Summary
Uncertainty in geometrical properties of fractures, when they are considered as the conductive paths for flow movement, affects all aspects of flow in fractured reservoirs. The connectivity of fractures, embedded in low-permeability zones, can control fluid movement and influence field performance. This can be analyzed using percolation theory. This approach uses the hypothesis that the permeability map can be split into either permeable (i.e., fracture) or impermeable (i.e., matrix) portions and assumes that the connectivity of fractures controls the flow. The analysis of the connectivity based on finite-size scaling assumes that fractures all have the same sizes. However, natural fracture networks involve a relatively wide range of fracture lengths, modeled by either scale-limited laws (e.g., log normal) or power laws.
In this paper, we extend the applicability of the percolation approach to a system with a distribution of size. For scale-limited distributions, we use the hypothesis seen in the literature that the connectivity of fractures of variable size is identical to the connectivity of fractures of the same size whose length is given by an appropriate effective length. It is then necessary to define the percolation probability based on the excluded area arguments. In this research work, we also validate the applicability of this idea to fracture networks having a uniform, Gaussian, exponential, and log-normal length distribution. However, in the case of the power-law length distribution, we have found that the scaling parameters (e.g., correlation length exponent) have to be modified. The main contribution is to show how the critical exponents vary as a function of the power-law exponent.
To validate the approach, we used outcrop data of mineralized fractures (vein sets) exposed on the southern margin of the Bristol Channel basin. We show that the predictions from the percolation approach are in good agreement with the results calculated from field data with the advantage that they can be obtained very quickly. As a result, they may be used for practical engineering purposes and may aid decision-making for real field problem.
Introduction
Many hydrocarbon reservoirs are naturally fractured. The conventional approach to investigate the impact of geological uncertainties on reservoir performance is to build a detailed reservoir model using available geophysical and geological data, upscale it, and then perform flow simulation. In fractured reservoirs, this can be done by using equivalent continuum models (i.e., dual porosity), discrete network models, or a combination of both [see Warren and Root (1963), Quenes and Hartley (2000), and Dershowitz et al. (2000)]. The nature of fluid flow in fractured reservoirs of low matrix permeability depends strongly on the spatial distribution of the conductive natural fractures.
We use the term "fracture" to mean any discontinuity within a rock mass that developed as a response to stress. Fractures exist on various length scales from microns to kilometres. They appear as tensile (e.g., joints or veins) or shear (e.g., faults) and can act as hydraulic conductors or barriers to flow movement. Conductive fractures may be connected in a complicated manner to form a complex network. The connectivity of such networks is a crucial parameter in controlling flow movement, which in turn depends on the geometrical properties of the network such as fracture orientation, spacing, or length distribution.
Equivalent Permeability Distribution for Fractured Porous Rocks: The Influence of Fracture Network Properties
