Ind. Eng. Chem. Process Des. Dev. 1988, 25, 164-168
164
Analog Computer Control of Benzene Chlorination Sohrab Rohanl Chemical Engineering Department, University of Saskatchewan, Saskatoon, Canada, S7N 0 WO
Analog computer control of a semibatch reactor was investigated both theoretically and experimentally. The reaction employed was the chlorination of benzene, and the controlled variable in all cases was the monochlorobenzene concentration. The manipulative variable was the heating water flow rate. Maximlzation of the monochlorobenzene concentration using Pontrya n’s maxknum principle resulted in operating at the minknum of the available operating temperature range (30-70 C). This isothermal optimal path was obtained by using a conventional PI temperature controller. Control along a linear path of the monochlorobenzene concentration with time was further investigated by using both feedback and open-loop feedforward controller schemes. The feedforward controller performed better than direct feedback controller. This was due to the detrimental effect of analysis time on the quality of control. A chromatographic column packed with tricrecyl phosphate supported on Silocel C22 reduced analysis time of the reaction products to 2 min.
P
The past few decades have seen considerable improvements in the control of purely batch reactors. Siebenthal and Aris (1964) used Pontryagin’s method for optimal control of batch and tubular reactors. Ray and A r i s (1967) considered adaptive control of the batch reactor. Recent works in the control of batch reactors are reported by Soni and Albright (1981), Armstrong and Coe (19831, and Mou and Cooney (1983). Little work, however, has been reported concerning semibatch reactor control in which one or more reactants are continuously added throughout the reaction period to an initially charged reactor. In the present work, optimal control of a semibatch reactor with a benzene chlorination reaction was attempted. Off-line maximization of the monochlorobenzene yield resulted in an isothermal optimal policy at the lower limit of the operating temperature range. Temperature control of a highly exothermic polymerization batch process using a conventional feedback controller is reported by Spellmann and Quinn (1975). A PI temperature controller in the present work ensured isothermal operation and monochlorobenzene yield maximization. A more challenging reaction path had to be chosen for evaluation of different control schemes to make the reaction follow the desired path. The response of monochlorobenzene to changes in the reaction temperature was sluggish with a small gain (eq 10). This was due to the weak temperature dependency of the reaction rate constants. Consequently, the desired path had to be selected based on system controllability considerations. A linear path of the monochlorobenzene concentration with time ensured system controllability and made implementation of different control schemes possible. In direct feedback control of the monochlorobenzene concentration, the gas-liquid chromatograph (GLC) analysis time was detrimental to the quality of control. In an attempt to decrease the analysis time, three different column packings are used tricresyl phosphate on Silocel C22, Apiezon L on Silocel C22, and Carbowax 20M on Silocel C22. Tricresyl phosphate supported on Silocel C22 gave the smallest time for the analysis of reaction products. System response under on-off and PI control with different analysis time was obtained experimentally. An open-loop feedforward controller based on an analog computer simulation of the chlorination process and the linear monochlorobenzene concentration path gave excellent response. Benzene chlorination was chosen due to its industrial importance, well-tabulated kinetics, and availability of the 0196-4305/86/1125-0164$01.50/0
reactants. Macmullin (1948) and Himoe and Stock (1969) reported kinetic data of the benzene chlorination reaction. Stock and Himoe (1969) studied the effect of various solvents and catalysts on the reaction.
Experimental Equipment The reactor was constructed from 1818 stainless steel. Good mixing was ensured by using an eccentrically placed 0.08-m paddle impeller and by baffles welded to the internal reactor wall. The chlorination reaction
was catalyzed by ferric chloride. At the commencementof each run, approximately 0.016 m3 of benzene was charged to the reactor together with 5 X m3 of nitrobenzene to improve catalyst effect. The catalyst was suspended in a perforated stainless steel tube within the reacting mixture, and chlorine was introduced through a circular distributor at the base of the reactor. The whole vessel was well-insulated, and temperatures within were monitored by iron-constantan thermocouples. Heat was supplied by hot water passing through a coil placed within the reacting mixture. The flow of hot water from a constant head tank was controlled by means of a lJ2-in. control valve and was monitored by using a differential pressure cell. Heating was accomplished by immersion heaters positioned in the hot water reservoir and controlled by a mercury contact thermometer placed in the reservoir tank. A cooling coil was also provided within the reactor and was supplied by refrigerated water. Four sample points were positioned at different points in the reactor, and each sample line was water-cooled to prevent vaporization. The sample was pumped continuously through a metering pump and an automatic sampling valve, thence being returned to the reactor. The valve was operated pneumatically by means of a timer and diverted a 10-8-m3sample into a GLC for analysis at predetermined intervals of time. The chromatograph was equipped with a catharometer detector and a 0.46-m column packed with Silocel C22 as the support, and tricresyl phosphate as the stationary phase. Helium was used as the carrier gas. The peaks of benzene, monochlorobenzene, and o-dichloro-
0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
Table I. Column Specification length, m stationary phase support outside diameter, mm inside diameter, mm net weight of packing, g net weight of silocel in column, g w t of tricresyl phosphate in column, g % loading carrier gas
0.457 tricresyl phosphate Silocel C 22 (120-150 mesh) 6.4 4.6 6.29 4.71 1.58
AC AhiALOG COMPUTER CLHS CONSTANT L E V E L HEATING SYSTEM DL DATA LOGGER
GLC GAS
.C U I 2
165
CHROMATOGRAPH
R REACTOR SU S C A d B B E R UNIT
r NOOH
25.1 helium
Table 11. Chromatographic Retention Times of Reaction Components carrier carrier gas 0gas flow inlet monochloro- dichlororate, pressure, benzene, benzene, benzene, cm3/s kN/m2 S S 8 8.6 193 20 65 225 8.9 275 18 59 161 10.9 310 16 39 148 12.5 345 15 45 123 15.2 379 14 44 116 16.1 414 12 42 112 19.2 482 9 39 105
benzene, using a carrier gas flow rate of 19.2 cm3/s, inlet pressure of 483 kN/m2, and column temperature of 423 K, were obtained after 9, 39, and 105 s, respectively. Column specifications and retention times are given in Tables I and 11. The hydrochloric acid gas produced in the reaction and any unreacted chlorine were absorbed by caustic soda in a packed column. A reflux condenser was fitted to the product gas line in order to prevent any chlorobenzene from escaping from the reactor. Experimental data were continuously scanned and printed by using a 20 channel data logger. The controllers were simulated by using a small, Pace TR-10 analog computer, possessing 20 amplifiers, 8 integrators, and 2 variable diode function generators working in 0-10 V. Chromatographic peaks of monochlorobenzene were converted to a 0-10-V signal by means of an automatic peak selector and integrator. The concentration signal measured at successive intervals was maintained by a zero-order hold element. Figure 1 shows the complete experimental setup. System Dynamic Response The following assumptions were made for the determination of the dynamic response of the system. (i) The chlorine enters the benzene ring by substitution of hydrogen only. (ii) The distribution of components is independent of the rate of introduction of chlorine. (iii) The resistance to mass transfer between chlorine in the gas and liquid phase is negligible (working at low chlorine flow rate). Hence, the changes of concentration in terms of the total number of kilomoles with time for the reaction constituents can be written
(3) (4)
Figure 1. Experimental setup.
’1
- NUMERICAL
a
-a 0
z
6
\
2
4 2
0
0
200
400
600
800
I000
DIMENSIONLESS TIME
Figure 2. Comparison of digital and the approximated analog process simulation results. 7’= 330 K, chlorine flow rate = 400 cm3/ min.
When assumption (iii) is applied, the number of kilomoles of chlorine at any instant is
Nc= xtrdt-X where X is the number of kilomoles of chlorine reacted. Differentiation of eq 5 with respect to time gives
cw, = rV - Nc(klNB+ k2NM+ k,ND) vdt
(6)
where
ki = Aie-Ei/RT (i = 1-3) An energy balance over the reactor leads to
(7)
AH3 T k S N c N D + UAAT + Qw (8)
Equations 1-8 were solved numerically by using Merson’s method. To simplify the analog computer simulation, it was assumed that the mole fraction of benzene decreased exponentially with time, Le.,
B = $8
(9) where the numerical value of /3 was taken as 0.012 (Carlson, 1965). This reduced the number of required nonlinear multipliers to one. Figure 2 shows good agreement between the approximated analog and digital simulation results which justifies the above assumption. Figure 3 indicates satisfactory agreement between the computed and the experimental results at two different operating temperatures. The isothermal operation was ensured by using a PI controller. Feedback Control (a) Bang-Bang Control. The feasibility of employing bang-bang optimal control in the case of pure batch re-
188
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
UH
1
A '
FYPFRIMFNTdl
..
,
Figure 5. Block diagram of the process under PI control:
1
?
F
4
8
TIME ( h )
Figure 3. Experimental and numerical results of monochlorobenzene concentration at two different temperatures. Chlorine flow rate = 800 cm3/min.
I -a
v4
,
z
1
f
t
c 31 t
--- UNCONTROLLED
-
E X P E RTDESIRED I M- EI No TmA Ln PATH RESULTS D
T - 2 m ~
2
RESPONSE
.
0 0
fly
I
TIME ( h )
fraction/h). The controller was an open-loop scheme based on the process model described by eq 1-9 with the following additional assumptions: (i) the rate of production of trichlorobenzene in the time considered was negligible and (ii) the rate of change of the concentration of unreacted chlorine in the reacting mixture was linear with respect to time. The resulting feedforward controller was wired on the analog computer. The heating water flow rate, QH, required to make the reaction follow the desired path was continuously computed. Considering eq 8, it is evident that to implement the feedforward controller, not only temperature but its time derivative is also required. This implies analog differentiation which is undesirable due to its effect on high frequency signals and signal noise. The problem was overcome by using the modified transfer function
Figure 4. Process response with on-off control.
y/x =
actors has been considered by Blakemore and Aris (1962) and Munick (1965). The possibility of using this simple control scheme to guide the reaction along the desired linear path was examined. The reacting mixture composition was determined at successive intervals of time by using the automatic sampling valve, chromatograph, and the peak selector-integrator network in series. The measured signal was compared with the output of a ramp generator representing the reaction desired path. Depending on the sign of the error, the heating water flow rate was increased to its maximum value or decreased to zero for the next sampling interval. The performance of this controller was examined for different sampling periods. The oscillatory nature of this control mode was substantially decreased with the reduction of the sampling interval (Figure 4). (b) PI Control. In order to eliminate the oscillatory nature of the response associated with on-off control, a P I controller was devised. The controller settings were determined by approximating the process by a first-order lag plus a time delay. The approximate transfer function was obtained by monitoring the monochlorobenzeneconcentration response to a step change in the heating water flow rate: 0.32e-14.5s Gp(S)
= 220s
+1
(10)
For a sampled-data system, the controller settings are a function of the model parameters and sampling period. Controller settings recommended by Mosler et al. (1967) with a sampling interval of 2 min were used in this work. Due to the very high controller gain, response of the process under PI control was similar to the on-off control scheme with a sampling time of 2 min. The block diagram of the process under PI control is shown in Figure 5. Feedforward Control The feedforward control criterion employed was to keep the monochIorobenzene concentration at the same linear path as with the feedback system (dNM/dt = 0.01 mol
S
7s
+1
(11)
which employs an integator in a feedback loop. The latter filters out the high frequency signals and could be chosen to maintain the noise output to a tolerable level. The necessary heat input to the reactor, QH, through the heating coil at any instant can be related to the reaction mixture temperature by using QH
= UAAT = qHPHCHS(TH,in - TP)
(12)
where
s = em - -1 em
and
Hence,
where TH,in is the constant inlet temperature of the heating coil. Knowing QH, then q H s can be obtained by using a nonlinear multiplier in the divide mode. The relationship between q H s and the valve actuating voltage was generated by a variable diode function generator (Figure 7). The effectiveness of the feedforward controller was tested by determining its ability to maintain the production of monochlorobenzene on the desired linear concentration path with respect to time. The analog computer was not able to simulate the process in real time because of the slow reaction rates. Thus, an incremental counter was constructed to set the computer into two different modes, "operate-hold" and "operate-reset". The process response under feedforward control is shown in Figure 8. Figure 9 shows the feedforward controller response in the presence of step changes in the
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
I
167
.L
h
TIME ( h )
Figure 8. Process response with feedforward control.
- - - UNCONTROLLED - DESIRED PRTH
RESPONSE
"OPERATE-HOLD': 79 sec
?C TIME ( h ) POTENTIOMETER SETTINGS
la : 2 I b = 029 2 0 = 0 122 FOR A CHLORINE F L O W R A T E O F 13.33 cm3/s
:
2b 30 3b 4a 4b
= 139
50 =
= .I2
5b
= 01
267 246 7 0 = 204 i
011 = 012
:
Figure 6. Analog circuit diagram of feedforward controller. INPUT VOLTAGE ( V O L T S )
v)
0 >
w 0
a
0
BREAK POINTS CURVE S E T UP ON FUNCTION GENERATOR THEORETICAL CURVE
-F I T T E D
i
0 -EL
Figure 7. Relation between control valve actuating voltage and qHS generated by a variable diode function generator.
chlorine flow rate. The step changes were introduced into the process analog simulator by manually adjusting potentiometer setting 2a in Figure 6 as soon as the step changes in the chlorine flow rate were introduced. Conclusions The chlorination of benzene is a complex reaction involving low reaction rates. Although a digital computer for control purposes seemed to be necessary, the TR-10 analog computer with its limited hardware capability proved to be sufficient to implement different control
Figure 9. Process response with feedforward control and variations in chlorine flow rate.
schemes successfully. The reaction is of importance to industry, but suitable precautions had to be taken due to the presence of benzene, chlorine, and the reaction products, both from the point of view of the human operator and the equipment. Corrosion was particularly severe. Figure 2 shows good agreement between the simplified process model for analog simulation with the numerical results. The agreement between experimental and numerical results was better at lower temperature (Figure 3). The rapid decrease in the solubility of chlorine in benzene and chlorobenzenes with an increase of temperature (being approximately 0.24 mol fraction at 258 K and 0.08 mol fraction at 335 K) explains the discrepancy between numerical and experimental results at higher temperature. The time delay associated with batch analyzers must be compensated for or reduced for successful feedback control. Analysis time was reduced to 2 min. The system was more sensitive to changes in the chlorine flow rate than in the hot water flow rate, but the latter was used as the manipulative variable due to the practical difficulties involved in controlling the chlorine flow rate. Maximization of monochlorobenzene resulted in an isothermal operation at the lower limit of the temperature range. In the feedback control of the process, due to the slow response of the monochlorobenzene concentration to changes in the operating temperature, a very high controller gain was necessary. The limiting case was the use of on-off control, which, however, resulted in an oscillatory response. Figure 4 indicates a stable response at a sampling interval of 2 min; however, increasing the sampling interval to 10 min made the response unstable. The open-loop feedforward control was superior to the feedback control even with the simplified analog model. This confirmed the absence of any unmeasured disturbances and the validity of the process model. However, the major problem in the feedforward control was the amplifiers drift. This was to a large extent overcome by employing an "operate-reset'' mode. The controller was very effective in suppressing the effect of variations in the
Ind. Eng. Chem. Process Des. Dev. 1986, 25, 168-171
168
chlorine flow rate, when such variations were introduced manually in the model. Implementation of the feedforward control would have been simpler if a digital control hardware was used.
8 R
T U V
X k 4 r S
t X
Y
benzene exponential decay index density, kg/m3 dimensionless time time constant, s
7
This work was partly supported by a grant from the National Sciences and Engineering Research Council of Canada. Nomenclature
B C E G K M N
P P
0
Acknowledgment
A
Symbols AH heat of reaction, kJ/kmol
Arrhenius frequency factor, dimensionless; area for heat transfer, m2 benzene mole fraction, NB/NB(O) heat capacity, kJ/(kgK) activation energy, kJ process transfer function constant monochlorobenzene mole fraction, NM/NB(O) number of kilomoles heat contribution due to chlorine feed, impeller action, condenser, and heat of solution of chlorine, kW universal gas constant, kJ/ (kmo1.K) temperature, sampling interval, s overall heat-transfer coefficient, kW/ (m2.K) initial volume of reacting mixture, m3 number of kilomoles of chlorine reacted at any instant reaction rate constant, m3/(kmol.s) volumetric flow rate, m3/s inlet flow rate of chlorine, kmol/s Laplace operator time, s input to noise filter output from noise filter
Subscripts
B C D H M P V
W Z i
benzene chlorine dichlorobenzene heating water monochlorobenzene reacting mixture valve cooling water trichlorobenzene reaction number
Registry No. Benzene, 71-43-2;monochlorobenzene,108-90-7.
Literature Cited Armstrong, W. S.; Coe, B. F. Chem. Eng. Prog. 1983, 7 9 , 56. Slakemote, N.; Aris, R. Chem. Eng. Sci. 1962, 17, 591. Carlson, A. Instrum. Control Syst. 1965, 38, 147. Himoe, A.; Stock, L. M. J . Am. Chem. SOC.1969, 9 1 , 1452. Macmullln, R. B. Chem. €ng. Prog. 1948, 4 4 , 183. Mosler, H. A.; Koppel, L. B.; Coughanowr, D.R. Ind. Eng. Chem. Process Des. Dev. 1967, 6 , 107. Mou, D. G.; Cooney, C. L. Biotechnol. Bioeng. 1983, 25, 225. Munick, H.AIChE J . 1965, 1 7 , 754. Ray, W. T.; Aris, R. Automatika 1987, 4 , 137. Siebenthal, C. D.; Aris, R. Chem. Eng. Sci. 1964, 19, 747. Soni, Y.; Albright, L. F. J . Appl. Polym. Sei., Appl. Polym. Symp. 1981, 3 6 , 113. Spellmann, R. A.; Quinn, J. B. ISA Trans. 1975, 74, 312. Stock, L. M.;Himoe, A. J . Am. Chem. Soc. 1961. 8 3 , 1973.
Received for review September 6 , 1984 Revised manuscript received February 25, 1985 Accepted July 10, 1985
Drying Characteristics of Morwell Brown Coal and Effects of Drying on Liquefaction Ryoro Toe1 and Hajlme Tamon' Department of Chemical Engineering, Kyoto Universiv, Kyoto 606, Japan
Katsuya Uehara and Saburo Matwmlya Toy0 Engineering Corporation, Kasumigaseki Building, 2-5, 3-Chome, Kasumigaseki, Chiyda-ku, Tokyo 100, Japan
Drying characteristics of Morwell brown coal were experimentally determined. About 80% of the waters contained in the coal was the free water and the capillary water, and the drying was easy. Though the coal was adsorptive and shrank during drying, the falling drying rate was proportional to water content. This result was useful to design a dryer. The effects of drying on coal liquefaction were investigated. During hot air drying below 164 O C , oxygen in the hot air did not affect the product yields and the hydrogen consumption during liquefactionand the composition of coal.
The total reserves of brown coal (lignite) around the world are nearly 2.5 X 10l2tons. Brown coal has a high water content and therefore a low energy density, so that it is correspondingly expensive in terms of transport. In order to take full advantage of the energy potential of the 0196-4305/86/1125-0168$01.50/0
coal, it is utilized as briquette and coal liquid. The dewatering is very important in these technologies. The dewatering such as the heating under pressure in saturated steam (the Fleissner process (Fleissner, 1927)) or oil a t around 200 OC (von Staden, 1927) has been con0 1985 American Chemical Society
