Ind. Eng. Chem. Res. 1994,33, 211-217
211
Effect of Initiator Characteristics on High-pressure Ethylene Polymerization in Autoclave Reactors Byung Gu Kwagt and Kyu Yong Choi' Department of Chemical Engineering, University of Maryland, College Park, Maryland 20742
The steady-state and transient behaviors of a high-pressure ethylene polymerization reactor have been analyzed for a continuous stirred autoclave reactor consisting of two reaction compartments. The nonlinear temperature dependence of the specific initiator consumption rate is modeled using the initiator efficiency factor which varies with reaction temperature. It is shown that there exists a critical reaction temperature a t which the steady-state process gain (reactor temperature change/ initiator feed rate change) changes its sign. When only the first reaction zone temperature is controlled by regulating the initiator injection rate, the second zone temperature is strongly affected by the first zone temperature for certain initiator types. It has also been shown that the volume ratio of the two reaction zones is an important reactor design parameter that affects the temperature rise in the second reaction zone. Dynamic closed loop reactor simulations have also been carried out to illustrate potential control problems when the reactor operating condition is changed from one steady state to another.
Introduction High-pressure free radical ethylene polymerization processes have been used in the polymer industry for years for the production of low-density polyethylene (LDPE). Although transition metal catalyzed low-pressureethylene polymerization processes (e.g., gas-phase and slurry-phase Ziegler-Natta processes) have gained in popularity in the polyolefin industry in recent years, a significant amount of low-density polyethylenes is still manufactured worldwide by high-pressure free radical polymerization processes. Moreover, some applications of high-activity transition metal catalysts to high-pressure reactor systems and the use of conventional high-pressure polyethylene reactors to produce copolymers have recently been reported, suggesting that high-pressure polyethylene technology should remain quite competitive in the coming years. High-pressure polyethylene processes are characterized by high reaction temperature (150-300"C)and pressure (1000-3000 atm). Both autoclave reactors and tubular reactors are widely used in the industry. It is known that polyethylenes manufactured by these processes differ in their molecular architecture and many of the important end use properties of polyethylenes manufactured by these processes are quite different. In autoclave polymerization processes, either single stage or multistage reactor systems are commonly used. When a multistage reactor is used, the reactor is typically a veritical cylindrical vessel with a large LID ratio. The reacting fluid is intensely mixed by an agitator shaft running down the center of the vertical reactor vessel with impeller blades. The overall reactor volume is generally small, and thus the reactor residence time is very short (e.g., less than 2-3 min). Various types of continuous autoclave ethylene polymerization reactors are described in patent literature. Since the polymerization pressure is so high, the reactor wall thickness is large and the polymerization reactor operation is essentially adiabatic. Thus, the heat of polymerization is
* To whom correspondence should be addressed. +
On leave from Lucky Ltd., Seoul, Korea.
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removed by the bulk flow on ethylene and polyethylene mixture in the reactor. It is well recognized that process models are useful for the design of optimal reactor operating conditions and reactor controls to obtain maximum polymer productivity and desired polymer properties. In developing a comprehensive process model for high-pressure ethylene polymerization, it is first required to develop a process model that gives an accurate prediction of the first level reactor performance variables such as temperature, polymer yield, and specific initiator consumption rate. Once these key reactor variables can be predicted by the model, one can further improve the process model to predict important polymer properties (e.g., molecular weight, molecular weight distribution, degree of short chain and long chain branching, etc.) and use the model to design a better product quality control system. Several authors (Georgakis and Marini, 1982;Marini and Georgakis, 1984;Chan et al., 1993) have proposed polyethylene reactor models and report that the steady state of a continuous autoclave polyethylene reactor is often open-loop unstable under typical industrial process operating conditions. Therefore, careful reactor controls are required for startup and steady-state operations. One of the well-known phenomena in high-pressure polyethylene processes is a rapid ethylene decomposition reaction, known as "decomp", when the reaction heat is not dissipated effectively. In such a case, the reactor temperature rises rapidly to the point (about 300-320 OC) where ethylene and polyethylene decompose explosively to lower molecular weight species such as carbon, methane, and hydrogen. It is to be pointed out that the decomposition reaction often occurs unexpectedly even after a long period of stable reactor operation with no clearly detectable abnormal symptoms in reactor process equipment. When the decomposition reaction takes place, the reactor pressure builds up quickly and the reactor must be vented, shut down, and flushed for a long period of time before a new startup is initiated. Quite obviously, the resulting economic loss will be quite significant. For the polymerization of ethylene in high-pressure processes, a variety of free radical generating initiators are used, depending upon the quality of the polyethylene 0 1994 American Chemical Society
212 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994
to be produced. Since initiator costs account for a significant fraction of total process operating costs, there is always a need to minimize the specific initiator consumption rate (SICR, grams of initiator injected/kilograms of PE produced) by employing optimal process operating conditions and initiator types. For some free radical initiators used in high-pressure ethylene polymerization processes (e.g., tert-butyl peroctoate, tert-butyl 3,5,5trimethylperhexanoate, di-tert-butyl peroxide (Seidl and Luft, 1981)),it has been reported that SICR is a nonlinear function of reaction temperature. For example, at low reaction temperatures the specific initiator consumption rate decreases with increasing reaction temperature; however, as the reaction temperature is further increased, the specific initiator consumption rate increases. This phenomenon has been observed even in a small laboratory scale polyethylene reactor [e.g., reactor volume = 15 mL (Seidl and Luft, 1981)l where a homogeneous mixture of initiators and monomers is injected in a single feed stream to the reactor. Such a nonlinear dependence of the specific initiator consumption rate on reaction temperature in a stirred autoclave reactor has been studied by several researchers. For example, Marini and Georgakis (1984) proposed that the initiator and the reacting fluid are not perfectly mixed in a large scale stirred autoclave reactor. In their modeling, a single autoclave reactor is divided into three CSTRs of different volumes. The first two CSTRs account for a very small fraction of the total reactor volume, and they represent the reactor volumes where the injected initiator is not fully mixed with the rest of the reactor fluid. The third CSTR accounts for the remaining reactor volume where most of the polymerization takes place. The division of the real reactor volume into three hypothetical zones is based on the measurements of the initiator injection velocity through a nozzle in the reactor and has an effet of lowering the overall initiator efficiency. In their work, the mixing parameters were determined using the size of a nozzle and the total flow rate of monomer and initiator solution through the nozzle. Chan and co-workers (1993) extended this approach to an autoclave ethylene polymerization process where monomers and initiators are supplied to the reactor through more than one injection port. In their model, the entire autoclave is represented by several volume elements, each of them consisting of a CSTR segment following by a plug-flow segment which is approximated as a finite number of small CSTRs in series. To model the effect of recirculation in the reactor, a recycle is allowed from one CSTR segment to the CSTR segment of the element above. The size and the number of these CSTR volume elements are the model parameters that can be adjusted to fit plant data. The authors have stated that reasonable estimates of these parameters can be obtained from the knowledge of reaction temperature profiles, initiator flow rates and stirrer geometry. van der Molen and van Heerden (1970)introduced a characteristic mixing time in calculating the specific initiator consumption rate with a fixed initiator efficiency factor. They assumed that at high temperatures, the initiator decomposes prematurely before the contents of the reactor are fully mixed, resulting in the wastage of radicals. Lorenzini et al. (1992)reported a polyethylene reactor model in which a partial segregation of the initiator stream was considered. They used the micromixing time as a parameter that was adjusted by optimal fitting to match experimental and model predicted values of the polymer production rates. The primary objective of this paper is to investigate the effect of initiator characteristics on the steady-state and
dynamic behaviors of a two-zone high-pressure continuuos autoclave polyethylene reactor through modeling and simulations. As described above, the effect of reaction temperature on the specific initiator consumption rate is nonlinear and thus a polyethylene reactor model should be capable of predicting such a behavior. In this work, we assume that the reaction mixture is perfectly backmixed but that the initiator efficiency varies with reaction temperature. It is well-known in free radical polymerization that initiators are not fully effective in initiating polymerization. Induced decomposition of initiator and some side reactions of the radicals formed by the initiator decomposition in the solvent cage are two of the most important reactions that lead to the wastage of initiator (Odian, 1991). In general, it is very difficult to identify these side reactions and to quantify the reaction kinetics. Thus, the initiator efficiency factor used in free radical polymerization is viewed as effective or apparent efficiency. Since the polymerization temperature is very high (e.g., 150-280 "C), it is not difficult to expect that some radicals generated by the thermal scission of the initiator may be engaged in side reactions, resulting in a waste of radicals and a decrease in the initiator efficiency. If these side reactions favor high reaction temperature, primary radicals will be wasted before the initiator molecules or radicals are completely mixed with the bulk reacting fluid. Thus, the initiator efficiencywill decrease accordingly and more initiator will be required to sustain a desired high reactor temperature. When a multicompartmented autoclave reactor is used for the polymerization, the variation in the initiator efficiency factor can significantly affect the temperature in the second or third reactors. Thus, it will be of practical interest to investigate the effect of a temperature dependent initiator efficiency factor on the performance of high-temperature and high-pressure ethylene polymerization reactors. To illustrate the aforementioned initiator effect, we have carried out model simulations for the two typical initiator systems that are widely used in high-pressure free radical polyethylene processes.
Reactor Model Let us consider a continuous stirred autoclave reactor that consists of two serially connected compartments of volume VI (zone 1)and V Z(zone 21, respectively. These two reaction zones are physically separated by a special device attached to a central shaft, and there is a negligible backflow of the fluid from zone 2 to zone 1. Pure ethylene and peroxide initiators diluted in an inert hydrocarbon solvent are supplied through separate injection ports to zone 1 only. The zone 1 temperature is controlled by regulating the initiator feedrate (qi). It is assumed that heat loss through the reactor walls is negligible and that physical parameters such as density and heat capacity of the reacting mixture are constant. The reactions considered in the modeling are initiator decomposition, chain initiation, chain propagation, and chain termination (combination termination only) reactions. This reaction scheme can be extended by including various chaintransfer reactions to account for branching reactions that affect many important polymer properties. In this work, we limit the scope of reactor modeling to the analysis of overall reactor behaviors and the assessment of the effect of proposed temperature variant initiator efficiencyfactor. Thus, no chain-transfer reactions are included in the kinetic scheme and polymer properties are not calculated. Then, the mass and energy balance equations for the two reaction zones take the following form:
Ind. Eng. Chem. Res., Vol. 33, No. 2,1994 213 Table 1. Numerical Values of Kinetic and Physical Parameters (P = 1700 atm)
zone 1
ku = 2.319 X lo1*exp(-42 732/RT) ka = 4.394 X 1016exp(-33 442/RT) k, = 5.8 X lo7e~p(-8646/RT)~ kt = 2.8 X 1028 exp(-339/RT)a
8-1 8-1
A",= -22 500
L/(mol 8) L/(mols) cal(L O C ) cal/mol
81 = 26
8
pcp= 300
Shirodkar and Tsien (1986).
(3)
zone 2 1 -dx4 - 1 ( x 1 - x4) + -R dt d2 Mf
P2
(4)
0' 200
In the above, the following dimensionless variables are used:
where Mf = feed monomer concentration, Mj = monomer concentration in the j t h zone, If = feed initiator concentration, Ij = initiator concentration in the j t h zone, Tf = feed monomer temperature, Tj = temperature in the jth zone, q = volumetric monomer feedrate, qi = volumetric initiator solution feedrate, d j = residence time in the jth zone, A", = heat of reaction, p = density, C, = heat capacity. In deriving the modeling equations, it has been assumed that the initiator solution feedrate (qi) is far smaller than the total monomer feedrate ( q ) . The rate of polymerization (Rpj)and the rate of initiator decomposition (Ru) in the j t h zone are given as follows: (7)
f i is the initiator efficiency factor. It is to be noted that the initiator feed rate is regulated by a feedback controller to keep the zone 1 temperature at its desired value and that the zone 2 temperature is not controlled. At steady state, the left-hand-side terms in the modeling equations are equal to zero and the resulting nonlinear algebraic equations are solved for given input conditions. The numerical values of kinetic parameters used in the model simulations are listed in Table 1.
Discussion of Results
In our simulation study, we shall consider two peroxide initiators A and B that are both widely used in the polymer industry. These initiators exhibit quite different initiation efficiency as reaction temperature is varied (see Table 1). The half-life of initiator A is longer than that of initiator B at a given reaction temperature, and initiator A is more suitable for high-temperature polymerization. When these
"
220
"
"
240 260 Temperature (C)
"
280
"
300
Figure 1. Initiator efficiency factors for initiator A and initiator B.
initiators are used in high-pressure ethylene polymerization processes, not all the radicals generated from these initiators are utilized to initiator chain growth reactions. Some radicals may undergo side reactions and thus the overall initiator efficiency is always less than 1.0. From the proprietary steady-state plant data of polymer yield at varying reaction temperatures, the initiator efficiency factors for these initiators have been estimated. If the steady-state reactor temperature, monomer conversion, feed initiator concentration, and initiator flow rate are known, one can use the steady-state mass balance equations for both monomer and initiator (eqs l and 2) to calculate the initiator efficiency factor. Of course one needs a sufficient amount of reactor data for several different temperatures with a given initiator system. Such operational data are readily available from the polyethylene plant. Figure 1 illustrates the initiator efficiency factors calculated for both initiators A and B as a function of temperature at 1700 atom using the plant data. Notice that the efficiency of initiator A changes significantly with reaction temperature whereas the efficiency of initiator B is low and relatively insensitive to reaction temperature. Due to this difference in the temperature dependence of initiator efficiency, the macroscopic behavior of the highpressure polyethylene reactor becomes quite different for these initiators. Steady-State Reactor Analysis. In the two-zone polymerization reactor system considered, only the zone 1temperature is controlled by regulating the initiator feed rate and the zone 2 temperature is determined by the conditions in zone 1. With the zone 2/zone 1volume ratio and the residence time in zone 1 fixed at 0.25 and 26 s, respectively, the steady-state reactor temperature vs initiator feed rate (scaled) profiles for both initiators have been calculated as shown in Figure 2. Here, the initiator concentration in the initiator feed solution is 5 w t 9% and the temperature dependent initiator efficiency factor determined from the plant data, as shown in Figure 1,is used for each initiator. For initiator A, the initiator feed rate decreases with an increase in the reaction temperature up to about 240 OC. At reaction temperatures above 240 "C,the initiator feed rate increases as the reaction
214 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 40
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Figure 2. Steady-state initiator feed rate vs zone 1temperature for initiator A and initiator B.
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Zone-1 Temperataure (C)
Figure 3. Specific initiator consumption rates for initiators A and B.
temperature is increased. For initiator B, a similar effect is seen but is not quite as pronounced as that for initiator A. In fact, the initiator B feed rate increases almost linearly with reaction temperature in the temperature range 220300 OC. The existence of a minimum initiator feed rate for initiator A can be easily understood from Figure 1: A t reaction temperatures above 240 "C, the initiator efficiency drops sharply. As a result, more initiator is needed to maintain the reaction temperature above 240 "C. The specific initiator consumption rate (SICR, grams of initiator injected/kilograms of PE produced) is an important measure of initiator productivity. The SICR value for zone 1can be easily obtained using the following expression: (9.1)
or
where J = pCp/(-AHr). (MW)i and (MW), are the molecular weights of initiator and ethylene, respectively. Figure 3 shows the SICR profiles for both initiators A and B with their efficiency factors represented as shown in Figure 1. Notice that initiator A clearly shows the minimum point at about 250 "C. If the initiator efficiency factor cfi) is kept constant, SICR calculated from eq 9.1 or 9.2 always decreases with an increase in temperature because the activation energy for propagation is larger than that for termination. Earlier reports on the polyethylene reactor modeling postulate that the initiator is
220
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Zone-1 Temperature (C) Figure 4. Steady-state zone 2 temperature as a function of zone 1 temperature.
not well mixed with the reacting fluid at high temperatures and thus the characteristic mixing time or segregated mixing models have been used to account for this effect. For initiator B, the initiator efficiency factor is only weakly dependent on temperature in the temperature range considered and no minimum SICR value is observed. The results shown in Figure 3 are quite consistent with the reports by Seidl and Luft (1981). They reported that such phenomena as shown in Figure 3 have been observed experimentally for many other initiators. No plausible explanations of the observed phenomena have been given, however. Recall that similar SCIR vs temperature plots were also obtained by Marini and Georgakis (1984) using a nonideal mixing model in which a single autoclave reactor was modeled as a series of three CSTRs of different volumes. Goto et al. (1981) included a side reaction in initiator decompositionand obtained similar SCIR profiles. Figures 2 and 3 indicate that the observed specificinitiator consumption rate profiles can also be explained by variant initiator efficiency even with an assumption of perfect backmixing. In fact, the net effect of imperfect backmixing of initiator and reacting fluid is to lower the concentration of radicals available for the chain propagation reaction. Thus, although the approach is different, there is a similarity between our proposition and the nonideal mixing models proposed by other workers in that both take into account the loss of radicals available for polymerization. When only the zone 1temperature is controlled by the initiator feed rate, the zone 2 temperature is totally dependent upon the zone 1temperature and the amount of undecomposed initiators transferred from it. Figure 4 shows the steady-state zone 2 temperature vs zone 1 temperature profiles for both initiator systems. For initiator B, the zone 2 temperature increasesalmost linearly with zone 1 temperature. For initiator A, the zone 2 temperature decreases as the zone 1 temperature is increased in the temperature range 200-235 "C. But for the zone 1 temperature above 235 "C, the zone 2 temperature increases as the zone 1temperature is increased. These phenomena can be better understood by examining the fractional initiator concentration ( w t of initiator/wt of initiator injected) profiles in both zone 1 and zone 2. Figures 5 and 6 show the initiator concentration profiles in zone 1 and zone 2 for initiators A and B, respectively. In zone 1,the initiator concentration drops monotonically with an increase in reaction temperature. However, when initiator A is used, the initiator concentration in zone 2 increases as the zone 1 temperature is increased to about 225 OC. This is because less initiator is needed at higher zone 1temperature and the radical concentration in zone 2 becomes low, leading to decreased reaction temperatures
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Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 215 330 1
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Figure 6. Fractional concentration of initiator B in zone 1and zone 2.
Figure 8. Effect of some 2/zone 1 volume ratio on monomer conversion in zone 1 for initiator A.
(see Figure 4). Thus, fractional initiator concentration increases in this temperature interval. At zone 1 temperatures above 225 OC,an increased amount of initiator is required and the radical concentration in zone 2 goes up, causing the zone 2 temperature to increase (Figure 4). Therefore, the fractional initiator concentration decreases in zone 2. When initiator B is used, the zone 2 temperature increases almost linearly as the zone 1 temperature increases, resulting in a monotonic decrease in the initiator concentration in zone 2. In fact, Figures 5 and6 illustrate why the entire autoclave reactor is divided into two compartments. By having a second compartment that exhibits higher temperature than the first compartment, the residual initiator concentration can be significantly reduced. If too much initiator residue remains in the product stream, undesirable reactions may take place in the subsequent polymermonomer separator units, causing a deterioration in polymer product quality. It will be shown in what follows that the zone 2/zone 1 volume ratio is an important reactor design parameter and that the second zone must be sized properly to prevent undesirably high reaction temperature or potentially catastrophic "decomp" reactions. Figure 7 illustrates the effect of the zone 2/zone 1 volume ratio on the reactor temperatures for the initiator A system. Here, the volume of zone 1 is fixed and only the zone 2 volume is varied. It is observed that as the volume ratio is increased the zone 2 temperature increases for a fixed zone 1 temperature, particularly in the zone 1 temperature range 200-250 "C. For large zone 2 volumes, the fluid residence time increases and as a result more initiators decompose to radicals, which in turn, accelerates the chain propagation reaction. Figure 7 also illustrates that the temperature difference between zone 1and zone 2 is quite large for low
zone 1temperatures. Once the reactor configuration (i.e., volume ratio V ~ / V I )is fixed, other reactor operating conditions such as initiator feed concentration or zone 1 temperature may have to be adjusted to avoid any undesirably high temperature in zone 2. The effect of the volume ratio on the overall monomer conversion with initiator A is illustrated in Figure 8. For zone 1temperatures below 235 "C, the zone 2 temperature becomes higher for lower zone 1 temperature (Figure 7) and as a result the monomer conversion increases as the zone 1 temperature is lowered. Note that the monomer conversion is linearly dependent upon zone 1reaction temperature in the temperature range 240-280 "C. Since only the zone 1 temperature is controlled by regulating the initiator injection rate, the overall monomer conversion vs zone 1temperature profiles as shown in Figure 8 would be useful in designing the reactor operating conditions. Another reactor operating parameter that affects the reactor performance is the ethylene feed rate or mean residence time. Figure 9 illustrates the effect of mean residence time in zone 1 on the feed rate of initiator A and zone 1 temperature. Here, curves 1,2, and 3 correspond to mean residence times of 17, 26 (base case), and 52 s, respectively. For high monomer feed rates or short residence times, larger amounts of initiator are needed and the steady-state zone 1 temperature becomes more sensitive to the variation in the initiator feed rate. If the temperature dependence of the initiator efficiency is not considered and constant initiator efficiency is assumed instead, the predicted reactor behavior becomes quite different from the foregoingmodel simulation results. Figure 10 illustrates the zone 1 and zone 2 temperature profiles for initiator A with a constant initiator efficiency factor of 1.0. Notice that for zone 1 temperatures above
216 Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 120 I
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Figure 11. Transient response of zone 1 and zone 2 temperatures to a setpoint change in zone 1 temperature from 260 to 275 O C . 300 1
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Zone-I Temperature (C) Figure 9. Effect of zone 1 residence time: curve 1,17 s; curve 2,26 s; curve 3, 52 s (initiator A).
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275 "C, the zone 2 temperature increases as the zone 1 temperature is increased, but for zone 1 temperatures below 275 "C, the zone 2 temperature increases sharply as the zone 1 temperature is lowered. At low zone 1 temperatures more initiator is required to maintain a desired reaction temperature and a large amount of undecomposedinitiator is transferred to zone 2 where rapid reaction takes place, leading to a high reaction temperature. Notice that the zone 2 temperature can easily exceed the upper limit of the reaction temperature where the "decompnreaction occurs. If zone 2 is eliminated to avoid an excessive temperature rise (i.e., single-zone reactor), the residual initiator concentration in the product stream can be undesirably high, causing operational and product quality problems in downstream units such as high- and low-pressure separators. Therefore, in designing the correct polymerization reactor operating conditions, a quantitative understanding of the temperature dependence of initiator efficiency as presented in the above will be quite useful. Transient Reactor Behavior. A few words are in order concerning the transient behavior of the reactor. In Figure 2, it has been shown for initiator A that the required initiator feed rate decreases as the desired steady-state zone 1 temperature is increased up to about 240 "C. In other words, the steady-state gain (AT/ Aqi) is negative below 240 "C, but the gain becomes positive at zone 1 temperatures above 240 "C. I t can be shown by the eigenvalue analysis of the linearized reactor model that the steady state below a zone 1 temperature of 240 "C is open-loop unstable. It is also intuitively obvious because Figure 2 indicates that a higher reaction temperature requires less initiator, which is against our normal ex-
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Figure 12. Transient response of zone 1 and zone 2 temperatures to a setpoint change in zone 1 temperature from 260 to 220 "C.
pectation that the reaction temperature should increase as more initiator is injected to the reactor. To illustrate potential reactor control problems caused by the sign change in the steady-state gain (AT/Aqi) values, we shall present two numerical examples of closed-loop dynamic model simulation results. Figure 11 shows the transient responses of zone 1 and zone 2 temperatures and the initiator A feed rate that was used as a manipulated variable. Here the efficiency of initiator A varies with temperature (see Figure 1) and the zone 1 temperature setpoint is changed from 260 to 275 "C with a PI (proportional-integral) controller. Notice that the zone 1 temperature is nicely controlled and a new zone 2 temperature is well within an acceptable temperature range. If zone 1 temperature setpoint is changed from 260 to 220 "C, with the same controller parameters as used in Figure 11, the reactor exhibits quite nonlinear dynamics as shown in Figure 12. Both zone 1 and zone 2 temperatures oscillate wildly, which should have the effect of yielding poor quality polymer products. Of course, the reactor response can be improved by using different controller parameters or more advanced controllers. What we would like to point out in these illustrative dynamic simulations is that understanding the nature of the steadystate behavior of the polyethylene reactor is of tremendous importance in designing reactor operating conditions and controlling the reactor dynamics. If a given reactor is used to produce a variety of polyethylene grades using different initiators and/or reactor operating conditions, it is imperative to understand the nonlinear nature of the reactor dynamics, the characteristics of the initiators being used, and the effect of the initiators on the reactor behaviors. Concluding Remarks
In this paper, we have proposed that the nonlinear dependence of the specific initiator consumption rate on
Ind. Eng. Chem. Res., Vol. 33, No. 2, 1994 217 the reaction temperature, as observed in high-pressure ethylene polymerization processes for certain types of initiators, can be predicted by using a temperature dependent initiator efficiency factor. The basic assumption is that as the reaction temperature increases, more primary radicals are wasted by unwanted side reactions. Unfortunately, however, there is a lack of understanding of the reaction chemistry associated with the side reactions that cause the loss of primary radicals at high polymerization temperatures. The temperature dependent initiator efficiency factors were determined from steady-state plant data, and the overall model predictions were in agreement with actual observations. For the two initiators that exhibit different initiation efficiencies, it has been shown that quite different qualitative reactor behaviors are predicted. It has been illustrated that in the two-zone autoclave reactor system considered in this paper, the reaction temperature in zone 2 is strongly affected by zone 1temperature. The volume ratio of the two reaction zones has also been found to be an important reactor design parameter. The closed-loop dynamic simulation studies indicate that reactor control strategies should be carefully designed depending upon the nature of the desired steadystate operating conditions that are affected by the initiator efficiency. The method used in our work can be easily extended to more complex multicompartmented reactor systems. What we have proposed in this work is different from other reported works where nonuniform mixing of initiator and reacting fluid has been regarded as the main cause for the observed nonlinearity in the temperature dependence of SICR. The net effect of using such nonideal mixing models is to lower the concentration of initiators or radicals that are available for the main propagation reaction. In our work, perfect backmixing has been assumed but the initiator efficiency factor has been assumed to vary with reaction temperature. It is possible that a complete micromixing of initiator and reacting fluid is not quickly established at high temperature, leading to more side reactions. In this context, we can say that both approaches are aimed at quantifying the loss of radicals in the reactor but from different angles. Thus, the proposed approach of analyzing the steady-state characteristics of a two-zone autoclave reactor offers another viewpoint for the quantification of complex reaction phenomena in high-pressure ethylene polymerization processes. The method used in this work can be easily applied to the analysis of a commercial scale polyethylene reactor without excessive additional plant tests.
Acknowledgment The financial support for this work by Lucky Ltd. (Seoul, Korea) is gratefully acknowledged. Nomenclature C , = heat capacity, cal/(g K) f i = initiator efficiency factor
AHr = heat of polymerization, cal/mol
Zf= feed initiator concentration, mol/L Ij = initiator concentration in the jth zone, mol/L k d = initiator decomposition rate constant, l/s k , = propagation rate constant, L/(mol s) kt = termination rate constant, L/(mol s) Mf= feed monomer concentration, mol/L Mj = monomer concentration in the jth zone, mol/L (MW), = molecular weight of ethylene, g/mol (MW)i = molecular weight of initiator, g/mol q = monomer feed rate, L/s qi = initiator solution feed rate, L/s RU = initiator decomposition rate in the jth zone, mol/(L e) R,j = polymerization rate in the jth zone, mol/(L e) SICR = specific initiator consumption rate, grams of initiator injected/kilograms of PE produced Tf= feed monomer temperature, K Tj = temperature of the jth zone, K Vi = volume of the jth zone, L Greek Letters Oj
p
= residence time in the jth zone, s = fluid density, g/L
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