Ind. Eng. Chem. Fundam.
439
1985,2 4 , 439-443
Dynamic Energy Conservation Aspects of Distillation Control Galen T. Stanley and Thomas J. McAvoy' Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742
Distillation accounts for a large percentage of the energy used in chemical and petroleum plants. The potential for energy savings is therefore great. Dual composition control has been shown to minimize energy requirements for a distillation tower. Steady-state results indicate savings of 1-5 %; however, industry has reported considerably larger energy savings of IO-30%. By using a dynamic simulation of a distillation tower in order to obtain a transient response from a disturbance and by examining how distillation towers are operated in industry, we can explain this discrepancy.
Introduction Distillation is the main separation process in the chemical industry. Its uses range from the separation of heavy crudes to the separation of liquefied air. It is an energy intensive process by definition. Energy must be supplied to the reboiler and removed in the condenser. Because of this large energy demand, distillation accounts for 3% of the total U.S. energy consumption (DOE, 1980). The energy savings potential for even a small increase in efficiency is therefore great. Only one of the compositions in many distillation towers is controlled. Single composition control is used because of the additional cost of controlling both compositions. The uncontrolled composition is kept above its product specification by setting one of the manipulative variables to a constant value high enough that the specification is not violated for any expected disturbances. In this paper the variable that is set is called the constant manipulative variable. Controlling both the distillate and the bottoms composition, i.e. dual composition control, results in minimum energy use for a distillation tower (Luyben, 1975). But the amount of energy that can be saved is in question. Steady-state calculations (Luyben, 1975) show energy savings of 1-5%, but reports from industry indicate considerably larger savings of 10-3070. Energy savings of 1-570 might not be enough to offset the added expense and difficulty of using dual composition control. It is therefore important to get a better understanding of the potential energy savings produced by dual composition control. The energy savings indicated by steady-state analysis are first calculated for the four towers considered in this study. The flow rates in a tower are calculated for both dual and single composition control for feed compositions that cover the range of expected upsets. The potential for energy savings resulting from the use of dual-ended control is calculated from the difference in energy input to the reboiler. Since the vapor rate from the reboiler is approximately equal to the energy input to the reboiler divided by the latent heat of vaporization, it is assumed that comparing the vapor rates will give an accurate indication of the energy savings. The problem with using the steady-state analysis is that towers are often disturbed from steady state by load changes affecting the tower. The transient peak resulting from a disturbance makes it necessary to overpurify the products in order that the product specifications are not violated even during the transient resulting from a disturbance (Shinskey, 1977). The vapor rates that are
Table I. Tower Data compotower nents approx 1 benzene2.4 toluene 2 methanol1.65 ethanol 3 isobutane1.4 n-butane 4 methanol4.0 water
01
product split 0.98-0.02
no. of trays
reflux ratio
17
1.3Rmi,
0.99-0.01
27
1.5R,in
0.99-0.01
40
1.4Rmin
0.995-0.005
25
1.ZR,,
necessary to keep the product compositions above their specifications during the transients are used to indicate the potential energy savings. A dynamic computer model of a distillation tower is solved to calculate these flow rates. It is shown that in some cases a steady-state analysis leads to erroneous conclusions about how much energy can be saved by using dual composition control. Review of Luyben's Steady-State Analysis The four different towers that are used in this study cover the range from moderate- to high-purity products. A range of tower product compositions is considered since it has been shown that different purity towers behave differently with respect to control (McAvoy and Weischedel, 1981). Important features of the towers are given in Table I. All towers are designed for a saturated liquid with XF = 0.5. Additional details about the towers are given by Stanley (1985). Towers 1 and 2 have been previously studied by Weischedel and McAvoy (1980) and labeled B and C by these authors. To determine the potential energy savings associated with dual composition control, a series of calculations are made to determine the steady-state tower flow rates over the range of expected feed composition upsets. The approach taken is the same as discussed by Luyben (1975). Three single composition control schemes are compared to dual composition control. These schemes are constant reflux L, constant vapor rate V, and constant reflux ratio LID. Feed composition and flow upsets are major disturbances affecting a tower. It is not, however, necessary to use dual composition control to minimize energy requirements for flow upsets (Luyben, 1975). It is possible to compensate for feed flow disturbances by manipulating ratios of the manipulative variables to the feed, i.e. V / F . Using such ratios results in a simple feed forward scheme that can correct for feed flow upsets. Therefore, only xF disturbances are considered. Following Luyben (1975), the vapor rate and the reflux rate required for both product compositions to meet their 0 1985
American Chemical Society
440
Ind. Eng. Chern. Fundarn., Vol. 24, No. 4, 1985 Table 11. Summary of Steady-State Percent Energy Savings Using Dual Composition Control
i
o Dual Control
b Fired R e f l u
tower
XD
1
0.98
0.02
2
0.99
0.01
XR
constant variable"
V L* LID V* L LID
3
0.99
0.01
4
0.995
0.005
V* L LID
V L* LID
energy savings, 70 xr = 0.6
xp = 0.4 xF = 0.5 7.4 0.0 0.0
2.7 1.7 18
0.0 4.7 38
1.9 0.0 0.0
0.3 1.7 22
0.0 4.5 45
1.2 0.0 0.0
0.0 0.43 26
0.3 2.6 55
17 0.0 0.0
8.0 2.2 32
0.0 3.5 67
"The best scheme is shown with an asterisk.
XF
XF
Figure 1. Comparison of steady-state vapor and reflux rates for dual vs. single composition control.
specifications are calculated for various feed compositions that cover the range of expected upsets. The steady-state flow rates for a typical tower under dual composition control are shown in Figure la. For single composition control the constant manipulative variable is fixed at its highest value calculated for dual composition control. Setting the constant manipulative variable a t this value ensures that the ancontrolled composition will not violate its specification for all expected xF upsets, provided they are slow. The flow rates for the three single composition control schemes are compared to the flow rates of dual composition control in Figure lb-d. The single composition control scheme with the smallest increase in the vapor rate a t the design feed concentration is then used for control. For the case shown in Figure 1the vapor would be held constant and the reflux would be used for control. The energy savings calculated from steady-state information are summarized in Table I1 for the four towers considered. The energy savings from use of dual composition control are less than 5% for these towers. Luyben (1975) also found that energy savings were very small in most cases. For many towers savings of this magnitude would not justify the additional expense and difficulty of using dual composition control. In essence, Luyben's (1975) method applies to the extreme case of very slow, i.e. steady state, disturbance forcing. Many control systems perform very well when subjected to such forcing. The problem with using only steady-state information is that it does not take into account the transient resulting from a disturbance. The transient makes it necessary to set the reflux and vapor rate even higher than is needed to just meet the product specification in the steady state. It is therefore necessary to include the dynamic responses of distillation towers to get a better understanding of the potential energy savings. A dynamic computer model of a distillation tower was developed to study the effect of including the transient response in the analysis of energy savings.
Digital Simulation The mathematical model used in the dynamic simulation is similar to the model used by McAvoy and Weischedel(l981). The following assumptions were made when developing the model: the vapor-liquid equilibrium is ideal, the energy equilibrium is fast, each tray is ideal, the column is adiabatic, the vapor holdup is negligible, and there is perfect mixing on each tray and in the reboiler. Using these assumptions, we can write the dynamic mass and energy balances for each tray in the tower as follows: overall mass balance dHn/dt = Ln+l + Vn-l - L, - V , (1) component mass balance dxnHn/dt = Xn+lLn+l+ Yn-1Vn-1 - XnLn - ~ energy balance dhn1H,/dt = h,+llL,+l
n v n(2)
+ hn-l"Vn-l - hnlL, - h,,'V,
(3)
The physical properties such as vapor pressure, enthalpies, etc., are obtained from correlations given in the literature (Perry, 1976; Smith and Van Ness, 1975), and these are given by Stanley (1985). One important change was made in the model used by Weischedel and McAvoy (1980). They assumed the energy balance was so fast that the right-hand side of eq 3 could be set to zero. This assumption resulted in unrealistic flow rates in some of the towers. For towers with a small number of trays such as towers 1 and 4,this assumption resulted in negligible error in the calculated compositions. But for tower 3 the flow rates would oscillate with increasing amplitude. The problem was traced to the assumption that dh,'Hn/dt was equal to zero. This assumption resulted in a small error in the calculated vapor rate from each tray in the tower. The error in the vapor rate would add throughout the tower so that the vapor rate at the top of the tower would then have an error proportional to the number of trays in the tower. This error in the vapor rates results in an error in reflux flow and eventually causes the mass on the trays to change, producing additional errors in the vapor flows. The error generation process involves a feedback loop which causes oscillations in the flow rates. For towers with a small number of trays the oscillations quickly died out without any error in the calculated compositions. However, for towers with a large number of trays the oscillations increased in amplitude giving unrealistic flow rates. This error was corrected by including the accumulation of energy on each tray as suggested by Luyben (1982). The accumulation comes from two sources: the accumulation
Ind. Eng. Chem. Fundam., Vol. 24, No. 4, 1985
/.99 '0°
x,
L
1.00
.96
x,
-
.99
,985
+
-
.I
- +
x,
.I
x,
.98
.02
.04
,015
.03
xo
xs .02 .01
r
.9s5y--
.98
.97
441
t
,000I 0
.o/
t
,005
1
10
1
20
I
I
I
30
40
50
TIME (MINI
Figure 2. Tower 1. Single composition control [(r~- V)]. K , = -19.0,TR = 9.01.
of mass on the tray and the change in the sensible heat on the tray. The right-hand side of eq 3 therefore becomes dh,lH,/dt
= H,dh,l/dt
+ h,'dH,,/dt
(4) The dh,'/dt term is approximated with a backward difference formula, and the dH;/dt term is eliminated by using eq 1. These changes in the energy equation result in a more accurate model without having to include dynamic energy equations which would make the resulting model very stiff. It is also assumed that the level loops in the reboiler and reflux accumulator are perfect. The dynamics of the reboiler are assumed to be so fast that varying steam flow is the same as manipulating the vapor rate directly. Dynamic Analysis of Energy Savings Potential To illustrate the problem with using only steady-state information, a simulation of tower 3, with xF step disturbances, is shown in Figure 2 using the control scheme resulting from Luyben's (1975) steady-state analysis. In this case the reflux is set so that XD = 0.983 when XF = 0.5. As can be seen, one of the product compositions,either XD or xB, violates its specification during much of the transient resulting from a disturbance. This transient violation is why products are overpurified in industry so that product specifications are always met. Another requirement for control is therefore used when one compares the potential energy savings of dual composition control. The requirement for acceptable control will be that the product specifications will not be violated even during the transient resulting from a step disturbance. It can be argued that the proposed dynamic requirement is just as extreme as Luyben's (1975) steady-state criterion. If sufficient tankage for blending is available and blending is acceptable, then some transient violation of product specifications can be tolerated. For actual towers the energy savings which can be achieved should lie between those calculated via the steady-state approach and those calculated via the approach proposed here. The proposed approach should
,000 0
I
1
1
1
16
32
48
64
1 80
TIME (MINI
Figure 3. Tower 3. Single composition control [(xD - L ) ] . K , = 18.0,2 ' ~ = 33.0.
provide an upper bound on energy savings. A trial and error calculation procedure is required to find the set point of the controlled composition and value for the constant manipulative variable when using the dynamically based criterion. An estimate is first made for these two parameters. A step change is then made in each manipulative variable to get the open-loop dynamic response of the tower. The resulting product composition curves are fitted to a fiisborder model with dead time. The time constants and dead times calculated are used to get approximate controller gains and reset times. The tower is then simulated with a step change in xF of iO.1 by using the approximate controller parameters. If the resulting control is too oscillatory or sluggish, the controllers are retuned to improve the performance. If the transient from the disturbance causes either product composition to violate its specification, then the product purities are adjusted until the peak for the transient just satisfies the product specification. Both positive and negative step changes in feed composition are necessary to assure that ceither distillate nor bottoms concentration violates the product specifications. The results of trial and error calculations for tower 3 are shown in Figures 3 and 4. For both dual and signal composition control the peak for the transient just meets the product specification and the controllers bring the compositions back to the set point with only slight oscillations. For single composition control, the XD set point had to be increased to 0.995 and the set point for xB was 0.0043. For dual control the xD set point only had to be increased to 0.994 and the XB set point was only 0.0062. The product specifications on the tower are xD = 0.99 and XB
= 0.01.
Choosing the best dual composition control scheme proved to be an involved task because of the large number of possible schemes. The best scheme depends on many factors such as the purity of the products and relative volatility. Several different dual composition control schemes were studied, and these are given in Table 111.
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Ind. Eng. Chem. Fundam., Vol. 24, No. 4, 1985
Table IV. Summary of Dynamic Energy Savings ____. best scheme tower dual single 70increase in energy 1 XD - L XD - V 0.4 XD -
I.‘ L
XB-
V
XB -
2
t1
.985
98
XD X B --
4
XI)
XB -
1
015
0
.XD
-L
17.5
XB-
V
a
B/V
I tower I
a VlF ,000
5.6
a Single-ended control could not keep the product compositions above the specifications for a 0.1 mole fraction change in xF.
r
o2
L B/ v -L
:i
V
XD-
16
48 T I M E fMfN)
32
Figure 4. Tower 3. Dual composition control. = 24.0. XB - R / V K , = 5.5> T R = 25.4.
64 XD:
/
10
/
D
80
K , = 60.0, T R
Table 111. Dual Composition Control Schemes scheme pairings name ref 1 xn-L,xB-\’ energy balance Wood (1973) 2 XD - D, XB - V material balance Shinskey (1969) Rijnsdorp (1965) 3 x , ) - L I D , xB - V reflux ratio 4 xI, - DjV, x B - V reflux ratio Ryskamp (1980) x,, - L , X B - B / V 5 6 X D - D , XB - B / V 7 \I) - D/V, xBHIV
It was found that the best control scheme also depended on the type of disturbance affecting the tower. For example, the energy balance scheme was found to work well for X F upsets but not for feed flow upsets. Cheung and Marlin (1982) have reported that the type of disturbance is important when choosing between energy and material balance schemes. The reasons why a control scheme will respond differently to different disturbances and how the best dual composition control scheme is determined are discussed in another paper (Stanley et al., 1985). Only the results for the best dual composition control scheme for x F upsets are presented here. The results of the dynamic simulations are summarized in Table IV. The energy savings predicted from steadystate calculations generally do not agree with the savings found when dynamics are included in the analysis. The amount of energy that can be saved depends on the tower. For tower 1, which is a moderate-purity tower, using dual composition control results in small energy savings of only 0.4% and therefore dual composition control would not be used. But as the number of stages and reflux ratio increases in a tower, the amount of energy savings also increases. The largest energy savings found is 17.5% for tower 3. Towers with high-purity requirements and low relative volatilities appear to be good candidates for large energy savings by using dual composition control. For towers with large throughputs even savings of a few percent might be enough to offset the additional costs of dual control
,05
2
Of
I
I
02
03
XB
Figure 5. Gain curve for
XB -
V.
For tower 4 it was not possible for a single composition controller to keep the product compositions above their specification for a f O . l change in xF. This lack of control could result in operators increasing the reflux to the maximum possible value to try to meet the specifications. The increased energy use would then be quite large, and dual composition control should therefore be used. If large upsets are infrequent and it is possible for the compositions to violate the product requirements for short periods and products are blended, it might be possible to use single composition control for this tower. If the disturbance affecting the tower is relaxed so that the controller is only required to keep the product composition above specifications for f0.05 changes in XF instead of f0.1 mole fraction, then the increased energy use for single-ended control is only 2% for tower 4. The small energy savings found for tower 4 when the requirements are relaxed is not true however for all towers. For example, tower 3 has only a small reduction in the energy savings, from 17.5to l6.6%, when disturbances in xF are f0.05. Part of the increased energy required by single-ended control can be explained by looking at the nonlinear gains in a distillation tower. The gain for the manipulative variable is defined as the change in the product composition divided by the change in the manipulative variable, e.g. d x D / d L . For distillation towers the gain of the manipulative variables decreases as the product purities increase as shown in Figure 5 . The controller is tuned for operation around a set point given by the product specifications. Since the gain for the controller is constant, the total loop gain changes with the product purity. When the controlled product is upset such that the product purity decreases, the gain of the loop increases. However, when
443
Ind. Eng. Chem. Fundam. 1985, 2 4 , 443-449
the upset is in the other direction, the gain of the loop will decrease and the control response will be sluggish. This sluggish response can be seen in Figure 3 for tower 3 when xD is controlled by reflux flow. As shown, the controlled response for a positive change in XF is much more sluggish than for a negative change. When the controlled composition response is sluggish, this causes the uncontrolled composition to have a large peak in its transient response. This peak makes it necessary to have the steady-state concentration much purer than the product specification. When dual composition control is used, the nonlinear gains in a tower do not affect the control system as much. When either product composition is upset in the direction of decreasing purity, the gain of that loop increases, helping the controller to prevent the composition from violating the specification. Comparing the set point concentrations of single and dual control in Figures 3 and 4 shows how much more the uncontrolled product, in this case xB, has to be overpurified. For single composition control the XB set point is 0.0045, and for dual control it is 0.0063 compared to the product specification of 0.01. Gain scheduling could be used for both dual and single composition control to help offset the problem of nonlinear gains and thereby reduce energy use. A more detailed explanation of nonlinear gains and gain scheduling in distillation towers is given by Tsogas and McAvoy (1985). Conclusions
Dynamic simulations of distillation towers have shown that for some towers the actual energy savings achieved with dual composition control can be much larger than those predicted by a steady-state analysis. The amount of energy savings varies depending on the tower. Predicting energy savings is difficult without actually simulating the tower dynamically, but some general guidelines can be stated. The energy savings from using dual composition control can be expected to be favorable for highpurity towers and for components with a low relative volatility. For towers with large throughputs dual composition control may be beneficial. Acknowledgment
time for this project was partially funded by the Computer Science Center for the University of Maryland. Nomenclature
B = bottoms flow D = distillate flow F = feed flow K = controller gain h> = molal enthalpy of liquid on tray n h," = molal enthalpy of vapor on tray n H, = liquid holdup on tray n L = reflux flow L, = liquid flow from tray n t = time TR = reset time V = vapor boilup V,, = vapor flow from tray n X B = bottoms composition (mole fraction) xD = distillate composition (mole fraction) xF = feed composition (mole fraction) x, = liquid composition on tray n (mole fraction) y , = vapor composition in equilibrium with x, (mole fraction) L i t e r a t u r e Cited "Energy Conservation in Distillation"; Department of Energy: Springfield, VA, 1980; DOElCS14431-72. Cheung, A.; Marlin, T. E., paper presented at Distillation Control Short Course, Lehigh University, Bethelehem, PA, May 1982. Luyben, W. Ind. Eng. Chem. Fundam. 1975, 1 4 , 321. Luyben, W., paper presented at Distillation Control Short Course, Lehigh University, Bethlehem, PA, May 1982. McAvoy, T. J.; Weischedel, K.,paper presented at the Proceedings of the 8th International Federation of Automatic Control Congress, Kyoto, Japan, 1981. Perry, R. H. "Chemical Engineers Handbook", 5th ed.; McGraw-Hill: New York, 1976. Rljnsdorp, J. Automatika 1965, 1 , 29. Ryskamp, C. Hydrocarbon Process. 1980, 59, 51. Shlnskey, F. G. Oil Gas J . 1969, 67, 76. Shinskey, F. G. "Distillation Control for Productivity and Energy Conservation"; McGraw-Hill: New York, 1977; Chapters 5-6. Smith, J.; Van Ness, H. "Introduction to Chemical Engineering Thermodynamics", 3rd ed.;McGraw-Hill: New York, 1975. Stanley, G. T. M.S. Thesis, University of Maryland, College Park, MD, 1985. Stanley, G. T.; McAvoy, T. J.; Marino-Gallarraga, M. A. Ind. Eng. Chem. Process Des. D e v . . In press. Tsogas, A.; McAvoy, T., paper presented at the Proceedings of the 2nd World Congress of Chemical Engineering, Montreal, Canada, Oct 1981; Chem . Eng . Commun ., in press. Weischedel, K.; McAvoy, T. J. Ind. Eng. Chem. Fundam. 1980, 19, 379. Wood, R. K.; Berry, M. W. Chem. Eng. Sci. 1973, 28, 1707.
This work was supported by the National Science Foundation under Grant CPE 8025301. The computer
Received for review April 5, 1984 Accepted February 28, 1985
Kinetic Study of Sulfate Reduction with Kraft Black Liquor Char John H. Cameron' and Thomas M. Grace The Institute of Paper Chemistiy, Appleton, Wisconsin 549 72
One of the principal reactions occurring in the Kraft recovery furnace is the reduction of sulfate with carbon. This paper presents the results of a kinetic study of sulfate reduction with Kraft black liquor char in a sodium carbonate melt. The reduction was found to be first order in the carbon content of the char, to be zero order in sulfate until only low levels of sulfate remain in the melt, and to have an activation energy of 122 kJ/mol. The following mechanism is proposed to account for these experimental results: Sulfate adsorbs on an active carbon site; it is reduced, forming either sulfide or an unstable reduced sulfur intermediate and carbon dioxide, and the reduced sulfur species then desorbs from the carbon surface.
Introduction
One of the principal steps in the Kraft pulping process is the recovery of the pulping chemicals. In the recovery furnace, the organic constituents of the spent pulping li0196-43 1318511024-0443$01 SO10
quor (black liquor) are burned and the sulfur compounds present are converted to sodium sulfide. One of the key reactions occurring in the furnace is the reduction of Na2S04to Na,S. This occurs in the bed of 0 1985 American Chemical Society
