Reaction rate time delays

Barrier Layers. Depending on composition, barrier layers can function simply as spatial separators or they can provide specified time delays by swelling at controlled rates or undergoing reactions such as hydrolysis or dissolution. Suitable barrier materials include cellulose esters and water-permeable polymers such as gelatin and poly(vinyl alcohol) (see Barrier polymers). 

Crisp and coworkers found that the development of surface crystallinity was related to the speed of set. The faster the reaction, the shorter was the inhibition period before surface crystallization took place. When the setting time of a cement was between two and three minutes, surface crystallinity developed in a few minutes. When it was seven minutes, surface crystallinity was delayed by three hours. The reaction rate was affected by the chemical composition and physical state of the cement components. Well-ignited zinc oxide, the presence of magnesium in the... 

Transient kinetic experiments have also been carried out to complement the information deduced from the steady-state measurements [33], Systematic variations were observed during the transition from the clean surface to the steady-state catalytic regime that correlate well with the overall reaction rates in the latter. Specifically, there is a time delay in the production of molecular nitrogen because of the need to buildup a threshold of atomic nitrogen coverage on the surface. This atomic nitrogen coverage, which could... 

Reaction rate experiments were conducted in NMR tubes sealed with Teflon valves. In an inert atmospere glovebox, catalysts and internal standard, TMS4C, were weighed into the tube, followed by addition of solvents and reactants. The tube was immediately inserted in the preheated (50 °C) probe of a 500 MHz Varian Unitylnova spectrometer. To acquire spectra the sample was irradiated twice with a 30° pulse, 5 sec acquisition time, and 120 sec delay. 

The outline of this paper is as follows. First, a theoretical model of unsteady motions in a combustion chamber with feedback control is constructed. The formulation is based on a generalized wave equation which accommodates all influences of acoustic wave motions and combustion responses. Control actions are achieved by injecting secondary fuel into the chamber, with its instantaneous mass flow rate determined by a robust controller. Physically, the reaction of the injected fuel with the primary combustion flow produces a modulated distribution of external forcing to the oscillatory flowfield, and it can be modeled conveniently by an assembly of point actuators. After a procedure equivalent to the Galerkin method, the governing wave equation reduces to a system of ordinary differential equations with time-delayed inputs for the amplitude of each acoustic mode, serving as the basis for the controller design. 

When the reduction of stored NO is accomplished at 150 °C, the reaction shows a significant induction period (Figure 13.17). The decrease in the H2 concentration is accompanied by the evolution of NH3 and of minor amounts of N2 however, a time delay is observed between product evolution and H2 uptake. Therefore, the rate of reaction is low at this temperature and a critical high surface concentration of activated hydrogen species is needed for the reaction to occur. The regeneration of the catalyst is not complete, since only 80% of the stored NO could be reduced after prolonged treatment with H2 at 150 °C. Also, the calculated overall N2 selectivity is very poor, below 20%, and ammonia represents the main reaction product. 

This is due to the fact that under isothermal conditions, the nth-order reaction presents its maximum heat release rate at the beginning of the exposure to initial temperature, whereas the autocatalytic reaction presents no heat release rate at this time. Thus, temperature increase is delayed and only detected later after an induction period, as the reaction rate becomes sufficiently fast. Hence acceleration, due to both product concentration and temperature increase, becomes very sharp. 

In the sixth and last step, the system is still considered to be purely conductive, with heat exchange at the wall to the surroundings and the zero-order approximation of the kinetics is replaced by a more realistic kinetic model. This technique is very powerful in autocatalytic reaction, since a zero-order approximation leads to the very conservative assumption that the maximum heat release rate is realized at the beginning of the exposure and maintained at this level, respectively increasing with temperature, during the whole time period. In reality, the maximum heat release rate is delayed, and only achieved later on. Thus, heat losses may lead to a decreasing temperature during the induction time of the autocatalytic reaction. 

Since the concentrations of reactants (Ma, Mp, Me and Mp,) in batch reactor are assumed to be measurable with a delay of one sampling time that is, at time k of the reactor, only information at time A — 1 is available. Thus, the EKF is applied to estimate the value of reactant concentration at current time k from their delayed measurements at sampling time k — 1. However, since it is expected to exhibit uncertainly in reaction rate constant (i.e. k and fcj) in real plant, the EKF is also used to estimate these uncertain parameters. The following equations, therefore, are appended for parameter estimation... 

A PBMR is a thermal reactor, thus delayed neutrons are the important factor in reactor response. A thermal reactor has a time constant of about 55 seconds. In the chemical plant, Section 2 and Section 3 have different response times. Section 2 has a response time on the order of 20 seconds, whereas Section 3 has a response time on the order of 500 seconds. The limiting reaction rate in the chemical plant is that of Section 3. Since the chemical plant is composed of cyclic processes, we know that the slowest reaction rate will occur in Section 3, the HI decomposition section. The response rate of Section 3 provides at least a first-order approximation of the overall plant response. 

The reaction begins without delay. The rate decreases as the degree of conversion increases. A graph showing vinyl concentration according to second order kinetics plotted against time gives a linear relationship (Fig. 5). 

As mentioned at the outset, chain reactions, relying on free radicals as chain carriers, are sensitive toward any substances that can destroy or trap such radicals. The interference with chain propagation can assume two forms. An added substance can reduce the reaction rate to almost nil or bring it to essentially a complete and permanent stop. This is called inhibition. It occurs if the inhibitor catches practically all free radicals produced by the initiator. Under different conditions, an added substance or impurity can delay the start of a chain reaction for some period of time, called an induction period, without affecting its later course. 

Ap/t = p = rate of change of pressure, (Ap)max = maximum pressure increase, p ax maximum rate of change of pressure, = Induction period = time delay from admission of reactants to attainment of Pmax, AT = Reactant temperature excess, T = wall temperature, T) = Compressed gas temperature, T, = ignition delay, / = light emission intensity, Iw-ai = period of maximum rate of reaction given that (I20-60) = kp", Q = heat release rate. 

In the SUPRAYIELD process, the delayed decompression is a degenerated flash process slowed down to such an extent that the period of time for going from a high primary pressure to a lower secondary pressure corresponds to the reaction time needed for the desired conversion of pentosan to furfural. To make this a practical proposition, the primary temperature must be high, say 240 °C, and the secondary temperature should not be below 180 °C as in this range the reaction rate would be too slow. 

Delayed-action catalysts have been made successfully. Buffered amine catalysts, where the activity of the amine has been reduced by the presence of an acid, have also been used. Acidic materials can be used to retard the urethane reaction. Hydrogen chloride and benzoyl chloride have been used in combination with amine-type catalysts to control reaction rates. A small percentage of acid can increase foaming time from 2.2 to 6 minutes (20). 

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