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#### 2.4.2 Simultaneous Solution and Enthalpy-Composition Diagram

If the temperature of the feed to the drum, TF, 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, hF, can be calculated, but the vapor and liquid enthalpies, Hv and hL, depend upon Tdrum, 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, Hv, hL, and Tdrum. 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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