Speaker
Description
Characterizing dissolved chemical migration in porous media through the Advection Dispersion Equation requires the knowledge of the fluid velocity field and of dispersivity values associated with diverse geomaterials which can make up the internal architecture of the system. Several studies have focused on the assessment of the impact on solute concentration dynamics of an incomplete knowledge of the fluid velocity field, the latter being typically due to uncertainty of hydraulic properties of the hosting media (e.g., permeability). Limited attention has been devoted to analyze the way uncertainty about spatial distribution of dispersivity values can propagate to uncertainty of solute concentration fields. Here, we address this issue by focusing on a simple one-dimensional domain filled with two distinct porous media and subject to a pulse injection of a tracer. We derive and solve numerically the equation governing the expected value and associated variance of solute concentration by considering uncertain dispersivity values and conceptualizing the domain as a random composite medium (where the location of the interface between the two materials can be uncertain). The solutions of such moment equations compare well against corresponding moments evaluated through a numerical Monte Carlo analysis. Our results suggest that in the investigated set-up (i) solute concentration variance exhibits a three peaks behavior, even in the presence of conditioning on a given location of the interface between the two materials and (iii) the actual sequence of the materials traveled by the solute impacts spatial distributions of expected value and variance of concentrations.
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