lgeh = logaritmo del gasto en educación por habitante, y linvh = logaritmo del insumo capital por habitante.
V. 3.1.3.4 Educación: macroeconomía y tipo de cambio
Solution:
For all three draw‐off stream trays, the tray pressure is evaluated first.
HGO draw off tray = 10 Flash zone pressure = 40 psia
HGO draw off tray is located 6 trays above the flash zone. Average pressure drop per tray = 0.32 psia per tray
HGO draw off tray pressure = 40 – 6 x 0.32 = 39.1 psia.
Similarly, LGO draw off tray pressure = 40 – (6 + 10) x 0.32 = 34.88 psia
Kerosene draw off tray pressure = 40 – (6 + 10 + 12) x 0.32 = 31.04 psia
Next, we evaluate the steam requirements in the side stream strippers.
Residue zone fresh steam flow rate (from flash zone calculations) = 2712.5 lbmol/hr
HGO zone fresh steam flow rate = 6125 x 0.5/18 = 170.13 lbmol/hr
LGO zone fresh steam flow rate = 11375 x 0.5/18 = 5687.5 lbmol/hr
Kerosene zone fresh steam flow rate = 14000 x 0.65/18 = 505.55 lbmol/hr
From mass balance table summarized previously,
Naphtha vapor flow rate = 898.03 lbmol/hr
Kerosene vapor flow rate = 670.9 lbmol/hr
LGO vapor flow rate = 391.1 lbmol/hr
HGO vapor flow rate = 181.63 lbmol/hr
I) HGO draw off tray temperature calculation
Moles overflow = 2.9 x 181.63 = 526.72 lbmol/hr
Hydrocarbon vapor flow rate = 898.03 + 670.9 + 391.1 + 181.63 = 2140 lbmol/hr
Steam flow rate = 2712.5 lbmol/hr (Only that steam that is reaching the HGO draw off tray is the steam that enters at the bottom of the main column).
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Therefore, partial pressure of hydrocarbons at HGO draw off tray = (2140 + 526.72)/(2140 + 526.72 + 2712.5) x 38.1 = 18.89 psia.
Now, the EFV of the Heavy gas oil is determined using Maxwell’s correlation. The procedure is not shown here. The obtained IBP from EFV curve is 561 oF.
From vapor pressure curves, estimated theoretical HGO draw off temperature at a partial pressure of 18.89 psia (instead of 14.7 psia) is 620 oF.
From Packie’s correlation, for an x‐axis data point of 561 oF, the y‐axis point (Table 4.1) is 83 oF.
Therefore, actual HGO draw off temperature = 620 – 83 = 537 oF.
II) LGO draw off tray temperature calculation
Moles overflow = 1.2 x 391.08 = 469.3 lbmol/hr
Hydrocarbon vapor flow rate = 898.03 + 670.9 + 391.1 = 1960.03 lbmol/hr (All HC vapors other than the HGO and residue products).
Steam flow rate = 2712.5 + 170.13 = 2882.64 lbmol/hr (This is the steam that enters at the residue zone and also in the HGO side stripper).
Therefore, partial pressure of hydrocarbons at HGO draw off tray = (1960.03 + 391.08)/(1960.03+391.08 + 288.26) x 34.2 = 15.66 psia.
Now, the EFV of the LGO is determined using Maxwell’s correlation. The procedure is not shown here. The obtained IBP from EFV curve is 485 oF.
From vapor pressure curves, estimated theoretical LGO draw off temperature at a partial pressure of 15.66 psia (instead of 14.7 psia) is 510 oF.
From Packie’s correlation, for an x‐axis data point of 510 oF, the y‐axis point (Table 4.1) is 60 oF. Therefore, actual HGO draw off temperature = 510 – 60 = 450 oF.
III) Kerosene draw off tray temperature calculation
Moles overflow = 0.9 x 670.9 = 603.81 lbmol/hr.
Hydrocarbon vapor flow rate = 898.03 + 670.9 = 1568.03 lbmol/hr (All HC vapors other than the LGO, HGO and residue products).
Steam flow rate = 3198.611 lbmol/hr
Therefore, partial pressure of hydrocarbons at HGO draw off tray = (1568 + 603.81)/(1568 + 603.81 + 3198.6) x 30.2 = 12.5 psia.
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From EFV, vapor pressure curves and packie’s correlation, actual draw off‐temperature = 320 oF.
4.7 Estimation of tower top temperature
The tower top temperature is very important to determine, as the know‐how of the temperature will lead to further delineating the condenser duty. The tower top temperature is determined from a dew point calculation. The procedure for the same is similar to that provided in the gasoline blending problem illustrated in the refinery mass balances chapter. The procedure for the same is outlined below:
a) Set the reflux drum temperature and pressure as 100 oF and 10 psig. Assume 5 psia pressure drop and hence, tower top pressure = 15 psig or 29.7 psia.
b) Assume external reflux as 0.8 times the total moles overhead product. Determine external reflux flow rate
c) Determine partial pressure of hydrocarbons in the tower top section.
d) Assume a tower top temperature of 250 oF. This value is required to determine the equilibrium constants (K) for different pseudo‐components.
e) As reflux will have a composition similar to the gas + naphtha fraction whose pseudo‐ component distribution is previously known, determine the vapor pressures of each pseudo‐ component as a function of its mid boiling point and API.
f) Determine mole fraction of each pseudo‐component.
g) Calculate equilibrium constant for each pseudo‐component as the ratio between its vapor pressure (determined from Maxwell’s vapor pressure correlations) and the partial pressure of the hydrocarbons (determined in step c)
h) Assume the determined mole fractions to correspond to the vapor stream. Eventually, determine liquid stream mole fraction using the expression x = y/K where K is the equilibrium constant.
i) Eventually, evaluate summation of all x values
j) For the last pseudo‐component, determine its new equilibrium constant using the expression K2 = K1 (sum of all x values).
k) From the K2 values, determine the new tower top temperature.
l) If significant differences exist between the new tower top temperature and assumed value (250 oF), then iterate the procedure until a converging tower top temperature is determined.
Q 4.6: For the Ecudaor CDU design problem, determine the tower top temperature.
Solution:
Tower top pressure = 29.7 psia
Vapor flow rate = (1+0.8) x 898.03 = 1616.46 lbmol/hr
Steam flow rate in the tower top section = 3704.1 lbmol/hr
Partial pressure of hydrocarbons in the tower top section = 1616.4/(1616.4 + 3704.1) x 29.7 = 9.02 psia.