Page 133 - Chemical process engineering design and economics

Process Circuit Analysis 117

After substituting Equations 3.3.42 and 3.3.43 into Equation 3.3.39, and with
some algebraic manipulation, we obtain the final form of the energy equation,
Equation 3.3.44.

yi,i r m 2V ( m 2V ^ 1
I —————————————— I K 2>i h 2V, ; —— + h 2Lii 1 1 ——— | | - h, = 0 (3.3.44)
(K 2ji - IHnWmO+l L raj I m l j J

The calculation procedure using Equations 3.3.38 and 3.3.44 is outlined in
Table 3.3.4.
Table 3.3.4: Procedure for Calculating the Temperature of a
Flashed Liquid _______________________________

1. Calculate the bubble-point temperature. Assume a temperature and then
calculate values for the equilibrium relations from Equations 3.3.22 and 3.3.23 in
Table 3.2.2. Next, calculate the vapor-phase mole fractions from Equations 3.3.20
and 3.3.21. Check the results using Equation 3.3.19. Assume a new temperature
and repeat the calculation until temperature converges to a desired degree of accu-
racy.

2. Similarly, calculate the dew-point temperature. Assume a temperature and then
calculate values for the equilibrium relations from Equations 3.3.27 and 3.3.28 in
Table 3.3.3. Next, calculate the liquid-phase mole fractions from 3.3.25 and
3.3.26. Check the results using Equation 3.3.24. Assume a new temperature and
repeat the calculation until temperature converges to a desired degree of accuracy.
3. Assume a temperature, T 2, between the bubble and dew point temperatures.

4. Calculate values for the equilibrium relations at T 2 from Equations 3.3.8 and
3.3.9 in Table 3.3.1.

5. Solve for the mole fractions for the liquid and vapor from Equations 3.3.3,
3.3.4, 3.3.6, and 3.3.7.

6. Substitute these values into Equation 3.3.38 and solve for m 2V/m } by trial.
7. Calculate the pure-component enthalpies from Equations 3.3.13 to 3.3.18 and
the enthalpy of the feed solution from Equation 3.3.10.

8. Check the guess of T by substituting all calculated quantities into the energy
2
balance, Equation 3.3.44.
9. Assume a new value of T, and repeat steps 3 to 7 until the energy equation is
2
satisfied within a sufficient degree of accuracy.

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