Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques

Abstract

Summary This paper presents the results of the 10th SPE Comparative Solution Project on Upscaling. Two problems were chosen. The first problem was a small 2D gas-injection problem, chosen so that the fine grid could be computed easily and both upscaling and pseudoization methods could be used. The second problem was a waterflood of a large geostatistical model, chosen so that it was hard (though not impossible) to compute the true fine-grid solution. Nine participants provided results for one or both problems. Introduction The SPE Comparative Solution Projects provide a vehicle for independent comparison of methods and a recognized suite of test data sets for specific problems. The previous nine comparative solution projects1–9 have focused on black-oil, compositional, dual-porosity, thermal, or miscible simulations, as well as horizontal wells and gridding techniques. The aim of the 10th Comparative Solution Project was to compare upgridding and upscaling approaches for two problems. Full details of the project, and data files available for downloading, can be found on the project's Web site.10 The first problem was a simple, 2,000-cell 2D vertical cross section. The specified tasks were to apply upscaling or pseudoization methods and to obtain solutions for a specified coarse grid and a coarse grid selected by the participant. The second problem was a 3D waterflood of a 1.1-million-cell geostatistical model. This model was chosen to be sufficiently detailed so that it would be hard, though not impossible, to run the fine-grid solution and use classical pseudoization methods. We will not review the large number of upscaling approaches here. For a detailed description of these methods, see any of the reviews of upscaling and pseudoization techniques, such as Refs. 11 through 14. Description of Problems Model 1. The model is a two-phase (oil and gas) model that has a simple 2D vertical cross-sectional geometry with no dipping or faults. The dimensions of the model are 2,500 ft long×25 ft wide×50 ft thick. The fine-scale grid is 100×1×20, with uniform size for each of the gridblocks. The top of the model is at 0.0 ft, with initial pressure at this point of 100 psia. Initially, the model is fully saturated with oil (no connate water). Full details are provided in Appendix A. The permeability distribution is a correlated, geostatistically generated field, shown in Fig. 1. The fluids are assumed to be incompressible and immiscible. The fine-grid relative permeabilities are shown in Fig. 2. Residual oil saturation was 0.2, and critical gas saturation was 0. Capillary pressure was assumed to be negligible in this case. Gas was injected from an injector located at the left of the model, and dead oil was produced from a well to the right of the model. Both wells have a well internal diameter of 1.0 ft and are completed vertically throughout the model. The injection rate was set to give a frontal velocity of 1 ft/D (about 0.3 m/d or 6.97 m3/d), and the producer is set to produce at a constant bottomhole pressure limit of 95 psia. The reference depth for the bottomhole pressure is at 0.0 ft (top of the model). The specified tasks were to apply an upscaling or pseudoization method in the following scenarios.2D: 2D uniform 5×1×5 coarse-grid model.2D: 2D nonuniform coarsening, maximum 100 cells. Directional pseudorelative permeabilities were allowed if necessary. Model 2. This model has a sufficiently fine grid to make the use of any method that relies on having the full fine-grid solution almost impossible. The model has a simple geometry, with no top structure or faults. The reason for this choice is to provide maximum flexibility in the selection of upscaled grids. At the fine geological model scale, the model is described on a regular Cartesian grid. The model dimensions are 1,200×2,200×170 ft. The top 70 ft (35 layers) represent the Tarbert formation, and the bottom 100 ft (50 layers) represent Upper Ness. The fine-scale cell size is 20×10×2 ft. The fine-scale model has 60×220×85 cells (1.122×106 cells). The porosity distribution is shown in Fig 3. The model consists of part of a Brent sequence. The model was originally generated for use in the PUNQ project.15 The vertical permeability of the model was altered from the original; originally, the model had a uniform kV/kH across the whole domain. The model used here has a kV/kH of 0.3 in the channels and a kV/kH of 10–3 in the background. The top part of the model is a Tarbert formation and is a representation of a prograding near-shore environment. The lower part (Upper Ness) is fluvial. Full details are provided in Appendix B. Participants and Methods Chevron. Results were submitted for Model 2 using CHEARS, Chevron's in-house reservoir simulator. They used the parallel version and the serial version for the fine-grid model and the serial version for the scaled-up model. Coats Engineering Inc. Runs were submitted for both Model 1 and Model 2. The simulation results were generated with SENSOR. GeoQuest. A solution was submitted for Model 2 only, with coarse-grid runs performed using ECLIPSE 100. The full fine-grid model was run using FRONTSIM, a streamline simulator,16 to check the accuracy of the upscaling. The coarse-grid models were constructed with FloGrid, a gridding and upscaling application. Landmark. Landmark submitted entries for both Model 1 and Model 2 using the VIP simulator. The fine grid for Model 2 was run with parallel VIP. Phillips Petroleum. Solutions were submitted for both Model 1 and Model 2. The simulator used was SENSOR. Roxar. Entries were submitted for both Model 1 and Model 2. The simulation results presented were generated with the black-oil implicit simulator Nextwell. The upscaled grid properties were generated using RMS, specifically the RMSsimgrid option. Streamsim. Streamsim submitted an entry for Model 2 only. Simulations were run with 3DSL, a streamline-based simulator.17 TotalFinaElf. TotalFinaElf submitted a solution for Model 2 only. The simulator used for the results presented was ECLIPSE; results were checked with the streamline code 3DSL. U. of New South Wales. The U. of New South Wales submitted results for Model 1 only, using CMG's IMEX simulator.

A locally conservative variational multiscale method for the simulation of porous media flow with multiscale source terms

“…It is taken from the top layer of the 10th SPE comparative solution project [17]. The fine grid on which the permeability is defined consists of 60 x 220 gridblocks.…”

Multiscale simulations of porous media flows in flow-based coordinate system

“…1) is a synthetic channelized reservoir generated using both multipoint geostatistics (for the channels) and two-point geostatistics (for permeability distribution within each facies). The second channelized system is one of the layers of the benchmark test (representing the North Sea reservoir), the Society of Petroleum Engineers comparative project [9] (upper Ness layers). These permeability fields are highly heterogeneous, channelized, and difficult to upscale.…”

“…These permeability fields are highly heterogeneous, channelized, and difficult to upscale. Because the permeability fields are [9] highly heterogeneous, they are refined to 400 × 400 to obtain accurate comparisons.…”

Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

“…Comparative Project (see [8]) that are modified to fit the domain dimensions L x = 256 and L y = 64. Examples of realizations for the permeability fields with long correlation lengths are shown in Figure 4.1.…”