Quantification of mixing and dynamic uncertainty for transport in heterogeneous porous media

Project Information

MixUQ

Grant agreement ID: 895152

DOI

10.3030/895152

Project closed

EC signature date 20 April 2020

Start date 1 December 2020

End date 28 February 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 160 932,48

EU contribution

€ 160 932,48

Coordinated by

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Spain

Periodic Reporting for period 1 - MixUQ (Quantification of mixing and dynamic uncertainty for transport in heterogeneous porous media)

Reporting period: 2020-12-01 to 2022-11-30

Summary of the context and overall objectives of the project

Heterogeneity in geological media spans several spatial scales, ranging from the complex arrangement of different geo-materials at the kilometer scale to the intricacy of the pore architectures below the millimeter scale. At the aquifer scale, heterogeneity in the hydraulic conductivity is the dominant factor. The latter underpins the complex spatial organization of the flow field whose spatial fluctuations drive the transport of dissolved chemicals in the subsurface.
In this context, spreading is a measure of the extension of a contaminant plume, while mixing refers to the degree of contaminant dilution. In heterogeneous formations, the prediction of plume spread is not sufficient to characterize mixing, because sub-plume-scale fluctuations in the concentration field are not negligible, i.e. mixing is incomplete (see figure). Furthermore, the hidden nature of the subsurface leads to uncertainty about the exact heterogeneous arrangement of the hydraulic conductivity of the aquifer. The latter must be projected onto the fate of solute to address central societal issues associated with the management of groundwater resources and risk assessment analysis.
The MixUQ project proposed a new way to reconcile the spreading and mixing dynamics of a solute plume transported within a heterogeneous aquifer (under incomplete mixing), while allowing the uncertainty quantification of its mixing state.

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

Predicting the fate of solute transported in Darcy’s scale heterogeneous media requires a detailed understanding of the transport mechanisms. Furthermore, predictions must be complemented by the quantification of the associated uncertainty.
Plume spreading has been the subject of intense investigations over the last decades. In this context, spatial-Markov models, which leverage on the spatial correlation of the velocity along streamlines in a divergence-free flow field (i.e. steady flow), have been successful in predicting the spreading of solute along the main flow direction. However, the transverse transport dynamics, in two-dimensional steady heterogeneous flow, exhibit a long-range anti-correlated nature which mines the adoption of a spatial-Markov model. We have developed a novel stochastic transport model to overcome the latter limitation. The proposed model incorporates the topological constrain of the flow field (i.e. long-range anti-correlation) that underpins the reduced transverse spreading (ultra-slow regime) of solute. The novel model, in conjunction with a spatial-Markov formulation of the longitudinal transport, allows to jointly predict the spreading behavior of solute along the main and transverse directions in mildly to highly heterogeneous formations. The framework has the potential to be extended to three-dimensional settings.
The heterogeneity-induced fluctuations in Darcy’s scale flow field promote the spreading of a plume (i.e. overall extension) in conjunction with its internal segregation into distinct sub-parcels: the mixing of the plume is incomplete (over the plume spreading scale). In many practical cases, the incomplete mixing of a plume lasts over several temporal scales during which plume spreading and mixing strongly differ. We proposed a novel framework to upscale solute mixing for a solute plume transported through a heterogeneous Darcy’s flow field. The mixing model recognizes the variability of the spreading process over the plume: different sub-plume parcels spread at different rates, especially during the advection-enhanced mixing regime. This aspect is key to properly quantifying the overall degree of mixing of a plume. Furthermore, the upscaled mixing model allows to predict the expected value and the standard deviation of the plume mixing state in case of uncertainty about the distribution of the hydraulic conductivity of the hosting aquifer. We tested the predictive capabilities of the mixing model, against results grounded on detailed numerical simulations, in case of mildly to highly heterogeneous formations finding a satisfactory match.
MixUQ has led to three main publications in scientific journals and three open-source software repositories for novel upscaled descriptions of solute spreading and mixing, as well as, for the uncertainty quantification of solute transport, and five presentations at international conferences.

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)

MixUQ advanced our state-of-the-art understanding, modeling and uncertainty quantification of the spreading and mixing dynamics of solute transported in Darcy’s scale heterogeneous geological formations. In particular, MixUQ extended:
1. The theoretical modeling of anomalous transport in two-dimensional heterogeneous geological formations by explicitly providing a novel stochastic model for the longitudinal and transverse spreading dynamics.
2. The understanding of the relationship between the spreading and mixing dynamics of a solute plume for mild to high degree of heterogeneity, by providing an upscaled mixing model that leverages on the variability of the spreading process at the sub-plume scale.
3. The uncertainty quantification of the fate of solute transported in heterogeneous formations, by providing an efficient modeling framework for assessing the uncertainty that plagues solute spreading and mixing.
The theoretical and modeling advances have led to a framework for predicting solute spreading and mixing in heterogeneous geological formations and the associated uncertainty. This integrated framework could potentially be a leading approach in the field of solute transport in heterogeneous porous media. Additionally, the concepts developed in MixUQ can be transferred to different hydrological settings, such as solute transport in riverine corridors, impacting our understanding of the role of the groundwater compartment on the solute transport in rivers.
The outcomes of MixUQ have an important societal role, by addressing the United Nations goal to provide universal access to clean drinking water and sanitation. In particular, MixUQ addressed the worldwide issue of aquifer contamination by providing efficient and integrated predictive models for the solute spreading and mixing processes and the assessment of their uncertainty which is crucial for risk analysis and resources management.

Spreading and Mixing