Flow and transport modelling in highly heterogeneous geological porous media

Flow and transport processes through porous media are ubiquitous both in natural and industrial environments. Ranging from diffusion in human tissue to oil recovery and CO2 storage, including the design of porous reactors, geothermal energy production, groundwater remediation, oil recovery and CO2 storage, the characterisation of fluid flow and solute transport at different scales represents the paradigm to better understand the mechanisms at the base of several processes. Due to the broad spectrum of applications, a vast empirical and numerical research field developed around transport in heterogeneous porous media. While on the numerical side, the mathematical models available for simulating transport at the micro and meso scales have shown good agreement with the empirical tests, the debate around modelling transport at the macro-scale is still open. One example is the unknown relation between system parameters and their values measured at different scales which is usually addressed as scale effect. Other examples are anomalous or non-Fickian transport phenomena and the validity range of macro-scale transport models. Our study focuses on the impact of the heterogeneous distribution of the subsurface properties on the transport of solute at the macro-scale. Initially we propose an analysis of transport in heterogeneous porous media generated with a random geostatistical algorithm. Subsequently this subject is expanded and applied to a real domain which was surveyed and reconstructed with a high level of resolution. Three-dimensional meso-scale numerical simulations performed with our open-source C++ library, built on top of the finite-volume library OpenFOAM, represent the main source of data to test macro-scale mathematical models

Book of Abstracts

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Flow and transport modelling in highly heterogeneous geological porous media

Flow and transport processes through porous media are ubiquitous both in natural and industrial environments. Ranging from diffusion in human tissue to oil recovery and CO2 storage, including the design of porous reactors, geothermal energy production, groundwater remediation, oil recovery and CO2 storage, the characterisation of fluid flow and solute transport at different scales represents the paradigm to better understand the mechanisms at the base of several processes. Due to the broad spectrum of applications, a vast empirical and numerical research field developed around transport in heterogeneous porous media. While on the numerical side, the mathematical models available for simulating transport at the micro and meso scales have shown good agreement with the empirical tests, the debate around modelling transport at the macro-scale is still open. One example is the unknown relation between system parameters and their values measured at different scales which is usually addressed as scale effect. Other examples are anomalous or non-Fickian transport phenomena and the validity range of macro-scale transport models. Our study focuses on the impact of the heterogeneous distribution of the subsurface properties on the transport of solute at the macro-scale. Initially we propose an analysis of transport in heterogeneous porous media generated with a random geostatistical algorithm. Subsequently this subject is expanded and applied to a real domain which was surveyed and reconstructed with a high level of resolution. Three-dimensional meso-scale numerical simulations performed with our open-source C++ library, built on top of the finite-volume library OpenFOAM, represent the main source of data to test macro-scale mathematical models

Filtered density functions for uncertainty assessments of transport in Groundwater

It is estimated that fifty percent of the drinking water is extracted from groundwater sources. But the groundwater quality is threatened by contaminants. Risk assessments are applied to geohydrological systems in order to estimate if they pose a risk through groundwater pollution. These risks not only depend on the impact of the contaminants, but also on the their propagation in the groundwater. Properties of the subsurface have a strong impact on the groundwater flow and therefore also on the transport of solutes. The scarcity of data together with the heterogeneity of the subsurface can cause the uncertainty of the transport predictions to be so large that they cannot be neglected. Consequently, the uncertainty needs to be included in the risk assessments. This is possible by using a geostatistical representation of the subsurface, which results in a probabilistic description of the transport processes. Probability density function (PDF) methods provide an integrated framework to predict the transport of solutes in which uncertainties are incorporated seamlessly. But PDF methods require the assumption of a statistically homogeneous conductivity field. This is problematic. Using spatially averaged quantities instead of stochastic averages, an alternative to PDF methods is found: the filtered density function (FDF) methods. The aim of the research presented here is to develop such an FDF method for predicting the transport in groundwater. Therefore, three steps are necessary. An efficient and accurate numerical solver for FDF equations needs to be developed. In a second step, the parameters contained by the equations have to be filtered. And finally, an appropriate mixing model needs to be found for approximating the unclosed mixing term. The mixing term is of particular interest because it has a direct impact on the uncertainty evolution. In summary, this work contributes towards the development of an FDF framework applied to the transport in groundwater

The Distribution of Atmospheric Pollutants in Europe: Optimal Use of Models and Observations with a Data Assimilation Approach

The research activity presented in this manuscript deals with the implementation of a methodology to merge in an optimal way atmospheric modelling and observations at different spatial scales. In particular, we approached the problem of assimilation of ground measurements and satellite columnar data and how the Data Assimilation (DA) could improve the chemical transport model (CTMs) and correct biases and errors in the chemical species forecast. The work focused on tropospheric ozone and the species linked to its formation, since they play a crucial role in chemical processes during photochemical pollution events. The study was carried out implementing and applying an Optimal Interpolation (OI) DA technique in the air quality model BOLCHEM and the CHIMERE CTM. The OI routine was chosen because it has given satisfactory results in air quality modelling and because it is relatively simple and computationally inexpensive. In the first part of the study we evaluated the improvement in the capability of regional model BOLCHEM to reproduce the distribution of tropospheric pollutants, using the assimilation of surface chemical observations. Among the many causes of uncertainties of CTMs simulations, a particular focus is given by uncertainties in emissions, that are known to be high. The scientific purpose was to analyse the efficacy of DA in correcting the biases due to perturbed emission. The work was performed using an Observing System Simulation Experiment (OSSE), which allowed the quantification of assimilation impact, through comparison with a reference state. Different sensitivity tests were carried out in order to identify how assimilation can correct perturbations on O3, induced by NOx emissions biased in flux intensity and time. Tests were performed assimilating different species, varying assimilation time window length and starting hour of assimilation. Emissions were biased quantitatively up to ± 50% and shifted temporally up to ± 2 hours. The analysis brought to the conclusions that NO2 assimilation significantly improves O3 maxima during the assimilation, making it almost independent on different emission scenarios. The assimilation impact lasts up to 36-40 hours after the end of the assimilation window. This is a considerable result, especially when it is taken into account that DA generally yields significantly better forecasts in the 6-12 hours range, but improvements vanish afterwards. The NO2 night-time chemistry has the role of maintaining the correction of O3 due to assimilation also in the following day. Assimilating NO2 and O3 simultaneously bring to rather better results, although the benefit lasts only a few hours after the end of the assimilation window. It was found that the best results are achieved assimilating observations during the photochemically active period (06-18 UTC). It was also found that temporally biased NOx emissions only slightly perturb O3 concentration during the photochemically active regime, while the perturbation is larger during night-time. Assimilation has a very low impact during the assimilation window and a negligible impact after its end. The second part of PhD research activity dealt with the evaluation of the impact of assimilation of satellite NO2 tropospheric columns on the distribution of pollutants at the ground level during photochemical pollution events at continental scale. In particular, we focused on the assimilation of observations from SCIAMACHY and from OMI, and its effect on ozone in the lowermost troposphere in Europe. For an effective improvement in assimilated fields it is particularly important the consistency between satellite and model resolution. SCIAMACHY and OMI have a considerable difference in spatial and temporal resolution, allowing to test the role of data resolution on the effectiveness of assimilation. The role of data resolution on the effectiveness of assimilation was investigated also changing the model resolutions. It was found the perturbation on NO2 field due to assimilation causes a modification on ozone field that appears more spatially variable and higher in some photochemical polluted areas. Similar effects are detected both for SCIAMACHY and OMI assimilation. Significative effects of assimilation on ozone can be appreciate in polluted areas at local scale. Focusing on specific subdomains, it was found that the effect of assimilation lasts, in general, 8 hours and in few cases until the reactivation of active photochemical period in the following day. This is a strong impact, considering that assimilation is performed at most once a day and it is probably linked to the model underestimate of ozone and its precursors in polluted areas with respect to those measured by SCIAMACHY and OMI. In wide and highly polluted areas assimilation achieves satisfactory results, comparing simulated ground ozone with independent ground measurements. In that region where OMI assimilation in the coarse and fine resolution simulations and SCIAMACHY assimilation were confronted, we could conclude that these different assimilation set-up are almost similar. Whereas, in more localised polluted areas (i.e. comparable to model and satellite resolution), OMI assimilation in the finer resolution simulation performs better with respect to OMI assimilation in the coarse resolution simulation and SCIAMACHY assimilation. As a general conclusive statement, assimilation can be an important tool to make the spatial and temporal distribution of pollutants more realistic and closer to the specific local differences with the caveat of horizontal resolution of the assimilated columns and model simulations

Coarse graining equations for flow in porous media: a HaarWavelets and renormalization approach

Coarse graining of equations for flow in porous media is an important aspect in modelling permeable subsurface geological systems. In the study of hydrocarbon reservoirs as well as in hydrology, there is a need for reducing the size of the numerical models to make them computationally efficient, while preserving all the relevant information which is given at different scales. In the first part, a new renormalization method for upscaling permeability in Darcy’s equation based on Haar wavelets is presented, which differs from other wavelet based methods. The pressure field is expressed as a set of averages and differences, using a one level Haar wavelet transform matrix. Applying this transform to the finite difference discretized form of Darcy’s law, one can deduce which permeability values on the coarse scale would give rise to the average pressure field. Numerical simulations were performed to test this technique on homogeneous and heterogeneous systems. A generalization of the above method was developed designing a hierarchical transform matrix inspired by a full Haar wavelet transform, which allows us to describe pressure as an average and a set of progressively smaller scale differences. Using this transform the pressure solution can be performed at the required level of detail, allowing for different resolutions to be kept in different parts of the system. A natural extension of the methods is the application to two-phase flow. Upscaling mobility allows the saturation profile to be calculated on the fine or coarse scale while based on coarse pressure values. To conclude, an alternative approach to upscaling in multi-phase flow is to upscale the saturation equation itself. Taking its Laplace transform, this equation can be reduced to a simple eigenvalue problem. The wavelet upscaling method can now be applied to calculate the upscaled saturation profile, starting with fine scale velocity data