Transient Fluid Temperature Estimation in Wellbores

Knowledge of transient temperature distribution in wellbore fluid is critical for the pressure transient tests during draw-down and shut-in processes. In absence or limitation of measurement devices installed on the wellbore, temperature estimation through soft sensors can properly fulfill the absence of these measurement devices. In this work, the heat transfer model for wellbore fluid is reduced to a set of hyperbolic PDEs and applying the method of characteristics and calculation of Riemann invariants, the observability of the temperature distribution is discussed for the governing set of hyperbolic PDEs. In case of oil well, the governing equations are reduced and discretized using method of characteristics and then reformulated in order to implement the observer. The developed model is used for Luenberger observer and Kalman filter synthesis using well-head temperature measurements. The observer is synthesized based on the reduced linear model and is examined on the high fidelity finite difference model of the wellbore fluid flow. The provided transient temperature estimation is enough accurate and reliable for on-line and real-time implementation in wellbore fluid.