Prediction of Temperature Propagation Along a Horizontal Well During Injection Period

Abstract

This paper presents a mathematical model describing the variation of temperature along the length of a horizontal well during the process of water injection. The model is obtained from a theoretical treatment accounting for both mass transfer and heat transfer between a horizontal well and a reservoir. The treatment is 1D linear in the wellbore and 1D radial in the reservoir. A numerical algorithm for reservoir temperature calculation is proposed and an analytical solution is derived on the basis of some realistic assumptions. The analytical solution can be used to generate the temperature profile in a horizontal injection well for any assumed distribution of injection profile along the length of the well, including injection profile that is uniform, skewed toward the heel or the toe, or exhibits some discontinuity (e.g., leakoff into a high permeability streak or fracture). This paper also presents comparison of temperature profiles obtained with the analytical solution given in this paper and those obtained with a numerical reservoir simulator with temperature option (ECLIPSE), which shows that the analytical solution yields reasonable temperature propagation profiles along the wellbore. The effects of injection rate and the injection profile are analyzed, and a quick in-situ injection patternrecognition method is proposed. Finally, examples are given to show the practical application of the theoretical model.