  The tendency of irreversible processes to generate entropy is the ultimate
driving force for the evolution of nature. In engineering, entropy production
is often used as a measure of usable energy losses. In this study we show that
the analysis of the entropy production patterns can help understand the vastly
diversified experimental observations of water-rock interactions in natural
porous media. We first present a numerical scheme for the analysis of entropy
production in dissolving porous media. Our scheme uses a greyscale digital
model of natural chalk obtained by X-ray nanotomography. Greyscale models
preserve structural heterogeneities with very high fidelity, which is essential
for simulating a system dominated by infiltration instability. We focus on the
coupling between two types of entropy production: the percolative entropy
generated by dissipating the kinetic energy of fluid flow and the reactive
entropy that originates from the consumption of chemical free energy. Their
temporal patterns pinpoint three stages of microstructural evolution. We then
show that the regional mixing deteriorates infiltration instability by reducing
local variations in reactant distribution. In addition, we show that the
microstructural evolution can be particularly sensitive to the initially
present transport heterogeneities when the global flowrate is small. This
dependence on flowrate indicates that the need to resolve the structural
features of a porous system is greater when the residence time of the fluid is
long.
