Transient fluid and heat flow modeling in coupled wellbore/reservoir systems
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This paper presents a transient wellbore simulator coupled with a semianalytic temperature model for computing wellbore-fluid-temperature profile in flowing and shut-in wells. Either an analytic or a numeric reservoir model can be combined with the transient wellbore model for rapid computations of pressure, temperature, and velocity. We verified the model with transient data from multiple gas and oil wells, where both surface and downhole data were available. The accuracy of the heat-transfer calculations improved with a variable-earth-temperature model and a newly developed numerical-differentiation scheme. This approach improved the calculated wellbore fluid-temperature profile, which, in turn, increased the accuracy of pressure calculations, at both bottomhole and wellhead. The proposed model accurately mimics afterflow during surface shut-in by computing velocity profile at each timestep and its consequent impact on temperature and density profiles in the wellbore. Surrounding formation temperature is updated every timestep to account for changes in heat-transfer rate between the hotter wellbore fluid and the cooler formation. Optional hybrid numerical differentiation routine removes the limitations imposed by the constant relaxation-parameter assumption used in previous analytic-temperature models. Copyright 2006, Society of Petroleum Engineers.