Summary
Investigating the impact of geological uncertainty (i.e., spatial
distribution of fractures) on reservoir performance may aid management
decisions. The conventional approach to address this is to build a number of
possible reservoir models, upscale them, and then run flow simulations. The
problem with this approach is that it is computationally very expensive. In
this study, we use another approach based on the permeability contrasts that
control the flow, called percolation approach. This assumes that the
permeability disorder of a rock can be simplified to either permeable or
impermeable. The advantage is that by using some universal laws from
percolation theory, the effect of the complex geometry which influences the
global properties (e.g., connectivity or conductivity) can be easily estimated
in a fraction of a second on a spread sheet.
The aim of this contribution is to establish the percolation framework to
examine the connectivity of fracture systems at a given finite observation
scale in 2D and 3D. In particular, we use numerical simulation to show
how the scaling laws of the connectivity derived originally for constant-length
isotropic systems can be expanded to cover more realistic cases including
fracture systems with anisotropy and fracture-length distribution. Finally, the
outcrop data of mineralized fractures exposed on the southern margin of the
Bristol Channel Basin was used to show that the predictions from the
percolation approach are in agreement with the results calculated from field
data but can be obtained very quickly. As a result, this may be used for
practical engineering purposes for decision making.
Introduction
Fractured reservoirs are very complex, containing geological heterogeneities
(i.e., fractures) on various length scales from microns to kilometers. These
heterogeneities have significant impact on the flow behavior and have to be
modeled to make reliable prediction of reservoir performance. However, we have
very few direct measurements of the flow properties (e.g., core and image-log
data) that are 1D and represent a very small volume of a typical reservoir.
Other type of data are more widespread (e.g., well-test or seismic data) but
generally are related indirectly to fracture distribution. The consequence is a
great deal of uncertainty about the spatial distribution of the fractures that
influence the flow and affect the reservoir performance. A major factor in
analysis of flow and transport in these reservoirs is the appropriate
representation of the heterogeneities that control flow (Bear et al. 1993).
The conventional approach to investigate the impact of geological
uncertainty on reservoir recovery is to build a detailed reservoir model using
geophysical and geological data, upscale it, and then perform flow simulation.
This is typically done by assuming either equivalent continuum models (i.e.,
dual porosity or dual permeability), discrete network models, or an integration
of both (Warren and Root 1963; Dershowitz et al. 2000). The fractures can be
assumed to be infinite (Snow 1969), which means that they are perfectly
connected, or finite in length (Sagar and Runchal 1982; Long and Witherspoon
1985). If fractures are poorly interconnected and the matrix rock is relatively
impermeable, the network formed by the fractures may control the flow. On the
other hand, if the matrix is relatively permeable and the fractures are regular
and highly interconnected, fractures and matrix could be treated as two
separate continuums occupying the entire domain (Warren and Root 1963). In
order to have a reliable estimation of reservoir performance parameters, it is
necessary to construct a number of possible reservoir models (with associated
probabilities) and then run flow simulations many times. The problem with this
approach is that it is computationally very expensive. Therefore, there is a
great incentive to produce much simpler physically-based models to predict
uncertainty in performance very quickly, especially for engineering
purposes.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
21 March 2005
- Revised manuscript received:
19 October 2006
- Manuscript approved:
21 November 2006
- Version of record:
20 June 2007
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