Reaction first-order irreversible

Although the right-hand side of Eq. (14-60) remains valid even when chemical reactions are extremely slow, the mass-transfer driving force may become increasingly small, until finally c — Cj. For extremely slow first-order irreversible reactions, the following rate expression can be derived from Eq. (14-60) ... 

The material balance for the single CFSTR in terms of for the first order irreversible reaction is... 

Consider a combination of CFSTR and plug flow systems as shown below for a first order irreversible reaction. 

Figure 5-38 shows plots of the dynamic response to changes in the inlet concentration of component A. The figure represents possible responses to an abrupt change in inlet concentration of an isothermal CFSTR with first order irreversible reaction. The first plot illustrates the situation where the reactor initially contains reactant at and... 

Fig ure 6-22. Temperature versus conversion for a first order irreversible reaction in an adiabatic continuous flow stirred tank reactor. 

The following assumptions were made (1) The gas bubbles are evenly distributed throughout the liquid phase and have constant radius and composition (2) the concentration of the gas-liquid interface is constant and equal to C (3) no gross variations occur in liquid composition throughout the vessel and (4) the gas is sparingly soluble, and, in the case of a chemical reaction, it is removed by a first-order irreversible reaction with respect to the dissolving gas. 

The treatment here is restricted to first-order irreversible reactions under steady-state conditions. Higher order reactions are considered by ARJS(30). 

Show that in steady-state diffusion through a film of liquid, accompanied by a first-order irreversible reaction, the concentration of solute in the film at depth r below the interface is given by ... 

Liquid phase oxidation reaction of acetaldehyde with Mn acetate catalyst can be considered as pseudo first order irreversible reaction with respect to oxygen, and the reaction occurred in liquid film. The value of kinetic constant as follow k/ = 6.64.10 exp(-12709/RT), k2 = 244.17 exp(-1.8/RT) and Lj = 3.11.10 exp(-13639/RT) m. kmor. s. The conversion can be increased by increasing gas flow rate and temperature, however the effect of impeller rotation on the conversion is not significant. The highest conversion 32.5% was obtained at the rotation speed of 900 rpm, temperature 55 C, and gas flow rate 10" m. s. The selectivity of acetic acid was affected by impeller rotation speed, gas flow rate and temperature. The highest selectivity of acetic acid was 70.5% at 500 rpm rotation speed, temperature of 55 C... 

The subscript refers to a spherical particle. One should also remember that we limited ourselves to a first-order irreversible reaction. Other expressions can be derived but are beyond the scope of this book. Nevertheless, Eq. (35) has important practical implications, since it is possible to discuss the effectiveness of the system by a single dimensionless parameter, (fig. Figure 5.35 shows the effectiveness factor as a function of O,. 

This technique is readily adaptable for use with the generalized additive physical approach discussed in Section 3.3.3.2. It is applicable to systems that give apparent first-order rate constants. These include not only simple first-order irreversible reactions but also irreversible first-order reactions in parallel and reversible reactions that are first-order in both the forward and reverse directions. The technique provides an example of the advantages that can be obtained by careful planning of kinetics experiments instead of allowing the experimental design to be dictated entirely by laboratory convention and experimental convenience. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

For first-order irreversible reactions and identical space times it is possible to obtain closed form solutions to differential equations of the form of 8.3.61. In other cases it is usually necessary to solve the corresponding difference equations numerically. 

The pyrolysis closely approximates a first-order irreversible reaction with a rate constant given by ... 

These stability considerations are not limited to first-order irreversible reactions. Figure 10.4 depicts the Qg and Qr curves for a reversible exothermic reaction. The intersections of the Qg curve and lines 3 and 4 represent stable... 

For a first-order irreversible reaction equation 11.2.9 becomes... 

A first order irreversible reaction is carried out in three CSTRs of equal volumes. The feed rate is V. A quantity aV ... 

A reversible reaction, At= B, takes place in a well-mixed tank reactor. This can be operated either batch-wise or continuously. It has a cooling jacket, which allows operation either isothermally or with a constant cooling water flowrate. Also without cooling it performs as an adiabatic reactor. In the simulation program the equilibrium constant can be set at a high value to give a first-order irreversible reaction. 

Two isothermal CSTRs are conneaed by a long pipe that acts like a pure deadtime of D minutes at the steadystate flow rates. Assume constant throughputs and holdups and a first-order irreversible reaction... 

Remark 4- Eq.(13) is valid only for a first order irreversible reaction A B. So, it is the easiest form to writing the energy balance in the reactor. 

In the present chapter, steady state, self-oscillating and chaotic behavior of an exothermic CSTR without control and with PI control is considered. The mathematical models have been explained in part one, so it is possible to use a simplified model and a more complex model taking into account the presence of inert. When the reactor works without any control system, and with a simple first order irreversible reaction, it will be shown that there are intervals of the inlet flow temperature and concentration from which a small region or lobe can appears. This lobe is not a basin of attraction or a strange attractor. It represents a zone in the parameters-plane inlet stream flow temperature-concentration where the reactor has self-oscillating behavior, without any periodic external disturbance. 

From the study presented in this chapter, it has been demonstrated that a CSTR in which an exothermic first order irreversible reaction takes place, can work with steady-state, self-oscillating or chaotic dynamic. By using dimensionless variables, and taking into account an external periodic disturbance in the inlet stream temperature and coolant flow rate, it has been shown that chaotic dynamic may appear. This behavior has been analyzed from the Lyapunov exponents and the power spectrum. 

The concentration and temperature Tg will, for example, be conditions of reactant concentration and temperature in the bulk gas at some point within a catalytic reactor. Because both c g and Tg will vary with position in a reactor in which there is significant conversion, eqns. (1) and (15) have to be coupled with equations describing the reactor environment (see Sect. 6) for the purpose of commerical reactor design. Because of the nonlinearity of the equations, the problem can only be solved in this form by numerical techniques [5, 6]. However, an approximation may be made which gives an asymptotically exact solution [7] or, alternatively, the exponential function of temperature may be expanded to give equations which can be solved analytically [8, 9]. A convenient solution to the problem may be presented in the form of families of curves for the effectiveness factor as a function of the Thiele modulus. Figure 3 shows these curves for the case of a first-order irreversible reaction occurring in spherical catalyst particles. Two additional independent dimensionless paramters are introduced into the problem and these are defined as... 

With conversions measured in terms of this may be looked on as a pseudo first-order irreversible reaction which on integration gives... 

First-order irreversible reaction, A products, any constant... 

Consider a two-step first-order irreversible reactions in series... 

We need reaction-rate expressions to insert into species mass-balance equations for a particular reactor. These are the equations from which we can obtain compositions and other quantities that we need to describe a chemical process. In introductory chemistry courses students are introduced to first-order irreversible reactions in the batch reactor, and the impression is sometimes left that this is the only mass balance that is important in chemical reactions. In practical situations the mass balance becomes more comphcated. 

Let us immediately apply this equation to the first-order irreversible reaction... 

We can use this solution for ary first-order irreversible reaction A products, r = kCA... 

Figure 2-5 Plots of Ca(1) und Cg(t) versus kt for the first-order irreversible reaction A— B,r = kCA in a batch reactor.

We have now developed mass balance equations for the three simple reactors in which we can easily calculate conversion versus time tbatch> residence time T, or position L for specified kinetics. For a first-order irreversible reaction with constant density we have solved the mass balance equations to yield... 

Ratio of Residence Times and Reactor Volumes in CSTR and PFTR versus Conversion for a First-Order Irreversible Reaction... 

The example in Figure 3-3 is for a first order irreversible reaction. We can generalize this to say that the PFTR requires a smaller reactor volume for given conversion for any... 

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