Summary
The exploitation of unconventional reservoirs complements the practice of
hydraulic fracturing, and with an ever-increasing demand in energy, this
practice is set to experience significant growth in the coming years.
Sophisticated analytic models are needed to accurately describe fluid flow in a
hydraulic fracture, and the problem has been approached from different
directions in the past 3 decades--starting with the work of Gringarten et al.
(1974) for an infinite-conductivity case, followed by contributions from
Cinco-Ley et al. (1978), Lee and Brockenbrough (1986), Ozkan and Raghavan
(1991), and Blasingame and Poe (1993) for a finite-conductivity case. This
topic remains an active area of research and, for the more-complicated physical
scenarios such as multiple transverse fractures in ultratight reservoirs,
answers are currently being sought.
Starting with the seminal work of Chang and Yortsos (1990), fractal theory
has been successfully applied to pressure-transient testing, although with an
emphasis on the effects of natural fractures in pressure/rate behavior. In this
paper, we begin by performing a rigorous analytical and numerical study of the
fractal diffusivity equation (FDE), and we show that it is more fundamental
than the classic linear and radial diffusivity equations. Thus, we combine the
FDE with the trilinear flow model (Lee and Brockenbrough 1986), culminating in
a new semianalytic solution for flow in a finite-conductivity vertical fracture
that we name the "fractal-fracture solution (FFS)." This new solution is
instantaneous and comparable in accuracy with the Blasingame and Poe solution
(1993). In addition, this is the first time that fractal theory is used in
fluid flow in a porous medium to address a problem not related to reservoir
heterogeneity. Ultimately, this project is a demonstration of the untapped
potential of fractal theory; our approach is flexible, and we believe that the
same methodology could be extended to different applications.
One objective of this work is to develop a fast and accurate semianalytical
solution for flow in a single vertical fracture that fully penetrates a
homogeneous infinite-acting reservoir. This would be the first time that
fractal theory is used to study a problem that is not related to naturally
fractured reservoirs or reservoir heterogeneity. In addition, as part of the
development process, we revisit the fundamentals of fractals in reservoir
engineering and show that the underlying FDE possesses some interesting
qualities that have not yet been comprehensively addressed in the
literature.
© 2013. Society of Petroleum Engineers
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History
- Original manuscript received:
27 January 2012
- Meeting paper published:
16 April 2012
- Revised manuscript received:
8 June 2012
- Manuscript approved:
31 August 2012
- Published online:
25 January 2013
- Version of record:
27 February 2013
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