Pore Network Modeling of Two Phase Flow in Vuggy Carbonates

Abstract

Carbonate reservoirs have more complex structures than silicate reservoirs because of depositional and diagenetic features. Secondary porosity enhancements due to fracturing or dissolution processes result complex porosity systems and thus complex flow patterns. Carbonates may contain not only matrix and fracture but also the vugs and cavities that are irregular in shape and vary in size from millimeters to centimeters in diameter. Although many of these vugs appear to be isolated from fractures, the mechanism of oil recovery from vugs in such a system is highly dependent on the location of the vugs and connections of the vugs to the matrix. Studies on pore network models of carbonate rocks available in literature generally consider regular grain lattices, disregarding secondary porosity features. In this study, two phase flow in vuggy carbonates was studied by developing a novel pore network model. The constructed model consists of matrix and vug sub-networks. Matrix blocks were constructed by pores with triangular crosssection and pore throats with circular cross-section where as vugs were represented by square cross-sections. By distributing pore and pore throat radii randomly, a spatially uncorrelated model was developed. It was observed that this model can successfully simulate primary drainage and secondary imbibition recovery processes like snap-off, piston like advance and pore body filling. Comparison of pore network results and several published experimental results showed the uses and applications of the proposed pore network model. It was concluded that this novel pore network model design successfully represents two phase flow in a vuggy carbonate rock. Introduction Understanding flow mechanisms and wettability behavior in porous media is crucial in estimating hydrocarbon recovery. Since relative permeability is significantly affected by wettability and pore structure, conventional experimental methods are not sufficient to elucidate the dependence of relative permeability on wettability. Thus, pore scale modeling of flow in porous media by assigning appropriate wettability conditions, can yield adequate results for relative permeability values and reasonable explanations for wettability effects. During the primary stages of pore scale modeling, sphere pack and bundle of tubes, approaches were utilized and use of pore networks in flow modeling was started by Fatt (1956)1,2,3. In his study, a pore network model, by combining both sphere pack and bundle of tubes approaches was proposed, and capillary pressure curves were obtained from pore network. After the pioneering study of Fatt (1956) 1,2,3, usage of pore network models and micro models became more popular in determination of relative permeability and capillary pressure curves. Enhancements in percolation theory for modeling flow properties (Heiba et al., 1983)4 and pore space extraction methods (Oren et al., 1997)5 were embedded in pore scale modeling studies and the use pore networks improved. Percolation theory was implemented in pore scale flow modeling studies for investigating effects of wettability on two phase relative permeability by using a Bethe network (Heiba et al., 1983)4. Also, by using the improvements in pore space extraction methods, Oren et al. (1997)5 successfully reconstructed a pore network for sandstones and by using extracted pore network model, capillary pressure and relative permeability curves were derived. They obtained good agreement with the experimental results of primary drainage and imbibition for both water wet and mixed wet porous media. Blunt (1997)6 examined the effects of wettability at pore scale by simulating displacement mechanisms, primary drainage, water injection and oil re-injection. By using different contact angle ranges for implementing wettability effects and different fractions of oil wet, water wet and mixed wet pores based on Kovscek et al. (1992)7, importance of oil films and wettability alteration on recovery was investigated. Three phase flow properties in mixed-wet porous media and the corresponding fluid configurations at pore scale were examined by Hui and Blunt (2000)8. They simulated primary drainage, waterflooding and gas injection. Three phase relative permeability curves obtained for a model consisted of triangular pores with different inscribed radiuses. They also examined effects of oil layer drainage and wettability (water wet, oil wet, gas wet and fractionally wet) on relative permeability and oil recovery.

Relative Permeability Measurement and Two-Phase Flow Visualization in Micromodels of Vugular Porous Media

“…This phase preferentially flows through the vugular space and connects the porous media. As expected, it has also been reported that the wetting phase preferentially saturates the porous matrix, and therefore its relative permeability is not significantly altered by the inclusion of vugs [9,32,69].…”

“…Numerical studies on 3D digital vuggy rocks have emulated the observations from the experimental studies described above, especially, in terms of early water breakthrough, strong anisotropy, hysteresis, and changes in the dynamics of pressure drop and flow pathways during waterflooding [14,24,69]. In addition, it has already been observed that the inclusion of vugs in the porous matrix has a significant impact on the relative permeability of the nonwetting phase, even in media with isolated vugs.…”

“…The experimental study conducted by Kusanagi et al [21] on vuggy carbonate rocks had already reported alterations in the shape of steady-state non-wetting phase relative permeability curves and their dependence on vug connectivity. However, direct comparisons with the relative permeability of the porous matrix without vugs have only been conducted through theoretical studies by Moctezuma-Berthier et al [9] and Akin and Erzeybek [69]. In our microfluidic approach to an oil-wet vugular porous medium, increases in the relative permeability to the non-wetting phase and no changes in the relative permeability to the wetting phase are evidenced for the first time with respect to an identical porous medium without vugs.…”

“…Concerning a rock with larger vug pores having 2D fracture-like distributions, the curve resulted in a straight line, like the X-shaped model usually used to represent the relative permeability in fractured porous media [70]. In that context, Akin and Erzeybek [69] using a 3D pore network model, postulated that when two or more vugs are close to each other or a vug is significantly longer than the other elements in the porous network, the medium acts as a fracture one leading to a nearly straight relative permeability curve.…”

“…However, despite best efforts, up to now it has not been possible to experimentally and systematically correlate the macroscopic behavior of two-phase flow observed in vugular porous media with pore-scale physics, and to make comparisons with respect to the behavior of an equivalent porous matrix without vugs. In core flooding experiments, due to difficulties in scanning the fluid flow at the pore scale and obtaining reliable samples [14,21]; and, in experiments on rock models, due to gross assumptions that limit the realism and, more importantly, to lack of information on the phase distribution throughout the porous medium [9,32,69].…”