Fluid Temperature in Fractures
Authors: Dysart G.R. , Whitsitt N.F. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
Knowledge of the actual temperature of a fluid in a fracture created with hydraulic pressure has been non-existent. The significance of having this data lies in the advantages of being able to predict not only acid spending times and related retardation effects, but also the viscosities of fracturing fluids. Viscosity values enter into the "C" factors used in fracture area calculations. Thus, an estimated viscosity can greatly affect predicted fracture areas and subsequently expected production increases.
This work develops a method of calculating temperatures of injected fluids at a given distance from the well bore in a fracture, and suggests how this information may be used fm better stimulation techniques.

Introduction
In the design of treatments for oil and gas wells no technique has been available to predict the temperature of the stimulation fluid as it moves outward in a fracture; yet the effect of temperature on acid spending times and on the viscosity of fracturing fluids is no mystery. Calculation procedures and chemical mixtures have been designed simply for original bottom-hole temperatures. It is known, however, that formation cooling takes place as a cool fluid is pumped down a well and into the formation. By assuming that any chemical or physical reactions occur at original formation temperature a temperature estimate may be in error as much as 260 deg. F, thereby affecting decisions as to the type of and retarder needed, and estimates of fluid viscosity and density which are temperature dependent.
The evaluation of the transient temperature distribution of fracturing fluid during a fracturing operation is a complex heat transfer problem. Certain assumptions regarding the nature of fluid flow in the fracture, and the mechanisms of heat transfer in both the fracturing fluid and the formation are necessary for the solution. The most accurate analysis of the problem requires the use of transient numerical procedures which involve the simultaneous solutions of a number of linear differential equations which describe the heat flow in both the fluid and the formation. Because of the heterogeneous nature of reservoir rocks, an averaging of the thermodynamic properties of the rock is necessary, and such variables create error in the cumbersome and exacting solution mentioned above.