Karstification corrosion along a karst fracture

Talking about karstification often the question arises why karst phenomena do not only occur at the surface but in greater depths as well. The reason is that the carbonate dissolution is a comparatively fast process, but still takes some time, while water may cover quite a long distance along a fracture. 

This shall be modeled with the following example. A fracture with an extension of 300 meters is given. Assume that, at the beginning of the simulation, this fracture is filled with groundwater that is in carbonate equilibrium. To simplify matters the following data shall be used pH 7.32 

Infiltrating rainwater now dissolves C02 according to the increased partial pressure of 1 Vol% in the unsaturated zone. Thus, the seepage water has the following characteristics pH 4.76 

This water enters the model fracture with a velocity of 10 m per 6 minutes. Calculate the carbonate dissolution in the 300 meter long fracture, that will be 

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