We develop a physically motivated approach to modeling displacement
processes in fractured reservoirs. To find matrix/fracture transfer functions
in a dual-porosity model, we use analytical expressions for the average
recovery as a function of time for gas gravity drainage and countercurrent
imbibition. For capillary-controlled displacement, the recovery tends to its
ultimate value with an approximately exponential decay (Barenblatt et al.
1990). When gravity dominates, the approach to ultimate recovery is slower and
varies as a power law with time (Hagoort 1980). We apply transfer functions
based on these expressions for core-scale recovery in field-scale
To account for heterogeneity in wettability, matrix permeability, and
fracture geometry within a single gridblock, we propose a multirate model
(Ponting 2004). We allow the matrix to be composed of a series of separate
domains in communication with different fracture sets with different rate
constants in the transfer function.
We use this methodology to simulate recovery in a Chinese oil field to
assess the efficiency of different injection processes. We use a
streamline-based formulation that elegantly allows the transfer between
fracture and matrix to be accommodated as source terms in the 1D transport
equations along streamlines that capture the flow in the fractures (Di Donato
et al. 2003; Di Donato and Blunt 2004; Huang et al. 2004).
This approach contrasts with the current Darcy-like formulation for
fracture/matrix transfer based on a shape factor (Gilman and Kazemi 1983) that
may not give the correct average behavior (Di Donato et al. 2003; Di Donato and
Blunt 2004; Huang et al. 2004). Furthermore, we show that recovery is
exceptionally sensitive to parameters that describe the physics of the
displacement process, highlighting the need to make careful core-scale
measurements of recovery.
Di Donato et al.(2003) and Di Donato and Blunt (2004) proposed a
dual-porosity streamline-based model for simulating flow in fractured
reservoirs. Conceptually, the reservoir is composed of two domains: a flowing
region with high permeability that represents the fracture network and a
stagnant region with low permeability that represents the matrix (Barenblatt et
al. 1960; Warren and Root 1963). The streamlines capture flow in the flowing
regions, while transfer from fracture to matrix is accommodated as source/sink
terms in the transport equations along streamlines. Di Donato et al.
(2003) applied this methodology to study capillary-controlled transfer between
fracture and matrix and demonstrated that using streamlines allowed
multimillion-cell models to be run using standard computing resources. They
showed that the run time could be orders of magnitude smaller than equivalent
conventional grid-based simulation (Huang et al. 2004). This streamline
approach has been applied by other authors (Al-Huthali and Datta-Gupta 2004)
who have extended the method to include gravitational effects, gas
displacement, and dual-permeability simulation, where there is also flow in the
matrix. Thiele et al. (2004) have described a commercial implementation
of a streamline dual-porosity model based on the work of Di Donato et al. that
efficiently solves the 1D transport equations along streamlines.
© 2007. Society of Petroleum Engineers
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