A Novel Framework Predicting Steady Flow and Solute Transport in Partially Saturated, Heterogeneous Media.

Project Information

USFT

Grant agreement ID: 101066596

DOI

10.3030/101066596

Project terminated on 28 September 2023

EC signature date 11 May 2022

Start date 1 June 2022

End date 31 May 2024

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 181 152,96

Coordinated by

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Spain

Periodic Reporting for period 1 - USFT (A Novel Framework Predicting Steady Flow and Solute Transport in Partially Saturated, Heterogeneous Media.)

Reporting period: 2022-06-01 to 2024-05-31

Summary of the context and overall objectives of the project

USFT set out to improve our understanding and quantifying abilities of flow, transport, and reaction processes in partially saturated heterogeneous media and their consequences on the relevant Darcy-scale for different multiphase conditions and flow dynamics, which is one of the leading open challenges in porous media research. In this project, we developed a novel framework to predict flow & transport processes at the micro and Darcy scales, in partially saturated media, from the basic pore structure parameters and general flow dynamics. First, we developed a new image analysis method and used it to analyze several experimental results of multiphase flow under different flow conditions in a multifluidic device. This study provided new insights into the interplay between stable and unstable processes in multiphase systems on the most basic pore system features (waterfilled pore size distribution, displacement mechanism, and velocity distribution). Furthermore, we used the image analysis method to extract different levels of phase configuration to construct network models of different complexity to evaluate the permeability, velocity distribution, hydraulic tortuosity, and dead-end (stagnant phase) fraction. As discussed in the following, these parameters are the minimal information needed to predict the complex non-Fickian transport in partially saturated media accurately. Second, we developed a Lagrangian CTRW upscaling framework for partially saturated media. This framework uses the velocities distribution, hydraulic tortuosity, and the fraction of stagnant dead-end phase to predict the breakthrough curve of non-reactive solutes. These accomplishments and their integration allow us to characterize diverse flow regimes in heterogeneous media within a unique, entirely predictive template (i.e. not parameterized by the transport parameters or the spatial pore-scale flow field). This interdisciplinary endeavor incorporates particle dynamic models, stochastic methods, CFD models, and analysis of microfluidic device experiments and numerical direct pore simulations

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Despite intensive research over the last five decades, understanding and predicting flow and hydrodynamic transport under variable fluid saturation and spatial heterogeneity have remained open questions. The last decade has seen enormous progress in imaging and characterising microscale structure and multiphase flow and transport processes. USFT has developed an effective image analysis method to characterise the pore space from binary 2D and 3D porous media images. This method uses the curvatures of the distance map (i.e. the Euclidean distance of each point from the nearest interface) to extract information about the pore space and segment the pores.

Building on this improvement, we were able to analyse thousands of images taken during gas and liquid flow experiments under different conditions in a milifluidic device, which has shown that the phase configuration dramatically affects the medium permeability. This finding suggests that the commonly used injective permeability-saturation curve assumption is incorrect. Moreover, this study demonstrates how the entrapped non-wetting phase enables the trapping of the wetting phase during drainage, forming a hysteretic behaviour in the fraction of the entrapped (non-percolated) phase. Furthermore, this study shows that the phase configuration and flow path changes with the different flow dynamics. However, these changes are related to local resistance forces and do not lead to a global dissipation of energy. These results have evidenced the shortcomings of classical flow and transport approaches for describing large-scale non-equilibrium phenomena.

It remained to be seen how the new knowledge on small-scale structures and processes can be used to derive upscaled models for unsaturated flow and transport that link microscale flow and medium properties to large-scale flow and transport. To this end, we used the image analysis tool to develop network models building on different levels of detailed information about the distribution of pore bodies' and throats' sizes and connectivity of the pores. The models, with different complexity, are suitable with different degrees of applicability to evaluate large scale parameters such as permeability, tortuosity, and flow velocity distribution.

For the upscaling of solute transport, we established a continuous time random walk model for a partially saturated media that accounts for a mobile-immobile mass exchange between stagnant and transmitting pores. This model accurately predicted the breakthrough curves of solute transport through the media compared to the results of detailed numerical flow and transport simulations. The advantage of the continuous time random walk is the much lower computational times required and the ability to evaluate the effect of the flow conditions on large scale (anomalous) transport and its characteristic parameters. For example, we demonstrated how the entrapped air increases the characteristic length of the media, the advective tortuosity, and the fraction of immobile area. Moreover, the Peclet number is strongly correlated to the trapping frequency and to the normalised mean trapping time.

Based on the achievements of USFT, a new framework will be developed that fuses i) insights regarding the effect of the flow dynamics on the phase configuration, ii) the network models relating the phase configuration to the hydraulic parameters and flow velocity distribution and iii) the integrated continuous time random walk that uses the network model outputs to evaluate the transport behaviour and residence time of solutes in partially saturated media.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

USFT advanced our state-of-the-art understanding, processing, and modelling of the flow and transport of solutes in unsaturated media. In particular, USFT extended:

1. The understanding of the effects of the flow dynamics on the multiphase configuration, localization, and hydraulic properties or partially saturated porous media:

a. The macroscale permeability of the media is affected by the phase configuration and not just by its content. This observation indicates a major limitation to the continuum approach modelling based on Buckingham's extension to Darcy's law.

b. However, the phases' configurations are not significantly affected by the injection dynamics for mean Capillary numbers in the range of 10-5 to 10-4. This surprising result suggests that the dynamic effect on the phase configuration is not governed by a global variational principle such as minimizing mechanical energy dissipation.

c. The initial phase configuration affects the quasi (or periodical) steady-state configuration, such that prevailing stagnant air clusters enable closing dead-end regions and the entrapment of water bodies, suggesting a hysteretic behaviour to the phase configuration.

2. The ability to effectively segment and extract detailed information about the pore space from binary images:

a. The distance map curvature can be used to locate critical points and to segment the pore space.

b. New image segmentation workflow.

3. The understanding of the applicability and limitations of network models to evaluate the relevant flow properties based on the model complexity:

a. Simple lattice models such as effective mean approximation rely on basic pore space features such as pore size distribution and mean coordination number. They can be used to evaluate the permeability but not the velocity distribution.

b. Random networks, accounting for the coordination number distribution, can be used to evaluate the hydraulic tortuosity of the media.

c. Estimating the flow velocity distribution (relevant to the dispersion of solute transport) requires evaluating the intra-pores velocity variability.

3. The modelling of solute transport in partially saturated media:

a. CTRW model captures the effect of trapping in stagnant regions and preferential transport on non-Fickian solute dispersion.

b. Entrapped air promotes preferential solute transport and solute trapping in stagnant regions.

c. Trapping frequency and trapping time depend on the interaction between advection and diffusion.

The outcomes of USFT have an essential societal role by addressing the United Nations' goal to provide universal access to clean drinking water and sanitation. In particular, USFT addressed the worldwide issue of aquifer contamination by providing efficient and integrated predictive models for solute spreading and transport through the critical zone, which is crucial for risk analysis, remediation planning, and resource management.