HosseiniMehr, Mousa (Department of Applied Mathematics, TU Delft, Delft, Netherlands) | Al Kobaisi, Mohammed (Department of Petroleum Engineering, Khalifa University of Science and Technology) | Vuik, Cornelis (Department of Applied Mathematics, TU Delft, Delft, Netherlands) | Hajibeygi, Hadi (Department of Geoscience and Engineering, TU Delft, Delft, Netherlands)
An algebraic dynamic multilevel (ADM) method for multiphase flow in heterogeneous fractured porous media using the projection-based embedded discrete fracture model (pEDFM) is presented. The fine-scale discrete system is obtained independently for matrix and each lower-dimensional fracture. On the fine-scale high resolution computational grids, an independent dynamic multilevel gird (i.e., ADM grid) is imposed. The fully implicit discrete system is mapped completely algebraically to this ADM grid resolution using sequences of restriction and prolongation operators. Multilevel multiscale basis functions are locally computed and employed to honor the heterogeneity contrasts of the fractured domain by interpolating the solution accurately. These basis functions are computed only at the beginning of the simulation to increase the computational efficiency. Once the ADM system is solved for all unknowns (i.e., pressure and saturation), the solution at ADM resolution is prolonged back to fine-scale resolution in order to obtain an approximated fine-scale solution. This dynamic multilevel system employs the fine-scale grid cells only at the sharp gradient of the solution (e.g., at the moving front). With two fractured test-cases (homogeneous and heterogeneous), the performance of ADM is assessed by comparing it to fine-scale results as reference solution. It will be shown that ADM is able to reduce the computational costs and provide efficiency while maintaining the desired accuracy.
Rocks are usually not homogeneous, but are made up of multiple components such as mineral grains and pore space. On a larger scale, the bulk properties of rocks will be some weighted combination of the small-scale components. This averaging or upscaling step is needed if we wish to understand the behavior of our laboratory data or extract useful parameters from field data such as logs or seismic measurements. Understanding the boundary constraints is an important factor in this process. The simplest bounds are provided by the constant strain and constant stress limits.
Upscaling, or homogenization, is substituting a heterogeneous property region consisting of fine grid cells with an equivalent homogeneous region made up of a single coarse-grid cell with an effective property value. Upscaling is performed for each of the cells in the coarse grid and for each of the grid properties needed in the reservoir flow-simulation model. Therefore, the upscaling process is essentially an averaging procedure in which the static and dynamic characteristics of a fine-scale model are to be approximated by that of a coarse-scale model. A conceptual illustration of the upscaling process is shown in Figure 1. Typically, 3D geological models contain detailed descriptions of the reservoir that can be hard to capture properly with a significantly coarser model. Currently, an average-sized flow simulation model consists of approximately 100,000 active grid cells. Hence, upscaling is a required part of current reservoir modeling workflows.
Crandall, Dustin (National Energy Technology Laboratory) | Gill, Magdalena (National Energy Technology Laboratory, LRST) | Moore, Johnathan (National Energy Technology Laboratory, LRST) | Brown, Sarah (West Virginia Geological and Economic Survey) | Mackey, Paige (National Energy Technology Laboratory, ORISE)
The behavior of fractured low-permeability rock in many subsurface formations is critical for unconventional resource extraction. Understanding how flow through individual fractures changes during shearing, and what influence heterogeneity of the rock has on shearing behavior, was the focus of our laboratory study. Computed tomography (CT) scanning of fractured rocks undergoing shear was coupled with numerical simulations of fluid flow through these fractures. We sheared multiple cores from the Marcellus and Eau Claire shales in a closed system with confining pressures of greater than 1000 psi. Samples were manually sheared in a step wise fashion. After each shearing event we assessed the bulk hydrodynamic response by measuring permeability through the core and performed a high-resolution CT scan to understand how the principal and secondary fractures were changing in the core volume. The mineralogy of each sample was examined via x-ray fluorescence.
A range of interdependent characteristics influence fracture network evolution and sample cohesion: mineralogy, lithological heterogeneity, principal fracture morphology, fracture asperities, and shearing direction in relation to bedding. We found that samples sheared parallel to bedding were less likely to develop extensive networks of secondary fractures, with secondary fracture growth contingent on the presence of large asperities. Fracture permeability tended to increase with continued shear and secondary fracture development, but a high variance existed between samples. In some instances, permeabilities decreased in response to shear-initiated aperture reduction due to fracture mating. Gouge formation is another factor contributing to the transmissivity decreases, particularly in shale-dominated fracture regions. The ability to study this complex behavior in a controlled fashion using CT scanning enables a view into processes that impact production in many unconventional formations. Findings show that small scale features and details can play a significant role in fracture behavior and should be accounted for.
Shale properties vary significantly and understanding how fractures evolve due to geomechanical stressing can improve our understanding of how to effectively stimulate a variety of formations.While hydraulic fracturing is a large-scale activity, the microfabric and heterogeneity of shale can control fracture evolution and flow properties. Upscaling the impact of microfabric and heterogeneity is poorly captured in most modeling and planning efforts; this disconnect between small scale features and large-scale operations is understandable. It is difficult to measure changes in fractures directly, difficult to implement upscaled equations of value, and difficult to know if studied laboratory/outcrop samples are representative of activities in the subsurface. This study describes the observed behavior of two distinctly different shales under controlled geomechanical stressing to examine what impact small features have on fracture evolution. By examining two shales with distinctly different structure and composition our goal is to understand when inclusions of micro-features in upscaling is critical to understanding system dynamics.
Two upscaling exercises performed in 2013-14 and 2017-18 on two onshore green fields with conventional to viscous oil are presented, for which the upscaling tried to compensate the effects of grid coarsening, in particular the increase of numerical dispersion and the decrease of heterogeneity. Our methodology was to adjust the water/oil relative permeabilities called pseudo KRs in the coarse scale simulation, in order to reproduce the behavior in terms of pressure, rates, saturations and concentrations of the fine scale model, which was using microscopic rock KRs based on laboratory data.
As the upscaling depends on the fluid injected, it was done separately for waterflood and polymer flood. When done with polymer flood, the concentration of polymer had to be history matched also mainly by adjusting the Todd-Longstaff mixing parameter in addition to the KRs. As upscaling is case dependent, it was performed on several geological models, varying heterogeneity and grid size, but also rock KRs and even precocity of the polymer flood after some waterflood, to test the robustness of the approach.
It was found that pseudo-KRs for waterflood could be slightly degraded for viscous oils, whereas the upscaling was more neutral for conventional oils. This correlates well with field observation for viscous oils, where water production occurs generally a bit quicker than what numerical simulation predicts when using rock KRs, in absence of upscaling.
For polymer floods, which were considered in secondary or early tertiary mode, pseudo KRs were generally improved, mainly because the polymer steepened the saturation fronts, which can be well represented only with small lateral grid size.
The result of both upscaling exercises was that the increment of polymer flood versus waterflood was noticeably higher when computed on high resolution modelling. This is equivalent to saying that when using pseudo KRs resulting from this high resolution matching, the polymer increment on coarse grid is significantly higher than if computed without pseudo KRs. This improves the economic evaluation of the project, increasing the willingness to de-risk and implement early polymer floods on these fields.
Carbonate reservoirs are extremely challenging for reservoir modeling and flow simulation due to their high heterogeneity and the complexity of controls on the porosity and permeability. The porosity and permeability may be connected or weakly connected, which can cause difficulties in coarse grid design and upscaling of flow. We report on the application of a recently developed "Diffuse Source" upscaling approach here applied to the upscaling of a high resolution 3D carbonate reservoir model. A high-resolution 3D geological model of the Amellago carbonate outcrop was utilized for analysis. This model, which has similar stratigraphy, structure and diagenetic controls as Middle East reservoirs, has proven to be a challenge for existing layer upgridding and flow-based upscaling approaches. We utilize flow-based "Diffuse Source" upscaling to obtain the intercell transmissibility and well indices, as this approach has improved localization and resolution compared to steady state calculations, and also allows us to distinguish between well connected and weakly connected sub-volumes. We report on the performance of the statistical layer upgridding approaches used to design the flow simulation grid from the underlying 3D geologic model, and the impact of the choice of the heterogeneity measure (velocity error, time of flight error, or a combination of the two).
Immiscible water-alternating-gas (iWAG) flooding is often considered as a tertiary recovery technique in waterflooded or about-to-be waterflooded reservoirs to increase oil recovery due to better mobility control and potentially favorable hysteretic changes to phase relative permeabilities. In such cases, typically, reservoir simulation models already exist and have been calibrated, often modifying saturation functions during the history matching stage. However, to utilize such models in forecasting iWAG performance, additional parameters may be required. These can be acquired by simulation of WAG coreflood experiments. While in many published cases, the parameter values obtained from matching experimental results are used without modification, this may not be advisable since the parameters are only valid at the core scale at which they were obtained. This paper discusses the challenge of systematically upscaling WAG parameters obtained at core scale to an existing full field model.
In this work, we use a multi-stage upscaling process from core scale to full field scale. The first stage uses a core scale model to match ‘representative’ core flood experiments and obtain WAG parameters. The second uses a well-to-well high-resolution 1D section of the full field model populated using gridblocks of core size to generate ‘reference’ WAG performance using the unaltered WAG parameters obtained from core. The third stage uses a similar 1D model but populated using gridblocks at full field model resolution to match the results from the reference model while adjusting the WAG parameters as little as possible. Finally, a model using the full field model resolution as well as the full field relative permeability functions which, it is assumed, have been tuned to match the history and account for dispersion is used to match the reference model results and obtain final upscaled WAG parameters.
The upscaled WAG parameters obtained at the end of this multi-stage process can be used at the field scale. This process allows clear quantification of the uncertainty associated with the upscaling process. Simulations at the third stage showed that once the full field to core scale grid size ratio exceeded a certain point (2500:1), there was a marked increase in the difference between upscaled and reference model results. It was found that if WAG parameters were changed in the full field model resolution model in order to match recovery results in the reference model, Land's parameter could change by up to 10% and relative permeability reduction factor could increase by up to 30% although it is expected that this will vary from case to case. It is therefore recommended to identify and use full field model resolutions to as close to the threshold as possible. The practice of using the core scale iWAG parameters in the full field model directly could under-estimate actual recovery, and overestimate injectivity. When considering the WAG mechanism alone, the value of the recovery underestimate increasing with pore volumes injected and, in our case, by up to 7% after injecting 1 pore volume of fluid.
This multi-stage simulation approach helps identify the adjustments required and uncertainties associated with simulating iWAG flooding in reservoir models. This approach utilizes options widely present in commercially available finite difference simulators, addresses the challenge of utilizing existing pseudo functions and provides a practical methodology through which iWAG performance forecasting can be improved.
High-resolution discretizations can be advantageous in compositional simulation to reduce excessive numerical diffusion that tends to mask shocks and fingering effects. In this work, we outline a fully implicit, dynamic, multilevel, high-resolution simulator for compositional problems on unstructured polyhedral grids. We rely on four ingredients: (i) sequential splitting of the full problem into a pressure and a transport problem, (ii) ordering of grid cells based on intercell fluxes to localize the nonlinear transport solves, (iii) higher-order discontinuous Galerkin (dG) spatial discretization with order adaptivity for the component transport, and (iv) a dynamic coarsening and refinement procedure. For purely cocurrent flow, and in the absence of capillary forces, the nonlinear transport system can be perturbed to a lower block-triangular form. With counter-current flow caused by gravity or capillary forces, the nonlinear system of discrete transport equations will contain larger blocks of mutually dependent cells on the diagonal. In either case, the transport subproblem can be solved efficiently cell-by-cell or block-by-block because of the natural localization in the dG scheme. In addition, we discuss how adaptive grid and order refinement can effectively improve accuracy. We demonstrate the applicability of the proposed solver through a number of examples, ranging from simple conceptual problems with PEBI grids in two dimensions, to realistic reservoir models in three dimensions. We compare our new solver to the standard upstream-mobility-weighting scheme and to a second-order WENO scheme.
Thomas, Sunil (Chevron Energy Technology Company) | Du, Song (Chevron Energy Technology Company) | Dufour, Gaelle (Chevron Energy Technology Company) | Mallison, Brad (Chevron Energy Technology Company) | Muron, Pierre (Chevron Energy Technology Company) | Rey, Alvaro (Chevron Energy Technology Company)
New developments in unstructured aggregation-based upscaling are presented that improve the flexibility of coarsening designs and enable a more integrated reservoir simulation workflow. Field cases and synthetic tests demonstrate the advantages of the method compared to legacy upscaling methods and fine scale simulations.
Aggregation-based upscaling has recently emerged as a favorable alternative to conventional upscaling methods in reservoir simulation workflows. We outline these developments and describe algorithms used to compute flexible aggregation schemes, coarse transmissibility, and upscaled well indices. The main value additions are,
the ability to selectively coarsen and adapt areal and vertical resolution based on geological features, areas of interest, and/or stratigraphic layer metrics resulting in improved accuracy, the improved simplicity and robustness resulting from avoiding the explicit creation of coarse grids and maintaining one grid for earth modeling and reservoir simulation workflows, and the broad applicability to fields modeled by many grid types including unstructured grids and discrete fracture models.
the ability to selectively coarsen and adapt areal and vertical resolution based on geological features, areas of interest, and/or stratigraphic layer metrics resulting in improved accuracy,
the improved simplicity and robustness resulting from avoiding the explicit creation of coarse grids and maintaining one grid for earth modeling and reservoir simulation workflows, and
the broad applicability to fields modeled by many grid types including unstructured grids and discrete fracture models.
The aggregation-based upscaling methodology is tested in the simulation of some synthetic benchmarks, and of full field models. Comparisons are provided to fine scale simulations in each case, and to legacy upscaling simulations, wherever practically feasible. The most important findings are the seamless integration afforded by the new workflow by eliminating the need for the coarse simulation grid, the significant savings in user interaction time and computational time, and the overall improvement in accuracy, when compared to legacy upscaling workflows. This is important because reservoir engineers operate on tight deadlines to complete projects, and because the logistical challenges of handling fine and coarse grids are significant for studies that involve multiple reservoir model realizations.
Islam, M. S. (Dhofar University in Oman and Fault Analysis Group, UCD School of Earth Sciences, University College Dublin in Ireland) | Manzocchi, T. (Fault Analysis Group and Irish Centre for Research in Applied Geosciences, UCD School of Earth Sciences, University College Dublin)
Most petroleum reservoirs contain faults, and a major technical challenge in full-field flow simulation is to represent the effects of 3D fault zone structure within the 2D fault surface represented in the industry standard commercial simulator. Geometrical upscaling (GU) is sometimes performed to include these fault zones implicitly in the upscaled model, and in this study, a comparison is made of the accuracy and flexibility of different geometrical upscaling methods. The existing template-based geometrical upscaling (TBGU) method is compared to a new flow-based geometrical upscaling (FBGU) method. In both methods, the faults are represented in the upscaled flow simulation model implicitly as neighbor and non-neighbor cell-to-cell connection transmissibilities, which are determined from 3D fault zone structures, but these transmissibilities are calculated in very different ways. Both approaches require a high-resolution flow simulation model (referred as truth model in this paper) containing complex 3D sub-seismic fault zone structure explicitly, which is then upscaled using the two methods to take into account the influences of the fault zone geometry as across-fault and along-fault flow. The accuracy of the upscaling methods is examined by comparing the flow behavior of the high-resolution flow simulation model with that of model versions upscaled in the two different ways. Individual well performance for the high-resolution truth and the upscaled models reveal significant differences between the two methods, and indicate that the flowbased geometrical upscaling technique is a more accurate means of including structurally complex fault zones into low-resolution upscaled flow simulation model.