Post Fracturing Temperature Recovery And Its Implication For Stimulation Design
Authors: Harrington Larry J. , Hannah Robert R. , Robert Beirute 
Published: December 2007

Abstract
In the last few years increasing emphasis has been placed on reducing post fracturing shut-in times. This trend has caused renewed interest in the relationship between breaker loadings and static fluid temperatures. Models of cooling profiles during fracturing have been extensively discussed in the literature, but scant attention has been paid to post fracturing temperature recovery. The problem has been discussed in a general way and one model has been proposed. This paper presents a somewhat different model and presents its development.
This paper will also discuss the application of this model to stimulation designs which require shortened breaking times. In addition, the relationship between fracture closure time and breaking times where crosslinked sand-laden gels are used will be brought out and the attendant danger of poor vertical proppant distribution will be discussed.

Introduction
During the late 1960's considerable work was done to develop models of the temperature of fluids in hydraulic fractures during their extension. The stimulation of deep hot wells had, by this time, become quite common and it was realized that a knowledge of these temperatures was essential for adequate design. Dysart and Whitsitt1,2, Wheeler3, and Sinclair4 presented models that predicted the cooling of the fracture by the injection of stimulation fluids.
The development of dependable crosslinked gels with virtually perfect sand support properties has displaced the earlier simple gels for a wide variety of applications. In particular, these gels have become popular for the massive hydraulic fracturing treatments in tight gas sands where fracture heights tend to be excessive and extend above and below the zone of interest.
Another complicating factor in the use of these gels is the demand for short post fracturing shut-in times which necessitates the addition of heavy concentrations of gel breaking additives into the fluid late in the treatment. These short shut-in times may be necessary due to the addition of gases such as CO2 or N2 which are subject to gravitational separation during the shut-in period. Additionally, in tight gas sands there is concern that prolonged shut-in times result in reduced load recovery rates and lower overall load recovery. This has been empirically established in some areas. Regardless of the reasons, shut-in times have been drastically reduced compared to accepted practice a few years ago.
The early thinning of these fluids presents no problems if the walls of the fracture have closed sufficiently to trap the suspended sand before serious viscous degradation has occurred. Where fracture closure is very slow due to very tight rock with extremely low matrix leak-off, early thinning of the frac fluid can allow significant separation of sand from the fluid and can result in portions of the formation being unpropped.
Where the well is opened prior to adequate breaking and before fracture closure, the sand will be produced with the fracturing fluid so breaking of the fluid is important.
Novotny5, in an excellent paper, discussed both temperature recovery and closure and presented models for both. In particular, many more extended shut-in pressure histories of the type shown in his paper should be made in order to better define closure.
This paper presents a model of the temperature recovery process and shows the mathematical development in the appendices. In addition, examples are given of typical recoveries experienced by fluids with different leak-off coefficients.