Patterns of entropy production in dissolving natural porous media with flowing fluid.

Y Yang,H O Sørensen,S L S Stipp,S Bruns

doi:10.1371/journal.pone.0204165

Abstract

The tendency for irreversible processes to generate entropy is the ultimate driving force for structure evolution in nature. In engineering, entropy production is often used as an indicator for loss of usable energy. In this study, we show that the analysis of entropy production patterns can provide insight into the diverse observations from experiments that investigate porous medium dissolution in imposed flow field. We first present a numerical scheme for the analysis of entropy production in dissolving porous media. Our scheme uses a greyscale digital model for chalk (an extremely fine grained rock), that was obtained using X-ray nanotomography. Greyscale models preserve structural heterogeneities with very high fidelity. We focussed 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, originating from the consumption of chemical free energy. Their temporal patterns pinpoint three stages of microstructural evolution. We then showed that local mixing deteriorates fluid channelisation by reducing local variations of reactant concentration. We also showed that microstructural evolution can be sensitive to the initial transport heterogeneities, when the macroscopic flowrate is low. This dependence on flowrate indicates the need to resolve the structural features of a porous system when fluid residence time is long.

Highlights

The production of entropy in irreversible processes drives the emergence and transformation of many structures in nature [1, 2]
We present an analysis of the patterns of entropy production in a dissolving natural porous medium, using a fixed initial microstructure
We studied 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

Summary

Introduction

The production of entropy in irreversible processes drives the emergence and transformation of many structures in nature [1, 2]. Spatial and temporal patterns of entropy production can help us understand the diversity and the self-organisation inherent to many complex systems [3, 4]. Reactive infiltration instability stems from positive feedback between the coupling of chemical reaction and mass transfer and induces the development of a wide variety of biotic and abiotic flow systems [6,7,8,9,10]. Predicting the development of flow systems in porous media is essential for many energy and environmental applications, such as geologic carbon storage [11], oil reservoir simulation [12], bioremediation [13] and in situ contaminant remediation [14]. Characterising the inherent heterogeneities of a porous material is important because infiltration instability can amplify transport heterogeneities indefinitely [15, 16]. It is desirable to use nondestructive, three dimensional imaging techniques, such as high

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