Mixed batch reactors

A well-mixed batch reactor has no input or output of mass. The amounts of individual components may change due to reaction, but not because of flow into or out of the system. A typical batch reactor is shown in Figure 5-3. 

Consider a well-mixed batch reactor with a key reactant A, during time t to time t -i- 6t, where 6t is very small. For a well-mixed batch system, assume the following ... 

For a well-mixed batch reactor, the design equation is... 

With respect to reaction rates, an element of fluid will behave in the ideal tubular reactor, in the same way, as it does in a well-mixed batch reactor. The similarity between the ideal tubular and batch reactors can be understood by comparing the model equations. 

Figure 14.3 A temporal superstructure for a multiphase well-mixed batch reactor.

For the case where all of the series reactions obey first-order irreversible kinetics, equations 5.3.4, 5.3.6, 5.3.9, and 5.3.10 describe the variations of the species concentrations with time in an isothermal well-mixed batch reactor. For series reactions where the kinetics do not obey simple first-order or pseudo first-order kinetics, the rate expressions can seldom be solved in closed form, and it is necessary to resort to numerical methods to determine the time dependence of various species concentrations. Irrespective of the particular reaction rate expressions involved, there will be a specific time... 

Write the component continuity equations for a perfectly mixed batch reactor (no inflow or outflow) with first-order isothermal reactions ... 

Jl An isothermal perfectly mixed batch reactor has consecutive first-order reactions... 

J2. A perfectly mixed batch reactor, containing 7500 lb of liquid with a heat capacity of 1 Btu/Ib °F, is surrounded by a cooling jacket that is filled with 2480 lb of perfectly mixed cooling water. 

Equations 7.10-7.12 are identical in forms with those for the uniformly mixed batch reactor, that is. Equations 3.15, 3.22, and 7.3, respectively. It is seen that the time from the start of a reaction in a batch reactor (t) corresponds to the residence time in a PFR (r). 

If the compositions vary with position in the reactor, which is the case with a tubular reactor, a differential element of volume SV, must be used, and the equation integrated at a later stage. Otherwise, if the compositions are uniform, e.g. a well-mixed batch reactor or a continuous stirred-tank reactor, then the size of the volume element is immaterial it may conveniently be unit volume (1 m3) or it may be the whole reactor. Similarly, if the compositions are changing with time as in a batch reactor, the material balance must be made over a differential element of time. Otherwise for a tubular or a continuous stirred-tank reactor operating in a steady state, where compositions do not vary with time, the time interval used is immaterial and may conveniently be unit time (1 s). Bearing in mind these considerations the general material balance may be written ... 

Mathematical modeling of systems for which characteristic variables are time-dependent only and not space-dependent is done by ordinary differential equations (ODEs). The situation is found in a nearly well-mixed batch reactor. There one may find differences in temperature or concentrations from one site to another due to imperfect mixing. When space changes are not important to the model, the process variables can be approximated by means of lumped parameter models (LPMs). When the... 

A well-mixed batch reactor is used for performing the isothermal liquid phase reaction... 

Batch Reactor. In a batch reactor there are no inlet or outlet streams In = Out = 0. The total feed is charged into the reactor at the beginning and no withdrawal is made until the desired conversion level has been reached. Hence a reaction process occurring in a batch reactor is an unsteady one. All variables change with time. In addition, we assume that it is a perfectly mixed batch reactor, so that the concentrations of the reaction components, reactants or products are the same over the whole reactor volume. This assumption allows us to consider applying the mole balance equation across the whole reactor. With the term reactor we mean the space where the reaction(s) take place. For liquid phase reactions the reactor volume is smaller than the size of the physical reactor. It is the volume of the liquid phase, where the reaction ) take(s) place. 

Crittenden JC, Hu S, Hand DW, Green SA. A kinetic model for H202/UV process in a completely mixed batch reactor. Water Res 1999 33 2315-2328. 

Equation (19-22) indicates that, for a nominal 90 percent conversion, an ideal CSTR will need nearly 4 times the residence time (or volume) of a PFR. This result is also worth bearing in mind when batch reactor experiments are converted to a battery of ideal CSTRs in series in the field. The performance of a completely mixed batch reactor and a steady-state PFR having the same residence time is the same [Eqs. (19-5) and (19-19)]. At a given residence time, if a batch reactor provides a nominal 90 percent conversion for a first-order reaction, a single ideal CSTR will only provide a conversion of 70 percent. The above discussion addresses conversion. Product selectivity in complex reaction networks may be profoundly affected by dispersion. This aspect has been addressed from the standpoint of parallel and consecutive reaction networks in Sec. 7. 

A major difficulty is that such hierarchies of molecular models are not exactly known. Recent work by Gillespie (2000, 2002) has established such a hierarchy for stochastic models of chemical reactions in a well-mixed batch reactor. This hierarchy is depicted in Fig. 3b. In particular, it was shown that the chemical master equation is deduced to a chemical Langevin equation when the population sizes are relatively large. Finally, the deterministic behavior can be... 

Preloading was done in 250-ml well-mixed batch reactors (amber bottles sealed with teflon septa). First, 10 to 15 mg of adsorbent was contacted with an organic matter solution (6 to 20 mg/L as organic carbon) for 14 to 45 days. After preloading, reactors were sampled with glass syringes, and the solution was filtered through a 0.45-micron polysulfone filter. 

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