Distillation columns composition response

Figure 5.214. The batch column was started with total reflux the reflux was then reduced to 0.25 at t = 75 and then increased (from 1.0 to 5.0 to 50.0) whenever the distillate tank composition XO fell below 0.9. The response of the plate compositions and the fraction distilled, FRAC, are shown.

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. 

Process dynamics is another important factor that must be considered. In a distillation column, for instance, the time elapsed between changing the reflux rate and observing a change in a product composition could be measured in hours. With this response time, and in the absence of dynamic prediction capability, the controller will start taking action hours after a disturbance occurs, and it would take even longer for the correction to take effect. Linear predictions are commonly used to forecast trends of process variables but many processes, particularly multistage separations, are often highly nonlinear. Substantial improvement can be achieved with a nonlinear model. 

In an ideal binary distillation column the dynamics of each tray can be described by first-order systems. Are these capacities interacting or not What general types of responses would you expect for the overhead and bottoms compositions to a step change in the feed composition ... 

Show qualitatively that the response of the bottoms composition of a distillation column to a step change in the vapor boilup, V, can exhibit inverse behavior. Consult Refs. 1 and 16. 

Chapter 12. Luyben [Ref. 1, Section 11.5] has a good discussion on the inverse response of the bottoms composition of a distillation column to a change in the vapor boilup. Iinoya and Altpeter [Ref. 17] discuss the characteristics of systems that exhibit inverse response and give a table of the most common physical situations (transfer functions) that give rise to inverse response. 

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... 

Distillation column models are well known to be nonlinear. This implies that a +10% step perturbation in the feed composition could display different dynamics and nonsymmetrical responses to a -10% step perturbation. Six different input sequences were studied and in each case, the computational time for computing the process transient was recorded, for both the open- and closed-loop configurations. 

Is the MRT (most responsive temperature) point in the distillation column expected to be above or below the feed point when the liquid feed composition is 70% light key component ... 

Modify Program ex56. m to study the dynamic response of the distillation column of section 5.6 under different heat duties and reflux ratios. What conclusions can you draw from this study Now repeat this study when the feed composition of toluene is. 2 mole fraction and. 4 mole fraction. 

A comparative study of the energy requirements and control properties of three thermally coupled distillation schemes and two conventional distillation sequences for the separation of ternary mixtures is presented. The responses to set point changes under closed loop operation with proportional-integral (PI) controllers were obtained. Three composition control loops were used, and for each separation scheme, the parameters of the PI controllers were optimized using the integral of the absolute error criterion. The effects of feed composition and of the ease of separability index were considered. The results indicate that there exist cases in which integrated systems may exhibit better control properties than sequences based on conventional distillation columns. 

Shunta compares the results with and without sampled-data interaction compensators for controlling both ends of a 20-tray distillation column. Figures 21.7a and 21.7b show the closed-loop responses of composition on trays 2 and 18 for set-point changes and Figures 21.7c and 21.7d for a 10 percent change in feed composition. Tlie improvement in control with interaction compensators is sign cant. 

Prominent examples include the exponential dependence of reaction rate on temperature (considered in Chapter 2), the nonlinear behavior of pH with flow rate of acid or base, and the asymmetric responses of distillate and bottoms compositions in a distillation column to changes in feed flow. Classical process control theory has been developed for linear processes, and its use, therefore, is restricted to linear approximations of the actual nonlinear processes. A linear approximation of a nonlinear steady-state model is most accurate near the point of linearization. The same is true for dynamic process models. Large changes in operating conditions for a nonlinear process cannot be approximated satisfactorily by linear expressions. 

As discussed in the previous section, temperature control gives much faster responses compared to composition control. In this two-column configuration, temperature control is used in the reactive distUlation column followed by temperature or composition control for the product column (second column). Because we are dealing with binary separation in the second column, two-temperature control is considered first. Figure 12.67 gives the temperature control schemes. For the reactive distillation column, the most sensitive tray, tray 9 (Ti g), is chosen for temperature control. The temperature is maintained at 385 K by... 

The program starts up the column at total reflux (R very high). After steady state is reached on all plates, vary the reflux ratio interactively and attempt to carry out the distillation in minimum time, while attempting to maintain a distillate composition, so far as is possible, that xq > 0.9 and note the response of the distillate composition, xq. 

Controlling Quality of Two Products Where the two products have similar values, or where heating and cooling costs are comparable to product losses, the compositions of both products should be controlled. This introduces the possibility of strong interaction between the two composition loops, as they tend to have similar speeds of response. Interaction in most columns can be minimized by controlling distillate composition with reflux ratio and bottom composition with boil-up, or preferably boil-up/bottom flow ratio. These loops are insensitive to variations in feed rate, eliminating the need for feedforward control, and they also reject heat balance upsets quite effectively. 

This composite calibration curve for seawater demonstrates the applicability of the cold-trap pre-concentration technique to low concentration ranges of mercury. Approximately 0.2 ng of mercury can be determined with a 25x scale expansion. Since the response depends on the vaporization and elution of trapped mercury from the column, the calibration curves were similar for other aqueous media including acidified (nitric acid) distilled deionized water. Therefore, this cold-trap procedure appears to separate effectively reducible mercury species from interfering substances that might be associated with differing solution matrices. 

The vapor pressxire controller has a far greater sensitivity to composition changes than a temperature controller (68, 332, 362), gives fast response, provides an accurate measurement in binary systems, and is relatively inexpensive. This technique is popular in services where pressure compensation of the control temperature is needed and is difficult to achieve, such as low-pressure (particularly vacuum) distillation and close separations. A typical example is ethanol-water columns (361). The technique is also useful where a good sensitivity of control temperature to composition and good correlation between product composition and control temperature are difficult to meet simultaneously (Sec. 18.2). 

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