www.optience.com 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.
The reaction network consists of two path types: Formation of C 2 species from methane, indicated in blue in the image below. Oxidation of all species yielding CO x 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:
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:
Experimental data retrieved from [1] covers the following effects: Methane and Oxygen conversion and product selectivities vs Space Time T=973K, P=110 kpa, CH 4 /O 2 feed = 3.0 W/F varying from 2 to 12 (kg s / mol) Methane and Oxygen conversion and product selectivities vs CH 4 /O 2 feed ratio T=1013K, P=130 kpa, W/F = 2.0 CH 4 /O 2 feed ratio varying from 2 to 12 Methane and Oxygen conversion vs CH 4 /O 2 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. 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:
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:
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:
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:
As seen above, C 2 H 4 and C 2 H 6 predictions need to be improved. In OCM-2.rex, we try to see if increasing the C 2 H 4 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 C 2 H 4 parity plot shows no significant improvement:. 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 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:
Comparing the previous parity results from OCM-1.rex file, we can see that C 2 H 4 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.