Fine-grid Simulations Research Articles

Why gravity improves waterflood recovery in oil-wet and mixed-wet reservoirs

Most past experimental and numerical research on water flooding has demonstrated a reduction in oil recovery in gravity dominated flow: gravity leads to the water slumping to the bottom of the reservoir with earlier water breakthrough and poor sweep efficiency. However, these studies were all performed on strongly water-wet systems: wherever the water has gone, the oil is at residual saturation so a reduction in sweep efficiency gives a reduction in recovery. In reality few if any reservoirs are strongly water-wet. If the rock is mixed or oil-wet, gravity improves the local displacement efficiency. Gravity reduces the mobility of injected water forcing downward water movement and better oil displacement laterally. When gravity dominates, once water reaches the bottom of the reservoir, it moves upwards in a gravity-stable displacement, with improved local displacement efficiency that can be quantified by linear Buckley-Leverett analysis. We show, using fine-grid simulations of water flooding in a two-dimensional homogeneous vertical cross-section with typical fluid and rock properties, that the overall recovery after ∼0.3 pore volumes of water injected is higher than without gravity for heavy oil-wet (unfavourable mobility) applications. This improvement is greater in light oil-wet (favourable mobility) applications and occurs even before water breakthrough counteracting the negative effect of poor sweep efficiency. Simulations on a heterogeneous reservoir model representing an oil field from the Middle East confirmed the significance of gravity on improving the displacement and overall oil recovery. The same considerations should pertain in reverse for gas storage: storage efficiency improves in gravity dominated flow.

A sub-grid gas–solid interaction model for coarse-grained CFD–DEM simulations

Computational fluid dynamics has been coupled with coarse-grained discrete element method (CFD–CGDEM) to study industrial-scale gas–solid fluidized beds. However, solving the fluid flow at a grid size of several coarse-grained particles (CGPs) cannot accurately predict the gas–solid interaction, and thus reasonable correction model is required. This study develops a sub-grid model to correct the gas–solid interaction and thereby improve the accuracy of coarse-grid CFD–CGDEM simulation. First, the fluid grids with the size of several CGPs are divided into the auxiliary three-dimensional sub-grids. Then, the CGPs are mapped onto the sub-grids by the weight function to reconstruct the local solid velocities and solid fractions of the sub-grids. After that, the simplified mass and momentum conservation equations are solved to resolve the local gas velocities of sub-grids. Finally, the drag on each CGP is corrected based on the local gas-phase hydrodynamics of sub-grids. Results show that the sub-grid model resolving the local gas velocity in all the three directions works better than that just in the main stream direction. The coarse-grid CFD–CGDEM simulations with this sub-grid model agree well with the experiment for the bubbling, turbulent and rapid fluidized beds. Besides, by solving the simplified conservation equations with graphics processing units, the coarse-grid CFD–CGDEM coupled with the sub-grid model achieves 674 times speedup compared to the fine-grid simulation, demonstrating a much more efficient method to study industrial-scale gas–solid fluidized beds.

Countercurrent Imbibition in Porous Media with Dense and Parallel Microfractures: Numerical and Analytical Study

Summary Countercurrent imbibition is the process in which the wetting fluid spontaneously displaces the nonwetting fluid, while the nonwetting fluid is recovered at the wetting fluid inlet. It is a major mechanism for the recovery of shale oil, shale gas, and tight oil. In shale and tight formations, microfractures are highly developed. Specifically, some typical formations, such as continental shales, consist of dense and parallel microfractures (DPFs). In DPF systems, microfractures are segregated by low-permeability matrix layers, while the very close distance betwen neighboring microfractures results in strong capillary correlation. The underlying assumptions of the classical dual-porosity (DP) model break down. Despite extensive studies on layered media, there is still no suitable model to describe imbibition in the DPF system at the representative elementary volume (REV) scale. In this study, we first numerically simulate countercurrent imbibition in DPF systems with fine grids, adopting typical continental shale parameters. For imbibition parallel to microfractures, two distinct stages are identified: an early stage where fractures are not correlated and a late stage where neighboring fractures are strongly correlated by capillarity. In both stages, cumulative oil production (Q) is proportional to the square root of imbibition time (t1/2), while the prefactors are very different. The late stage is the dominant stage in oil recovery. We note that the matrix permeability rarely contributes to imbibition parallel to microfractures at the late time, indicating that the matrix’s role here is to store fluid rather than to provide flow resistance. In addition, we rationalize the failure of the classical DP model, as it significantly overestimates fracture-matrix fluid exchange near the displacement front. Similarly, for imbibition perpendicular to microfractures, Q is also proportional to t1/2 in the late stage. After elucidating the mechanisms of fracture-fracture capillary interaction, we successfully derive analytical solutions for uni-directional countercurrent imbibition kinetics in DPF systems at the late stage, for imbibition parrallel and perpendicular to microfractures, respectively. We accordingly propose an equivalent REV scale model and examine it with fine-grid simulations. We highlight the importance of adopting anisotropic relative permeability in this DPF system at REV scale for reservoir simulation rather than simply adopting anisotropic absolute permeability. This presents a new challenge for numerical simulations at reservoir scale.

The Influence of Terrain Smoothing on Simulated Convective Boundary-Layer Depths in Mountainous Terrain

Many applications rely on a correct estimation of the convective boundary layer (CBL) depth over mountainous terrain, but often these applications use numerical model simulations. Although models inevitably smooth terrain, the amount of smoothing depends on grid spacing. We investigate the behavior of the CBL in coarse- and fine-grid models applied to mountainous terrain by using output from an operational mesoscale modeling system and by performing quasi-idealized simulations. We investigate different areas in different climate zones using different CBL top derivation methods, grid spacing ratios, planetary boundary layer (PBL) schemes, and terrain smoothing. We find that when compared to fine-grid simulations, CBL depths are systematically larger in coarse domains over mountaintops, and to a lesser extent in valleys. On average, differences between coarse- and fine-domains over mountaintops could reach around 10%. In certain locations, differences could be as high as 25%. We attribute the result to terrain smoothing. Similarly, when using a coarse-grid CBL height (relative to mean sea level) interpolated using fine-grid terrain information, there is good agreement with fine-grid CBL depths over mountaintops and less agreement in valleys. Our results have implications for applications that use output from coarse model grids in mountainous terrain. These include inverse modeling studies (e.g., greenhouse gas budget estimations or integrated water vapor transport), PBL evaluation studies, climate research, air quality applications, planning and executing prescribed burns, and studies associated with precipitation over mountainous terrain.

A corrected filtered drag model considering the effect of the wall boundary in gas-particle fluidized bed

The databases used to construct traditional mesoscale drag models is usually obtained from fine-grid simulation results in the full-periodic domains, ignoring the function of the wall boundary. In actual fluidized bed reactors, the presence of wall boundary can significantly affect the heterogeneous structures in near-wall areas, thereby affecting the drag force. Therefore, this work aims to further enhance the performance of the prediction results of existing filtered drag model by introducing the influence of the wall boundary. Based on the mesoscale drag force model published in previous literature, a correction coefficient considering the influence of the distance from the grid to the wall boundary is proposed. The applicability of the new corrected model is further enhanced by introducing the influence of solid volume fractions and slip velocities. Simple posteriori validations are systematically conducted in various common fluidized beds including the bubbling bed, the turbulent bed, and the fast bed to assess the predictive capability of the newly proposed correction drag model.

Data-driven correction of coarse grid CFD simulations

Computational fluid dynamics is a cornerstone of the modern aerospace industry, providing important insights through aerodynamic analysis while reducing the need for expensive experiments and tests. A consistent spatial discretization on so-called grids approximates the analytical solution of the partial differential equation with increasing number of discrete points. But computing a rigorous amount of CFD simulations on fine grids can be a daunting task due to the high computational cost involved. Thus, it is of interest to find methods which generate accurate results while keeping computational costs low. This work proofs that machine learning as a post-processing tool is capable of improving the accuracy of coarse grid simulations. The results show that three machine learning models with varying complexity, namely random forest, neural network, and graph neural network, are capable of finding patterns in coarse grid simulations. These patterns are used for a vertex-wise prediction of the discretization error to approximate the field variables of interest of the corresponding fine grid simulation mapped onto the coarse grid. Initial training and testing is performed on the two dimensional RAE2822 airfoil leading to corrected flow fields, improved surface integrals and coefficients, even when shocks are present. Additional tests are performed on the RAE5212 airfoil, showing the generalization limits of the trained models. Finally, the training and prediction is showcased on a three dimensional geometry. The proposed method promises to reduce computational expenses while increasing the accuracy of the coarse grid results which works locally, e.g. it corrects the error for each vertex individually and is therefore not restricted by the number of grid points. The presented results obtained by the machine learning models during post-processing are a promising baseline for more integrated developments, where the models will interact in a dynamic fashion with the flow solver to further improve coarse grid simulations.

On the differences between periodic domain and fluidized bed

To understand the effects of macroscale constraints on fluidization, we investigate the differences between the periodic domain and realistic bed by using fine-grid simulations. The differences in these two systems are highlighted by identifying three force-balance conditions with respect to the gas-phase, solid-phase and the mixture, respectively. Specifically, these three conditions are not satisfied at the microscale, but satisfied at the macroscale in both systems; Over the mesoscale, the gas-phase force balance is established in the periodic domain and in the fluidized bed at bubbling states, but not at turbulent states, whereas the solid-phase and the mixture force balance conditions are established only in the periodic domain, not in the realistic bed. The influence of the bounding wall can be implicitly included by introducing the gas-phase pressure gradient, turbulent kinetic energies (TKEs) of gas and solids phases, and drift velocity as the markers for the drag force.

Theoretical and numerical analysis of drag force at the interface between the dilute and dense phases

Resolving the sharp interface between the dilute and dense phases in gas–solid flows is a bottleneck in fine-grid simulations. This study addresses this issue through the theoretical analysis of an infinite gas–structure interface with arbitrary flow directions. The drag force at the interface is decomposed into three parts: the homogeneous drag forces of the dilute and dense regions and a stress divergence difference term. All the three parts are expressed as the functions of the solid volume fractions, particle Reynolds numbers, and stress divergences of the interface grid and its adjacent grids. The developed theoretical drag models at the interface are verified and improved based on particle-resolved direct numerical simulations (PR-DNSs) of flows past plug-like structures. The models are then tested against PR-DNSs of flows past bubble-containing, spherical, ellipsoidal structures. They yield significantly better performance than the traditional Beetstra et al.'s model [Beetstra et al., “Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres,” AIChE J. 53(2), 489–501 (2007)].

Upscaling Low-Salinity Benefit from Laboratory Scale to Field Scale: An Ensemble of Models with a Relative Permeability Uncertainty Range

Summary The distribution of low-salinity benefit for an ensemble of models is required to evaluate low-salinity enhanced oil recovery (OREC) projects. To enable this, low-salinity pseudorelative permeability curves are required to estimate the benefit of low-salinity waterflooding at the field level. We present how the low-salinity benefit can be propagated through an ensemble of full-field models in which each simulation case could have a set of distinctive high-salinity pseudos. A 0.5-ft vertical resolution sector and its 10-ft upscaled counterpart are used. Relative permeability curves and the low-salinity benefit from corefloods are used in the high-resolution sector to create profiles. Pseudohigh- and low-salinity curves are generated for the upscaled sector by history matching high-salinity and incremental low-salinity profiles. Low-salinity benefit is typically measured from corefloods and the same benefit is often assumed at the field scale. Our results show that generating low-salinity curves for high-salinity pseudos using low-salinity benefit from corefloods slightly underestimates the true low-salinity benefit at field scale estimated from high-resolution models. This conclusion is consistent for two extreme relative permeability scenarios tested (i.e., a high-total-mobility unfavorable fractional flow and low-total-mobility favorable fractional flow). Including capillary pressure in high-resolution models was crucial. We would have come to another conclusion if we had not used capillary pressure in fine-grid simulation as approximately one-third of the benefit of low-salinity waterflooding was attributable to more favorable capillary pressure under low-salinity injection. We demonstrate how a set of high-salinity relative permeability data obtained from corefloods, which encompasses a range for fractional flow and total mobility, can be included in ensemble modeling appropriately and how low-salinity benefit could be estimated for such an ensemble. It is adequate to generate low-salinity curves for bounding high-salinity sets of curves. The bounding low-salinity curves can then be used to estimate low-salinity curve for any interpolated high-salinity curve. This workflow significantly simplifies the process of generating the distribution of low-salinity benefit corresponding to an ensemble of models which may be calibrated to limited history.

A New Projection-Based Integrally Embedded Discrete Fracture Model and Its Application in Coupled Flow and Geomechanical Simulation for Fractured Reservoirs

The embedded discrete fracture model (EDFM) has been popular for the modeling of fractured reservoirs due to its flexibility and efficiency while maintaining the complex geometry of fracture networks. Though the EDFM has been validated for single-phase flow simulations, some recent cases show that the EDFM might result in apparent errors in multiphase flow situations. The projection-based embedded discrete fracture model (pEDFM) and the integrally embedded discrete fracture model (IEDFM) are two recently developed methods, which intend to improve the accuracy of the EDFM. In this study, a projection-based integrally embedded discrete fracture model (pIEDFM) is proposed, which combines the advantages of the pEDFM and the IEDFM. Similar to the pEDFM, the pIEDFM uses a kind of additional connections between fracture and nonneighboring matrix cells to obtain more physically authentic velocity fields. As a significant improvement, a semi-analytical cone-shaped pressure distribution that follows the IEDFM is adopted in the pIEDFM to capture the sharp pressure change near the fracture surfaces. Comparisons with benchmark results and explicit-fracture fine grid simulation results show that the pIEDFM provides accurate solutions using a moderate amount of grids. The proposed pIEDFM is also applied to coupled flow and geomechanical simulation for fractured reservoirs. Comparison of our coupled simulation results with that of the EDFM shows that the pIEDFM is applicable for the coupled simulation, and the different methods for matrix-fracture transmissibility between the pIEDFM and the EDFM may lead to deviations in stress fields predicted by geomechanical modeling, which eventually affects the oil production, water cut, and oil saturation profiles.

Exploring a unified EMMS drag model for gas-solid fluidization

Gas-solid fluidization is characterized by pervasive, dilute-dense two-phase flow structures, which need mesoscale drag modeling to account for their subgrid effects. The classic formulation of the energy-minimization multi-scale (EMMS) drag modeling requires a semi-empirical correlation of cluster diameter. To avoid using such a phenomenological description of mesoscale structures, in this work, we propose a two-level averaging approach: First, the mean drag in a fine-grid cell is defined as a weighted sum of the drag force in both the dilute and dense phases; Then, the second-level averaging is performed at the coarse-grid scale, where the unified EMMS drag is defined, and determined by performing a series expansion with respect to the phase-mean points of both the dilute and dense phases, respectively. The unified EMMS drag is validated with comparison to fine-grid simulation in a periodic domain and coarse-grid simulation of realistic fluidized beds, both showing fair agreement.

Large Eddy simulation of tracer gas dispersion in a cavity

This paper assesses the prediction of inert tracer gas dispersion within a cavity of height (H) 1.0 m, and unity aspect ratio, using large Eddy simulation (LES). The flow Reynolds number was 67 000, based on the freestream velocity and cavity height. The flow upstream of the cavity was laminar, producing a cavity shear layer which underwent a transition to turbulence over the cavity. Three distinct meshes are used, with grid spacings of (coarse), (intermediate), and (fine) respectively. The Smagorinsky, WALE, and Germano-Lilly subgrid-scale models are used on each grid to quantify the effects of subgrid-scale modelling on the simulated flow. Coarsening the grid led to small changes in the predicted velocity field, and to substantial over-prediction of the tracer gas concentration statistics. Quantitative metric analysis of the tracer gas statistics showed that the coarse grid simulations yielded results outside of acceptable tolerances, while the intermediate and fine grids produced acceptable output. Interrogation of the fluid dynamics present in each simulation showed that the evolution of the cavity shear layer is heavily influenced by the grid and subgrid scale model. On the coarse and intermediate grids the development of the shear layer is delayed, inhibiting the entrainment and mixing of the tracer gas into the shear layer, reducing the removal of the tracer gas from the cavity. On the fine grid, the shear layer developed more rapidly, resulting in enhanced removal of the tracer gas from the cavity. Concentration probability density functions showed that the fine grid simulations accurately predicted the range, and the most probable value, of the tracer gas concentration towards both walls of the cavity. The results presented in this paper show that the WALE and Germano-Lilly models may be advantageous over the standard Smagorinsky model for simulations of pollutant dispersion in the urban environment.

Optimization-based upscaling for gravity segregation with 3D capillary heterogeneity effects

Multiphase flow driven by gravity and capillary forces occurs in various applications pertaining to aquifers, the vadoze zone and hydrocarbon reservoirs. In particular, these processes have been under investigation for modeling CO2 migration in geosequestration applications. Solving such multiscale problems can be extremely computationally demanding and therefore upscaling is often employed. However, a recent study by Rabinovich and Cheng, 2020 showed that implementation of conventional upscaling methods fails to reproduce fine-grid simulations of gravity-capilary driven flow. This work presents a new upscaling method based on an effective property formula for permeability (k), power law averaging in the capillary limit for relative permeability, and an optimization approach for capillary pressure (Pc). The new method is tested on various example cases and coarse-grid simulations are shown to match fine-grid ones with sufficient accuracy. The challenge of upscaling the flows is found to be related to entry pressure trapping and the optimization upscaled Pc is shown to have a unique structure allowing to model the trapping. The method is global, requiring a fine-grid simulation for calibration of the optimized parameters. However, we show that the method reduces computational time dramatically if calibrated parameters are used in cases in which the fine-grid solution is unknown, such as for varying k realizations.

A dynamic multiphase turbulence model for coarse-grid simulations of fluidized gas-particle suspensions

The Spatially-Averaged Two-Fluid Model (SA-TFM) is a functional multiphase turbulence model aimed at predicting the influence of unresolved meso-scale structures on the macro-scale flow properties in coarse-grid simulations of gas-particle flows. In this study, we highlight the general applicability of the SA-TFM model due to the dynamic estimation of the model coefficients through test-filters, the anisotropic treatment of the Reynolds-stresses and the drag force correction, and additional wall-friction boundary conditions for the particle-phase velocity, Reynolds-stress and turbulent kinetic energy. The dynamic approach derives information on the unresolved meso-scale flow properties from the resolved macro-scale variables without the need for any intensive prior considerations of the specific flow structure. Thereby, the drift velocity, a measure for the drag-reduction due to the presence of meso-scale structures is estimated from the turbulent kinetic energies of the phases and the variance of the solids volume fraction. We validate the dynamic anisotropic SA-TFM against highly resolved fine-grid Two-Fluid Model simulation data and experimental measurements of Geldart type A and B particles in bubbling to turbulent flow regimes. In the course of this extensive study, we find that the predictions for the macro-scale flow properties, such as slip-velocity, bed expansion, volume fraction distribution, and mass-flux, are in good agreement with the experimental and fine-grid simulation data in a vast number of cases, ranging from unbound fluidization to pilot-scale fluidized beds, thus, implying a wide applicability of the dynamic model independent of the underlying grid-size.

Dynamics of droplet migration in oscillatory and pulsating microchannel flows and prediction and uncertainty quantification of its lateral equilibrium position using multifidelity Gaussian processes

The dynamics of a droplet in oscillatory and pulsating flows of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, surface tension, and channel flow rate have been explored by simulating the drop within a microchannel. These types of flows introduce new equilibrium positions for the drop compared to steady flows with similar conditions. The simulation results are very sensitive to the grid resolution due to the unsteady behavior of the base flow. Therefore, a set of fine grids have been used in this study to capture the physics of this problem more accurately. However, these fine grids make the computations significantly expensive. Therefore, a multifidelity Gaussian processes method with two levels of fidelity has been used to predict the results of the remaining fine-grid simulations along with their uncertainties based on their correlations with those of the coarse-grid cases over a wide range of input parameters.

High-resolution simulation of oscillating bubble plumes in a square cross-sectioned bubble column with an unsteady k-ε model

How to choose the interphase force and turbulence models is still an open question for Eulerian simulation of bubbly flows. It is well accepted that an unsteady k-ε model that can simulate the meandering bubble plumes in a flat bubble column reactor (BCR) but fails to capture this phenomenon in a three-dimensional (3D) BCR. This work presents a GPU-accelerated fine-grid simulation with an unsteady k-ε model with a Lattice Boltzmann Method (LBM) based mixture model developed by Shu et al. (2020b) for a square cross-sectioned BCR. A good quantitative agreement between the numerical results and experimental data from the literature is achieved without a lift force. This work highlights that GPU-accelerated fine-grid simulations with an unsteady k-ε model can predict the bubble plumes in 3D BCRs, and that the lift force is not used in this case. The reason why lift is not needed in this case is discussed.

Development of data-driven filtered drag model for industrial-scale fluidized beds

Simulations of large-scale gas-particle flows using coarse meshes and the filtered two-fluid model approach depend critically on the constitutive model that accounts for the effects of sub-grid scale inhomogeneous structures. In an earlier study (Jiang et al., 2019), we had demonstrated that an artificial neural network (ANN) model for drag correction developed from a small-scale systems did well in both a priori and a posteriori tests. In the present study, we first demonstrate through a cascading analysis that the extrapolation of the ANN model to large grid sizes works satisfactorily, and then performed fine-grid simulations for 20 additional combinations of gas and particle properties straddling the Geldart A-B transition. We identified the Reynolds number as a suitable additional marker to combine the results from all the different cases, and developed a general ANN model for drag correction that can be used for a range of gas and particle characteristics.

A Source Clustering Approach for Efficient Inundation Modeling and Regional Scale Probabilistic Tsunami Hazard Assessment

For coastal regions on the margin of a subduction zone, near-field megathrust earthquakes are the source of the most extreme tsunami hazards, and are important to handle properly as one aspect of any Probabilistic Tsunami Hazard Assessment (PTHA). Typically, great variability in inundation depth at any point is possible due to the extreme variation in extent and pattern of slip over the fault surface. In this context, we present an approach to estimating inundation depth probabilities (in the form of hazard curves at a set of coastal locations) that consists of two components. The first component uses a Karhunen-Loeve expansion to express the probability density function (PDF) for all possible events, with PDF parameters that are geophysically reasonable for the Cascadia Subduction Zone (CSZ). It is then easy and computationally cheap to generate a large $N$ number of samples from this PDF; doing so and performing a full tsunami inundation simulation for each provides a brute force approach to estimating probabilities of inundation. However, to obtain reasonable results, particularly for extreme flooding due to rare events, $N$ would have to be so large as to make the tsunami simulations prohibitively expensive. The second component tackles this difficulty by using importance sampling techniques to adequately sample the tails of the distribution and properly re-weight the probability assigned to the resulting realizations, and by grouping the realizations into a small number of clusters that we believe will give similar inundation patterns in the region of interest. In this approach, only one fine-grid tsunami simulation need be computed from a representative member of each cluster. We discuss clustering based on proxy quantities that are cheap to compute over a large number of realizations, but that can identify a smaller number of clusters of realizations that will have similar inundation depths. The fine-grid simulations for each cluster representative can also be used to develop an improved strategy, in which these are combined with cheaper coarse-grid simulations of other members of the cluster. We illustrate the methodology by considering two coastal locations: Crescent City, CA and Westport, WA.

Grid-dependence study for simulating propeller crashback using large-eddy simulation with immersed boundary method

Simulating the flow around a propeller using large-eddy simulation (LES) with the immersed boundary (IB) method is challenging and computationally expensive. In this work, we carry out the grid-dependence study of LES with IB for simulating a propeller in crashback mode using four sets of gradually refined grids. The simulation results show that the grid-resolution requirements for accurately predicting different flow quantities are different. Specifically, it is found that the side-force coefficient and the averaged streamwise velocity are less sensitive to grid resolutions as compared with the thrust force coefficient and the turbulence kinetic energy, respectively. Furthermore, it is found that the computed results in the near wake region and the region around the blade are more sensitive to grid resolutions as compared with the far wake region, where the predictions from the four different grids are similar to each other. This suggests that a coarse grid simulation is adequate if only the far wake region is of interest, while a fine grid simulation is required if one cares about the flow around the blade and the flow in the near wake region.

Pseudorelative Permeabilities for Simulation of Unstable Viscous Oil Displacement

Summary Relative permeabilities are well understood for light oils involving stable displacement. However, conflicting arguments have been presented in the literature regarding relative permeabilities for viscous oils. Most nonthermal viscous oil displacements are unstable. Depending on the magnitude of mobility ratio, displacement is influenced by varying degrees of viscous instability, often referred to as fingering. For viscous oils (>500 cp), even a polymer flood must be designed at partially stable conditions (mobility ratio > 1) to maintain an economical processing rate [% pore volume (PV) injected (PVI) per year]. Typically, viscous fingering is difficult to model in full-field simulation because of the large grid sizes used. To design and optimize a partially stable polymer or waterflood, it is critical to correctly upscale the laboratory-generated relative-permeability curves for reservoir simulation. In recent years, such models have been published in the Society of Petroleum Engineers literature. Unfortunately, most of these models require multiple fitting parameters (at least three). In this work, we present a simplified technique that requires systematic change in only one parameter to generate upscaled relative permeability curve for a given viscosity ratio. Using fine-grid simulations, we show that the flow at high-viscosity ratio is channelized even in a core perceived to be homogeneous at laboratory scale. This happens because of small-scale heterogeneities that are present in every rock. Upscaling averages these fine variations in heterogeneities, causing the grids to be overswept, thus overpredicting recovery. To compensate for this shortcoming, it is recommended to upscale the relative-permeability curves in the simulation model.