1924
Ind. Eng. Chem. Res. 1987, 26, 1924-1930
On-Line Optimization Using a Two-Phase Approach: An Application Study Chun Y. Chen' and Babu Joseph* Chemical Engineering Department, Washington University, St. Louis, Missouri 63130 A two-phase approach for on-line optimization of chemical processes was proposed by Jang e t al. This approach addresses some crucial difficulties encountered with chemical processes such as imperfect models, nonlinearity, presence of operating constraints, and the multivariable nature of most processes. T h e approach was adapted for application to an industrial scale problem, namely, the optimal operation of a packed tubular reactor for the production of ethylene oxide. This application exhibits many characteristics cited above which makes on-line optimization a challenging problem. Results using a simulation study show that the two-phase approach holds considerable promise. The paper concludes with suggestions regarding the application of the proposed approach to industrial processes. Considerable progress has been made in the field of chemical process control in the last decade. The availability of low-cost microcomputers is revolutionizing the field of instrumentation and control hardware. Process engineers now have access to vast amounts of operational information and computing power. Networking allows access to larger computers from the plant operating site. Plant managers are increasingly looking into ways of reducing energy consumption, raw materials, waste, and production costs using these newly acquired capabilities. This is evidenced by the recent publications from industry extolling virtues of computer control and plant optimization (Haggin, 1984; Cutler and Perry, 1983; Prett and Gillette, 1979; Webb et al., 1978; Smith and Brodman, 1976; Morari et al., 1980). The term on-line optimization is used here to indicate the continuous reevaluation and alteration of operating conditions of a process so that the economic productivity of the process is maximized subject to the operating constraints. In the hierarchical approach to the control of process systems, the optimization layer lies between the regulatory layer and the production scheduling layer. The results of the optimization layer are implemented by changing the set points of the regulatory controllers. The economic payoffs resulting from even small improvements in the process performance are economically significant because of the large amount of material being processes. For a typical ethylene plant with a capacity of about 1X IO9 lb/year, a 1%improvement in yield can lead to savings of as much as $1.5 X 106/year. Cutler and Perry (1983) estimate that (based on actual implementation) the economic value added by the process can be improved by 3-5% through the on-line optimization techniques. For a plant that breaks even a t about 70% capacity this 3-5% improvement is quite significant. Although a variety of techniques have been proposed in the literature for on-line optimization, the model-based approaches have proven to be superior. The main problem here is with errors in modeling that affect the performance of the on-line optimization scheme. The two-phase approach, presented in Jang et al. (1987), attempts to solve this problem by incorporating an identification phase to reconcile the plant/model mismatch. The objective of this article is to evaluate this approach in a study involving the on-line optimization of a packed tubular reactor for the production of ethylene oxide. This process was selected
* Author t o whom correspondence should be addressed.
Present address: National Chung-Cheng University, Taiwan, Republic of China. 0888-5885/87/2626-1924$01.50/0
because it represents a highly nonlinear process that is difficult to model. Of particular interest to us is the performance of the algorithm using imperfect models. The study is conducted by using a simulation model of the plant and then attempting to optimize its operation by using a series of process models with deliberately introduced modeling errors, model uncertainties, and model parameters which were assumed to be unknown. This mimics what might happen in a real application.
Two-Phase Approach A brief summary of the two-phase approach toward on-line optimization is given here to maintain continuity of the paper. For details the reader is referred to the article by Jang et al. (1987). The on-line optimization problem can be stated in abstract form as follows: Given an operating plant with measurements 9 and a set of manipulable inputs m (these may be set points of regulatory controllers), determine the values of m as a function of time which will maximize some measure of the profitability of the plant, while meeting the operational constraints of the process. The two-phase approach begins by postulating a model for the plant of the form 1 = fi(x,m,p,t) (la) fdx,m,p,t) = 0 Ob) with observations y modeled by Y = g(x,m,p,t) (lc) and constraints modeled by h(x,m,p,t)I 0 (Id) The variables are defined as follows: x, state variables; m, manipulated inputs; p , unknown parameters and unmeasured disturbances. No other restrictions are placed on the model. This is quite significant since we can inorporate models based on physical and chemical laws describing the events in the system. This type of model will have a wider range of applicability and physically more meaningful variables to identify. However, the computational complexity increases with detailed models, so a compromise has to be made between the level of detail used and the number of parameters to be estimated on-line. The first phase of the two-phase approach consists of identifying the unknown parameters and unmeasured disturbances entering the process by using all available process measurements. In the second phase, this identified model is used to determine the optimum operating strategy. The two phases are repeated periodically in 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1925
7 I
y
,
optimum meratine
4
Disturbanc,es
\ I-
PLANT
T-
I
Primary Outputs
Measurements
Compare :he actual measurements wilh
the model predictions
Identification phase
I
: I
Figure 1. Schematic of the two-phase approach to on-line optimization.
tandem to follow continually changing input disturbances and process parameters. The identification problem can be stated as follows: Given a set of observations, 9, determine the values of unknown parameters and input disturbances, p , and the current state of the system, x , such that the difference between model predictions and plant observations is minimized. As shown in Jang et al. (1987), this reduces to a constrained optimization problem which can be solved by nonlinear programming techniques. The optimization problem can be stated as follows: Given an objective function, Q , ( x , n , p , t )determine , the operating conditions, m(t),such that Q, is maximized (or minimized) subject to the model equations and constraints given in eq la-ld. Implementation. The two-phase algorithm is implemented as shown in Figure 1. The identification phase is activated whenever a preset discrepancy between model predictions and plant measurements arise. This could be caused by a change in one of the inputs entering the process or a change in one of the parameters such as catalyst activity. The identification phase estimates the new set of variables, p , which is used by the optimization phase. If the plant dynamics are relatively fast compared to the frequency of the input disturbances, then the plant will be operating a t steady state most of the time (except for small perturbations which are corrected by the regulatory controllers). In this case, the on-line optimization problem is simplified since we need to consider only steady-state models. As we will see below, the example chosen in this application study can be treated this way.
Process Description The example we have chosen for study is the optimal operation of the ethylene oxide reactor. The basic reaction chemistry is R1:
gas phase
CZH4 + ‘ / 2 0 2
C2H40
AH = -117 kJ/gmol with undesirable side reactions: CzH4 3 0 2 2C0, + 2Hz0 R2: A H = -1334 kJ/gmol
+
-
-
C2H40+ 5/202 2C02 + 2Hz0 AH = -1217 kJ/gmol The selectivity of ethylene oxide is in the range 50-80 70. R3:
The oxidation is carried out in packed tubular reactors cooled on the outside along with an inert diluent gas such as nitrogen. Approximately 60-80% of the ethylene is converted. The unconverted ethylene is separated and recycled. In this paper we will focus our attention on the on-line optimization of the ethylene oxide reactor. The presence of undesired side reactions in the EO reactor puts greater emphasis on the optimization problem since higher conversion (as may be required by higher demand) generally means greater amounts of valuable feedstock will be lost as carbon dioxide. Substantial changes in yield and selectivity can occur as the catalyst activity and other process parameters change. For the purposes of this study, the productivity, defined as production of ethylene oxide per unit of ethylene feed, is selected as the objective function. The reactor is of the shell-and-tube type, with thousands of tubes of 20-50-mm inside diameter. The reaction tube lengths are 6-12 m, and contact times range from 1 to 5 s. These tubes are filled with a silver-based supported catalyst of 3-10-mm diameter and supported on a carrier material with a surface area usually < 1 m2/g. The yield (moles of product produced per moles of ethylene consumed) is normally 60-77% depending on catalyst type, per pass conversion, reactor design, and operating conditions (Cawse et al., 1978). Industrial operating conditions are as follows. Reaction temperatures may range from 200 to 350 “C, but in practice temperatures from 260 to 290 “C are commonly used when air is the oxidant and temperatures as low as 230 “C are employed when pure oxygen is used. The reaction proceeds at pressures of 1-3 MPa (10-30 atm) with pressure drops of 40-150 kPa. Plant Simulation. In order to conduct the experiments in optimization, the following approach is adopted. A detailed model of the reactor is generated. This model will serve as a “simulated plant”. The two-phase algorithm is implemented by using simplified models to emulate the approximations one must make in modeling a real plant. We recognize that this is only an approximation of actually testing the algorithm, yet a great deal can be learned about the effect of model simplifications, as will be shown later. To keep the discussion simple, we will refer to the simulated plant as the “plant”. The plant simulation model is based on the following assumptions. 1. Intraparticle temperature and concentration gradients are negligible. This is reasonable for small-diameter catalyst pellets used in EO reactor. 2. The only transport mechanism operating in the axial direction is the overall flow itself. This assumption is reasonable because of the very high gas velocities present. 3. The bulk gas velocity is constant. This would be valid when the Nzconcentration used in the feed is large. 4. Physical properties such as density, heat capacity, heat of reaction, and heat-transfer coefficient are assumed to be independent of temperature. 5. The partial pressure gradients between the catalyst surface and bulk gases are negligible. 6. The pressure drop through the bed is negligible. The assumptions can be removed at the expense of adding the complexity of the model. However, since the objective here is not to match the behavior of an ethylene oxide reactor precisely, a model that retains the major process characteristics should yield meaningful test results. The resulting pseudohomogeneous reactor model consists of four coupled nonlinear partial differential equations
1926 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 Table 11. Operating Data on the EO Reactor reactor dimensions reactor length, L = 6 m tube diameter, 2ro = 0.03 m inlet conditions kmol/m3 C,,,, = 1.0, CB,in= 0.0, Cref = 8.283 X T I , = 1.01, T,,,, = 0.85, Tref= 535 K gas flow rate, u = 2.166 m/s, coolant flow rate, u, = 2.5 m/s outlet conditions CA = 0.17085, C B = 0.67887 T = 0.856 33, T, = 0.85007 (countercurrent flow) conversion of C2H4 = 0.829 155, yield of C2H40 = 0.818 744
Table I. Reaction Kinetic Data Used in This Work activation energy E,, J/mol 6.069 X lo4 9.228 X lo4 E,, J/mol 8.480 X lo4 E3,J/mol preexponential factor 2.8 k l , kmol/ (m%) k,, kmol/(m2.s) 7.0 X lo2 14.4 k S , kmol/ ( m 2 4 heat of reaction -1.17 X 10’ AH1,J/kmol -1.334 X lo9 AH,, J/kmol -1.217 X lo9 AHs, J/kmol adsorption equilibrium const 7.155 x 10-4 KE, bar-, 3.3 x 10-5 KEO,b a r 2
-___--___\.
I
representing material balances for ethylene and ethylene oxide and energy balances for the reactor and the coolant: ethylene balance:
-1
Finite-Difference Model
I
6 CoIIo Pts
I
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0 3 C O l l O PtS
I I I
I
I W
a
I
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2
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ethylene oxide balance:
W
%
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F
energy balance on reactor: 1l o04 ]
1021 ’
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00
/
I I 1
1
02
1
1
1
1
1
I
04 06 08 REACTOR LENGTH WL)
I
I I O
Figure 2. Steady-state temperature profile for different sets of collocation points. Also shown is the finite-difference solution.
...a+
energy balance on coolant:
The coolant flow is assumed to be countercurrent to the reactant flow. The rate equations are given by (Stoukides and Vayenas, 1981) KEPEPo~ rl = k , (6) + KEPEP02,in (7) r, = k ,
KEOpE02
1 + KEOPEO’ The rate constants are listed in Table I. Solution Procedure. The model of the ethylene oxide reactor is discretized in the axial direction by using orthogonal collocation. The resulting spatially discretized equations are of the form
where N = number of collocation points and i = 1,2, 1. These equations were solved by using the ACSL integration package (Mitchell and Gauthier, 1981). The reactor dimensions used and typical operating conditions are shown in Table 11. Figure 2 shows the solution from the collocation approximation to the steady-state profile obtained by numerical integration of the steady-state equations. As the number of points is decreased, obvious inaccuracies result, while points more than 10 do not provide any appreciable improvement. The nonlinear simplified model of order 10 ( N = 10 in eq 9) could accurately represent the reactor dynamically and track the new steady state when reactor inlet condition changes. Dynamic simulation studies using the above model showed that the reactor responds quickly to input disturbances with time constants of the order of a minute or less. The reactor would respond in almost steady state for disturbances which vary at a slower rate. For such disturbances, we can design the optimizing controllers based on the steady-state models alone. Steady-State Optimization Studies. The effects of inlet feed temperature and coolant inlet temperature on the steady-state reactor outputs, such as ethylene oxide and carbon dioxide produced, ethylene conversion, and yield of ethylene oxide, etc., were further investigated. This can be used to estimate the optimal operating conditions of the process. (i) Effect of Feed Temperature. Increasing the inlet feed temperature decreases the yield and sharply increases the carbon dioxide produced. From Figure 3, we see that the feed temperature around 535 K (at P = 10 atm, T, = 470 K, U = 255 J/(m2.s.K)) maximizes the ethylene oxide produced. There is a sharp drop in ethylene oxide pro-
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1927
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520
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FEED TEWPERANRE (K)
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= 9 I45 x I
510
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kmole/m3 I
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550 570 COOLANT TEMPERATURE
530
l
i
l
590
Figure 5. Ethylene oxide produced vs. coolant temperature for different gas velocities.
OPERATlhC COVDlTlOhi
OPTIMIZATION USING THE IDEKTIFIED MODEL
2.52-
Figure 3. Effect of inlet feed temperature on ethylene oxide and COBproduced in the reactor (P= 10 atm).
--- ------0.50r ---
1
PLANT
MODELS
Figure 6. Strategy for testing the two-phase approach on the EO reactor.
produced as a function of inlet coolant temperature taking and u as parameters. Both variables affect the location of the optimum as well as the optimum production rate. A decreased catalyst activity requires an increase in the coolant temperatures to maintain the optimum. The maximum ethylene oxide produced decreases with increasing gas velocity.
22
fC ,, I
490
9 145 x
kmole/m3
:
I
510
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I
550
I
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570
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COOLANT TEMPERATURE
Figure 4. Ethylene oxide produced vs. coolant temperature for various catalyst activities.
duction at high temperatures mainly due to increased conversion to COP. (ii) Effect of Coolant Temperature. The situation is similar to that of the inlet feed temperature. The coolant temperature around 485 K (at P = 10 atm, Ti, = 535 K, U = 255 J/(m2.s.K)) maximizes the ethylene oxide produced. For the optimizing control (optimization) problem, we need to understand the effect on the reactor performance by the long-term disturbances, such as catalyst activity and gas feed flow rate. Figures 4 and 5 show the ethylene oxide
Application of the Two-Phase Approach to the EO Reactor The two-phase approach was applied to the simulated plant above. The test strategy is schematically shown in Figure 6. Here we distinguish between two types of models. The models used in the identification and optimization phase were deliberately chosen to be approximations to the model used in the simulated plant. Thus, we are able to evaluate the efficiency of the algorithm when there are plant/model misinatches which are inherently present in any application. The simulated plant model used in this study was based on an eight-point collocation model and used the kinetic rates given in (6)-(8). Approximate Models Used. In order to evaluate the effect of plant/model mismatches, two types of approximations were introduced. (i) The first type is approximations introduced by using a smaller number of collocation points. This would reduce the number of equations used in the identification phase and hence reduce the computational load. (ii) The second type is approximations to reaction kinetic expressions. This was selected to see how well the two-
1928 Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 Table 111. Identified Parameters and CPU" Time Using (a) Model AM1 and (b) Model AM2 a s a Function of the Number of Collocation Points Used catalyst activities void N PI P7 sn fraction, t CPU, s SD Section a 1 0.7711 1.4243 1.0056 0.0843 5.50 0.07241 2 0.7909 1.2623 1.0044 0.2444 10.48 0.0577 4 1.0185 0.9552 0.9988 0.3756 23.97 0.0075 6 0.9948 0.9958 1.0000 0.3667 53.17 0.0062 8 0.9905 1.0047 1.0000 0.3606 87.80 0.0008 plant 1.0 1.0 1.o 0.3500 1
2 4 6 8
1.00 1.00 1.00 1.00 1.00
Section 1.1462 -0.0083 1.1143 -0.0288 1.000 1.0094 1.000 1.0188 1,000 1.0174
b 0.3066 0.3704 0.33421 0.31796 0.31991
8.20 16.92 28.95 62.49 119.37
0.0771 0.0666 0.0212 0.0148 0.0142
Table IV. Optimum Values and CPU Times Used for Model AM1 producN tivity T,,, K Toin conversion yield CPU, s 1" 2 0.75615 296.324 533.86 0.9893 0.7644 22.93 4 0.80548 426.238 481.61 0.9250 0.8708 43.12 6 0.80667 357.253 492.65 0.9353 0.8636 101.14 8 0.80693 324.640 497.17 0.9368 0.8633 160.81 No results could be obtained in this case since the identified model was incorrect.
(ii) the time taken to complete the identification on a VAX 750 computer; (iii) the standard deviation, SD, of the error in estimation computed as
"CPU times are given for a VAX 11/750 computer. n
phase approach would handle gross simplifications in the reactor model. Two approximations were studied. approximate model AM1: rl = k1KEPEPo2
7'2
= K~KEPEPo,
r3 = ~ & E # E o ~ / ( ~ + KEOPEO~)
,=1
(10)
approximate model AM2: rl = klKEPE
r2 = k2KEpE
r3 = k3KEf12
(11)
The second model neglects the dependence on oxygen concentration and the contribution of the denominator in the thrid reaction. Parameters Used in Model Identification. Some of the variables which are likely to change with time were selected as adjustable parameters in the model identification step. The two parameters that are used in this work are the catalyst activity p r and the void fraction t in the reactor. The activity is defined separately for each of the three reactions by using the equation r1' = PTI (12) where r, = rate computed from initial estimates of kl, KE, etc., and r,' = actual rate used in the model equations. Plant Measurements Used. The following sets of measurements were used for the identification phase: (i) temperature measurements at the eight collocation points; (ii) concentration measurement at reactor inlet and reactor exit; (iii) coolant temperatures also at the eight collocation points; (iv) flow measurements at reactor inlet and coolant inlet. Results of Identification Phase. The identification problem can be stated as follows: given measurements of input and output flow rates, composition, and temperatures, determine the set of parameters, p, and e, which will minimize the square of the error, defined as the difference between observations and model predictions, i.e., min Cb, - pJ2 P d
(13)
I
This optimization is subject to all the constraints arising from the model equations listed in (9). This problem was solved by using GRG I1 code (Lasdon et al., 1980). Table I11 summarizes the results of the identification runs using models AM1 and AM2. The table compares the following items: (i) the estimated values of identified parameters for various models;
SD is a measure of the fit between the plant data and model predictions. An idea of the relative significance of SD can be obtained by looking a t Figure 2, which shows that the temperature varies about 14% over the entire reactor. Thus, an SD of 0.07 represents a poor fit. Model AM1 is clearly superior to model AM2. Also increasing the number of collocation points in both models leads to closer agreement between plant data and the model predictions. The last two lines in Table IIIb show that there is little improvement by increasing the number of collocation points from six to eight, which means that this error is a result of the approximation made in the kinetic rate expressions. Large values of SD obtained when the number of collocation points are small indicate that we may not be able to use these models effectively in on-line optimization. CPU times increase with increasing dimensionality of the model, as expected. But the time taken for identification is small (less than a minute on a VAX 11/750), which indicates the feasibility of using these types of models for on-line work. Results of the On-Line Optimization Studies. The above process of model identification was combined with the optimization phase to verify the ability of the twophase approach to achieve optimum operation. The objective function selected is the productivity of the reactor defined as Q =
moles of EO produced moles of ethylene fed
The independent variables over which the optimization is carried out were (1)Tin= reactor inlet temperature, (2) T,,,, = coolant inlet temperature, (3) Fo, = oxygen feed rate, (4) F N 2 = nitrogen feed rate, (5) Fco, = carbon dioxide feed rate. The following constraints were also imposed on the optimization: 0.02 C XE C 0.10,0.04 C Xo2 C 0.08,0.72 C XN, C 0.89, 0.05 C Xco2 C 0.10. These constraints were selected from suggested operating ranges in the literature. The optimization was carried out by using GRG I1 (the same code used in the identification phase). Satisfactory results were obtained by using model AM1 (results are shown in Table IV), whereas model AM2 failed to converge in some instances or resulted in operating conditions far
Ind. Eng. Chem. Res., Vol. 26, No. 9, 1987 1929 Nevertheless, good results were achieved with the reduced order models also. The approximations made in the reaction kinetics played a more significant role. Here too much simplification can lead to models that do not fit the observed data very well. A careful evaluation of the simplifications employed in approximate models is suggested. This can be done with plant data and/or detailed off-line simulation models.
0.82
l h
I
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Acknowledgment Partial support provided by the National Science Foundation through Grant CPE 82-19701 is gratefully acknowledged. Chen wishes to acknowledge the financial support by the Government of Taiwan, Republic of China.
0.581 \ t
l
l
l
,
l
l
d
13 14 15 16 17 18 1,9 2 0 C 2 H 4 FEED RATExIO**5 (KMOLE/SEC)
Figure 7. Performance of on-line optimizer as a function of varying production capacity (using model AM1, four collocation points).
below the theoretical optimum. Referring to Table I11 again, we note that stringent conditions on the model fit are required in this application. A good way to check the validity of the model is to compare the observed and model predicted temperature profiles. In the case of model AM1, only one failure is noted in Table IV. The results using N = 2 are not very satisfactory either. The ability of model AM1 to follow changes in the optimum was tested by perturbing the reactor ethylene feed. Figure 7 shows the results. Starting with an ethylene feed of 1.4 X kmol/s, the feed is increased in stepwise fashion to a feed rate of 2.0 X mol/s. Also plotted on the graph is theoretical optimum based on precise knowledge of the plant operation. Without on-line optimization, the productivity drops significantly. On-line optimization using the two-phase appraoch is able to achieve operation close to the theoretical maximum, the difference being caused by the error in identification and due to the approximations made in the model. Conclusions The two-phase approach was capable of reaching and following the optimum operating conditions of the ethylene oxide reactor, It was found that the method can tolerate and cope with a certain level of approximation in the model used. This we believe is critical in real applications since we rarely have exact models or exact plant parameters. The identification phase is able to cope with these plant/model mismatches through adjustment of the model parameters. The study also showed that the plant/model mismatch cannot be too large. A measure of the plant/model mismatch is the goodness of fit between plant data and model predictions. This should be evaluated based on expected error over a range of operating conditions and comparing this error to the expected variations in the quantity being estimated. Thus, if a temperature is being fit, the error in its estimation should be compared against its variation over the range of operating conditions. The time taken in the identification and optimization phases is of the order of a minute of a VAX 11/750, and hence it is quite feasible to implement this on line. The additional savings obtained by reducing the order of the model is small and not significant for this application.
Nomenclature A , = cross-sectional area for coolant flow around tube, m2 A , = coefficients resulting from orthogonal collocation CA = dimensionless concentration of ethylene CB = dimensionless concentration of ethylene oxide CA* = concentration of ethylene, kmol/m3 CB* = concentration of ethylene oxide, kmol/m3 C = heat capacity of coolant, J/(kgK) 8;= heat capacity of fluid, J/(kg.K) = heat capacity of catalyst, J/(kg of cata1yst.K) = reference concentration, kmol/m3 d = diameter of catalyst particle, m lf = activation energy of reaction i, J/mol FA = feed rate of component A, kmol/s KE = adsorption equilibrium constant, bar-2 KEo = adsorption equilibrium constant, bar-2 k , = rate constant of reaction i , kmol/ (m2-s) L = reactor length, m m = manipulated variable P = reactor pressure, atm Pe = perimeter of the tube, m PE = partial pressure of ethylene, atm Po2 = partial pressure of oxygen, atm Pol,,,, = partial pressure of oxygen in feed, atm Q = dimensionless variable = u,/u R, = gas constant = 0.083139, bar-m3/(kmol,K) re = rate of reaction of ethylene, kmol/(s.m3) r,, = reactor radius, m T = dimensionless reactor temperature T , = dimensionless coolant temperature R* = reactor temperature, K T,* = coolant temperature, K Tref= reference temperature, K t = dimensionless variable = t*u/L t* = time, s U = overall heat-transfer coefficient, J / (m*-s.K) u = fluid velocity, m/s u, = coolant velocity, m/s x = state variable xA = mole fraction of component A y = measured variable 9 = plant measurements z = reactor length, m Greek Symbols 0 = dimensionless variable = UPJ/(p,C,,A,u) e = void volume fraction of reactor E = dimensionless variable = z / L w = dimensionless variable = 2UL/(pC,r,p) r = dimensionless variable = p f C p f / p C p yl = dimensionless variable = E,/R,T,,, p = catalyst activity ps = density of catalyst bed, kg of catalyst/m3 pf = density of fluid, kg/m3 p c = density of coolant, kg/m3 SZ = productivity tH,= reaction enthalpy of i , J/kmol
8, &
Ind. Eng. Chem. Res. 1987, 26, 1930-1935
1930
Subscripts E = ethylene EO = ethylene oxide i = reaction i
in = inlet condition O2 = oxygen Registry No. EO, 75-21-8. Literature Cited Cawse, J. N.; Henry, J . P.; Swartzlander, M. W.; Wadid, P. H. "Ethylene Oxide", In Encyclopedia of Chemical Technology, 3rd ed.; Wiley: New York, 1978; Vol. 9, pp 432-471. Cutler, C. R.; Perry, R. T. Comp. Chem. Eng. J . 1983, 7 ( 5 ) ,663. Haggin, J. Chem. Eng. N e w s 1984, 62, 14. Jang, S . S.; Joseph, B.; Mukai, H. A I C h E J . 1987, 33(1),26.
Lasdon, S., Warren, A. D.; Ratner, M. W. GRG2 User's Guide; Department of General Business, University of Texas a t Austin: Austin, 1980. Mitchell and Gauthier Associates, Inc. A C S L User's Guide; ACSL: Concord, MA, 1981. Morari, M.; Arkun, Y.; Stephanopoulos, G.; A I C h E J . 1980, 26(2), 220. Prett, D. M.; Gillett, R. D. Paper presented at AIChE 86th National Meeting, Houston, 1979. Smith, C. L.; Brodman, M. T. Chem. Eng. 1976, 83, 14. Stoukides, M.; Vayenas, C. G. J . Catal. 1981, 69, 1689. Webb, P. U.; Lutter, B. E.; Hair, R. L. Chem. Eng. Prog. 1978, 74, 6. Received for review July 26, 1985 Reuised m a n u s c r i p t received September 24, 1986 Accepted June 26, 1987
Improved Perfluoroalkyl Ether Fluid Development William R. J o n e s , Jr.* National A e r o n a u t i c s a n d S p a c e A d m i n i s t r a t i o n , Lewis Research C e n t e r , Cleveland, Ohio 44135
K a z i m i e r a J. L. Paciorek, J a m e s H.N a k a h a r a , M a r k E. S m y t h e , a n d Reinhold H.K r a t z e r U l t r a s y s t e m s , I r v i n e , California 92714
The feasibility of transforming a commercial liner perfluoroalkyl ether fluid into a material stable in the presence of metals and metal alloys in oxidizing atmospheres at 300 "C without the loss of the desirable viscosity-temperature characteristics was determined. T h e approach consisted of thermal oxidative treatment in the presence of catalyst t o remove weak links, followed by transformation of the thus created functional groups into phospha-s-triazine linkages. A dynamic process amenable t o scale-up was developed. T h e experimental material obtained in 66% yield from the commercial fluid was found to exhibit, over an 8-h period a t 300 " C in the presence of Ti(4A1,4Mn) alloy, thermal oxidative stability better by a factor of 2.6 X lo3, based on volatiles evolved (0.4 mg/g) than the commercial product. T h e viscosity and molecular weight of the developed fluid were unchanged by the above exposure and were essentially identical with that of the commercial material. No metal corrosion occurred with the experimental fluid a t 300 "C. The material thus developed can be used as a lubricant, fluid, or grease, in applications where oxidizing atmospheres and extremes of temperature, -55 t o +300 " C , are encountered in the presence of metals and metal alloys. No material exhibiting all these properties is available a t present. Both in aeronautical systems and space applications, there is a need for wide liquid ranges and high viscosity index fluids that are stable thermally and oxidatively above 300 "C, the applications being in hydraulics and lubrication, e.g., greases. Unbranched perfluoroalkyl ether fluids available today, as exemplified by Fomblin Z (Montedison Co. products) (Sianesi et al., 1973), of the general approximate formula CF30(CF2CF,0),(CF20),CF3possess the required liquid ranges but are unfortunately unstable in oxidizing atmospheres a t elevated temperatures, particularly in the presence of metals (Jones et d . , 1982,1983; Paciorek et al., 1981, 1983; Snyder et al., 1981). This decomposition is accompanied by evolution of gaseous products and metal corrosion. These materials do exhibit high thermal stability and chemical inertness and possess viscosity indexes above 300 (Caporiccio et al., 1982; Sianesi et al., 1971). The last property makes these compositions indispensable for applications where extremes of temperatures are encountered. Additives, phospha-s-triazines and phosphines, have been developed (Jones et al., 1982, 1983; Paciorek et al., 1981, 1983; Snyder et al., 1979, 1981) which virtually eliminate the degradation of these fluids up to 288 "C for short periods of time. It would be preferable to have a fluid which does not require 0888-5885/87/2626-1930$01.50/0
an additive and has even higher thermal oxidative stability than those attained to date. Thus, the objective of this work was to prove the feasibility of modifying Fomblin Z type fluids to obtain a fluid with comparable temperature viscosity characteristics, yet stable in the presence of metals in oxidizing atmospheres at least to 300 "C. Experimental Details a n d Procedures General. The perfluoralkyl ether fluid employed in this study was Fomblin Z fluid, MLO-79-196 (MW, 6400; viscosity at 40 "C, 80.85 CS(product of Montedison)), and was obtained through the courtesy of Dr. C. Tamborski and C. E. Snyder, Air Force Wright Aeronautical Laboratories. All solvents used were reagent grade and were dried and distilled prior to use. Operations involving moisture- or air-sensitive materials were carried out either in an inert atmosphere enclosure (Vacuum Atmospheres Model HE93B), under nitrogen by-pass, or in vacuo. Infrared spectra were recorded either neat (on liquids) or as gas spectra on gases and volatile liquids or in solution, the latter for the quantitative determinations, by using a Perkin-Elmer infrared spectrophotometer Model 1330. The molecular weights were determined in hexafluoro0 1987 American Chemical Society
