This paper presents the algebraic dynamic multilevel method (ADM) for compositional flow in three dimensional heterogeneous porous media in presence of capillary and gravitational effects. As a significant advancement compared to the ADM for immiscible flows (Cusini et al., 2016) [33], here, mass conservation equations are solved along with k-value based thermodynamic equilibrium equations using a fully-implicit (FIM) coupling strategy. Two different fine-scale compositional formulations are considered: (1) the natural variables and (2) the overall-compositions formulation. At each Newton's iteration the fine-scale FIM Jacobian system is mapped to a dynamically defined (in space and time) multilevel nested grid. The appropriate grid resolution is chosen based on the contrast of user-defined fluid properties and on the presence of specific features (e.g., well source terms). Consistent mapping between different resolutions is performed by the means of sequences of restriction and prolongation operators. While finite-volume restriction operators are employed to ensure mass conservation at all resolutions, various prolongation operators are considered. In particular, different interpolation strategies can be used for the different primary variables, and multiscale basis functions are chosen as pressure interpolators so that fine scale heterogeneities are accurately accounted for across different resolutions. Several numerical experiments are conducted to analyse the accuracy, efficiency and robustness of the method for both 2D and 3D domains. Results show that ADM provides accurate solutions by employing only a fraction of the number of grid-cells employed in fine-scale simulations. As such, it presents a promising approach for large-scale simulations of multiphase flow in heterogeneous reservoirs with complex non-linear fluid physics.@en

Heterogeneous reservoirs often have poor sweep efficiency during flooding. Although polymer flooding can be used to improve the recovery, in-depth diversion might provide a more economical alternative. Most of the in-depth diversion techniques are based on the propagation of a system that forms a gel in the reservoir. Premature cross-linking of the system prevents the fluid from penetrating deeply into the reservoir and as such reduces the efficiency of the treatment. We studied the effect of using a polyelectrolyte complex (PEC) to (temporarily) hide the cross-linker from the polymer molecules. In addition to studying the cross-linking process in bulk, we demonstrated its behaviour at the core scale (1 m length) as well as on the pore scale. The gelation time in bulk suggested that the PEC could effectively delay the time of the cross-linking even at high brine salinity. However the delay experienced in the core flood experiment was much shorter. Tracer tests demonstrated that the XL polymer, which is a mixture of PEC and partially hydrolyzed polyacrylamide, reduced the core pore volume by roughly 6.2% (in absolute terms). The micro-CT images showed that most of the XL polymer was retained in the smaller pores of the core. The large increase in dispersion coefficient suggests that this must have resulted in the creation of a few dominant flow paths isolated from each other by closure of the smaller pores.

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Field-scale simulation of flow in porous media in presence of incomplete mixing demands for high-resolution computational grids, much beyond the scope of state-of-the-art simulators. Hence, the upscaling-based Todd and Longstaff (TL) approach is typically used, where coarse grid cells are employed with effective mixing fluid properties and parameters found by matching results obtained with fully resolved reference simulations. Dynamic local grid refinement (DLGR) techniques, on the other hand, only employ fine-scale grid resolution where the fully mixed assumption is not valid. The rest of the domain is then solved at coarser resolutions, where the fully mixed assumption is valid. Here, we assess the accuracy and the robustness of DLGR- and TL-based simulations of miscible displacements in homogeneous and heterogeneous porous media. Due to the intrinsic uncertainty within the unstable displacement nature of the studied incomplete mixing processes, the performance of the methods is also investigated based on a range of acceptable solutions rather than relying only on a single reference one. Systematic numerical results illustrate that the DLGR method is much more robust and accurate than the upscaling-based TL approach, and employs only a small fraction of fine-scale reference grids. Especially, the TL upscaling results (though history matched with computationally expensive fine-scale results) are very sensitive to the change of the simulation parameters. Based on this study, we propose a dynamic multilevel simulation strategy for efficient and reliable large-scale simulation of the complex incomplete mixing processes.@en

The partitioning inter-well tracer test (PITT) is a method to determine average oil saturation between an injector-producer pair. Tracer tests can be used to quantify incremental oil recovery in enhanced oil recovery (EOR) pilots and for reservoir surveillance purposes. Various interpretation methods can be applied: peak arrival time comparison, Residence Time Distribution Analysis (RTDA), extrapolation methods and projection methods. Various sensitivities influence the outcome, accuracy and consistency of these methods. First and foremost, reservoir geometry and heterogeneity have significant impact on the shape of the tracer response curve, and on the accuracy of the subsequent oil saturation estimation. The presence of multiple flow paths can be clearly identified from tracer responses and oil saturation of each flow path can be determined individually by use of extrapolation and projection methods. Thus, potential permeability baffles or barriers can be identified and static reservoir models can be improved by evaluating tracer response data. Further key sensitivities are sampling duration, sampling frequency and measurement errors. An incomplete tracer response can lead to significant loss of accuracy of oil saturation determination by RTDA. A low sampling frequency has severe impact on the accuracy of oil saturation estimation, especially if large measurement errors are present. For timely execution of an EOR project, an early estimation of oil saturation is desirable. In this study, a new and robust analytical projection method is proposed that enables early time estimation of oil saturation based on limited data. The projection method is based on a translation of the non-partitioning tracer response curve to the partitioning tracer curve using a time and amplitude scalar. Robustness of this method is achieved by performing a least squares optimization that takes into account all available data in order to find optimal fitting time and amplitude scalars for tracer data translation. This projection method provides accurate early time oil saturation estimations based on limited partitioning tracer data. Especially if responses are incomplete, contain multiple peaks caused by reservoir heterogeneities, have a low sampling frequency and contain large measurement errors, the least squares projection method provides a more accurate oil saturation estimate than the other methods.@en

The size distribution and swelling kinetics of copolymer nano-spheres extracted from an W/O emulsion was studied with dynamic light scattering (DLS) and transmission electron microscopy (TEM). TEM results were compared against DLS results. It was demonstrated that the size distribution for agglomerates (clusters) of particles match well with the size distribution obtained from DLS. Hence, less time consuming DLS tests can be used for the estimation of the size of nano-spheres in the future. Next, a novel procedure for the study of agglomeration and swelling rates separately with TEM was designed. The results of the study revealed that the spheres agglomerate and swell over time. The kinetics of the agllomeration is used for a population balance model to predict the size of spheres over time. This approach helps to understand how well the spheres can propagate in an oil reservoir over time.@en

A dynamic multilevel compositional solver (C-ADM) is introduced for fully- (and sequentially-) implicit systems arising from compositional displacements in natural porous media. The fully (or sequential) implicit system is first described at a fine-scale resolution, where phases are allowed to consist of different components (based on thermodynamics equilibrium). In addition, heterogeneous capillary functions (defined based on Leverett’s J-function) and gravitational effects are both considered, adding significantly to the non-linear complexity of the processes. Given this complex fine-scale system for a heterogeneous reservoir, C-ADM defines a dynamic multilevel system, based on an error criterion, where the grid resolution is defined based on the physics of the process as well as geological complexities and location of wells. Once this multilevel grid is defined, sequences of prolongation and restriction operators are employed to obtain an accurate and efficient multilevel system. CADM allows for a general set of prolongation operators, e.g., constant, bilinear (or polynomial), and multiscale basis functions. The restriction operators, however, are constructed based on a mass-conservative finite-volume formulation at all levels. For several challenging test cases it is shown that C-ADM employs only a small fraction of the fine-scale grids to provide an accurate description of the process. C-ADM casts a promising approach in the application of dynamic grid refinement methods for real-field applications. @en

An algebraic dynamic multilevel method (ADM) is developed for fully-implicit (FIM) simulations of multiphase flow in heterogeneous porous media with strong non-linear physics. The fine-scale resolution is defined based on the heterogeneous geological one. Then, ADM constructs a space-time adaptive FIM system on a dynamically defined multilevel nested grid. The multilevel resolution is defined using an error estimate criterion, aiming to minimize the accuracy-cost trade-off. ADM is algebraically described by employing sequences of adaptive multilevel restriction and prolongation operators. Finite-volume conservative restriction operators are considered whereas different choices for prolongation operators are employed for different unknowns. The ADM method is applied to challenging heterogeneous test cases with strong nonlinear heterogeneous capillary effects. It is illustrated that ADM provides accurate solution by employing only a fraction of the total number of fine-scale grid cells. ADM is an important advancement for multiscale methods because it solves for all coupled unknowns (here, both pressure and saturation) simultaneously on arbitrary adaptive multilevel grids. At the same time, it is a significant step forward in the application of dynamic local grid refinement techniques to heterogeneous formations without relying on upscaled coarse-scale quantities @en

In order to improve oil recovery from water flooded heterogeneous oil reservoirs, different chemical enhanced oil recovery (cEOR) technologies can be applied. One of the recently developed cEOR technologies for the improvement of oil recovery is based on prefabricated polymeric nano-spheres. These spheres are able to swell over time through absorption of brine. Literature review on the flow of the nano-spheres in porous media showed that the mechanism of oil displacement from heterogeneous as well as homogenous porous media is not well established. One of the proposed mechanisms is that prefabricated polymeric particles might reduce the residual oil saturation Sor (Goudarzi et al. 2014). To validate this, a series of core flood experiments was carried out in order to study this mechanism in both a heterogeneous Boise outcrop and homogeneous Bentheimer outcrop. Saturation of the cores with highly viscous crude oil was done at 50°C using the porous plates method. After the oil saturated core was water flooded at 1 ft/day, a bump flood was performed. It helped to achieve the residual oil saturation in the core. Subsequently, several slugs of the nano-spheres were injected into the core in order to study the influence of the nano-spheres on the residual oil saturation. In addition to that, the propagation of the nano-spheres in the core was studied via a pressure drop measurement at different sections of the core and by effluent collection. The results of the experiments show that the oil displacement from a core with nano-spheres after a bump flood is marginal. Some oil extraction with nano-spheres might have happened due to restricting the flow in the highly permeable zones of the core. The subsequent injection of water could potentially result in improved microscopic sweep efficiency and increased oil production. However, in our experiments this effect was not significant. Our results do not show that nano-spheres significantly reduce the residual oil saturation of the core. Additional measurements showed that the nano-spheres are mostly retained in the inlet section of the core and the propagation of the nano-spheres in porous media is slow. Therefore, the effect of the extra oil recovery is likely limited to the inlet section of the core. There is currently limited description in the literature on the oil recovery mechanism by polymeric nano-spheres. It has a large impact on how the behaviour of the nano-spheres in porous media needs to be modelled and on the screening of candidate reservoirs for the conditions described in the experiments. In our experiments we have seen no significant reduction of residual oil saturation and slow propagation. Further work is required to evaluate the conditions under which the performance of the nano-spheres can be improved.@en