Distillation columns tray hydraulics

Packed fractional distillation columns run in the batch mode are often used for low-pressure drop vacuum separation. With a trayed column, the liquid holdup on the trays contributes directly to the hydraulic head required to pass through the column, and with twenty theoretical stages that static pressure drop is very high, e.g., as much as 100-200 mm Hg. 

You may wonder why we would ever be satisfied with anything less than a very accurate integration. The ODEs that make up the mathematical models of most practical chemical engineering systems usually represent a mixture of fast dynamics and slow dynamics. For example, in a distillation column the liquid flow or hydraulic dynamic response occurs fairly rapidly, of the order of a few seconds per tray. The composition dynamics, the rate of change of hquid mole fractions on the trays, are usually much slower—minutes or even hours for columns with many trays. Systems with this mixture of fast and slow ODEs are called stiff systems. 

The digital simulation of a distillation column is fairly straightforward. The main complication is the large number of ODEs and algebraic equations that must be solved. We will illustrate the procedure first with the simplified binary distillation column for which we developed the equations in Chap. 3 (Sec. 3.11). Equimolal overflow, constant relative volatility, and theoretical plates have been assumed. There are two ODEs per tray (a total continuity equation and a light component continuity equation) and two algebraic equations per tray (a vapor-liquid phase equilibrium relationship and a liquid-hydraulic relationship). 

Tung, L.S. and Edgar, T. F., "Development and Reduction of a Multivariable Distillation Column Model with Tray Hydraulics,"... 

Site the Distillation Column. This includes the hydraulic aanlysis to establish operating mages, pressure drop, and mass transfer efficiency. The result is a set of dimensious, including columa diameter and height, number of actual trays (or height of packed bed), details of internal devices, and profiles of temperature and pressure. 

For example, the cost of a distillation column can be assembled from the cost of elements vertical cylindrical vessel, plus internals (trays or packing), reboiler, condenser, and reflux drum. The height of the shell can be determined from the number of trays and inter-stage height. The column diameter can be found by hydraulic calculations based on the flooding point. In this way, the volume of the cylindrical part can be easily evaluated. The volume of auxiliary vessels, as drum and reboiler, can be estimated from the residence time, typically of 10 minutes. 

An important example of a physical process that shows inverse response is the base of a distillation column with the reaction of bottoms composition and base level to a change in vapor boilup. In a binary distillation column, we know that an increase in vapor boilup V must drive more low-boiling material up the column and therefore decrease the mole If action of light component in the bottoms xg. However, the tray hydraulics can produce some unexpected results. When the vapor rate through a tray is increased, it tends to (1) back up more liquid in the downcomer to overcome the increase in pressure drop through the tray and (2) reduce the density of the liquid and vapor Ifoth on the active part of the tray. The first effect momentarily reduces the liquid flow rates through the column while the liquid holdup in the downcomer is... 

The hydraulic capacity of trayed distillation columns is always limited by either a high liquid entrainment, or by an overload of downcomers. The technology of high capacity trays deals with these two fundamental limits by reducing the entrainment or by releasing the loads of downcomers. Both are generally connected (HUls, 2001). 

The rigorous column models allow the design engineer to carry out tray sizing and hydraulics calculations for the basic types of distillation trays and for some types of random and structured packing. Different commercial simulators use different tray sizing correlations, but they all follow a method similar to that described in Chapter 11. 

For example, in distillation we generally do not attempt to control a temperature or composition in the base of the column by manipulating reflux. There is typically a liquid hydraulic lag of 6 seconds per tray, so a change in reflux to the top of a 50-tray column does not change the liquid flow at the bottom of the column for about 5 minutes. The dynamic performance of this loop is poor, so we do not pair bottoms composition with reflux no matter what the RGA tells us to do. On the other hand, the vapor boilup affects all sections of the column quite quickly, so it can be paired with a controlled variable at the top of the column with no dynamic problem. 

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