Molar balance for reactor systems

Molar balance is very important concept for chemical engineering undergraduate students. For reactor systems in chemical engineering, this phenomenon is widely applied. This theory is helped to calculate flow rates, reaction rates in industrial applications.

In the previous chapter we learned about types of reactor systems used in chemical engineering.

Types of reactor systems

  1. Batch reactor
  2. Continuous stirred tank reactor ( CSTR )
  3. Plug flow (tubular) reactor (PFR)
Reaction system types

Molar balance equation

There may be a inflow and a outflow in a reactor and reactions are happening inside the reactor. Therefore molar balance equation includes several terms to describe each of those processes. General molar balance equation is figured below.

molar balace equation

In the molar balance equation, there are two terms such asmolar generation and molar consumption. Both of them exists in opposite directions in the equations. Instead of both of them we only use molar generation which represent both generation and consumption together.

We represent
Generation as + Generation
Consumption as - Generation

Now our equation is reduced as below.

molar balace short equation

Below figure shows us reactor system with inflow and outflow. We choose one species A for our demonstration.

Reaction system inflow outflow

First, A enters into the system through inflow. Then one or several reactions are happened in the system. Finally remaining A comes out from the system.

For calculate generation we consider small part of volume in the system.

rate of reaction in dv

If A is disappearing/ reducing / consumption (due to reacting)
Generation term become negative

negative generation rate

Accumulation in the reactor

Some reactantant or product can be accumulated inside the reactor. Assume that there are NA moles at time t in the reactor. We can write the accumulation rate as below.

accumulation term

Molar balance equation for any reactor

Finally, we write the general equation for any reactor system as below.

general molar balance equation for any reactor

Molar balance for continuous stirred tank reactor

Assumptions

If rate of reaction ( rA ) is same in everywhere in the reactor ( no spatial variation ), rA becomes constant

.reacton rate constant

If process is in steady state,

According to those assumptions out molar balance equation for continuous stirred tank reactor

continuous stirred tank reactor

Molar balance for plug flow reactor (PPR)

Conditions of the PPR change along the reactor.

plug flow reactor

Select a small volume part and we take our selected specie as A. Inflow of reactor is FA|V and outflow is FA|V+ ΔV

Assumptions

He we consider steady state. ( dNA/dt = 0)

According to those assumptions out molar balance equation for continuous stirred tank reactor

Molar balance for plug flow reactor

Molar balance for batch reactor

There are no inflow or outflow in the batch reactor. Initially, we filled the reactor by reactants and take out products (reactants may be present in products if reaction had not completed. ) after the reaction. Therefore FA = 0 and FAO = 0
But reaction rate (rA) is different in everywhere in the reactor

Molar balance for batch reactor

Summary of molar balace equations of reactors

summary of Reactor systems


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