Processes in Karst Systems

1 Introduction.- 1 Introduction.- 1.1 The Process of Karstification.- 1.2 Approaches to an Explanation of Karst Development.- 1.3 Organization of the Book.- I Basic Principles from Physics and Chemistry.- 2 Chemistry of the System H2 O-CO2 -CaCO3.- 2.1 Reactions and Equilibria.- 2.2 Boundary Conditions for Achieving Equilibrium.- 2.2.1 The General Case.- 2.2.2 Change of Boundary Conditions.- 2.2.3 Saturated CaCO3 Solutions.- 2.2.4 Mixing of Saturated Waters in the Closed System.- 2.2.5 Influence of Foreign Ions on Calcite Dissolution.- 3 Mass Transport.- 3.1 The Random Walk Problem as Principle for Diffusional Mass Transport.- 3.2 The Laws of Diffusion.- 3.2.1 Some Basic Solutions.- 3.3 Diffusive and Advective Mass Transport.- 3.3.1 Diffusion in Turbulent Flow.- 3.3.2 Hydrodynamic Dispersion.- 3.4 Diffusion Coefficients and Their Magnitudes.- 3.4.1 Molecular Diffusion.- 3.4.2 Eddy Diffusion.- 3.4.3 Hydrodynamic Dispersion.- 4 Chemical Kinetics.- 4.1 Rate Laws of Elementary and Overall Reactions.- 4.1.1 Elementary Reactions.- 4.1.2 Overall Reactions.- 4.1.3 Temperature Dependence of Rate Constants.- 4.2 Approaching Equilibrium.- 4.2.1 Irreversible Reactions.- 4.2.2 Reversible Reactions.- 4.3 The Kinetics of the Reaction H2 O + CO2 ? H++HCO?;3.- 4.3.1 Examples.- 4.4 Mixed Kinetics.- 5 Hydrodynamics of Flow.- 5.1 Laminar and Turbulent Flow.- 5.1.1 The Law of Bernoulli.- 5.1.2 Laminar Flow.- 5.1.3 Turbulent Flow.- 5.1.4 An Example of Hydraulic Characteristics of Karst Aquifers.- 5.1.5 Flow Through Porous Media.- II Principles of Dissolution and Precipitation of CaCO3.- 6 Dissolution and Precipitation of Calcite: The Chemistry of the Heterogeneous Surface.- 6.1 Experimental Methods of Calcite Dissolution.- 6.1.1 Rotating Disc System.- 6.1.2 Batch Experiments.- 6.1.3 Measurement of Dissolution Rates.- 6.2 The Kinetics of Calcite Dissolution.- 6.2.1 Three Regions of Calcite Dissolution.- 6.2.2 The Mechanistic Model of Plummer, Wigley and Parkhurst (PWP Model).- 6.2.3 Comparison of the Mechanistic Model with Other Experiments.- 6.3 Kinetics of Calcite Precipitation.- 6.4 Dissolution Close to Equilibrium.- 7 Modelling the Kinetics of Calcite Dissolution and Precipitation in Natural Environments of Karst Areas.- 7.1 Statement of the Problem.- 7.2 The Mass Transport Equation.- 7.3 Dissolution and Precipitation Kinetics in the Open System.- 7.3.1 Calculation of Dissolution and Precipitation Rates.- 7.3.2 Results for the Open System.- 7.4 Dissolution and Precipitation Kinetics in the Closed System.- 7.4.1 Calculation of the Rates.- 7.4.2 Results for the Closed System.- 7.5 The Influence of the Diffusion Boundary Layer to Dissolution and Precipitation Rates in Turbulent Flow.- 7.5.1 Calculation of Dissolution and Precipitation Rates.- 7.5.2 Experimental Verification.- 7.6 Dissolution in Natural Systems.- 7.6.1 Influence of Foreign Ions on Dissolution Rates Far from Equilibrium.- 7.6.2 Influence of Lithology on Dissolution Rates.- 7.6.3 Dissolution in Porous Media.- III Conceptual Models of Karst Processes.- 8 Karst Systems.- 8.1 Fractures and Discontinuities in Limestone Rocks.- 8.1.1 Joints.- 8.1.2 Faults.- 8.1.3 Bedding Planes.- 8.2 Structural Segments and Tectonic Control of Caves.- 8.3 Karst Aquifers.- 8.4 Caves.- 8.5 Development of Caves.- 9 Models of Karst Development from the Initial State to Maturity.- 9.1 Pressure Fields in Fractures and Their Influence on the Development of Early Channels.- 9.2 The Network Linking Models of Ewers.- 9.2.1 The Low Dip Model.- 9.2.2 The High Dip Model.- 9.2.3 The Restricted Input Model.- 9.3 Dissolution Kinetics and the Concept of Penetration Length.- 9.3.1 The Concept of Penetration Length.- 9.3.2 Penetration Lengths in Turbulent Flow.- 9.4 Karst Development from the Initial State to Maturity.- 9.5 Geomorphological Theories from the Viewpoint of the Mathematical Model.- 9.6 Experimental Models.- 9.7 Karst Processes on the Surface.- 9.7.1 The Formation of Dolines and Shafts.- 9.7.2 Karst Denudation.- 9.7.3 Denudation Rates on Bare Rock at the Surface and in Caves.- 10 Precipitation of Calcite in Natural Environments.- 10.1 Speleothems: Growth and Morphology.- 10.2 Stalagmites.- 10.2.1 Morphology of Stalagmites.- 10.2.2 Growth Rates of Stalagmites and Related Diameters.- 10.3 Calcite Precipitation in Surface Streams.- 11 Conclusion and Future Perspective.- References.