Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques

Abstract

Abstract This paper presents the results of the Tenth 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 pseudoisation 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 datasets for specific problems. The previous nine comparative solution projects1–9 have focussed on black-oil, compositional, dual porosity, thermal or miscible simulations, as well as horizontal wells and gridding techniques. The aim of the tenth 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 web site10. The first problem was a simple 2000 cell 2D vertical cross section. The tasks specified were to apply upscaling or pseudoization methods and 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 that it would be hard, though not impossible, to run the fine grid solution and use classical pseudoisation 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 pseudoisation techniques, for example11–14. Description of Problems Model 1 The model is a 2-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 762 meters long by 7.62 meters wide by 15.24 meters thick. The fine scale grid is 100×1×20 with uniform size for each of the grid blocks. The top of the model is at 0.0 metres with initial pressure at this point of 100 psia. Initially the model is fully saturated with oil (no connate water). 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. 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 on 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 0.3 m/d (about 1 foot/day or 6.97 m3 per day), and the producer is set to produce at a constant bottom pressure limit of 95 psia. The reference depth for the bottom hole pressure is at 0.0 meters (top of the model). The tasks specified were to apply upscaling or pseudoization method in the following scenarios:2D - 2D uniform 5×1×5 coarse grid model2D - 2D nonuniform coarsening. Max 100 cells. Directional pseudo relative permeabilities were allowed if necessary. Model 2 This model has a sufficiently fine grid to make 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 selection of upscaled grids.