First-order chemical

Gaussian plume models are easy to use and require relatively few input data. Multiple sources are treated by superimposing the calculated contributions of individual sources. It is possible to include the first-order chemical decay of pollutant species within the Gaussian plume framework. For chemically, meteorologically, or geographically complex situations, however, the Gaussian plume model fails to provide an acceptable solution. 

As with the case of energy input, detergency generally reaches a plateau after a certain wash time as would be expected from a kinetic analysis. In a practical system, each of its numerous components has a different rate constant, hence its rate behavior generally does not exhibit any simple pattern. Many attempts have been made to fit soil removal (50) rates in practical systems to the usual rate equations of physical chemistry. The rate of soil removal in the Launder-Ometer could be reasonably well described by the equation of a first-order chemical reaction, ie, the rate was proportional to the amount of removable soil remaining on the fabric (51,52). In a study of soil removal rates from artificially soiled fabrics in the Terg-O-Tometer, the percent soil removal increased linearly with the log of cumulative wash time. 

Fig. 6. Film model for diffusion with simultaneous irreversible first-order chemical reaction [after Lightfoot (L5)].

Mass Transfer Accompanied by Irreversible First-Order Chemical Reaction... 

A slightly different approach was taken by Gill (G15), who considered the case of a bubble moving through a stationary liquid with mass transfer accompanied by simultaneous first-order chemical reaction. His assumptions were as follows ... 

Fig. 10. Numerical solutions of the forced-convection mass-transfer equation for the case of irreversible first-order chemical reaction [after Johnson et al. (J4)] (Solid lines— rigid spheres dashed lines—circulating gas bubbles).

A first-order chemical reaction takes place in a reactor in which the catalyst pellets are platelets of thickness 5 mm. The effective diffusivity De for the reactants in the catalyst particle is I0"5 m2/s and the first-order rate constant k is 14.4 s . 

The turnover time may be thought of as the time it would take to empty the reservoir if the sink (S) remained constant while the sources were zero (tqS = M). This time scale is also sometimes referred fo as "renewal time" or "flushing fime." In the common case when the sink is proportional to the reservoir content (S = kM), the turnover time is the inverse of the proportionality constant (k ), which is analogous to first-order chemical kinetics. 

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. 

P. G. Seybold, L. B. Kier, and C.-K. Cheng, Simulation of first-order chemical kinetics using cellular automata. 7 Chem. Inf. Comput. Sci. 1997, 37, 386-391. 

The idea that disinfechon could be treated as a first-order chemical reachon led to ideas equating the effect of heat on the process to the effect of heat on chemical reactions. 

Although the methods that are discussed in this chapter deal explicitly with the disposition of dmgs in animals and humans, their scope is much wider. In general, these methods can be applied to study the transport of substances within parts of a system provided that these transports can be described by zero or first order kinetics. This applies, for example, when the rate of change of the amount in one part of the system depends linearly on the amounts present in all the various parts of the system. Applications are found commonly in first order chemical reactions. 

Figure 2.5. Step response of a stirred tank with first-order chemical reaction (V=l, t =1,...

At steady-state conditions, the rate of supply of S by diffusion is balanced by the rate of consumption by chemical reaction, where assuming a first-order chemical reaction... 

Assuming the case of a first-order chemical reaction, (r = - k Ca), and a non-compressible liquid system, the generalised mass and energy balance equations reduce to... 

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

It is important to understand that the time constant xp of a process, say, a stirred tank is not the same as the space time x. Review this point with the stirred-tank heater example in Chapter 2. Further, derive the time constant of a continuous flow stirred-tank reactor (CSTR) with a first-order chemical reaction... 

A first-order chemical reaction occurs isothermally in a reactor packed with spherical catalyst pellets of radius R. If there is a resistance to mass transfer from the main fluid stream to the surface of the particle in addition to a resistance within the particle, show that the effectiveness factor for the pellet is given by ... 

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

The utility of RTD theory is best illustrated by its treatment of first-order chemical reactions. For this case, each fluid element can be treated as a batch reactor.15 The concentration... 

Because die outlet concentrations will not depend on it, micromixing between duid particles can be neglected. The reader can verify this statement by showing that die micromixing term in the poorly micromixed CSTR and the poorly micromixed PFR falls out when die mean outlet concentration is computed for a first-order chemical reaction. More generally, one can show that die chemical source term appears in closed form in die transport equation for die scalar means. 

Relaxation Derived as an Analogue to First-Order Chemical Kinetics... 

Applying a standard treatment of first-order chemical kinetics, the rate of disappearance of the excited Si molecules, Jtotab is given by ... 

First-order chemical reaction preceding a reversible electron transfer. The process in which a homogeneous chemical reaction precedes a reversible electron transfer is schematized as follows ... 

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