Pressure and temperature gradients are created around wellbores during waterflooding or when fluids are injected in connection with any other secondary or tertiary recovery process. These gradients result in changes in earth stresses, which in turn cause hydraulic fracturing pressures to change.

In this paper, analytical solutions have been used to determine the stresses resulting from radially symmetrical temperature and pressure changes around a wellbore. These stresses are required to predict the change in fracture extension pressure that is caused by the injection process. Exact, closed-form solutions are given for the stresses. These have been evaluated with a computer, and more convenient empirical formulas have been fitted to the calculated results. Solutions for discrete cylindrical or disk-shaped regions of changed temperature and pressure are shown. Also, the solutions can be adapted to annular elements of finite thickness that are convenient for incorporation to an r-z-type computer program. Such a program could then be used to compute the stresses resulting from temperature and pressure fields that vary gradually in the radial direction.

This paper gives examples to illustrate the effect of injecting a large volume of liquid that is cooler than the insitu reservoir, as is common when waterflooding. The cooling can have a large effect on lateral earth stresses, and for some conditions vertical hydraulic fracturing pressures can be significantly reduced.

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