Geothermal Two-phase Flow in Horizontal Pipes

This paper reanalysed the 255 sets of geothermal two-phase flow data of Freeston et al (1983). A new void fraction correlation is proposed in this paper. The new correlation is derived from the analysis of two-phase flow velocity distribution using the Seventh Power Law as: To predict the two-phase pressure drop, an equivalent pseudosingle-phase flow having the same boundary layer velocity distribution is assumed. The average velocity of the equivalent single-phase flow is used to determine the wall friction factor and hence the two-phase pressure drop. This method gives very good agreement with the experimental data. The average velocity of the equivalent single-phase flow is also a very good correlating parameter for the prediction of geothermal twophase pressure drops in a horizontal straight pipe. INTRODUCTION Geothermal resources suitable for power production are mainly of the wet type that requires the separation process for use in conventional steam turbines. The separation process can take place anywhere between the wellhead and the powerhouse. Separation at the wellhead allows high separation pressure but lower steam output due to higher wellhead pressure (WHP). On the other hand, separator near the turbine has low steam pressure but more quantity of steam. Hence the separation pressure determines the turbine inlet pressure and the utilisation efficiency of the resource. Since the two-phase well fluid pressure drop in the transmission line between the wellhead and the separator affects these two important parameters, it is important to design the two-phase pipelines to transport the two-phase fluid as efficiently as possible. James (1968) and Takahashi et al. (1970) showed that there were economic advantages using long two-phase transmission pipelines. From experience at Wairakei, this has the added advantage of solving the steam pipe corrosion problem due to the steam condensate. However, there is a minimum length of steam pipe required upstream of the steam turbines to scrub the steam of salts carryover from the separation process and for steam pressure control. Although there are many theories and correlations available for predicting two-phase pressure drop, most of them were based on small pipe diameter (<60 mm) and high heat transfer rate conditions for single-component flows else they are twocomponent, two-phase flows. For geothermal application (large diameter, low heat transfer rate and single-component), Harrison’s (1975) correlation, based on geothermal data, is the most suitable. Freeston et al. (1983) studied geothermal two-phase pressure drops in 100 mm diameter straight pipe and fittings, collected 255 sets of valuable data. However, attempts to correlate twophase pressure gradients in a straight pipe as a function of liquid phase velocity give divergent result (see Figure 1). Figure 1: Measured pressure gradient versus liquid phase velocity (prior to the introduction of PC) of Freeston et al (1983). It has to be pointed out that these results were computed prior to the availability of powerful Personal Computer (PC) and spreadsheet software. Steam-water properties were correlated from steam tables. Mundakir (1997) reevaluated the data on a PC using a spreadsheet software, and steam-water properties were obtained from the computer software Engineering Equation Solver (EES) by Klein and Alvarado (1994). The correlation with liquid phase velocity improved significantly as shown in Figure 2. However, attempts to correlate pressure drop across pipe fittings showed no consistent results with liquid phase velocity. Mundakir’s (1997) attempt to correlate the measured pressure gradient of the straight pipe as a function of a two-phase pressure coefficient [(/2ρV)TP.] gave divergent results similar that of Figure 1. This paper is an attempt to find a better correlating parameter for the two-phase pressure drop data of Freeston et al. (1983). 8 / 7 8 / 7 ) )( )( 1 1 ( 1       − = − g f f g x μ μ ρ ρ α α y = 0.0537x + 0.2598x R = 0.6709