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

  pip install mkin4py==version_no

• Example: Stoltze’s 17-Step Ethylene Epoxidation MK system

  import mkin4py
  import numpy as np
  
  # Environment Conditions
  T = 500; #K
  P = 2; #bar
  gas_constant = 8.31456e-3 # Gas Constant - kJ/(mol×K)
  
  # Set the environment conditions
  mkin4py.environment.set_temperature(T)
  mkin4py.environment.set_gas_constant(gas_constant)
  mkin4py.environment. set_pressure(P)
  
  # Stoichiometric Matrix
  ms = [
  [-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 mS
  nprod = [2, 3, 4, 5] # Product Rows in mS
  stoichs = np.concatenate((nreac,nprod)) # Reactants and Products are not under PSSH
  mkin4py.mkmodel.create(np.shape(ms)[0],np.shape(ms)[1],stoichs) # Initialize the model
  mkin4py.mkmodel.set_ms(ms) # Set the stoichiometry matrix
  
  # Species labels
  splabels = ['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 parameters
  mkin4py.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 Fraction
  mkin4py.mkmodel.set_concentrations(y) # Set the *free*-species concentrations

• Evaluation:

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

• Output:

  ...
  Convergence achieved time:  2.25999999046
  Coverage
  [[  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]]