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Register a new userTemporal pattern of entropy production induced by reactive infiltration instability in natural porous media
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Authors
Yi Yang
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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.
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Reactive infiltration instability (RII) drives the development of many natural and engineered flow systems. These are encountered e.g. in hydraulic fracturing, geologic carbon storage and well stimulation in enhanced oil recovery. The surface area of the rocks changes as the pore structure evolves. We combined a reactor network model with grey scale tomography to seek the morphological interpretation for differences among geometric, reactive and apparent surface areas of dissolving natural porous materials. The approach allowed us to delineate the experimentally convoluted variables and study independently the effects of initial geometry and macroscopic flowrate. Simulations based on North Sea chalk microstructure showed that geometric surface not only serves as the interface for water-rock interactions but also represents the regional transport heterogeneities that can be amplified indefinitely by dissolutive percolation. Hence, RII leads to channelization of the solid matrix, which results in fluid focusing and an increase in geometric surface area. Fluid focusing reduces the reactive surface area and the residence time of reactants, both of which amplify the differences in question, i.e. they are self-supporting. Our results also suggested that the growing and merging of microchannels near the fluid entrance leads to the macroscopic fast initial dissolution of chemically homogeneous materials.
The dissolution of porous materials in a flow field shapes the morphologies of many geologic landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive regions in a dissolving medium, is a prerequisite for studying dissolution kinetics. Despite its fundamental importance, the dynamics of a dissolution front in an evolving natural microstructure has never been reported. Here we show an unexpected spontaneous migration of the dissolution front against the pressure gradient of a flow field. This retraction stems from the infiltration instability induced surface generation, which can lead to a reactive surface dramatically greater than the ex situ geometric surface. The results are supported by a very good agreement between observations made with real time X-ray imaging and simulations based on static images of a rock determined by nanoCT. They both show that the in situ specific surface area of natural porous media is dependent on the flow field and reflects a balancing between surface generation and destruction. The reported dynamics challenge many long-held understanding of water-rock interactions and shed light on reconciling the discrepancies between field and laboratory measurements of reaction kinetics.
The reactive-infiltration instability, which develops when a porous matrix is dissolved by a flowing fluid, contains two important length scales. Here we outline a linear stability analysis that simultaneously incorporates both scales. We show that the commonly used thin-front model is a limiting case of a more general theory, which also includes convection-dominated dissolution as another special case. The wavelength of the instability is bounded from below, and lies in the range 1mm to 1km for physically reasonable flow rates and reaction rates. We obtain a closed form for the growth rate when the change in porosity is small.
When reactive fluids flow through a dissolving porous medium, conductive channels form, leading to fluid breakthrough. This phenomenon is important in geologic carbon storage, where the dissolution of CO2 in water increases the acidity and produce microstructures significantly different from those in an intact reservoir. We demonstrate the controlling mechanism for the dissolution patterns in natural porous materials. This was done using numerical simulations based on high resolution digital models of North Sea chalk. We tested three model scenarios, and found that aqueous CO2 dissolve porous media homogeneously, leading to large breakthrough porosity. In contrast, CO2-free solution develops elongated convective channels in porous media, known as wormholes, and resulting in small breakthrough porosity. We further show that a homogeneous dissolution pattern appears because the sample size is smaller than the theoretical size of a developing wormhole. The result indicates that the presence of dissolved CO2 expands the reactive subvolume of a porous medium, and thus enhances the geochemical alteration of reservoir structures and might undermine the sealing integrity of caprocks when minerals dissolve.
We develop a theory for the problem of high pressure air injection into deep reservoirs containing light oil. Under these conditions, the injected fluid (oxygen + inert components) is completely miscible with the oil in the reservoir. Moreover, exothermic reactions between dissolved oxygen and oil are possible. We use Kovals model to account for the miscibility of the components, such that the fractional-flow functions resemble the ones from Buckley-Leverett flow. This allows to decompose the solution of this problem into a series of waves. We then proceed to obtain full analytical solutions in each wave. Of particular interest {is the case where} the combustion wave presents a singularity in its internal wave profile. Evaluation of the variables of the problem at the singular point determines the macroscopic parameters of the wave, i.e., combustion temperature, wave speed and downstream oil fraction. The waves structure was observed previously for reactive immiscible displacement and we describe it here for the first time for reactive miscible displacement of oil. We validate the developed theory using numerical simulations.
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