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Multiple reactant concentrations

Volumetric heat generation increases with temperature as a single or multiple S-shaped curves, whereas surface heat removal increases linearly. The shapes of these heat-generation curves and the slopes of the heat-removal lines depend on reaction kinetics, activation energies, reactant concentrations, flow rates, and the initial temperatures of reactants and coolants (70). The intersections of the heat-generation curves and heat-removal lines represent possible steady-state operations called stationary states (Fig. 15). Multiple stationary states are possible. Control is introduced to estabHsh the desired steady-state operation, produce products at targeted rates, and provide safe start-up and shutdown. Control methods can affect overall performance by their way of adjusting temperature and concentration variations and upsets, and by the closeness to which critical variables are operated near their limits. [Pg.519]

The acid-base reaction is a simple example of using the mixture fraction to express the reactant concentrations in the limit where the chemistry is much faster than the mixing time scales. This idea can be easily generalized to the case of multiple fast reactions, which is known as the equilibrium-chemistry limit. If we denote the vector of reactant concentrations by and assume that it obeys a transport equation of the form... [Pg.256]

In general, concentrations of the products are divided by the concentrations of the reactants. In the case of gas-phase reactions, partial pressures cire used instead of molar concentrations. Multiple product or reactant concentrations are multiplied. Each concentration is raised to an exponent equal to its stoichiometric coefficient in the balanced reaction equation. (See Chapters 8 and 9 for details on balanced equations and stoichiometry.)... [Pg.203]

The semibatch can also be used to control the kinetics in multiple reaction sequences. The selectivity may be shifted to one reaction by adding a reactant slowly. This keeps one reactant concentration high with respect to the other. [Pg.465]

Most textbook discussions of effectiveness factors in porous, heterogeneous catalysts are limited to the reaction A - Products where the effective diffusivity of A is independent of reactant concentration. On the other hand, it is widely recognized by researchers in the field that multicomponent single reaction systems can be handled in a near rigorous fashion with little added complexity, and recently methods have been developed for application to multiple reactions. Accordingly, it is the intent of the present communication to help promote the transfer of these methods from the realm of the chemical engineering scientist to that of the practitioner. This is not, however, intended to be a comprehensive review of the subject. The serious reader will want to consult the works of Jackson, et al. [Pg.211]

For exothermic reactions (fi > 0) a sufficient temperature rise due to heat transfer limitations may increase the rate constant Ay. and this increase may offset the diffusion limitation on the rate of reaction (the decrease in reactant concentrations CA), leading to a larger internal rate of reaction than at surface conditions CAs. This, eventually, leads to 17 > 1. As the heat of reaction is a strong function of temperature, Eq. (9.24) may lead to multiple solutions and three possible values of the effectiveness factor may be obtained for very large values of /I and a narrow range of catalytic reactions, (3 is usually <0.1, and therefore, we do not observe multiple values of the effectiveness factor. The criterion... [Pg.458]

The type of reasoning that has been given here can be extended to take into account reaction orders different from uni y and multiple-reactant, one-step chemistry. For a one-reactant proce of reaction order n, w is proportional to the reactant concentration (in the reaction zone) to the nth... [Pg.161]

In addition to the performance variations with reactant concentration and gas hourly space velocity (GHSV), there can be multiple steady states observed. Generally, a reactor in which a single, exothermic reaction is occurring will operate in one of two stable steady states. Additionally, an unstable steady-state solution to the mass... [Pg.337]

At steady state, the rate and current density of an electrocatalyst in a MER are uniform. In a CER, however, reactant concentration declines along the reactor and current decreases under potentiostatic control for non-zero-order, single, or multiple reactions. Current nonuniformity in a CER becomes more pronounced with decreasing reduction or increasing oxidation potentials (60-62). With slow diffusive transport in porous catalysts, significantly lower potentials are necessary to reach the same degree of nonuniformity as in the absence of pore diffusion (61). [Pg.318]

This is the most wide spread and extensively investigated type of multiplicity. It is associated with exothermic reactions. In fact, this type of multiplicity results from some sort of non-monotonic behaviour associated with the change of the rate of reaction under the simultaneous variation of reactants concentration and temperature accompanying the reactions taking place within the boundaries of the system (the reactor). For the case of exothermic reactions, as the reaction proceeds the reactants deplete which tends to cause a decrease in the rate of reaction while at the same time, heat release increases the temperature and thus causes the rate of reaction to increase through the Arrhenius dependence of the rate of reaction upon temperature. These two conflicting effects on the rate of reaction associated with the conversion of reactants lead to a non-monotonic dependence of the rate of reaction upon the reactant concentration. This in turn leads to the possibility of multiple steady... [Pg.322]

Chemical relaxation techniques have been employed to study the rates of elementary reaction steps. The two most useful variables for the system control are the concentrations of the reactants and the reactor temperature. The dynamic responses from the system after the changes of these variables are related to the elementary steps of the catalytic processes. Chemical relaxation techniques can be divided into two general groups, which are single cycle transient analysis (SCTA) and multiple cycle transient analysis (MCTA). In SCTA, the reaction system relaxes to a new steady-state and analysis of this transition furnishes information about intermediate species. In MCTA, the system is periodically switched between two steady-states, e.g. by periodically changing the reactant concentration. [Pg.292]

In conclusion, one solves two coupled first-order ODEs for the molar density profile of reactant A under isothermal conditions, without considering the thermal energy balance. Then, a volumetric average of the rate of conversion of reactant A to products due to multiple chemical reactions is obtained by focusing on the reactant concentration gradient at the external surface of the catalyst ... [Pg.752]

In our first example, there was just one reactant and one product. When there are multiple species on either side of the equation, the numerator is the produa of product concentrations and the denominator is the product of reactant concentrations—with each concentration raised to the appropriate power, that IS, the stoichiometric coeffident... [Pg.595]


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Reactant concentrations

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