1810
Ind. Eng. Chem. Res. 1995,34, 1810-1822
Experimental Verification of the Equilibrium Stage Model for the Dynamics of the Multicomponent Distillation Considering the Effects of Energy Loss Ch. Kruse,* G. Fieg3 G. Wozny,' L. JerominJ and W. Johannisbauer' COGNIS GmbH, Postfach 130164, 40551 Diisseldorf, Germany, Henkel KGaA, 40191 Diisseldorf, Germany, and Institut fur Prozess- und Anlagentechnik, TU Berlin, 10623 Berlin, Germany
This paper on the dynamics of multicomponent distillation is based on experimental investigations in a laboratory-scale distillation column. The concentration and temperature profiles are obtained a t the steady-state operating point, and the transition behavior is observed by systematically changing the relevant operating variables. The general scope of these experiments is to evaluate and study the concentration and temperature profiles measured along the column height. The developed methodology for sampling at vacuum is explained. The experimental results are compared with theoretical calculations obtained by means of steady-state and dynamic simulation. The influence and the importance of heat losses on the steady-state and dynamic behavior at high temperature levels are investigated and discussed. The aim of these studies is to prove the steady-state and dynamic simulation tool on the basis of the equilibrium stage model. It is found that the simulation results agree closely with those obtained experimentally. This refers to the concentration and temperature profiles as well as to the calculated and the experimentally used reboiler heat input. In order to achieve this good agreement, heat losses along the column height have to be taken into account in the simulation. Consequently, the consideration of heat losses is of great importance for the determination of HETP values in packed columns.
Introduction The design and operation of chemical plants can be simplified considerably and accelerated by using computer-based design procedures. Highly developed flow sheet programs are now available for the chemical industry in the field of plant design. With their help, plant design engineers can estimate an optimal steadystate process design. However, the effects of internal couplings on the dynamic behavior of a plant cannot be studied (Gilles et al., 1986). For this reason, the dynamic process simulation gains increasing importance in the chemical industry and plant design. Aside from steady-state simulation tools, suitable software tools for dynamic simulation have been increasingly developed and have been extensively reviewed in recent years (Wozny and Jeromin, 1991). Especially in the context of process control and process automation, dynamic simulation plays an important role. An analysis of the numerous publications shows that the many studies of practical examples stretch from subjects ranging from the analysis of the mathematical models applied (Gani et al., 1986; Wozny et al., 1987; Patwardhan and Edgar, 1993) to the evaluation of the numerical methods of the solution employed and to the studies of hydrodynamics (Wang and Cameron, 1993; Gunn and Al-Saffar, 1993). Only a few papers describe experimental investigations that are aimed at verifying the numerical results obtained (Fieg et al., 1992; Fieg et al., 1993; Berber and Karadurmus, 1989). Therefore, often only the product concentrations or temperature profiles have been used
* To whom correspondence should be addressed at COGNIS GmbH. FAX: 0049-211-798-8955. Henkel KGaA. 8 Institut fur Prozess- und Anlagentechnik.
to prove the developed simulation model. Due to the nonlinearity between temperature and concentration for multicomponent mixtures, the meaningfulness of the steady-state temperatures and the dynamic behavior of the temperature profiles, caused by disturbances or feed changeover operations, are always restricted. However, the question arises: Why is it necessary to verify the model along the column height? Firstly, the columns are normally overdesigned, i.e. equipped with too much packing. If an accurate model is used for design, the investment costs can be reduced. Secondly, complex and coupled columns may be constructed with multiple feeds or side streams. Selecting the appropriate tray for these additional streams requires from a process or production engineer a careful consideration of many factors. It is, of course, a huge advantage if they can place these additional streams exactly on the optimal stages. For this purpose, knowledge of the concentration profiles along the column height is helpful. Finally, if a column does not operate in an assumed way, an accurate tool can be used for trouble-shooting and provides important insights into the understanding. The verification of the developed tools by means of concentration profiles along the column height seems to be necessary and useful. The aim of this paper is to verify the developed model and to get additional valuable information about the temporal and local spreading of disturbances or changes on the relevant process variables with the help of product sampling along the height of the column. The experimental findings are compared with steady-state and dynamic simulation results using the model of equilibrium stage, in both cases considering the influence of heat losses. Heat losses play a particularly important role in laboratory-scale distillation columns because of the numerous nonlagged measuring points (temperature, pressure, and concentration). These heat
0888-588519512634-1810$09.0010 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34,No. 5, 1995 1811
v,-1
fYj.l,l
4-1
1
and component i corresponding to Figure 1. 5-21
total mass balance
component balance
energy balance d(HUjhL I
f
I
+ hu .hG J = F,hfj+ VJ+lhVj+l+
dt
Murphree-stage efficiency
equilibrium relationship (theoretical stage)
y*. . = KvL. J.PjCjc Jtc
Figure 1. Basis of the simulation model.
losses can be considerably reduced for most production plants by using suitable insulation. Moreover, production plants often have no samplers along the column height, but samples can be frequently found on laboratory-scale distillation columns. Large heat losses at production plants occur mainly due to faulty or wet insulation. The consideration of heat losses might play an important role for the scaleup in order to avoid mistakes in the planning and startup. The aim is to quantitatively estimate heat losses in the distillation columns. This problem is only well-known qualitatively from numerous publications. The objective is to demonstrate and examine methods for estimating heat losses quantitatively and to demonstrate their influence on the temperature and concentration profiles. The mathematical model, the assumptions, and the experimental methods are described in more detail below. The equilibrium stage model is used for packing columns. It was shown that this model can be used for tray and packing columns equally if energy losses are considered. The good agreement between the theroretical results and the experimental findings confirms the equations used and the assumptions taken.
Simulation Model The mathematical model used is based on the wellknown laws of conservation (energy balance and mass balance) and equilibrium relationships. Heat losses can also be considered in the model. These equations are formulated for each stage (Figure 1) and for the peripheral systems (condenser and reboiler) (Fieg et al., 1992; Wozny et al., 1987). The stages are numbered from the top of the column (the first stage) to the bottom (the last stage). As a result, the following system of algebraic and differential equations is obtained for stage j
(5)
The equilibrium constant KvLj,j is a function of the temperature Tj,the pressure pj, and the liquid concentration xj,i
The activity coefficients can be calculated, for example, by means of the NRTL or UNIQUAC model. In our investigations, the used fatty alcohols can be assumed to be ideal mixtures. Therefore, the activity coefficients are y = 1. The vapor pressure of the pure component can be calculated with the Antoine equation:
The properties and parameters of the pure components are summarized in Table 1. summation equation N >j,i i=l
=1
where j = 1, ..., N J (NJ is the number of theoretical stages) and i = 1,..., N (N is the number of components). An intensive heat and mass transfer occurs on each stage of the column. At high contact times, the vapor and liquid phases are assumed to be in equilibrium. The departure from equilibrium is assumed to be caused by insufficient contact times of vapor and liquid. This difference can be considered with the Murphree-tray efficiency in the case of tray columns. The separation stages of the packed columns are determined with the help of HETP values. Thereby, the Murphree-stage efficiency is 1. The model equations are based on the following simplified assumptions: constant pressure profile in the
1812 Ind. Eng. Chem. Res., Vol. 34, No. 5 , 1995 Table 1. Physical Properties and Parameters of the Used Pure Components
formula molecular weight critical temperature ("C) critical pressure (bar) critical volume (cmVmo1) enthalpy of evaporation (kJ/mol) melting point ("C) boiling point at 1 atm ("C) density at 25 "C, 1bar (kg/m3) Antoine parameter A Antoine parameter B Antoine parameter C
octanol (CS)
decanol (ClO)
dodecanol (ClZ)
tetradecanol (c14)
(c16)
octadecanol (ClS)
eicosanol (CZO)
CsHisO 130.23 379.35 28.6 489.59 46.90 -15.15 195.20 821.545 15.5535 2902.53 -137.10
CioHzzO 158.283 413.85 24.0 599.583 50.264 6.9 231.11 826.37 15.4762 3145.08 -148.53
ClZH260 186.337 443.85 20.6 716.692 52.512 23.80 264.64 829.65 15.5734 3459.14 -150.78
C14H300 214.394 470.55 17.95 828.00 55.402 38.0 295.634 824.27 15.5103 3638.32 -159.53
C16H340 242.444 494.85 15.9 943.346 57.983 49.30 324.08 819.17 15.6529 3908.23 -164.83
C18H380 270.498 516.85 14.4 1060.784 60.371 57.90 349.79 813.75 14.1497 3216.71 -205.91
C20H420 298.551 527 12.0 1120.0 62.43 65.40 362.63 815.91 15.8233 3912.10 -203.10
Table 2. Variables and Used Equations variables
equations per theoretical stage
T,1
enthalpy balance 1 stoichiometric equation 1 total mass balance 1 component balance n vapor-liquid equilibrium n Murphree-tray efficiency n
v,1
LJ 1 xJsL
y:,i YJJ
n n
stages of 1 m Sulzer packing DX amounts to 18, requiring a top pressure of 20 mbar and an F factor of 1.5 (kg/(s2/m))1/2.The respective physical properties of fatty alcohols are taken from an internal data bank (Henkel Co.). The plant used is not equipped with collectors or dispensers. The reflux drum has a volume of only 50 mL. The bottom holdup is up to 1.5 dm3.
column, ideally mixed liquid phase, and negligible storage effect of the gas phase.
huJ = 0
(9)
+
The 3n 3 variables are solved with the system of equations (Table 2). In the first step, the corresponding system of equations is solved simultaneously for steadystate conditions with the Newton-Raphson algorithm. The steady-state solution obtained (temperature, flow, and concentration profiles) is the starting point for the subsequent dynamic calculation. In each time step, the differential equations are transformed with the modified Euler procedure, giving a new variable vector of the form
o 5 in the turbulent zone h*L= 0.57'Fr1'3 The separation stages are determined with the help of the data in the brochure (Sulzer Co., 1991). According to that, 1 m of the Sulzer packing BX corresponds to ca. seven theoretical stages. The number of theoretical
Description of the Laboratory Column Figure 2 shows the laboratory setup used in the present study. The distillation column has a diameter of 70 mm. It is packed with two types of packings, namely BX and DX, from Sulzer Chemtech, Winterthur, Switzerland. The packing heights are 1.5 and 1.0 m, respectively; the packing is installed in 0.5 m high segments. The column is made of glass and has a double jacket. To reduce heat losses, the space in between is evacuated and the column is mirror-coated. The feed is introduced into the column at a packing height of 1m. The feed is subject to preliminary heating by means of an electrical heating element. The reboiler heat is provided by four electrically adjustable heating elements. The reboiler is insulated with glass wool in order to reduce heat losses. A wattmeter measures the energy input. The condenser is located about 2.5 m higher than the reboiler. It is operated as a total condenser. The vapors condense at the top of the column and flow back to a reflux divider located below. This consists of a collector and a magnetic outlet fitting on a rotatable mounting. An adjustable magnetic timer regulates periodic switching between discharge from (distillate stream) and return to (reflux stream) the column. The unit is equipped with a laboratory process control system from Munzer and Diehl Electronic, Overath, Germany. The control system allows for the measurements of analogue quantities and the regulation and storage of relevant process variables (top pressure, differntial pressure, temperatures along the column height). According to the small quantities involved (on the order of 1kgh), the mass flows (distillate, feed) are determined with the help of a stopwatch and a balance. The process variables are controlled with PID controllers. The unit is fitted with sampling points as shown in Figure 2. The three additional samplers are placed at packing heights of 2.0, 1.5, and 0.5 m and are classified into stage numbers 5 (first measuring point), 10 (second measuring point), and 20 (third measuring point) corresponding t o the given details from the brochure of the Sulzer Co. This equipment allows for the determination of steady-state as well as dynamic concentration profiles along the column height. The
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1813
,-----
--------I L - - - - >
r - - - - -b =.
1111
m
--------I
------0,5 m Sulzer packing BX 0,5 m Sulzer packing DX
U
bottom product B
Figure 2. Laboratory-scale distillation column.
packing (8)
\
column wall (4) (evacuated and mirror- coated)
Figure 3. Sampling method.
I
I sampling glass flask (evacuated) (7)
composition of the samples taken is analyzed with a gas chromatograph (Hewlett-Packard,model 5890, series I1 with 7673 injector). Fieg et al. (1992)give more details about the laboratory distillation column.
Method of Sampling Distillation columns are often equipped with samplers only.at the top and bottom. So dynamic simulation tools
1814 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 Table 3. Parameter and Process Variables
concentratlon/% by wt.
Feed Parameters feed rate feed plate feed pressure feed temperature feed ClO ClZ c14
c16
C18
czo
1.5 k g h stage 11 20 mbar 160 "C feed I PWfeed I1 Ps % by wt
90
diameter rectification section stripping section 30 theoretical plates Operation Parameter top pressure reflux rate temperature reflux ratio holdup condenser reboiler reboiler heat input (w)
60
l!Y2E!!
64
20
33 0.5
10 01
70 mm 1.5 m Sulzer BX 1.0 m Sulzer DX
6
11
16
70 -
-rim.
60 -
* C12-exp.
.
50 -
A
40 30 20 10
C18-exp.
~
~
Figure 4. Steady-state concentration profiles; comparison between simulation and experiment. (a, upper) feed I Pk. (b, lower) feed I1 Ps.
Table 4. Steady-State Concentration Profiles" product concentration % distillate stage 5 bywt sim exp sim exp
stage 10 sim exp
stage 20 sim exp
Feed I Pk 0 0 0 0 Clz 77.4 77.1 27.9 19.8 25.55 28.3 0.19 0.17 C14 21.4 21.9 71.9 80.2 71.95 70.5 75.3 97.03 2.0 0.8 8.4 1.7 C16 0 0 0.1 Cis 0 0 0 0 0.5 0.4 15.93 1.1 Czo 0 0 0 0 0 0 0 0 c 1 0 1 . 2 - -
bottom sim exp 0
0
0
0
9.3 9.5 25.6 28.6 64.3 61.7 0.8 0.2
Feed I1 Ps 0.99 Clz 0.4 C14 2.4 C16 96.3 ClO
Cis
Czo
0 0 1.3 0.2 2.6 0.38 96.1 99.42 0.01 0 0.18 0 0 0
0 0 0.42 0.32 1.34 0
0 0
0 0 0 0 0 0 99.26 93.44 94.37 82.6 89.6 2.5 0.32 6.2 3.99 17.2 10.41 96.5 0 0 0 0.2 0 1.25 0
0
0
0.1
0 0 0
4.54 94.14 1.32
a Comparison between simulation (sim) and experiment (exp) neglecting heat losses.
Table 5. Reboiler Heat Inpup
(w) Qreb Qdifference (w)
started up with the appropriate saturated fatty alcohol,
C14-exp. C16-exp.
~
Qreb
Experiments Steady-State Studies. The distillation column is
26
80 -
0.711.6 0.25 L 1.5 L 1100/1350
On the basis of this chosen and explained sampling and sample methodology, it can be guaranteed that only liquid drains into the flask. Disturbances in pressure changes can be avoided in this way. The samples are taken in time intervals of 10-20 min.
21
stage number
20 mbar 80 "C
can be proven only for these peripheral systems (condenser and reboiler). Disturbances and their effects can only be observed with the help of temperature profiles. Sampling over the column height supplies additional information about the dynamic behavior in the column. This makes a validation of the used simulation model possible. Sampling proves to be difficult, particularly at vacuum-operated columns. Even small mistakes in the preparation and the sampling lead to unwanted disturbances of pressure in the column, sensitively affecting the steady-state or transition period of the column. The unit was fitted with three additional samplers as shown in Figure 2, aside from the samplers at the top and bottom of the column. Figure 3 shows the sampling methodology used in the present study. The central part is a small glass tube (1)which is inside the column opened and bent in the form of a funnel (2). The glass tube is held by a connection piece (3) in the column wall (4). Consequently, the funnel (2) is always arranged in the middle of the section. In this place, a part of the liquid is collected. First, the liquid is dammed in the funnel because the valve (5) is closed during normal operation. Outside the column behind the valve, a 50 mL flask (7) is installed and evacuated at column vacuum before the sample can be let out from the funnel in the flask. Afterward, the valve is closed. The flask pressure is set to the ambient pressure. The procedure described is repeated for every sample a t the desired time points. The measured concentration is interpreted as an integral (eq 14) with respect to time, even though only a few seconds are needed to fill the funnel once again with liquid.
I
70b\nf---i
2.5 17 10 24 0.5 Packing
t
a
measured simulation (W)
feed I Pk 1050 210 840
feed I1 Ps 1350 410 940
Comparison between simulation and experiment.
either palm kernel (Pk)or palm stearic (Ps). First of all, the steady-state operation points are investigated for both cases. In the first case, a mixture of Clo-Czo fatty alcohol (Pk) is used. The main components are C12-Cl8. The top pressure is 20 mbar. At a feed rate of 1.5 kg/h and a reflux ratio of 0.7, a distillate is removed at a rate of ca. 1kg/h. Other process variables are shown in Table 3. When the steady-state condition
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1816
Legend
- simulation
+ ,C 12 exp. A
C 14 exp. ‘ IC 16 exp. IC 18 exp.
distill ate
r n
€!
ur
llme lmln
tlmo lmln
,feed
I
stage 20
bottom product
Figure 5. Dynamic concentration profiles; comparison between simulation and experiment (product changeover from Pk to Ps).
of the plant has been reached in terms of temperature profile and product composition, samples of the product are taken by means of a special device on the distillation column. The samples along the column height form the concentration profile in the column. The compositions relate to the liquid phase. The distillate product
consists of the fatty alcohol, C12 (77%) and c14 (22%)in the steady state. The bottom product mainly contains elf, (28.6%) and C18 (61.7%). In the second case, a mixture of C ~ O - C ~(Ps) O was used. The main components are the fatty alcohols c16 (64%) and cl8 (33%). Compared with the first case, the reboiler heat input is
1816 Ind. Eng. Chem. Res., Vol. 34,No.5, 1995
Qloss
= 14,7-19,l W
Qloss
= 14,7-19,l W
Qloss
= 15,6-19,5 W
Qloss
t
Qloss
= 15,6-19,5 W Qloss= 31,3-38,9 W
Stage 5
= 31,4-39,5 W
Stage 10
= 15,7-19,5 W
= 15,7-19,7 W
Qloss
Qloss
= 15,7-19,7 W
Qloss
Qfoss
= 17,l-20,4 W
++
Qloss
= 17,l-20,4 W
I Qloss= 18,9-22,7 W
++
t
= 34,2-40,7 W
Qloss
Stage 20
Qloss= 18,9-22,7 W
Legend
GIloss=
from Feed / (Pk) to Feed // (Ps) temperature measuring point sampling point
t Qloss
= 10 W per stage
Figure 6. Heat losses along the column height.
increased and a new reflux ratio on the order of 1.6 is chosen. The top pressure, the distillate rate, and the feed rate are retained (Table 3). The cl6 fatty alcohol content in the distillate is approximately 96%, whereas the bottom product has a corresponding content of 94% cl8.
Dynamic Studies. Because of customers’ requests and specific features of the plant, it is common practice in industry to manufacture two or more products from one raw material. Usually these products differ in their composition. In the first test, the plant is allowed to reach a steady state with the corresponding set point. Then the relevant process variables are changed. After a certain transition period, a new product is obtained. The new desired values are set. This dynamic process is called product changeover in the following discussion. Such a product changeover operation is based on a simultaneous change in the feed concentration and the feed rate. As a result, all the material remaining in the column needs to be removed, particularly when highpurity products are desired. In the following example, a product changeover operation from the fatty alcohol Pk to the fatty alcohol Ps is studied, including a change
in the feed concentration. First the desired steady-state operation point for Pk has to be reached. The distillate product consists of a mixture of the components C12 (77%)and c14 (22%)as mentioned above. This steadystate condition with Pk is the starting point for the following studies. The feed is changed to Ps,the reboiler heat input is increased to the corresponding new value, and the new reflux ratio is adjusted from 0.7to 1.6. The bottom level and the feed flow around the electrical heating elements are not decreased during the product changeover operation. During the studies, the distillate receiver (50 mL) is not used. At the beginning of the product changeover, the remaining old product (Pk)in the unit amounts to 2 L. As a consequence of this mixture, consisting of new and old feed, and the increasing reboiler heat input, the concentrations change in the column until the new steady-state operation point for Ps is achieved. The c16 concentration in the distillate amounts to 96%; the c18 concentration in the bottom product is 94%. The top pressure, the feed temperature, and the reflux flow temperature are kept constant during the product changeover. The process parameters necessary for
Ind. Eng. Chem. Res., Vol. 34,No. 5 , 1995 1817 Table 6. Steady-State Concentration Profiles"
concrntrrtlon /% by wt. 100
product concentration
90
%
60
70
- alm.
* C12-axp.
80
.
50
A
40
'
30
C14-eXp. C16-Oxp. C10axp.
20 10 0
distillate
stage 5 exp
bywt sim exp sim
1
6
11
16
21
28
atage number concentration /% by wt.
iL 60
t
X
I
,
10 0
stage 20 sim exp
bottom sim exp
Feed I Pk ClO 1.2 0.09 0 0 0 0 0 0 0.17 0 0 Clz 77.4 77.1 20.6 19.8 19 28.3 0 C14 21.4 21.9 79.3 80.2 78.1 70.5 94.8 97.03 9.3 9.5 0 0.01 1.7 0.8 1.8 1.7 25.6 28.6 Cle 0 1.2 0.4 3.4 1.1 64.3 61.7 0 0 0 Cis 0 0 0.8 0.2 0 0 0 0 0 0 Czo 0 Feed I1 Ps ClO 0.99 0 0.02 0 0 0 0 0 0 0 Clz 0.4 1.3 0.01 0 0.01 0 0 0 0 0 C14 2.4 2.6 0.34 0.42 0.26 1.34 0 0 0 0 Cle 96.3 96.1 99.53 99.26 94.37 94.37 89.5 89.6 2.5 4.54 Cis 0.01 0 0.1 0.32 5.33 3.99 10.34 10.41 96.5 94.14 0 0 0 0.03 0 0.26 0 1.25 1.32 Czo 0 a Comparison between simulation (sim) and experiment (exp) considering heat losses.
60
50
stage 10 sim exp
1
6
11
16
21
26
rtrge number
Figure 7. Steady-state concentration profiles; comparison between simulation and experiment. (a, upper) feed I Pk.(b, lower) feed I1 Ps.
carrying out the experimental studies are listed in Table 3. The distillate rates are calculated with the presented simulation tool. The corresponding reboiler heat input is determined experimentally. The dynamic spreading of the disturbances is recorded in the form of changes in the temperature and concentration profiles as a function of time. Numerous samples are taken along the distillation column, and their compositions are analyzed. Three different kinds of disturbances and their dynamic behavior are analyzed: step change in feed concentration, step change in reboiler heat input, and step change in reflux ratio.
Results The results of the experimental studies are compared with steady-state and dynamic simulation. With the described mathematical model, not only can steady-state simulation results be obtained, but dynamic processes can also be studied. Such simulations give insight on the time dependent behavior of a distillation column. Steady-StateResults. The steady-state simulations with the feeds Pk and Ps are shown in Figure 4a,b and are compared respectively with the experimental findings in Table 4. The solid lines represent the results obtained by steady-state and dynamic simulation, whereas the symbols illustrate the experimental measurements of the concentration profiles. As can be seen, the results show insufEcient agreement between the calculated and experimental concentration profiles. This refers to both the Pk and Ps feeds. Merely a comparison at the peripheral systems (condenser and reboiler) shows good agreement for the product specifications. The deviation between the simulated and measured profiles for Pk and Ps can be seen particularly for the
C14 fatty alcohol. The experimental concentration of C14 in the rectification section is on the order of 80%; its content increases in the stripping section up to 97% in comparison with the simulation results predicting only 74% C14 in the rectification and stripping section. High changes in the concentration profile arise, especially on stage numbers 1-5 and 26-30. Inside the column, there are regions without changes in the concentration which are only interruped by the feed on stage 12. The deviation between the simulated and measured steadystate concentration profiles for the feed Ps can only be seen in the stripping section. While the experimental c16 concentration is in this section ca. 90%, the calculated content does not reach more than 82% here. The comparison in the rectification section shows good agreement within the margin of accuracy of the measurements. On the 5th stage, the c16 concentration increases to 99% and decreases in the distillate to 96% become because the low-boiling components c1&14 enriched when they approach the top of the column. High changes in the steady-state concentration profiles appear on stage numbers 21-30. In this section, the content of c16 decreases from 90 to 5% in the bottom product. The sections with the same concentrations are only interrupted by the feed on the 12th stage. Dynamic Results. On the basis of these steadystate results, dynamic simulations are carried out for a product changeover operation from Pk to Ps. The results are shown in Figure 5 at the corresponding locations along the column as a function of time. As in the steady state, the comparison between the experimental findings and the dynamic simulations shows unsatisfactory agreement. That was to be expected on the basis of the steady-state studies. Only the comparison of the dynamic behavior of the peripheral systems (condenser and reboiler) during the transition period indicates good agreement between simulation and experiment. In contrast to Pk, Ps has a higher content of high-boiling components CldCl8. Because of a higher reboiler heat input at the beginning of the product changeover operation, the composition of the low-boiling components C12/C14increases, particularly in the top of the column. This effect can be seen especially in the rectification section of the column. After a certain period, the low-boiling content decreases fast because of the initial products already being removed from the column. Then the c16 concentration increases steadily until the desired specification of 96% in the
1818 Ind. Eng. Chem. Res., Vol. 34, No. 5,1995 Legend
-
................. ................
- simulation
+ C 12 exp.
..................
distiI late
A
................ ..................
-I-
C 14 exp. V C 16 exp.
................... . . . . . . . . . . . . . . . .
..................
C 18 exp.
. . . . . . . . . . . . . . . .
-
-
200
150
100
250
llme lmln
stage 5
...
.;.
d
...
. . . :_ ....
...
..........
tlmm lmln
--
100
-
- -
....................
_
stage 10
feed
.................... . , _ . . . . . . . . . . . . . _ , _. . . . .................... ..... ..,... .......... ............ ........ ....................... ...... . . . . . . . . . . . . . . . . . . L
f
10-
i .
.
. . . . . . . . . . . . . . . . . . . . * - . , - , , ? 250 SO 100 ?SO 200 lmln
11-
-
I
I
_
. : -
'
.
'
_
..................... . . . . . . . . . . . . .L . . . . . . . . . . .....................
stage 20
........................ . . . . . . . . . . . . .: . . . . . . . . . . ........................ . . . . . . . . . . . . .: . . . . . . . . . .
.=A ' 50
-
I
. -
'
. -.
100
' A 1.50
,
-
a
&
200
2.50
Ilme lmln ..-
,os.
eo,
f
OO
. . . . . . . . . . . . . . . . . . . . .
.:
. . .:. . . . . . . . . . . . . . : . . . . ......................
50
100
*so
200
2.50
llme lmln
Figure 8. Dynamic concentration profiles; comparison between simulation and experiment (product changeover from Pk to Ps).
distillate is reached. The cl(3concentration decreases correspondingly in the bottom product. As can be seen in Figure 5, the content of c16 is already about 90% on the 20th stage. These short transition periods are characteristic for packed columns because the liquid holdup is much lower than in the case of tray columns. In the bottom (reboiler system), the relatively long transition period has to be explained. The liquid holdup in the bottom of the column is one of the critical factors. It is on the order of magnitude of 1.5 L (measured volumetrically). In this context, it is also worth mentioning that the laboratory column does not possess a reflux drum (50 mL) with a holdup corresponding to the bottom of the column. Therefore, the transition period of the top of the column (condenser system) is comparable to that of the packing. The new steady-state operation is already reached within 75 min, except for the bottom, and the product changeover operation is finished in these sections. The differences, seen in Figures 4a,b and 5, between the simulation and the experimental findings will be subject of a critical
analysis. These deviations refer to both the steady-state and the dynamic simulations. It can be shown that these deviations can be attributed to heat losses and their influence on the behavior of the laboratory distillation column. The reboiler heat input calculated and used in the experimental studies is summarized in Table 5. A comparison of the corresponding values yields differences on the order of magnitude of 890-940 W. These results indicate the importance of the consideration of heat losses. The influence and the importance of heat losses on concentration profiles along the distillation column are investigated and analyzed in the Appendix.
Simulation Considering Heat Losses The heat losses estimated and shown in Figure 6 are now considered for the steady-state and the dynamic simulation. The results obtained are shown in Figure 7a,b and 8. The steady-state operation points for Pk and Ps are illustrated in Figure 7a,b a t the correspond-
Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 1819
.'I
200
. l . . . /-..
. . .. .
,60
tempereture i°C
1
250,
etege 2 exp.
!ol 50
A etege 20 exp.
, 1
6
11
16 stage number
21
,
I
1
etage 30 exp.
,
26
tamDereture PC
temperature /'C 250
I1
I I
stage 2
i'"
50 --~lIhwl hul IO.*-
-
0'
1
6
11
I6
21
Mtn h u t l D u I
26
stage number
Figure 9. Comparison of steady-state temperature profiles considering and not considering heat losses. (a, upper) feed I Pk. (b, lower) feed I1 Ps.
ing control points as a function of time and are summarized in Table 6. In contrast to Figure 4a,b the comparison between the simulated and measured steadystate concentration profiles shows good agreement, especially in the stripping section of the column. The experimental C14 concentration of 97% (stage 20,Omin) is nearly obtained by simulation (Figure 7a). As can be seen in Figure 7b7 the agreement between the simulation and experimental findings is improved, particularly for the C I concentration ~ (89.6%) in the stripping section (stage 20) for the fatty alcohol Ps. The peripheral systems still show good agreement, and no changes can be noted in comparison to the previous calculations in which the heat losses along the column height are neglected. On the basis of these steady-state results and their good agreement between simulation and experiment in the following, dynamic simulations are carried out considering heat losses. The dynamic simulation results are shown in Figure 8 as a function of time corresponding to the respective measuring points. A comparison of the simulated and experimentally measured transition profiles during the product changeover operation shows good agreement now. This refers t o qualitative and quantitative statements within the margin of accuracy of the measurements. The influence of the heat losses can be seen, especially for the dynamic transition period of the C14 fatty alcohol on stage 10 ranging from initial 70% (0 min) to 88% (20 min) and a t steady state to less than 1%,for example. At the peripheral systems, changes in the dynamic behavior cannot be noted in comparison to the simulation results neglecting heat losses. In Figure 9a7b,steady-state temperature profiles for Pk and Ps are compared considering and neglecting heat losses. Figure 10a7bshows the corresponding dynamic transition behavior of the temperature profiles during
Conclusion This article presents a systematic approach for steadystate and dynamic investigations of packed laboratoryscale distillation columns. The developed methodology allows for the systematic evaluation of the heat losses with respect to temperature and concentration profiles for two different feeds. Certainly, the experiments carried out and the analysis indicate the necessity of the consideration of heat losses along the column height. It was shown clearly that the influence of the heat losses cannot be seen in the steady-state and dynamic temperature profiles. Steady-state and dynamic simulations carried out in view of these effects indicate good agreement between calculated and experimental findings. Changes in the peripheral systems (condenser and reboiler) cannot be noted considering or not considering heat losses. In both cases, the comparison between experiment and simulation agrees well. Moreover, experimental studies were carried out for a product changeover operation from Pk to Ps. With
1820 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995
the new feed, Ps relevant process variables (the reflux ratio and the reboiler heat input) were changed. For the analysis of product concentrations, additional samples along the column height at three different segments during the dynamic transition period were taken and analyzed. In addition to temperature profiles, further and valuable information was obtained for the spreading of purposeful changes of relevant process variables or disturbances. A reasonable agreement with dynamic simulations can be achieved. As can be shown, heat losses along the column height, especially at the temperature- and concentration-measuring points, have to be considered in order to improve the agreement with dynamic simulations. Hence, the dynamic transition behavior was correctly described qualitatively and quantitatively. The good agreement between simulated and experimental findings confirms that the used equilibrium stage model applied to packed columns, taking into account the corresponding heat losses. With the steady-state or dynamic temperature profiles, these effects cannot be observed. Because laboratory-scale columns are often equipped with numerous different kinds of measuring points (temperatures, pressure, and concentrations), the influence of heat losses is very important. At production plants, these heat losses are avoided with suitable insulation. Furthermore, considering heat losses is very important for the scaleup from the laboratory distillation column to the production plant to avoid mistakes in the preliminary stages of the planning, projecting, and startup. It should be noted that the shown results can be used for an improved automation concept for startup and product changeover operations of distillation columns (Kruse et al., 1993) and have significant impact on the minimizing of development costs.
Acknowledgment The authors would like to thank the BMFT (Bundeministerium fur Forschung und Technik), Germany, and the AIF (Arbeitsgemeinschaft industrieller Forschungsvereinigung), Germany, for providing financial support for this work. The authors also express their gratitude to Mr. S. Pelkonen (Neste Oy's Foundation) for his assistance during the preparation of this manuscript, to the anonymous reviewers of this paper, and to the associate editor (Prof. J. D. Seader) for their helpful comments.
Nomenclature A = surface (m2) A = Antoine parameter in eq 7 a = specific surface of packing (m2/m3) B = bottom product rate (kg/s) B = Antoine parameter in eq 7 C = Antoine parameter in eq 7 c = heat capacity ((kJ/kg)/K) D = distillate rate (kg/s) d = diameter (m) f = feed concentration (mol %) F = feed rate (kmovs) g = gravitational constant (m/s2) h = enthalpy (W) H = height (m) h* = holdup (m3/m3packing) HU = liquid holdup (kmol) hu = vapor holdup (kmol) K = equilibrium constant k = overall heat transfer coefficient ((W/m2)/K)
L = liquid flow (kmovs) 1 = length (m) M = Murphree tray efficiency n = number of insulating layers N = number of components N J = number of theoretical stages p = pressure (mbar) Pk = feed I: palm kernel fatty alcohol Ps = feed 11: palm stearic fatty alcohol Q = duty (W) r = radius (m) R = reflux ratio t = time (SI T = temperature ("C) u = specific liquid load ((m3/m2)/s) U = site stream (kmoYs) V = vapor flow (kmol/s) w = velocity of air ( d s ) x = liquid concentration (mol %) y = vapor concentration (mol %) Greek Symbols
a = heat transfer coefficient ((W/m2)/K)
/3 = thermal coefficient of expansion in eqs 12,20,22(1K) /3 = factor (eq 8) A = difference 0 = temperature ("C)
1 = thermal conductivity ((W/m)/K) Y = kinematic viscosity (m2/s) n = cycle constant e = density (kg/m3) Subscripts
a = outside calc = calculated cond = condenser cy1 = cylinder exp = experimental forc = forced convection free = free convection i = inside i = component j = stage number L = liquid phase lam = laminar loss = loss reb = reboiler sampl = sampling point temp = temperature-measuring point total = total turb = turbulent V = vapor phase Superscripts
' = pure component * = equilibrium VL = vapor-liquid equilibrium - = average value Dimensionless Quantities
Froude number Fr = uL2(a/g) Grashoff number Gr = g13AO/v2//3 Nusselt number N u = aaZ/Aair Prandtl number P r b = veclil Reynolds number Reair = wd/v (eqs (16, 17, 23) Reynolds number Re = uIja/vL (eqs 9, 10)
Appendix Importance and Influence of Heat Losses. As emphazized earlier, the column is made of glass and has
Ind. Eng. Chem. Res., Vol. 34, No. 5,1995 1821 a vacuum-insulated double jacket. The column surface temperature reaches 35 "C during the operation. The column, consisting of several separate segments, has numerous uninsulated temperature-measuring and -sampling devices as can be seen in Figure 3. Each column segment is equipped with two opposite-lying temperature-measuring points. In addition, three further samplers (arrangement in Figure 3) and two further temperature-measuring points for the feed input, the condenser, and the reboiler are added. It might be expected that the heat losses will be particularly high at these mentioned places of the column. In what follows, these heat losses are estimated by calculation considering free and forced convection (caused by air draft). Their influence on the steady-state and dynamic concentration profile will be derived. To calculate the average heat transfer coefficient at forced convection, an air velocity of Wair = 0.5 d s is assumed. The contribution of heat losses by thermal radiation is neglected with regard to the free and forced convection because of small surfaces and temperature differences. An estimation yields heat transfer coefficients on the order of less than 0.4 (W/m2)/K (VDI, 1991). The following heat transfer coefficients are considered closer. Heat Losses of the Column Wall. The heat losses a t free convection result from differences in density as a consequence of temperature differences. The dimensionless heat transfer coefficient can be estimated with eq A.l (VDI, 1991):
Nu = flGr,Pr)
(A.1)
Heat Losses of the Temperature-Measuring Points and Samplers. To calculate an average heat transfer coefficient a t free convection for the horizontal cylinder, the following equation is used:
Nufiee= (0.60 with
With the given equations, the heat transfer coefficient for the temperature-measuring points and samplers is on the order of a, = 23-23.5 (W/m2)/K. Heat Losses of the Condenser and Reboiler. The condenser is regarded as an uninsulated circumflowed cylinder with a surface temperature of ca. 80 "C. Equations A.5-A.8 are used t o estimate the heat transfer coefficient for free and forced convection. For this, an average coefficient is calculated on the order of a, = 14.6 (W/m2)/K. The reboiler is approximately regarded as a hollow sphere. The heat transfer a t free convection is calculated with the following Nusselt function:
Nufree= 2
(A.2)
with
For a vertical cylinder, the Nusselt number is determined by eq A.4. The calculation of the average Nusselt
+
NucJI= NUplate 0.975 h
(A.4)
function a t forced convection is carried out with the same equation as for the overflowed flat plate using the characteristic length I = n(0.5d)
+ 0.33 (Gr Pr)1/4Pr1/4
Nuforc= 2
+ 0.6Re0.5Pr1/3
NUforc,turb
-
1
+
0.037Re'.'Pr 2.443Re-'%'rW3 - 1)
(A.5)
3
+~
k=
-I
I
- (A.13)
(A.6)
The superposition of free and forced convection yields to increasing heat transfer = (NU,,
(A.12)
The average heat transfer coefficient is thereby a, = 9.7 (W/m2)/K. The measured heat transfer coefficient at the inner wall for fatty alcohols is about 1700 (W/ m2)/K (Nitsche, 1994). The thermal conductivity A of glass is between 1.3 and 1.6 (W/m)/K. Thereby, the inner heat transfer and the heat conduction through the glass wool is assumed to be so good that the temperature differences can be neglected. Hence, the total resistance is practically only controlled by the transition resistance from the surface of the measuring point to the surroundings. So the heat conducted is determined mainly by this resistance. The influence on the heat flow by changing the inner heat transfer coefficient cannot be noted. The heat transmission coefficient is calculated with eq A.13 for hollow spheres because half of the reboiler surface is insulated with glass wool. 1 I
Nuforc,lam = 0.6646Pr1/3
(A.ll)
The corresponding heat transfer coefficient for forced convection in the laminar and turbulent region is calculated with eq A.12
This coefficient in the laminar and turbulent zone at free convection can be described as
Nufree= (0.825 + 0.387[Gr Pr fl(Pr)11/6}2
+ 0.387[Gr Pr f3(Pr)11'6}2 (A.9)
u ~ ~ ~ :(A.8) ) ~ ~
The estimation results an outerwall heat transfer coefficient of a, = 21 (W/m2)/Kand heat losses on the order of ca. 10 W per theoretical stage for a 3.2 m column height and a diameter of 0.09 m.
The values of the thermal conductivity for glass wool are on the order of 0.075 (W/m)/K. From that follows an overall heat transfer coefficient of ca. k = 7.6 (W/ m2)/K. The physical characteristics for air were taken from VDI (1991). The calculation of the heat losses is carried out with eq A.14. Qoss
= a $ S s d a c e ( o i - air)
(A.14)
The characteristic dimensions for estimating heat transfer area are summarized in Table I. The heat losses resulting from temperature-measuring points and samplers are shown in Tables I1 (Pk)and I11 (Ps). The
1822 Ind. Eng. Chem. Res., Vol. 34, No. 5, 1995 Table I. Calculated Heat Transfer Areas
cylinder
hollow sphere
temperaturemeasuring point sampling point column wall condenser reboiler
Literature Cited
diameter length heat transfer 1 (m) areaA(m2) d (m) 0.03 0.05 0.0047
0.03 0.09 0.09 0.168
0.1 3.2 0.5 -
0.02827 0.0942 0.905 0.08867
Table 11. Heat Losses at the Temperature-Measuring Points and Samplers (Feed I Pk) stage no. temp ("C) 2 153.72 5 162.32 7 162.56 10 162.82 20 175.48 29 190.90
Qiws temp (W)
Qioss samp (W)
31.27 31.39 34.23
14.67 15.63 15.67 15.69 17.12 18.85
&total iosa (W)
292.15
-
Table 111. Heat Losses at the Temperature-Measuring Points and Samplers (Feed I1 Ps) stage no. temp ( " 0 2 193.44 5 196.28 7 196.83 10 198.67 20 204.30 29 224.86
(W) 19.13 19.45 19.52 19.73 20.37 20.69
Qioss temp
Qioss samp (W)
38.91 39.45 40.73 -
Qtohi loaa
(W)
360.87
Table IV. Estimated Heat Losses along the Column Height heat losses
feed I Pk
feed I1 Ps
column wall (W) measuring points (W) condenser (W) reboiler (W) Qloas c a ~ c(W) Qloss exp (W)
280 360 120 160 920 940
280 290 120 130 830 840
total heat losses along the column height are summarized in Table IV.The heat losses for feed I Pk are on the order of 830 W and for feed I1 Ps are ca. 920 W. Considering these heat losses in the simulation calculations, the reboiler heat input agrees closely with the one found in the experimental studies. Figure 6 shows clearly the heat losses along the column height.
Berber, R.; JSaradurmus, E. Dynamic Simulation of a Distillation Column Separating a Multicomponent Mixture. Chem. Eng. Commun. 1989,84,113-127. Fieg, G.; Wozny, G.; Jeromin, L. Experimental and theoretical studies of the steady-state and dynamic behaviour of packed columns. Chem. Eng. Process. 1992,31, 377-383. Fieg, G.; Wozny, G.; Kruse, Ch. Experimental and Theoretical Studies of the Dynamics of Startup and Product switchover Operations of Distillation Columns. Chem. Eng. Process. 1993, 32,283-290. Gani, R.;Ruiz, C. A.; Cameron, I. T. A Generalized Model for Distillation. Comput. Chem. Eng. 1986,10, 181-198. Gilles, E. D.; Holl, P.; Marquardt, W. Dynamische Simulation komplexer chemischer Prozesse. (Dynamic simulation of complex chemical processes.) Chem.-Zng.-Tech. 1986,58,268-278. Gunn, D. J.; Al-Saffar, H. B. S. Liquid Distribution in Packed Columns. Chem. Eng. Sci. 1993,48,3845-3854.Internal data bank; Henkel KGaA: Diisseldorf, Germany. Kruse, Ch.; Fieg, G.; Wozny, G. Aufwand-mutzenanlayse von Anfahr- und Produktwechselvorgkgen an Rektifikationskolonne. Presented at the internal group meeting of the GVC Technical Committee Prozess- und Anlagentechnik, Luneburg, Germany, October 25,26, 1993. Mackowiak, J. Fluiddynamik von Kolonnen mit modernen Fiillkorpern und Packungen fur Gas I Fliissigkeitssysteme; Salle Sauerlander: Aarau, 1991. Nitsche, M. Personal notification. Patwardhan, A. A.; Edgar, T. F. Nonlinear Model Predictive Control of a Packed Distillation Column. Znd. Eng. Chem. Res. 1993,32,2346-2356. Sulzer Co. Trennkolonnen fur Destillation und Absorption (Chemtech brochure). VDZ-Warmeatlas;VDI Verlag: Auflage, 1991;Vol. 6 Chapters E and F. Wang, F. Y.; Cameron, I. T. Dynamics of Fractionators with Structured Packing. Chem. Eng. Commun. 1993,119,231-259. Wozny, G.; Jeromin, L. Dynamische Prozesssimulation in der industriellen Praxis. (Dynamic process simulation in industrial practice.) Chem.-Zng.-Tech. 1991,63,313-326. Wozny, G.; Witt, W.; Jeromin, L. Dynamics of Distillation with High Product Purities. Chem. Eng. Technol. 1987,10,338-348.
+
Received for review May 27, 1994 Revised manuscript received November 16, 1994 Accepted February 16, 1995@ IE940341J Abstract published in Advance ACS Abstracts, April 1, 1995. @
