Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

Based on thermodynamic considerations we derive a set of equations relating the seepage velocities of the fluid components in immiscible and incompressible two-phase flow in porous media. They necessitate the introduction of a new velocity function, the co-moving velocity. This velocity function is a characteristic of the porous medium. Together with a constitutive relation between the velocities and the driving forces, such as the pressure gradient, these equations form a closed set. We solve four versions of the capillary tube model analytically using this theory. We test the theory numerically on a network model.

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number Ca, and at Ca ∼ 10 −8 the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method. method [2, 3] to keep track of the fluid interface locations, have been used. The lattice-Boltzmann method is another popular choice, see e.g. [4]. These methods can provide detailed information on the flow in each pore. They are, however, computationally intensive and this restricts their use to relatively small systems.Pore network models have proven to be useful in order to reduce the computational cost [5], or enable the study of larger systems, while still retaining some pore-level detail. In these models, the pore space is partitioned into volume elements that are typically the size of a single pore or throat. The average flow properties in these elements are then considered, without taking into account the variation in flow properties within each element.Pore network models are typically classified as either quasi-static or dynamic. The quasi-static models are intended for situations where flow rates are low, and viscous pressure drops are neglected on the grounds that capillary forces are assumed to dominate at all times. In the quasi-static models by Lenormand et al. [6], Wilkinson and Willemsen [7] and Blunt [8], the displacement of one fluid by the other proceeds by the filling of one pore at the time, and the sequence of pore filling is determined by the capillary entry pressure alone.The dynamic models, on the other hand, account for the viscous pressure drops and thus capture the interaction between viscous and capillary forces. As three examples of such models, we mention those by Hammond and Unsal [5], Joekar-Niasar et al.[9] and Aker et al. [10]. A thorough review of dynamic pore network models was performed by Joekar-Niasar and Hassanizadeh [11].The pore network model we consider here is of the dynamic type that was first pre...

We present in detail a set of algorithms for a dynamic pore-network model of immiscible two-phase flow in porous media to carry out fluid displacements in pores. The algorithms are universal for regular and irregular pore networks in two or three dimensions and can be applied to simulate both drainage displacements and steady-state flow. They execute the mixing of incoming fluids at the network nodes, then distribute them to the outgoing links and perform the coalescence of bubbles. Implementing these algorithms in a dynamic pore-network model, we reproduce some of the fundamental results of transient and steady-state two-phase flow in porous media. For drainage displacements, we show that the model can reproduce the flow patterns corresponding to viscous fingering, capillary fingering and stable displacement by varying the capillary number and viscosity ratio. For steady-state flow, we verify non-linear rheological properties and transition to linear Darcy behavior while increasing the flow rate. Finally we verify the relations between seepage velocities of two-phase flow in porous media considering both disordered regular networks and irregular networks reconstructed from real samples.

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a twodimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm. B Alex HansenAlex.Hansen@ntnu.no Isha Savani