G8540 Modeling of Geochemical Processes

Faculty of Science
Spring 2002
Extent and Intensity
1/2. 3 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Ing. Jiří Faimon, Dr. (lecturer)
Guaranteed by
doc. Ing. Jiří Faimon, Dr.
Department of Geological Sciences – Earth Sciences Section – Faculty of Science
Contact Person: doc. Ing. Jiří Faimon, Dr.
Prerequisites (in Czech)
( G5080 Geochemistry I && G6080 Geochemistry II ) || SOUHLAS
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course provides the basic knowledge and skills in the field of mathematical and computer modeling. Especial care is devoted to the modeling of geochemical equilibrium systems. There is presented PHREEQC, professional geochemical software. The part of the course is applied to the modeling of dynamic systems. Basic non-linear models are demonstrated (Lotka-Volterra, Brusselator). Mathematic methods and understanding of modeling principles are emphasized. Numeric calculations are accomplished in the MS Excel and Mathematica software. The dynamic modeling of open systems, in which transport and chemical reaction are coupled, is briefly discussed.
Syllabus
  • Basic ideas: Physical reality. Subjective ideas. Observations and experiments. Phenomenological approach. Real model. Physical model. Mathematical model.

    Problem formulation - model development: Conservation principles, mass /energy/ balances /input, resources, output, accumulation/, equilibrium equations, rate equations /flux balances.

    Model simplification: System definition, balance area, time-period. Significant and non-significant influences.

    Closed and opened systems: States, processes, chemical equations, matrix form, vector form, inversion matrix, matrix solution of linear equation system.

    Phase rule: Chemical species, Physical phases, degree of freedom. Simple systems. Example: carbonate system.

    Components as mathematical variables: Independent equations. Basis species. Secondary species. Chemical equations. Mass action equations. Charge balances. Mass balance. Change of basis.

    Equilibrium systems: Functions of more variables. Minimization. Newton's method. Steepest descent method. Constrained minimization. Taylor's series. Gradient. Jacobian. Hessian. Newton-Raphson's method.

    Model of carbonate system: Thermodynamical database. Basis of variables. Model of calcite-CO2-H2O system. Numerical solution.

    PHREEQC software: Modeling of basic interactions and processes with professional software.

    Dynamic systems: Reservoirs and mass fluxes. Single reservoir system, residence and response times, steady states. Multi-reservoir systems. Linear systems (Matrix solution of differential equation linear system. Eigen values. Eigen vectors. Characteristic equation. Homogenous and non-homogeneous systems). Non-linear systems (Multiple steady states, stability and non-stability. Oscillations. Numerical solution of nonlinear equation system. Euler's methods. Runge-Kutta's methods).

    Non-linear models: Brusselator, Lotka-Volterra. Phase space. Attractor. Numerical solution.

    Opened dynamic systems: Transport (advection, diffusion). Reaction and transport. Numerical solution of partial differential equations. Finite difference method. Bondary conditions.

Literature
  • BETHKE, Craig. Geochemical reaction modeling : concepts and applications. New York: Oxford University Press, 1996, xvii, 397. ISBN 0195094751. info
  • ALBARÉDE, Francis. Introduction to geochemical modeling. 1st pub. Cambridge: Cambridge University Press, 1995, 543 s. ISBN 0-521-45451-4. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2000, Spring 2001.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2002/G8540