Figure 6-4 shows the cold feed distillation tower of Figure 6-3. The inlet stream enters the top of the tower. It is heated by the hot gases bubbling up through it as it falls from tray to tray through the downcomers. A flash occurs on each tray so that the liquid is in near-equilibrium with the gas above it at the tower pressure and the temperature of that particular tray.
As the liquid falls, it becomes leaner and leaner in light ends, and richer and richer in heavy ends. At the bottom of the tower some of the liquid is circulated through a reboiler to add heat to the tower. As the gas goes up from tray to tray, more and more of the heavy ends get stripped out of the gas at each tray and the gas becomes richer and richer in the light ends and leaner and leaner in the heavy ends (just the opposite of the liquid). The gas exits the top of the tower.
The lower the temperature of the inlet liquid, the lower the fraction of intermediate components that flash to vapor on the top trays and the greater the recovery of these components in the liquid bottoms. However, the colder the feed, the more heat is required from the reboiler to remove light components from the liquid bottoms. If too many light components remain in the liquid, the vapor pressure limitations for the liquid may be exceeded. Light components may also encourage flashing of intermediate components (by lowering their partial pressure) in the storage tank. There is a balance between the amount of inlet cooling and the amount of reboiling required.
Typically, the liquid out the bottom of the tower must meet a specified vapor pressure. The tower must be designed to maximize the molecules of intermediate components in the liquid without exceeding the vapor pressure specification. This is accomplished by driving the maximum number of molecules of methane and ethane out of the liquid and keeping as much of the heavier ends as possible from going out with the gas.
Given inlet composition, pressure, and temperature, a tower temperature and the number of trays that produce a liquid with a specified vapor pressure can be chosen as follows:
1. Assume an initial split of components in the inlet that yields the desired vapor pressure. That is, assume a split of each component between the tower overhead (gas) and bottoms (liquid). There are
various rules of thumb that can be used to estimate this split in order to give a desired vapor pressure. Once the split is made, both the assumed composition of the liquid and the assumed composition of
the gas are known.
2. Calculate the temperature required at the base of the tower to develop this liquid. This is the temperature at the bubble point for the tower pressure and for the assumed outlet composition. Since the composition and pressure are known, the temperature at its bubble point can be calculated.
3. Calculate the composition of the gas in equilibrium with the liquid. The composition, pressure, and temperature of the liquid are known, and the composition of the gas that is in equilibrium with this liquid
can be calculated.
4. Calculate the composition of the inlet liquid falling from Tray 1. Since the composition of the bottom liquid and gas in equilibrium with the liquid is known, the composition of the feed to this tray is also known. This is the composition of the liquid falling from Tray 1.
5. Calculate the temperature of Tray 1. From an enthalpy balance, the temperature of the liquid falling from Tray 1, and thus the temperature of the flash on Tray 1, can.be calculated. The composition is
known, the enthalpy can be calculated. Enthalpy must be maintained, so the enthalpy of the liquid of known composition falling fom Tray 1 must equal the sum of the enthalpies of the liquid and gas flashing from it at known temperature.
6. This procedure can then be carried on up the tower to Tray N, which establishes the temperature of the inlet and the gas outlet composition.
7. From the composition of the inlet and gas outlet the liquid outlet, composition can be calculated and compared to that assumed in step 1.
8. The temperature or number of trays can then be varied until the calculated outlet liquid composition equals the assumed composition, and the vapor pressure of the liquid is equal to or less than that
assumed. If the vapor pressure of the liquid is too high, the bottoms temperature must be increased.
