A dispersion-free numerical procedure for the solution of nonlinear conservation equations based on exact solutions of the Riemann Problem by the Random Choice Method is reviewed. This paper is concentrated on the displacement of oil by water in a onedimensional porous rock, however, the technique applies equally well to a variety of physical problems where accurate modelling of the evolution of discontinuities / shock waves is imperative. For immiscible displacement, the nonlinear part of the conservation equation is an empirical function with error bounds. The effect of representing the (unknown) smooth nonlinearity function by a tabulated version is studied, accompanied by a proof for the structural stability of the problem with respect to small perturbations in the nonlinear function.
The mechanisms of fluid flow in fractures in a chalk and fracture closure were studied both by pure flow simulation, and by coupled flow and rock mechanics simulation. Simulated fracture flow as such, and different ways to model the closure are discussed. Since the fractures are basically one-dimensional objects, they are only to a small degree affected by boundary conditions, and the closure can equally well be modelled as a function of fluid pressure as of strain – a considerable simplification. Explicit fracture modelling does not seem to be necessary to obtain reliable simulated results.Key words: Chalk, fractures, fracture closure, coupled simulation
Based on exact strain calculations from a simplified coupled flow – stress simulation run, the reservoir is subdivided into a number of “pseudo soil regions” such that in each sub-region compaction is a function of fluid pressure only, while still honouring the original soil properties. This revised compaction model is tailored for the flow simulator framework, and when used in that setting the flow simulator computes a compaction state which is as good as identical to the “exact” state computed from strain, in (almost) every grid cell. The construction process is always possible, and an error tolerance can be set such that coupled simulations can be guaranteed to run in explicit mode (no pore volume iterations needed) without loss of accuracy. The overall gain is a flow simulator computed compaction field which is accurate at all times (not only at stress steps), and which can be computed with significantly less computer effort than with the standard approachKey words: Compaction, Reservoir simulation, coupled simulation, computational mechanics
In simulation models for reservoirs containing a thin oil zone, an alternative to the established approach of aligning the simulation grid layers with geological layers (“geo-grid”), is to use a model with horizontal grid layers, at least covering the oil zone, and possibly also all or parts of the gas cap and water zone. The motivation for this approach is that as the high resolution part of the grid can be concentrated to regions of fluid contact movement, an improved representation of contact movement and cusping / coning into horizontal wells can be expected. The main drawback is obviously that the geological description and petrophysics will be poorer resolved than on a traditional grid, which is built in a manner tailored to honour these features. The aim of this study has been to classify the benefits and drawbacks of using horizontal grids in thin-oil-zone reservoir models, and in the cases where such grids actually are used, to identify some recommended practice.The main conclusions from the study can be summarized as,•True horizontal wells are better represented on a horizontal grid. In a geo-grid all well completions are approximated to the nearest cell centre, which is an error source which may be significant.•Using the same areal resolution, comparable results were obtained with geo-grids and horizontal grids. Gas production and partly also water production was better resolved on the horizontal grid.•For comparable grids the computer processing time was about 30-50% lower for the horizontal grid than the geo-grid. Results from a geo-grid with local grid refinement near the horizontal wells were almost identical to the horizontal grid case, but very costly in terms of computer time.•Recommended strategies for the horizontal gridoIn the oil zone it was found that one meter thick layers was the best compromise between accuracy and computing timeoThe use of horizontal layers in the gas cap and water zone depends on the process. In general, high resolution horizontal layers should be used to capture contact movement.oIn this study the gas cap was in expansion mode, while the water zone was an active aquifer.oAlmost identical results were achieved with only two horizontal layers in the gas cap, with a high resolution horizontal grid in the gas cap, and using geo-layers in the gas cap. Hence, as the gas is in expansion mode, the resolution or gridding strategy for the gas zone does not seem to be important.oDuring production, the oil-water contact moves upwards and downwards in a complex manner. This was best captured by using a horizontal grid with slowly increasing layer thicknesses from the oil-water contact downwards, covering about 20% of the water zone thickness, and geo-layers below.Key words: Reservoir simulation, thin oil zone, horizontal wells, horizontal grid
The impact of simulation grid size and dimension has been studied for two-phase flow withvarying relative permeability, using three different reservoir simulatorKey words: Upscaling, homogeneous, two-phase, ECLIPSE, IMEX, STARS