Summary
We have developed a new constrained optimization approach to the coarsening
of 3D reservoir models for flow simulation. The optimization maximally
preserves a statistical measure of the heterogeneity of a fine-scale model.
Constraints arise from the reservoir fluids, well locations, pay/nonpay
juxtaposition, and large-scale reservoir structure and stratigraphy. The
approach has been validated for a number of oil and gas projects, where flow
simulation through the coarsened model is shown to provide an excellent
approximation to high-resolution calculations performed in the original
model.
The optimal layer coarsening is related to the analyses of Li and Beckner
(2000), Li et al. (1995), and Testerman (1962). It differs by using a more
accurate measure of reservoir heterogeneity and by being based on recursive
sequential coarsening instead of sequential refinement. Recursive coarsening is
shown to be significantly faster than refinement: the cost of the calculation
scales as (NX.NY.NZ) instead of (NX.NY.NZ)². The more accurate measure of
reservoir heterogeneity is very important; it provides a more conservative
estimate of the optimal number of layers than the analysis of Li et al. The
latter is shown to be too aggressive and does not preserve important aspects of
the reservoir heterogeneity. Our approach also differs from the global methods
of Stern and Dawson (1999) and Durlofsky et al. (1996). It does not require the
calculation of a global pressure solution, nor does it require the imposition
of large-scale flow fields, which may bias the analysis (Fincham et al. 2004).
Instead, global flow calculations are retained only to validate the reservoir
coarsening.
Our approach can also be used to generate highly unstructured,
variable-resolution computational grids. The layering scheme for these grids
follows from the statistical analysis of the reservoir heterogeneity. Locally
variable resolution follows from the constraints (reservoir structure, faults,
well locations, fluids, pay/nonpay juxtaposition). Our reservoir simulator has
been modified to allow a fine-scale model to be initialized and further
coarsened at run time. This has many advantages in that it provides both
simplified and powerful workflows, which allow engineers and geoscientists to
work with identical shared models.
Introduction
The development of (coarsened) reservoir simulation models from
high-resolution geologic models remains an active field of research (Darche et
al. 2005; Nilsson et al. 2005; Fincham et al. 2004; Li and Beckner 2000; Stern
and Dawson 1999; Li et al. 1995; Durlofsky et al. 1996). These studies are
motivated by a desire to understand the errors introduced when a
high-resolution model is upscaled or, equivalently, to use an error analysis to
find the optimal coarsened grid. If coarsened too far, the reservoir
description many be overly homogenized, providing biased performance
predictions. If coarsened too little, the cost of the simulation model may
remain too high, limiting the utility of the model for detailed engineering or
sensitivity studies. In the current study, we propose a statistical error
analysis for layer coarsening, which guides us to an optimal layering scheme.
Specifically, the error analysis provides us with a sequence of possible
layering schemes, with a calculated error for each. The scheme with the minimum
number of layers that reduces variance but does not introduce bias into the
solution by over-homogenization is the optimal scheme.
© 2006. Society of Petroleum Engineers
View full textPDF
(
3,146 KB
)
History
- Original manuscript received:
15 July 2005
- Revised manuscript received:
18 January 2006
- Manuscript approved:
12 June 2006
- Version of record:
20 August 2006
View Cart
