Continuous Stirred Tank Reactor (CSTR)

The Cstr model simulates a continuous stirred tank reactor. This type of reactor model may be used to simulate a packed bed reactor, when the length to diameter ratio is small, or when a packed bed reactor is operating under differential conditions. The code integrates the following governing equation

\[\rho V \frac{dY_k}{dt} = \dot{q}_{in} \rho_{in} Y_{k,in} - \dot{q}_{out} \rho Y_k + \dot{s_k} M_k A_s + \dot{\omega_k}M_k V\]

Here $Y_k$ is the mass fraction of species $k$, $\rho$ is the density (kg/m$^3$) of the mixture, $V$ is the reactor volume (m$^3$), $M_k$ is the molecular weight of species $k$ (Kg/mol), $\dot{q}$ is the volumetric flow rate (m$^3$/s), $\dot{s}_k$ is the molar production rate (mol/m$^2$-s) of species $k$ due to surface reactions, $\dot{\omega}_k$ is the molar production rate (mol/m$^3$-s) of species $k$ due to gas phase reactions, and $A_s$ is the surface are in $m^2$ The subscripts in and out respectively refers to the inlet and outlet conditions. The outlet volumetric flow rate is related to the inlet volumetric flow rate according to

\[\dot{q}_{out} = \frac{q_{in} \bar{M_in} }{\bar{M}}\]

Here $\bar{M}$ refers the average molecular weights. The above equation for outlet volumetric flow rate is valid only when there is no mass accumulation within the reactor.

Running the code

The code is invoked by using the following method.

On the Julia REPL

julia>using ReactionEngine
julia>cstr("cstr.xml","../lib/")

Input file

The method takes file_path and the path to lib directory as the arguments. The file_path points to the input XML file. The structure of the XML input file is shown below.

<?xml version="1.0" encoding="ISO-8859-1"?>
<cstr>
    <gasphase>CH4 H2O H2 CO CO2 O2 N2</gasphase>
    <molefractions>CH4=0.25,H2O=0.25,N2=0.5</molefractions>
    <T>1073.15</T>
    <p>1e5</p>
    <volume>1e-5</volume>
    <flow-rate>1.66e-6</flow-rate>
    <As>5e-3</As>
    <time>10</time>
    <surface_mech>data/ch4ni.xml</surface_mech>
</cstr>

The meaning of different tags is specified below.

• <cstr> : The root XML tag for Cstr
• <gasphase> : list of gas-phase species. The species names must be separated by white spaces or tab
• <molefractions> : inlet mole fraction of the gas-phase species. Instead of mole fractions, mass fractions may also be specified. In that case, the tag must be <massfractions>. You must ensure that the sum of mass or mole fractions specified is unity. There are no internal checks to ascertain this.
• <T>: operating temperature in K
• <p>: initial pressure in Pa
• <volume> : reactor volume in m$^3$
• <flow-rate> : volumetric flow rate in m$^3$/s
• <As> : surface area available for surface reactions m$^2$
• <time> : integration time in s
• <surface_mech> : name of the surface reaction mechanism. Must be specified along with the path

Output

The code generates two output files in the same directory where the input file cstr.xml is present. The file gas_profile.dat contains the mole fraction of the gas phase species as a function of time. The file surf_profile.dat contains the surface coverages of adsorbed species as a function of time. In addition to these two files, the code also generates terminal output, which shows integration progress. The terminal output is nothing by the integration time.

An example terminal output is shown below

julia> cstr("test/cstr/cstr.xml")
0.0000e+00
5.4134e-12
7.3599e-12
1.0969e-11
..
..
..
9.3568e+00
9.6322e+00
9.9232e+00
1.0000e+01
Solver Integration: Success

A sample output of gas_profile.dat is shown below

         t           T           p         rho         CH4         H2O          H2          CO         CO2          O2          N2
0.0000e+00  1.0732e+03  1.0000e+05  2.5240e-01  2.5000e-01  2.5000e-01  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  5.0000e-01
5.4134e-12  1.0732e+03  1.0000e+05  2.5240e-01  2.5000e-01  2.5001e-01  1.4392e-15  1.4653e-29  1.9600e-41  1.8072e-32  4.9999e-01
7.3599e-12  1.0732e+03  1.0000e+05  2.5240e-01  2.5000e-01  2.5001e-01  3.6770e-15  2.9837e-29  3.0298e-40  5.6564e-32  4.9999e-01
...
...
9.9232e+00  1.0732e+03  1.0000e+05  2.2739e-01  1.7569e-01  1.5482e-01  1.6954e-01  2.8553e-02  2.0940e-02  3.9303e-19  4.5046e-01
1.0000e+01  1.0732e+03  1.0000e+05  2.2738e-01  1.7566e-01  1.5479e-01  1.6961e-01  2.8572e-02  2.0942e-02  4.0255e-19  4.5044e-01

A sample output of surf_profile.dat is shown below

         t           T        (NI)       H(NI)       O(NI)     CH4(NI)     H2O(NI)     CO2(NI)      CO(NI)      OH(NI)       C(NI)     HCO(NI)      CH(NI)     CH3(NI)     CH2(NI)
0.0000e+00  1.0732e+03  6.0000e-01  0.0000e+00  0.0000e+00  0.0000e+00  4.0000e-01  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00  0.0000e+00
5.4134e-12  1.0732e+03  6.0847e-01  3.0035e-04  3.3271e-05  1.1713e-09  3.9096e-01  2.8741e-33  6.1498e-21  2.3380e-04  1.1015e-12  2.3785e-23  8.9706e-13  4.7230e-11  8.9960e-12
7.3599e-12  1.0732e+03  6.1146e-01  4.2230e-04  5.9785e-05  1.1839e-09  3.8776e-01  6.0780e-32  1.8970e-20  3.0273e-04  2.9147e-12  8.4330e-23  1.7009e-12  6.0154e-11  1.5013e-11
...
...
...
9.9232e+00  1.0732e+03  6.2063e-01  1.7493e-01  3.9236e-03  8.4466e-10  2.7702e-04  3.7430e-06  2.0019e-01  3.0447e-05  2.3741e-05  6.4247e-12  2.0465e-11  2.6758e-10  1.1674e-10
1.0000e+01  1.0732e+03  6.2056e-01  1.7494e-01  3.9209e-03  8.4442e-10  2.7693e-04  3.7428e-06  2.0024e-01  3.0431e-05  2.3746e-05  6.4295e-12  2.0465e-11  2.6755e-10  1.1672e-10