Reactor Types in the Reaction Engineering Interface

The mass balances that are set up in the Reaction Engineering interface are simplified versions of the general mass transport equation. The main assumption is that the reactor is perfectly mixed, meaning that any variations in compositions within the reactor are neglected.

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Mass Balance Equation

Energy Balance

The energy balances solved in the Reaction Engineering interface are derived from the general energy balance of a system. The utilized equation follows the perfect mixing assumption and is dependent on the selected reactor as described below.


	Theory for Heat Transfer

The following reactor types are available in the Reaction Engineering interface (the Chemistry interfaces does not contain reactor models):

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Batch

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Batch, Constant Volume

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CSTR, Constant Mass/Generic

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CSTR, Constant Volume

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Semibatch

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Plug Flow

Batch

In the batch reactor no mass enters or leaves the system. Common for all reactor models is that reacting fluids in the gas phase are assumed to behave as ideal gases. Liquid mixtures are assumed to be ideal and incompressible.

The species mass balances are given by:

(2-44)

which takes into account the effect of changing volume. In Equation 2-44, ci (SI unit: mol/m3) is the species molar concentration, Vr (SI unit: m3) denotes the reactor volume, and Ri (SI unit: mol/(m3·s)) is the species rate expression.

For an ideal reacting gas, the energy balance is:

(2-45)

In Equation 2-45, Cp,i (SI unit: J/(mol·K)) is the species molar heat capacity, T (SI unit: K) is the temperature, and p (SI unit: Pa) the pressure. On the right-hand side, Q (SI unit: J/s) is the heat due to chemical reaction, and Qext (SI unit: J/s) denotes heat added to the system. The heat of reaction is:

where Hj (SI unit: J/mol) is the enthalpy of reaction, and rj (SI unit: mol/(m3·s)) the reaction rate.

For an incompressible and ideally mixed reacting liquid, the energy balance is:

(2-46)


	Ibuprofen Synthesis: Application Library path Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/ibuprofen_synthesis

Batch, Constant Volume

The constant volume batch reactor is the default reactor. It assumes a closed, perfectly mixed system of constant volume. The species mass balances are:

For an ideal reacting gas, the energy balance is given by Equation 2-45. For an incompressible and ideally mixed reacting liquid, the energy balance is given by Equation 2-46.


	Neutralization of Chlorine in a Scrubber: Application Library path Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/chlorine_scrubber

CSTR, Constant Mass/Generic

The continuous stirred tank reactor (CSTR) has reacting species entering and leaving the reactor by means of inlet and outlet streams. The reactor is again assumed to be perfectly mixed, so that the species concentrations of the exit stream are the same as the concentrations in the reactor volume.

The species mass balances for the CSTR are given by:

(2-47)

In Equation 2-47, cf,m (SI unit: mol/m3) is the species molar concentration of the associated feed inlet stream vf,m (SI unit: m3/s). Vr (SI unit: m3) denotes the reactor volume and is a function of time.

The reactor volume as a function of time is given by:

(2-48)

In Equation 2-48, vp (SI unit: m3/s) denotes the volumetric production rate. It is given by Equation 2-49 for ideally mixed liquids and by Equation 2-50 for ideal gases.

(2-49)

(2-50)

where νij is the stoichiometric coefficient of species i in reaction j, Mi (SI unit: kg/mol) denotes the species molecular weight, ρi (SI unit: kg/m3) the species density, and Ri (SI unit: mol/(m3·s)) is the reaction rate of species i.

When this reactor model is solved for constant mass, the reactor model assumes that the volumetric flow rate of the outlet stream, v (SI unit: m3/s), is adjusted in such a way that the total mass of the reactor is held constant:

(2-51)

In contrast, when the model is set to be solved for generic conditions a specific outlet flow stream can be set.

The energy balance for an ideal reacting gas is:

(2-52)

For an incompressible and ideally mixed reacting liquid, the energy balance is:

(2-53)


	Ideal Stirred Tank Reactor System: Application Library path Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/tank_flow_system

CSTR, Constant Volume

This reactor type is a CSTR reactor where the reactor volume is constant.

The species mass balances are given by:

(2-54)

Assuming constant reactor volume:

and setting the volumetric outlet rate to:

(2-55)

Equation 2-54 can be rewritten as:

(2-56)

The volumetric production rate, vp, is defined as in Equation 2-49 and Equation 2-50.

The energy balance is the same as for the CSTR with Constant Mass/Generic reactor type (Equation 2-53).


	Startup of a Continuous Stirred Tank Reactor: Application Library path Chemical_Reaction_Engineering_Module/Tutorials/cstr_startup

Semibatch

In the semibatch reactor, reactants enter the reactor by means of one or several feed inlet streams.

The species mass balances are given by:

(2-57)

The reactor volume is a function of time given by:

(2-58)

The volumetric production rate, vp, is defined as in Equation 2-49 and Equation 2-50.

An energy balance over the Semibatch reactor results in the same energy balance expression as for the CSTR reactor types (Equation 2-53).


	Semibatch Polymerization: Application Library path Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/semibatch_polymerization

Plug Flow

In the plug flow reactor the species concentrations and the temperature vary with position. For a tubular reactor configuration, plug flow assumes concentration and temperature gradients to only develop in the axial direction but not in the radial direction of the reactor.

The species mass balances are given by:

(2-59)

where Fi (SI unit: mol/s) is the species molar flow, V (SI unit: m3) is the reactor volume, and Ri (SI unit: mol/(m3·s)) denotes the species rate expression.

In order to evaluate the rate expressions Ri, which are functions of the species concentrations, the physics interface calculates:

where v (SI unit: m3/s) is the volumetric flow rate.

For liquids, the volumetric flow rate is given by:

where Mi (SI unit: kg/mol) denotes the species molecular weight and ρi (SI unit: kg/m3) the species density

For ideal gases:

so that

where p (SI unit: Pa) is the constant pressure.

Neglecting pressure drop, the energy balance for an ideal reacting gas, as well as an incompressible and ideally mixed reacting liquid is given by:

(2-60)

Equation 2-60 is similar to the energy balance for the batch reactors (Equation 2-46), but with a reactor volume dependence instead of a time dependence.


	Nonisothermal Plug-Flow Reactor: Application Library path Chemical_Reaction_Engineering_Module/Tutorials/nonisothermal_plug_flow