CXd = coefficient of fluid stream deflection at lower surface of distributor a0 = coefficient of fluid stream deflection a t bed upper boundary = coefficient of resistance for bed support 6,6 = thickness of distributor t = local mean voidage €0 = unperturbed voidage 6‘ = voidage perturbation 6d = local mean voidage in porous distributor K = ratio of support pressure drop to that across bed in ynperturbed state bC = critical wavelength A,-- = bulk viscosity of particle phase in unperturbed state bf = shear viscosity of fluidizing fluid PO” = shear viscosity of particle phase in unperturbed
state p = ratio of fluid density to solid density @ = density of fluidizing fluid p s = density of solid material Symbols with and without circumflex denote corresponding dimensional and dimensionless variables, respectively. L i t e r a t u r e Cited Anderson, T. 6.. Jackson, R., Ind. fng. Chem., Fundam.. 8, 528 (1967). Beavers, 0. S., Joseph, D. D.. J. FluMMech., 30, 197 (1967). Clift. R., Grace, J. R.. Weber, M. E., lnd. Eng. Chem., Fundam., 13, 45 (1974). Medlin, J., Wong, KW., Jackson, R., Ind. fng. Chem., Fundam., 13, 247 (1974). Saffman. P.G., Stud. Appl. Math., 50, 93 (1971).
Receiued for reoiew December 2,1974 Accepted May 19,1975
Steady-State Energy Conservation Aspects of Distillation Column Control System Design William L. Luyben Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 180 15
Energy consumption in distillation column operation is minimized by controlling compositions at both ends of the column. This dual composition control can, however, present dynamic stability and interaction problems. This study points out that the energy savings may often not be worth the increased cost and complexity of instrumentation. Simple, stable alternative control schemes, where reflux-to-feed rate or steam-to-feed rate ratios are maintained and overfractionation is deliberately used, sometimes consume very little additional energy. Steady-state calculations are employed to evaluate the incentive, or lack of incentive, for dual composition control.
Introduction Recent rapid increases in fuel costs have stimulated extensive redesign of many processes. These design changes normally involve increasing capital investment in order to reduce energy operating costs. Since distillation columns are often major energy consumers in plants, the process design, operating strategies, and control systems of distillation columns are being intensively studied. The old bruteforce, energy-inefficient control strategies are being reevaluated. For a simple two-product distillation column, energy consumption is minimized when both products are held at specified purities. Controlling only one product composition and using excess reflux or vapor boilup to guarantee that the other product is always a t or above its desired purity results in more energy consumption. Therefore, from a steady-state energy consumption standpoint, it is desirable simultaneously to control both product compositions in a distillation column. This is called “dual composition,control”. Figure 1 illustrates a typical control system. However, dual composition control can lead to dynamic control problems. Interaction between the two composition control loops can result in closed-loop stability difficulties. Instrumentation complexity and cost increase if interaction compensators (decouplers) are required. Engineering costs are also significantly increased if dynamic simulation stud-
ies, detailed control system design, and/or plant tests are required. I t is important to note also that dual composition control is not needed in order to minimize energy consumption when feed rate changes occur. Throughput disturbances can be simply handled by ratioing reflux or heat input to feed rate while controlling one product composition. Feed composition variations are the principal disturbances that require a dual composition control system in order to minimize energy consumption. Therefore the energy savings of dual composition control must come primarily from achieving the minimum vapor boil-up/feed ratio ( V / F )as feed composition disturbances are encountered. Steady-State Calculations T o quantitatively determine the economic incentive for dual composition control, a series of steady-state distillation calculations should be made to compute VlF ratios for various control systems over a suitable range of feed compositions. The three alternative control systems or operating strategies are constant reflux operation, constant-heatinput operation, or constant-product-composition operation. The last will yield the lowest VlF ratios, but the first two cases must be calculated to see if the incentive for dual composition control is significant enough to justify potential dynamic problems and increased instrumentation costs. Ind. Eng. Chem., Fundam., Vol. 14, No. 4. 1975 321
a = 2 I.
l i
CONSTANT
D
N, = 4 6 X,/X,
N, = 21
= 0.999/0.001
t
xo
it i
1.0
-
t
'V/F
AV
i
-
1.6
Figure 1. Typical dual composition control system.
a = 2
N,=
23
N,
It
-
R/
1.2
F
1.1
L
0. B 1.2
0.4
0.6
0.6
0. T
XF
Figure 3. Energy requirements for three different control systems.
1.4
-
Av
V / F'
1.0
3.
1.4
1.2
1.0
L
R/F\
I
0.3
0.8
0.4
0.0
0.7
XF
Figure 2. Energy requirements for three different control systems.
( 1 ) Constant-Product-Composition Case. Calculate the vapor boilup V and reflux R required to achieve the specified product purities X D and XB as feed composition XF varies over a typical operating range experienced in the plant. These calculations are performed for a fixed column, i.e., one with a fixed number of total trays NT and a con322
Ind. Eng. Chem., Fundam., Vol. 14, No. 4, 1975
stant feed plate location N F . The top curves in Figure 2 give the V I F and RIF ratios required to maintain X D and X B at 0.95 and 0.05, respectively, for a 23-tray column fed on the 11th tray in a system having a constant relative volatility of 2. The maximum V l F ratio (1.505) occurs in this case at the top of the X F range studied. (2) Constant Vapor Boilup Case. Fix the vapor boilup at the maximum value calculated for any of the cases in (1) above, and hold one product composition constant (either XD or X B ) by manipulating reflux. Since excess vapor boilup is being used, the composition of the uncontrolled product will always be better than specification purity. The middle curves in Figure 2 show how the RIF ratio changes for this fixed V l F operation. At a feed composition of 0.50 the V I F ratio is 0.094 higher using a fixed VIF ratio than using dual composition control. This represents a 6.7% increase in energy consumption at this feed composition. Less energy will be wasted a t higher feed compositions, and more at lower feed compositions. (3) Constant Reflux Case. Fix the reflux rate at the maximum value calculated for any of the cases in (1)above, and hold one product composition constant by manipulating vapor boil-up. Since excess reflux is used, the uncontrolled product purity will always exceed specification. The bottom curves in Figure 2 show how the VlF ratio changes for this fixed RIF case. At X F = 0.50 the VlF ratio is only 0.0074 higher (0.5%) than the minimum dual-composition case. Thus for this particular column, a constant reflux-tofeed control system will be very nearly as energy-efficient as dual composition control (if X F = 0.50 is the average feed composition that the column operates with).
a = 1.2 CONSTANT
I.
1.4
1
NT981 Xo / X ,
a =2
N, 8 4 0
0.95/0.05
V/ F
2.
CONSTANT
t
I\
: ’\?
\
V
1.4,.
