Three-Phase Upscaling in Capillary and Viscous Limit
Arild Lohne, George A. Virnovsky · 2006
Abstract Three phase flow properties are important for correct modeling and prediction of such IOR processes as WAG and blow-down/depletion after waterflooding. On the core-scale, these properties can generally be obtained directly from experiments, from pore-scale modeling of three-phase flow, or from empiric formulae (like the Stone's) interpolating two sets of two-phase data into the three-phase saturation region. For usage in simulators core scale properties have to be scaled up to reflect heterogeneities smaller than the simulation grid-blocks. These upscaled three-phase properties, similarly to their two-phase counterparts, are rate-dependent. We describe the upscaling procedure and efficient algorithms for three "easy-to-compute" asymptotic cases: VL-viscous limit (viscous dominance), CL-capillary limit (dominance of capillary forces), and VE-vertical equilibrium (flow dominated by gravity and capillarity). Upscaled 3-phase relative permeabilities for different geological flow units from a North Sea field are analyzed. At VL, upscaled relative permeabilities to all phases will in general depend on two saturations if contrasts in relative permeabilities are present at the finer scale. This dependency may in many cases be small and ignored, but not always. At CL, upscaled krw and krg will remain functions of one saturation each, as long as the oil phase is mobile in every part of the porous medium. When oil reaches its immobile saturation in part of the medium, both krw and krg will turn into full three-phase functions depending on two saturations. For the examples presented the size of the domain with full three-phase functions covers up to about half of the three-phase domain. The three-phase dependency was very weak for water in all the tested cases, while for gas very strong effects could be observed.