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The tendency of irreversible processes to generate entropy is the ultimatedriving force for the evolution of nature. In engineering, entropy productionis often used as a measure of usable energy losses. In this study we show thatthe analysis of the entropy production patterns can help understand the vastlydiversified experimental observations of water-rock interactions in naturalporous media. We first present a numerical scheme for the analysis of entropyproduction in dissolving porous media. Our scheme uses a greyscale digitalmodel of natural chalk obtained by X-ray nanotomography. Greyscale modelspreserve structural heterogeneities with very high fidelity, which is essentialfor simulating a system dominated by infiltration instability. We focus on thecoupling between two types of entropy production: the percolative entropygenerated by dissipating the kinetic energy of fluid flow and the reactiveentropy that originates from the consumption of chemical free energy. Theirtemporal patterns pinpoint three stages of microstructural evolution. We thenshow that the regional mixing deteriorates infiltration instability by reducinglocal variations in reactant distribution. In addition, we show that themicrostructural evolution can be particularly sensitive to the initiallypresent transport heterogeneities when the global flowrate is small. Thisdependence on flowrate indicates that the need to resolve the structuralfeatures of a porous system is greater when the residence time of the fluid islong.

Temporal pattern of entropy production induced by reactive infiltration instability in natural porous media