The Effect of Temperature On Stimulation Design
Authors: Whitsitt N.F. , Dysart G.R. 
Published: December 2007

During hydraulic fracturing, fluid viscosity, acid spending times, and inhibitor performance are adversely affected by the high temperatures existing in deep wells. However, when fluids are pumped down tubing at normal rates, tubing temperature drops drastically. Presented here is a method of predicting the dynamic temperature changes that occur during stimulation.

Introduction
Many producing oil and gas wells requiring stimulation treatments have high bottom-hole temperatures. This is illustrated in Table 1, which lists the approximate well depths where formation temperatures reach or exceed 200 degrees F. In almost all of these areas, wells of these depths are being, or soon will be stimulated either by hydraulic fracturing or by acidizing techniques. In fact, stimulation of wells having bottom-hole temperatures of about 350 degrees F has already begun in some areas. In order for these types of treatments to effect the greatest production increases, the thermal environment must be understood, and its effect on treatment fluids, chemicals, and additives must be considered. It is important, for instance, to know the relationship between the effects of the thermal environment during treatment and fracture fluid viscosity, fracture proppant settling rates, solid blocking agent performance, proppant settling rates, solid blocking agent performance, acid reaction rates, and acid retarder requirements. In designing methods of stimulation, the effect that transient temperature conditions will have on these properties has not been considered. This neglect will properties has not been considered. This neglect will cause considerable error, which will be demonstrated by comparisons in this paper. Before the effects of temperature-dependent factors on stimulation design can be accurately established, it is first necessary to determine what the thermal environment actually is during a fracturing operation. With existing technology it is impossible to measure temperatures in the fracture passages themselves. It is possible, however, to measure the temperature in the wellbore during or immediately after a stimulation operation. Such measurements show that the wellbore walls are cooled dramatically by the passage of cool fluids. This result has been predicted by Ramey as well as others in their analytical approaches to this problem. Good correlations have been made between problem. Good correlations have been made between theoretical and field-measured data. Although it is known that wellbore cooling takes place during the fracturing process, attempts to place during the fracturing process, attempts to calculate the temperature in the fracture itself during stimulation had not been published until the early work presented in Ref. 6. That study was the first, presented in Ref. 6. That study was the first, somewhat elementary, but important step in the development of a representative thermal model. Since then, a much more representative thermal model bas been developed to describe the temperature in a vertical fracture and the adjacent formation. The following discussion describes the development of this thermal model. The analytical solution, obtained through the introduction of some simplifying assumptions, bas the convenience of being usable without the need of numerical analysis techniques and digital computing equipment.

Development of the Solution
The hydraulic fracturing of a formation involves applying sufficient fluid pressure in the wellbore to overcome the stresses in the formation. In wells that have high temperatures, the least principal stresses generally are in the horizontal plane. This will cause vertical fractures to occur.
JPT
P. 493