Fast Estimation of Connectivity in Fractured Reservoirs Using Percolation Theory
- Mohsen Masihi (Sharif University of Technology) | Peter Robert King (Imperial College) | Peyman Reza Nurafza (Imperial College)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2007
- Document Type
- Journal Paper
- 167 - 178
- 2007. Society of Petroleum Engineers
- 4.3.4 Scale, 5.6.4 Drillstem/Well Testing, 5.8.6 Naturally Fractured Reservoir, 4.1.2 Separation and Treating, 5.6.5 Tracers, 1.6.9 Coring, Fishing, 5.1 Reservoir Characterisation, 5.3.2 Multiphase Flow, 5.5.2 Core Analysis, 5.5.3 Scaling Methods, 4.1.5 Processing Equipment, 5.1.2 Faults and Fracture Characterisation
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- 966 since 2007
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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.
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.
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