Gray
General Description
The twophase flow correlation by Gray (1971)^{1} was originally presented in the manual for a computer program on sizing of surface controlled subsurface safety valves (SCSSV). The correlation is meant for lean gascondensate wells with liquid as a dispersed phase (mist flow). The correlation includes an expression for the liquid hold up, and a modification of the pipe roughness to account for liquid adhesing to the pipe wall which increases friction forces.
The liquid hold up is calculated from
where with \(R=v_{sL}/v_{sg}\), \(N_{v}=\rho_m^2v_{m}^2/(g\sigma(\rho_L\rho_g))\), and \(N_d=g(\rho_L\rho_g)d_h^2/\sigma\).
The modification to the pipe roughness \(k\) is calculated by where \(k_0=28.5\sigma/(\rho_m v_m^2)\), with the limit \(k_{eff}\geq 2.77\times 10^{5}\).
Pressure Gradient Calculations
The correlationspecific properties in the pressure gradient are set to the following
Density in the gravity gradient \(\rho_g=\rho_s\)
Density in the friction gradient \(\rho_f=\rho_m\)
Density in the acceleration gradient \(\rho_a=\rho_s\)
Friction factor \(f_D\) is calculated with \(N_{Re}=\rho_m v_m d/\mu_m\) and \(k_{eff}/d_h\) instead of \(k/d_h\).

H.E. Gray. Vertical Flow Correlation in Gas Wells. Userâ€™s Manual for API 14B Surface Controlled Subsurface Safety Valve Sizing Computer Program. American Petroleum Institute, 2 edition, 1978. ↩