Pore-scale velocities in three-dimensional porous materials with trapped immiscible fluid

Chaotic Transport of Solutes in Unsaturated Porous Media

Unsaturated porous media, characterized by the combined presence of several immiscible fluid phases in the pore space, are highly relevant systems in nature, because they control the fate of contaminants and the availability of nutrients in the subsoil. However, a full understanding of the mechanisms controlling solute mixing in such systems is still missing. In particular, the role of saturation in the development of chaotic solute mixing has remained unexplored. Using three-dimensional numerical simulations of flow and transport at the pore scale, built upon X-ray tomograms of a porous medium at different degrees of liquid (wetting)-phase saturation, we show the occurrence of chaotic dynamics in both the deformation of the solute plume, as characterized by computed chaos metrics (Lyapunov exponents), and the mixing of the injected solute. Our results show an enhancement of these chaotic dynamics at lower saturation and their occurrence even under diffusion-relevant conditions over the medium's length, also being strengthened by larger flow velocities. These findings highlight the dominant role of the pore-scale spatial heterogeneity of the system, enhanced by the presence of an immiscible phase (e.g., air), on the mixing efficiency. This represents a stepping stone for the assessment of mixing and reactions in unsaturated porous media.

Upscaling Mixing-Controlled Reactions in Unsaturated Porous Media

We study mixing-controlled chemical reactions in unsaturated porous media from a pore-scale perspective. The spatial heterogeneity induced by the presence of two immiscible phases, here water and air, in the pore space generates complex flow patterns that dominate reactive mixing across scales. To assess the impact of different macroscopic saturation states (the fraction of pore volume occupied by water) on mixing-controlled chemical reactions, we consider a fast irreversible reaction between two initially segregated dissolved species that mix as one solution displaces the other in the heterogeneous flow field of the water phase. We use the pore-scale geometry and water distributions from the laboratory experiments reported by Jiménez-Martínez et al. (Geophys. Res. Lett. 42: 5316-5324, 2015). We analyze reactive mixing in three complementary ways. Firstly, we post-process experimentally observed spatially distributed concentration data; secondly, we perform numerical simulations of flow and reactive transport in the heterogeneous water phase, and thirdly, we use an upscaled mixing model. The first approach relies on an exact algebraic map between conservative and reactive species for an instantaneous irreversible bimolecular reaction that allows to estimate reactive mixing based on experimental conservative transport data. The second approach is based on reactive random walk particle tracking simulations in the numerically determined flow field in the water phase. The third approach uses a dispersive lamella approach that accounts for the impact of flow heterogeneity on mixing in terms of effective dispersion coefficients, which are estimated from both experimental data and numerical random walk particle tracking simulations. We observe a significant increase in reactive mixing for decreasing saturation, which is caused by the stronger heterogeneity of the water phase and thus of the flow field. This is consistently observed in the experimental data and the direct numerical simulations. The dispersive lamella model, parameterized by the effective interface width, provides robust estimates of the evolution of the product mass obtained from the experimental and numerical data.

Sensitivity-based Parameter Calibration of Single- and Dual-continuum Coreflooding Simulation Models

Our study is keyed to the development of a viable framework for the stochastic characterization of coreflooding simulation models under two- and three-phase flow conditions taking place within a core sample in the presence of preferential flow of the kind that can be associated with the presence of a system of fractures. We do so considering various modeling strategies based on (spatially homogeneous or heterogeneous) single- and dual-continuum formulations of black-oil computational models and relying on a global sensitivity-driven stochastic parameter calibration. The latter is constrained through a set of data collected under a water alternating gas scenario implemented in laboratory-scale coreflooding experiments. We set up a collection of Monte Carlo (MC) numerical simulations while considering uncertainty encompassing (a) rock attributes (i.e., porosity and absolute permeability), as well as (b) fluid–fluid/ fluid–solid interactions, as reflected through characteristic parameters of relative permeability and capillary pressure formulations. Modern moment-based global sensitivity indices are evaluated on the basis of the MC model responses, with the aim of (i) quantifying sensitivity of the coreflooding simulation results to variations of the input uncertain model parameters and (ii) assessing the possibility of reducing the dimensionality of model parameter spaces. We then rest on a stochastic inverse modeling approach grounded on the acceptance–rejection sampling (ARS) algorithm to obtain probability distributions of the key model parameters (as identified through our global sensitivity analyses) conditional to the available experimental observations. The relative skill of the various candidate models to represent the system behavior is quantified upon relying on the deviance information criterion. Our findings reveal that amongst all tested models, a dual-continuum formulation provides the best performance considering the experimental observations available. Only a few of the parameters embedded in the dual-continuum formulation are identified as major elements significantly affecting the prediction (and associated uncertainty) of model outputs, petrophysical attributes and relative permeability model parameters having a stronger effect than parameters related to capillary pressure.

Distribution of liquid flow in a pore network during evaporation

The variation of the distribution of the liquid flow in porous media during evaporation is still a puzzle. We resolve it with the pore network modeling approach. The distribution of the evaporation-induced liquid flow in a pore network composed of about 2.5 million pores is determined. The probability density function of the magnitude of the normalized liquid flow rate is obtained. For the low normalized liquid flow rate, the probability density function is power-lawlike. The power-law exponent depends on both the liquid saturation and the location of the moving meniscus in the main liquid cluster. The evaporation-induced liquid flow in the pores in the pore network can be correlated. Whether the liquid flow distributions in various zones in the pore network are similar or not relies significantly on the location of the moving meniscus in the main liquid cluster. The functions depicting the relation between the power-law exponent and the local liquid saturation for the zones adjacent to and away from the open side of the pore network are different. These findings from the pore scale studies provide insights into developing the accurate continuum model for evaporation in porous media.

Phase Saturation Control on Mixing-Driven Reactions in 3D Porous Media

Transported chemical reactions in unsaturated porous media are relevant to environmental and industrial applications. Continuum scale models are based on equivalent parameters derived from analogy with saturated conditions and cannot appropriately account for incomplete mixing. It is also unclear how the third dimension controls mixing and reactions. We obtain three-dimensional (3D) images by magnetic resonance imaging using an immiscible nonwetting liquid as a second phase and a fast irreversible bimolecular reaction. We study the impact of phase saturation on the dynamics of mixing and the reaction front. We quantify the temporally resolved effective reaction rate and describe it using the lamellar theory of mixing, which explains faster than Fickian (t^0.5) rate of product formation by accounting for the deformation of the mixing interface between the two reacting fluids. For a given Péclet, although stretching and folding of the reactive front enhance as saturation decreases, enhancing the product formation, the product formation is larger as saturation increases. After breakthrough, the extinction of the reaction takes longer as saturation decreases because of the larger nonmixed volume behind the front. These results are the basis for a general model to better predict reactive transport in unsaturated porous media not achievable by the current continuum paradigm.