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Reactive transport processes in a porous medium will often both cause changes to the pore structure, via precipitation and dissolution of biomass or minerals, and be affected by these changes, via changes to the material’s porosity and permeability. An understanding of the pore structure morphology and the changes to flow parameters during these processes is critical when modeling reactive transport. Commonly applied porosity–permeability relations in simulation models on the REV scale use a power-law relation, often with slight modifications, to describe such features; they are often used for modeling the effects of mineral precipitation and/or dissolution on permeability. To predict the reduction in permeability due to biomass growth, many different and often rather complex relations have been developed and published by a variety of authors. Some authors use exponential or simplified Kozeny–Carman relations. However, many of these relations do not lead to fundamentally different predictions of permeability alteration when compared to a simple power-law relation with a suitable exponent. Exceptions to this general trend are only few of the porosity–permeability relations developed for biomass clogging; these consider a residual permeability even when the pore space is completely filled with biomass. Other exceptions are relations that consider a critical porosity at which the porous medium becomes impermeable; this is often used when modeling the effect of mineral precipitation. This review first defines the scale on which porosity–permeability relations are typically used and aims at explaining why these relations are not unique. It shows the variety of existing approaches and concludes with their essential features.

Many subsurface engineering technologies or natural processes cause porous medium properties, such as porosity or permeability, to evolve in time. Studying and understanding such processes on the pore scale is strongly aided by visualizing the details of geometric and morphological changes in the pores. For realistic 3D porous media, X-Ray Computed Tomography (XRCT) is the method of choice for visualization. However, the necessary high spatial resolution requires either access to limited high-energy synchrotron facilities or data acquisition times which are considerably longer (e.g. hours) than the time scales of the processes causing the pore geometry change (e.g. minutes). Thus, so far, conventional benchtop XRCT technologies are often too slow to allow for studying dynamic processes. Interrupting experiments for performing XRCT scans is also in many instances no viable approach. We propose a novel workflow for investigating dynamic precipitation processes in porous media systems in 3D using a conventional XRCT technology. Our workflow is based on limiting the data acquisition time by reducing the number of projections and enhancing the lower-quality reconstructed images using machine-learning algorithms trained on images reconstructed from high-quality initial- and final-stage scans. We apply the proposed workflow to induced carbonate precipitation within a porous-media sample of sintered glass-beads. So we were able to increase the temporal resolution sufficiently to study the temporal evolution of the precipitate accumulation using an available benchtop XRCT device.

The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Flow through heterogeneous landfills that include macropores may occur under Reynolds numbers higher than those where Darcy’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.

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.

The dynamic interaction between subsurface flow and soil mechanics is often simplified in the stability assessment of variably saturated landslide-prone hillslopes. The aim of this study is to analyze the impact of conventional simplifications in coupling and modeling strategies on stability assessment of such hillslopes in response to precipitation using the local factor of safety (LFS) concept. More specifically, it investigates (1) the impact of neglecting poroelasticity, (2) transitioning from full coupling between hydrological and mechanical models to sequential coupling, and (3) reducing the two-phase flow system to a one-phase flow system (Richards’ equation). Two rainfall scenarios, with the same total amount of rainfall but two different relatively high (4 mm h−1) and low (1 mm h−1) intensities are considered. The simulation results of the simplified approaches are compared to a comprehensive, fully coupled poroelastic hydromechanical model with a two-phase flow system. It was found that the most significant difference from the comprehensive model occurs in areas experiencing the most transient changes due to rainfall infiltration in all three simplified models. Among these simplifications, the transformation of the two-phase flow system to a one-phase flow system showed the most pronounced impact on the simulated local factor of safety (LFS), with a maximum increase of +21.5% observed at the end of the high-intensity rainfall event. Conversely, using a rigid soil without poroelasticity or employing a sequential coupling approach with no iteration between hydromechanical parameters has a relatively minor effect on the simulated LFS, resulting in maximum increases of +2.0% and +1.9%, respectively. In summary, all three simplified models yield LFS results that are reasonably consistent with the comprehensive poroelastic fully coupled model with two-phase flow, but simulations are more computationally efficient when utilizing a rigid porous media and one-phase flow based on Richards’ equation.

The injection of fluids into the subsurface takes place in the context of a variety of engineering applications such as geothermal power generation, disposal of wastewater, CO 2 storage and enhanced oil recovery. These technologies involve not only the underground emplacement of fluids in a geologic formation but also affect the stress state of these rocks. If the rock’s strength is surpassed, these stress changes can even lead to failure. In this context, we present a conceptual approach to model fault reactivation in porous media. As a starting point for developing and implementing this approach, the already existing combined hydro- and geomechanical model within the open-source simulator DuMu x was chosen. For the evaluation of shear slip on the fault plane, the classical Mohr–Coulomb failure criterion is used. Based on the energy balance from Kanamori (Earthquake thermodynamics and phase transformations in the earth’s interior, international geophysics, vol 76. Academic Press, London, pp 293–305, 2001 ), where a slip event on fault is described as a transformation of elastic energy into seismic waves, heat and an amount of energy required to cause fracture, we interpret failure as a dissipation of elastic energy. Furthermore, seismic data allow to infer a constant stress drop over a wide range of scales (Abercrombie and Leary in Geophys Res Lett 20(14):1511–1514, 1993 ). These findings are incorporated into our model by altering the material properties during the slip event. In detail, the linear elastic material law is replaced by a visco-elastic behaviour, which reproduces the characteristics mentioned above. This, in turn, leads to additional displacements, which are interpreted as the slip on the fault plane. Our results indicate that this pragmatic approach is capable of modelling fault reactivation without resolving the fault as a discrete surface but as a elements representing a fault zone instead.

Attachment of bacteria in porous media is a complex mixture of processes resulting in the transfer and immobilization of suspended cells onto a solid surface within the porous medium. Quantifying the rate of attachment is difficult due to the many simultaneous processes possibly involved in attachment, including straining, sorption, and sedimentation, and the difficulties in measuring metabolically active cells attached to porous media. Preliminary experiments confirmed the difficulty associated with measuring active Sporosarcina pasteurii cells attached to porous media. However, attachment is a key process in applications of biofilm-mediated reactions in the subsurface such as microbially induced calcite precipitation. Independent of the exact processes involved, attachment determines both the distribution and the initial amount of attached biomass and as such the initial reaction rate. As direct experimental investigations are difficult, this study is limited to a numerical investigation of the effect of various initial biomass distributions and initial amounts of attached biomass. This is performed for various injection strategies, changing the injection rate as well as alternating between continuous and pulsed injections. The results of this study indicate that, for the selected scenarios, both the initial amount and the distribution of attached biomass have minor influence on the Ca 2 + precipitation efficiency as well as the distribution of the precipitates compared to the influence of the injection strategy. The influence of the initial biomass distribution on the resulting final distribution of the precipitated calcite is limited, except for the continuous injection at intermediate injection rate. But even for this injection strategy, the Ca 2 + precipitation efficiency shows no significant dependence on the initial biomass distribution.

Convective dissolution of CO2${\\text{CO}}_{2}$is a well‐known mechanism in geological storage of CO2${\\text{CO}}_{2}$ . 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${\\text{CO}}_{2}$concentration were used to compute scenario‐specific results for effective CO2${\\text{CO}}_{2}$entry rates into an idealized fracture with varying aperture, temperature, and CO2${\\text{CO}}_{2}$concentration at the gas‐water interface. The results were analyzed in terms of dimensionless quantities. They revealed a Rayleigh invariance of the effective CO2${\\text{CO}}_{2}$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${\\text{CO}}_{2}$entry rates, which can then be used, in perspective, in upscaled models. We have studied convective CO2${\\text{CO}}_{2}$dissolution for two different fracture settings; the first one relates to karstification scenarios, where CO2${\\text{CO}}_{2}$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${\\text{CO}}_{2}$storage, where the literature provides only studies on convective CO2${\\text{CO}}_{2}$dissolution for porous‐media flow with Darcy regimes. Plain Language Summary Carbon dioxide (CO2${\\text{CO}}_{2}$ ) dissolves into water when the latter is in contact with a gaseous, CO2${\\text{CO}}_{2}$ ‐rich atmosphere. This process is characteristic for karst systems, where CO2${\\text{CO}}_{2}$originating from microbial activity in the soil is enriched in the atmosphere of caves or karstic void spaces. It is furthermore an important storage mechanism for CO2${\\text{CO}}_{2}$in deep geological reservoirs where the greenhouse gas is injected for mitigating global warming. When water is stagnant or without significant base flow, the dissolution process is governed by so‐called convective dissolution, where convection cells are triggered by instabilities in the water body due to density differences caused by dissolved CO2${\\text{CO}}_{2}$ . Convective dissolution is well understood, but it is still challenging to predict how much CO2${\\text{CO}}_{2}$dissolves over time. While literature studies on convective dissolution have been focused on porous rocks, we investigate here open fractures, where flow patterns are much more complex. Using computationally expensive numerical simulations, we created a data basis for developing an approach to estimate effective CO2${\\text{CO}}_{2}$entry rates. A crucial finding is that these rates are invariant to a key dimensionless number, the Rayleigh number, which in this case describes the instability of a water body due to CO2${\\text{CO}}_{2}$dissolution. Key Points Convective mixing of CO2 in water‐filled fractures shows 3D effects and cannot be described with porous‐media Darcy‐models Non‐dimensionalization reduces the parameter space for estimating effective CO2 flux rates due to convective dissolution Fully developed fingering regimes after a certain time and fracture length reveal a Rayleigh invariance of the effective CO2 fluxes

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.