A component and overall mole balance are performed:
$$
n_i^F = n_i^L + n_i^V,
$$
$$
n^F = n^L + n^V,
$$
where \(n\) is the number of moles, the superscripts F, L and V refer to the feed, liquid and vapor streams and the subscript \(i\) = m or w refers to a component (methanol or water).
Overall and component energy balances with the reference state \(T_{ref}\) = 25°C and \(P_{ref}\) = 1 bar:
$$
H_{in} = H_{out},
$$
$$
H^F = H^L + H^V,
$$
$$
H_i^F = H_i^L + H_i^V,
$$
where \(H\) is enthalpy (kJ).
The enthalpies of each stream are calculated using heat capacities \(Cp\) (kJ/(mol K)) and heat of vaporization \(\Delta H^{vap}\) (kJ/mol):
$$
H^F = \Sigma n_i^FCp_i^L(T_{in}-T_{ref}),
$$
$$
H^L = \Sigma n_i^LCp_i^L(T_{out}-T_{ref}),
$$
$$
H^V = \Sigma n_i^V(Cp_i^V(T_{out}-T_{ref}) + \Delta H_i^{vap}).
$$
The flash drum has a single equilibrium stage, so the exiting liquid and vapor streams are at the same temperature, \(T_{out}\).
Saturation pressure \(P^{sat}\) of the components in vapor-liquid equilibrium is calculated using the Antoine equation:
$$
P_i^{sat} = 10^{A_i - \frac{B_i}{T+C_i}},
$$
where \(A_i\), \(B_i\) and \(C_i\) are Antoine constants for each component, and \(P^{sat}\) is in bar.
Raoult's law is used for the exit streams to find the vapor-liquid equilibrium compositions:
$$
x_iP_i^{sat} = y_iP,
$$
where \(x_i\) and \(y_i\) are the liquid and vapor mole fractions.
The sum of the mole fractions times their saturation pressures is the total pressure \(P = x_mP_m^{sat} + x_wP_w^{sat}.\)
+ 
on Mac
or 
+ 
on Mac
or