Summary
A new macroscale pressure definition is investigated through a series of
upscaling calculations for two-phase flow in porous media. This definition is
taken from previous theoretical work by the authors and aims at correcting for
systematic subscale heterogeneities including those generated by nonlinear
dependencies on (heterogeneous) saturation distributions. Traditional intrinsic
phase-averaged pressure leads to nonmonotone and multivalued upscaled
constitutive functions (e.g., discontinuous upscaled-relative-permeabilities
exceeding unity). Using both analytical and numerical calculations, the new
macroscale pressure definition is shown to lead to better-behaved upscaled
functions.
Introduction
One of the most important challenges in the simulation of multiphase flow
processes, such as oil and gas recovery, is the large disparity between the
resolution of the geological characterization and the smallest feasible grid
size in a typical numerical simulation. Modern geostatistical approaches
frequently produce realizations of the geology with details down to the
submeter scale. Computational capabilities of modern multiphase flow simulators
are typically limited to approximately a million grid cells. For a medium-sized
oil field, this translates to a grid resolution on the scale of tens of meters.
As a consequence, some form of coarsening or upscaling is necessary to relate
the geological description to parameters defined at the grid-block scale.
Several approaches to upscaling are currently under active development. In
these methods, macroscale flow equations are defined, for which effective
parameters must be obtained. These macroscale effective parameters are
typically chosen such that the solution of some small-scale flow problem is
honored; for reviews see Barker and Thibeau (1997) or Christie (2001). Recent
developments have looked at enhancing this approach by optimizing the choice of
macroscale grid, as well as introducing higher-order spatial moments (such as
variance and covariance) of saturation and flow into the macroscale effective
functions (Durlofsky 1998). The general framework of upscaling to obtain
effective parameters forms the basis of the discussion in this paper.
© 2009. Society of Petroleum Engineers
View full textPDF
(
661 KB
)
History
- Original manuscript received:
29 September 2007
- Revised manuscript received:
30 January 2008
- Manuscript approved:
16 February 2008
- Published online:
17 December 2009
- Version of record:
12 March 2010
View Cart
