Characteristic reaction time constant

The reaction system, the experiment procedure, and the analytical method used for the determination of micromixing in the TIJ mixer are the same as those described in the last section of this book but Mahajan et al. correlated their experimental data not with impinging velocity w() but with the jet Reynolds number Re. Also, the researchers employed the measure of increasing both the initial concentration CBo and the reaction temperature to raise the sensitivity of the procedure. The characteristic reaction time constant tK = 200 ms at 25 °C and CBo = 2.5 mM, while rR = 65 ms at 35 °C and CB0 = 4.7 mM, which can be used to bound the micromixing times, rM, no greater than them, respectively. 

Under the inherent assumption that the mass fractions of the reactants are not changing, further interesting insights can be obtained by rearranging Eq. (7.22). If the reaction proceeds at a constant rate corresponding to T(), a characteristic reaction time rr can be defined as... 

This equation, sometimes called the test equation in texts on numerical differential equations [13], has an important resemblance to chemical kinetics. Specifically, the rate of disappearance of y is proportional to y itself. As X (i.e., the rate constant) increases, the shorter the characteristic reaction time. The general solution to this problem is obviously... 

A similar study of the reaction of acetylene with iron supported on quartz was made by Maksimov et al. (240). The Mossbauer spectrum before reaction with acetylene was a spectral doublet characteristic of iron silicate. After reaction at 1270 K for 50 sec the sample was quenched to room temperature, and in the subsequent Mossbaucr spectrum a new peak was noted. The intensity of this peak increased with increasing reaction time up to 0.1 hr, after which time the intensity remained constant. In this case, it was only possible to study the rate of this surface reaction using a series of low-temperature quenches, since the characteristic reaction time was the order of time required to obtain the Mossbauer spectrum. 

The modified Stanton criterion compares the characteristic reaction time with the thermal time constant of the reactor. The time can be eliminated from the equations by building the ratio ... 

A simple, homogeneous (slow) first-order reaction was considered. Simulations were carried out for cases with and without impeller in the same cubical reactor. Initial and boundary conditions are shown in Fig. 7.20. It can be seen that the mean residence time of the reactor is 10 s. Three cases with different first-order reaction rate constants (0.01s", 0.1s", 1.0s" ) were simulated (samples of the results are listed with Fig. 7.20). Results of simulations with an impeller velocity of 5 m s" are discussed first. As expected, for the lowest reaction rate constant, where the characteristic reaction time scale is much higher than mean residence time, the simulated results agree quite well with the analytical solution obtained based on the assumption of a completely mixed reactor. Even for the case of characteristic reaction time scale of 10 s (which is the same as the residence time), deviation from the analytical solution (of predicted outlet concentration of reactant) is just about 1% (for the case with rate constant 0.1 s" ). As the reaction time scale becomes smaller than residence time (rate constant 1.0 s" ), deviation increases and is equal to 33% If the reaction... 

The main difficulty in determining the reaction rate r is that the extent is not a measurable quantity. Therefore, we have to derive a relationship between the reaction rate and the appropriate measurable quantity. We do so by using the design equation and stoichiometric relations. Also, since the characteristic reaction time is not known a priori, we write the design equation in terms of operating time rather than dimensionless time. Assume that we measure the concentration of species j, Cj(t), as a function of time in an isothermal, constant-volume batch reactor. To derive a relation between the reaction rate, r, and Cj(t), we divide both sides of Eq. 6.2.4, by obtain... 

In other words, E is not a function of conversion or molar densities. The characteristic chemical reaction time constant is 25 min. The temperature is the same in each case. The following reactor configurations are employed. 

One liquid-phase chemical reaction occurs in an isothermal configuration of PFRs. The chemical kinetics are second order and irreversible [i.e., lEt = 2(Ca) ], and the characteristic chemical reaction time constant A. is 5 min. Rank the configurations listed in Table PI-3 from highest final conversion of reactant A in the exit stream of the last PFR in series to lowest final conversion in the exit stream of the last PFR. In each case, the volumetric flow rate is 10 L/min and Ca, miet is the same. Calcnlate the final conversion of reactant A in the exit stream of the third PFR in series for case 7. 

As expected, a shorter reactor is required to achieve the same final conversion when the characteristic chemical reaction time constant u> is smaller and the effectiveness factor E is larger. Since the integral in equation (22-27) that contains the dimensionless kinetic rate law reduces to a constant when the final conversion of... 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

The Damkoehler number Da represents the ratio of a characteristic reaction time to the kinetic time constant of the reaction and is therefore a measure for the reaction time. The attribute characteristic refers to the individual definition necessary for each... 

The Damkohler number [7], Da = Hk( ref/F, is the ratio of a characteristic liquid residence time (H/F) to the characteristic reaction time (1/kf f), where, k( is the rate constant for the reference reaction, (p = V/F, is the fraction of liquid feed that is vaporized. Using these parameters in (6.3), we get... 

This is the ratio of the characteristic liquid residence time to a characteristic reaction time, kf is the forward rate constant at a reference temperature, No reaction occurs in the limit Doj — 0 and reaction equilibrium is achieved as Duj —> oo. At intermediate Daj, the stage operates in the kinetically controlled regime. Incorporating j and Doj in (6.8), we find... 

The ignition/extinction results and responses to changes in load provide information about the time scales for the response of the fuel cell. The time constant for transitioning to steady state during startup is 100 s. Five of the key time constants associated with PEM fuel cells are listed in Table 3.1.They include the characteristic reaction time of the PEM fuel cell (ti), the time for gas phase transport across the diffusion layer to the membrane electrode interface (T2), the characteristic time for water to diffuse across the membrane from the cathode to the anode (ts), the characteristic time for water produced to be absorbed by the membrane (T4), and the characteristic time for water vapor to be convected out of the fuel cell (T5). Approximate values for the physical parameters have been used to obtain order of magnitude estimates of these time constants. 

On the basis of the rate constants measured, the following characteristic reaction times result ... 

Characteristic Reaction Time. As shown in Example 13-1, mixing can affect the selectivity of a reaction, not just the rate. Reactions that show selectivity are usually two-step reactions which are either consecutive or parallel. One reaction is usually so fast that it is mixing controlled. The second reaction has a characteristic time constant of the order of the local mixing time. The reaction time is usually given by... 

The heat-transfer coefficient between the measuring kettle and the thermostat has a defined, finite value in accordance with which the heat transfer between their fillings occurs in a definite way The process is marked by a characteristic thermal time constant Trti,. Just so, a definite transfer coefficient exists for the heat flow from the reaction mixture into the temperature sensor, i.e. the heat flow is also marked by a characteristic time constant Tp. 

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