What is the name for the measure of the interconnectedness of spaces in a material and how it controls how readily a rock or sediment will transmit fluids?

Permeability

permeability of any  medium or substance is directly proportional to its  fluid transmission ability  

Explanation:

Permeability measures the ability of any medium or substance to allow transmission of any substance through it  

The higher is the amount of free space with in any substance and medium, the higher is its ability to transmit other substances through it and hence higher is the permeability.  

Thus, permeability of any  medium or substance is directly proportional to its  fluid transmission ability  

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