Changes in Earth Stresses Around a Wellbore Caused by Radially Symmetrical Pressure and Temperature Gradients

Abstract

Abstract 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 in-situ 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. Introduction Thermal stresses can have a significant effect on engineering design because they can cause materials to fail. Many novel processes have been proposed for drilling and breaking rocks that make use of this fact. It is only recently, however, that the role of thermal stresses has been appreciated in the fracturing of geothermal and petroleum reservoirs. Several studies have been concerned with thermal stresses generated in geothermal wells. These studies indicate that thermal stresses open secondary fractures in the rock that substantially reduce the resistance to flow, thereby increasing the efficiency of the system. Other investigators have studied the effect that thermal stresses have on the results of in-situ earth stress measurements made by the hydraulic fracturing method. Another study predicted the thermal stresses resulting from hot-water injection into a cool reservoir. Others have proposed methods to exploit thermal stresses in the reservoir. It has been suggested that heating the reservoir will alter the in-situ earth stresses so that, in some circumstances, the horizontal stresses can be made to exceed the vertical stresses. If a fracture propagated under these conditions, the fracture would be horizontal, which is sometimes preferable to a vertical fracture. The purpose of this paper is to compute the earth stresses resulting from the injection of cool water into a warmer formation and then to deduce how the altered stresses will affect the hydraulic fracturing pressure. Initiation and propagation of hydraulic fractures are known to be controlled to a large degree by the magnitude of the earth stress that acts perpendicular to the plane of the fracture. It has been recognized for some time that the fluid pressure field in the surrounding reservoir rock will have an effect on the earth stress in the vicinity of a hydraulic fracture. During ordinary hydraulic fracturing operations, however, leakoff is controlled so that injected fluid volumes will be minimized. As a result, pressure and temperature changes in the rock surrounding the fracture do not ordinarily have a very significant effect on the fracturing operation. therefore, the primary concern has been the effect that temperature has on fracturing fluid rheology and leakoff behavior. There is another general problem of interest, where hydraulic fracturing occurs in connection with injection of large volumes of fluid, such as when waterflooding of when applying other secondary or tertiary recovery processes. For these cases, an extensive region of changed temperature or pressure can be created, and the effects on earth stresses and hydraulic fracturing processes are significant. The problem of calculating earth stress changes resulting from fluid injection is not trivial. the stress change at any position is not a point function, but rather it depends on the entire temperature and pressure fields. In this paper we review briefly the basic thermoelastic and poroelastic relationships for stress and strain. Because of an analogy between pressure and temperature effects, solutions for earth stress changes are valid for both pressure and temperature fields if the parameters are properly interpreted. SPEJ P. 129^