Modeling of geochemical processes

                                             J. Faimon

                                 Modeling of geochemical processes
                                           An Introduction

                                             J. Faimon



Reality and subjective vision 

Observation and experiment

Model



Previous concept

*      model -- a real object in the lesser scale;

    an attempt to imitate original



*      applications in engineering:

     behavior of the model was extrapolated to the behavior of the original object (a presumption
that both behavior will be similar)

 

*      Risk that the model behavior is different

     Similarity Theory, Dimensional Analysis (dimensionless  variables, size analysis) 

                                 Modeling of geochemical processes
                                          An Introduction

Modern concept

*      model  is imaginary -- it reflects the physical idea  

    Model replaces the physical reality with an identical mathematical description.



*      Models describe the behavior of physical system in the given range of variables
and precession. Model is not identical with real object.



*      We periodically find that model is not valid for certain  range of variables or that it is
not precise enough! Based on these facts, new model  is derived -- model more precise (often more
complicated a less visual).



Actual physical principles (theories, theorems, hypothesis) "satisfactory" describe the behavior of
natural systems; at least, in the range of the condition at which they were verified!

   

Example: gas equation        pV = nRT

     The model introduces ideal gas. 

     Any real gas does not respect this equation (model).

     In general, however, the model (equation) is frequently used!

If its preciseness is not satisfactory, the more precise model

based on the more complicated picture (van derWaals model). 

Sometimes a reality is described without any picture, based on mathematical description
(phenomenological approach).



Model development 

A. Formulation of a physical model   

     Formulation of a vision, simple as possible; validated by an experiment 

The tools

*      balances (mass balances, energy balances, charge balances...) 

*      equilibrium equations /heat -, chemical -, phase- equilibrium/

*      rate equations /mass fluxes/

 Tools are often combined!



*      a vicinity is assumed to be constant (temperature, pressure...)

*      system is considered to by homogenous (stirring, diffusion...),

*      continuous system is replaced by discontinuous one  

*      variables are presumed to be constant (surface area, pH....) 

*      dependences are understood as linear (linearization... )

*      random changes of some variables are neglected (stochastic model is replaced by deterministic
model) 

After reaching basic behavior and properties, model can be improved (model complicates)!



B. Mathematical solution

Mathematical solution of the model results into the solving of systems of differential equations --
linear or non-linear (numeric methods, computers)