Modeling Two-Phase Fluid and Heat Flows in Geothermal Wells

Abstract

Abstract 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-pattern-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. Introduction Historically, pressure-traverse computation in geothermal wellbores followed a trend similar to that in wells producing hydrocarbons. This similarity is appreciated by noting that all the principal flow regimes, bubbly, slug, churn, and annular, are common to both systems. Some of the authors of early studies adopted a hybrid approach; that is, the slip between steam and water phases is computed with a different model in each flow regime. One potential difficulty of this approach is that the transition between the flow regimes may not be smooth, thereby triggering discontinuity. The early studies of Gould (1974), Chierici et al. (1981), Ambastha and Gudmundsson (1986a, 1986b), Chadha et al. (1993), among others, fall into the hybrid-approach category. A few authors, such as Upadhayay et al. (1977), used different models in their entirety to find the one most reliable. Orkiszewski's correlation (1967) appeared to have an edge in their study. In a more recent study, Acuña and Arcedera (2005) expressed a similar sentiment while discussing one field example. However, this view is not universal as Tanaka and Nishi (1988) showed in a study with 16 wells, containing varying amounts of CO2. Despite reporting comparative studies, most authors dealt with a very few wells, thereby leading to an important question: is the number of field tests sufficient to draw statistically significant conclusions with regard to superiority of one model over any other? To compound the problem, the dataset were incomplete; that is, both bottomhole temperature (BHT) and geothermal gradient went often unreported. Any comparative study involving models' relative performance is akin to the one used extensively in the petroleum literature. However, the number of wells in the petroleum industry dwarfs those that are available in geothermal production, thereby posing challenges in identifying reliable models for pressure-traverse computation.