(699d) Transient Temperature Distribution Estimation in Wellbore Fluid
Transient temperature and pressure tests are crucial for petroleum wellbore monitoring and maintenance of oil flow lines and facilities. Transient flow and temperature occur during drawdown and shut-in processes . As fluid velocity in wellbore changes, the fluid dissipates heat to the surrounding earth formation. Since temperature variation affects the oil density, momentum and pressure, real-time knowledge of transient temperature is necessary for wellbore analysis . Distributed Temperature Sensors (DTS) are used in the state-of-the-art completed and realized wellbores. These sensors provide on-line temperature profile measurements along the wellbore. Although DTS systems provide high resolution temperature measurements, the technology is new and not available for existing mature oil and/or gas wells. The real-time transient temperature estimation and monitoring using available wellhead temperature measurements and a reliable wellbore model is a suitable substitute for DTS systems. In this work, the wellbore fluid flow and heat transfer model is considered as a set of hyperbolic partial differential equations arising from the transport processes in oil/gas wellbore. The method of characteristics and the Riemann invariants are utilized and implemented in order to evaluate the model behaviour and features. Observability of transient temperature using wellhead temperature measurements are investigated and discussed. The temperature dynamic model is simplified for incompressible oil flow in wellbore and reduced to the heat transfer model given by a one dimensional hyperbolic PDE. Subsequently, the Luenberger observer and Kalman filter approaches are used for on-line transient temperature profile estimation in the wellbore fluid. The hyperbolic temperature model is reformulated to standard linear time invariant form using the method of characteristics and then the observer is designed for real-time temperature estimation. Motivated by realistic set of available measurements, the state estimation is based on the temperature measurement available at the wellhead (point measurement), and the estimated transient temperature profile is provided. In addition, the temperature estimation is examined by assuming stochastic uncertainties in the model and the measurement, and the temperature reconstruction is realized by standard Kalman filter. Finally, the Luenberger observer and Kalman filter are applied on a high fidelity finite difference model to evaluate the efficiency of the proposed temperature estimation strategies.
 A. R. Hasan and C. S. Kabir. Wellbore heat-transfer modelling and applications. Journal of Petroleum Science and Engineering, 86-87:127-136, 2012.
 A. R. Hasan, C. S. Kabir, and D. Lin. Analytic wellbore temperature model for transient gas well testing. SPE Reservoir Evaluation & Engineering, 8(3):240-247, 2005.
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