On the Choice of Primary Variables in Transient Geothermal Wellbore Modelling

Abstract

Transient flow in a geothermal wellbore is modelled using equations for conservation of mass, momentum and energy. Additional constitutive equations that describe phase slip, heat transfer and frictional effects are also required for model closure. The transient wellbore simulator described in this paper solves discrete two-phase conservation equations numerically using the Newton-Raphson procedure. Additionally, the constitutive equation describing phase slip is included in the set of equations to be solved implicitly. This method requires four primary variables, however, the best choice of the primary variables is not clear. This paper discusses the use of different combinations of primary variables in our transient geothermal wellbore simulator. The numerical performance of each model is assessed using a set of problems that have been developed to test the transient simulator. This suite of test problems covers a range of operating conditions and serves as a benchmark for future simulator development. It was found that using pressure, temperature (swapped with saturation for two-phase conditions), vapour velocity and liquid volume flux resulted in the best numerical performance for all cases tested.