Pressure propagation rate

Relationship Among Critical Discharge Rate, Pressure Propagation Rate, and Sonic Velocity... 

The effect of temperature, pressure, and oil composition on oil recovery efficiency have all been the subjects of intensive study (241). Surfactant propagation is a critical factor in determining the EOR process economics (242). Surfactant retention owing to partitioning into residual cmde oil can be significant compared to adsorption and reduce surfactant propagation rate appreciably (243). 

As propagation rates of gassy reactions are pressure dependent, so are gasless reactions temp dependent. This temp dependence has been... 

The rate of pressure rise is indicative of the flame front propagation rate and thus of the magnitude of the explosion. The pressure rate or slope is computed at the inflection point of the pressure curve, as shown in Figure 6-15. The experiment is repeated at different concentrations. The pressure rate and maximum pressure for each run are plotted versus concentration, as shown in Figure 6-16. The maximum pressure and maximum rate of pressure rise are determined. Typically, the maximum pressure and pressure rates occur somewhere within the range of flammability (but not necessarily at the same concentration). By using this relatively simple set of experiments, the explosive characteristics can be completely established in this example the flammability limits are between 2% and 8%, the maximum pressure is 7.4 bar, and the maximum rate of pressure rise is 360 bar/s. 

Deflagration tests run under ambient pressure are relatively rudimentary. They provide information concerning only the propagation rate of deflagration after forced initiation. Examples of these tests are the UN deflagration test [143], dedicated to classification of organic peroxides, and the UN trough test [145], dedicated to classification of fertilizers. 

On increasing the pressure, the rate of diffusion of the radicals to the walls decreases and therefore the rate of destruction of radicals also slows down while the rate of propagation and branching increases. Thus due to a considerable rise in concentration of radicals the rate of reaction increases enormously leading to an explosion. This is called lower explosion limit and depends upon the size and shape of the vessel. 

The life-time, r, of the radicals can be determined from the ratio of overall rates of polymerization measured at the steady- and unsteady state as a result of intermittent illumination by the rotating sector. In Fig. 3.3-10 the rate constant, kp, of chain propagation (left) and kh that of termination (right), are plotted versus the pressure. Both rate constants increase with increasing temperature. The energy of activation of chain propagation is Ep = 37 kJ/mol, and that of chain termination is E, = 9.9 kJ/mol. The influence of pressure is... 

Methyl branching also occurs in the preparation of many polymers. Ordinarily methyl branches are present in only trace amounts, barely detectable by the most sensitive 13C-NMR(69), and they have no effect on polymer properties. But if the polymerization is carried out at atmospheric pressure or less, methyl branching becomes much more common (69). It may originate from isomerizarion at the active site. This isomerization is probably not favored but does occur very rarely (Scheme 2). Low pressure decreases the propagation rate, allowing each chain to spend more time around the active site, thus increasing the probability of such side reactions. Internal... 

Calculations which relate the concentration limits to losses by thermal radiation lead to the conclusion that, as the pressure is raised, the minimum possible propagation rate decreases proportionally to p-1/2. Unfortunately, we do not have the data necessary to compare this assertion with experiment. Reliable measurements of the flame velocity (especially for slow flames) at non-atmospheric pressures are rarely encountered. 

Initial pressure affects maximum explosion pressure and rate of pressure rise. If the initial pressure is increased above atmospheric pressure, there will be a proportional increase in the maximum explosion pressure and in the rate of pressure rise. Reducing the initial pressure will cause a corresponding decrease in maximum explosion pressure until finally an explosion reaction can no longer be propagated through the gas mixture. 

On the basis of this observation and of the preliminary results reported by Bor-diga et al. (210), Groppo et al. (183) repeated the experiment reported in Fig. 24 in presence of a CO poison, with the hope of lowering the propagation rate and hence increasing the concentration of the initial species. The result is shown in Fig. 25, which is the analogue of the experiment reported in Fig. 24, but performed in the presence of a CO poison (1 kPa of C2FI4 in the presence of a CO equilibrium pressure of 65 Pa). The complex series of bands shown in Fig. 25 is very similar to... 

Figure 16 shows the pressure drop across the core as a function of pore volume of nitrogen gas injected. The highest pressure drop is always observed before the gas breakthrough (it is worth noting, for the C,A0S system, the faster propagation rate of oil is accompanied by a more rapid increase in the pressure drop). 

FIGURE 7.6 Fatigue crack propagation rate (daldN) vs. stress intensity factor range (AK) relationships measured in low-pressure hydrogen gas for two low-alloy steels with different tensile strengths. " ... 

The effect of pressure on the rate of free radical propagation reactions has been studied in homopolymerizations only for styrene. Since aV is negative for this reaction, the apphcation of pressure increases the propagation rate. Nicholson and Norrish (12) list the propagation rate constant for styrene as 72.5 liters-mole- —sec.- at atmospheric pressure and 30° C. This increases to 206 liters-mole —sec. at 2000 atm. and 400 hters-mole —sec. at 3000 atm. From these data it is possible to calculate the value of AV for the propagation step to be —13.3 cc. per mole. Walling and Pellon (16) report a value of —11.5 cc. per mole for the same reaction measured by a different technique. 

From an extended set of SP-PLP experiments carried out at temperatures between 190 and 230 °C and at pressures between 1950 and 2900 bar, Schweer [24] derived expressions for the temperature, pressure, monomer conversion (X), and viscosity (t)) dependence of termination and propagation rate coefficients for the ethene homopolymerization, eqs (4.6-2) and (4.6-3). 

The terminal model approach may also be used to investigate the pressure dependence of cross-propagation rate coefficients kjj. As pressure-dependent studies are restricted to Te, only the activation volume of ea. A0(A ea). may be estimated from experimental data ... 

Figure 4.6-12 Variation of the propagation rate coefficient kp with (a) temperature at ambient pressure and (b) pressure at 30°C for the following monomers methyl methacrylate (MMA), butyl methacrylate (BMA), and dodecyl methacrylate (DMA) methyl acrylate (MA), butyl acrylate (BA), and dodecyl acrylate (DA) for references see text.

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