Time-average reaction rate

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

Soil water flow is decidedly episodic. During dry times the water solutions in the soil are probably fairly concentrated and not very reactive. Time-averaged reaction rates should be roughly proportional to the fraction of time reacting minerals are in contact with thermodynamically imdersaturated (and reactive) water. In a study of the relationship between denudation rate and runoff for rivers draining igneous and metamorphic rock in Kenya, Dunne (1978) obtains the relationship of (denudation rate in tons/km per year) = 0.28 (runoff in mm/ year)°. ... 

Figure 3. Time-averaged reaction rate as a function of period. Key (concentration wave amplitude) Q, 0.24 , 0.12 and-----------, steady-state rate.

Figure 3. Effect of cycle-period on time-average reaction rate. Key Time-average Ht, 0.75 and cycle split, 0.4.

The CO oxidation over noble metal catalyst has been studied most intensively under both steady-state operation and periodic operation. Cutlip [47] studied the CO oxidation on a Pt/Al203 catalyst in a gradientless reactor. The observed time-averaged reaction rates... 

Most reactions slow down as the reactants are used up. In other words, the average reaction rate decreases as the reaction proceeds. The reaction rate may also change over the time interval during which the change in concentration is being measured. 

Reactor production rate depends on average reaction rate and the fraction of the time the reactor is not operating. With a batch reactor the reaction rate starts small, increases to a rather constant value, sometimes increases further to a maximum, and then decreases rapidly as the monomer concentration falls. 

When a reaction generates gas, chemists can monitor the volume of gas produced. In Investigation 6-A, you will determine average reaction rates by recording the time taken to produce a fixed volume of gas. You will perform several trials of the same reaction to investigate the effects that temperature, concentration of reactants, and surface area of reactants have on the reaction rate. You will also perform one trial using a different reactant. 

The average reaction rate is obtained by dividing the change in concentration of a reactant or a product by the time interval in which the change takes place. 

This partial differential equation is made ordinary by taking its Laplace transform. It is then solved for the transform of u and the transform of the total reaction rate for the particle calculated. There is no need to invert this transform, for what we want is the average reaction rate in the bed and this is the integral of the product of the reaction rate after a time a and the probability of the particle having age a. Because the ages are exponentially distributed, this is none other than the Laplace transform with the dimensionless transform variable set equal to 1. The end result is that the Damkohler number is... 

The average reaction rate is the change in concentration either reactant or product per unit time during a time interval ... 

This is found from the absolute value of the slope of a curve of concentration vs. time. An estimate of the reaction rate at time t may be found from the average reaction rate over a small time interval surrounding t. For those familiar with calculus notation, the following equations define reaction rate, but calculus is not needed for this skill ... 

Entrapped Hb within a layered activities of 2.46 and 8.13 times enhancements in the 20 min average reaction rates in toluene and acetonitrile solvents, respectively The layered spongy Co304 was integrated [18]... 

The extension of the two-mode axial dispersion model to the case of fully developed turbulent flow in a pipe could be achieved by starting with the time-smoothed (Reynolds-averaged) CDR equation, given by Eq. (117), where the reaction rate term R(C) in Eq. (117) is replaced by the Reynolds-averaged reaction rate term Rav(C), and the molecular diffusivity Dm / is replaced by the effective diffusivity Dej- in turbulent flows given by... 

The Reynolds-averaged reaction rate Rav(c) could be evaluated by using simple closure models of Bourne and Toor (1977), Brodkey and Lewalle (1985), Li and Toor (1986), Dutta and Tarbell (1989), etc. It should also be pointed out that the spatial averaging presented here is independent of the methodology using which Rilv(c) and D v are evaluated, or in other words, spatial averaging follows time averaging. 

The important result is that the two-mode models for a turbulent flow tubular reactor are the same as those for laminar flow tubular reactors. The two-mode axial dispersion model for turbulent flow tubular reactors is again given by Eqs. (130)—(134), while the two-mode convection model for the same is given by Eqs. (137)—(139), where the reaction rate term r((c)) is replaced by the Reynolds-averaged reaction rate term rav((c)). The local mixing time for turbulent flows is given by... 

Reaction data for the reaction between butyl chloride (C4HgCI) and water (H2O) is given in Table 17-1. Calculate the average reaction rate over this time period expressed as moles of C4H9CI consumed per liter per second. 

You are given the initial and final concentrations of C4HgCI and the initial and final times. You can calculate the average reaction rate of the chemical reaction using the change in concentration of butyl chloride in four seconds. In this problem, the reactant butyl chloride is consumed. 

In the gas-phase reaction I2 -l- CI2 21C1, the [I2] changes from 0.4(X)M at time = 0 to 0.300M at time = 4.00 min. Calculate the average reaction rate in moles I2 consumed per liter per minute. 

Given the following data for the decomposition of hydrogen peroxide, calculate the average reaction rate in moles H2O2 consumed per liter per minute for each time interval. 

For fast and intermediate reactions, the time-averaged reaction source term will contain some additional terms. These additional terms need to be modeled to close the set of equations. For example, consider the case of a single second-order reaction with instantaneous rate given by... 

The average reaction rate for airy brief time interval t during the above reaction is ... 

We could estimate this rate constant by finding average reaction rates in each small time interval and assuming this rate occurs halfway between the two concentrations ... 

The average reaction rate is the change in reactant (or product) concentration over a change in time, Af. The rate slows as reactants are used up. The instantaneous rate at time t is obtained from the slope of the tangent to a concentration vs. time curve at time t. The initial rate, the instantaneous rate at f = 0, occurs when reactants are just mixed and before any product accumulates. The expression for a reaction rate and its numerical value depend on which reaction component is being monitored. 

In a system described by a local random matrix model there can be corrections to the RRKM prediction for the average reaction rate. Assuming that the total reaction time is the sum of the RRKM contribution and a correction, and using = f dt e Ja ... 

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