mkin4py 1.0

A package for linearly defining and solving microkinetic catalytic systems.

mkin(microkinetics) 4 py(thon)

A package for linearly defining and solving micr okinetic catalytic systems.

Description

A microkinetic package translated from the Linearized Microkinetic Catalytic System Solver

By the author:

Gabriel S. Gusmão <[e-mail]>

under Dr. Phillip Christopher <[e-mail]> 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

Features

• 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)

On the way

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)

Instructions

• 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]]