User:Grup5CQ/sandbox/Numerical Methods Chemical Kinetics

Chemical equilibrium and kinetic calculations are crucial for modeling chemical processes in a wide range of applications such as industrial, environmental, and geological. These include, for example, combustion and reactive flow in engines pore-scale reactive transport phenomena, speciation calculations in aquatic systems, cement chemistry, polluted groundwater remediation, hydrothermal geochemistry and ore forming processes, biochemical processes in cells, plotting of phase equilibria diagrams in petrology and metallurgy, reactive transport simulations at nuclear waste disposal sites, geologic carbon storage in deep saline aquifers and other formations ,geothermal energy utilization, combinations of the latter two, and enhanced oil recovery.

Due to the complexity of the coupled physical and chemical processes of interest nowadays, in which several thousands of chemical equilibrium and kinetic calculations might be needed in a computer simulation, the computational methods for such chemical calculations need to be efficient and robust.

Numerical methods are a computational, nunerical way to solve differential equations. In order to solve a chemical kinetics problem we need: initial values for concentrations, values for rate constants, and an explicit formula for the rate

TENUA PROGRAM
Tenua program is a simple program with an intuitive interface to simulate chemical reactions.

TENUA allows the users to plot easily concentrations vs.time, if the rate constant and initial concentrations are known. This program may also calculate rate constants from experimental data. It allows you to write out chemical reactions and calculate the concentrations of all the species over time. It can also compare the simulation to real data and automatically calculate the correct rate constants and other parameters to fit the data.

In this web-site you can see an example of TENUA: https://www.d.umn.edu/~psiders/courses/chem4641/kineticsim/index.html

KINETICUS PROGRAM
Kineticus program is a more complex numerical program especifically tailored to chemical kinetics, allows for far more complex solutions than Tenua, but which may not be free of charge.

Kintecus is a powerful Industrial Strength/Research Grade chemical modeling software for simulation and optimization/regression of combustion, nuclear, biological, enzyme, atmospheric and many other chemical kinetic and equilibrium processes.

PYTHON PACKAGES
Python is a programming language that lets you work quickly and integrate systems more effectively. Python uses packages that are collections of Python modules containing an additional __init__.py file. The __init__.py distinguishes a package from a directory that just happens to contain a bunch of Python scripts. Some of such packages are NumPy, Pendulum, Python imaging Library, MoviePy.

Euler and Runge-Kutta
The overall goals of the field of numerical analysis in the design and analysis of techniques to give approximate but accurate solution are hard to get. It is therefore, important to be able to estimate the error involved in such approximation.

Euler’s method is simple but inaccurate and time steps must be very short. Runge-Kutta is less imple but very accurate and time steps may not be so short.

Starting from initial values for time (t=0) and concentration ([A](t=0)=[A]0) a table of values for time and concentrations is built.

In mathematics and computational science, the Euler method is a first-order numerical procedure for solving ordinary differential equation (ODEs) with a given initial value. It is the most basic explicit method of numerical integration of ordinary differential equation and is the simplest Runge-Kutta method. The Euler method is named after Leonhard Euler (1707).

The Runge-Kutta method is also a second order Runge-Kutta Method using Taylors series expansion to derive it, like modified Euler’s method.