Design Equations for Continuous Flow Reactors

The previous post dealt with the design equations for a batch reactor, this post will look at the most common reactor types, Continuous Flow Reactors like CSTR and PFR.

Flow reactors work on the principle of continuous flow technology to carry out continuous chemical reactions. Reagents are continuously added to a flow reactor vessel inlet whilst product is constantly collected at the reactor outlet, hence a continuously flowing stream of reactants and outputs occur

A continuous flow reactor embodies the principles of flow chemistry. Flow reactors are designed to operate at a continuous steady state, thus the internal stream, temperature, reagent feed and flow rates are all constant, to produce a continuous flow of chemical reactant material that generates a continuous product output.

A flow reactor is more versatile and efficient reactor than the batch reactor. Continuous flow reactors also overcome problems surrounding scalability, poor heat transfer, safety, sustainability and lack of control found with batch production.

If we assume a reaction between A and B to produce C and D:

The general mass balance equation is:

mass in - mass out + generation = accumulation

The mass balance for the above continuous flow process is thus:

Continuous Flow Reactor Working Mechanism

• The flow reactor administers the integration of two or more reactive compounds, which are then mixed and flowed through a highly controlled stream to generate a continuous reaction. 

• Flow reactions take place in tubular system, whether through a capillary or micro-structured device made from a non-reactive material. Coiled tubing is commonly added to aid both mixing and heat transfer. Temperature control is then maximized by adding heat or coolant transfer fluid.

• The core principle of all flow reactors is the same, involving a continuous flowing mechanism, however, there are different types of flow reactors chosen depending on the application but still the principles remain the same.

Type of Mixing in Flow Reactors

• Passive Mixing: This relies on the fluid velocity of each reagent, combining with a particular vessel geometry in order to generate mixing between reagents.

• Active Mixing: This relies on external energy like from an agitator, which mixes all reactants (similar to how the contents of a batch vessel are mixed with an overhead stirrer). 

Advantages of Flow Reactors

• Advanced heat transfer, improved mixing leading to faster reactions,

• Easier scalability when compared to batch production,

• Improved safety with better management of hazardous reagents,

• Improved sustainability; lower energy consumption and cost, lower solvent use and low emissions.

1) Continuous Stirred Tank Reactor (CSTR)

This is an agitated vessel used that has a continuous feed of reactants and a continuous discharge of the reaction mixture (product). The feed and discharge rates are controlled to maintain constant reaction conditions (concentration, temperature and reaction rate) ensuring a consistent product stream is produced.

The behavior of of CSTR is usually modelled by that of an "ideal CSTR" with the assumption of perfect mixing i.e., the reagent is instantaneously and uniformly mixed throughout the reactor upon entry into the reactor. Thus, the output composition is identical to the material composition inside the reactor which is a function of residence time and reaction rate.

Some advantages of a CSTR are:

• Runs at a steady state with a continuous flow of reactants and products.
• Feed assumes a uniform composition throughout the reactor.
• The exit stream has the same composition as in the tank.

The design equation of a CSTR is as follows:

2) Plug Flow Reactor (PFR)

Plug flow is an important characteristic of flow reactors, where any two molecules entering the reactor at time zero, exit at a similar time. 

The PFR reactor model provides an effective means of controlling reaction time while optimizing the separation of reactants and products. 

A Good plug flow is essential for good performance in all but a few applications and means that fluid travels through the reactor in a time-orderly way and without back-mixing. Reactors which employ plug flow chemistry are commonly referred to as plug flow reactors or PFR reactors.

Advantages of PFR reactors are as follows:

• Efficient reaction time control - as products are removed from the reactor on formation.
• Efficient utilization of reactor volume as the reacted material is not retained within the reactor.
• Optimum reaction yield and purity due to efficient heat and mass transfer properties and removal of products on formation, reducing by-products.
• Low start-up and shutdown losses due to the smaller volumes involved.

Assumptions of PFR reactors

• As the plug flows through a plug flow reactor, the fluid is perfectly mixed in the radial direction but not in the axial direction (forwards or backward). 
• Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small continuous stirred tank reactor, limiting to zero volume.

The design equation of a PFR is as follows: