Tubing Temperature Correlations For Injection And Production Based On Simulation And Field Experience
Authors: Erpelding Peter , Miller R.A. 
Published: October 2008

ABSTRACT
A finite difference model was developed and used to simulate transient heat transfer in wells undergoing injection and production processes. The tubing temperature profiles from these simulations were then reduced to a set of algebraic equations to provide simple and effective temperature versus depth and temperature versus time estimates. Results from field tests are also presented and compared in order to validate the finite difference model.

INTRODUCTION
Accurate temperature prediction for dowuhole tubulars has become increasingly important due to the potential cost savings associated with more preeise optimization of string design. Much of the attention in the literature has focused on accurate cementing temperature modeIs, while very little mention has been given to fracture stimulation or production temperature predictions.
In an effort to predict tubing temperature profiles during injection and production, an axisymmetric 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. However, numerical simulation requires substantial input, and accuracy can only be assured if all input parameters are known. In certain situations, though, an engineer may find that a usable finite difference code or accurate well thermal properties are unavailable. In these eases, good correlations can provide similar results at substantial cost and time savings. In other situations, an engineer may need to predict the temperatures resulting from an increase in flow rate, or perhaps predict the temperatures for a fracture stimulation on a well for which production data is already available. The equations presented here can be used to accurately predict the temperatures resulting from such operations.

PROCEDURE
In order to develop a method to quickly estimate tubing temperatures during injection and production, it was necessary to identify the most sensitive input variables so that an appropriate correlation could be formulated. Using the finite difference model, the significant variables were found to ix the volumetric flow rate, depth, time, undisturbed static temperature profile, well geometry, flowing fluid properties, and formation thermal properties. Results from field tests were also compared in order to validate the finite difference model.
Table-1 Comparison of FD Model With Field Tests(Available in full paper)
A modified version of the injection model proposed by Ramcyl was used as the basis for providing the tubing temperature profiles. The model was modified by replacing the analytical time function with a function predicted by the finite difference simulations. The model was further simplified by allowing the overall heat transfer coefficient to be infinite (see Appendix), thus allowing the wellbore thermal effects to be included in the time function. An equivalent model for production was also developed (see Appendix) and shares the same time function as the injection model.