We present a comprehensive dataset of two-phase flow Lattice-Boltzmann simulations, generated using over 100 million GPU hours, covering a wide range of wetting conditions, capillary numbers, and porous geometries. While multiphase flow has traditionally been studied through laboratory experiments, the growing power of computational simulations provides a scalable and efficient alternative. Our simulations, validated against synchrotron beamline experiments, reveal key insights into the effects of wettability, ganglion dynamics, and flow behaviors that can be used to either substantiate current upscaling theories or develop new approaches. The dataset includes 50 relative permeability curves and over 25,000 distinct fluid configurations. Acquiring equivalent data through experiments would be impractical using current techniques, and the computational resources required far exceed those typically available without direct access to high-performance facilities. This open-access dataset enables broad collaboration within the porous media research community and offers a valuable foundation for future studies on pore-scale transport, relative permeability prediction, and data-driven modeling approaches.

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number (Ca∼1×10−5), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

Summary Equinor has performed an extensive laboratory program using Cretaceous pre-salt carbonate samples from offshore Santos basin, Brazil to investigate oil recovery (EOR/IOR) mechanisms from low salinity water flooding. The program comprises a set of spontaneous imbibition experiments and uses high-resolution micro-CT to image the fluid distributions inside the cores. This way it is possible to observe in detail, the pore scale displacement mechanisms and saturation changes over time. The experiments show that the great salinity contrast between the formation brine and sea water yields an immediate and a gradual increase in water saturation inside the core with enhanced recovery of oil. Furthermore it gives rise to an osmosis process that leads to swelling of trapped formation water. This swelling causes a redistribution of fluids and increases the contact area inside the rock where wettability change can occur resulting further oil production. From these observations, it is concluded that both wettability change and osmosis contribute to enhance oil recovery and are not mutually exclusive. Indeed, the osmosis process can accelerate and enhance the wettability change which can be a powerful recovery method in pre-salt carbonate reservoirs that are naturally oil wet and contain formation water of very high salinity.

Direct pore scale simulations of two-fluid flow on digital rock images provide a promising tool to understand the role of surface wetting phenomena on flow and transport in geologic reservoirs. We present computational protocols that mimic conventional special core analysis laboratory (SCAL) experiments, which are implemented within the open source LBPM software package. Protocols are described to simulate unsteady displacement, steady-state flow at fixed saturation, and to mimic centrifuge experiments. These methods can be used to infer relative permeability and capillary curves, and otherwise understand two-fluid flow behavior based on first principles. Morphological tools are applied to assess image resolution, establish initial conditions, and instantiate surface wetting maps based on the distribution of fluids. Internal analysis tools are described that measure essential aspects of two-fluid flow, including fluid connectivity and surface measures, which are used to track transient aspects of the flow behavior as they occur during simulation. Computationally efficient workflows are developed by combining these components with a two-fluid lattice Boltzmann model to define hybrid methods that can accelerate computations by using morphological tools to incrementally evolve the pore-scale fluid distribution. We show that the described methods can be applied to recover expected trends due to the surface wetting properties based on flow simulation in Benntheimer sandstone.

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

Relative permeability and capillary pressure are key properties within special core analysis and provide crucial information for full field simulation models. These properties are traditionally obtained by multi-phase flow experiments, however pore scale modelling has during the last decade shown to add significant information as well as being less time-consuming to obtain.Pore scale modelling has been performed by using the lattice-Boltzmann method directly on the digital rock models obtained by high resolution micro-CT images on end-trims available when plugs are prepared for traditional SCAL-experiments. These digital rock models map the pore-structure and are used for direct simulations of two-phase flow to relative permeability curves.Various types of wettability conditions are introduced by a wettability map that opens for local variations of wettability on the pore space at the pore level. Focus have been to distribute realistic wettabilities representative for the Norwegian Continental Shelf which is experiencing weakly-wetting conditions and no strong preference neither to water nor oil. Spanning a realistic wettability-map and enabling flow in three directions, a large amount of relative permeability curves is obtained. The resulting relative permeabilities hence estimate the uncertainty of the obtained flow properties on a spatial but specific pore structure with varying, but realistic wettabilities.The obtained relative permeability curves are compared with results obtained by traditional SCAL-analysis on similar core material from the Norwegian Continental Shelf. The results are also compared with the SCAL-model provided for full field simulations for the same field. The results from the pore scale simulations are within the uncertainty span of the SCAL models, mimic the traditional SCAL-experiments and shows that pore scale modelling can provide a time- and cost-effective tool to provide SCAL-models with uncertainties.

We present a review of pore-scale simulations of immiscible fluid transport with focus on two of the most popular approaches: lattice Boltzmann modeling for direct simulations on digital models of the pore space and simulations on network models extracted from the pore space. This review focuses on covering basic theory and implementation strategies and gives the readers input and motivation to start their own pore-scale simulations and relate them to realistic porous media. We present a review of recent and relevant applications and how a digital workflow that combines advanced pore-scale imaging and simulations can give very useful input to different fields of science and industry, including reservoir characterization. Given the large span in methods and applications, this review does not aim to cover all methods or applications. However, it covers popular methods and describes to some extent their applicability to different types of transport problems.

Computation of two-phase flow in porous media with low capillary numbers is challenging due to slow convergence and the presence of spurious currents at the phase interfaces that are greater than the viscous flow. The relative permeability of such systems is a critical parameter for upscaling flow properties but requires steady state flow configurations at low capillary numbers; a computationally slow problem to calculate. By using a morphologically coupled multiphase Lattice Boltzmann Method (LBM), it is observed that phase distributions converge an order of magnitude faster (1,000-50,000 timesteps) than flow fields (250,000-350,000 timesteps) during capillary dominated regimes. The proposed method couples a quasi-static, morphological method with direct LBM simulation that combines the efficiency of morphological calculations with the accuracy of direct simulation. The system fluid distribution is initialised morphologically instead of using simulated forced primary drainage to reduce dynamic simulation time and remove saturation end effects. The approach preconditions the simulation towards steady state conditions and the LBM routine relaxes the phase distributions until phases are stable. The steady state velocity fields are obtained by solving for flow in each stable connected phase distribution with a fast Semi Analytical Laplace solver to overcome spurious currents. A morphological Shell Aggregation method is then applied, condensing the displacing phase as a shell over pre-existing phase distributions and allowed to again reach phase equilibrium. Results obtained from the simulations are consistent with experimental relative permeability curves and phase morphology obtained from Gildehauser sandstone. This method allows rapid computation of phase distributions and relative permeability for capillary dominated flows. Shell Aggregation typically reaches steady state within 50,000-150,000 LBM timesteps opposed to 250,000-350,000 by spinodal decomposition for the tested 500 cubed Bentheimer sandstone and 150 cubed sand pack samples. Solving for flow in each connected phase body after Shell Aggregation LBM reaches steady state is furthermore shown to require down to 1,000-10,000 LBM timesteps at the expense of some interfacial physics.

We have performed numerical pore scale simulations and detailed analysis of the resulting configuration, distribution and amount of residual oil in the pore space of a reservoir rock during and after water-flooding. The simulations were performed using a multiphase lattice-Boltzmann (LB) solver on a digital rock model which had been constructed from high-resolution 3D micro-CT images. The micro-CT images were acquired from a sandstone reservoir. Using this type of simulation it is possible to follow and map fluid configurations during displacement in detail, and thus analyze and quantify the fluid distributions inside the pores. In our study we looked at both water wet and intermediate wet conditions, each of which was simulated for four different interfacial tensions, giving rise to a total of eight simulated cases. In each case the final residual oil configuration was recorded after injecting approximately three pore volumes (PV) of water. We then identified individual oil clusters and computed statistics such as cluster length and size distribution. The results indicated that the interfacial tension has a clear impact on the residual oil saturation and configuration. This applies even for intermediate values of interfacial tension, i.e. not only ultra-low values. There are also clear differences between the water wet and the intermediate wet cases in terms of the production curves and oil cluster distribution. INTRODUCTION Although water flooding has been used for decades to recover oil, many questions and uncertainties remain with respect to oil recovery and trapping mechanisms at the pore scale. Wettability and the balance between viscous and capillary forces are major factors controlling the displacement and distribution of fluids in porous rocks, [1]. Several chemical enhanced oil recovery (EOR) techniques have been designed to increase the microscopic displacement efficiency and mobilize trapped oil by altering wettability and interfacial tension. The potential of such EOR methods depend strongly on the distribution of oil in the pore space. This, in turn, is closely linked to the cluster size and length on which a viscous pressure gradient can act [2].

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.

Digital pore scale images of the reservoir rocks from the Utsira formation have been modelled. The Utsira Formation on the Norwegian Continental Shelf that is already being used for CO2 sequestration. This is a saline sand aquifer of Miocene to early Pliocene age, which is covered by some 700 meters of shales and sands. The aquifer is large and CO2 is being injected into the aquifer at a depth of 1012 meters below the sea floor by a highly deviated 3 km long well from the Sleipner Field. Direct dynamic CO2/water simulations have been conducted with all relevant fluid and flow properties. From these simulations steady and un-steady state constitutive relations (relative permeability, end-point saturations) are obtained. Clear flow rate and viscosity effects are revealed from these data, which again affects the storage capabilities of the reservoir rocks.

Summary We present results from simulations of two-phase flow directly on digitized rock-microstructure images of porous media using a lattice Boltzmann (LB) method. The implemented method is performed on a D3Q19 lattice with fluid/fluid and fluid/solid interaction rules to handle interfacial tension and wetting properties. We demonstrate that the model accurately reproduces capillary and wetting effects in pores with a noncircular shape. The model is applied to study viscous coupling effects for two-phase concurrent annular flow in circular tubes. Simulated relative permeabilities for this case agree with analytical predictions and show that the nonwetting-phase relative permeability might greatly exceed unity when the wetting phase is less viscous than the nonwetting phase. Two-phase LB simulations are performed on microstructure images derived from X-ray microtomography and process-based reconstructions of Bentheimer sandstone. By imposing a flow regulator to control the capillary number of the flow, the LB model can closely mimic typical experimental setups, such as centrifuge capillary pressure and unsteady- and steady-state relative permeability measurements. Computed drainage capillary pressure curves are found to be in excellent agreement with experimental data. Simulated steady-state relative permeabilities at typical capillary numbers in the vicinity of 10−5 are in fair agreement with measured data. The simulations accurately reproduce the wetting-phase relative permeability but tend to underpredict the nonwetting-phase relative permeability at high wetting-phase saturations. We explain this by pointing to percolation threshold effects of the samples. For higher capillary numbers, we correctly observe increased relative permeability for the nonwetting phase caused by mobilization and flow of trapped fluid. It is concluded that the LB model is a powerful and promising tool for deriving physically meaningful constitutive relations directly from rock-microstructure images.

We propose that steady-state two-phase flow in porous media may be described through a formalism closely resembling equilibrium thermodynamics. This leads to a Monte Carlo method that will be highly efficient in studying two-phase flow under steady-state conditions numerically.

We report on experimental studies of steady-state two-phase flow in a quasi-two-dimensional porous medium. The wetting and the nonwetting phases are injected simultaneously from alternating inlet points into a Hele-Shaw cell containing one layer of randomly distributed glass beads, initially saturated with wetting fluid. The high viscous wetting phase and the low viscous nonwetting phase give a low viscosity ratio M=10(-4). Transient behavior of this system is observed in time and space. However, we find that at a certain distance behind the initial front a "local" steady-state develops, sharing the same properties as the later "global" steady state. In this state the nonwetting phase is fragmented into clusters, whose size distribution is shown to obey a scaling law, and the cutoff cluster size is found to be inversely proportional to the capillary number. The steady state is dominated by bubble dynamics, and we measure a power-law relationship between the pressure gradient and the capillary number. In fact, we demonstrate that there is a characteristic length scale in the system, depending on the capillary number through the pressure gradient that controls the steady-state dynamics.

Using numerical simulations, we study immiscible two-phase flow in a pore network reconstructed from Berea sandstone under flow conditions that are statistically invariant under translation. Under such conditions, the flow is a state function which is not dependent on initial conditions. We find a second-order phase transition resembling the phase inversion transition found in emulsions. The flow regimes under consideration are those of low surface tension-hence high capillary numbers Ca-where viscous forces dominate. Nevertheless, capillary forces are imminent, we observe a critical stage in saturation where the transition takes place. We determine polydispersity critical exponent tau=2.27+/-0.08 and find that the critical saturation depends on how fast the fluids flow.

We study experimentally the case of steady-state simultaneous two-phase flow in a quasi-two-dimensional porous media. The dynamics is dominated by the interplay between a viscous pressure field from the wetting fluid and bubble transport of a less viscous, nonwetting phase. In contrast with more studied displacement front systems, steady-state flow is in equilibrium, statistically speaking. The corresponding theoretical simplicity allows us to explain a data collapse in the cluster size distribution as well as the relation |nablaP| proportional, sqrt[Ca] between the pressure gradient in the system and the capillary number.

When immiscible wetting and nonwetting fluids move in parallel in a porous medium, an instability may occur at sufficiently high capillary numbers so that interfaces between the fluids initially held in place by the porous medium are mobilized. A boundary zone containing bubbles of both fluids evolves, which has a well-defined thickness. This zone moves at constant average speed toward the nonwetting fluid. A diffusive current of bubbles of nonwetting fluid into the wetting fluid is set up.