit or refrac behaviour to correctly quantify the changes in SRV. It is shown that although the existing techniques work reasonably well at low matrix permeability, the error margin goes up as the permeability increases. In Eagle Ford, the permeability is high enough to warrant using this new analysis method. Existing analyses methods primarily use diagnostic plots (superposition time) and are only applicable to frac-hits or refracs prior to boundary dominated flow (BDF) regime. This proposed method is valid over different flow regimes & larger permeability ranges. The analysis method recommended in this study allows the operators to better analyse the efficiency and benefits of their refracs, as well as detrimental impact of frac-hits from infilling and downspacing the wells.

Summary In tight-gas sandstone, the productivity of a well is sometimes quite different from that of a nearby well. Several mechanisms for this observation have been advanced. Of interest in this paper is the possibility that a small change in water saturation can change the gas-phase permeability significantly in rocks with small porosity and very small permeability. We quantify the effect of small saturations of the wetting phase on nonwetting-phase relative permeability by modeling the geometry of the wetting phase. We also show how a porosity-reducing process relevant in tight-gas sandstones magnifies this effect. The basis for these observations is a model of the grain-scale geometry of low-porosity sandstones. The model is built from a dense random packing of spheres modified geometrically to simulate quartz-overgrowth cementation. To compute phase geometry and permeability, we use a physically representative network model extracted from the model rock. At small saturations (at or near the drainage endpoint), the wetting phase exists largely in the form of pendular rings held at grain contacts. Pore throats correspond to the constriction between groups of three grains, each pair of which can be in contact. Thus, the existence of these pendular rings decreases the void area available for flowing nonwetting phase. Because the hydraulic conductance of the throat varies with the square of the void area, the effect on permeability is disproportionate to the volume occupied by the rings. Convention holds that connate water has little effect on oil or gas permeability because it occupies the smaller pores. Comparing predictions for unconsolidated model rocks with those for cemented model rocks allows one to reconcile this view with the sensitivity reported in the field and the laboratory. Introduction In tight-gas sandstone, the productivity of a well is sometimes quite different from that of a nearby well. Wells also can be very sensitive to small amounts of water, whether from an aquifer associated with the reservoir, from hydraulic fracturing, or from other completion operations. Although the effect of water saturation on the effective permeability to gas has been the subject of numerous experiments (Byrnes et al. 1979; Jones and Owens 1980; Sampth and Keighin 1982; Walls et al. 1982; Ward and Morrow 1987; Chowdiah 1988), a fully mechanistic explanation has not yet been offered for why the effect appears larger in tight-gas reservoirs. In this paper, we explore the possibility that the grain-scale geometry of tight gas is responsible. Small wetting saturation is mainly an irreducible wetting phase that exists in two morphologies (Bryant and Johnson 2003). One is volumes of water held in the smallest pores. The other is pendular rings held at grain contacts or liquid bridges held between two grains separated by a gap. The former forces gas to flow around the filled pores, decreasing the average connectivity of the gas phase. The latter reduces the area open to gas (the nonwetting phase) as it passes through a pore throat. It is possible to quantify the effects of these topological and geometrical changes on gas-phase permeability with the methods described in the next section. The important feature of the method is that its input is based on a geologic description (sorting, type, and extent of cementation). Thus, the insights gained can be useful in explaining regional variations in well performance, if regional trends in diagenetic alteration are known.