Modeling and Simulation

Kinetic and reactor models of OCM on mixed metal oxide catalysts have been published including simplified models with a few steps of reactions and complex ones with over a hundred free radical reactions.  From Baerns’ model of ten reaction steps, we developed a simplified model.  We modified rate equations and kinetic parameters based on our experimental observations and plotted the simulated and experimental data together.  We applied the model to predict the trends of residence time, conversion and selectivity as well as effects of operating conditions.  We also tested the model to simulate a two-reactor process and high pressure process, which shows the model’s validity and limits by comparison with experimental data.

Matlab 7.3.0 (R2006b) is the software we used for the simulation and parameter estimation with the ODE solver and optimization toolbox.

 

I              REACTION SCHEME, KINETIC MODEL

We chose eight reactions, including three primary and five secondary ones, for our model (Figure 1).  Similar to Baerns’s model based on La2O3/CaO catalyst, ethane formation from methane (reaction 1) is the primary reaction followed by a secondary reaction of ethane to ethylene (reaction 2) for manganese oxide based catalyst. Partial oxidation of methane to CO (reaction 6) and deep oxidation to CO2(reaction 7) as primary reactions, are consistent with the experimental observations.  Further oxidations of ethylene to CO (reaction 3) and CO to CO2 (reaction 4) are accounted for lower hydrocarbon selectivity and higher CO2 selectivity for long residence times.  The consumption of ethane is mostly through transformation to ethylene; the direct oxidation of ethane to COis relatively slow.  However, the step of homogeneous dehydrogenation of ethane to ethylene in Baerns’ model is dropped from our model since reaction 2 is sufficient to account for consumption of ethane during the parameter estimation process.  The steam reforming of ethylene (reaction 5) is kept but its contribution to the product distribution is relatively small.  For most models in the literature, the C3+ hydrocarbons are included in the C2 yield.  To try to account for 5-10% C3+ selectivity, reaction 8 is included in our model, as propylene is the major C3+hydrocarbon product.

 

 

Scheme 1.  Reaction scheme for the simplified OCM model.

 

Reaction 1:                          2 CH4 + ½ O2 ===> C2H+ H2O

Reaction 2:                          C2H6 + ½ O2 ===> C2H4 + H2O

Reaction 3:                          C2H4 + 2 O2 ===> 2 CO + 2 H2O

Reaction 4:                          CO + ½ O===> CO2

Reaction 5:                          C2H4 + 2 H2O ===> 2 CO + 4 H2

Reaction 6:                          CH4 + O2 ===> CO + H2O + H2

Reaction 7:                          CH4 + O2 ===> CO+ 2 H2O

Reaction 8:                          CH4 + C2H4 ===> C3H6 + H2

 

II.                  RATE EQUATIONS AND KINETIC PARAMETERS

The modified rate equations for the eight reactions in the model are listed below. The Hougen-Watson type rate equations are used for r1, r4, r6, and r7, while methane coupling step is considered for both O2 and CO2 adsorption, and only CO2 adsorption is accounted for by r4 (CO to CO2), r6 (CH4 to CO) and r7 (CH4 to CO2).  For r2, r3, r5, r8, power-law rate equations are taken.  The power-law orders are estimated from 80-20 batch I catalyst by using as the first guess parameters from Baerns’ model.  The same procedure was also used to estimate the O2 and CO adsorption equilibrium constants and adsorption enthalpy values.

 

III.                  SIMULATION OF EXPERIMENTS FOR THIS CATALYST

As extensive experimental study has been done on this catalyst (first batch), a set of seventeen experimental data with a variety of conditions such as temperature, residence time, and feed ratios are used to obtain kinetic parameters.  First test of the kinetic model is to check the fitting of the simulation results to the experimental results.  During modeling, seven output variables are chosen for comparison of simulation with experiment: methane conversion (X_CH4), oxygen conversion (X_O2), ethylene selectivity (S_C2H4), ethane selectivity (S_C2H6), C3 selectivity (S_C3), CO selectivity (S_CO), CO2 selectivity (S_CO2).  From these results, further calculation can give S_C2 (S_C2H4 plus S_C2H6), S_C2+ (S_C2 plus S_C3), S_COx (S_CO plus S_CO2), and C2+_Yield (X_CH4 multiply S_C2+).  The comparison of the simulation and experimental results is shown in Figures 1 and 2.

 

experiment