Reactant consumption

A thermal oxidizer is a chemical reactor in which the reaction is activated by heat and is characterized by a specific rate of reactant consumption. There are at least two chemical reactants, an oxidizing agent and a reducing agent. The rate of reaction is related both to the nature and to the concentration of reactants, and to the conditions of activation, ie, the temperature (activation), turbulence (mixing of reactants), and time of interaction. 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

Also, a specific analysis for the intermediate itself may be developed. It may be detectable at levels below those discernible as discrepancies in the mass balance. If the concentration of. the intermediate is very low, Eqs. (1-5) and (1-6) hold. If not, then reactant consumption and product buildup occur at different rates. Such complications will be considered in Chapters 3 and 4. Most complexities in kinetics involve reactive intermediates. Relatively few reactions of significance occur in a single step, so issues concerning intermediates will recur throughout this book. 

He also notes a situation where the rate constant for product buildup appears to be larger than that for reactant consumption. This signals intervention of an intermediate and is a special case of Eq. (4-25). The chemical equations are... 

That the rates of reactant consumption and product growth are equal in the steady state is a consequence of setting d[Vjdt = 0. We can see this from the mass conservation relation,... 

In the premixed case and for lean conditions (equivalence ratio less than 1), the volumetric rate of reactants consumption q can be estimated from the light emission intensity I of excited radicals like C or CH [28,33] and OH [34] in the reachon zone. This can be used effectively to measure the volumetric rate of reactants consumption ... 

Fine chemicals are often manufactured in multistep conventional syntheses, which results in a high consumption of raw materials and, consequently, large amounts of by-products and wastes. On average, the consumption of raw materials in the bulk chemicals business is about 1 kg/kg of product. This figure in fine chemistry is much greater, and can reach up to 100 kg/kg for pharmaceuticals (Sheldon, 1994 Section 2.1). The high raw materials-to-product ratio in fine chemistry justifies extensive search for selective catalysts. Use of effective catalysts would result in a decrease of reactant consumption and waste production, and the simultaneous reduction of the number of steps in the synthesis. 

Adler, J. and Enig, J.W., 1964, The Critical Conditions in Thermal Explosion Theory with Reactant Consumption, Combustion and Flame 8, 97. 

Most reactor operations involve many different variables (reactant and product concentrations, temperature, rates of reactant consumption, product formation and heat production) and many vary as a function of time (batch, semi-batch operation). For these reasons the mathematical model will often consist of many differential equations. 

One rather unfortunate aspect of the M + hydrocarbon (and M + OX) reactions mentioned thus far is that the products of the reactions were not detected directly, but were instead inferred via the pressure and temperature dependencies of the measured rate constants for metal reactant consumption and by comparison to ab initio calculations. Exceptions are the reactions of Y, Zr + C2H4 and C3H6, for which the Weisshaar group employed the 157 nm photoionization/mass spectrometry technique to identify the products of the reaction as those resulting from bimolecular elimination of H2.45 47 95... 

In the simplest form of the theory, reactant consumption is ignored, i.e. [A] = [A]q. This is often a reasonable assumption, but allowance can be made for depletion of reactant by reaction before explosion if necessary [16-18],... 

The Frank-Kamenetskii theory has been extended to allow for reactant consumption [16—18], other geometries [19, 20] and heat transfer by convection as well as conduction, this being particularly important in gaseous systems when the Rayleigh number Ra > 600 [21]. ... 

Conserving mass explicit incorporation of reactant consumption... 

We may now allow for reactant consumption explicitly by restoring the exponential decay, p = p0e- °. In dimensionless terms this means recognizing that p is a time-dependent parameter, p = /i0e . The governing rate equations are... 

We will regard a and 6 as functions of the reactant concentration as expressed in fi and assume that they change on a fast timescale compared with reactant consumption (small e), i.e. we apply the pseudo-stationary-state hypothesis. The pseudo-stationary-state condition da/dt = dO/dz = 0 yields the following simultaneous equations ... 

Some typical oscillatory records are shown in Fig. 4.6. For conditions close to the Hopf bifurcation points the excursions are almost sinusoidal, but this simple shape becomes distorted as the oscillations grow. For all cases shown in Fig. 4.6, the oscillations will last indefinitely as we have ignored the effects of reactant consumption by holding /i constant. We can use these computations to construct the full envelope of the limit cycle in /r-a-0 phase space, which will have a similar form to that shown in Fig. 2.7 for the previous autocatalytic model. As in that chapter, we can think of the time-dependent... 

We now know that if a system on the upper branch of the isola, just below the Hopf bifurcation point, is given a small perturbation which remains within the unstable limit cycle, it will decay back to the upper solution. If, however, the perturbation is larger, so we move to a point outside the cycle, we will not be able to get back to the upper solution the system must move to the other stable state, with no reactant consumption. 

Fig. 9.3. Stationary-state concentration profiles aS5(p) for a reaction-diffusion cell with a single cubic autocatalytic reaction (a) D = 0.1157, only small extents of reactant consumption arise (b) D = 0.0633, a higher extent of reactant consumption occurs, particularly towards the centre...

Critical conditions in thermal expin theory with reactant consumption 3 C S60... 

Until recently the major problems in the study of combustion have been analytical since it is essential to determine products in the earliest stages of reaction when secondary reactions involving products can be shown to be unimportant. Generally this implies reactant consumptions below 0.1 or 1%. Only gas chromatography is capable of adequate sensitivity, selectivity, and quantitative accuracy under these conditions. However, even gas chromatography has not been able to deal effectively with the analysis of peroxides, and there is need for more work in this field. 

The reactions when ferric chloride or ferric acetylacetonate is present occur in three stages (1) an initial fast reaction decreasing in rate, (2) an arrest during which the oxidation rate may be very low, and (3) a "sigmoid phase in which an autocatalytic reaction is finally overtaken by reactant consumption. With the ferric (bissalen) chloride complex, the reaction was accelerated but Stages 1 and 2 did not appear (curve 340R, Figure 2). 

When quoting a reaction rate, it s important to specify the reactant or product on which the rate is based because the rates of product formation and reactant consumption may differ, depending on the coefficients in the balanced equation. For the decomposition of N205,4 mol of N02 form and 2 mol of N205 disappear for each mole of 02 that forms. Therefore, the rate of formation of 02 is one-fourth the rate of formation of N02 and one-half the rate of decomposition of N205 ... 

Thus the reactant consumption function C(Ca) on the right-hand side of (3.23) is a straight line with slope a, or C Ca) = a Ca, and the reactant supply function S(Ca) on the left-hand side of (3.23) is S(Ca) = Cas — Ca- We can easily solve (3.23) graphically to find the steady-state solution Cass, since the steady state occurs when C(Cass) = S(Cass), or at the intersection of the two lines. 

F. Cell Reactant Consumption Time Faradaic Mole Density (I/(nFAc)) 10 2 moi m"V1 Specific Mole Density (ph) 10 3 mohm 2 10° s... 

M 35] [protocol see [119]] A protein conformation kinetic study of the small protein ubiquitin was performed both in the continuous and in a stopped-flow mode at low reactant consumption [119], The bifurcation mixer was used prior to an IR flow cell for data monitoring. The change of conformation from native to the A-state was followed when adding methanol under low pH conditions to the protein solution. In the continuous mode, long data acquisition could be made and the reaction time was determined by the flow rate and the volume interconnecting zone between the mixer and IR flow cell, which was small, but not negligible. In the stopped-flow mode, the reaction time resolved was dependent on the time resolution of the FTIR instrument. 

Less conservative criteria for runaway can be found by removing the assumption of negligible reactant consumption. Along this line, a class of runaway criteria has been devised by linking the reactor behavior to suitable geometric features of the temperature-time history. 

J. Adler and J.W. Enig. The critical conditions in thermal explosion theory with reactant consumption. Combustion and Flame, 8 97-103, 1964. 

In order to explain the mechanism of the Fisher-Tropsch reaction, some authors derived the Langmuir-Hinshelwood or Eley-Rideal types of rate expressions for the reactant consumption, where in the majority of cases the rate-determining step is supposed to be the formation of the building block or monomer, methylene [134],... 

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