Continuous constant density reactions

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

Polymerization Results. Preliminary polymerization runs were conducted to evaluate the effect of Initiator concentration, temperature, and continuous-phase density on the rate of reaction as well as the ultimate molecular weight of the polymer. Continuous-phase density could be varied in two ways 1) by varying the pressure at constant temperature and ethane/propane ratio, and 2) by varying the ethane/propane ratio at constant temperature and pressure. In all of these polymerizations, the acrylamide ratio was 1.0, water was 3.5, and the total dispersed-phase volume fraction was 0.16. 

First, it is apparent that the density of the ethane/propane continuous phase, rather than the molecular coxtqposition, determines the stability of the microemulsion. Stable microemulsions can be prepared in mixtures of ethane and propane over the entire concentration range. This allows examination of the effect of continuous-phase density on reaction rate, etc., while temperature and pressure remain constant. 

Given the two continuous reactors in this chapter, the CSTR and the PFR, it is natural to compare their steady-state efficiencies in converting reactants to products. For simplicity, consider a constant-density, liquid-phase reaction with nth-order, irreversible reaction rate... 

We assume we keep the flow of the tracer small enough that we do not disturb the existing flow pattern in the reactor. We expect to see a continuous change in the concentration of the effluent stream until, after a long time, it matches the concentration of the feed stream. We are by now experts on solving this type of problem, especially in this simple situation without chemical reaction to complicate matters. Assuming constant density, the differential equation governing the concentration of dye in the reactor follows from Equation 4.38... 

A jacketed continuous stirred tank reactor characterized by an irreversible exothermic reaction A —> B (Dash et al., 2003 Luyben, 1990). Assuming heat losses and constant densities to be negligible, the equations governing the system are as follows ... 

Spielman and Levenspiel (1965) appear to have been the earliest to propose a Monte Carlo technique, which comes under the purview of this section, for the simulation of a population balance model. They simulated the model due to Curl on the effect of drop mixing on chemical reaction conversion in a liquid-liquid dispersion that is discussed in Section 3.3.6. The drops, all of identical size and distributed with respect to reactant concentration, coalesce in pairs and instantly redisperse into the original pairs (after mixing of their contents) within the domain of a perfectly stirred continuous reactor. Feed droplets enter the reactor at a constant rate and concentration density, while the resident drops wash out at the same constant rate. Reaction occurs in individual droplets in accord with nth-order kinetics. 

For simple irreversible reactions, a (semi) analytical solution of the continuity and energy equations is possible. Douglas and Eagleton [1962] published solutions for zero-, first-, and second-order reactions, both with a constant and varying number of moles. For a first-order reaction with constant density, the integration proceeds as follows ... 

A batch of 180 kg of pure ethyl alcohol (density = 0.789 kg/dm ) was stored in a container. Pumping of an aqueous solution of acetic acid (42.6 wt% acetic acid density 0.958 kg/dm ) into the container was initiated. A continuous, constant inflow of 1.8 kg/min was maintained for 120 min. The reaction temperature was 100°C. The reaction... 

Appendix 3.Ill contains the equivalents of these equations for different variables (e.g., f and t), for heterogeneous catalytic reactions, and for the constant-density case. The numbering of the equations in Appendix 3.IIIA continues from Eqn. (3-33) above. 

The graphical interpretation of the design equations for the two ideal continuous reactors has been illustrated using fractional conversion to measure the progress of the reaction. The analysis could have been carried out using the extent of reaction with Eqns. (3-18) and (3-34). Moreover, for a constant-density system, the analysis could have been carried out using the concentration of Reactant A, Ca, with Eqns. (3-24) and (3-37). 

We will begin the discussion of continuous reactors with the ideal CSTR, first with a constant-density example and then with a variable-density example. The ideal PFR then will be treated, for the constant-density and then the variable-density case. To point out the differences between constant- and variable-density systems, and the differences between how the different reactors are treated, all of our analysis will be based on Reaction (4-B) and the rate equation given by Eqn. (4-13). 

For a continuous reactor, y is the molar flow for batch reactors, it is the molar amount of substance or concentration. For systems with a constant density, the molar quantities can simply be replaced by concentrations. Thus, any model predicts the stoichiometric relation y = yo, + On the other hand, experimentally recorded concentrations exist for the components in the system. The task is now to find an optimal extent of reaction, which would minimize the difference for the entire data set. 

Water in its supercritical state has fascinating properties as a reaction medium and behaves very differently from water under standard conditions [771]. The density of SC-H2O as well as its viscosity, dielectric constant and the solubility of various materials can be changed continuously between gas-like and liquid-like values by varying the pressure over a range of a few bars. At ordinary temperatures this is not possible. For instance, the dielectric constant of water at the critical temperature has a value similar to that of toluene. Under these conditions, apolar compounds such as alkanes may be completely miscible with sc-H2O which behaves almost like a non-aqueous fluid. 

When a detonation wave passes through an explosive, the first effect is compression of the explosive to a high density. This is the shock wave itself. Then reaction occurs and the explosive is changed into gaseous products at high temperature. These reaction products act as a continuously generated piston which enables the shock wave to be propagated at a constant velocity. The probable structure of the detonation zone is illustrated in Fig. 2.3. 

In general, the properties of supercritical fluids make them interesting media in which to conduct chemical reactions. A supercritical fluid can be defined as a substance or mixture at conditions which exceed the critical temperature (Tc) and critical pressure (Pc). One of the primary advantages of employing a supercritical fluid as the continuous phase lies in the ability to manipulate the solvent strength (dielectric constant) simply by varying the temperature and pressure of the system. Additionally, supercritical fluids have properties which are intermediate between those of a liquid and those of a gas. As an illustration, a supercritical fluid can have liquid-like density and simultaneously possess gas-like viscosity. For more information, the reader is referred to several books which have been published on supercritical fluid science and technology [1-4],... 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

But if reactants or products of the desired reaction are lost and/or if undesrred compounds are formed by side reactions (i.e. yield and selectivity will be reduced), it is necessary to avoid any overstepping of the limiting current density. Especially in case of changing conditions (batch operation) with a rising degree of conversion - here, the most significant parameter will be the decreasing reactant concentration - a continuous adjustment of the current density is indispensable. Then it will be better to work at a constant electrode potential than at constant cell current (see Sect. 23.23). 

The same reactions considered in Prob. 6.17 are now carried out in a single, perfectly mixed, isothermal continuous reactor. Flow rates, volume and densities are constant,... 

We also account for density, heat capacity, and molecular weight variations due to temperature, pressure, and mole changes, along with temperature-induced variations in equilibrium constants, reaction rate constants, and heats of reaction. Axial variations of the fluid velocity arising from axial temperature changes and the change in the number of moles due to the reaction are accounted for by using the overall mass conservation or continuity equation. 

At constant potential, in a simple reaction with no surface intermediates, the i—t line will tend to become constant after the double-layer charging is over. If at this time the current density is well below the limiting current density, iL (Section 7.9.10), there should be nothing to interfere with the continuation of the steady-state constant current. If the current density after double-layer charging is above the limiting current, the current will decline with time. This is discussed quantitatively in Chapter 8. 

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