Holger Class

Zusammenfassung

Abstract Convective dissolution of CO2 \$CO\_2\$ is a well-known mechanism in geological storage of CO2 \$CO\_2\$. It is triggered by gravitational instability which leads to the onset of free convection. The phenomenon is well studied in porous media, such as saline aquifers, and the literature provides substantial evidence that onset times and effective flux rates can be estimated based on a characterization of instabilities that uses the Darcy velocity. This work extends the study of convective dissolution to open water-filled fractures, where non-Darcy regimes govern the induced flow processes. Numerical simulations using a Navier-Stokes model with fluid density dependent on dissolved CO2 \$CO\_2\$ concentration were used to compute scenario-specific results for effective CO2 \$CO\_2\$ entry rates into an idealized fracture with varying aperture, temperature, and CO2 \$CO\_2\$ concentration at the gas-water interface. The results were analyzed in terms of dimensionless quantities. They revealed a Rayleigh invariance of the effective CO2 \$CO\_2\$ flux after the complete formation of a quasi-stationary velocity profile, that is, after a certain entry length. Hence, this invariance can be exploited to estimate the effective CO2 \$CO\_2\$ entry rates, which can then be used, in perspective, in upscaled models. We have studied convective CO2 \$CO\_2\$ dissolution for two different fracture settings; the first one relates to karstification scenarios, where CO2 \$CO\_2\$ is the dominant driving force, and were stagnant-water conditions in fractures have not yet received attention to date. The second setting is inspired from geological CO2 \$CO\_2\$ storage, where the literature provides only studies on convective CO2 \$CO\_2\$ dissolution for porous-media flow with Darcy regimes.

Zusammenfassung

Alterations in the pore morphology of porous materials cause changes to the characteristic hydraulic properties, which are mostly non-linear and inherently difficult to predetermine. Assuming the alterations are known with sufficient accuracy, the relation between the altered pore structure, measured in terms of porosity, and intrinsic permeability may be determined by simulations with enormous computational effort. We focus on microfluidic experiments during the course of which the pore space becomes increasingly occupied with solid precipitate over elapsed process time. To analyze these domains, we present a novel geometry-informed drag formulation which allows for solving pseudo-3D Stokes equations for image-based input data of clogging porous media with accuracy and efficiency. In a pre-processing step, local pore space properties are analyzed and employed to spatially vary the magnitude of the drag term, which reflects the influence of neglected 3D effects. Calibration and validation is achieved through fully 3D Finite Difference Stokes simulations of different benchmark cases. With the proposed formulation we achieve the high accuracy of the pseudo-3D methods as far as permeability is concerned (<30% deviation), but also with respect to local velocities, for a microfluidic domain throughout the clogging process. Noteworthy, the computational cost is being reduced to less than 1%. Combining the efficiency of a Stokes 2D simulation and accuracy of a 3D model the presented approach is rendered an interesting option to investigate remaining open questions, for example on anisotropy of effective hydraulic parameters during the clogging process.

Zusammenfassung

Abstract By employing kinetic interface sensitive (KIS) tracers, we investigate three different types of glass-bead materials and three natural porous media systems to quantitatively characterize the influence of the porous-medium grain-, pore-size and texture on the specific capillary-associated interfacial area (FIFA) between an organic liquid and water. By interpreting the breakthrough curves (BTCs) of the reaction product of the KIS tracer hydrolysis, we obtain a relation for the specific IFA and wetting phase saturation. The immiscible displacement process coupled with the reactive tracer transport across the fluid–fluid interface is simulated with a Darcy-scale numerical model. Linear relations between the specific capillary-associated FIFA and the inverse mean grain diameter can be established for measurements with glass beads and natural soils. We find that the grain size has minimal effect on the capillary-associated FIFA for unconsolidated porous media formed by glass beads. Conversely, for unconsolidated porous media formed by natural soils, the capillary-associated FIFA linearly increases with the inverse mean grain diameter, and it is much larger than that from glass beads. This indicates that the surface roughness and the irregular shape of the grains can cause the capillary-associated FIFA to increase. The results are also compared with the data collected from literature, measured with high resolution microtomography and partitioning tracer methods. Our study considerably expands the applicability range of the KIS tracers and enhances the confidence in the robustness of the method.

Zusammenfassung

Dissolved CO2 in karst water is the key driving force of karstification. Replenishment of CO2 concentrations in karst water occurs by meteoric water that percolates through the vadose zone, where CO2 produced from microbial activity is dissolved. CO2 can thus be transported with the percolating water or in the gas phase due to ventilation in karst systems. We measured seasonally fluctuating CO2 concentrations in the air of a karst cave and their influence on aqueous CO2 con- centrations in different depths of a stagnant water column. The observed data were compared to numerical simulations. The data give evidence that density-driven enhanced dissolution of gaseous CO2 at the karst water table is the driving force for a fast increase of aqueous CO2 during periods of high gaseous concentrations in the cave, whereas during periods of lower gaseous concentrations, the decline of aqueous CO2 is limited to shallow water depths in the order of 1 m. This is significant because density-driven CO2 dissolution has not been previously considered relevant for karst hy- drology in the literature. Attempts at reproducing the measured aqueous CO2 concentrations with numerical modeling revealed challenges related to computational demands, discretization, and the high sensitivity of the processes to tiny density gradients.

Zusammenfassung

Enzymatically induced calcium carbonate precipitation is a promising geotechnique with the potential, for example, to seal leakage pathways in the subsurface or to stabilize soils. Precipitation of calcium carbonate in a porous medium reduces the porosity and, consequently, the permeability. With pseudo-2D microfluidic experiments, including pressure monitoring and, for visualization, optical microscopy and X-ray computed tomography, pore-space alterations were reliably related to corresponding hydraulic responses. The study comprises six experiments with two different pore structures, a simple, quasi-1D structure, and a 2D structure. Using a continuous injection strategy with either constant or step-wise reduced flow rates, we identified key mechanisms that significantly influence the relationship between porosity and permeability. In the quasi-1D structure, the location of precipitates is more relevant to the hydraulic response (pressure gradients) than the overall porosity change. In the quasi-2D structure, this is different, because flow can bypass locally clogged regions, thus leading to steadier porosity–permeability relationships. Moreover, in quasi-2D systems, during continuous injection, preferential flow paths can evolve and remain open. Classical porosity–permeability power-law relationships with constant exponents cannot adequately describe this phenomenon. We furthermore observed coexistence and transformation of different polymorphs of calcium carbonate, namely amorphous calcium carbonate, vaterite, and calcite and discuss their influence on the observed development of preferential flow paths. This has so far not been accounted for in the state-of-the-art approaches for porosity–permeability relationships during calcium carbonate precipitation in porous media.

Zusammenfassung

Abstract Dissolution trapping plays a significant role in CO2 geological storage. When CO2 dissolves in aquifer brines, the aqueous solution is heavier than the underlying resident brine. This results in convective instability in the form of CO2-rich fingers, which accelerates dissolution. It was recently shown that background flow affects CO2 dissolution by suppressing the development of convective fingers. However, there was a discrepancy between computational results and measurements, with the computational results demonstrating a decrease in the dissolution rate and the laboratory measurements showing no significant effect. Here, we attempted to understand this difference by exploring the relations between the transport mechanisms that facilitate convective mixing. We investigated the role of background flow by using numerical simulations that were validated by laboratory measurements and analytical solutions. Simulations were generated for the same porous medium and fluid pair used in the experiments, keeping the Rayleigh number constant, while changing the background velocity and the Peclet number. Studying the flux components revealed three distinct regimes characterized by the Peclet to Rayleigh ratio Pe/Ra. When Pe/Ra < 0.77, natural convection dominated, and dissolution remained approximately constant. When the background flow was large (Pe/Ra > 2), dissolution was controlled by pure forced convection and increased with Pe/Ra. In the intermediate range (0.77 < Pe/Ra < 2), both natural convection and forced convection were important.

Zusammenfassung

Flow through heterogeneous landfills that include macropores may occur under Reynolds numbers higher than those where Darcy&rsquo;s law is valid. Extensions, such as a Forchheimer approach, may be required to include inertial effects. Our aim is developing predictive models for such landfills that are built from the low-level radioactive waste and debris of dismantled nuclear power plants. It consists of different materials, which after crushing result in a spatially heterogeneous distribution of porous-media properties in the landfills. Rain events or leakage, for example, may wash out radionuclides and transport them with the water flow. We investigate here the water flow and consider an inclusion of macropores. To deal with possibly high velocities, we choose the Forchheimer model and, taking different Forchheimer coefficients into account, compare it to the Darcy model. The focal points of the study are (i) the influence of the macropores on the flow field and (ii) the impact of the choice of the Forchheimer coefficient both on the solution and the computational effort. The results show that dependent on their size, macropores can dominate the flow field. Furthermore, Forchheimer coefficients introducing more inertial effects are associated with considerably higher runtimes.

Zusammenfassung

Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a response to this, an active field of research has developed over the past decades, focusing on the development of mathematical models and numerical methods to describe and simulate the flow processes in fractured rock. In this work, we present a comparison of different finite volume-based numerical schemes for the simulation of flow in fractured porous media by means of numerical experiments. Two novel vertex-centered approaches are presented and compared to well-established numerical schemes in terms of convergence behavior and their performance on benchmark studies taken from the literature. The new schemes show to produce results that are in good agreement with those of established methods while leading to less degrees of freedom on unstructured simplex grids.

Zusammenfassung

Enzymatically induced calcite precipitation (EICP) is an engineering technology that allows for targeted reduction of porosity in a porous medium by precipitation of calcium carbonates. This might be employed for reducing permeability in order to seal flow paths or for soil stabilization. This study investigates the growth of calcium-carbonate crystals in a micro-fluidic EICP setup and relies on experimental results of precipitation observed over time and under flow-through conditions in a setup of four pore bodies connected by pore throats. A phase-field approach to model the growth of crystal aggregates is presented, and the corresponding simulation results are compared to the available experimental observations. We discuss the model's capability to reproduce the direction and volume of crystal growth. The mechanisms that dominate crystal growth are complex depending on the local flow field as well as on concentrations of solutes. We have good agreement between experimental data and model results. In particular, we observe that crystal aggregates prefer to grow in upstream flow direction and toward the center of the flow channels, where the volume growth rate is also higher due to better supply.

Zusammenfassung

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

Zusammenfassung

Abstract Enzymatically induced calcite precipitation (EICP) in porous media can be used as an engineering option to achieve precipitation in the pore space, for example, aiming at a targeted sealing of existing flow paths. This is accomplished through a porosity and consequent permeability alteration. A major source of uncertainty in modeling EICP is in the quantitative description of permeability alteration due to precipitation. This report presents methods for investigating experimentally the time-resolved effects of growing precipitates on porosity and permeability on the pore scale, in a poly-di-methyl-siloxane microfluidic flow cell. These methods include the design and production of the microfluidic cells, the preparation and usage of the chemical solutions, the injection strategy, and the monitoring of pressure drops for given fluxes for the determination of permeability. EICP imaging methods are explained, including optical microscopy and X-ray microcomputed tomography (XRCT), and the corresponding image processing and analysis. We present and discuss a new experimental procedure using a microfluidic cell, as well as the general perspectives for further experimental and numerical simulation studies on induced calcite precipitation. The results of this study show the enormous benefits and insights achieved by combining both light microscopy and XRCT with hydraulic measurements in microfluidic chips. This allows for a quantitative analysis of the evolution of precipitates with respect to their size and shape, while monitoring their influence on permeability. We consider this to be an improvement of the existing methods in the literature regarding the interpretation of recorded data (pressure, flux, and visualization) during pore morphology alteration.

Zusammenfassung

Calcium oxide/Calcium hydroxide can be utilized as a reaction system for thermochemical heat storage. It features a high storage capacity, is cheap, and does not involve major environmental concerns. Operationally, different fixed-bed reactor concepts can be distinguished; direct reactor are characterized by gas flow through the reactive bulk material, while in indirect reactors, the heat-carrying gas flow is separated from the bulk material. This study puts a focus on the indirectly operated fixed-bed reactor setup. The fluxes of the reaction fluid and the heat-carrying flow are decoupled in order to overcome limitations due to heat conduction in the reactive bulk material. The fixed bed represents a porous medium where Darcy-type flow conditions can be assumed. Here, a numerical model for such a reactor concept is presented, which has been implemented in the software DuMux. An attempt to calibrate and validate it with experimental results from the literature is discussed in detail. This allows for the identification of a deficient insulation of the experimental setup. Accordingly, heat-loss mechanisms are included in the model. However, it can be shown that heat losses alone are not sufficient to explain the experimental results. It is evident that another effect plays a role here. Using Bayesian inference, this effect is identified as the reaction rate decreasing with progressing conversion of reactive material. The calibrated model reveals that more heat is lost over the reactor surface than transported in the heat transfer channel, which causes a considerable speed-up of the discharge reaction. An observed deceleration of the reaction rate at progressed conversion is attributed to the presence of agglomerates of the bulk material in the fixed bed. This retardation is represented phenomenologically by mofifying the reaction kinetics. After the calibration, the model is validated with a second set of experimental results. To speed up the calculations for the calibration, the numerical model is replaced by a surrogate model based on Polynomial Chaos Expansion and Principal Component Analysis.

Zusammenfassung

Abstract Density-driven dissolution of carbon dioxide in water is a well-known and much described mechanism in geological sequestration of this greenhouse gas. It is remarkable that such enhanced dissolution does not receive attention in karst hydrology and speleology. Models and hypotheses on karst development are complex and consider many different processes. We focus here on the influence of CO2 partial gas pressures at the interface between atmosphere and karst water on the dynamics of dissolved CO2 concentrations below the water table. Seasonal variations of microbial soil activity and root respiration or barometric-pressure changes cause fluctuations in CO2 partial pressures. Dependent on the existence and strength of a karst-water background flow, fingering regimes might be triggered causing enhanced dissolution of CO2. This allows replenishment of CO2, and, thus, dissolutional power even deep in the water body without the need for percolating water to transport dissolved CO2. We present and discuss simplified and generic experimental and computational scenarios to strengthen our claim, and we try to give answers to: how much? and under which circumstances? The applied numerical model solves the Navier-Stokes equation with water density dependent on CO2 concentration and temperature. We show that calculated CO2 mass fluxes into the water bodies are dependent on the ratio of Péclet to Rayleigh numbers (Pe/Ra) and show a local minimum around Pe/Ra = 1, i.e. when natural and forced convection are about equal. Concluding, we claim that there is sufficient reason to consider density-driven dissolution as a process of relevance in karstification if circumstances are given.

Zusammenfassung

Subsurface flow and geomechanics are often modeled with sequential approaches. This can be computationally beneficial compared with fully coupled schemes, while it requires usually compromises in numerical accuracy, at least when the sequential scheme is non-iterative. We discuss the influence of the choice of scheme on the numerical accuracy and the expected computational effort based on a comparison of a fully coupled scheme, a scheme employing a one-way coupling, and an iterative scheme using a fixed-stress split for two subsurface injection scenarios. All these schemes were implemented in the numerical simulator DuMux. This study identifies conditions of problem settings where differences due to the choice of the model approach are as important as differences in geologic features. It is shown that in particular transient and multiphase flow, effects can be causing significant deviations between non-iterative and iterative sequential schemes, which might be in the same order of magnitude as geologic uncertainty. An iterated fixed-stress split has the same numerical accuracy as a fully coupled scheme but only for a certain number of iterations which might use up the computational advantage of solving two smaller systems of equations rather than a big monolithical one.

Zusammenfassung

Carbon dioxide density-driven dissolution in a water-filled laboratory flume of the dimensions 60 cm length, 40 cm height, 1 cm thickness, was visualized using a pH-sensitive color indicator. We focus on atmospheric pressure conditions, like in caves where CO2 concentrations are typically higher. Varying concentrations of carbon dioxide were applied as boundary conditions at the top of the experimental setup, leading to the onset of convective fingering at differing times. The data were used to validate a numerical model implemented in the numerical simulator DuMux. The model solves the Navier&ndash;Stokes equations for density-induced water flow with concentration-dependent fluid density and a transport equation, including advective and diffusive processes for the carbon dioxide dissolved in water. The model was run in 2D, 3D, and pseudo-3D on two different grids. Without any calibration or fitting of parameters, the results of the comparison between experiment and simulation show satisfactory agreement with respect to the onset time of convective fingering, and the number and the dynamics of the fingers. Grid refinement matters, in particular, in the uppermost part where fingers develop. The 2D simulations consistently overestimated the fingering dynamics. This successful validation of the model is the prerequisite for employing it in situations with background flow and for a future study of karstification mechanisms related to CO2-induced fingering in caves.

Zusammenfassung

Predicting shear failure that leads to the reactivation of faults during the injection of fluids in the subsurface is difficult since it inherently involves an enormous complexity of flow processes interacting with geomechanics. However, understanding and predicting induced seismicity is of great importance. Various approaches to modelling shear failure have been suggested recently. They are all dependent on the prediction of the pressure and stress field, which requires the solution of partial differential equations for flow and for geomechanics. Given a pressure and corresponding mechanical responses, shear slip can be detected using a failure criterion. We propose using characteristic values for stress drops occurring in a failure event as sinks in the geomechanical equation. This approach is discussed in this article and illustrated with an example.