Heat Transfer Effects in Deep Well Fracturing

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Abstract
In evaluating reservoirs for fracturing, the effects of heat transfer should be taken into account. If there appears to be significant heat blockage, any of several changes may be made in the design of the fracture treatment; thus fracturing could be extended to formations that might otherwise be passed over as being poor candidates. Introduction The consideration of heat transfer in designing stimulation treatments has become important as more wells having reservoir temperatures in the 200 degrees to 400 degrees F range become candidates for stimulation. This is particularly true because the viscous fracturing fluids often needed for effective stimulation are fluids that have highly temperature-sensitive viscosities. In the fracturing process, cool fluids are pumped at high rates into a crack in a hot reservoir; some of this fluid leaks out of the fracture into the formation. The temperature difference between the reservoir and the fluid in the fracture causes heat flow from the reservoir to the fracture. At first it was assumed that in this heat transfer the fluids were instantaneously heated to reservoir temperature at a point entering the fracture. This approach, which neglected transient heating, represented the most severe conditions from a design viewpoint and could preclude effective stimulation of some wells. The first attempts to include transient effects in calculating temperature profiles of vertical and horizontal fractures considered only conduction; the convective mode of heat transfer associated with fluid leakoff was neglected. In 1969 Whitsitt and Dysart presented a more realistic approachone that accounted for both conduction and convection in vertical fractures. Fluid was allowed to leak off linearly from zero at the wellbore to a maximum at the tip of the fracture. They used the concept of "heat blockage" to describe the effect of a cool transpiring fluid leaking out of the fracture into the formation. A leakoff fluid moving in a direction opposite that of the conductive heat transfer tends to insulate or block the flow of heat to the fluid remaining in the fracture. The model that Whitsitt and Dysart used to represent the fluid leakoff did not realistically represent the processes that occur during fracturing. A better model for the fluid leakoff was presented by Wheeler, who assumed that the rate of fluid leakoff was uniform along the fracture. Although the idea is not rigorously sound, his model more nearly represented the actual physical situation. The analytical solution for the conductive and convective heat transfer in vertical fractures that was defined by Wheeler has been used in the present study to assess the effect of various factors upon the temperature distribution within the fracture. The predicted temperature profiles can be used as a basis predicted temperature profiles can be used as a basis for modifying the design of specific fracture treatments. Temperature Profiles for Different Fracturing Fluids In using Wheeler's analytic solution (see Appendix A) for heat transfer in vertical fractures to calculate temperature profiles, it must be specified that the entering fluid temperature and the reservoir temperature are the boundary conditions. The reservoir temperature can be measured or approximated by depth and temperature gradient information. The temperature of the fluid at the surface can be measured, but the heating that occurs as the fluid flows down the tubing will cause the entering fluid temperature to be higher. JPT P. 1484

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