Feedpoint viscosity in geothermal wellbore simulation

We consider the appropriate way to average reservoir and wellbore viscosities at a feedpoint, when simulating production in a geothermal well. Large differences in these values can arise when flashing occurs in a liquid-dominated reservoir, which may manifest as non-monotonic flowrates in simulated output curves. Integrating Darcyʹs law for flow to a feed from wellbore to reservoir gives an integral average for the reciprocal of viscosity as a function of pressure that is consistent with the productivity index formulation used in the geothermal wellbore simulators GWELL and SwelFlo. The average is related to the concept of pseudopressure, and various approximations to the integral average are considered, with the result that a trapezoidal rule provides a quick and accurate method. The critical shape of the dependence of average viscosity on wellbore and reservoir pressures is calculated, that separates monotonic from non-monotonic flowrate behaviour, and is found to plot as a straight line. The integral average also reveals that intuition is correct – flow to a feed is monotonic in the pressure there, despite possibly dramatic changes in viscosity.