Ideal Stirred Tank Reactor System

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Ideal Stirred Tank Reactor System

In the chemical and biochemical industries, for instance in fermentation processes, reactors having well-mixed conditions and liquid level control are common.

This example shows how to use the Reaction Engineering interface to model a 0D ideal system of tank reactors in series, with controlled feed inlet and product outlet streams. The volume change in each reactor is monitored and controlled.

Model Definition

This model solves for a liquid-phase first order irreversible reaction A → B where

(1)

In Equation 1, r is the reaction rate (SI unit: mol/(m3·s)), k is the rate constant (SI unit: 1/s), and cA is the concentration of A.

The reaction takes place in a system of two ideal reactors in series. The first reactor tank has a volume capacity of vtank1 = 1 m3 and the second vtank2 = 1.5 m3 initially.

Initially the reactors are charged only with solvent. A is fed with solvent to the first tank with a volumetric flow rate of vf1 = 1 m3/min. The volumetric flow rate at the outlet of the first tank is set to vout1 = 0.9 m3/min. This whole stream is fed to the second tank in the system, vf2 = vout1. The second tank also has a fresh supply of A with solvent entering at a rate of vf2 = 0.5 m3/min. In a similar way as for the first reactor, the outlet flow is also set to vout2 = 1 m3/min. Figure 1 shows the reactor system in detail.

Figure 1: The reactor system.

The mass balance for species i in each reactor is shown in Equation 2:

(2)

Vr denotes the reactor volume (SI unit: m3), Ri is the species rate expression (SI unit: mol/(m3·s)). Subscripts f and out indicate the feed inlet and the outlet, respectively. j and k are the number of feed inlet and outlet streams, respectively.

The volume depends on the volumetric production rate vp and the regulated inlet and outlet volumetric flow rates as shown in Equation 3:

(3)

The model incorporates two stop conditions: If any of the reactor volumes is 1 % or less of the initial volumes, the computations stop.

Results and Discussion

In Figure 2 and Figure 3, the concentrations of the species in the two tanks are shown.

Figure 2: Concentrations of A and B in tank 1 and tank 2.

The variation of the tank volumes is shown in Figure 3. With a known diameter of the reactor, the liquid level can be calculated from this volume. Given the inlet and outlet flows, this system will fill up the tanks considerably.

Figure 3: Tank volumes.

The results show only some system aspects that can be investigated with the Reaction Engineering interface. This application can also be utilized as a starting point for studying, for instance, startup and steady-state process conditions.

Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/tank_flow_system

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select .

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In the tree, select .

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Global Definitions

Add a set of global parameters by importing their definitions from a data text file.

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In the window, under click .

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In the window for , locate the section.

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

Start with the first reactor. Select the reactor type to model the first reactor.

Reaction Engineering (re)

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type A=>B.

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Locate the section. In the kf text field, type kf_reaction.

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In the window, click .

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In the window for , locate the section.

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In the M text field, type Mn_A.

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In the window, click .

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In the window for , locate the section.

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In the M text field, type Mn_B.

Add a solvent (water) to the first tank.

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type S.

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Locate the section. From the list, choose .

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Locate the section. In the M text field, type Mn_S.

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In the ρ text field, type density_S.

in the section substitutes the constant mass condition. Choose this to set a constant value of the volumetric outlet rate, v.

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In the window, click .

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In the window for , locate the section.

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Find the subsection. From the list, choose .

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In the v text field, type v_outlet1.

Initial Values 1

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In the window, click .

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In the window for , locate the section.

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In the Vr0 text field, type Vr_init_tank1.

Set only solvent in the first tank initially.

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Locate the section. In the table, enter the following settings:


Species	Concentration (mol/m^3)
S	cinit_S

Add one stream to the first tank.

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In the toolbar, click

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In the window for , locate the section.

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In the vf text field, type v_inlet.

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Locate the section. In the table, enter the following settings:


Species	Concentration (mol/m^3)
A	cinlet_A1
S	cinlet_S

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In the window, right-click and choose .

Reaction Engineering 2 (re2)

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In the window, right-click and choose .

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In the dialog box, click .

Duplicating the first reactor and changing the necessary parameters that distinguishes the first from the second reactor.

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In the window, click .

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In the window for , locate the section.

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Find the subsection. In the v text field, type v_outlet2.

Initial Values 1

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In the window, expand the node, then click .

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In the window for , locate the section.

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In the Vr0 text field, type Vr_init_tank2.

The stream to the second reactor is equal to the whole outlet stream from the first reactor.

Feed Inlet 1 - from Tank 1

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In the window, click .

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In the window for , type Feed Inlet 1 - from Tank 1 in the text field.

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Locate the section. In the vf text field, type v_outlet1.

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Locate the section. In the table, enter the following settings:


Species	Concentration (mol/m^3)
A	re.c_A
B	re.c_B
S	re.c_S

Feed Inlet 2 - Fresh

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In the toolbar, click

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Add a second stream to the second reactor to model the fresh feed.

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In the window for , type Feed Inlet 2 - Fresh in the text field.

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Locate the section. In the vf text field, type v_fresh2.

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Locate the section. In the table, enter the following settings:


Species	Concentration (mol/m^3)
A	cfresh2_A
S	cinlet_S

Step 1: Time Dependent

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type range(0,0.1,120).

Solution 1 (sol1)

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In the toolbar, click

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Stop the computations if any of the two reactor volumes is empty.

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In the window, expand the node.

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Stop expression	Stop if	Active	Description
comp1.re.Vr<=Vr_init_tank1*0.01	True (>=1)	√	Stop expression 1

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In the table, enter the following settings:


Stop expression	Stop if	Active	Description
comp1.re2.Vr<=Vr_init_tank2*0.01	True (>=1)	√	Stop expression 2

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Locate the section. From the list, choose .

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Clear the check box.

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In the toolbar, click

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Concentrations in Tanks

Follow these steps to create Figure 2.

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In the window for , type Concentrations in Tanks in the text field.

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

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Locate the section. From the list, choose .

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In the window, expand the node, then click .

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In the window for , type Tank 1 in the text field.

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

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

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In the table, enter the following settings:


Legends
A in tank 1
B in tank 1

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Right-click and choose .

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In the window for , type Tank 2 in the text field.

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Click in the upper-right corner of the section. From the menu, choose .

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Click in the upper-right corner of the section. From the menu, choose .

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Locate the section. In the table, enter the following settings:


Legends
A in tank 2
B in tank 2

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In the toolbar, click

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Follow these steps to create Figure 3.

Volume in Tanks

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In the window, under click .

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In the window for , type Volume in Tanks in the text field.

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Locate the section. From the list, choose .

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Locate the section. From the list, choose .

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In the window, expand the node, then click .

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In the window for , type Tank 1 in the text field.

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Click in the upper-right corner of the section. From the menu, choose .

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Locate the section. From the list, choose .

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Locate the section. From the list, choose .

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In the table, enter the following settings:


Legends
Tank 1

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Right-click and choose .

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In the window for , type Tank 2 in the text field.

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Click in the upper-right corner of the section. From the menu, choose .

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Locate the section. In the table, enter the following settings:


Legends
Tank 2

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In the toolbar, click

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