mkin4py 1.0

A package for linearly defining and solving microkinetic catalytic systems.

==============
**mkin4py**
==============

*mkin(microkinetics) 4 py(thon)*

|star| |watch| |fork| |github|

.. image:: https://img.shields.io/pypi/l/mkin4py.svg
:height: 100px
:width: 200 px
:scale: 50 %
:alt: alternate text
:align: right

.. image:: https://img.shields.io/pypi/v/mkin4py.svg
:height: 100px
:width: 200 px
:scale: 50 %
:alt: alternate text
:align: right

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]>

|ld|

|rg|

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**

.. code-block:: python

pip install mkin4py==version_no

- **Example**: Stoltze's 17-Step Ethylene Epoxidation MK system

.. code-block:: python

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**:

.. code-block:: python

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**:

.. code-block:: python

...
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]]

.. |github| image:: https://img.shields.io/github/followers/gusmaogabriels.svg?style=social&label=Follow
:scale: 25%
:target: https://github.com/gusmaogabriels

.. |fork| image:: https://img.shields.io/github/forks/gusmaogabriels/mkin4py.svg?style=social&label=Fork
:scale: 25%
:target: https://github.com/gusmaogabriels/mkin4py/fork

.. |star| image:: https://img.shields.io/github/stars/gusmaogabriels/mkin4py.svg?style=social&label=Star
:scale: 25%
:target: https://github.com/gusmaogabriels/mkin4py/stargazers

.. |watch| image:: https://img.shields.io/github/watchers/gusmaogabriels/mkin4py.svg?style=social&label=Watch
:scale: 25%
:target: https://github.com/gusmaogabriels/mkin4py/watchers

.. |rg| image:: https://www.researchgate.net/images/public/profile_share_badge.png
:height: 55 px
:width: 166 px
:scale: 30 %
:target: https://www.researchgate.net/profile/Gabriel_Gusmao?cp=shp

.. |ld| image:: https://static.licdn.com/scds/common/u/img/webpromo/btn_viewmy_160x25.png
:height: 25 px
:width: 160 px
:scale: 50 %
:target: https://br.linkedin.com/pub/gabriel-saben%C3%A7a-gusm%C3%A3o/115/aa6/aa8