A two-phase feed to the gas-liquid separator (or flash drum), shown in Fig. E13.10, consists of a mixture of two hydrocarbons. Because the vessel pressure P is lower than the feed pressure, the feed flashes as it enters the separator. Using the following information and a degrees of freedom analysis, do the following:
(a) Determine the model degrees of freedom,N_F.
(b) Determine the control degrees of freedom,N_FC.

Available Information:
1. The flash drum operates is o thermally with the two phases in equilibrium.
2. Each phase is perfectly mixed.
3. The mass flow rates are in units of kg/min and the compositions (e.g., w_F ) are expressed as mass fractions.
4. Each flow rate can be adjusted by a control valve (not shown).
5. For the uncontrolled process, the exit flow rates are related to vessel conditions by empirical equations that have the following forms: G = f₁ (P) and L = f₂ (h).

Gas G, wG Feed F, wF Liquid L, wL Figure E13.10