Wellbore Thermal and Mechanical Fingerprinting
Authors: Erpelding P. 
Published: October 2008

ABSTRACT
A method is presented such that two parameters can be used to fully describe the thermal characteristics of a tubing string undergoing an injection or production process. For a given well, these parameters remain the same regardless of tubing size, flow rate, flowing substance, and flowing condition (injection or production). Simple algebraic equations are used to determine these well parameters using existing injection or production temperature data. These parametersean then be used to predict the resulting thermal and mechanical response of any change in geometry or flow.

INTRODUCTION
Obtaining accurate temperature predictions is a prerequisite for modem drilling. As wells are drilled deeper, higher temperatures and pressures are encountered. Consequently, the designer must use great care in calculating the loads for a casing or tubing string. A safe design can only be achieved if the designer has confidence in the loads that are calculated and the material that is used. The mechanics of casing and tubing design requires knowledge of three basic profiles: internal pressure, external pressure, and temperature. In many circumstances, the temperature profile provides the greatest uncertainty in determination of the load. The method presented here allows the engineer to use known temperature data from a single well flowing condition to determine the well fingerprint. With the fingerprint information in hand the engineer can then accurately predict the temperature response of the tubing string for any injection and production flowing condition that may take place later in the life of the well. Assuming the internal and external pressure profiles are known, the well is also mechanically finger printed since the tubing string mechanics are tied directly to temperature.

PROCEDURE
In an effort to develop the concept of a thermal fingerprint, an axis symmetric finite difference model was developed. The model was developed following standard finite difference practices and provides the ability to accurately simulate virtually any well configuration under any sequence of flowing or static conditions. The results from field tests were used to validate the finite difference model. Ten individual wells were fingerprinted using the results from over 500 finite difference models.
The following equations were developed in previous work1 and are used to determine the fingerprinting parameters a & b, For injection of a liquid, the tubing temperature as a function of depth and time is:
(Mathematical equation) (Available In Full Paper)

CONCLUSIONS
Using available field data, users employing the thermal fingerprinting technique can now develop well specific time functions to accurately predict the thermal behavior during injection and production processes. Simple mechanical principle scan then be used to determine the tubing loads and movements. However, the methods presented here are not a complete solution. The accuracy of the temperature predictions is degraded as the injection and production events occur over shorter periods of time (&lt; 3 hours). In addition, the equations presented do not allow for flow sequencing, prediction of shut-in periods, or for multiple tubing sections with geometry changes. Reliable temperature and mechanical predictions for these conditions requires more complicated models.