# Ideal reactor

Chemical reactions take place in the chemical reaction process in reactors instead. Since the hydrodynamics of such reactors is extremely complicated, these reactors are considered idealized . This is called the ideal reactor (abbreviated to IR).

This means that mathematically difficult to grasp real conditions, which in practice always exist within a certain framework, e.g. B. incomplete backmixing or turbulent flow with laminar areas on the reactor wall, can be replaced by simple conditions, e.g. B. by complete backmixing or ideal plug flow . This enables concentration or temperature curves to be obtained as an analytical solution to the balance - differential equations .

In general, a distinction is made between the following ideal reactors:

## Discontinuous operation

In discontinuous operation , the empty reactor is filled with the starting materials and any solvents that may be required , and the chemical reaction starts. After the reaction has ended, the contents with the products and the remaining starting materials are removed. The reactor is cleaned before it is used again. When a reactor is used so it is referred to as a batch reactor (ger .: batch reactor ).

### The discontinuous, ideal stirred tank

In an ideal discontinuous stirred tank (Engl .: Stirred tank reactor  (STR) or batch reactor ), the reaction mass is presented. The composition in the reactor or the concentrations then change over time:

${\ displaystyle {\ frac {\ partial c} {\ partial t}} \ neq 0}$.

There is an ideal , so any rapid mixing of the reactor contents. This means that the concentrations and the temperature are the same at every location in the reaction space at every discrete point in time:

${\ displaystyle {\ frac {\ partial c} {\ partial x}} = 0}$and ,${\ displaystyle {\ frac {\ partial T} {\ partial x}} = 0}$

the state is therefore spatially, but not temporally, “ gradient free”.

## Continuous operation

In continuous operation , the reactor is continuously filled with new starting materials at one point and these are continuously removed at another point together with the products formed.

### Continuous, ideal stirred kettle (KIK)

With the continuous, ideal stirred tank reactor  (CSTR), complete back-mixing takes place. Here, “ideal” is also understood to mean that the starting materials flowing in are mixed with the mass in the “stirred tank” reaction chamber at an infinitely high speed.

The mass concentrations of all substances (including the products) are constant in terms of location and time both in the boiler itself and in the outlet ( stationary in terms of location and time = "space- time stationary "):

${\ displaystyle {\ frac {\ partial c} {\ partial x}} = 0}$ and ${\ displaystyle {\ frac {\ partial c} {\ partial t}} = 0}$

This is positive for reaction engineering and kinetic investigations, because stationary measured values ​​can be recorded better or more precisely.

Because the respective starting materials react with one another in the reactor and the starting material is thus consumed, the amount per unit volume (i.e. the concentration) of the starting materials in the reaction space will be lower than in the feed stream. Therefore, there is a “jump in concentration” at the point of entry. H. as soon as the educts enter the boiler, their concentration has immediately dropped to the lower concentration in the boiler:

${\ displaystyle c_ {boiler}

Due to the volume flow through the boiler, the reaction mass has a limited residence time in the reaction space - and this "to make matters worse" is characterized by a likelihood of leaving, ie not discretely, but in a "bandwidth" = residence time distribution . For reactions of a positive order , the specific product output is therefore always smaller than in an ideal reactor.

By connecting several KIK in series to form a cascade, such a system approaches the behavior of the ideal reactor as the number of stirred tanks increases: from ten stirred tanks, no difference can be measured in real cases.

### Ideal flow tube (IR)

In an idealized, tubular reactor [ plug-flow reactor  (PFR) or plug-flow tubular reactor  (PFTR)] there is a plug flow . One can imagine this flow as a migration of a very long series of very thin slices of the reaction mass through the pipe, which have no exchange of material or heat with one another .

Here the material conversions take place along the flow path x, the concentrations of the substances change along the pipe:

${\ displaystyle {\ frac {\ partial c} {\ partial x}} \ neq 0}$

At a certain point x in the pipe, however, the same concentrations are present at every point in time (since the reaction takes place at the same speed within all the discs):

${\ displaystyle \ left. {\ frac {\ partial c} {\ partial t}} \ right | _ {x} = 0}$

If you look at the course of the reaction within a certain disc during its migration through the pipe , you can look at it in the same way as in a discontinuous, ideal stirred tank:

${\ displaystyle {\ frac {\ partial c} {\ partial t}} \ neq 0}$

Within a single slice (radius R, variable r), all concentrations and the temperature are spatially constant at a certain point in time:

${\ displaystyle {\ frac {\ partial c} {\ partial r}} = 0}$ and ${\ displaystyle {\ frac {\ partial T} {\ partial r}} = 0}$