Heat transfer limitations

Copolymerization is effected by suspension or emulsion techniques under such conditions that tetrafluoroethylene, but not ethylene, may homopolymerize. Bulk polymerization is not commercially feasible, because of heat-transfer limitations and explosion hazard of the comonomer mixture. Polymerizations typically take place below 100°C and 5 MPa (50 atm). Initiators include peroxides, redox systems (10), free-radical sources (11), and ionizing radiation (12). 

P. Vin2 and C. A. Busse, "Axial Heat Transfer Limits of Cylindrical Sodium Heat Pipes Between 25 W/cm and 15.5 kW/cm, " International Heat Pipe Conference, Stuttgart, Germany, 1973. 

The LDPE reactor is sometimes termed heat transfer limited in conversion. While this is true, the molecular weight (or melt index)—conversion relationship is not since this work shows that a selected initiator can allow conversion improvements to be made under adiabatic conditions for a specified molecular weight. The actual limitation to conversion is the decomposition temperature of the ethylene and given that temperature as a maximum limitation, an initiator (not necessarily commercial or even known with present initiator technology) can be found which will allow any product to be made at the rate dictated by this temperature. Conceptually, this is a constant (maximum) conversion reactor, runnirg at constant operating conditions where the product produced dictates the initiator to be used. 

Recycling of partially reacted feed streams is usually carried out after the product is separated and recovered. Unreacted feedstock can be separated and recycled to (ultimate) extinction. Figure 4.2 shows a different situation. It is a loop reactor where some of the reaction mass is returned to the inlet without separation. Internal recycle exists in every stirred tank reactor. An external recycle loop as shown in Figure 4.2 is less common, but is used, particularly in large plants where a conventional stirred tank would have heat transfer limitations. The net throughput for the system is Q = but an amount q is recycled back to the reactor inlet so that the flow through the reactor is Qin + q- Performance of this loop reactor system depends on the recycle ratio qlQin and on the type of reactor that is in the loop. Fast external recycle has... 

The concept of linear burning rate is not confined to the reaction of a gas with a solid. The fuses on fireworks are designed to bum at a constant linear rate. The flame front on solid rocket fuel progresses at a constant linear rate. Both examples have two reactants (a fuel and an oxidizer) premixed in the soUd. Heat transfer limits the burning rate. These materials are merely fast burning. Unlike explosives, they not do propagate a sonic shockwave that initiates further reaction. 

The following are some of the reasons that microreactors can be be used (i) reduced mass and heat transfer limitations, (ii) high area to volume ratio, (iii) safer operation, and (iv) ease of seating up by numbering out. The advantages of scaling down zeolite membranes are that it could be easier to create defect-free membranes and... 

Four mmoles of malononitrile and benzaldehyde were introduced in a batch stirred tank reactor at 323 K with toluene as solvent (30 ml). Then 0.05 g of aluminophosphate oxynitride was added. Samples were analysed by gas chromatography (Intersmat Delsi DI200) using a capillary column (CPSilSCB-25 m). Care was taken to avoid mass or heat transfer limitations. Before the reaction no specific catalyst pretreatment was done. 

The catalytic experiments were performed at the stationnary state and at atmospheric pressure, in a gas flow microreactor. The gas composition (NO, CO, O2, C3H, CO2 and H2O diluted with He) is representative of the composition of exhaust gases. The analysis, performed by gas chromatography (TCD detector for CO2, N2O, O2, N2, CO and flame ionisation detector for C3H6) and by on line IR spectrometry (NO and NO2) has been previously described (1). A small amount of the sample (10 mg diluted with 40 mg of inactive a AI2O3 ) was used in order to prevent mass and heat transfer limitations, at least at low conversion. The hourly space velocity varied between 120 000 and 220 000 h T The reaction was studied at increasing and decreasing temperatures (2 K/min) between 423 and 773 K. The redox character of the feedstream is defined by the number "s" equal to 2[02]+[N0] / [C0]+9[C3H6]. ... 

GP 11] [R 5] A judgement on heat-transfer limitations on the reaction rate according to the Anderson criterion was made [121]. This inequality predicts no such limitations in the boundary layer when the Anderson criterion is smaller than 1. Using process parameter data applied in a number of experiments, the highest value found was 2.2 10 so that no heat-transfer limitations have to be assumed. 

At this point it is instructive to consider the possible presence of intraparticle and external mass and heat transfer limitations using the methods developed in Chapter 12. In order to evaluate the catalyst effectiveness factor we first need to know the combined diffusivity for use... 

Finally, to conclude our discussion on coupling with chemistry, we should note that in principle fairly complex reaction schemes can be used to define the reaction source terms. However, as in single-phase flows, adding many fast chemical reactions can lead to slow convergence in CFD simulations, and the user is advised to attempt to eliminate instantaneous reaction steps whenever possible. The question of determining the rate constants (and their dependence on temperature) is also an important consideration. Ideally, this should be done under laboratory conditions for which the mass/heat-transfer rates are all faster than those likely to occur in the production-scale reactor. Note that it is not necessary to completely eliminate mass/heat-transfer limitations to determine usable rate parameters. Indeed, as long as the rate parameters found in the lab are reliable under well-mixed (vs. perfect-mixed) conditions, the actual mass/ heat-transfer rates in the reactor will be lower, leading to accurate predictions of chemical species under mass/heat-transfer-limited conditions. 

The amount of heat actually taken up by the particles was an important quantity, as tubes operate under heat transfer limited conditions near the tube inlet. Fig. 30 shows a plot of Q against r, where Q was the total energy flow into the solid particles, for the entire segment. For inlet conditions, Q varied strongly at lower r, but was almost constant at higher values. As rcut/rp decreased from 0.95 to 0.0 and the effectiveness factor increased from nearly zero to one, the active solid volume increased by a factor of 7. If the solid temperature had remained the same, the heat sink would also have had to increase sevenfold. This could not be sustained by the heat transfer rate to the particles, so the particle temperature had to decrease. This reduced the heat sink and increased the driving force for heat transfer until a balance was found, which is represented by the curve for the inlet in Fig. 30. 

All reactor-cells used had a volume of 30 ml and have been shown to be well mixed over the range of flowrates employed in the present study (22). Both external and internal mass and heat transfer limitations have been shown to be negligible (12,22). Reactants were certified standards of ethylene diluted in N2 and Matheson zero grade air. They could be further diluted in N2. Reactants and products were analyzed by one line Gas Chromatography. The carbon dioxide concentration in the product stream was also continuously monitored using a non-dispersive IR CO2 Analyzer (Beckman 864). 

As one limiting case, let us assume no heat transfer limitations so that the pressure inside the bubble is invariant at Pvp(To). Then, using Eqs. (8) and (9), as shown by Plesset and Zwick (1954),... 

In reality, Eqs. (13) and (14) should be solved simultaneously with Eqs. (8) and (9), but no analytical solution is available. However, we can examine the asymptotic solutions to Eqs. (13) and (14) to determine the bubble growth rate when heat transfer limits the growth, i.e., when P r) — Pq and r Tb so no inertial effects are present. For this extreme,... 

This physical limitation is the result of mass and heat transfer limitations, which are stoichiometrically related to product formation. The vertieal dotted line in Figure 11.1 symbolizes the limitation which is a conseqnence of the faet that the eoneentration of the biocatalyst is bound to certain defined limits, for instanee solnbihty in case of isolated enzymes and space in case of suspended eells. Fignre 11.1 also shows that the biocatalyst should have a minimum speeifie aetivity to be able to operate the bioreactor close to its physical ceiling. 

Dissociation (Section 3.3), which is typically heat transfer limited with... 

The different hydrate dissociation models that have been developed by various research groups are summarized in Table 7.10. The majority of these models are based on heat transfer limited dissociation. Some of the models have been developed to incorporate both heat transfer and kinetics. 

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