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| Titel |
Two-dimensional numerical investigations on the termination of bilinear flow in fractures |
| VerfasserIn |
A. E. Ortiz R., R. Jung, J. Renner |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1869-9510
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| Digitales Dokument |
URL |
| Erschienen |
In: Solid Earth ; 4, no. 2 ; Nr. 4, no. 2 (2013-10-11), S.331-345 |
| Datensatznummer |
250084936
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| Publikation (Nr.) |
 copernicus.org/se-4-331-2013.pdf |
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| Zusammenfassung |
| Bilinear flow occurs when fluid is drained from a permeable matrix by
producing it through an enclosed fracture of finite conductivity
intersecting a well along its axis. The terminology reflects the combination
of two approximately linear flow regimes: one in the matrix with flow
essentially perpendicular to the fracture, and one along the fracture itself
associated with the non-negligible pressure drop in it. We investigated the
characteristics, in particular the termination, of bilinear flow by
numerical modeling allowing for an examination of the entire flow field without
prescribing the flow geometry in the matrix. Fracture storage capacity was
neglected relying on previous findings that bilinear flow is associated with
a quasi-steady flow in the fracture. Numerical results were generalized by
dimensionless presentation. Definition of a dimensionless time that, other
than in previous approaches, does not use geometrical parameters of the
fracture permitted identifying the dimensionless well pressure for the
infinitely long fracture as the master curve for type curves of all
fractures with finite length from the beginning of bilinear flow up to fully
developed radial flow. In log–log scale the master curve's logarithmic
derivative initially follows a 1/4-slope straight line
(characteristic for bilinear flow) and gradually bends into a horizontal
line (characteristic for radial flow) for long times. During the bilinear
flow period, isobars normalized to well pressure propagate with the fourth and
second root of time in fracture and matrix, respectively. The
width-to-length ratio of the pressure field increases proportional to the
fourth root of time during the bilinear period, and starts to deviate from
this relation close to the deviation of well pressure and its derivative
from their fourth-root-of-time relations. At this time, isobars are already
significantly inclined with respect to the fracture. The type curves of
finite fractures all deviate counterclockwise from the master curve instead
of clockwise or counterclockwise from the 1/4-slope straight
line as previously proposed. The counterclockwise deviation from the master
curve was identified as the arrival of a normalized isobar reflected at the
fracture tip 16 times earlier. Nevertheless, two distinct regimes were
found in regard to pressure at the fracture tip when bilinear flow ends. For
dimensionless fracture conductivities TD < 1, a significant
pressure increase is not observed at the fracture tip until bilinear flow is
succeeded by radial flow at a fixed dimensionless time. For TD > 10, the pressure at the fracture tip has reached substantial fractions of
the associated change in well pressure when the flow field transforms
towards intermittent formation linear flow at times that scale inversely
with the fourth power of dimensionless fracture conductivity. Our results
suggest that semi-log plots of normalized well pressure provide a means for
the determination of hydraulic parameters of fracture and matrix after
shorter test duration than for conventional analysis. |
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