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General Description

The two-phase 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 gas-condensate 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 correlation-specific 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 \(k/d_h\).

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