A Two-Phase Flow Simulation of Discrete-Fractured Media using Mimetic Finite Difference Method - Volume 16 Issue 3 - Zhaoqin Huang, Xia Yan, Jun Yao

Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts.

Caves in fractured-vuggy reservoir usually contain lots of filling medium, so the two-phase flow in formations is the coupling of free flow and porous flow, and that usually leads to low oil recovery. Considering geological interpretation results, the physical filled cave models with different filling mediums are designed. Through physical experiment, the displacement mechanism between un-filled areas and the filling medium was studied. Based on the experiment model, we built a mathematical model of laminar two-phase coupling flow considering wettability of the porous media. The free fluid region was modeled using the Navier-Stokes and Cahn-Hilliard equations, and the two-phase flow in porous media used Darcy's theory. Extended BJS conditions were also applied at the coupling interface. The numerical simulation matched the experiment very well, so this numerical model can be used for two-phase flow in fracture-vuggy reservoir. In the simulations, fluid flow between inlet and outlet is free flow, so the pressure difference was relatively low compared with capillary pressure. In the process of water injection, the capillary resistance on the surface of oil-wet filling medium may hinder the oil-water gravity differentiation, leading to no fluid exchange on coupling interface and remaining oil in the filling medium. But for the water-wet filling medium, capillary force on the surface will coordinate with gravity. So it will lead to water imbibition and fluid exchange on the interface, high oil recovery will finally be reached at last.

A vug is a small cavity in a porous medium that is relatively larger than interparticle pore spaces. Vuggy porous media are common in carbonate petroleum reservoirs and karst aquifers. Although small, the vugs can significantly affect the porosity and permeability of a rock. The real rock cores and outcrops indicate that the cumulative size distributions of interparticle pores and vugs both follow the fractal scaling law. In this paper, a two-scale fractal permeability model for natural vuggy porous media is developed based on the fractal characteristics of interparticle pores and vugs. In the proposed model, the interparticle pores of rock matrix are described as a bundle of tortuous capillary tubes. The vugs are embedded in rock matrix and are regarded as equipotential bodies, which change the tortuosity of matrix capillary tubes. Then, different matching relations between matrix capillary tubes and vugs are conducted to predict the permeability of a vuggy porous medium. The results show that the predicted permeability varies within a certain range. The maximum permeability is the case of larger vugs matching with the larger capillary tubes, and the minimum permeability is the converse case. The most probable permeability is calculated based on a set of random matching relations by using the Monte Carlo method. The validity of the proposed model is verified by comparing with experimental results and reference data in the literature. The parameter sensitivity analysis indicates that the fractal dimension of capillary tubes and their tortuosity, and the maximum diameter of capillary tubes and vugs have significant effects on the predicted permeability.

For fault-controlled fractured-vuggy reservoirs, the development characteristics of bottom water flooding and water and gas injection flooding under multi-well conditions must be clarified due to the structural complexity. To address this issue, we designed and manufactured fault-controlled physical experimental models based on the geological model of Tarim Oilfield and conducted flooding experiments. The results demonstrate significant variations in bottom water flooding characteristics due to differences in flow capacity within fractures, cavity area in caves, and filled area in caves under different filling modes. Different bottom water rates exhibit varying abilities to overcome gravity and breakthrough capillary resistance, significantly impacting the bottom water flooding characteristics. During the bottom water flooding period, the positioning of production wells primarily affects the macroscopic sweep range, while the filling modes significantly influence the distribution of remaining oil within individual caves. Throughout the three periods of multi-well water and gas injection, the early water injection stage mainly focuses on mobilizing “insufficiently controlled remaining oil” and some “attic remaining oil,” and the middle gas injection stage primarily targets the attic remaining oil. Finally, the late water injection stage aims to lift the oil–gas–water interface and improve oil displacement efficiency. Furthermore, different water and gas flooding directions affect displacement resistance in each channel and the longitudinal sweep range. This paper identifies the direction for the life cycle production of fault-controlled fractured-vuggy reservoirs and presents a mechanistic explanation.