1836
Ind. Eng. Chem. Res. 1998, 37, 1836-1840
PROCESS DESIGN AND CONTROL On Control of Distillation Columns with Input Multiplicity Alex Zheng* Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-3110
Vince Grassi and George Meski Air Products & Chemicals, Inc., 7201 Hamilton Bloulevard, Allentown, Pennsylvania 18195-1501
In this paper, we report an input multiplicity behavior observed in the simulation of a practical extractive distillation column (tray) involving three components. Some tray temperatures, including the one selected for control, are nonmonotonic with respect to input variables such as reboiler duty and entrainer flow. Thus, for a fixed tray temperature, several input values are possible. Its implication for temperature control is discussed. It should be noted that the column temperature profile is monotonic. 1. Introduction Distillation columns exhibit many interesting behaviors. For example, it has been shown by simulations, theories, and experiments that multiple steady states (i.e., two or more steady states for a fixed set of operating parameters) can exist for columns with binary or ternary mixtures (e.g., Magnussen et al. (1979), Prokipakis et al. (1981), Rovaglio and Doherty (1990), Bekiaris et al. (1993), Kienle et al. (1995), Koggersbol et al. (1996), Guettinger et al. (1997), etc.). Their implications for design and control of distillation columns have been discussed by Morari (1996). The steady-state multiplicity described in all these papers is the output multiplicity (i.e., the existence of several steady-state outputs for a fixed set of inputs). Another type of multiplicity, input multiplicity (i.e., the existence of several steady-state inputs for a fixed set of outputs), potentially more important for process control, does not seem to have been reported in the literature for distillation columns. It should be pointed out that the theory for the input multiplicity as well as its applications to reactors have been well studied (e.g., Koppel (1982, 1985), Balakotaiah and Luss (1985), Dash and Koppel (1989), etc.). Jacobsen (1994) discussed the implications of input multiplicity for the system dynamics. Koppel (1982) gave an excellent discussion on why the input multiplicity imposes more practical control problems than the output multiplicity. In this paper, we describe such a behavior, observed in simulation studies, for an extractive distillation column with three components (Grassi (1992) discusses various unusual behaviors of extractive distillation columns) and discuss its practical implications for temperature control. Temperature control is important as it is frequently used to indirectly control product compositions for a distillation column. It is popular in * To whom all correspondence should be addressed. Phone: (413)545-2916. Fax: (413)545-1647. E-mail: zzheng@ ecs.umass.edu.
industry since it is much cheaper to install and to maintain than on-line composition analyzers. The main disadvantage is that, for many reasons (e.g., feed composition disturbance and column pressure variations), perfect temperature control does not guarantee perfect composition control. The following behavior has been observed on a column with two feeds and three components: At the steady state, tray temperatures in some section of the column are nonmonotonic with respect to reboiler duty and entrainer flow which are typically manipulated to control tray temperatures. For example, when reboiler duty is increased with all other column parameters constant, some tray temperatures increase initially but decrease upon further increase of reboiler duty. For all the cases studied, the column temperature profile is monotonic. What is practically important is that this behavior occurs within the section of the column where a tray temperature may be selected as the controlled variable. To the best of our knowledge, the behavior has not been reported for a double feed column in the literature. Patwardhan and Edgar (1993) observed a similar behavior between distillate (and bottom) product compositions and reboiler duty for a packed column (it is not clear from reading the paper whether this behavior was observed on the simplified model or the rigorous model). However, for the column discussed in this paper, the relationships between bottom (and distillate) product compositions and reboiler duty are monotonic. 2. Column Description and Controlled Variable Selection In this section, we briefly describe the column and its operating conditions. For confidentiality reasons, the column configurations, as well as component properties, have been altered. However, the main qualitative features have been preserved. In addition, we briefly go through the process of how a tray temperature is selected for control (Downs (1992)).
S0888-5885(97)00673-8 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/16/1998
Ind. Eng. Chem. Res., Vol. 37, No. 5, 1998 1837
Figure 1. Column configuration and nominal operating conditions. Table 1. Antoine Coefficients for Components A, B, and C and Binary Parameters for the Wilson Model Figure 2. Ideal temperature profile at the nominal operating conditions.
(a) Antoine Coefficientsa c1 c2 c3 c4 c5
A
B
C
71.74 -5302 -7.332 6.24 × 10-17 6
134.7 -6056 -19.42 2.862 × 10-2 1
73.65 -7258 -7.304 4.165 × 10-6 2
(b) Binary Parameters for the Wilson Modelb bij
A
B
C
A B C
0 -40 -1100
-10 0 -1800
400 -550 0
a ln(p) ) c + c /T + c ln(T) + c Tc5 where p is the pressure in 1 2 3 4 pascal and T is the temperature in Kelvin. b ln γi ) 1 - ln ∑jAijxj - ∑j[Ajixj/∑kAjkxk] and Aij ) e-bij/RT.
2.1. Column Description. Consider the column shown in Figure 1. The column has 70 trays (trays 2-71), a total condenser (tray 1), and a partial reboiler (tray 72). The column operates with a pressure drop of 0.1 psia per tray, and the condenser pressure is 170 psia. Murphee tray efficiency is assumed to be 60% for trays 2-71 and 100% for trays 1 and 72. The feed (at tray 35) contains three components which are denoted by A, B, and C. The purpose of this column is to separate A from B and C. Since boiling points of components A and B are close, more heavy component C is added (at tray 10) as an entrainer to improve the separation of A and B. Notice that A and B do not form an azeotrope under the operating conditions shown in Figure 1. This column has two specifications:
