Bernd Flemisch

Release 3.9.0 of DuMux, DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media. DuMux is a free and open-source simulator for flow and transport processes in and around porous media. It is based on the Distributed and Unified Numerics Environment DUNE.

Vertical equilibrium (VE) models have been introduced as computationally efficient alternatives to traditional mass and momentum balance equations for fluid flow in porous media. Since VE models are only accurate in regions where phase equilibrium holds and traditional simulations are computationally demanding, hybrid methods have been proposed to combine the accuracy of the full-dimensional approach with the efficiency of VE model. However, coupling both models introduces computational overhead that can make hybrid simulations slower than fully traditional ones. To address the computational overhead introduced by coupling interfaces in hybrid models, we utilize data-driven surrogates to accelerate the overall scheme. To this end, we predict the gas plume distance and coarse-level mobilities in the VE model, and also enhance the computation of the coupling scheme via surrogates. We focus on surrogate models with short inference times to minimize computational overhead during frequent function calls. The proposed approach preserves key physical properties, such as mass conservation, despite the deployment of data-driven models, while substantially reducing simulation runtimes. Overall, combining data-driven methods with the hybrid VE scheme yields an enhanced model that outperforms traditional simulations in speed while introducing only negligible errors.

The usability of enzymatically induced calcium carbonate precipitation (EICP) as a method for altering porous media properties, soil stabilization, or biocementation depends on our ability to predict the spatial distribution of the precipitated calcium carbonate in porous media. While current REV-scale models can reproduce the main features of laboratory experiments, they neglect effects like the formation of preferential flow paths and the appearance of multiple polymorphs of calcium carbonate with differing properties. We show that extending an existing EICP model by the conceptual assumption of a mobile precipitate, amorphous calcium carbonate (ACC), allows for the formation of preferential flow paths when the initial porosity is heterogeneous. We apply sensitivity analysis to understand the influence of characteristic parameters of ACC that are uncertain or unknown, and compare two model variations based on different formulations of the ACC detachment term to analyze the plausibility of our hypothesis. An arbitrary polynomial chaos (aPC) surrogate model is trained based on the full model and used to reduce the computational cost of this study.

In general, modelling bedload transport requires a full coupling between shallow water equations and sediment balance equations. Nevertheless, splitting approaches can be applied, depending on the time step size and the degree of interaction between flow and mobile bed. This work employs an implicit time discretisation to implement both a fully coupled and a splitting approach. The currently available approaches utilise an appropriate calculation of the numerical flux at the cell faces, e.g. Roe’s scheme, in order to ensure a full coupling. However, this work demonstrates that a fully coupled approach can also be achieved through an implicit time discretisation, as it combines the shallow water and the sediment balance equations into a system of non-linear equations, thereby ensuring full coupling between shallow water flow and bedload transport. The full coupling via implicit time discretisation has the advantage of being applicable to arbitrary bedload transport problems. In contrast, the existing fully coupled approaches are only applicable to uniform bedload transport and are not suitable for mixed size bedload transport with several grain classes or in situations where modifications to the bedload discharge rate are required, such as secondary currents or gravitational transport. Unlike the fully coupled approach, the splitting approach solves the shallow water equations and the sediment balance equations sequentially, resulting in two non-linear systems per time step. This work compares the two presented coupling approaches in terms of computational cost and with regard to the applicability of the splitting approach. The comparison indicates that, where applicable, the splitting approach often offers a superior performance compared to the presented fully coupled approach, particularly in cases involving several grain classes.

Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the dynamics of a system. While conventional full-dimensional models have the ability to represent dynamics, they come at the cost of high computational effort. We aim to combine the efficiency of the vertical equilibrium model and the accuracy of the full-dimensional model by coupling the two models adaptively in a unified framework and solving the emerging system of equations in a monolithic, fully-implicit approach. The model domains are coupled via mass-conserving fluxes while the model adaptivity is ruled by adaptive criteria. Overall, the adaptive model shows an excellent behaviour both in terms of accuracy as well as efficiency, especially for elongated geometries of storage systems with large aspect ratios.

The usability of enzymatically induced calcium carbonate precipitation (EICP) as a method for altering porous-media properties, soil stabilization, or biocementation depends on our ability to predict the spatial distribution of the precipitated calcium carbonate in porous media. While current REV-scale models are able to reproduce the main features of laboratory experiments, they neglect effects like the formation of preferential flow paths and the appearance of multiple polymorphs of calcium carbonate with differing properties. We show that extending an existing EICP model by the conceptual assumption of a mobile precipitate, amorphous calcium carbonate (ACC), allows for the formation of preferential flow paths when the initial porosity is heterogeneous. We apply sensitivity analysis and Bayesian inference to gain an understanding of the influence of characteristic parameters of ACC that are uncertain or unknown and compare two variations of the model based on different formulations of the ACC detachment term to analyse the plausibility of our hypothesis. An arbitrary Polynomial Chaos (aPC) surrogate model is trained based on the full model and used to reduce the computational cost of this study.

In the context of CO2 injection wells, several factors have the potential to compromise well injectivity, which under the most unfavorable circumstances can result in well loss. These factors include formation, drying and salt precipitation. The degree of scaling is primarily determined by capillary transport phenomena due to evaporation kinetics, effects that are largely ignored in reservoir simulators. In the present work, we have developed and implemented drying and evaporation kinetics in a reactive continuum transport model based on DuMuX. The model considers all aspects of the processes, including capillary-driven countercurrent transport of dissolved solids and their subsequent precipitation. This comprehensive approach allows the model to provide a realistic description *of the processes occurring in the borehole environment. In cases where experimental data sets were incomplete, a qualitative comparison was made between the model and the available experimental data sets. Stochastic sensitivity analysis was used to identify the key parameters that define the zone of countercurrent flow and the potential for formation damage. The work thus provides a model capable of realistically simulating formation drying, including drying and precipitation kinetics. In the case of supercritical CO2 injection and for an assumed homogeneous sandstone formation, the mutual mass transfer coefficient, the salinity, and the injection rate were found to be the most influential parameters in determining the ultimate salt precipitation along the core sample and the respective size of the drying zone. In contrast to the results of the equilibrium model, the results of our model indicate a more uniform distribution of salt precipitates throughout the core.