Revisiting the Classical Problem of Transient Temperature Prediction in Complex Deepwater Wellbores with a New Semi-Analytical Approach

Abstract

Abstract Transient temperatures in arbitrarily complex wellbores are preicted by using a semi-analytical approach based on the Laplace Transformation of the set of governing equations from the flowing stream across the multiple layers of the wellbore and out into the formation. We investigate flowing and shut-in (static) scenarios consider sequentially linked thermal operations. The methodology can be applied to subsea deviated wellbores with variable lithology and geothermal gradients, and without invoking any of the several simplifying that have characterized previous studies. Wellbore temperatures are extracted from the solutions of the coupled heat transfer equations in the wellbore and the formation by inverting a set of Laplace transforms with sequential updating to capture the temporal variation of natural convection in fluid-filled annuli. Natural convection in these annuli and in the static fluid conduit during a shut-in period is explicitly modeled by taking considering the non-Newtonian behaviour of typical annular fluids. The transient heat transfer in the formation is determined by a time dependent temperature boundary condition at the wellbore-formation interface, and a zero heat flux boundary condition at a farfield location that is spatially consistent with the duration of the specified thermal operation. The former boundary condition is analytically treated by the Duhamel superposition principle. Having obtained the analytical solution to the formation heat transfer, the efficiency of the Gaver-Stehfest function sampling algorithm to invert the Laplace transforms is demonstrated. The methodology is demonsrated by applying it to a complex deepwater 30,000 ft MD deviated well in the Gulf of Mexico. The S-shaped trajectory traverses a thick salt layer with variable geothermal gradients. We show that in comparsion to finite-difference methods, the semi-analytical approach (using Laplace Transforms) can use much larger time sub-intervals to provide a given level numerical accuracy. This aspect of numerical efficiency arises as a consequence of the inherent numerical stability of the approach. This results in a reduction in computational time by several orders of magnitude without a corresponding sacrifice in accuracy. Production, Injection and Shut-In operations are modeled. The advantages of the present approach are more pronounced for short term scenarios such as drill-stem tests where the transients have not yet decayed to a steady state. Even though complex subsea wellbores are the focus of the approach, the formulation can be applied to an arbitrary wellbore configuration including land-based and platform wells.