22
I&. Eng. Chem. process ~ e s DW. .
it may be important in forming protective surface layers. Acknowledgment The authora are indebted to the operators of the SRC-I Pilot Plant at Wilsonville, AL, for their help in providing the tower liquid samples and process information. The work reported herein is a part of the Kentucky Energy Resource Utilization Program conducted by the University of Kentucky Institute for Mining and Minerals Research (IMMR)for the Kentucky Department of Energy (KDoE). R&stry NO.NI-&C1,12125-02-9; (NHJzC03, 506-87-6;1050 carbon steel, 12731-95-2;304L stainless steel, 12611-86-8;cresol, 1319-77-3; 3b-dimethylphenol, 108-68-9; 3,4-dimethylphenol, 95-65-8; 3,4-lutidine, 583-58-4. Literature Cited Barnett, W. P.; Sa@&% A. A.; Davis, 8. H.; Baumert, K. L.; submitted for puMlcetlon in Fuel, 1982. Baylor, V. B.; Ketser, J. R.; Lsslle, B. C.; Allen, M. D.; Swfndemen, R. W. Analyds of T-105 Fractknetkn Column F a k e at the Wllsonvkb, AL, Went Refind Coal (SRC) Pwot Plant. Oak RMge Naibnal Laboratory, Oak Rldge, TN, ORNLilM-7327, July 1980. Canfidd, D. R.; Ibarra, S.; McCoy. J. D. Hy&ocarbon Process. July 1979, 58, 203. Davis, 8.: Thomes, G.; S a w ,A.; Jewkt, C.; Baumsft. K. Dlstlllation Tower Conosh: chermcal Anaglyds of Solvent Refined Coal Rocem Samples for C h W , AcMic, and Basic Compounds, IMMR180-053, Instnute for
i e w , 22, 22-31
Mining and Minerals Research, Lexington, KY, A p 1980. Davis, 8. H.;Sam.A. A.. to be presented at Corrosh/S3, Natlonal Assoc l a W of Conosbn Engineers Annual Meeting, 1983. Fontana. M. G.; CLeene, N. D. “Corrosion Enginwing”, 2nd ed.; McQraw-HiIl: New York, 1978. Jewkt, C., presentation at the workshop on CorroslonlEroslon in Coal Liqus factkn Pilot Plants, Oak Rldge, TN, Nov 29, 1979. Johnson, T.; Sa*. A. A.; Davls, B. H. DlstiHatlon Tower Corrosion: Synergistk Effects of Chlorine and Phsnolc Compounds in Coal Llqulds, IMMR4gPD23-80, Institute for Mkrlng and Mlneriais Research, Lexington, KY, Mar 1980. Keiser, J. R.; Judkins, R. R.; Baybr, V. B.; Canfield. D. R.: Barentt, W. P. Mater. Perform. May 1982, 21, 47. Sa*, A. A.; Davis, B. H.; Rlley, D.; Spencer, D.: Furman, R.; Clagget, J. “Annual Report, A Kentucky Energy Resource uwiretkn Program. July 1, l98Wune 30, 19S1”: IA.+M811061 Institute for Minlng and Minerals R s search, Lexington. KY, Dec 1981, pp 2-15. Sag&, A. A.; Davls, B. H. Mechanisms of Corrosion and A b y Response In Coal Llquld Systems Containing Chlorides, in “CorrosIon1ErosionlWear in Fossll Energy Fuel Systems”;Natbnal Aseoclation of Corrosion Engineers, Houston, TX, to be published in 1982a. Sag&, A. A.; Davb,B. H. HyctDcerbon Process. Jan. 1982b, 61, 98. Shalvoy, R. B.; Davis, B. H.; Freeman, 0. B.; Sag&& A. A. J. Vac. Scl. Techno/ 1982, 20, 1080. Sorell, 0.;LendvaKintner, E.; Buchhehn, G. M. kleter. Pwf”.apt 1982. 21, 23. Meterlala Performance In the EDS Coal Liquefaction Pilot Plant: Ilinds No. 8 Coal. Wachter, A.: StHlman, N. Trans. Electrochem. Soc. 1945, 87, 183.
Received for review February 20, 1981 Accepted June 7, 1982
Control of F l M z e d Bed Reactors. 1. Modeling, Simulation, and Single-Loop Control Studies Randall C. McFarlane, Terrence W. Hoffman, Paul A. Taylor, and John F. MacGregor’ Depamnent of Chemical Engln&ng,
McMaster Unlverslty, Uamllton, Ontarlo, Canada L8S 4L7
I n this paper a dynamic model is developed for a pilot plant fluidized bed reactor carrying out highly exothermic hydrogenoiysisreactions. The model is used to tune and to examine the performance of sirnple single-loop cascade controllers, and some preliminary on-line computer control runs are performed to evaluate further the problems in controlllng these reactors over an extended range.
Introduction In recent years considerable research on the control of temperatures, conversion, and selectivities in packed bed and tubular reactors has been published. Much less has been reported on the control of fluidized bed reactors with the exception of the literature on controlling the temperature and overall conversion in fluidized catalytic crackers where the emphasis has been on investigating the interactions between the regenerator and the reactor. Although fluidized bed reactors are in some ways less sensitive to process disturbances, they do exhibit nonlinear and time varying characteristics which give rise to control problems over an extended range of operation. This is the first paper in a series which will deal with the control of a fluidized bed reactor carrying out some complex and highly exothermic hydrogenolysis reactions. The model considered is general enough and the pilot plant reactor used is large enough that the results should represent reasonably well the main features of industrial fluidized bed reactors. The main objectives of this paper are: (i) to develop a dynamic model for the reactor system based on material and energy balances and to estimate
some of the parameters from reador data; (ii) to investigate the unsteady-state and nonlinear characteristics of the reactor through simulation; (iii) to tune and to evaluate the performance of some simple cascade controllers for temperature and selectivity using the model, and (iv) to perform some preliminary on-line computer control runs on the pilot plant using these simple controllers. All of the above investigations will illuminate some of the difficulties in controlling these reactors over a range of operating conditions and will provide a base case for the control of the reactor using single-loop conventional controllers against which more advanced controllers can be compared. Subsequent papers will deal with adaptive and suboptimal nonlinear controllers aimed at overcoming some of the deficiencies exhibited by these preliminary schemes. Process Description The Chemical Reaction Network. The reactions considered are those of the hydrogenolysis of normal butane in a fluidized bed of nickel-impregnated silica gel catalyst. The butane hydrogenolysis reactions were extensively studied by Orlikas et al. (1972). They showed
0196-4305/83/1 122-0022$01.50/0 0 1982 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 23
I
,,s
t
I
E-
1----"--1DAH,LIN (360s e d
i I I
I
I
I
T,I:
I FLOWRATE
IRATIO
oil system. This system consists of 1.27-cm tubing spiralled at 5-cm centers around the reactor wall and around approximately half of the disengaging section. Heat transfer between the coils and the reactor wall is enhanced by a heat-transfer caulking. To heat up the reactor and to maintain ita temperature during reaction, a number of electrical immersion heaters are installed in the circulating oil tank. Fine control over the temperature of the oil entering the coils is achieved by control of the cooling air flow in an air-cooled heat exchanger. The entire reactor system can be operated either manually at the site or remotely under computer control using one of the minicomputers in the department's computer control laboratory (a NOVA 1200 in this case). Under either mode of control all data collection is performed by the computer. A more detailed description of the reactor is given by Shaw (1974).
A Dynamic Model for the Reactor System When developing a model for a system it is important to keep in mind to what use the model will be put. For control purposes a high level of model complexity is not usually required; a model which is able to predict the dominant dynamic effects will usually suffice. With this in mind and knowing that eventually the model is to be used in on-line computer control schemes, we try to strike a balance between the requirement of an accurate mechanistic model of the fundamental transport phenomena in the system and a simple and easily solved model suitable for use in a computer control scheme. Reaction Kinetics. Orlikas et al. (1972) developed a mechanistic kinetic model for the reaction system described in eq l and showed that it gave very good predictions of conversion and selectivities over a wide range of conditions. These expressions and their parameters were used directly in this study. Only the catalyst activity term had to be reestimated for our system. The reader is referred to this reference for the detailed kinetic expressions. The main characteristics of the reactors are that they are all highly exothermic (AHHR N -40 kcal/mol) and have large activation energies (AI3 N 40 to 60 kcal/mol), leading to a doubling of the reaction rates for about every 3 "C increase in reaction temperature. In very simplified terms the kinetic expressions behave roughly to a firstorder dependence on the butane concentration and to a negative second-order dependence on the hydrogen concentration. Fluidized Bed Reactor Model. Prior experimental and steady-state modeling studies were carried out on this reactor by Shaw et al. (1972,1973). They found that the simple, two-phase model of Orcutt et al. (1962) described the conversion and product distribution (selectivity) with acceptable accuracy even though other models provided a better representation of the reactor under certain conditions. We have based our dynamic model upon the Orcutt model because of its simplicity. The model contains the following assumptions: (1) There are two phases in the reactor: a bubble phase and an emulsion phase. (2) Reaction occurs only in the emulsion phase. (3) The emulsion phase is perfectly mixed. (4) The bubbles are of constant diameter and pass through the bed in plug flow at velocity ub, and there is no breakup or coalescence of bubbles. (5) All gas in excess of that required for minimum fluidization flows as bubbles. (6) The bed is isothermal. (7) Mass transfer between the bubble and emulsion phases occurs at a uniform rate over the bed height. This two-phase representation is illustrated in Figure 2. Material Balances: Bubble Phase. For any compo-
-!p: ------------: I
I I
Figure 1. Schematic of the pilot plant equipment and control configurations.
that these highly exothermic hydrogenolysis reactions could be represented by the following set of four seriesparallel equimolar reactions (three of which are stoichiometrically independent) CdH10 + H2 C3H8 + CHI 2CzH6 C4H10 + H2 C3H8 + H2 CzHs + CH4 C2H6 + H2 2CH4 (1) The fluidized Bed Reactor System. A schematic diagram of the fluidized bed reactor system is shown in Figure 1. The reaction section containing the catalyst is 0.20 m in diameter and 1.83 m high. Above this is a 0.46 m diameter disengaging section. An external cyclone removes any solid that leaves this section and returns it via a dip leg. The butane and hydrogen feed rates are controlled separately from the minicomputer and then combined and preheated to reaction temperature (e255 "C) in a hot oil preheater. The hot feed gas then enters the bottom cone of the reador which is packed with stainless steel rings and passes into the reaction section through a distributor plate drilled with 230 0.14-cm holes. The nickel catalyst is supported on silica gel particles (10% Ni by weight) with diameters ranging from about 70 to 300 pm. The depth of the catalyst bed under static conditions is approximately 0.47 m. The reactor bed temperatures are measured using thermocouples inserted at several heights. Radial traverses with these thermocouples indicated that the bed was nearly isothermal, except in the immediate vicinity of the wall, as long as the gas velocity was in excess of ten times that required for minimum fluidization. The reactor is maintained under constant pressure, and the effluent gas is sampled every 360 s and analyzed with an on-line Beckman process gas chromatograph. The complete chromatographic analysis cycle requires 360 s for completion, thereby introducing a considerable dead-time in obtaining the concentration measurements. This is an important consideration later in the control studies. Cooling of the reactor is accomplished with a circulating +
+
-
24
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 p r o d u c t gas
Simultaneous solution of this set of differential equations (5) gives the emulsion phase concentrations through the reactor. If one knows the division of flow into each phase, the bed exit concentration can then be calculated from the solution of the set of eq 3 and 5. Disengaging Section. Since the concentrations are measured by a process chromatograph at the exit of the reactor, the dynamics of the disengaging section are also important, and they were modeled as a perfectly mixed tank. Empirical Correlations. Several empirical correlations were available from the literature for predicting certain physical phenomena in the bed. (i) Bubble diameter as a function of bed height was given by Kat0 and Wen (1969) as
Since the Orcutt model assumes a constant bubble diameter with respect to height, an integrated average value of Db was calculated from this expression as described by Shaw et al. (1973). (ii) The bubble rise velocity was predicted from (Shaw et al., 1973) ub
= 0.711(gDb)1'2
+ (us- umf)
(7)
(iii) The interchange rate between the bubble and the emulsion phases was calculated from the correlation (Kobayashi et al., 1965)
8 = 71 ' ( v b / D b ) feed
gas,
'C
0
Figure 2. Two-phase representation of a fluidized bed reactor.
nent i in the bubble phase its concentration as a function of the height (h) through the bed is given by dC2 (i = 1, 2, 3) (2) U b V b X = Q(C,' - Chi)
where 7 is a parameter that was estimated from reactor conversion/selectivity data. Enthalpy Balances. Reactor Contents. On the assumption that the gas and the catalyst particle temperatures are equal (TR), a combined gas/solid phase enthalpy balance can be written as (WCPB
with initial conditions C$ = Cd at h = 0. Q is the transfer or interchange rate for any component between a bubble of volume v b and the emulsion. Since v b , ub, C,i, and Q are assumed to be independent of height in the bed, the bubble material balance equations in (2) can be integrated from h = 0 to h = H to give the exit bubble concentrations as
(3) Emulsion Phase. For any component i a material balance over the entire perfectly mixed emulsion phase yields dC,' Ve= umfA,(C,' - C,') dt N b U b V b As(C0' - C ~ , H-~i)V , (i = I, 2, 3) (4) Substituting (3) into (4) then gives the emulsion phase concentrations as
+
(8)
+ €V/s cpg)-dTR = dt
Reactor Wall. The reactor wall, cooling coils, and supporting structure in contact with the wall were judged to have a mass sufficient to make their dynamic effect an important consideration in the temperature dynamics of the overall system. Lumping these elements into a single mass (M,) at a uniform temperature (Tw), an enthalpy balance yields
Cooling Coils and Air-Cooled Heat Exchanger. The temperature response of these heat-exchange units was shown to be rapid in relation to the rest of the system, and therefore the instantaneous outlet oil temperatures were calculated from the steady-state relationships for a heat exchanger with a constant heating/cooling source temperature. Parameter Estimation Although many of the parameters in the foregoing model were readily available in the literature, or had been previously well estimated from statistically designed kinetic experiments (Shaw et al., 1972; Orlikas et al., 1972), there
Id.Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 25
290
280 270
I
0 TR data
Tw
1 I
a
Toil
- model predictions
260
250 240
-
230
-
220
-
210
-
200
I
I
r
I
I
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I
100
200
300
400
500
600
700
800
I
900
I
I
1000
1100
I
1200
I
1300
1400
TIME (seconds)
Figure 3. Comparison between the model predictions for various reactor temperatures and experimental data. Table I. Parameters of the Model and Their Least-Squares Estimates Obtained from Unsteadystate Reactor Data parameters
symbol
estimate
wall heat transfer coefficient coil heat transfer coefficient apparent mass of the reactor wall heat loss to environment catalyst activity
hwAw
21.4cal/(s K)
hdc
17.36 cal/(s K)
M&,,
3000 cal/K
Qlos
0.0165 cal/s
k/k,
1.87
still remained a number of unknown parameters that had to be estimated from data collected on the fluidized bed reactor itself. These are listed in Table I. As is usual with exothermic (or endothermic) reactions, some of these reactor model parameters will be very highly correlated if only temperature data under reaction conditions are used in the estimation (Jutan et al., 1977). This can be seen from the structure of eq 9, where the parameters (h,Jw) and k/koappear in the last two terms, respectively, which represent the rate of heat removal and the rate of heat generation. Any parameter values for (h&,) and k/ko which make these terms almost equal in magnitude and opposite in sign will provide an almost equally good fit to the data. To help to reduce this correlation, two sets of data were used, one taken under nonreacting conditions (i.e., the butane feedrate was suddenly set to zero and maximum cooling applied to the reactor) and another taken under reacting conditions where both the hydrogen/butane feed ratio and the cooling oil temperature were varied. At this preliminary stage of the investigation the exit concentration data were not available from the chromatograph, and so the parameter estimates werepbtained by minimizing the sum of squares (2- Z)T(Z- 2)where ZT = (TRT,TwT,ToilT)and 2 is the estimate of 2 from the model. The parameter estimates obtained are listed in
Table I, and in Figure 3 it is shown that the resulting model predictions are quite reasonable.
Control Objectives and Univariate Controllers A desirable overall objective would be to control the production or consumption rates of all five species at desired values specified at any given time by optimizing some profitability function. Since only three of the reactions in (1)are stoichiometrically independent, this can be accomplished effectively by controlling the production rates of only three of these species. There are potentially four manipulated variables: the oil temperature, the inlet feed temperature, and the hydrogen and butane feed rates. However, there are operational constrainta which limit the freedom of control action: the reactor temperature must be maintained within certain bounds to avoid quenching or runaway of the reactions; the effective speed of response of the system to changes in the various manipulatable inputs is very different (that due to the reactant feed rates being very much faster than that due to either of the temperature variables); the temperature difference between the cooling oil and reactor should be large enough to provide sufficient heat removal but not so large as to produce excessive heat losses; and the total flow rate of the gases should be high enough to ensure adequate fluidization of the catalyst without being so high that slugging or excessive bypassing occurs. In this paper a first attempt is made at controlling this nonlinear, coupled, multivariable process by using a set of univariate controllers as shown in Figure 1. The highly exothermic nature of the reactor coupled with the large activation energies meant that direct control of the reactor temperature, TR,was a necessity for safe and stable operation. This was accomplished by manipulating the ratio of hydrogen to n-butane feed rates. The total flow rate was kept constant so as to keep the state of fluidization constant. The other manipulatable variables, oil temperature and inlet feed temperature, could not be used for this purpose since their effect on T R was slowed by heat
26
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983
No. of control interval temperature loop (30s)
No. of control i n t e r v a l s ,
=
n,
temperature loop (30s) t.: = 11
Figure 4. Response of the reactor temperature control system to temperature step set point changes with the PI controller tuned for w = 0 and w = 1 (simulation).
U
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