Fractional packing model for hydraulic conductivity derived from sediment mixtures

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Abstract
Petrophysical relations are derived to predict porosity and hydraulic conductivity from grain size distributions considering particle packing in sediment mixtures. First, we develop a fractional packing model for porosity that considers the fraction of intrapore fines that occur as the fines content increases. Then, a fractional packing Kozeny‐Carman relation for hydraulic conductivity is developed by examining which particle sizes dominate the pore structure, and which averaging procedure best represents the mean grain diameter in any given sediment mixture. The relations developed here perform well for a wide range of sediment mixtures regardless of confining pressure. Graphs are presented that show hydraulic conductivity versus weight fraction of fines for mixtures of coarse‐ and fine‐grained sediment commonly observed in the field, such as clayey gravel and silty sand. These graphs show that the wide range of hydraulic conductivity values reported for sediment mixtures can display a 5 order of magnitude variation over a few percent fines. Finally, a field scale application using grain size distributions from a quantitative depositional model shows that these petrophysical relations successfully predict more than 90% of hydraulic conductivity values to within 1 order of magnitude over 7 orders of magnitude of spatial variability.