Analytical Temperature Modeling for Early Detection and Rate Estimation of CO2 Wellbore Leakage

Wellbore leakage of CO₂ injected into a storage zone can induce significant temperature anomalies. These arise from expansion of the leaking fluid associated with the pressure drop across the leak, known as the Joule-Thomson effect. These temperature anomalies provide a signal that has the potential to understand the nature and rate of wellbore leakage of CO₂. In principle, these signals can be used to estimate the rate of CO₂ leakage. However this requires careful numerical evaluations of the temperature signal considering conductive and convective heat transfer. We investigate the strength of the temperature signal as a function of leakage rate and develop a control volume analysis to develop their relationship. The thermal model analyzes quickly detectable temperature signal that can be used to estimate the leakage rate soon after CO₂ breakthrough occurs along the wellbore. The applicable range of this approach is identified from the results of specific examples. The nature of the thermal signal is sensitive to the balance between the Joule-Thomson effect and heat conduction. The ratio of these two effects and the Graetz Number can be used to identify universal criteria for the applicability of modeling these thermal signals. A general procedure to apply this approach to a practical problem is detailed.