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.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
20 February 2006
- Meeting paper published:
12 June 2006
- Revised manuscript received:
7 August 2007
- Manuscript approved:
13 August 2007
- Version of record:
20 March 2008
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