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Summary Modeling the dynamic fluid behavior of low-salinity waterflooding (LSWF) at the reservoir scale is a challenge that requires a coarse-grid simulation to enable prediction in a feasible time scale. However, evidence shows that using low-resolution models will result in a considerable mismatch compared with an equivalent fine-scale model with the potential of strong, numerically induced pulses and other dispersion-related effects. This work examines two new upscaling methods that have been applied to improve the accuracy of predictions in a heterogeneous reservoir where viscous crossflow takes place. We apply two approaches to upscaling to bring the flow prediction closer to being exact. In the first method, we shift the effective-salinity range for the coarse model using algorithms that we have developed to correct for numerical dispersion and associated effects. The second upscaling method uses appropriately derived pseudorelative permeability curves. The shape of these new curves is designed using a modified fractional-flow analysis of LSWF that captures the relationship between dispersion and the waterfront velocities. This second approach removes the need for explicit simulation of salinity transport to model oil displacement. We applied these approaches in layered models and for permeability distributed as a correlated random field. Upscaling by shifting the effective-salinity range of the coarse-grid model gave a good match to the fine-scale scenario, while considerable mismatch was observed for upscaling of the absolute permeability alone. For highly coarsened models, this method of upscaling reduced the appearance of numerically induced pulses. On the other hand, upscaling by using a single (pseudo)relative permeability produced more robust results with a very promising match to the fine-scale scenario. These methods of upscaling showed promising results when they were used to scale up fully communicating and noncommunicating layers as well as models with randomly correlated permeability. Unlike documented methods in the literature, these newly derived methods take into account the substantial effects of numerical dispersion and effective concentration on fluid dynamics using mathematical tools. The methods could be applied for other models where the phase mobilities change as a result of an injected solute, such as surfactant flooding and alkaline flooding. Usually these models use two sets of relative permeability and switch from one to another as a function of the concentration of the solute.
Summary Numerical fidelity is required when using simulations to predict enhanced-oil-recovery (EOR) processes. In this paper, we investigate the conditions that lead to numerical errors when simulating low-salinity (LS) waterflooding (LSWF). We also examine how to achieve more accurate simulation results by scaling up the flow behavior in an effective manner. An implicit finite-difference numerical solver was used to simulate LSWF. The accuracy of the numerical solution has been examined as a function of changing the length of the grid cell and the timestep. Previously we have shown that numerical dispersion induces a physical retardation such that the LS front slows down while the formation water front speeds up. We also report for the first time that pulses can be generated as numerical artifacts in coarsely gridded simulations of LSWF. These effects reflect the interaction of dispersion, the effective-salinity range, and the use of upstream weighting during calculation, and can corrupt predictions of flow behavior. The effect of the size of the timestep was analyzed with respect to the Courant condition, traditionally related to explicit numerical schemes and also numerical stability conditions. We also investigated some of the nonlinear elements of the simulation model, such as the differences between the concentrations of connate water salinity and the injected brine, effective-salinity-concentration range, and the net mobility change on fluids through changing the salinity. We report that to avoid pulses it is necessary, but not sufficient, to meet the Courant condition relating timestep size to cell size. We have also developed two approaches that can be used to scale up simulations of LSWF and tackle the numerical problems. The first method is dependent on a mathematical relationship between the fractional flow, effective-salinity range, and the Péclet number and treats the effective-salinity range as a pseudofunction. The second method establishes an unconventional proxy method equivalent to pseudorelative permeabilities. A single table of pseudorelative permeability data can be used for a waterflood instead of two tables, as is usual for LSWF. This is a novel approach that removes the need for relative permeability interpolation during the simulation. Overall, by avoiding numerical errors, we help engineers to more efficiently and accurately assess the potential for improving oil recovery using LSWF and thus optimize field development. We also avoid the numerical pulses inherent in the traditional LSWF model.
Abstract We investigate the effect of heterogeneous petrophysical properties on Low Salinity Water Flooding (LSWF). We considered reservoir scale models, where the geological properties were obtained from a giant Middle East carbonate reservoir. The results are compared against a typical sandstone model. We simulated low salinity induced wettability changes in field scale models in which the petrophysical properties were randomly distributed with spatial correlation. We examined a wide range of geological realisations which mimic complex geological structures. Sandstone was simulated using a log-linear porosity-permeability relation with fairly good correlation. A carbonate reservoir from the Middle East was simulated where a much less correlated porosity permeability relationship was obtained. The salinity of formation water was set to typically observed values for the sandstone and carbonate cases. A number of simulations were then carried out to assess the flow behaviour. We have found that the general trend of permeability-porosity correlation has a key role that could mitigate or aggravate the impact of spatial distributions of petrophysical properties. We considered models with a log-linear permeability-porosity correlation, as generally observed for sandstone reservoirs. These are likely to be directly affected by the spatial distribution more than models with a power permeability-porosity correlation, which is often reported for flow units of carbonate reservoirs. The scatter of data in the permeability-porosity correlations had a relatively small impact on the flow performance. On the other hand, the effect of heterogeneity decreases with the width of the effective salinity range. Thus, uncertainty in carbonate reservoirs arises due to the ambiguity of spatial distribution of permeability and porosity would be less affects the LSWF predictability than in sandstone case. Overall, the incremental oil recovery due to LSWF was higher in the carbonate models than the sandstone cases. We observe from uncertainty analysis that the formation waterfront was less fingered than the low salinity waterfront and the salinity concentration. The dispersivity of salinity front and the water cut can be estimated for models with various degrees of heterogeneity. The outcome of the study is a better understanding of the implications of heterogeneity on LSWF. In some cases the behaviour can appear like a waterflood in very heterogeneous cases. It is important to assess the reservoir effectively to determine the best business decision.
Summary Low‐salinity waterflooding (LSWF) is a promising process that could lead to increased oil recovery. To date, the greatest attention has been paid to the complex oil/water/rock chemical reactions that might explain the mechanisms of LSWF, and it is generally accepted that these result in behavior equivalent to changing oil and water mobility. This behavior is modeled using an effective salinity range and weighting function to gradually switch from high‐ to low‐salinity relative permeability curves. There has been limited attention on physical transport of fluids during LSWF, particularly at large scale. We focus on how the salinity profile interacts with water fronts through the effective salinity range and dispersion to alter the transport behavior and change the flow velocities, particularly for the salinity profile. We examined a numerical simulation of LSWF at the reservoir scale. Various representations of the effective salinity range and weighting function were also examined. The dispersion of salinity was compared with a theoretical form of numerical dispersion based on input parameters. We also compared salinity movement with the analytical solution of the conventional dispersion/advection equation. From simulations we observed that salinity is dispersed as analytically predicted, although the advection velocity might be changed. In advection‐dominated flow, the salinity profile moves at the speed of the injected water. However, as dispersion increases, the mixing zone falls under the influence of the faster‐moving formation water and, thus, speeds up. To predict the salinity profile theoretically, we have modified the advection term of the analytical solution as a function of the formation- and injected‐water velocities, Péclet number, and effective salinity range. This important result enables prediction of the salinity transport by this newly derived modification of the analytical solution for 1D flow. We can understand the correction to the flow behavior and quantify it from the model input parameters. At the reservoir scale, we typically simulate flow on coarse grids, which introduces numerical dispersion or must include physical dispersion from underlying heterogeneity. Corrections to the equations can contribute to improving the precision of the coarse‐scale models, and, more generally, the suggested form of the correction can also be used to calculate the movement of any solute that transports across an interface between two mobile fluids. We can also better understand the relative behaviors of passive tracers and those that are adsorbed.
Abstract As an enhanced oil recovery method (EOR), chemical flooding has been implemented intensively for some years. Low Salinity WaterFlooding (LSWF) is a method that has become increasingly attractive. The prediction of reservoir behaviour can be made through numerical simulations and greatly helps with field management decisions. Simulations can be costly to run however and also incur numerical errors. Historically, analytical solutions were developed for the flow equations for waterflooding conditions, particularly for non-communicating strata. These have not yet been extended to chemical flooding which we do here, particularly for LSWF. Dispersion effects within layers also affect these solutions and we include these in this work. Using fractional flow theory, we derive a mathematical solution to the flow equations for a set of layers to predict fluid flow and solute transport. Analytical solutions tell us the location of the lead (formation) waterfront in each layer. Previously, we developed a correction to this to include the effects of numerical and physical dispersion, based on one dimensional models. We used a similar correction to predict the location of the second waterfront in each layer which is induced by the chemical's effect on mobility. In this work we show that in multiple non-communicating layers, material balance can be used to deduce the inter-layer relationships of the various fronts that form. This is based on similar analysis developed for waterflooding although the calculations are more complex because of the development of multiple fronts. The result is a predictive tool that we compare to numerical simulations and the precision is very good. Layers with contrasting petrophysical properties and wettability are considered. We also investigate the relationship between the fractional flow, effective salinity range, salinity dispersion and salinity retardation. This work allows us to predict fluids and solute behaviour in reservoirs with non-communicating strata without running a simulator. The recovery factor and vertical sweeping efficiency are also very predictable. This helps us to upscale LSWF by deriving pseudo relative permeability based on our extension of fractional flow and solute transport into such 2D systems.
Abstract Numerical stability and precision are required when using simulations to predict Enhanced Oil Recovery processes and these can be difficult to achieve for Low Salinity Water Flooding (LSWF). In this paper we investigate the conditions that lead to numerical instabilities when simulating LSWF. We also examine how to achieve more precise simulation results by upscaling the flow behaviour in an effective manner. An implicit finite difference numerical solver was used to simulate LSWF. The stability and precision of the numerical solution has been examined as a function of changing the grid size and time step. We used the Peclet number to characterise numerical dispersion with these changes. Time step length was compared with the Courant condition. We also investigated some of the nonlinear elements of the simulation model such as the differences between the concentrations of connate water salinity and the injected brine, effective salinity concentration range and the net mobility change on fluids through changing the salt concentration. We observe that numerical solution of LSWF tends to be conditionally stable, with problems occurring as a function of the range of effective salinity concentration relative to the initial reservoir water and the injected brine concentrations. We observe that the Courant condition is necessary but not sufficient. By definition, the precision of the numerical solution decreased when increasing numerical dispersion but this also resulted in slowing down the low salinity water and increased the velocity of the formation water further reducing precision. These numerical problems mainly depend on fluid mobility as a function of salt concentration. We conclude that the total range and the mid-concentration of effective salinity affect the stability and precision of the numerical solution, respectively. In this work, we have developed two approaches that can be used to upscale simulations of LSWF and tackle the numerical instability problems. The first method is based on a mathematical form that gives the relationship between the fractional flow, effective salinity concentration and the Peclet number. The second method is that we have established an unconventional proxy method that can be used to imitiate pseudo relative permeabilities. This work enables us for the first time to simulate LSWF by using a single table of pseudo relative permeability data, instead of two tables as traditionally done in previous studies. This removes the need for relative permeability interpolation during the simulation and will help engineers to more efficiently and accurately assess the potential for improving oil recovery using LSWF and optimise the value of the field development. We also avoid the numerical instabilities inherent in the traditional LSWF model.
Abstract Low Salinity Water Flooding (LSWF) is an emergent technology developed to increase oil recovery. Many laboratory tests of LSWF have been carried out since the 1990's, but modelling at the reservoir scale is less well reported. Various descriptions of the functional relationship between salt concentration and relative permeability have been presented in the literature, as have the differences in the effective salinity range over which salt content takes effect. This paper focuses on these properties and their impact on the fractional flow of LSWF. We present observations that help characterise the flow behaviour in a more general form, simplifying the interpretation of results. We explain how numerical or physical diffusion of salt affects the velocity of the waterflood front, and how this can be predicted from fractional flow analysis. We have considered various linear and non-linear shapes of the function relating salinity to relative permeability and different effective salinity ranges using a numerical simulator applied at the reservoir scale. The results are compared to fractional flow theory in which both salt and water movement is assumed to be shock-like in nature. We observe that diffusion of the salt front is an important process that affects the fractional flow behaviour depending on the effective salinity range. The simulator solution matches the analytical predictions from fractional flow analysis under the condition that the mid-point of the effective salinity range is at the mid-point between the formation and injected salt concentrations. However, an effective behaviour similar to adsorption/desorption occurs when these mid-point concentrations are not coincidental. The outcome is that the fronts representing high and low salinity water travel with altered velocities and at different saturations. We find that we can predict this behaviour from the input data alone as an augmented form of the fractional flow theory including the concept of retardation or acceleration as occurs for adsorption and desorption for other injectants. We use the analytical solution to the advection-diffusion equation and find that the changes in behaviour depends on the Peclet number. The result of our work is that we have produced an updated form of the fractional flow model of LSWF, to include the impact of salt front diffusion on the movement of fluids. A new factor is introduced, similar to adsorption in polymer flooding. We have developed a new mathematical formula, empirically, to estimate the magnitude of this factor. The new form can be used to modify the effects that numerical or physical diffusion have on the breakthrough times of high and low salinity water fronts during LSFW. This will improve predictive ability and also reduce the requirement for full simulation.