This paper presents a transient wellbore simulator coupled with a semianalytic temperature model for computing wellbore-fluid-temperature profiles 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 simulator with transient data from 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 simulator accurately mimics afterflow during surface shut-in by computing the velocity profile at each timestep and its consequent impact on temperature and density profiles in the wellbore. Surrounding formation temperature is updated in every timestep to account for changes in heat-transfer rate between the hotter wellbore fluid and the cooler formation. The optional hybrid numerical-differentiation routine removes the limitations imposed by the constant relaxation-parameter assumption used in previous analytic-temperature models.
Both forward and reverse simulations are feasible. Forward simulations entail computing pressure, temperature, and velocity profiles at each wellbore node to allow matching field data gathered at any point in the wellbore. In contrast, reverse simulation allows translating pressures from one point to another in the wellbore, such as wellhead to bottomhole condition.