A New Simulator For the Calculation of the In Situ Temperature Profile During Well Stimulation Fracturing Treatments
Authors: Kamphuis Harry , Davies David R. , Roodhart Leo P. 
Published: March 2010

Abstract
Many essential parameters in hydraulic fracturing operations such as the viscosity of the fracturing fluid and the effectiveness of certain breakers, are strongly dependent on temperature. A finite-difference computer program has been developed that accurately computes temperature profiles in a propagating fracture. It is based on a rigorous description of the heat transfer processes involved:the heat influx from the fracture wall is computed numerically via a special coordinate transformation of the energy balance equation for the rock,the temperature of the frac fluid and the adjacent rock face are allowed to be different (particularly relevant for wide fractures).local time derivatives in the energy balance are fully accounted for.
The code and the underlying model are valid for the full range of conditions encountered in the field, e.g.:high leak-off rates of the fracturing fluid (high permeability rock),low heal conductivity of the rock (certain carbonates)
It was found that fractures are often significantly cooler than previously reported results. Consequently, the proppant carrying capacity of the frac fluid will be better and it is possible to carry out successful treatments (good proppant placement and reduced impairment) more cost-effectively. The size of prepad stages for cooling can often be reduced. Further, the temperature recovery profile after proppant placement can aid in the design of resin coated proppant systems.

Introduction
Many essential parameters in hydraulic fracture simulation operations are strongly dependent on the temperature level prevailing locally in the hydraulically created fracture. In fracturing treatments, the temperature affects:the viscosity of frac fluids and thereby the settling rate of the proppant.The stability of multiphase frac fluid (foams, emulsions).Crosslinker effectiveness.Viscosity breaker effectiveness.Fracture geometry (depending on the fracture propagation model assumed)
These will in turn affect the ultimate productivity improvement achieved by the fracture stimulation treatment. Knowledge of the fracture temperature profile is thus requires for optimal design of the frac fluid formation (e.g. type of crosslinker) and/or the treatment stages (e.g. the size of a pre-pad sometimes required to cool the formation).
The heat transfer processes taking place during a hydraulic fracture treatment are depicted in Figure q. Cold fluid is pumped into the fracture, where it cools the fracture face and the interior of the rock adjacent to the fracture by conduction and by leak-off.
Simultaneously, the fluid heats up as it travels through the fracture because if conduction of heat from reservoir towards the fracture, and, in the case of acid fracturing, by the heat produced by the etching of the rock by the acid.
A variety of models have been published in the open literature describing temperature profiles in the fracture for hydraulic fracturing treatments during the pumping stage(1–9), and after the pumping stage prior to closure of the fracture(10, 11) and for acid fracturing treatments(12, 13) In virtually every theory published simplifications had to be made to arrive at a workable semianalystical expression for the temperature. In this work, many restricting assumptions have been avoided. i.e.: