Rate of pressure change

Fig. 4. Plot of maximum rate of pressure change for propane VPO showing NTC region 5.33 kPa propane, 13.33 kPa O2. Courtesy of Blackwell Scientific...

Pressure. The absolute pressure is unlikely to have a direct effect on attrition unless it affects the amount of adsorbed surface layers. But there is again an effect on the gas density that is similar to the effect of temperature mentioned above. Moreover, the rate of pressure change may have more influence. 

L. R. Sochet The term used by Dr. Mayo— the maximum rate of pressure change —leads to ambiguity. It is better to talk of the sudden but temporary increase in the over-all rate of reaction which occurs at the same time as an increase in light emission, after the maximum rate of reaction (Figure 1). 

The reaction starts at a low rate as shown by the rate of pressure change and accelerates in the manner commonly associated with degenerate branching. 

The distance rate of pressure change for a unit-volume of gas at a radial distance R is... 

H0 a monotonous decrease in pressure with time is observed, being sharper at higher levels. Data about the rate of pressure change indicate that in a foam which is away from its hydrostatic equilibrium, a linear Ap(H) dependence is realised, the pressure remaining constant and corresponding to the level H0 (Ap is the difference between atmospheric and border pressure). At levels below H0 the pressure increases during the initial period and after a certain period of time begins to decrease. 

Fig. 47. Rates of pressure change outside the ignition limits (after Ashmore and Tyler [276]). 100 mm 2H2 + O2 20 mm diameter quartz vessel temp. = 360 °C. (By courtesy of The Combustion Institute.)...

Lewis and von Elbe have ignited CO/O2 mixtures in the centre of spherical reaction vessels, and have obtained data on the rate of propagation of the flame and the rate of pressure change in the vessel. From such results the burning velocity S, can be calculated [4], according to the thin flame approximation, from eqn. (120),... 

T 45 mm diam., 278 ml vol. NO2 in equilibrium with dissociation products. Zero rate of pressure change initially hence initial rate due to reaction (Ixxvi) alone. d[N02 ]/df measured photometrically. Found —d[N02]/ df oc [CO] 0 -0.02 X [N02]° -°° Rate coefficient in good agreement with ref. 485. ... 

The initial period of acceleration is not very evident if the initial O2 /fuel ratio is high. For ratios greater than unity the maximum rate of pressure decrease (pm a x) is attained somewhere between one-quarter and one-third of the total reaction. Most investigators have found Pmax oxygen independent (except for O2 /fuel ratios very much less than unity) and approximately second order with respect to the initial aldehyde pressure (Table 1). The overall activation energy (based on the maximum rate of pressure change) between 90 and 150 °C is about 15 kcal. mole" (Table 2). 

For aged vessels k had a value of 12.8 x 10" torr min and d(HCHO)/dt was approximately twice the rate of pressure change for HNO3 cleaned surfaces or for reactions in the presence of mercury vapour k was 9.1 X 10" (torr) min" and the rate of formaldehyde consumption was very much greater than twice the rate of pressure change. 

The sensitivity of the relationship between the rates of pressure change and formaldehyde consumption to surface conditions means that it is desirable that the kinetics should be discussed in terms of aldehyde loss rather than of pressure change. This has not always been done, and consequently it is difficult to compare many of the reported activation energies for the oxidation. These (Table 8) cover a large range, the spread being a further indication of the sensitivity of this oxidation to surface and reaction conditions. 

Fig. 2. The influence of temperature on 6, the induction period in minutes, and Pmax maximum rate of pressure change in torr. min" of combustion of alcohols [26]. Alcohol pressure (at 295 °C), 40 torr oxygen pressure (at 295 °C) 200 torr. O, n-butanol , iso-butanol , sec-butanol x, fcrf-butanol.

Methanol is somewhat less reactive than its higher homologues and slow combustion takes place at a conveniently measurable rate only above 390 °C. In uncoated pyrex vessels [7], or vessels coated with boric acid or potassium chloride [8], reaction begins immediately without a true induction period and accelerates to a maximum rate. This maximum is increased by the addition of inert gas and is proportional to the square of the initial methanol concentration, (in boric acid coated vessels this power is about 2.5) but independent of oxygen concentration over a wide range of conditions. The overall activation energy (calculated from the effect of temperature on the maximum rate of pressure change) is about 40 kcal.mole" in coated vessels and about 53—61 kcal.mole in uncoated ones. 

The induction periods and maximum rates of pressure change of iso-and sec-butanol are very similar under all conditions examined by Cullis and Warwicker [26]. The products in the induction period at 295 °C are methyl ethyl ketone and hydrogen peroxide, together with a little acetaldehyde, and, at 400 °C, some formaldehyde. 

Fuel Temp. (°C) Partial pressure Induction period (min) Max. rate of pressure change (torr. min" ) Activation energy (of max. rate) (kcal. mole" ) Ref. 

Fig. 6.3. First evidence for a region a negative temperature dependence of reaction rate in a closed vessel. The ordinate refers to the rate of change of reactant concentration, deduced from the fractional rate of pressure change. (After Pease [4].)...

The autocatalytic nature of the reaction (see Chapters 1 and 5), which may be a limitation on the validity of the underlying assumption about a constant reaction stoichiometry (i.e., constant y and z), requires there to be a specific reference point at which the rate of pressure change may be compared. The usual reference is taken to be the maximum rate of pressure change in each experiment (pmax)- This approach has been exploited extensively over the years, and there are very many other examples to be found in the literature (Table 6.1). For example, Wu et al. [15], investigating the gaseous oxidation of butane in the temperature range 470-810 K, were... 

Fig, 6,4. Relationship between the maximum rate of pressure change (pmax) and reciprocal inclination time (100/P) as a function of closed vessel temperature and the time to the attainment of the maximum rate of pressure change, the induction time (t,). (After Shu... 

Knox and Norrish [7] showed that, during the oxidation of ethane in a closed vessel, the vessel temperature at which pmax exhibited a maximum and a minimum coincided with a maximum and a minimum of an associated temperature change, AT (Fig. 6.5). Whilst these observations are a qualitative confirmation that there is a negative temperature dependence of overall rate for ethane oxidation, the relationship of the rate of pressure change in a closed vessel under non-isothermal conditions to the reaction rate is a complicated one [37]. Differentiating (6.5) with respect to time gives the rate of pressure change. 

Supplementary points that relate to Fig. 6.5 are (i) whether or not, the maximum rate of pressure change is a useful practical parameter for the interpretation of the reaction rate under non-isothermal conditions, and (ii) whether or not, the range of vessel temperatures within which the ntc is found to exist from pressure measurements is a satisfactory representation even if there is some quantitative discrepancy from the rate of reactant consumption. The correction term in equation (6.9) may not be negligible, and it is certainly not constant, since it is known that the intervention of temperature change during the autocatalytic oxidation of alkanes causes the maximum rate of reactant consumption to occur at increasing extents of reaction [38, 39]. 

A condition for the maximum rate of pressure change during reaction under non-isothermal conditions is obtained by differentiating (6.7) with respect to time and equating it to zero [37]. 

By substituting (6.3) and its first and second differentials with respect to time in (6.10) the condition for a maximum rate of pressure change during non-isothermal reaction corresponds to... 

Clearly, some caution must be exercised in the interpretation of data which involve measurements of rates of pressure change under non-isothermal conditions. Unfortunately, whether or not self-heating has occurred in... 

A number of useful points emerged from this exercise, the main kinetic conclusions of which are discussed in detail elsewhere [227]. For present purposes we may note that a negative temperature dependence of reaction rate, simulated as a rate of pressure change in a closed vessel, was predicted to exist in a similar temperature range to that observed experimentally. Moreover, multiple cool-flames, in satisfactory accord with the experimental observations, were also predicted. The underlying kinetic structure which gave rise to the ntc of rate was of the form. 

Rate of temperature change Rate of pressure change Agitator or pump speed Batch time... 

SURGE TANK - Container connected to the low-pressure side of a refrigerating system which increases gas volume and reduces rate of pressure change. 

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