Oscillations, conversion

Achieving steady-state operation in a continuous tank reactor system can be difficult. Particle nucleation phenomena and the decrease in termination rate caused by high viscosity within the particles (gel effect) can contribute to significant reactor instabilities. Variation in the level of inhibitors in the feed streams can also cause reactor control problems. Conversion oscillations have been observed with many different monomers. These oscillations often result from a limit cycle behavior of the particle nucleation mechanism. Such oscillations are difficult to tolerate in commercial systems. They can cause uneven heat loads and significant transients in free emulsifier concentration thus potentially causing flocculation and the formation of wall polymer. This problem may be one of the most difficult to handle in the development of commercial continuous processes. 

One of the most promising ways of dealing with conversion oscillations is the use of a small-particle latex seed in a feed stream so that particle nucleation does not occur in the CSTRs. Berens (3) used a seed produced in another reactor to achieve stable operation of a continuous PVC reactor. Gonzalez used a continuous tubular pre-reactor to generate the seed for a CSTR producing PMMA latex. 

A recent paper by Kiparissides, et al. (8) details a mathematical model for the continuous polymerization of vinyl acetate in a single CSTR. Operating conditions were shown to exist in which either steady-state operation or sustained conversion oscillations would occur for vinyl acetate. Experimental results for both cases were successfully simulated by their model. In addition, regulatory conversion control policies were considered in which both initiator feed rate and emulsifier feed rate were used as manipulated variables (Kiparissides (9)). The problem of conversion control in the operating region in which sustained conversion oscillations occur is one of significant commercial importance. Most commonly, however, a uniform concentration of emulsifier is required in the emulsion recipe and, hence, emulsifier flow rate cannot be used as a manipulated variable. 

The rate of growth of particles depends on the concentration of the reagents in the particles, radicals and monomer, and on the propagation rate constant. The gel effect, which causes the termination rate constant to be lower at higher conversions, can cause higher free radical concentrations in the particles and thus higher particle growth rates. This effect also contributes to conversion oscillations. 

Greene et nl. (1976) demonstrated that strong initial overshoots and conversion oscillations could, in some cases, he avoided by careful start-up. The reactor was started either with a seed latex from a previous run or full of distilled water. Both procedures were successful in achieving steady operation in some cases. In other cases, however, significant transients were observed after a smooth start-up. 

Continuous processes involving tubular reactors have been reported in the literature (General References 2, 7, and ). Continuous tubular reactors have been used in three ways. Gonzalez (9) used a tubular prereactor to feed a CSTR system. The tubular prereactor served as a particle nucleation system and thus solved the problem of conversion oscillations often observed in CSTR systems. A tubular prereactor also can be used to generate a higher particle concentration than would be produced with the same recipe in a CSTR system. 

A technique has been developed for the continuous measurement of emulsion surface tension based on the pressure necessary to form a bubble in liquid. Details of the method may be found in Schork and Ray [24]. With a laboratory prototype of the bubble tensiometer, it has been possible to measure surface tensions continuously to within 1 to 2% [24]. A commercial instrument based on these principles is now available. Figures 5.5 and 5.7 demonstrate the use of the bubble tensiometer to monitor the surface tension of methyl methacrylate emulsion during continuous and batch polymerization. It will be noted that during conversion oscillation the surface tension oscillated as well, in accordance with the discrete initiation mechanism often postulated to explain this phenomenon. 

The same type of oscillations seen in laboratory-scale reactors have been reported for industrial copolymerization reactors (Keane, 1972). In a model of vinyl acetate polymerization in an industrial-scale reactor, Teymour and Ray (1992b) discovered a wide range of dynamical behavior, including a perioddoubling route to chaotic oscillations. Oscillations in temperature ranged in amplitude from 70 to 140 °C. The extent of conversion oscillated from about 0.5 to almost 1. Obviously, behavior of this type would be detrimental to the operation of a plant. 

In this study fast warm-up has been selected as the most important design criterion. The converters are compared by the time needed to achieve 50 percent conversion in the NEDC test. The criterion is fulfilled only if the conversion continues the rice after it achieves 50 percent. Thus, the criterion excludes cases where the 50 percent conversion is only temporarily exceeded. Light-off for catalyst 2 is complicate. In the beginning conversion oscillates between zero and over 80 percent several seconds until it stabilises. The results are shown in table 2. 

Even when there are no disturbances in the feed or in the reactor conditions, a cooled CSTR may still show some instability. This has been studied extensively by Fortuin and coworkers, who found that sustained oscillations or limit cycles may occur. Apparently there exist several possible steady states, that all satisfy eq. (8.8). It may happen that the reactor temperature and the conversion oscillate between two steady states. Under particular conditions, a slight disturbance may be magnified, resulting either in a runaway or in complete extinction of the reaction. Several of these phenomena were demonstrated both by simulation and by real experiments (Vermeulen and Fortuin, 1986, Vleeschhouwer and Fortuin, 1990). 

Gonzalez (6,7) used a tubular pre-reactor upstream of a CSTR to generate a particle seed to feed into the CSTR. The motivation for this work was to control the conversion oscillations often observed in CSTR systems. A tube-CSTR series has a number of potential advantages which will be reviewed in this paper. 

Because the rate coefficients of reactions I and II are directly proportional to the concentration of the corresponding product B respectively C, stages I and II are autocatalytic reactions, i.e. during the run of the conversion oscillations can be originated. To start the reaction, B and C must exist at least in marginal amounts or be produced by intrinsic parallel reactions. Here the latter option is neglected simplifying the illustration of the conversion, which is in any case not simple but already, apart from that, a mathematically and analytically complex. 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

It should be noted that, whereas ferroelectrics are necessarily piezoelectrics, the converse need not apply. The necessary condition for a crystal to be piezoelectric is that it must lack a centre of inversion symmetry. Of the 32 point groups, 20 qualify for piezoelectricity on this criterion, but for ferroelectric behaviour a further criterion is required (the possession of a single non-equivalent direction) and only 10 space groups meet this additional requirement. An example of a crystal that is piezoelectric but not ferroelectric is quartz, and ind this is a particularly important example since the use of quartz for oscillator stabilization has permitted the development of extremely accurate clocks (I in 10 ) and has also made possible the whole of modern radio and television broadcasting including mobile radio communications with aircraft and ground vehicles. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

Lick Observatory. The success of the LLNL/AVLIS demonstration led to the deployment of a pulsed dye laser / AO system on the Lick Observatory 3-m telescope (Friedman et al., 1995). LGS system (Fig. 14). The dye cells are pumped by 4 70 W, frequency-doubled, flashlamp-pumped, solid-state Nd YAG lasers. Each laser dissipates 8 kW, which is removed by watercooling. The YAG lasers, oscillator, dye pumps and control system are located in a room in the Observatory basement to isolate heat production and vibrations from the telescope. A grazing incidence dye master oscillator (DMO) provides a single frequency 589.2 nm pulse, 100-150 ns in length at an 11 kHz repetition rate. The pulse width is a compromise between the requirements for Na excitation and the need for efficient conversion in the dye, for which shorter pulses are optimum. The laser utilizes a custom designed laser dye, R-2 perchlorate, that lasts for 1-2 years of use before replacement is required. 

Abstract Optical Parametric Oscillators provide a very efficient source of tunable coherent radiation. The principle of different kinds of OPOs are described. OPOs are used in astronomy for Laser Guide Star systems, and they may be used for other nonlinear optics applications in astrophysics, such as frequency conversion or parametric amplification. 

Changes in thermal stability and mass due to the formation of CdS nanoparticles in LB films were examined [180]. The LB films were formed onto gold-coated quartz oscillators from monolayers of arachidic acid or nonacosa-10,12-diynoic acid on CdCH containing subphases. The films were exposed to H2S gas until the mass change indicated complete conversion of Cd to CdS. The thermal stability of the H2S-treated films was reduced, with significant mass loss initiating at 55°C, compared to minimal mass loss in the untreated films up to at least 80°C under mild vacuum. The average CdS-particle size... 

When a sound wave, propagated by a series of compression and rarefaction cycles, passes through a liquid medium it causes the molecules to oscillate aroimd their mean position. During the compression cycle the average distance between molecules is reduced and, conversely, it is... 

Figure 2 shows the result of an experiment without photocatalyst where the reactor tenperature was maintained at 97°C during the run. Note that conversions of methane remain relatively constant at - 4% and production of hydrogen, methanol, oxygen, and carbon monoxide remain constant during the ejqjeriment. The large oscillations in the conversion of methane and the production of methanol were not observed during this ejqjeriment. 

When finger agnosia was present, there were more errors with the nonpreferred hand (2.05 mean errors) than with the preferred hand (1.88 mean errors). Fewer than 10 percent of the sample showed performances on the hand dynamometer below the normative standards. Conversely, nearly 50 percent of the sample showed below normal performances on the finger oscillation test, a finding that suggests that fine motor dysfunction is more prevalent as a result of PCP and other drug abuse than gross motor dysfunction. 

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