Applying High-Resolution Numerical Schemes in Reservoirs Described by Complex Corner-Point Grids

Abstract

Abstract Higher order numerical schemes are necessary to get good front resolution when modelling reservoirs using practical block sizes. Methods for such schemes presented to date have focussed on situations where the grids are somewhat regular. To be useful, implementations are required that can apply in situations when the gridding is complex, such as when corner point grids are involved that have non-regular cells, grid refinements are used, and when faults exist. This work discusses the implementation of higher order accurate methods in a corner point setting when refinements and faulting are present, and includes a discussion of how to maintain numerical stability. The implementation is carried out in an equation of state-based fully compositional reservoir simulator that uses complex corner point grids with faulting and refinements, thereby making higher order methods available for field scale reservoir modelling. The numerical schemes use two point flux calculations and can be up to second order accurate in space in smooth regions, the latter being regions where the various component, phase saturation and pressure distributions (and hence phase velocities) are smoothly varying. A Total Variation Diminishing (TVD) flux limiter is required to maintain numerical stability. Such limiters are applied to the inter-cell flows in each component's mass balance equation to control throughput and to ensure overall stability of the resulting numerical scheme. The application of flux limiters also guarantees that the computed properties remain within their physical ranges. TVD limiters must be applied carefully when complex grids are encountered as cells have varying dimensions and can be partially contacted by neighbouring grid cells on several faces. Special consideration needs to be given to how the limiters are to be evaluated in these situations. This usage extends TVD technology beyond what has already been done in reservoir simulation, and makes its use practical for complicated field scale models. The results of several simulations are demonstrated. In particular, the ability of the techniques to better resolve sharp fronts can be seen. This leads to a more accurate prediction of overall fluid movements, including fluid contamination and mixing, breakthrough timing, and front and/or fluid bank movement in the reservoir. A more precise evaluation of ultimate recovery for the reservoir is obtained, which leads to the opportunity to improve overall recovery. The techniques described here can greatly enhance the accuracy of compositional reservoir simulation, and it is shown how these capabilities can be brought to the realm of field scale modelling with complex corner point grids.