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Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
confirmed by taking photomicrographs of individual gel particles. Gels 3 and 7 had a large variety of pore diameters and sizes while gel 4 had pores so small as to be beyond the resolution of the electron microscope (30 A). Gel 4,with a low permeability limit, was suitable only for classification of alkanes. Gel 3 was suitable for classifying high alkanes and low molecular weight polystyrenes (less than 8300). Gel 7 was capable of classifying low to medium molecular weight polystyrenes (lo3to 5 X lo4) but did not give a very good separation of alkanes. This GPC performance further bears out the previous observations about pore size. Alkanes in the molecular weight range up to about 500 are very small molecules compared to polystyrene so that a smaller pore size gel will suffice to separate them and is generally more discriminatory. The larger polystyrene molecules require a gel with much larger pores to effect a separation or classification. The chromatographic performance of the present pilot-scale synthesized gels was remarkably similar to that of the bench-prepared gels of Moore (1964) and Freeman (1974) when the recipe modifications used in the present preparations are taken into account. However it was not possible to synthesize a gel using a completely polar diluent (100% 1-decanol) due to agglomeration of the gel particles. This meant that a gel capable of classification in the high polymer range (greater than lo5molecular weight) could not be made using this synthesis method. However, the successful synthesis of the other gels augurs well for the commercial production of a material which is becoming more and more useful in the rapid and accurate determination of molecular weight distributions of polymers. Conclusions The feasibility of pilot-scale synthesis of macroporous styrene-divinylbenzene copolymers has been demonstrated
and the optimum reaction conditions have been determined. Though particle size distributions were in general rather broad, the particles were good separatory agents in the range of alkanes and low to intermediate molecular weight polystyrenes. Acknowledgment James C. Watters acknowledges the financial assistance in the form of a teaching assistantship and instructorship awarded to him by the University of Maryland for the duration of the work described in this paper. Nomenclature (I) = concentration of initiator d = mean droplet diameter DVB = divinylbenzene EVB = ethylvinylbenzene izd = initiator dissociation rate constant iz, = propagation rate constant k = termination rate constant for microgel radicals n""= mole fraction of DVB in monomer mixture PVA = poly(viny1 alcohol) t = time X = fractional conversion of monomers at time t Literature Cited Brandrup, J., Immergut, E. H., Ed., "Polymer Handbook", 2nd ed, Wiiey-lnterscience, New York, N.Y., 1975. Fondy, P. L., Bates, R. L., AIChE J., 9(3), 338 (1963). Freeman, D. H., "The Study of Chemical Interactions as Applied to Forensic Science", Technical Report, Universily of Maryland, College Park, Md., 1974. Moore, J. C., J . Polym. Sci., Part A , 2, 835 (1964). Storey, B. T., J . Polym. Sci., Part A , 3, 265 (1965). Trommsdorff. E., "Colloquium on High Polymers", Freiburg, 1944. Trommsdorff, E., Kohie, H., Logolly, P., Makromol. Chem., I,269 (1948). Watters, J. C., Ph.D. Thesis, University of Maryland, College Park, Md., 1977.
Received for review July 31, 1978 Accepted March 24, 1979
Evaluation of Use of Syngas for Coal Liquefaction Rand F. Batchelder and Yuan C. Fu' Pittsburgh Energy Technology Center, U S . Department of Energy, Pittsburgh, Pennsylvania 75273
Coal liquefaction processes by direct catalytic liquefaction or extractive hydrogenation could benefit economically by using syngas in place of hydrogen. Data are presented to show that the hydrotreating of bituminous coal using
syngas and steam with CoMo-K,CO, catalyst gave product oil similar to that obtained from the hydrotreating using H2 and Co-Mo catalyst. A comparative process evaluation has been made for the direct catalytic liquefaction of coal using H, and syngas. Summaries of mass balance, energy balance, and cost estimation are presented. The use of syngas reduces the capital and operating costs by eliminating shift convertors and gas purifying systems and thus could reduce the process cost of SYNTHOIL and H-coal by about 14%. The process economics could b e further improved by the use of a high-pressure coal gasification process for the syngas production.
Introduction With the feasibility of coal liquefaction having been demonstrated over 40 years ago, the major emphasis since then has been on process modifications and catalyst development to improve the process economics (Bergius, 1922). Cost analysis of a typical coal liquefaction process (Kattel, 1975) reveals that as much as 30% of the overall cost is related to hydrogen production. There have been some attempts to use carbon monoxide or carbon mon-
oxide-containing gas for liquefying lignite (Appell et al., 1972),liquefying bituminous coal (Fu and Illig, 1976), and hydrotreating hydrocarbonaceous liquids (Vernon and Pennington, 1973). The proposed modification is to use syngas (H2 + CO) and steam instead of H2 as feed gas to the reactor. The advantages of this modification are presented. The bench scale approach in the direct liquefaction of coal consists of treating a slurry of coal in solvent under
This article not subject to U S . Copyright. Published 1979 by the American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979 595 Table I. Hydrotreating of Bituminous Coal' (Coal: SRC Liquid = 1:2.3, 3000 psi, 450 "C, 1 5 min) syngas (H,:CO = 2 : l )
% K,C03 surface area, m2/g conversion, % oil yield, % asphaltene formed, % S in oil product, 5% kinematic viscosity, cSt at 60 " C syngas or H, consumed, SCF/lb of maf coal
H2
CoMoK,CO,b
CoMoK,C03b
CoMoK,C03C
CoMoBaAcb
NiMoK,C03b
NH,Mo
11.2 74 94 68 42 0.40 20
5.0 133 90 60 42 0.44 18
7.7 136 90 63 32 0.41 18
(9.9)f 141 89 61 24 0.41 16
10.1 140 89 59 32 0.40 21
90 51 19 0.37 13
123 94 71 30 0.39 15
153 91 62 25 0.33 13
93 62 37 0.44 20
8.6
9.9
10.0
10.0
9.0
11.2
10.7
11.6
10.2
-
CoMod
-
CoMoe
NH,Mo
-
-
' Data are given in weight percent of maf coal. CoMo or NiMo impregnated with K,CO, solution. Laboratory prepared sample with K , C 0 3 substituted for alumina. Harshaw 0402. e Laboratory prepared sample with the same composition as Harshaw 0402. f Percent barium acetate. high H2pressure at temperatures of 400-475 "C. The large coal molecules fragment thermally and are hydrogenated via hydrogen transfer from a donor solvent. The liquid product is formed as the H/C atomic ratio of coal increases from 0.7 to an approximate value of 0.4-1.0. Lighter liquid products could be formed with additional H2 uptake. A catalyst would serve to promote hydrogenation and desulfurization processes during liquefaction. The required H2, usually 3-6 wt 70 of the coal feed, is produced by gasification of coal and residual char to produce a synthesis gas. The synthesis gas as produced is a mixture of H2,CO, H 2 0 , and some C02. The "raw" syngas is then passed through a shift converter to produce C 0 2 and additional Ha. Since the gas still contains about 2-370 residual CO, further processing will be required before the gas can be used with a CO-sensitive catalyst (Vernon and Pennington, 1973). Synthesis Gas Concept The syngas approach is to bypass the expensive gas purification and shift conversion step and send the product from the gasifier directly to the liquefaction reactor along with the recycle gas and added steam. The CO in the feed gas reacts with steam to form H2 (CO + H 2 0 H2 + C02) in the liquefaction reactor rather than separately in the water-gas shift system. This can be accomplished by utilizing a bifunctional catalyst in the liquefaction reactor, consisting of the conventional CoMo-Si02-A1203 for liquefaction and desulfurization, which is impregnated with K2C03to catalyze the shift reaction. The obvious advantage of this modification is the elimination of the capital and operating cost of the purification and shift steps. In addition, there will be a slight improvement in the thermal efficiency of the process. There is a need, however, for a larger recycle gas cleanup step capable of removing both H2S and C02. Before the process can be considered viable it must be proven that the liquefaction activity in the presence of CO, H2, and H 2 0 is comparable to that with H2. To evaluate the effect of substituting synthesis gas for H2,we decided at first to look at the SYNTHOIL process. The Experimental Section explains how the direct catalytic coal liquefaction performance using H2 and H2-CO was compared in a set of autoclave experiments. The results of a batch reactor cannot be simply used to predict the steady-state conditions in a continuous commercial reactor. An attempt was made, however, to calculate flow conditions for coal liquefaction processes using H2 and H2-CO on the same basis using autoclave data. The objective is a preliminary study to evaluate and compare the potential merit of using syngas rather than to calculate the accurate results for a commercial process. The evaluation of
-
SYNTHOIL by Kattel(1975) was used as the basis for the conceptual design. Experimental Section and Results The concept of liquefying coal with syngas was tested in a stirred autoclave. The autoclave was charged with 30 g of West Virginia bituminous coal, 70 g of Solvent Refined Coal process solvent, 10 g of H 2 0 , and 2-3 g of crushed CoMo-K2C03 catalyst. The autoclave was then charged with a 2:l H2-CO gas mixture to 1500 psig, heated to 450 "C (operating pressure 2800-3000 psi), held at 450 "C for 15 min, and then rapidly cooled by running water through an immersed cooling coil. The CoMo-K2C03 catalysts were prepared in three ways: (1)by blending ground CoMo-Si02-A1203 catalyst (Harshaw 0402T) with K2C03powder, (2) by impregnating the CoMo catalyst with aqueous carbonate solution, and (3) by introducing K2C03early in the preparation of CoMo catalyst in place of silicated alumina and keeping the ratios of Co and Mo to alumina constant. We have also tested CoMo catalysts impregnated with sodium carbonate, potassium acetate, and barium acetate, NiMo catalyst impregnated with KZCO3, and NH,Mo catalyst. Some results have been presented previously (Fu and Illig, 1976). Table I shows some representative results as well as hydrotreating data obtained with pure H2 and CoMo-Si02-A1203 catalyst. The performances with H2-CO and H2 compare rather closely in all categories except that the asphaltene levels and kinematic viscosities appear to be somewhat higher for the synthesis gas product. This may not be of great significance if the product were to be used as boiler fuel. Process Evaluation Using the yields obtained from the autoclave experiments and the process parameters of the SYNTHOIL process, material balances were derived for both the H2-CO and H2 systems. An energy balance was then calculated for the H2-CO process scheme. Finally, an economic comparison of the two alternatives was performed, based on an economic evaluation of the SYNTHOIL process made by Kate11 (1975). The benefit of using a high-pressure gasifier (such as in the Texaco process) and a modification of the Exxon Donor Solvent Process using syngas were also examined. A. Direct Catalytic Liquefaction of Coal. The flowsheet for the modified direct catalytic liquefaction process is shown in Figure 1. Synthesis gas from the gasifier is sent directly to the liquefaction reactor eliminating the shift and purification steps. Steam is added to the liquefaction reactor to promote the water-gas shift reaction. Now that this reaction is taking place in the
596
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979
STREAM COMPOSITION COMPONENT1 Ibs (vol%l MAF COAL 15 I I 4 ASH CHAR
~
1600 16.6
1
Ibs ~ ( v o l % Ibs ~
l(vol%)l
Ibs
I
O I 1600
' 1073
' ( v o l % l l lbs
i 1
1
261 COMPOSITION I I
I
I 5 07
58 179
16081
(0051 (053) (7341
,
02
0I
( 1 321
(043) (005)
1
scf
81820
676IO
76350
1
Table 11. Product Yields and Analysis a t Steady State (Basis 100 lb of Maf Coal Feed) syngas
H,
Input maf coal H,
co
H*O total H, or H, + CO consumption, SCF
100.00 100.00 1.17 3.19 35.20 0.00 25.81 0.00 -~
162.18 661
103.79 615
output 11.37 71.38 9.08 55.31 2.54 0.50 6.00
C,-C, oil H2O
co
2
H2S
"3 char
~~
162.18 elemental
coal
C
73.8 5.2 7.2 1.3 3.8 8.2 0.5
H 0 N S ash moisture
10.80 17.87 5.99 0.00 2.54 0.59 _6.00 __ 103.79
product product oil oil 88.3 7.5 2.6 1.2 0.4
-
-
88.3 7.7 2.5 1.1 0.4 -
1
55
I
359
(100) 6864
330
2479 l(26001
(I 26)
202
0
1 124356 (1001
114481
1
1 (0541
55 1 (090)
(100) 6920 I3030
(100) 7780
liquefaction reactor, the C 0 2 produced there must be removed in the recycle gas cleanup step. Therefore, the recycle gas cleanup step must be designed to remove both C 0 2 and H2S. It is desirable to produce a concentrated stream of H2S to allow efficient use of the Claus process for converting H2Sto sulfur. The concept employed in the Giammarco-Vetrocoke process (Riesenfeld and Mullowney, 1959) for acid-gas removal meets these requirements, but its effectiveness on a commercial scale is untested. It will remove both C 0 2 and H2S from a gas stream and process it into two separate streams of C 0 2 and H2S. The aqueous stream from the vapor-liquid separators is sent to an ammonium sulfate and sulfuric acid recovery process. The product slurry from the high-temperature separator is centrifuged. The underflow from the centrifuge is sent to a char de-oiling process for recovery of oil entrained in the solids. Unconverted char from this step is sent to the gasifier for further carbon utilization. Mass Balance. The basis of the flowsheet calculation is briefly described in the Appendix. There are two major problems associated with the batch autoclave data: (1)the solvent is not a recycle solvent derived a t the identical steady state condition, and (2) the material balance is usually poor with a recovery in the range of 94-9870. Batch data from the autoclave experiments were used in the calculation as shown in the Appendix. The conversion of CO is calculated by assuming water-gas shift equilib-
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979 597 Table 111. Overall Mass Balance
COAL H E A T i X C HRA hEC EC- 7KE - Y S
H,/CO
H2
In
RECYCLE
2000.0 141.4 187.0 558.2 2886.6
2000.0 108.9 223.5 0 380.3 2112.7
249.1 118.9 169.6 365.0 946.4 1037.6 2886.6
30.4 159.9 169.8 692.1 626.0 1034.5 2712.7
0
~
'-FUEL
OIL
raw coal gasifier steam feed gasifier 0, feed shift converter steam reactor water feed total
TpRoc i
~
GAS
out water condensate waste water slag fuel gas H,S + CO, oil product total
rium at 475 " C (28 "C approach) with a H2:CO:H20feed of 2:1:0.4. The resulting yields for a continuous reaction are shown in Table 11. The flowsheet derived from these yields is shown in Figure 1. The overall mass balances for the H2-CO and H2 processes were obtained on the basis of one ton of West Virginia bituminous coal feed (see Table 111). The mass balance over the reactor, which operates at 4000 psig and 450 "C, is based on the simulated yields. The design parameters used in the study are listed in the Appendix. It was assumed that the recycle gas scrubber provided complete removal of C 0 2 and H2S. The flow and composition of the off-gas from the vapor-liquid separators were estimated from vapor-liquid equilibria of the various components with the liquid oil at the separator temperatures of 150 and 40 "C. The gasifier mass balance was based on the total gas demand, coal and char feed, operating condition of 450 psi and 982 "C, 95% carbon conversion, and a water-gas shift equilibrium at 1010 "C (28 ' C approach). Energy Balance. The thermal efficiency of the SYNTHOIL Process has been estimated by Akhtar et al. (1974). The energy balance for the H2-CO process was computed and is shown in Figure 2. It is based on the net heats of combustion at the specified temperature of each stream, neglecting pressure effects. The net heats of combustion of the coal (12390 Btu/lb), oil (16300 Btu/lb), and the char (4500 Btu/lb) were obtained experimentally. The heat capacities for coal, char, ash, and oil were obtained from IGT's Coal Conversion Data Book (1976). The energy balance across the reactor was calculated using eq 6 in the Appendix, assuming an adiabatic reaction with an estimated heat loss. The conceptualized plant is totally self-sufficient with the coal being the only energy input. The plant contains its own steam and
DA'A
?AS15
GCC
eTL
hPuT
COAL *EA-
CF
COM@UjTlOh 9 L T l
Figure 2. Thermal balance.
electricity plant. The overall thermal efficiency is 75.6 '70 as compared to values of 67.8% (Kattel, 1975) and 74.9% (Akhtar et al., 1974) for the SYNTHOIL process using H2 The advantage of the syngas system is a result of the elimination of the inefficient two-stage shift reactors. Economics. The methods used to perform the economic analysis of the two alternative cases followed those used in Katell's report. The main objective of this economic evaluation is to obtain a relative cost comparison of the two processes rather than to yield accurate estimates. The sequence of steps in the evaluation was as follows: (1)size major equipment, (2) cost major equipment, (3) use standard factors to cost miscellaneous equipment, (4) calculate utility balance, (5) size and cost utility sections, (6) determine operating costs, and (7) do a discounted cash flow analysis over the life of the plant to determine the product selling price at various rates of return and coal prices. The analysis was carried out for both the CO-H2 and H2 cases. A unit cost table, which shows the cost distribution among the various sections of the process, is shown in Table IV. Two major differences are apparent in the unit cost table. The recycle gas cleanup and byproduct recovery sections in the H2-C0 process are more expensive than that in the H2 process because of the necessity of removing C 0 2 in addition to H2Sin this stage. The cost of the shift and purification section is $1.90/bbl in the H2 process, but is totally absent in the H2-CO system. Thus the H2-CO system results in a net cost advantage of $1.59/bbl or about 14% of the total process cost. High Pressure Gasifier. A beneficial modification to the H2-C0 process is to employ a high pressure gasifier to be operated at a pressure in the range of 2500-3000 psi, equivalent to that required in a liquefaction reactor. This change would further increase the thermal efficiency and
Table IV. Unit Cost, $/Bbl of Product Oilatb coal and paste hydroPrep genation
heat exchange
operating
0.90
2.10
0.67
capital
0.67
2.18
1.18
credits
0
2.37
0
process cost
1.57
-
1.91
1.85
recycle gas char gasishift and byproduct flue gas cleanup de-oiling fication purification recovery processing 0.51 0.17 0.42 0.22 - 0.11 0 0.82 0.39
0.21
1.99
0.36
0.17
0.32
0
0.31 0.42 0.42
0.43 0.43
0.53
0
- 0.23
- 0.11
0.25
2.16
coal cost oil cost Basis: 25 000 bbl/day; W.Va. coal, $25/ton; 15% return on investment.
H,.
0 1.21 0 0.69 0 0 1.90
0.73 0.84
0.63
total
___7.12
8.10 5.83 6.43 - 3.03 - 3.03 9.92 11.50
9.45 19.37 20.95
The italicized values designate the cost using
,
598
Ind. Eng. Chern. Process Des. Dev., Vol. 18, No. 4, 1979
Table VI. Coal Liquefaction by Solvolysis (Solvent:coal= 2.3:1, 3000 psi, 450 '(3, 1 5 Min)
SOLVEYT HIDROTREAT YG STELll
1
1L -
4 2
~
$
'-
A
synga (H,:CO = 2 : l ) solvent SRC treated SRC conversion, % 89 90 asphaltene formed, % 42.7 32.6 S in oil product, % 0.64 0.54 kinematic viscosity, 30.1 22.7 cSt at 60 " C
30.
W
r, .-I
H2 treated SRC 89 91 49.3 25.6 0.65 0.44 30.8 14.8
SRC
Figure 3. Solvolysis of coal using syngas. Table V. Hydrotreating o f SRC Solvent (425 "C. 60 min) syngas original (H,:CO = 2 : l ) catalyst H,O added, pts/100 pts initial pressure, psi operating pressure, psi product analysis, % C H N S
0 kinematic viscosity, cSt at 6 0 "C
H, COMO-K~CO, CoMo 10 0 1220 1520 2600 2450
88.8 7.4 1.1 0.65 2.05 12.2
89.1 7.6 1.0 .42 1.88 7.8
Elemental Balance for Continuous Reaction. Yi = yield, (lb of i out - lb of i in)/lb of maf coal: F;k = wt
89.4 8.0 0.8 .14 1.66 5.4
improve the economics. From the energy balance (Figure 2) we see that 2% of the input energy exists as latent heat in the hot gasifier output. Also 2% of the input energy is used to compress the gasifier product gas. By employing a high-pressure gasifier all of the latent heat is recovered, the inefficient gasifier heat exchanger is eliminated, the make-up gas compressor is not required, and the reactor preheat duty is reduced. Thus the use of higher pressure gasifier increases thermal efficiency by about 4%. A minor offsetting change is the increased pressure of O2 and steam necessary to feed the gasifier. B. Extractive Hydrogenation of Coal. Coal liquefaction processes by extractive hydrogenation such as the Exxon Donor Solvent Process can also be benefited economically by using syngas in place of H2. A conceptual process scheme is presented in Figure 3. Coal is dissolved in a recycling solvent in the absence of catalyst under H2-C0 pressure, and part of the liquid product is subsequently hydrotreated with syngas and steam in the presence of CoMo-K2C03 catalyst to make the recycle solvent. Experimental data were obtained by initially hydrotreating an SRC solvent with syngas and steam in the presence of CoMo-K2C03 catalyst and subsequently using this hydrotreated solvent to extract coal in the absence of catalyst. Table V shows the autoclave experimental results of hydrotreating the SRC solvent with syngas and H2. Table VI shows the comparison of using the syngas hydrotreated solvent and the H2 hydrotreated solvent for coal solvolysis under H2-C0 and H2 pressures, respectively. From both tables, no significant difference in the quality of the product oil or solvent was observed between the syngas and H2 systems. Appendix Design Calculations. The flowsheet upon which the design calculations are based is shown in Figure 4.
Assumptions. (1) The yields of C1-C4 gas (Yclq ) and char ( YChar) and the elemental compositions of C1-d4, oil, and char observed in the autoclave experiment are used in the continuous reaction design. (2) The yield of carbon monoxide is calculated assuming the water-gas shift reaction to be at equilibrium at 477 "C (28 "C approach) with a H,:CO:H20 reactor feed of 2.05:1:0.4.It is also assumed that carbon dioxide is involved only in the water-gas shift reaction, thus YCo,= -Yco. ( 3 ) The remaining unknowns are YHp,YH,O, YH2s,Y" , and Yoi1. These are determined by solving eq 1-5 simuftaneously. The other unknown, Tout,is solved from eq 6. Design Parameters. 0il:coal ratio = 2.12; SCF/lb slurry reactor feed = 15.8;reactor feed rate = 280 lb/h-ft3 catalyst; reactor inlet temp = 425 "C; reactor inlet press = 4200 psig; reactor exit temp = 449 OC; reactor exit press = 4000 psig; process heater eff = 80%: electric generation eff = 40%. Economic Evaluation. Based on April 1977 CE Index; 15% discounted cash flow. Literature Cited Akhtar, S..Lacey, J. J., Weintraub, M., Reznik, A. A., Yavorsky, P. M., "The SYNTHOIL Process-Material Balance and Thermal Efficiency", Paper No. 356, Bureau of Mines, Pittsburgh Energy Research Center, Dec 1974. Appell, H. R., Miller, R. D., Wender, I., presented before the Division of Fuel ChemisQ, 163rd National Meeting of the American Chemical Society, Boston, Mass., Apr 10-14, 1972.
Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 4, 1979 Bergius, F., German Patent 303272 (1922). Fu, Y. C., Illlg, E. G . , Ind. Eng. Chern. Process Des. Dev., 15, 392 (1976). IGT, "Preparation of a Coal Conversion Systems Technical Data Book". Final Repod FE-1730-21, 1976. Kattel, S., "SYNMOIL Process-LiquM Fuel from Coal Plant", Report No. 75-20, Bureau of Mines, Morgantown, W. Va., Jan 1975.
599
Riesenfeld, F. C., Mullowney, J. F., Oil Gas J . , 57(20), 86 (1959). Vernon, L. W., Pennington, R . E.. U.S. Patent 3719588 (1973).
Received for review September 11, 1978 Accepted M a r c h 12, 1979
Feedback Control of a Two-Input, Two-Output Interacting Process Mohan Bhalodia Exxon Co. U.S.A., Linden, New Jersey
Thomas W. Weber' State University of New York at Buffalo, Amherst, New York 14260
A model for a two-input, two-output interacting process is described which characterizes the four open-loop responses by six time constants and two interacting gain factors. The system parameters are reformulated in terms of the
normalized amplitude ratio and critical frequency of each loop. Proportional-integral controllers are used in two feedback control loops. The optimum behavior for a step input disturbance in one loop is determined where the criterion function is the sum of the integrals of the square of the error for each loop. The Continuous Cycling Method of controller tuning is applied to the model. A simultaneous and several sequential schemes are tested and the results are compared with those of the optimum settings. Tuning parameters for gain and reset time are suggested. The gain parameter is about the same as that suggested by Ziegler and Nichols (1942) for single loops, but the reset time parameter is one-fourth as large.
Introduction Multivariable control systems, in which there are several output variables under feedback control, are rather common. For example, in a simple distillation column, it may be necessary to control both the overhead and bottoms compositions. This can be achieved by manipulating the reflux ratio and the boilup rate. A fluid catalytic cracking unit requires close control of the heat and carbon balances by manipulating the catalyst circulation rate or feed temperature and the air rate to the regenerator. In both of these examples, there is some interaction between the controlled variables and the manipulated variables. Interactions vary to a considerable degree in their severities. In driving an automobile, both direction and speed are under control, but the interaction between these variables is normally negligible when the pavement is dry and the speed is within the legal limit. On the other hand, there is a strong interaction between the overhead and bottoms compositions of a distillation column. In addition to these two controlled variables, there would be several others such as pressure and the liquid levels in the reflux drum and reboiler. All of these control loops interact to some extent, but some of these interactions are weak and of no great importance. Multivariable control systems have not received the same degree of attention as single variable systems because they suffer from the same "curse of dimensionality" as multivariable optimization problems. To make matters worse, many system models and configurations are possible. In spite of these obstacles, the studies described in this paper are based on a model that can reasonably represent the behaviors of many different processes. This model is then used to gain some insight into the behavior of multiple loops under optimum conditions and to develop 0019-7882/79/1118-0599$01.00/0
some procedures for tuning multivariable control loops using the Continuous Cycling Method (CCM) of Ziegler and Nichols (1942). Literature Review Most of the research in multivariable control has been concerned with the decoupling of interactive loops using specially designed networks, with emphasis on the servo problem of decoupling the loops for changes in set point. If perfect decoupling is achieved, a change in set point for one variable will only affect the controlled variable associated with that set point, and all other controlled variables will be unaffected. In process control, the regulator problem is very often of more importance since changes in set point may be made only occasionally while load disturbances are occurring continuously. Two methods of analysis have been used in the design of noninteracting control systems. One is the transfer function or the frequency domain approach, and the other is the state variable or time domain approach. MacFarlane (1970) outlined some basic features of multivariable controller design and various techniques available. He emphasized the importance of using both the time domain and frequency domain approaches. Early research concentrated on the use of transfer functions. Freeman (1957) outlined a procedure for determining the controller transfer functions based on those of the process and the desired overall responses. In a second paper, Freeman (1958) discussed problems of physical realizability and stability. Kavanagh (1957) presented solutions to two servo design problems, one in which there was a specified response to a given input, and the other with an unspecified response. Kavanagh (1958) also considered the problem of the response of the system 0 1979
American Chemical Society
