Temperature Prediction for Hydraulically Fractured Oil and Gas Wells
Authors: Liu X. , Yang H. 
Published: November 2021

Abstract
It is a common practice in the oil and gas industry to improve well production by creating hydraulic fractures in petroleum bearing formations. In order to maintain the fracture open in the formation as a flow path for oil and gas production, it is generally created by injecting a viscous fluid mixed with propping materials such sands or ceramic particles, which are all called proppants. It is very important to have a precise knowledge of the temperature profiles both in the wellbore and in the fracture because temperature affects gel loading (required polymer concentration in the fluid), fluid rheology, the ability for the fluid to carry proppants, and the condition for the gelled fluid to break down after the operation.
Several models have been developed in the literature to predict wellbore and fracture temperature profiles, and most of them are analytical. Since an analytical solution cannot handle variable fluid and rock properties and variable pumping rates, a unique numerical scheme is developed in this study to solve the PDE’s that govern the heat transfer both in the wellbore and in the fracture, and the surrounding earth. Since the coordinate system for temperature calculations in the wellbore is different from that in the fracture, two heat transfer models are coupled together to solve the entire problem. In addition to the effects of convective and conductive heat transfer in the well and the fracture, the models also rigorously consider fluid flow and heat transfer in the porous formation surrounding the well and the fracture.
The models were first verified by analytical results for constant flowrate injection. One can easily measure the wellbore temperature at any location by running a temperature gauge inside the well, but no one has directly measured with the current technology the fluid temperature profile inside a narrow hydraulic fracture (which is usually less than one inch in width at the wellbore) far beyond the wellbore limit. In this study, the following temperature survey data were used to infer the fluid temperature inside a fracture: A temperature gauge was run into a well and was set inside the wellbore at the location where the hydraulic fracture was anticipated to be created outside the wellbore; and the well was put into production (or flowback) immediately after the hydraulic fracturing operation. Within a couple of minutes during the flowback, the fluid passing through the temperature gauge was actually from inside the fracture. The models were then verified by the actual temperature survey data during pumping and flowback.
The heat transfer models were finally integrated into a hydraulic fracture design simulator that is widely used in the oil and gas industry. The numerical scheme developed to solve the models in this study has been implemented in such a way that it is not only accurate for calculating the temperature profiles, but that it also runs fast for real-time analysis and monitoring during the hydraulic fracturing operations. To authors’ knowledge, it is the first attempt in the literature to verify a heat transfer model for hydraulic fracturing using actual measured data inferred from the temperature of the fluid flowed back from inside a created hydraulic fracture.