Two-Phase Flow Correlation for Vertical Geothermal Well Using Dimensional Analysis

Abstract

The flowing bottom-hole pressure of a geothermal well is the sum of the flowing wellhead pressure, the pressure exerted by the weight of the fluid column, the kinetic energy change, and the energy losses resulting from heat transfer and friction. In this study, we propose a model which was derived using the dimensional analysis method to estimate the flowing pressure at any point along a geothermal well. The correlation includes several important parameters which have significant effect in fluid flow system in geothermal well such as mixture density, total mass flow rate, enthalpy, pipe diameter, and pressure gradient. For validation purpose, the measured flowing bottom-hole pressure of several wells in Iceland was compared with the one calculated using the proposed model. The differences of flowing bottom-hole pressure are ranging from 2.016% to 12.63%. The comparison results show that the proposed model is viable to estimate the flowing bottom-hole pressure. The model allows the application of temperature gradient change by multisegment calculation procedure. There are little differences of flowing bottom-hole pressure calculation that are computed using the whole wellbore and two segment calculation due to round off errors. The average difference is 0.23%.