Absolute Permeability Upscaling Assessment in Different Coarsening Levels inReservoirs with Various Heterogeneities and Displacement Processes

Upscaling is an effective solution to overcome time and resource limitations in dynamic reservoir simulation. In thisstudy, eight absolute permeability upscaling methods were evaluated, namely: arithmetic, geometric, harmonic-arithmetic,renormalization, pressure-solver, unbiased, sequential unbiased, and sequential pressure-solver methods. Thelast three methods, introduced here for the first time, are numerical approaches in which the diffusivity equation issolved over local fine grid-blocks under the corresponding boundary condition of the coarse grid-blocks, and theequivalent permeability is then calculated using Darcy’s equation. By implementing six water-flooding scenariosover three synthetically generated reservoirs, the effects of a broad range of mobility ratios (۰.۲ to ۲۰), capillarypressure, and reservoir heterogeneity on the performance of upscaling methods were investigated. Moreover, it wasobserved that average boundary pressure errors were high and increased rapidly with up-scaling level from ۲% at level۲ to ۳۵% at level ۱۶. Furthermore, a similar trend was observed for the average reservoir pressure, but it has muchsmaller error which goes up to ۷% at highest upscaling level. Therefore, it is necessary to apply near-well/boundaryupscaling methods to improve pressure distribution. The overall error never exceeded ۰.۵% with respect to heterogeneityand capillary pressure effects, whereas at MR = ۰.۲, it increased to about ۵–۶% for oil and ۱.۵% for water productionrate. In most scenarios, numerical methods produced smaller overall error compared with analytical methods.Ultimately, in general, unbiased and sequential unbiased estimation were found to be the superior numerical methodsand arithmetic and harmonic-arithmetic methods were identified as the superior analytical methods.

Keywords:

Upsscaling , Absolutes Permeability , analytical method , numerical method , Heterogeneity , displacement process