In Fig. 13-25, if P2 and the feed-stream conditions (i.e., F, z, T1, P1) are known, then the calculation of T2, V, L, yt, and x, is referred to as an adiabatic flash. In addition to Eqs. (13-12) to (13-14) and the total mole balance, the following energy balance around both the valve and the flash drum combined must be included:
Taking a basis of F = 1.0 mol and eliminating L with the total mole balance, Eq. (13-17) becomes f2{V T2) = Hf- V(HV - Hl) - Hl = 0 (13-18)
With T2 now unknown, Eq. (13-17) becomes f1{V T2) = X Zi(1 -K = 0 (13-19)
A number of iterative procedures have been developed for solving Eqs. (13-18) and (13-19) simultaneously for V and T2. Frequently, and especially if the feed contains components of a narrow range of volatility, convergence is rapid for a tearing method in which a value of T2 is assumed, Eq. (13-19) is solved iteratively by the isothermal-flash procedure, and, using that value of V, Eq. (13-18) is solved iteratively for a new approximation of T2, which is then used to initiate the next cycle until T2 and V converge. However, if the feed contains components of a wide range of volatility, it may be best to invert the sequence and assume a value for V, solve Eq. (13-19) for T2, solve Eq. (13-18) for V, and then repeat the cycle. If K values and/or enthalpies are sensitive to the unknown phase compositions, it may be necessary simultaneously to solve Eqs. (13-18) and (13-19) by a Newton or other suitable iterative technique. Alternatively, the two-tier method of Boston and Britt [Comput. Chem. Eng., 2, 109 (1978)], which is also suitable for difficult isothermal-flash calculations, may be applied.
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