If the temperature of the feed to the drum, T_{F}, is the specified variable, the mass and energy balances and the equilibrium equations must be solved simultaneously. You can see from the energy balance, Eq. (2-7) why this is true. The feed enthalpy, h_{F}, can be calculated, but the vapor and liquid enthalpies, H_{v} and h_{L}, depend upon T_{drum}, y, and x, which are unknown. Thus a sequential solution is not possible.

We could write Eqs. (2-3) to (2-8) and solve seven equations simultaneously for the seven unknowns y, x, L, V, H_{v}, h_{L}, and T_{drum}. This is feasible but rather difficult, particularly since Eqs. (2-3) and (2-4) and often Eqs. (2-8) are nonlinear, so we resort to a trial-and-error ...

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