A Critical Review of the Use of Pseudorelative Permeabilities for Upscaling

Abstract

Summary The properties and limitations of different dynamic pseudorelative permeability methods are summarized. Severe difficulties common to all methods are discussed: choosing the number and locations of the coarse-grid rock types, defining the simulations from which the pseudos are generated, and the dependence of the pseudos on well rates and positions. It is concluded that, in practice, pseudos cannot be used reliably to scale up from a "fine-grid" geological model to a "coarse-grid" fluid-flow model except for cases where capillary or gravity equilibrium can be assumed at the coarse-gridblock scale. Scaling up from the core scale to the geological model is more likely to be possible because capillary forces are more important at smaller scales. A practical approach to the dynamic upscaling problem is outlined, but one should not expect that the effects of the detail in the geological model will be captured more than qualitatively. Introduction Multiphase fluid-flow simulations of oil reservoirs are computationally very intensive. With currently available computers, most oil companies cannot afford to run routine fluid-flow simulations with more than about 10 5 gridblocks. This implies an average gridblock size on the order of 100m areally and perhaps 1 to 10 m vertically. Each gridblock thus represents a part of the reservoir that is heterogeneous. Historically, little information on the structure of the reservoir at this scale was available, so there was little motivation to do anything but ignore the heterogeneity not explicitly represented in the model. Nowadays, modern reservoir imaging techniques and advances in geological modeling are providing more detailed reservoir descriptions. Geological reservoir models are being built with up to 10 7 gridblocks (the size of these models is also limited by computational constraints). These models may be used directly for fluid-in-place and connectivity calculations with little computational difficulty. Single-phase flows, such as well tests or depletion of dry gas reservoirs with no aquifer influx, may possibly be simulated on grids of this size. But for multiphase flows, which occur in the majority of hydrocarbon reservoirs, the detailed geological information must be incorporated into a coarser, fluid-flow simulation model by means of some upscaling technique.

Modeling of subgrid effects in coarse‐scale simulations of transport in heterogeneous porous media

“…This, in turn, can lead to a lack of robustness in the coarse-scale description. See Christie [1996] and Barker and Thibeau [1997] for further discussion of the overall approach. Recent work has demonstrated that the calculation of pseudo relative permeabilities using local boundary conditions based on effective medium theory can lead to significantly improved coarse-scale results [Wallstrom et al, 2000].…”

“…Most such methods either attempt to minimize, and then neglect, subgrid effects [Durlofsky et al, 1996 or require the a priori estimate of the global flow field from which upscaled (or pseudo) flux functions are computed [Christie, 1996;Barker and Thibeau, 1997]. The present method does model subgrid effects, but it does not require a priori estimates of the global flow field.…”

Scale dependency of dynamic relative permeability–satuartion curves in relation with fluid viscosity and dynamic capillary pressure effect

“…Indeed the scale dependency and methods for upscaling of P c -S w , K r -S w and s-S w relationships had been the subjects of intense study in the literature [7,[51][52][53][54][55][56]. Barker and Thibeau [51] and Renard and De Marsily [54] suggested that the constitutive relationship should be used at the same scale as that of a predictive model but the practicality would only be attained with upscaling. In this regard, Gasda and Celia [52] proposed correction for the coarse grid simulation so that it could match better with the fine grid simulations.…”

Large-scale Invasion Percolation with Trapping for Upscaling Capillary-Controlled Darcy-scale Flow

“…In general, all dynamic pseudofunctions, produced at large scales, where viscous forces become important, depend on boundary conditions and the underlying gridding properties. They are only correct for the specific grid and flow conditions used to derive them (Barker and Thibeau 1997;Barker and Dupouy 1999).…”