mkin4py 1.0

A microkinetic package translated from the Linearized Microkinetic Catalytic System Solver

By the author:

Gabriel S. Gusmão <gusmaogabriels@gmail.com>

under Dr. Phillip Christopher <christopher@engr.ucr.edu> advisement.

For detailed information, refer to code comments or associated publication. Gusmão, G. S. & Christopher, P., A general and robust approach for defining and solving microkinetic catalytic systems. AIChE J. 00, (2014).; http://dx.doi.org/10.1002/aic.14627

The 17-Step Ethylene Epoxidation by Stegelmann et al. has been used as example. Stegelmann, C., Schiødt, N. C., Campbell, C. T. & Stoltze, P. Microkinetic modeling of ethylene oxidation over silver. J. Catal. 221, 630–649 (2004).

1. Set-up the environment conditions (temperature, pressure, gas constant)
2. Create a MK (microkinetic model object) - Define its dimensions: number of reactants (rows) and elementary reactions (columns) involved in the stoichiometry matrix, and parse the rows that refer to free-species (non-adsorbed) - Parse the stoichiometry matrix (must be of size number of reactants × number of elementary reactions) - Set the kinetic parameters: Activation Energies and Pre-exponential factors (must be of the size of the involved elementary reactions) - Set the fixed concentration of free-species (molar fraction in non-adsorbed phase) - Parse the string-labels of involved species (array of size of number of species)
3. Solve the ensuing LP (linear problem) - For now, there is only a Newton-type method available. - Standard iterative-procedure adopted for solving the inner-loop LP (Quasi-minimum residue)

The convergence parameters are set as default in the module solver in .params

• Linearization

The project makes use of explicit routines for the calculation of the MK model derivatives

• Jacobian: Available as standard.
• Hessian: Used in the convex two-step method (details in the aforementioned reference)

1. Additional LP solvers in “switchable” fashion.
2. Evolutionary methods for the definition of best convergence parameters for stiff problems (when TOF`s are close to the machine precision)

• Installation

  pipinstallmkin4py==version_no

< L>＞P＞{STR 1 } $实例< /强>：Stoltze的17步乙烯环氧化MK体系

importmkin4pyimportnumpyasnp# Environment ConditionsT=500;#KP=2;#bargas_constant=8.31456e-3# Gas Constant - kJ/(mol×K)# Set the environment conditionsmkin4py.environment.set_temperature(T)mkin4py.environment.set_gas_constant(gas_constant)mkin4py.environment.set_pressure(P)# Stoichiometric Matrixms=[[-1,1,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1],\
[-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,1,-1,0,0,1,-1,0,0,1,-1,1,-1],\
[1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,2,-2,-2,2,-1,1,1,-1,-1,1,0,0,0,0,1,-1,-6,6,0,0,-1,1,-1,1,-5,5,1,-1,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,-4,0,0,0,0,1,-1,3,-3,-2,2,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,-1,1],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,0,0,0,0,2,-2,0,0,-1,1,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,2,-2,0,0,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,1,-1,0,0,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,1,-1,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,-1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0,0,0],\
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1,-1,1,0,0,0,0,0,0],\
];nreac=[0,1]# Reactant Rows in mSnprod=[2,3,4,5]# Product Rows in mSstoichs=np.concatenate((nreac,nprod))# Reactants and Products are not under PSSHmkin4py.mkmodel.create(np.shape(ms)[0],np.shape(ms)[1],stoichs)# Initialize the modelmkin4py.mkmodel.set_ms(ms)# Set the stoichiometry matrix# Species labelssplabels=['O2','C2H4','C2H4O','CH3CHO','CO2','H2O','*','O2*','O*','OH*',\
'H2O*','CO2*','C2H4*','O·O*','C2H4·O*','CH2CH2O·O*','C2H4O·O*','CH3CHO·O*',\
'CH2CHOH·O*','CH2CHO·O*']mkin4py.mkmodel.set_splabels(splabels)# Set species labels# Pre-exponential Factors of Eelementary Reactions (1/s)va=[2.71e5,1.1e12,4.0e12,8.0e14,2.0e7,1.3e15,7.2e7,\
2.2e11,9.0e14,5.3e14,1.95e8,4.8e12,1.13e13,2.11e12,\
9.0e12,4.5e10,2.9e13,2.6e9,2.0e20,5.3e13,7.2e7,2.2e11,\
4.0e11,3.1e14,2.6e13,1.3e9,1.0e20,5.5e13,1.4e10,1.0e11,\
3.6e14,1.0e8,5.9e14,1.4e9]# Activation Barriers for Elementary ReactionS (kJ/mol)vea=[5.7000,47.3000,75.0000,157.5000,20.0000,96.9000,0,37.1000,112.0000,\
183.3000,0,39.1000,95.0000,93.5000,95.0000,204.3000,41.9000,4.4000,\
11.0000,791.6000,0,30.1000,32.0000,42.8000,86.0000,106.1000,0,906.6000,\
65.6000,50.0000,38.9000,0,46.6000,0]# Set the kinetic parametersmkin4py.mkmodel.set_kinetic_params(np.array(va,ndmin=2).T,np.array(vea,ndmin=2).T)y=[0.5,0.5,0,0,0,0]# Reactants and Products Initial Fractionmkin4py.mkmodel.set_concentrations(y)# Set the *free*-species concentrations

• 评估：

  sol=mkin4py.solver.solve.rk4()# 4th-order Runge-Kutta method coupled within the LP solved via QMR# Outuptsprint'...'printsol['msg'],'time: ',sol['time']print'Coverage'printsol['coverage']print'Rates'printsol['rates']

• 输出：

  ...Convergenceachievedtime:2.25999999046Coverage[[5.00000000e-01][5.00000000e-01][0.00000000e+00][0.00000000e+00][0.00000000e+00][0.00000000e+00][4.39342950e-01][1.19743307e-03][1.07992516e-01][1.10447591e-01][2.99730332e-09][7.70711567e-10][1.00256049e-01][9.78269843e-02][1.32727193e-01][9.64368428e-03][3.28419897e-08][4.59118359e-13][5.65562897e-04][1.12150752e-15]]Rates[[-4.24252190e+01][-2.49532633e+01][1.29732696e+01][5.58723011e-04][2.39588699e+01][2.39588699e+01][0.00000000e+00][3.65929509e-13][0.00000000e+00][4.32857086e-11][2.76796815e-16][2.87485591e-11][0.00000000e+00][-2.27373675e-13][-4.65661287e-10][9.86479981e-16][0.00000000e+00][-1.60491195e-13][4.65661287e-10][-1.42115222e-11]]