Pore-scale simulation of remaining oil distribution in 3D porous media affected by wettability and capillarity based on volume of fluid method

Highlights

• Direct pore-scale modelling of two-phase flow in three-dimensional porous media by VOF method.

• The evolution of remaining oil was investigated by considering wettability, viscous force and capillary number.

• Phase circulation phenomenon was simulated and two circulation patterns were found which can be interconverted.

• Preferred conditions for improving the oil recovery rate was discussed in detail.

Abstract

Characterizing the trapped phase in porous media is essential for many engineering applications, such as enhanced oil recovery, nuclear storage, and geological sequestration of CO₂. This study aims to study the distribution, evolution, and influencing factors of the remaining oil in the process of water flooding at the pore scale. The single-connected pore space model was established by reconstructing the real micron CT scanned images of carbonate rocks. The VOF (volume of fluid) method using FSF (filtered surface force) formulation was adopted on OpenFOAM platform to simulate the oil-water two-phase flow process at the pore scale. Different wettability and capillary number were considered in the model. The accuracy of the model was proved by comparing with previous experimental results. The results showed that in the process of water flooding, the complex pore structure would lead to the generation of remaining oil, and the phase circulation phenomenon can be observed in the remaining oil and presents two distribution forms: co-current driven flow and lid-cavity driven flow. It also revealed that the phase recirculation increases the viscous dissipation. Further research also showed that the two forms of recirculation could be transferred by changing the wettability and that a higher capillary number was more beneficial for reducing the remaining oil saturation.

Introduction

Understanding multiphase flow in porous media is essential in various fields, such as enhanced oil recovery, groundwater remediation, nuclear storage, and geological sequestration of CO₂ (Herring et al., 2013; Iglauer et al., 2011; O'Neill and Mudawar, 2020; Wang et al., 2020; Yang et al., 2020b). Water flooding is a common method to enhance oil recovery in the petroleum industry while taking advantage of water injection can displace oil out of formation and profoundly enhance the oil recovery. Water and oil flow in reservoir formation is a typical scenario of multiphase flow in porous media. Multiphase flow in porous media controlled by capillary forces, viscous forces, and gravitational forces involves complex fluid dynamics, including the rising and shrinking of fluid interfaces and phase-changing behavior. Those complex fluid dynamics bring forth the remaining oil in pore space, thus reducing the recovery rate. Therefore, a pore scale model addressing the formation and mobilization of remaining oil in pore space is essential.

One of the major challenges in characterizing the porous media of rocks is how to show the pore structure characteristics of rocks and the flow behavior of fluids on the micro-scale ($10^{-6}\sim 10^{-9}m$). Digital rock physics (DRP) (Andrew et al., 2014; Blunt et al., 2013; Gao et al., 2017; Liu et al., 2017; Yang et al., 2019b) has emerged in the past decade as a potential way to address the challenge in combination with the use of X-ray computer tomography ($\mu \text{CT}$) and computational methods to generate numerical models of fluid flows in real rocks. At the pore scale, several methods have been developed to model the two-phase flow in porous media, mainly including the Pore Network Model (PNM) (Blunt, 2001; Chandler et al., 1982; Li et al., 2014; Song et al., 2020; Wenhui et al., 2018; Yang et al., 2019a), the Lattice Boltzmann Method (LBM) (Tang et al., 2018; Yang et al., 2018; Yang et al., 2019c; Zhang et al., 2019; Zhao et al., 2016), the Lattice Boltzmann Methods for Porous Media (LBPM) (McClure et al., 2021), the Direct Hydrodynamic simulation (DHD) (Koroteev et al., 2014), the grid-independent Smoothed Particle Hydrodynamics method (SPH) (Yang et al., 2020a), grid-based methods, including Finite Volume Method (FVM) (Alizadeh and Fatemi, 2021; Shams et al., 2018) and Finite Element Method (FEM) (Wang et al., 2019; Yang et al., 2021). Grid-based methods are often used in conjunction with various algorithms to simulate fluid-fluid interfaces, such as Volume of Fluid methods (VOF) (Ferrari and Lunati, 2013; Pinilla et al., 2021; Raeini et al., 2015; Raeini et al., 2012; Renardy et al., 2001), Level Set methods (LS) (Ferrari et al., 2017), and Phase Field method (PF) (Zhang et al., 2021; Zhu et al., 2019a; Zhu et al., 2019b). In recent years, some researchers have even extended the study of pore scale two-phase flow to molecular scale by applying molecular simulation methods (Li et al., 2019; Moud et al., 2019; Song et al., 2018; Yang et al., 2020c). PNM is effective in the calculation because it simplifies the geometric and physical properties of a model. The advantage of LBM is that no explicit interface tracking or contact angle model is required, but numerical instability may occur when simulating multiphase flow with a high density and viscosity ratio. The advantages of the grid-independent method are high stability, easy to implement, and the ability to handle complex interface motions. However, it is not always possible to compute efficiently when dealing with large three-dimensional systems. The VOF method's advantage is that the volume fraction is introduced to represent the phase interface implicitly. The method does not require a complex phase interface tracking algorithm, which is very important for calculating two-phase flow modeled by complex geometric shapes, especially in porous media.

Researchers tend to apply those numerical models to analyze the flow of two-phase fluid in porous media through obtaining the relative permeability curve (Xu et al., 2016), which has been proved to be an effective method. The influence of rock wettability and capillary number on the flow of two-phase fluid can be reflected on the relative permeability curve, manifested as the change of percolation capacity of two-phase fluid, thus showing different distribution patterns of the relative permeability curve (Fan et al., 2019). The conventional ways of analysis tend to focus on the overall properties. There are complex interfacial phenomena, velocity distribution patterns, interfacial drag force, capillary force, and so on in the single pore space flow, which we definitely cannot ignore. As for the remaining oil in the pore space, recirculation phenomena were reported in many published works (Alamooti et al., 2020; Crevacore et al., 2016; Roman et al., 2020; Zhou et al., 2019), which shows different properties under different conditions, and these properties will greatly affect the distribution of the remaining oil, thus affecting the recovery rate (as shown in Fig. 1). At the same time the drag force on the interface also affects the distribution of remaining oil.

Heshmati and Piri (2018) studied the occupancy rate and velocity field of pore fluid under the condition of two-phase flow in different micromodels and believed that there is a slip boundary between two-phase fluids in porous media. The fluid interface and injection velocity together have an impact on the occurrence state of the displaced phase. Raeini et al. (2014) simulated the two-phase flow using the VOF method and studied the effect of snap-off and layer flow in corner space of porous media; on this basis, the introduction of the concept of capillary field, the characterization of capillary force, makes the study of the influence of pore structure on a larger scale fluid flow possible. Guo et al. (2019) simulated the remaining oil distribution in porous media under different wetting conditions by applying the phase-field method and show that water-wet condition is the preferred condition to improve oil recovery when performing water flooding. Zhou et al. (2019) simulated the flow field and transport field in two-dimensional rough fractures and analyzed the mass transfer process in fractured porous media. The results had shown that when recirculation zones were present in the flow field, it could act as a retention area to affect the transport processes at the main flow channel profoundly and usually appeared near the fluid-solid boundary, such as rough fracture walls. Roman et al. (2020) have also found out that when fluids flowing in pore space, the interface between fluids can also exist in two forms: one interface is similar to the concrete wall, resulting in the formation of remaining oil in the pore corner space; another interface can generate recirculation inside the remaining oil in the corner space, dragging the oil phase out of the corner and finally affecting the occurrence of the oil phase

In general, previous research works lacks the discussion on the role of recirculation inside oil clusters. They have not discussed how to mobilize the oil clusters when considering other properties. Previous research works mainly focus on the velocity profile inside the trapped phase. The impact of wettability, capillary number and the drag force on the interfaces has not been studied well.

In our research work, the VOF method using the FSF (filtered surface force) interface model and OpenFOAM, a well-known and widely used open-source CFD (computational fluid dynamics) software, was used to simulate the flow process of oil-water two-phase in the single-connected pore space model extracted from a carbonate digital core. To prevent non-physical numerical solutions from appearing in the model, we set the simulation time step to be $1\times 10^{-6}$s. PISO (Pressure-Implicit with Splitting of Operators) algorithm was used for coupling velocity, pressure, and volume fraction. The pore space model was reconstructed and built from the micro-CT scanned image of carbonate rock from the Feixianguan formation deposited at Triassic age. Using micro-CT scanning technology, we obtained a scanned image of the carbonate rock. A section reflecting the characteristics of pore structure was extracted from the scanned core images, a single-connected pore space model was established, and a grid was built for it. We simulated the two-phase flow on the model and studied the flow behavior under different wettability. Simultaneously, the formation process of remaining oil in pore space under different wettability conditions is also analyzed. Finally, the influence of different capillary number on two-phase flow was studied.

The following parts of this paper are organized as follows: Section 2 introduces the applied methodology, the setup process of the porous media model, and numerical model details. Section 3 discusses the validity of the model and the simulation results. Section 4 summarizes the conclusions of this work.