Modeling two-phase fluid and heat flows in geothermal wells
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This study presents a robust model for two-phase flow in geothermal wells using the drift-flux approach. For estimating the static head, we use a single expression for liquid holdup, with flow-pattem-dependent values for flow parameter and rise velocity that gradually changes near the transition boundaries to avoid discontinuity in the estimated gradients. Frictional and kinetic heads are estimated with the simple homogeneous modeling approach. As the geothermal fluids ascend up the well, loss of both momentum and heat occur. The consequent pressure loss often leads to flashing and increase in steam fraction (quality) despite heat loss. Accurate estimation of heat loss, which leads to significant changes in fluid properties influencing pressure-drop is, therefore, important in modeling flow in geothermal wells. Heat transfer from the wellbore fluid to the surrounding formation is rigorously modeled by treating the wellbore as a heat sink of finite radius in an infinite-acting medium (formation) and accounting for the resistances to heat transfer offered by various elements of the wellbore. We present a comparative study involving the new model and those that are often used for geothermal wells. These models include those of Ansari et al., Orkiszewski, Hagedorn and Brown, Beggs and Brill, and the homogeneous model. The main ingredient of this study entails the use of a small but reliable dataset. Statistical analyses suggest that all the models behave similarly, although the proposed model offers marginally greater accuracy and simplicity of use. Uncertainty of performance appears to depend upon the quality of data input, rather than the model characteristics. Copyright 2009. Society of Petroleum Engineers.