Prediction of the entropy production and pressure losses in two-phase flow from the mixing length theory

The case of vertical two-phase flow is examined under the light of the mixing-length theory which was succesfully applied to turbulent flows. The purpose of the analysis is to obtain the pressure distribution along the geothermal wells. The well is modeled as a vertical pipe carrying a fluid of variable density; the density distribution is described by two parameters. The conservation equations are written in boundary layer coordinates and the pressure losses are computed through the entropy production function. The two-phase friction factor is defined and calculated and through this the pressure distribution of the geothermal well is obtained. Finally a comparison is made of the results emanating from this model to other theoretical predictions and known experimental data