The evaporator shown in Fig. 13.5 is used to concentrate a dilute solution of a single, nonvolatile solute in a volatile solvent by evaporating solvent using heat supplied by a steam coil. Three process variables can be manipulated: steam pressure, Ps, product flow rate, B, and vapor flow rate of

Question

The evaporator shown in Figure below is used to concentrate a dilute solution of a single, nonvolatile solute in a volatile solvent by evaporating solvent using heat supplied by a steam coil. Three process variables can be manipulated: steam pressure,[latex] P_{s}[/latex], product flow rate, B, and vapor flow rate of solvent, D. The chief DVs are feed composition, [latex]x_{F}[/latex], and feed flow rate, F. The compositions are expressed as mole fractions of solute, and the flow rates are in molar units.
Propose multiloop control strategies for two situations:
(a) The product composition [latex]x_{B}[/latex] can be measured on-line
(b) [latex]x_{B}[/latex] cannot be measured on-line

Accepted Answer

Case (a): Product Composition [latex]x_{B}[/latex] Is Measured On-Line
First, we select the CVs. Because the chief objective for an evaporator is to produce a product stream with a specified composition, mole fraction [latex]x_{B}[/latex] is the primary CV (Guideline 3). Liquid level h must be controlled because of operating constraints and safety considerations (Guideline 2). If the level is too high, liquid could be entrained in the solvent stream; if the level is too low, the tubes of the steam chest would be exposed to vapor, rather than liquid, a potentially dangerous situation. In this latter situation, the heat transfer rate from the steam to the evaporator liquid would be significantly lower, and thus overheating and damage to the steam chest could result. Pressure P should also be controlled, because it has a major influence on the evaporator operation (Guideline 2). Large pressure variations affect the temperature T and could shift the boiling regime from film boiling to nucleate boiling, or vice versa. This type of regime shift could produce a major process upset. For these reasons, three CVs are selected: [latex]x_{B}[/latex], h, and P.
Next we select the MVs. Because the feed conditions cannot be adjusted, the obvious MVs are B, D, and [latex]P_{s}[/latex]. Product flow rate B has a significant effect on h, but relatively small effects on P and [latex]x_{B}[/latex]. Therefore, it is reasonable to control h by manipulating B (Guideline 6) unless B is only a small fraction of F (for example, less than 10%). In this latter case, it would be desirable to have F become an MV. Vapor flow rate D has a direct and rapid effect on P but has less direct effects on h and [latex]x_{B}[/latex]. Thus, P should be paired with D (Guideline 6). This leaves the [latex]P_{s}-x_{B}[/latex] pairing for the third control loop. This pairing is physically reasonable, because the most direct way of regulating [latex]x_{B}[/latex] is by adjusting the evaporation of solvent via the steam pressure (Guideline 8).
Finally, we consider which process variables to measure. Clearly, the three CVs should be measured. It is also desirable to measure the three MVs because this information is useful for controller tuning and troubleshooting. If large and frequent feed disturbances occur, measurements of disturbance variables F and [latex]x_{F}[/latex] could be used in a feedforward control strategy that would complement the feedback control scheme. It is not necessary to measure [latex]T_{F}[/latex], because sensible heat changes in the feed stream are typically small compared to the heat fluxes in the evaporator.
A schematic diagram of the controlled evaporator for Case (a) is shown in first Figure on the right.

Case (b): Product Composition Cannot Be Measured On-Line
The CVs are the same as in Case (a), but, because the third controlled variable [latex]x_{B}[/latex] cannot be measured, standard feedback control is not possible. A simple feedforward control strategy can be developed based on a steady-state component balance for the solute,
[latex]0=\bar{F}\bar{x}_{F}-\bar{B}\bar{x}_{B}[/latex]
where the bar denotes the nominal steady-state value. Rearranging gives
[latex]\bar{B}=\bar{F}\frac{\bar{x}_{F}}{\bar{x}_{B}} [/latex] (1)
Equation (1) provides the basis for the feedforward control law. Replacing [latex]\bar{B} \space and \space \bar{F}[/latex] by the actual flow rates, B(t) and F(t), and replacing [latex]\bar{x}_{B}[/latex] by the set-point value, [latex]x_{Bsp}[/latex], gives
[latex]B(t)=F(t)\frac{\bar{x}_{F}}{x_{Bsp}} [/latex] (2)
Thus B is adjusted based on the measured value of F, the set point [latex]x_{Bsp}[/latex], and the nominal value of the feed composition, [latex]\bar{x}_{F}[/latex].
The MVs are the same as for Case (a): D, B, and [latex]P_{s}[/latex]. Bottom flow rate B has already been used in the feedforward control strategy of Equation (2). Clearly, the P-D pairing is still desirable for the reasons given for Case (a). This leaves h to be controlled by adjusting the rate of evaporation via [latex]P_{s}[/latex]. A schematic diagram of the controlled evaporator is shown in second Figure on the right.
This control strategy has two disadvantages. First, it is based on the assumption that the unmeasured feed composition is constant at a known steady-state value.
Second, because the feedforward control technique was based on a steady-state analysis, it may not perform well during transient conditions. Nevertheless, this scheme provides a simple, indirect method for controlling a product composition when it cannot be measured.

Question 13.4: The evaporator shown in Fig. 13.5 is used to concentrate a d...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions