Stimulation Design Applications Of A Technique To Locate Successive Fluid Segments In Fractures
Authors: Hannah Robert R. , Harrington Larry J. , Anderson Robert W. 
Published: December 2007

Abstract
This paper will discuss an analytical technique that predicts the final fracture location of predetermined fluid volumes. This information can then predetermined fluid volumes. This information can then be plotted versus a pumping temperature profile. By means of this plot the maximum temperatures to which a fluid segment is exposed can be reasonably predicted. predicted. This information can be used to schedule various materials, both types and quantities, according to their predicted temperature exposures. This method will help to avoid over-designed treatments and lends itself to the most economical design that will achieve stimulation objectives.

Introduction
Fracturing design techniques along with mechanical equipment and materials have improved rapidly within the last fifteen years. Attempts to stimulate reservoirs with marginal capacities has led to extremely large fluid volumes in reservoirs with over 200 degrees F BHT. These temperatures combined with long pumping times led to the development of water-based fracturing fluids that would withstand the thermal degradation of viscous properties experienced by mare conventional polymer-based properties experienced by mare conventional polymer-based fracturing fluids. A key element in these systems is the use of higher polymer concentrations and chemicals designed to slow the loss of viscous properties. In gelled fluid technology, thermal properties. In gelled fluid technology, thermal tolerance and stability are functions not only of polymer type but also of polymer concentration. polymer type but also of polymer concentration. These systems are expensive and have become a significant item of stimulation cost.
Methods of calculating approximate fracture temperatures during pumping have been presented in the literature. These methods consider the cooling effects caused by loss of fluid through the fracture wall. This results in a temperature gradient along the fracture length from a few degrees above surface water temperature at the wellbore to BHT at the fracture tip.
These methods allowed more rational designs based on more realistic fracture temperatures but there were obvious weaknesses. If the average fracture temperature were used, all fluid pumped ahead of this average temperature point had poorer fluid properties than predicted. At the same time, the fluid behind this average point would have much better properties than indicated by the average temperature. The viscous properties of these fluids effect several important areas of the fracturing process including proppant transport, fluid process including proppant transport, fluid leakoff, and fracture width. Another area of concern involves breaker scheduling and reasonable shut-in times. For long pumping times breakers scheduled for average temperatures may lead to a premature break of the early fluid pumped while later fluid would break too slowly. Breakers scheduled for the absolute bottom hole temperatures may lead to very long break times in the immediate wellbore area. A more rational approach to breaker scheduling was needed to overcome these problems.
Some fracturing designs have accounted for the progressively cooler environment by arbitrarily progressively cooler environment by arbitrarily decreasing polymer loading and increasing breaker loading at pre-selected points. This technique does consider the changing fracture environment but is based strictly on the judgment of the individual designing the treatment.
This paper presents a mathematical model that will approximately predict the location of selected fluid segments in terms of distance from the wellbore. This information combined with a temperature profile along the fracture length provides a very profile along the fracture length provides a very useful tool for scheduling polymers, breakers, or other materials. This allows the selection of practical minimum viscosities and the selection of practical minimum viscosities and the selection of breaker schedules to allow an approximately uniform break time.