Ind. Eng. Chem. Process Des. Dev. 1984, 23, 857-859 TERNARY DISI’ILLATION CONTROL MEASURED VARIABLES TRIPLE PENALTY ON REFLUX TOLUENE IN ,TLUENEIN BOTTOM 8.91 4 96
1
1300
1200
I 100 1000
900
800
700
600
I
I 0.0 REFLUX
I
I
10.0 49.27
0.0
I
10.0
I
0.0 REBOIL
1
10.0
I 00
10.0
49.92
Figure 5. Closed loop response of controlled variables: reflux constrained. TERNARY DlSTlLLAION CONTROL -TED VARIABLES TRIPLE PENALTY ON REFLUX REBOIL REFLUX RATIO DUTY 49 92
,
i :?
450
550
!3/FEB/83 130902
SIDE DRAW
now
,
49 71 45 0
55.0
857
ditional actuators and acceptance of the fact that this particular system is uncontrollable. Strict comparison of the performance of this control scheme to that of Doukas and Luyben is not possible here as they applied their designed linear control scheme to a nonlinear process model. In addition, they performed feed rate and composition disturbance tests, but they did not provide the process causality which would allow replication of their tests. Conclusions An application of the Direct Nyquist Array method to the design of control schemes for non-square systems has been demonstrated. The compensator design technique is borrowed from optimization theory and the resulting control scheme minimizes a quadratic performance index. It has been shown that good control performance is achieved and that actuator movement can be constrained. Nomenclature e = error vector u = control output vector (changes) K = process gain matrix C = error penalty matrix B = control penalty matrix D = pre-compensating decoupler matrix G = process transfer function matrix Q = compensated process transfer function matrix F = compensated process return-difference matrix Registry No. Benzene, 71-43-2; toluene, 108-88-3; xylene, 1330-20-7.
Literature Cited
I
45.0
TOLUENE IN
I
1
55.0
45.0
8.91
I
55.0
I
45.0 TOLUENE IN
I
55.0
4.96
Figure 6. Closed loop response of manipulated variables: reflux constrained.
in Figures 3 and 4 was repeated. Figure 5 shows the process response to the same 5% change in setpoint, of toluene in bottoms, as before. The performance was essentially the same as before but the variables equilibrated at slightly different values. Figure 6 shows that the reflux ratio was exercised over only 5% of its range in this case, a significant improvement in the performance. In comparing this approach to that of Doukas and Luyben, a trade-off must be made between the cost of ad-
Boyle, T. J. TAPPZ 1978, 61 (1). 77-8. Cutler, C. R.; Ramaker, B. L. American Institute of Chemical Engineers, 86th National Meeting, Houston, 1979. Doukas, N.; Luyben. W. Anal. Insfrum. 1978, 76, 51-8. Kouvaritakis, B.; Edmunds, J. M. “Alternatives for Linear Multivariable Control”; National Engineering Consortium, Inc.: Chicago, 1978; Paper 4.2, p 229. MacFarlane, A. G. J.; Kouvaritakis, B.; Edmunds, J. M. “Alternatives for Linear Multivariable Control”; National Engineering Consortium Inc.: Chicago, 1978; Paper 4.1, p 189. Marchetti, J. L.; Mellichamp, D. A.; Seborg, D. E. American Institute of Chemical Engineers, 74th Annual Meeting, New Orleans, 1981. Rosenbrock. H. H. “Computer-aided Control System Design”; Academic Press: London, 1974. Treiber, S. “Canadian Conference on Industrial Computer Systems”; Hamilton, Ont., May 3-5, 1981.
Shell Canada Limited Process Computer Applications Department Toronto, Ontario, M5S-2H8,Canada
Steven Treiber*
Received for review May 5, 1983 Accepted November 22,1983 Closed Loops Inc., 65 Queen Street West, Suite 1105. Toronto, Ontario M5H 2M5, Canada.
Modeling of Hydrogenation of Glucose in a Continuous Slurry Reactort A model for a continuous slurry reactor has been developed for the case of Langmuir-Hinshelwood type kinetics applicable to hydrogenation of glucose. The model predictions have been compared with pilot plant data on this system which agree well with the predicted results assuming that liquid flows in a plug flow.
Introduction Catalytic hydrogenation of glucose is an industrially important reaction as the productaorbitol-is a versatile NCL Communication No. 2856.
0 196-4305/84/ 1123-0857$01.50/0
chemical intermediate. A summary of the literature of this reaction is presented by Brahme (1972) and a detailed kinetics is reported by Brahne and Doraiswamy (1976). Generally, this process employs a slurry reactor operated either in a batch or a continuous manner. Continuous 0 1984 American Chemical Society
858
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 4, 1984
Table I. Conditions and Parameter Values Used for Simulation of Glucose Hydrogenation Using Raney-Ni Catalyst A. Reactor Diameter height
42 mm 1.0 m
B. Operating Conditions liquid (slurry) velocity, u1 1 x lo4 t o 4 x 5 x IOT3m/s gas velocity, ug inlet glucose concentration 0.7-4 kmol/m3 temperature 420-453 K pressure 2.026 X lo4 kPa catalyst loading 2-14 kg/m3
m/s
C. Physical Properties particle density 4500 kg/m3 10 mw average diameter of cat. particles porosity of cat. 0.51 viscosity of glucose solution 9.2 X lo4 kg/m s liquid density 1200 kg/m3 surface tension of glucose solution 0.05 N/m diffusivity of H2in glucose solution 9.5 X lo4 m2/s "At 453 K.
operation is preferable for large capacity plants and for obtaining good quality product. The published reports on modeling of a continuous slurry reactor (Goto and Smith, 1978; Ramachandran and Smith, 1979;Ramachandran and Chaudhari, 1980, 1983) mainly deal with simple reaction kinetics and no attempts to analyze reactions with nonlinear L-H type kinetics have been made so far. In this note a theoretical model for continuous hydrogenation of glucose has been developed considering the nonlinear L-H type rate equation applicable to this system. The performance of the model has been compared with experimental pilot-plant data available in our laboratory. The continuous slurry reactor model proposed is likely to be useful for scaleup as well as in prediction of effect of operating variables on reactor performance.
Theoretical Model The kinetics of hydrogenation of glucose has been studied by Brahme and Doraiswamy (1976) using RaneyNi catalyst in a stirred slurry reactor. They proposed following rate equation
where,
QA
is the rate of reaction mol/kg cat s.
In modeling of a three phase slurry reaction, gas-liquid, liquid-solid, and intraparticle diffusion with surface chemical reaction are important steps. However, under conditions of glucose hydrogenation (see Table I), liquidsolid and intraparticle mass transfer resistances are found to be negligible (Brahme and Doraiswamy, 1976). Therefore, in developing a continuous reactor model, liquid-solid and intraparticle diffusion effects were assumed to be negligible. In addition, it was assumed that catalyst distribution is uniform, gas feed consists of pure hydrogen, and that isothermal conditions prevail in the reactor. Also since pure hydrogen is generally used, mixing in the gas phase is considered to be unimportant. In order to account for liquid phase backmixing, a mixing cell approach proposed by Ramachandran and Smith (1979) was used in this work. Using this approach, the two extremes of plug flow and backmixed flow as well as the intermediate cases can be analyzed. In a mixing cell model, the three-phase slurry reactor is visualized as a number of backmixed reactors ( N cells) in series. Following the approach described by Ramachandran and Smith (1979) and Ramachandran and Chaudhari (1983))the equations for outlet concentrations of species A (hydrogen) and B (glucose) can be derived for a particular cell as bli (1 + K*UlO) (2) blo = 1 UlO(K*+ qa,) a10
=
+ - m2 + [mZ2 - 4mlm3]'/* 2m1
where ml = (1 + agi)(K*+ qar)
m2 = 1 + cygl
no. 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15
glucose concn, kmol/m3
cat. loading, kg/m3
1.6 2.2 2.4 2.4 2.4 2.6 2.6 2.7 2.7 2.8 3.0 3.0 3.4 3.4 4.0
3.66 3.88 0.83 3.40 2.22 0.70 3.24 1.08 3.69 3.47 1.46 2.35 2.08 2.27 1.84
13.2 14.0 3.0 12.3 8.0 2.5 11.68 3.90 13.30 12.50 5.26 4.22 7.50 8.18 6.64
At pressure = 10 130 kPa; all other runs a t pressure = 20 260 kPa.
(4)
+ arbli- (K* + qa,) (ali + a g l )
(5)
m3 = - (ali + agi)
(6)
and Substituting eq 3 in eq 2 gives the value of blo for a particular cell. The procedure for calculation of the conversion in the entire reactor is then as follows. For cell 1,bli = 1and ali = 0 if the feed liquid contains no dissolved hydrogen. Then using eq 3 and 2 , alo and blo can be obtained. These are then used as ali and bli for the second cell. The calculations are continued for N cells and the conversion in the reactor is calculated as (7) XB = 1 - (blO)Nth cell
Table 11. Comparison of Pilot-Plant Data with Model Predictions liquid rate u1 x 104, m/s
(3)
temp, K 428 428 443 420 424 463 421 453 429 423 443 438 425 428 413
obsd 96.5 86.5 99.7 77.0 88.0 99.9 70.0 99.8 65.0 67.0 99.0 75.0 81.0 77.0 65.0
glucose conversion, % predicted backmix plug flow model model 87.6 95.9 78.2 82.6 77.5 93.8 71.0 75.0 78.8 90.6 80.6 96.2 68.6 72.4 81.7 96.1 61.0 62.4 62.0 64.0 78.0 91.3 64.8 72.1 67.5 75.2 66.8 72.6 57.6 69.4
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 850
If the reactor is completely backmixed, N = 1 should be used while for a case of plug flow of the liquid N = 20 is a reasonable approximation. For intermediate situations N can be approximated as (PeL/2). This model can also be used to predict the extent of backmixing in the reactor by matching the model predictions with experimental data with N as a model parameter. Comparison of Model Predictions with Pilot Plant Data The pilot plant scale experiments were carried out in a continuous high-pressure slurry reactor and the details of reaction conditions and reactor are given in Table I. In order to predict the performance of the reactor using theoretical model described above, the rate constants in eq 1were used from the work of Brahme and Doraiswamy (1976). Accordingly, the values of kll and KA were calculated from the following equations kll = 7.75 exp(-24 244/RgT) (8) and
KA = 4.5
X
lo-* exp(38456/RgT)
(9)
The physical properties of the catalyst and glucose solution are given in Table I. The solubility of H2 in glucose solution was calculated from the following correlation (Brahme, 1972) A* =
P
-exp( -8.140 101.3
ali = dimensionless concentration of A entering a particular
cell, Az/A* alo = dimensionless concentration of A leaving a particular
cell, Alo/A* A* = concentration of A (hydrogen) in the liquid in equilibrium with the gas, kmol/m3 Ali = concentration of A in liquid entering a particular cell, kmol/m3 bli = dimensionless concentration of B (glucose) in liquid entering a particular cell, Bli/Bli,l blo = dimensionless concentration of B in liquid leaving a particular cell, Blo/Bli,l Bli = concentration of B in the liquid entering a particular cell, kmol/m3 Blo = concentration of B in liquid leaving a particular cell, kmol/m3 DEL = liquid phase axial dispersion coefficient, m2/s k l l = second-order reaction rate constant, ma kg-' (kmol)-' S-1
k L = liquid film mass transfer coefficient, m/s
K* = KAA* KA = adsorption equilibrium constant of A, m3/kmol ml, m2,m3 = constants defined by eq 4 to 6 N = number of cells, a parameter of the mixing cell model PeL = Peclet number for liquid, defined as u ~ L / D E L q = concentration ratio defined as vA* B1,,l QL = volumetric flow rate of liquid, m /s R = gas constant, J/mol K temperature of the reactor, K u1 = superficial velocity of liquid, m/s VR = volume of a single cell (reactor volume = NVR), m3 1u = mass of catalyst per unit volume of the reactor, kg/m3 XB = conversion of B
i
fl=
'>
+ (364,57/T) - 0.1193 log 101.3
(10)
The values of gas-liquid mass transfer coefficient ( ~ L U B ) were calculated using the correlation of Kawagoe et al. (1975). Using these data and the mixing cell model described above, the conversion of glucose in a continuous reactor was predicted for backmixed flow ( N = 1)and plug flow of liquid ( N = 20) for conditions under which pilot plant data were available. The results are presented in Table 11. It can be seen that most of these data agree well with the plug flow model, but it is also important to note that for most of the runs, the difference in the predictions of plug flow and backmix model is small, the maximum difference being only 17.4%. This indicates that for a conservative design, backmix model (which predicts lower performance) may also be satisfactory. For glucose hydrogenation, the effect of liquid phase backmixing does not seem to be very significant. However, further work in this area is required to arrive at general design guidelines for continuous slurry reactors. Nomenclature aB = effective gas-li uid interfacial area per unit volume of Ali/A* reactor, m7/m3
Greek Letters
agl = parameter defined as kLa,VR/QL a, = parameter defined as wkllBli,lVR/QL v = stoichiometric coefficient
= local rate of chemical reaction per unit weight of catalyst, kmol/ kg s
52A
Registry No. D-Glucose, 50-99-7; D-sorbitol, 50-70-4.
Literature Cited Brahme, P. H. Ph.D. Thesis, Bombay University, 1972. Brahme, P. H.; Doralswamy, L. K. Ind. Eng. Chem. Process Des. D e v . 1978, 15, 130. Goto, S.; Smith, J. M. AIChE J . 1978, 24, 286. Kawagoe, M.; Nakao, K.; Otake. T. J . Chem. Eng. Jpn 1975, 8 , 254. Ramachandran, P. A.; Chaudhari, R. V. Chem. Eng. 1980, 7 4 , 1. Ramachandran, P. A.; Chaudhari. R. V. "Three-Phase Catalytic Reactors": Oordon and Breach Sci. Publishers: London, 1983. Ramachandran, P. A,; Smith, J. M. Chem. Eng. J . 1979, 17, 91.
National Chemical Laboratory Poona 41 1 008, India
Prabhakar H. Brahme Raghunath V. Chaudhari Palghat A. Ramachandran*
Received for review September 18, 1981 Revised manuscript received January 10, 1984 Accepted February 9, 1984
