COMSOL 6.4 - Nonisothermal Plug-Flow Reactor

This example considers the thermal cracking of acetone, which is a key step in the production of acetic anhydride. The gas phase reaction takes place under nonisothermal conditions in a plug-flow reactor. As the cracking chemistry is endothermic, control over the temperature in the reactor is essential in order to achieve reasonable conversion. Furthermore, it is illustrated how to affect the conversion of acetone by means of a heat exchanger supplying energy to the system, and how the conversion of acetone is affected by mixing inert into the feed inlet stream.

The example details the use of the predefined Plug flow reactor type in the Reaction Engineering interface of the Chemical Reaction Engineering Module. This model reproduces the results in Ref. 1.

Model Definition

The model simulates the step in the gas-phase production of acetic anhydride where cracking of acetone (A) into ketene (K) and methane (M) occurs:

The rate of reaction is

where the rate constant is given by the Arrhenius expression

For the decomposition of acetone described above, the frequency factor is A1 = 8.2·1014 (SI unit: 1/s), and the activation energy is E1 = 284.5 (SI unit: kJ/mol). Together with the reacting species, nitrogen can also be present as an inert in the system.

The chemical reaction takes place under nonisothermal conditions in a plug-flow reactor, illustrated schematically in Figure 1.

Figure 1: The Plug-flow reactor.

Species mass balances are set up as

(1)

where Fi is the species molar flow rate (SI unit: mol/s), V is the reactor volume (SI unit: m3), and Ri is the species rate expression (SI unit: mol/(m3·s)). Concentrations needed to evaluate rate expressions are described by

where v is the volumetric flow rate (SI unit: m3/s). By default, the Reaction Engineering interface treats gas phase reacting mixtures as being ideal. Under this assumption the volumetric flow rate is given by

where p is the pressure (Pa), Rg denotes the ideal gas constant (8.314 J/(mol·K)), and T is the temperature (SI unit: K).

The reactor energy balance is

(2)

In Equation 2, Cp,i represents the species molar heat capacity (SI unit: J/(mol·K)), and ws is the shaft work per unit volume (SI unit: J/(m3·s)). Q denotes the heat due to chemical reaction (SI unit: J/(m3·s)) and is described by

where Hj is the heat produced by reaction j. The term Qext represents external heat added or removed from the reactor. The present model treats both adiabatic reactor conditions, that is

and the situation where the reactor is equipped with a heat exchanger jacket. In the latter case Qext is given by

where U is the overall heat transfer coefficient (SI unit: J/(m2·s·K)), a is the effective heat transfer area per unit of reactor volume (SI unit: 1/m), and Tamb is the temperature of the heat exchanger medium (SI unit: K). The Reaction Engineering interface automatically sets up and solves Equation 1 and Equation 2 as the predefined Plug flow reactor type is selected. As input to the balance equations you need to supply the chemical reaction formula, the Arrhenius parameters, the species thermodynamic properties, as well as the inlet molar feed of reactants.

Working with Thermodynamic Polynomials

The Reaction Engineering interface uses the following set of polynomials as default expressions describing species thermodynamic properties:

(3)

(4)

(5)

Here, Cp,i denotes the species’ heat capacity (SI unit: J/(mol·K)), T the temperature (K), and Rg the ideal gas constant, 8.314 (J/(mol·K)). Further, hi is the species’ molar enthalpy (SI unit: J/mol), and si represents its molar entropy (SI unit: J/(mol·K)). A set of seven coefficients per species are taken as input for the polynomials above. The coefficients a1 through a5 relate to the species heat capacity, the coefficient a6 is associated with the species enthalpy of formation (at 0 K), and the coefficient a7 comes from the species entropy of formation (at 0 K).

The format outlined by Equation 3, Equation 4, and Equation 5 is referred to as CHEMKIN or NASA format (Ref. 2). This is a well-established format, and database resources list the needed coefficients for different temperature intervals. Many web-based data resources exist for CHEMKIN thermodynamic data and otherwise. For a collection of databases, see Ref. 3. It is therefore often a straightforward task to assemble the thermodynamic data required and then import it into your reaction model.

Creating a Thermodynamic Data File

CHEMKIN thermodynamic files typically contain blocks of data, one block for each species. Such a data block is illustrated in Figure 2 for gas phase acetone.

Figure 2: Thermodynamic data block on the CHEMKIN format.

The first line starts with the species label, given with a maximum of 18 characters, followed by a 6 character comment space. Then follows a listing of the type and number of atoms that constitute the species. The G indicates gas phase data. The line ends with listing of three temperatures, defining two temperature intervals. Lines 2 through 4 contain two sets of the polynomial coefficients, a1 through a7. The first set of coefficients is valid for the upper temperature interval, and the second for the lower interval.

A complete CHEMKIN thermodynamics file has the structure illustrated in Figure 3.

Figure 3: Thermodynamic data file on the CHEMKIN format.

The keyword thermo always starts the text file. The subsequent line lists three temperatures, defining two temperature intervals. These intervals are used if no intervals are provided in the species specific data. Then follows the species data blocks, in any order. The keyword end is the last entry in the file.

The data file reproduced in Figure 3 is used in the model. It was constructed by creating a text-file with species data blocks from the Sandia National Labs Thermodynamics Resource.

Using Subsets of Thermodynamic Coefficients

In some instances, not all coefficients a1 through a7 are available. Coefficients may also be on a format differing from the NASA or CHEMKIN style. Input parameters can still be put on the form of Equation 3, Equation 4, and Equation 5, as illustrated below.

For species A, K, M, and N2, Ref. 1 lists polynomials for the heat capacity on the form:

Furthermore, the species enthalpies of formation at Tref = 298 K are provided:


Species	a1'	a2'	a3'	h(298)
A	26.63	0.183	-45.86e-6	-216.67e3
K	20.04	0.0945	-30.95e-6	-61.09e3
M	13.39	0.077	-18.71e-6	-71.84e3
N2	6.25	8.78e-3	-2.1e-8	0

The data in the table above can be correlated with the polynomials given by Equation 3 and Equation 4 by noting the relations:

(6)

(7)

Using Equation 6 and Equation 7, you find the coefficients to enter in the Reaction Engineering interface.


Species	a1	a2	a3	a6
A	3.20	2.20e-2	-5.52e-6	-2.79e4
K	2.41	1.14e-2	-3.72e-6	-8.54e3
M	1.61	9.26e-3	-2.25e-6	-9.87e3
N2	0.752	1.06e-3	-2.53e-9	-2.71e2

Read more about how to work with thermodynamic data in the section Transport Properties in the Chemical Reaction Engineering Module User’s Guide.

Results and Discussion

A 5 m3 plug-flow reactor is simulated both for adiabatic conditions and with heat exchange. The reactor is fed with pure acetone at 1035 K. 18.8 mol/m3 acetone is set to enter with a volumetric flow of 2 m3/s. Figure 4 shows the reactor temperature as a function of the reactor volume for both cases. In the adiabatic case, with no additional heating, the reactor temperature decreases along the reactor length since the cracking reaction is endothermic. On the other hand, the temperature profile as a heat exchanger supplies energy increases after first passing through a minimum. This is explained by Figure 5 where the reaction rates are shown. The minimum is due to the energy demand of the cracking reaction being dominant initially. However, as the reaction rate drops off, the heat exchanger starts to heat up the system. The heating rate decreases with the temperature difference between the heat exchanger medium and reacting fluid.

Figure 4: The reactor temperature (K) as a function of reactor volume (m3) for the two investigated cases.

Figure 5: The reaction rates (mol/(m3·s)) as functions of reactor volume (m3) for the two investigated cases.

Figure 6 shows the conversion of acetone. The reactor conversion is considerably lower at the reactor outlet in the adiabatic case than with heat exchange.

Figure 6: The conversion of acetone (%) as a function of reactor volume (m3) for the two investigated cases.

If the feed inlet stream contains an additional amount of nitrogen inert the conversion of A becomes more efficient at adiabatic conditions. This is shown for three different molar fractions of acetone in the inlet in Figure 7. The explanation is that the inert acts as a heat supply to the endothermic reaction.

Figure 7: The conversion of acetone (%) as a function of reactor volume (m3) for 100 mol%, 50 mol%, and 10 mol% of acetone in the feed inlet stream.

References

1. H.S. Fogler, Elements of Chemical Reaction Engineering, 3rd ed., Prentice Hall PTR, example 8-7, pp. 462–468, 1999.

2. S. Gordon and B.J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouquet Detonations, NASA-SP-273, 1971.

3. See, for example https://www.comsol.com/chemical-reaction-engineering-module#specs

Chemical_Reaction_Engineering_Module/Tutorials/nonisothermal_plug_flow

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