Study of the Effect of Wetting on Viscous Fingering Before and After Breakthrough by Lattice Boltzmann Simulations

We present a suite of numerical simulations of two-phase flow through a 2D model of a porous medium using the Rothman-Keller Lattice Boltzmann Method to study the effect of viscous fingering on the recovery factor as a function of viscosity ratio and wetting angle. This suite involves simulations spanning wetting angles from non-wetting to perfectly wetting and viscosity ratios spanning from 0.01 through 100. Each simulation is initialized with a porous model that is fully saturated with a "blue" fluid, and a "red" fluid is then injected from the left. The simulation parameters are set such that the capillary number is 10, well above the threshold for viscous fingering, and with a Reynolds number of 0.2 which is well below the transition to turbulence and small enough such that inertial effects are negligible. Each simulation involves the "red" fluid being injected from the left at a constant rate such in accord with the specified capillary number and Reynolds number until the red fluid breaks through the right side of the model. As expected, the dominant effect is the viscosity ratio, with narrow tendrils (viscous fingering) occurring for small viscosity ratios with M ≪ 1, and an almost linear front occurring for viscosity ratios above unity. The wetting angle is found to have a more subtle and complicated role. For low wetting angles (highly wetting injected fluids), the finger morphology is more rounded whereas for high wetting angles, the fingers become narrow. The effect of wettability on saturation (recovery factor) is more complex than the expected increase in recovery factor as the wetting angle is decreased, with specific wetting angles at certain viscosity ratios that optimize yield. This complex phase space landscape with hills, valleys and ridges suggests the dynamics of flow has a complex relationship with the geometry of the medium and hydrodynamical parameters, and hence recovery factors. This kind of behavior potentially has immense significance to Enhanced Oil Recovery (EOR). For the case of low viscosity ratio, the flow after breakthrough is localized mainly through narrow fingers but these evolve and broaden and the saturation continues to increase albeit at a reduced rate. For this reason, the recovery factor continues to increase after breakthrough and approaches over 90% after 10 times the breakthrough time.

Systematic Modelling of Unstable Displacement

Modelling unstable displacement is a challenge which may lead to large errors in reservoir simulations. Field scale coarse grid simulations therefore need to be anchored to more reliable fine grid models which capture fluid displacement instabilities in a physically correct manner. In this paper, a recently developed approach for accurately modelling viscous fingering has been applied to various types of unstable displacement. The method involves estimation of dispersivity of the porous medium and length scale of the model to determine the required size of the simulation grid cell. Fractional flow theory is then applied to obtain the correct saturation of the injected phase in the unstable fingers formed due to the adverse mobility ratio. Unstable displacement experiments have been history matched using 2D-imaging of in-situ saturation as a calibration of our method, before carrying out sensitivity calculations on the effect of fluid viscosity, and rock heterogeneity. Our modelling approach allows us to carry out simulations using a conventional numerical simulator using elementary numerical methods (e.g. single-point upstreaming). The methods used to model instability (Sorbie et al, 2020) was originally developed for immiscible water/oil systems. The current paper now presents new results applying this approach to unstable gas displacements, where adverse viscosity ratios may be even higher than in water/oil systems. The displacement with injected gas is shown to be influenced by mass exchanges between the gas and oil as the alternating fluids (water and gas) are injected in WAG processes. Swelling of fingers delay the gas front and WAG processes divert the injected gas and improve sweep efficiency. We have also modelled water-oil displacement at adverse mobility and shown the benefit which is obtained by reducing the instability by adding polymers to viscosify the injected water. The impact of rock heterogeneity has different effect depending on buoyancy forces and the degree of crossflow into the high permeable zones. This paper extends our novel approach to modelling the fine scale distribution of the injected fluids in adverse mobility ratio displacements. This approach has now been applied to both, gas/oil and water/oil systems where viscous fingering is present, either at extremely adverse mobility ratios and/or for reservoirs where the permeability field is very heterogeneous.

Modeling Acid Fracturing Treatments in Heterogeneous Carbonate Reservoirs

The goal of acid fracturing operations is to create enough fracture roughness through non-uniform acid etching on fracture surfaces such that the acid fracture can keep open and sustain a high enough acid fracture conductivity under the formation closure stress. A detailed description of the rough acid-fracture surfaces is required for accurately predicting the acid-fracture conductivity. In this paper, a 3D acid transport model was developed to compute the geometry of acid fracture for acid fracturing treatments. The developed model couples the acid fluid flow, reactive transport and rock dissolution in the fracture. We also included acid viscous fingering in our model since the viscous fingering mechanism is commonly applied in acid fracturing to achieve non-uniform acid etching. Carbonate reservoirs mainly consists of calcite and dolomite minerals but the mineral distribution can be quite heterogeneous. Based on the developed model, we analyzed the effect of mineral heterogeneity on the acid etching process. We compared the acid etching patterns in different carbonate reservoirs with different spatial distributions of calcite and dolomite minerals. We found that thin acid-etched channels can form in carbonate reservoirs with interbedded dolomite layers. When the reservoir heterogeneity does not favor growing thin acid-etched channels, we investigated how to utilize the acid viscous fingering technique to achieve the channeling etching pattern in such reservoirs. Through numerical simulations, we found that thin acid-etched channels can form inside acid viscous fingers. The regions between viscous fingers are left less etched and act as barriers to separate acid-etched channels. In acid fracturing treatments with viscous fingering, the etching pattern is largely dependent on the perforation spacing. With a proper perforation design, we can still achieve the channeling etching pattern even when the reservoir does not have interbedded dolomite layers.

Study of Fingering Dynamics of Two Immiscible Fluids in a Homogeneous Porous Medium with Considering Wettability Effects Using a Pore-Scale Multicomponent Lattice Boltzmann Model

In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M<1, the viscous fingering regime appears by driving the invading fluid through the pore structures due to the viscous force and capillary force. However, by increasing the dynamic viscosity ratio and the capillary number, the invading fluid penetrates even in smaller pores and the stable displacement regime occurs. By the increment of the capillary number, the pressure difference between the two sides of the porous medium increases, so that the pressure drop Δp along with the domain at θ=40∘ is more than that of computed for θ=80∘. The present study shows that the value of wetting fluid saturation Sw at θ=40∘ is larger than its value computed with θ=80∘ that is due to the more tendency of the hydrophilic medium to absorb the wetting fluid at θ=40∘. Also, it is found that the magnitude of Sw computed for both the contact angles is decreased by the increment of the viscosity ratio from Log(M)=−1 to 1. The present study demonstrates that the S-C LBM is an efficient and accurate computational method to quantitatively estimate the flow characteristics and interfacial dynamics through the porous medium.