A comprehensive coupled wellbore/reservoir simulator was developed to study the behavior of single-phase oil flow in the wellbore. The wellbore is modeled numerically where mass, momentum, and energy of the fluid are conserved, while the reservoir fluid flow is treated analytically. Energy transport occurs through tubulars, cement sheaths, and the formation by conduction. However, both conductive and convective heat-transport mechanisms are operative for the annular fluid. Heat losses through seawater and air are also modeled for a well producing in an offshore environment.
A sensitivity study shows that heat loss through seawater becomes significant for long submerged tubulars (< 2,000 ft), but is marginal for shorter pipes because of the fluid's short residence time. Further, a deviated well loses more heat to formation than its vertical counterpart for the same reason. Of the major variables, thermal conductivity of the annular fluid plays a key role in heat retention and, therefore, the wellhead temperature (WHT). We have identified the phenomenon of thermal storage. This storage behavior is associated with heat absorption or desorption by cement sheaths and tubulars and is reflected as the time taken to attain equilibrium WHT for a given flow rate. A longer storage period occurs at low flow rates because of lower associated fluid enthalpy.
Field data were used to demonstrate various applications of the simulator. We showed that both drawdown and buildup data of bottomhole pressure (BHP), wellhead pressure (WHP), and WHT can be modeled successfully given the tubular, completion, and reservoir data. Conversely, given the wellhead measurements (WHP and WHT), BHP values comparable to those measured can be computed.