COMSOL 6.4 - Startup of a Continuous Stirred Tank Reactor

Startup of a Continuous Stirred Tank Reactor

The hydrolysis of propylene oxide into propylene glycol is an important chemical process with 400,000 metric tons produced worldwide each year. Propylene glycol finds wide application as a moisturizer in foods, pharmaceuticals, and cosmetics.

In this example, the startup phase of a continuous stirred tank reactor (CSTR), used to produce propylene glycol, is modeled. The nonisothermal process is described by a set of coupled mass and energy balances that are easily set up and solved in the Chemical Reaction Engineering Module. The model highlights the use of the predefined CSTR reactor type in the Reaction Engineering interface, and also shows how to enter the thermodynamic data needed for the energy balances.

This example reproduces results found in Ref. 1.

Model Description

Propylene glycol (C3H8O2) is produced from the reaction of propylene oxide (C3H6O) with water (H2O) in the presence of an acid catalyst:

The reaction rate (SI unit: mol/(m3·s)) is first order with respect to the activity of propylene oxide:

where the rate constant is temperature dependent according to the Arrhenius expression:

(1)

The Arrhenius parameters in Equation 1 are A1 = 4.71·109 s−1 and E1 = 75.358 kJ/mol.

The liquid phase reaction takes place in a continuous stirred tank reactor (CSTR) equipped with a heat-exchanger. Methanol (CH3OH) is also added to the mixture but does not react. It is further assumed that the reactor volume is constant over time.

Figure 1: A perfectly mixed CSTR for the production of propylene glycol. The CSTR is a predefined reactor type in the Chemical Reaction Engineering Module.

The time evolution of the nonisothermal reacting system is given by several coupled balance equations. The species mass balances are:

(2)

In Equation 2, ci is the species molar concentration (SI unit: mol/m3), Vr denotes the reactor volume (SI unit: m3), Ri is the species rate expression (SI unit: mol/(m3·s)), and vf is the volumetric flow rate of the feed inlet (SI unit: m3/s). v is the volumetric flow of the species exiting the reactor and is defined as:

vp is the volumetric production rate, arising due to differences in molar mass, Mi, and densities, ρi, of the species.

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

where Cp,i is the species molar heat capacity (SI unit: J/(mol·K)), and T is the temperature (SI unit: K). On the right-hand side, Q represents the heat due to chemical reaction (SI unit: J/s), and Qext denotes heat added to the system (SI unit: J/s), for instance by a heat exchanger. The last term signifies heat added as species flow through the reactor. In this term, hi is the species molar enthalpy (SI unit: J/mol).

This example assumes that the species heat capacities, Cp,i, represent an average over the temperature interval. The associated species’ enthalpies are then given by:

where hi(Tref) is the standard heat of formation at the reference temperature Tref.

The heat of reaction is given by:

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

The heat added by the heat exchanger is given by:

where F is the molar flow rate (SI unit: mol/s), U is the overall heat transfer coefficient (SI unit: J/(K·m2·s)), and A represents the heat exchange area (SI unit: m2). The subscript x refers to the heat exchanger medium, which in this case is water. Tx is the inlet temperature of the heat exchanger medium.

The following table summarizes additional parameters describing the reactor setup and process conditions:


Parameter	Value	Description
Vr	1.89 m3	Reactor volume
vf	3.47·10-3 m3/s	Volumetric flow rate
cf,C3H6O	2903 mol/m3	Concentration of propylene oxide in feed stream
cf,H2O	36291 mol/m3	Concentration of water in feed stream
cf,CH3OH	3629 mol/m3	Concentration of methanol in feed stream
c0,H2O	55273 mol/m3	Initial concentration of water in the reactor
ρC3H6O	830 kg/m3	Density of propylene oxide
ρH2O	1000 kg/m3	Density of water
ρC3H8O2	1036 kg/m3	Density of propylene glycol
ρCH3OH	792 kg/m3	Density of methanol
Cp,C3H6O	146.5 J/(mol·K)	Heat capacity of propylene oxide
Cp,H2O	75.4 J/(mol·K)	Heat capacity of water
Cp,C3H8O2	192.6 J/(mol·K)	Heat capacity of propylene glycol
Cp,CH3OH	81.6 J/(mol·K)	Heat capacity of methanol
Cpx	75.4 J/(mol·K)	Heat capacity of heat exchanger medium
href,C3H6O	-153.5·103 J/mol	Enthalpy of formation of propylene oxide at Tref
href,H2O	-286.1·103 J/mol	Enthalpy of formation of water at Tref
href,C3H8O2	-525.6·103 J/mol	Enthalpy of formation of propylene glycol at Tref
href,CH3OH	-238.6 J/mol	Enthalpy of formation of methanol at Tref
Tf	297 K	Feed stream temperature
T0	340 K	Initial reactor temperature
Tref	293 K	Reference temperature
Tx	289 K	Temperature of heat exchanger medium at inlet
Fx	126 mol/s	Heat exchanger medium molar flow
UA	8441 J/(s·K)	Heat exchange parameter

The model described here is readily set up and solved using the predefined CSTR reactor with constant volume in the Reaction Engineering interface available in the Chemical Reaction Engineering Module.

Results and Discussion

Figure 2 shows the concentration of propylene oxide (SI unit: mol/m3) as a function of reaction time.

Figure 2: Concentrations of reactant propylene oxide (mol/m3) during the first 4 hours of operation.

The corresponding development of the reactor temperature is shown in Figure 3.

Figure 3: Reactor temperature (K) during the first 4 hours of operation.

Initially both the reactant concentration and the temperature oscillate around their respective steady-state values (472 mol/m3 and 337 K, respectively). The model predicts that the reactor temperature passes a maximum value higher than the steady-state temperature. From a safety perspective it is therefore relevant to look closer at possible sets of initial conditions to see if process operation limits are violated. In the process modeled here, it is undesirable to exceed a reactor temperature of 355 K to avoid undesirable side reactions and not damage reactor equipment. Figure 4 shows the concentration-temperature phase plane for three initial condition scenarios: (cC3H6O = 0, T0 = 297 K), (cC3H6O = 0, T0 = 340 K), and (cC3H6O = 1400, T0 = 340 K).

Figure 4: Trajectories in the concentration-temperature phase plane for three sets of initial conditions.

The plot shows that all investigated initial conditions converge to the same steady state. However, starting with cC3H6O = 1400 mol/m3 and T0 = 340 K leads to violation of the temperature safety limits.

Reference

1. H.S. Fogler, Elements of Chemical Reaction Engineering, 3rd ed., Prentice Hall PTR, Example 9-4, pp. 553–559, 1999.

Chemical_Reaction_Engineering_Module/Tutorials/cstr_startup

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Add a set of model parameters by importing their definitions from a data text file provided with the .

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file cstr_startup_parameters.txt.

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file cstr_startup_variables.txt.

Select the -CSTR, constant volume for a liquid mixture and include the . That is, nonisothermal conditions apply.

Reaction Engineering (re)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

In the Qext text field, type Q_xch.

Click to expand the section. From the list, choose .

Locate the section. Find the subsection. In the Vr text field, type Vr_tank.

Reaction 1

In the toolbar, click

Add the reaction. Note that the reaction in this example is of first order in regard to propylene oxide, not the default stoichiometric reaction order.

In the window for , locate the section.

In the text field, type C3H6O+H2O=>C3H8O2.

Locate the section. From the list, choose .

In the rj text field, type re.kf_1*re.c_C3H6O.

Locate the section. Find the subsection. In the text field, type 1.

Locate the section. Select the checkbox.

In the Af text field, type Af_reaction.

In the Ef text field, type Ea_reaction.

Species 1

In the toolbar, click

In the window for , locate the section.

In the text field, type CH3OH.

Species: C3H6O

In the window, click .

In the window for , locate the section.

In the ρ text field, type rho_C3H6O.

Species: H2O

In the window, click .

In the window for , locate the section.

In the ρ text field, type rho_H2O.

Species: C3H8O2

In the window, click .

In the window for , locate the section.

In the ρ text field, type rho_C3H8O2.

Species: CH3OH

In the window, click .

In the window for , locate the section.

In the ρ text field, type rho_CH3OH.

Feed Inlet 1

In the toolbar, click

Define the inlet feed stream of the CSTR.

In the window for , locate the section.

In the vf text field, type v_feed.

In the Tf text field, type Tfeed.

Locate the section. In the table, enter the following settings (clear all the checkboxes in the rightmost column):


Species	Concentration (mol/m^3)	Enthalpy	Species enthalpy (J/mol)
C3H6O	cfeed_C3H6O	Species enthalpy	subst(re.h_C3H6O, re.T, re.feed1.Tf)
CH3OH	cfeed_CH3OH	Species enthalpy	subst(re.h_CH3OH, re.T, re.feed1.Tf)
H2O	cfeed_H2O	Species enthalpy	subst(re.h_H2O, re.T, re.feed1.Tf)