apb

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The prediction and mitigation of annular pressure build up in a wellbore during injection and production are recurring challenges in petroleum engineering. The annular pressure build up has been studied continuously over the past decades because the understanding and underlying APB mechanism is essential for developing any mitigation technology.
The first step of understanding the APB mechanism is to predict temperature profiles in the wellbores accurately. Almost all practical methods for calculation of temperature profiles in the wellbores go back to the work by Ramey (1962) on wellbore heat transmission published in early 1960’s.
In that paper, Ramey presented an analytical equation for wellbore temperatures based on a simplified heat balance. Assuming steady-state flow of an incompressible single phase fluid, he dropped the kinetic energy term.
Edwardson et al. (1961) developed methods to calculate formation temperature disturbances attributable to mud circulation during drilling operations. The method was mathematically expanded by solving of the differential equation of heat conduction and the calculated results reasonably confirmed field data. It was concluded that, in general, the temperature disturbances caused by circulating mud are small beyond 10ft from the wellbore, but are quite significant near the wellbore.
In 1989, Mitchell et al. presented a model to predict downhole temperature during the operations by reducing the differential equations of energy and momentum conservation to algebraic equations, and by solving these algebraic equations subject to the appropriate boundary using a numerical solution process. They indicated that wellbore simulation can provide more reliable estimates of well loads and flowing fl...

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...the Grashof number were studied starting from the solution for mixed convection without viscous dissipation. It was reported that viscous dissipation enhances the effects of buoyancy and vice versa.
The effects of viscous dissipation and the yield shear stress on the asymptotic behavior of the laminar forced convection in a circular duct for a Bingham fluid were investigated by Khatyr et al. (2002). Three types of wall boundary conditions, namely: variable heat flux distributions, constant wall temperature and convection with an external isothermal fluid were considered. The same asymptotic values of the the Nusselt number were reported for the boundary conditions of constant wall temperature and convection with an external isothermal fluid. It was illustrated that in the convective boundary conditions, the value for Nusselt number is independent of the Biot number.

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