The calculation for a point on the flash curve that is intermediate between the bubble point and the dew point is referred to as an isothermal-flash calculation because T2 is specified. Except for an ideal binary mixture, procedures for calculating an isothermal flash are iterative. A popular method is the following due to Rachford and Rice [J. Pet. Technol., 4(10), sec. 1, p. 19, and sec. 2, p. 3 (October 1952)]. The component mole balance (Fz, = Vy, + Lx,), phasedistribution relation (K, = y,/xi), and total mole balance (F = V + L) can be combined to give
Equation (13-14) is solved iteratively for V/F, followed by the calculation of values of x, and y, from Eqs. (13-12) and (13-13) and L from the total mole balance. Any one of a number of numerical root-finding
procedures such as the Newton-Raphson, secant, false-position, or bisection method can be used to solve Eq. (13-14). Values of K are constants if they are independent of liquid and vapor compositions. Then the resulting calculations are straightforward. Otherwise, the Ki values must be periodically updated for composition effects, perhaps after each iteration, using prorated values of x, and y, from Eqs. (13-12) and (13-13). Generally, the iterations are continued until the calculated value of V/F equals to within ±0.0005 the value of V/F that was used to initiate that iteration. When converged, X Xt and X yt will each be very close to a value of 1, and, if desired, Ti can be computed from an energy balance around the valve if no heat exchanger is used. Alternatively, if T1 is fixed as mentioned earlier, a heat exchanger must be added before, after, or in place of the valve with the required heat duty being calculated from an energy balance. The limits of applicability of Eqs. (13-12) to (13-14) are the bubble point, at which V = 0 and x, = zt, and the dew point, at which L = 0 and yt = zt, at which Eq. (13-2) reduces to the bubble-point equation
and the dew-point equation
For a binary feed, specification of the flash-drum temperature and pressure fixes the equilibrium-phase concentrations, which are related to the K values by
X1 = (1 - K2)/(K1 - K2) and y1 = (KK - K1)/(K - K1)
The mole balance can be rearranged to
If K1 and K2 are functions of temperature and pressure only (ideal solutions), the flash curve can be calculated directly without iteration.
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