Summary
A new transient analytical model has been developed to study the temperature
and stress distribution induced by nonisothermal fluid injection, particularly
conventional waterflooding. In the model, the transient pressure, temperature,
and stress fields are computed consecutively. The pressure field has been
computed by using either the exponential integral solution for a unit mobility
ratio displacement or Ramey’s composite reservoir model for a nonunit mobility
ratio pistonlike displacement. The transient temperature field has been
computed by using a model that can account for both the overburden heat losses
and transversal heat dispersion within the reservoir. The stress distribution
has been calculated with a method presented for a plane strain in a hollow
cylinder.
The results implied that the thermoelastic changes in the cooled zone could
affect the surrounding stress fields in a profound manner. For instance, for a
porous medium with stiff material (such as carbonate reservoirs) owing to
cooling by the injected cold water, large-scale tensile stresses arise and may
induce new fractures (or propagate existing ones) far into the reservoir. In
addition, a major tangential stress concentration develops just in front of the
cooled zone; hence, shear yield is highly likely to occur ahead of the thermal
front.
The 2D treatment of the temperature field makes the new method superior to
the previous analytical models, where only a 1D field has been used.
Introduction
Stress distributions in a reservoir directly affect the integrity or failure
of reservoir rock. Rock failure can be engineered to improve well injectivity
or productivity. Undesired failures, on the other hand, can cause significant
reductions in the sweep efficiency of secondary- and enhanced-oil-recovery
processes. Therefore, an understanding of stress distribution during injection
processes is of great importance to design engineers.
Consider, for example, a waterflooding operation in which a fluid that is
significantly colder than the reservoir rock and fluids is injected into the
reservoir. During waterflooding, the initial stress distribution is changed
because of two principal factors. First, injection of water changes the
reservoir pressure distribution. Second, the temperature difference between the
injected fluid and initial reservoir temperature causes additional changes in
the form of thermal stress.
The influence of thermal stresses in fracturing geothermal reservoirs has
been appreciated fairly early (Murphy 1979). The studies concerning geothermal
reservoirs noted that thermal stresses may lead to the opening of secondary
fractures. Such fractures reduce the resistance to flow and, hence, increase
the injectivity of the wells.
Transient stress-distribution studies resulting from injection into oil
reservoirs have also started quite early (Geertsma 1978; Paslay and Cheatham
1963; Deily and Owens 1969). The analogy between pressure and thermal effects
has long been recognized (Lubinksi 1954). Seth and Gray (1968) formalized this
analogy between the pressure and thermal effects on stress distribution in an
oil reservoir during production. Later, Perkins and Gonzalez (1984, 1985) used
the same analogy to study thermoelastic stresses around a wellbore. They have
developed analytical solutions and indicated possible use of their solutions to
predict the change in fracture propagation. The classical work of Haimson and
Fairhurst (1967) presented an analytical solution for a plane-strain case to
study initiation and extension of hydraulic fractures. The works of Bratli and
Risnes (1981) and Risnes et al. (1982) considered stresses around a wellbore
with special considerations of fluid flow in unconsolidated sands. The
analytical solutions developed by Bratli and Risnes (1981) have been summarized
and simplified to apply to the case of flow into a wellbore in an infinite
reservoir by Fjaer et al. (1992).
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
8 December 2004
- Revised manuscript received:
7 September 2005
- Manuscript approved:
18 September 2005
- Version of record:
20 May 2006
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