oxidative coupling of methane - optience
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Oxidative Coupling of Methane
Objective: Parameter Estimation for Methane to Ethylene reaction In this example, we build a simplified reaction network for the Oxidative Coupling of Methane (OCM)
and estimate the kinetic parameters based on data from [1]. We start with a basic model and the
model is refined sequentially to improve empirical accuracy. You may download the zip file containing
the rex files analyzed next.
Features Illustrated ● Building a Macro-kinetic Reaction Network
● Manipulation of weighting factors with automated procedures.
● Reaction Traffic tool used to compare the relative magnitude of reaction paths
Reaction Model Oxidative Coupling of Methane is generally accepted as a combination of catalytic and gas-phase
reactions. The reaction network for this system as shown in [1] is below:
The complete model from [1] includes 50+ elementary reactions. Gas phase reactions include radical
species and detailed microkinetics are considered for the reactions on the catalyst surface. While the
detailed microkinetic model proposed in [1] can be formulated in REX using the Detailed Catalyst
feature as shown here, we focus this example on building an empirical macrokinetic model. This
model contains bulk species only: radicals and surface intermediates are not considered. The
experimental data from from [1] are used for the kinetic estimation.
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The reaction network consists of two path types:
● Formation of C2 species from methane, indicated in blue in the image below.
● Oxidation of all species yielding COx indicated in green:
Setting up the first Mass Action Model (OCM-1.rex)
In the Units Configuration node, the rate basis is selected to be Catalyst Mass; Partial Pressure is
chosen for the concentration term in the rate expression. Other units selected are shown below:
In the Compounds node, we define all the species. Optional information for atom counts may also be
entered in the Compounds→Formula node. All reactions are considered irreversible:
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The compound orders are defined in node Chemistry→Kinetics→Parameters node for every reaction.
We choose order=1 for all reactants in a reaction.
Experimental Data The experiments are carried out in a fixed bed reactor (modeled as a PFR), where pressure and
temperature are Interpolated from Data. Those specifications are defined in the Reactor node, where
the gas flow is chosen as float so that it can be calculated by REX to match the pressure setpoint:
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Experimental data retrieved from [1] covers the following effects:
● Methane and Oxygen conversion and product selectivities vs Space Time
○ T=973K, P=110 kPa, CH4/O2 feed = 3.0
○ W/F varying from 2 to 12 (kg s / mol)
● Methane and Oxygen conversion and product selectivities vs CH4/O2 feed ratio
○ T=1013K, P=130 kPa, W/F = 2.0
○ CH4/O2 feed ratio varying from 2 to 12
● Methane and Oxygen conversion vs CH4/O2 feed ratio at different temperatures
○ P=130 kPa, W/F = 2.0
○ Temperature values: 944K, 973K and 1013K
The experimental data is available in the Experiments→Measurements→SetName nodes of the
provided rex files.
Setting up the parameter estimation
All reactions are selected as Estimate in Estimation node, and bounds are open in
Estimation→Parameters node for pre-exponential and activation energies.
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In the Weights node, we select all the compounds to be reconciled, except water. Hybrid weights are
generated with the Ignore Zero option enabled. This ensures that the weights are kept at zero for the
measurements whose experimental values are zero.
When running this model, the total weighted Least Square Error (LSQ) for this model is around 10-3.
In order to have better scaling of the objective function, we increase all weights by a factor of 1000.
This is done in the Advanced tab of the Weights node. First, we include all checkboxes, so that the
change is done for all compounds and sets. A quick way to include all checkboxes in a column is by
pointing to the column header, then using the right click mouse button and selecting the Check All
option. For example for the CH4 column:
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The same must be done for the other compound columns to have all checkboxes included. Another
option is to include one checkbox, then copy this checkbox ( Ctrl-C works or by right click on the
mouse) and paste the include flag to a region of checkboxes (Ctrl-V works). Once the required
checkboxes are selected, the “Multiply by Custom Weight” option is chosen in the Modification Type
combo. A factor of 1000 is entered in the Custom Weight box followed by the Apply button as shown
below:
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The OCM-1.rex file already includes this modification. A log with the changes done on the weights
can be seen in the History tab on Weights node.
Estimation Results
After running the estimation model, we obtain the objective function to be 7.06.The parameter values
from the solution are shown in the Results→Parameters node:
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You may note that several reactions have very small pre-exponential values with high activation
energy. These reactions have negligible traffic and thus can be eliminated without affecting model
predictions. We continue analyzing the model predictions by inspecting the parity plots in the
Results→Model-Data Comparison node:
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As seen above, C2H4 and C2H6 predictions need to be improved.
In OCM-2.rex, we try to see if increasing the C2H4 weights by a factor of 10 (in the Advanced tab of
the Weights node) can improve the fit. However, despite running the model with the increased
weights, the C2H4 parity plot shows no significant improvement:
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Next, we try to optimize the compound orders for the reactions in OCM-3.rex. We initially had all
orders fixed to one; now we open them between 0.5 and 2 in the Estimation→Parameters node. This
gives a better weighted LSQ value of 3.56. The resulting parameters are below:
Some orders have hit their bounds. You may experiment with relaxing the bounds to see if further
improvement can be obtained.
In the final trial, we fix the orders close to the solution obtained from previous run. The orders are
fixed to either 0.5, 1 or 2 by setting them closest to the optimal value. For example, reaction CH4-to-
C2H6 will have orders fixed fo 0.5 for CH4 and for O2. We also un-include the reactions that have
negligibly small rates: C2H6-to-CO2, C2H6-to-CO and C2H4-to-CO. They can be un-included from
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either the Chemistry→Reactions or Chemistry→Kinetics node; the latter is shown below and the
corresponding rex file is OCM-4.rex:
This simplified model has a weighted LSQ of 3.72 which is slightly higher than the previous model
with open bounds on the compound orders. The parameter values and resulting parity charts are
shown next:
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Comparing the previous parity results from OCM-1.rex file, we can see that C2H4 match has
improved, while all other compounds predictions remain reasonably good as before. The carbon
traffic in Reaction Traffic node allows us to qualitatively compare the relative importance of the
reaction paths in the resulting reaction network:
Further studies You may start from the mass action model in OCM-1.rex and add Langmuir Hinshelwood kinetics and
compare these results with the model from OCM-4.rex. You may also build a first principles model
based on the surface reactions by using the Detailed Catalyst model in REX.
References 1. Sun, J., Thybaut, J.W., Marin, G.B., (2008) Microkinetics of Methane Oxidative Coupling. Catalysis
Today, Vol 137, 90-102.