A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.
We use fast synchrotron x-ray microtomography to investigate the pore-scale dynamics of water injection in an oil-wet carbonate reservoir rock at subsurface conditions. We measure, in situ, the geometric contact angles to confirm the oil-wet nature of the rock and define the displacement contact angles using an energy-balance-based approach. We observe that the displacement of oil by water is a drainagelike process, where water advances as a connected front displacing oil in the center of the pores, confining the oil to wetting layers. The displacement is an invasion percolation process, where throats, the restrictions between pores, fill in order of size, with the largest available throats filled first. In our heterogeneous carbonate rock, the displacement is predominantly size controlled; wettability has a smaller effect, due to the wide range of pore and throat sizes, as well as largely oil-wet surfaces. Wettability only has an impact early in the displacement, where the less oil-wet pores fill by water first. We observe drainage associated pore-filling dynamics including Haines jumps and snap-off events. Haines jumps occur on single-and/or multiple-pore levels accompanied by the rearrangement of water in the pore space to allow the rapid filling. Snap-off events are observed both locally and distally and the capillary pressure of the trapped water ganglia is shown to reach a new capillary equilibrium state. We measure the curvature of the oil-water interface. We find that the total curvature, the sum of the curvatures in orthogonal directions, is negative, giving a negative capillary pressure, consistent with oil-wet conditions, where displacement occurs as the water pressure exceeds that of the oil. However, the product of the principal curvatures, the Gaussian curvature, is generally negative, meaning that water bulges into oil in one direction, while oil bulges into water in the other. A negative Gaussian curvature provides a topological quantification of the good connectivity of the phases throughout the displacement.
This paper presents a pore-scale model proposed for numerical simulation of fines migration in porous media. The model simulates the behavior of spherical particles with different radii in flow by coupling lattice Boltzmann method (LBM) as a computational fluid dynamics (CFD) solver for the simulation of the fluid flow with a rigid body physics engine responsible for the simulation of the particulate transports. To achieve this, the basic LBM algorithm was extended to treat the curved particle boundaries, and a fluid-particle force interaction was implemented in order to account for the exerted force acting on the particles by the fluid and subsequent particulate movements. The accuracy and reliability of the proposed numerical model were successfully validated by simulating Poiseuille flow and Stokes flow and comparing the simulation results with those of the analytical solution. Thereafter, it was employed to simulate the migration of fine particles through synthetic 2D porous media. The simulation results were also presented to investigate the influence of fines migration on the porosity and permeability of the medium, and more interestingly on the hydraulic tortuosity as a criterion for changes in preferential flow path. As will be shown, the developed numerical method is able to successfully capture major retention mechanisms responsible for fines migration associated formation damage including external cake formation by the large particles, internal cake formation by the small particles, pore plugging, and surface deposition. This work provides a framework for further investigations regarding pore-scale phenomena associated with fines migration in the porous media.
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