Two of the four manipulated variables listed above must be used to maintain liquid inventories in the reflux drum and in the column base. Therefore, we are left with just two manipulated variables that can be used to control compositions in the column.
No matter what "manipulated variables" are chosen to control what "controlled variables," there are basically two fundamental manipulated variables that affect compositions. These are "feed split" and "fractionation."
Feed split means the fraction of the feed removed as either distillate or bottom product. The D/F and B/F ratios can be manipulated either directly (as proposed by Shinskey in his "material balance control" scheme) or indirectly. The steady-state effectiveness of both the direct and indirect schemes is identical. In either case feed split has a very strong effect on product composition. A slight change in feed split can change product compositions very drastically, particularly when product purities are high.
Fractionation also affects product composition. Fractionation means the degree of separation. It varies with the number of trays in the column, the energy input to the reboiler, and the intrinsic difficulty of separating the components. For a fixed column operating at a fixed pressure with given chemical components, heat input to the reboiler is the only variable that can be used. Heat input can be used directly; alternatively reflux can be adjusted, if this is more convenient, since reflux and heat input are tied together through overall energy and mass balances.
We will discuss the pros and cons of various choices of control schemes in more detail in later chapters.
The vast majority of industrial distillation columns are equipped with trays or plates (sometimes called "decks" in the petroleum industry) located every 1—3 feet up the column. These trays promote mass transfer of light components into the vapor flowing up the column and of heavy components into the liquid flowing down the column. Vapor-liquid contacting is achieved by a variety of devices. The most widely used trays in recent years have been sieve trays and valve trays because of their simplicity and low cost.
Sieve trays are simple flat plates with a large number of small holes. Vapor flows up through the holes, preventing the liquid from falling through. Liquid flows across each tray, passes over a weir, and drops into a "downcomer," which provides liquid for the tray below through an opening at the base of the downcomer. See Figure 2.3. Valve trays are built with a cap that fits over the hole in the tray and that can move up and down, providing more or less effective hole areas as vapor flow rate changes.
This fairly complex process of flow of vapor up the column and of liquid across each tray and down- the column is called tray "hydraulics." It is important in control system design because it imposes very important constraints on the range of permissible liquid and vapor flow rates. If liquid cannot flow down the column, or if vapor-liquid contacting is poor, the separating ability of the column drops drastically.
Vapor flows from one tray up through the tray above it because the pressure is lower on the upper tray. Thus there is an increase in pressure from the top of the column to its base. Liquid must flow against this positive pressure gradient. It is able to do so because the liquid phase is denser than the vapor phase. A liquid level is built up in the downcomer to a height sufficient to overcome the difference in static pressure between the tray onto which the liquid is flowing and the tray from which it is coming.
ACTIVE TRAY AREA
ACTIVE TRAY AREA
This pressure difference depends on the vapor pressure drop through the tray (which varies with vapor velocity, number and size of holes, vapor density, etc.) and the average liquid height on the tray (which varies with liquid flow rate, outlet weir height, etc.).
Tray "flooding"* occurs when the liquid height in the downcomer equals or exceeds the height between trays (tray spacing). This is usually due to excessive boilup (vapor rate) but sometimes may be caused by excessive reflux. The control system must keep the column from flooding. Therefore, there are maximum vapor and liquid rates.
On the other end of the scale, if vapor rates are reduced too much, the vapor pressure drop through the openings in the tray will be too small to keep the liquid from weeping or dumping down through the holes.f If this occurs, vapor—liquid contacting is poor and fractionation suffers. The same thing occurs if liquid rates are so low (as they often are in vacuum columns) that it becomes difficult to hold enough liquid on the tray to get good vapor-liquid contacting.
These hydraulic constraints can be handled in control system design by using maximum and minimum flow limiters on heat input and reflux. A measurement of column pressure drop can also be used to prevent flooding.
Distillation columns can be used to separate chemical components when there are differences in the concentrations of these components in the liquid and vapor phases. These concentration differences are analyzed and quantified using basic thermodynamic principles covering phase equilibrium. Vapor—liquid equilibrium (VLE) data and analysis are vital components of distillation design and operation.
The liquid phase of any pure chemical component, species /, exerts a certain pressure at a given temperature. This pressure is called the pure component "vapor pressure" Pr It is a physical property of each component.
Vapor-pressure data are obtained by laboratory experiments where both liquid and vapor phases of a pure component are held in a container (see Figure 2.4). Pressure is measured at various temperatures. The temperature at which the pure component exerts a pressure of one atmosphere is called its "normal boiling point." Light components have low normal boiling points and heavy components have high normal boiling points.
* For a further discussion of flooding, see pages 424—430 of reference 8.
t This occurs at about 60 percent of design vapor rates for sieve trays and about 25 percent of design vapor rate for valve trays.
When the data are plotted on linear coordinates (see Figure 2.5), a nonlinear dependence of vapor pressure on temperature is obtained. Vapor-pressure data often can be described by the Antoine equation*:
Pj = vapor pressure of/th component in any pressure units
(commonly mm Hg, psia, atmospheres, kPa) T = absolute temperature (degrees Kelvin or Rankine)
Aj and Bj = constants over reasonable range of temperatures
Therefore, vapor-pressure data are usually plotted using coordinates of log pressure versus reciprocal of absolute temperature as illustrated in Figure 2.6. Note that the constants A, and B, must be determined for each pure component.
Vapor pressure and temperature measurement
Vapor pressure and temperature measurement
* A three-constant version of the Antoine equation is used in Chapter 10.
They can be easily calculated by knowing two vapor-pressure points (Px at and P2 at T2). When working with a distillation column, 1\ and T2 are usually selected to be near the temperatures at the top and at the bottom of the column.
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