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Pore-to-Darcy scale upscaling of multiphase flow is one of the major unresolved problems in many fields of porous media research. While this problem involves very fundamental aspects, there are many practical and application-driven challenges as well, such as the accurate prediction of Darcy-scale multiphase effective properties, e.g., relative permeability by pore-scale flow simulation on the basis of the imaged pore geometry, e.g., via X-ray computed micro-tomography. Validation of pore-scale modeling methods against experimental data by comparison of measured against simulated relative permeability curves has proven to be insufficient. Comparison of the fluid topology, in particular, the non-wetting phase topology, is a much more reliable criteria as relative permeability shows a very strong correlation with connectivity. While percolation-based quasi-static modeling approaches operating in the capillary limit have proven moderately successful in drainage, they largely fail to predict fluid connectivity in imbibition. We show that a fully coupled visco-capillary simulation, using a free-energy based lattice Boltzmann approach, correctly predicts fluid connectivity in imbibition, which was not predicted correctly by a quasi-static approach in a previous study on the same dataset. The respective relative permeability data shows a close match with results from Darcy-scale core flooding experiments while there is a major mismatch from quasi-static approach. The results once more highlight the close connection between relative permeability and fluid topology and suggest that topological measures are much more meaningful validation criteria for pore-scale simulation. The results also show that the direct simulation approach described in this paper, using appropriate initial and boundary conditions, correctly predicts Darcy-scale effective properties.

We generate a novel reference dataset to quantify the impact of numerical solvers, boundary conditions, and simulation platforms. We consider a variety of microstructures ranging from idealized pipes to digital rocks. Pore throats of the digital rocks considered are large enough to be well resolved with state-of-the-art micro-computerized tomography technology. Permeability is computed using multiple numerical engines, 12 in total, including, Lattice-Boltzmann, computational fluid dynamics, voxel based, fast semi-analytical, and known empirical models. Thus, we provide a measure of uncertainty associated with flow computations of digital media. Moreover, the reference and standards dataset generated is the first of its kind and can be used to test and improve new fluid flow algorithms. We find that there is an overall good agreement between solvers for idealized cross-section shape pipes. As expected, the disagreement increases with increase in complexity of the pore space. Numerical solutions for pipes with sinusoidal variation of cross section show larger variability compared to pipes of constant cross-section shapes. We notice relatively larger variability in computed permeability of digital rocks with coefficient of variation (of up to 25%) in computed values between various solvers. Still, these differences are small given other subsurface uncertainties. The observed differences between solvers can be attributed to several causes including, differences in boundary conditions, numerical convergence criteria, and parameterization of fundamental physics equations. Solvers that perform additional meshing of irregular pore shapes require an additional step in practical workflows which involves skill and can introduce further uncertainty. Computation times for digital rocks vary from minutes to several days depending on the algorithm and available computational resources. We find that more stringent convergence criteria can improve solver accuracy but at the expense of longer computation time.

Intermittent fluid flow has recently been identified as an important transport mode for processes involving subsurface multiphase fluids such as CO 2 storage and natural gas production. However, due to experimental limitations, it has not been possible to identify why intermittency occurs at subsurface conditions and what the implications are for upscaled flow properties such as relative permeability. We address these questions with observations of nitrogen and brine flowing at steady-state through a carbonate rock. We overcome previous imaging limitations with high-speed (1s resolution), synchrotron-based X-ray micro-computed tomography combined with pressure measurements recorded while controlling fluid flux. We observe that intermittent fluid transport allows the non-wetting phase to flow through a more ramified network of pores, which would not be possible with connected pathway flow alone for the same flow rate. The volume of fluid intermittently fluctuating increases with capillary number, with the corresponding expansion of the flow network minimising the role of inertial forces in controlling flow even as the flow rate increases. Intermittent pathway flow sits energetically between laminar and turbulent through connected pathways. While a more ramified flow network favours lowered relative permeability, intermittency is more dissipative than laminar flow through connected pathways, and the relative permeability remains unchanged for low capillary numbers where the pore geometry controls the location of intermittency. However, as the capillary number increases further, the role of pore structure in controlling intermittency decreases which corresponds to an increase in relative permeability. These observations can serve as the basis of a model for the causal links between intermittent fluid flow, fluid distribution throughout the pore space, and the upscaled manifestation in relative permeability.

When nonwetting fluid displaces wetting fluid in a porous rock many rapid pore-scale displacement events occur. These events are often referred to as Haines jumps and any drainage process in porous media is an ensemble of such events. However, the relevance of Haines jumps for larger scale models is often questioned. A common counter argument is that the high fluid velocities caused by a Haines jump would average-out when a bulk representative volume is considered. In this work, we examine this counter argument in detail and investigate the transient dynamics that occur during a Haines jump. In order to obtain fluid–fluid displacement data in a porous geometry, we use a micromodel system equipped with a high speed camera and couple the results to a pore-scale modeling tool called the Direct HydroDynamic (DHD) simulator. We measure the duration of a Haines jump and the distance over which fluid velocities are influenced because this sets characteristic time and length scales for fluid–fluid displacement. The simulation results are validated against experimental data and then used to explore the influence of interfacial tension and nonwetting phase viscosity on the speed of a Haines jump. We find that the speed decreases with increasing nonwetting phase viscosity or decreasing interfacial tension; however, for the same capillary number the reduction in speed can differ by an order of magnitude or more depending on whether viscosity is increased or interfacial tension is reduced. Therefore, the results suggest that capillary number alone cannot explain pore-scale displacement. One reason for this is that the interfacial and viscous forces associated with fluid–fluid displacement act over different length scales, which are not accounted for in the pore-scale definition of capillary number. We also find by analyzing different pore morphologies that the characteristic time scale of a Haines jump is dependent on the spatial configuration of fluid prior to an event. Simulation results are then used to measure the velocity field surrounding a Haines jump and thus, measure the zone of influence, which extends over a distance greater than a single pore. Overall, we find that the time and length scales of a Haines jump are inversely proportional, which is important to consider when calculating the spatial and temporal averages of pore-scale parameters during fluid–fluid displacement.