Development of a Wellbore Flow Simulator (WELCARD-II) Applicable up to Annular-Mist Flow in Geothermal Wells

Investigation about Friction Factor

Abstract

A wellbore flow simulator (WELCARD-II) for liquid-single and two-phase flows in geothermal wells has been developed, which is applicable to the flow regimes up to annular-mist flow. The applicability of many constitutive equations for friction factor to actual geothermal wells and the availability of the wellbore simulator have been investigated by the comparison of computational results with measured values of borehole temperature and pressure in the Kakkonda geothermal field in Japan. The results are as follows.
1) In the domain of liquid-single flow, the calculation by the wellbore simulator with Blasius's equation for friction factor (λ=0.3164 Re^-0.25) at Re≤3.0×10⁶ and Weisbach's equation for friction factor (λ=0.0144+0.0095/j^1/2) at Re>3.0×10⁶ was very satisfactory.
2) In the domain of two-phase flow, the calculation by the wellbore simulator with the equation for friction factor (λ=0.032) at Rem≤2.6×10⁷ and the equation for friction factor (λ=0.046Rem^-0.2) at Rem>2.6×10⁷ was also very satisfactory.
3) WELCARD-II is applicable to the two-phase flow in the wellbore up to annular-mist flow regime and has the advantage of overcoming the problems in calculations such as non-continuity of temperature/pressure profiles at flow regime boundaries.