Summary
Fractured-reservoir relative permeability, water breakthrough, and recovery
cannot be extrapolated from core samples, but computer simulations allow their
quantification through the use of discrete fracture models at an intermediate
scale. For this purpose, we represent intersecting naturally and stochastically
generated fractures in massive or layered porous rock with an unstructured
hybrid finite-element (FE) grid. We compute two-phase flow with an implicit
FE/finite volume (FV) method (FE/FVM) to identify the emergent properties of
this complex system.
The results offer many important insights: Flow velocity varies by three to
seven orders of magnitude and velocity spectra are multimodal, with significant
overlaps between fracture- and matrix-flow domains. Residual saturations
greatly exceed those that were initially assigned to the rock matrix. Total
mobility is low over a wide saturation range and is very sensitive to small
saturation changes. When fractures dominate the flow, but fracture porosity is
low (10−3 to 1%), gridblock average relative permeabilities, kr,avg, cross over
during saturation changes of less than 1%. Such upscaled kr,avg yield a convex,
highly dispersive fractional-flow function without a shock. Its shape cannot be
matched with any conventional model, and a new formalism based on the
fracture/matrix flux ratio is proposed.
Spontaneous imbibition during waterflooding occurs only over a small
fraction of the total fracture/matrix-interface area because water imbibes only
a limited number of fractures. Yet in some of these, flow will be sufficiently
fast for this process to enhance recovery significantly. We also observe that a
rate dependence of recovery and water breakthrough occurs earlier in
transient-state flow than in steady-state flow.
Introduction
Oil is difficult to recover from fractured reservoirs; however,
approximately 60% of the world’s remaining oil resources reside in
heterogeneously deformed formations (Beydoun 1998). The production dilemma is
reflected in complex pressure and production histories, unpredictable couplings
of wells independent of their spatial separation, rapidly changing flow rates
and the risks of rapid water breakthrough, and low final recovery (Kazemi and
Gilman 1993).
Qualitatively, the main production obstacle is simple to conceptualize
(Barenblatt et al. 1990): while the oil resides in the pores of the rock
matrix, production-induced flow will occur predominantly in the fractures.
However, they typically contribute less than 1% to the total fluid-saturated
void space and are therefore rapidly invaded by the injected fluid. Once
short-circuited by the injectant, the injection/production stream entrains only
the oil that enters the fractures as a consequence of countercurrent imbibition
(CCI) (Lu et al. 2006). The efficiency of this process is relatively well
constrained by experimental work (Morrow and Mason 2001) and reproduced
accurately by transfer functions (Lu et al. 2006). Rate predictions for
fractured reservoirs require a further estimate of the area of the
fracture/matrix interface captured by a shape factor (Kazemi et al. 1992).
However, in cases where this measure is relatively well-constrained, predicted
transfer rates appear to greatly exceed actual values . This observation
suggests that, at any one time in the production history, transfer occurs over
only a small part of the fracture/matrix interface. Furthermore, as is
indicated by packer tests and temperature logs, only a small number of
fractures contribute to the flow during production (Long and Billaux 1987,
Barton 1995). This is confirmed by field-data-based numerical flow models
(Matthäi and Belayneh 2004, Belayneh et al. 2006), highlighting that viscous
flow in the rock matrix is usually significant, even if the fractures are well
interconnected. All these findings conflict with the simple conceptual model,
even qualitatively. How shall we replace it with something more accurate for
the prediction of the behavior of fractured reservoirs?
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
7 December 2004
- Meeting paper published:
31 January 2005
- Revised manuscript received:
19 March 2007
- Manuscript approved:
12 July 2007
- Version of record:
20 December 2007
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