Liquid column dynamics

Dynamic Modelling of Plug-Flow Contactors Liquid-Liquid Extraction Column Dynamics... 

Figure 4.19. Liquid-liquid extraction column dynamic representation.

Now, from its essential notion, we have the feedback interconnection implies that a portion of the information from a given system returns back into the system. In this chapter, two processes are discussed in context of the feedback interconnection. The former is a typical feedback control systems, and consists in a bioreactor for waste water treatment. The bioreactor is controlled by robust asymptotic approach [33], [34]. The first study case in this chapter is focused in the bioreactor temperature. A heat exchanger is interconnected with the bioreactor in order to lead temperature into the digester around a constant value for avoiding stress in bacteria. The latter process is a fluid mechanics one, and has feedforward control structure. The process was constructed to study kinetics and dynamics of the gas-liquid flow in vertical column. In this second system, the interconnection is related to recycling liquid flow. The experiment comprises several superficial gas velocity. Thus, the control acting on the gas-liquid column can be seen as an open-loop system where the control variable is the velocity of the gas entering into the column. There is no measurements of the gas velocity to compute a fluid dynamics... 

Generally, trays work better in applications requiring high flows, because plate efficiencies increase with increased vapor velocities, and therefore increase the influence of the reflux to feed ratio on overhead composition. Column dynamics is a function of the number of trays, because the liquid on each tray must overflow its weir and work its way down the column. Therefore, a change in composition will not be seen at the bottoms of the tower until some time has passed. 

Subsequently, we used Aspen Dynamics for time-domain simulations. A basic control system was implemented with the sole purpose of stabilizing the (open-loop unstable) column dynamics. Specifically, the liquid levels in the reboiler and condenser are controlled using, respectively, the bottoms product flow rate and the distillate flow rate and two proportional controllers, while the total pressure in the column is controlled with the condenser heat duty and a PI controller (Figure 7.4). A controller for product purity was not implemented. 

The liquid holdup is largely measured by a tracer technique. In this technique the total liquid holdup (dynamic -4- static) is obtained by multiplying the liquid flow rate by the mean residence time. There are a large number of holdup correlations reported in the literature. Since some correlations are for the total liquid holdup and some for the dynamic holdup, proper precautions should be taken in using these correlations. The liquid holdup has been defined in terms of either void volume or the total volume of the column. 

In other areas of technology such as chromatographic separations, and hydrometallurgy which may often involve resin transfer (movement) operations, fluidized beds, and truly countercurrent contact of resin and liquid, the acquisition of design data is more often through a fluid dynamic and mass transfer approach to describe, and thereby scale up, column designs in order to realize commercial practices. A text of this nature is neither the vehicle for, nor can it do justice to, such an important topic and the reader is referred to the bibliography for a more detailed account of column dynamics. 

Sircar, S. Myers, A.L. Liquid adsorption operations equilibrium, kinetics, column dynamics and applications. Sep. Sd. Technol. 1986, 21, 535-562. 

The adsorption of water from a binary or multicomponent liquid mixtures is characteristically different from that from gaseous phase because the pore space within the alumina is always filled with a liquid mixture. Nevertheless, the key characteristics (equilibria, kinetics and ad(de)sorption column dynamics) for adsorption of trace and bulk water from a liquid mixture is very well studied. 

Column dynamics for ad(de)sorption of water from liquid mixtures... 

The basic equations of column dynamics were introduced in Section 13.6 in the context of developing a convergence strategy for a steady-state solution. For a full representation of column dynamics, these equations are rewritten here in a slightly modified form and additional equations are introduced to complete the model. The equations refer specifically to a column tray with liquid and vapor holdups. The vapor holdup is negligible compared to the liquid holdup and is usually omitted from the equations. The liquid and vapor on the tray are each assumed of uniform composition. 

Distillation control schemes may be analyzed either on a steady-stale (sensitivity analysis) or on a dynamic basis. The latter requires a dynamic model that takes into account the dynamic response of the column and the control loope. An example of a dynamic model is described by McCune and Gailier,6 but il should be apparent from the material presented enrlier that the holdup characteristics of distillation columa devices can vary widely, and snch variation should be accommodated by the model. The development of the naw high-efficiency packings has caused a new look at the system dynamics when the liquid holdup in the column is quite low, and thus the existing models for trays may not be adjustable to application to packings. The use of a tray-type dynamic model is described in the article by Gailier and McCune 7 so work to date has been reported for packed column dynamic models. 

Measuring device. This can be a variable capacitance differential pressure transducer (Section 13.3), measuring the pressure of a liquid column of height h. The dynamic response of the sensor is given by eq. (13.9). Let Ap = ah, where a is a constant. Then take... 

Figure 21.2 shows the LV configuration for the two-point composition control of a binary distillation column discussed in Example 20.9. After assigning manipulated variables to regulate the vapor and liquid inventories, the boilup rate, V, and the reflux flow rate, L, remain available to control the distillate and bottoms product compositions, and Xg, respectively. To assess the controllability and resiliency of this configuration, the disturbances are taken to be the feed composition, Xp, and the flow rate, F. The column dynamics are approximated by a linear model in transfer function form (Sandelin et al., 1990) ... 

Cassanello M, Larachi F, Kemoun A, Al-Dahhan MH, Dudukovic MR (2001) Inferring liquid chaotic dynamics in huhble columns. Chem. Eng. Sci., 56 6125-6134. 

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