New advances in coupled fluid dynamics, heat and solute transport, and biogeochemical reactions in soils, the vadose zone, and below



Physical (e.g. flow and transport), chemical (e.g. red-ox reactions) and biological (e.g. bio-mineralization) processes play a critical role in controlling reactive transport of contaminants in soils, the vadose zone, and deeper subsurface permeable media, for example during (bio)remediation operations. The characterization and modeling at different scales of such coupled processes in subsurface environments has motivated the development of novel experimental approaches, from laboratory to field, that are capable of quantifying the physical, chemical and biological properties of heterogeneous structures and of the related physical processes at different scales. Detailed experimental investigation and evidence of complex subsurface processes allow testing and validating new measurement techniques, and provide datasets with sufficient resolution and/or high spatial coverage to make the validation of coupled processes theories and numerical models possible.

The session will provide the opportunity for a multidisciplinary discussion based on recent advances in the experimental characterization and modeling of single and multiphase flows (including flows of non-Newtonian fluids), as well as conservative and reactive solute transport and bacterial activity, in porous and fractured media. Examples of such coupled subsurface processes include the dynamics of single and multiphase flows, NAPL dissolution and transport, mixing and mixing-controlled reactions, heat transfer, contaminant (bio)degradation, precipitation/dissolution reactions, bacterial dynamics and biofilm growth. Experiments featuring high resolution measurements with novel sensors, analytical, and imaging techniques, as well as novel modeling and upscaling techniques, will be addressed prominently.

Co-organized by HS13
Convener: Yves Meheust | Co-conveners: Vittorio Di Federico, Florian Doster, Maria Klepikova
vPICO presentations
| Wed, 28 Apr, 09:00–10:30 (CEST)

vPICO presentations: Wed, 28 Apr

Chairpersons: Yves Meheust, Vittorio Di Federico, Maria Klepikova
Block 1: solicited talk
Joaquin Jimenez-Martinez, Ishaan Markale, and Andrés Velásquez-Parra

Coupling of unsaturated flows and surface reactions, including sorption and desorption, takes place in environmental contexts such as soils and the unsaturated zone. Lower sorption coefficients than those observed from batch experiments are found in natural soils. However, a deep understanding of this coupling is missing. To achieve this objective, we designed microfluidics experiments and performed direct numerical simulations based on experimental images at the microscale. We explore the effects of fluid flow dynamics and reaction kinetics on the effective kinetics. We have observed that an increase in the air volume within the porous medium promotes more heterogeneous fluid flow velocities, controlling the mixing of the transported reactant and resulting in a non-monotonic effective kinetic of the surface reaction.

How to cite: Jimenez-Martinez, J., Markale, I., and Velásquez-Parra, A.: Effective kinetics and phases saturation impact on surface reactions in porous media, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8994,, 2021.

Block 2
Huhao Gao, Alexandru Tatomir, Nikolaos Karadimitriou, Holger Steeb, and Martin Sauter

Porous media surface roughness strongly influences the transport of solutes during drainage, due to the formation of thick water films (capillary condensation) on the porous media surface. In the case of interfacial-reacted, water-based solutes, these water films increase both the production of the solute, due to the increased number of fluid-fluid interfaces, and the loss of the solute by the retention in the stagnant water films. The retention of the solute in flowing water is described by a mobile mass retention term. This study applies the pore-scale direct simulation with the phase-field method based continuous solute transport (PFM-CST) model on the kinetic interfacial sensitive (KIS) tracer reactive transport during primary drainage in a 2D slit with a wall with variable fractal geometries. The capillary-associated moving interface is found to be larger for rough surfaces than smoother ones. The results confirm that the impact of roughness regarding the film-associated interfacial area can be partly, or totally masked, in a drained slit. It is found that the mobile mass retention term is increased with larger volumes of capillary condensed water films. To conclude, it is also found that the surface roughness factor has a non-monotonic relationship with the overall production rate of solute mass in moving water.

How to cite: Gao, H., Tatomir, A., Karadimitriou, N., Steeb, H., and Sauter, M.: Pore-scale study of effects of surface roughness on the transport of interfacial reactive tracers during primary drainage process, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3495,, 2021.

Alessandro Comolli, Anne De Wit, and Fabian Brau

The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.

Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field vr(r,z) describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.


                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.



[1] L. Gálfi, Z. Rácz, Phys. Rev. A 38, 3151 (1988);

[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);

[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).

How to cite: Comolli, A., De Wit, A., and Brau, F.: Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-5697,, 2021.

Alexandre Puyguiraud, Lazaro Perez, Juan J. Hidalgo, and Marco Dentz

We utilize effective dispersion coefficients to capture the evolution of the mixing interface between two initially segregated species due to the coupled effect of pore-scale heterogeneity and molecular diffusion. These effective dispersion coefficients are defined as the average spatial variance of the solute plume that evolves from a pointlike injection (the transport Green function). We numerically investigate the effective longitudinal dispersion coefficients in two porous media of different structure heterogeneity  and through different Péclet number regimes for each medium. We find that, as distance traveled increases (or time spent), the solute experiences the pore-scale velocity field heterogeneity due to advection and transverse diffusion, resulting in an evolution of the dispersion coefficients. They evolve from the value of molecular diffusion at early time, then undergo an advection dominated regime, to finally reach the value of hydrodynamic dispersion at late times. This means that, at times smaller than the characteristic diffusion time, the effective dispersion coefficients can be notably smaller than the hydrodynamic dispersion coefficient. Therefore, mismatches between pore-scale reaction data from experiment or simulations and Darcy scale predictions based on temporally constant hydrodynamic dispersion can be explained through these differences. We use the effective dispersion coefficients to approximate the transport Green function and to quantify the incomplete mixing occurring at the pore-scale. We evaluate the evolution of two initially segregated species via this methodology. The approach correctly predicts the amount of chemical reaction occuring in reactive bimolecular particle tracking simulations. These results shed light on the upscaling of pore-scale incomplete mixing and demonstrates that the effective dispersion is an accurate measure for the width of the mixing interface between two reactants. 

How to cite: Puyguiraud, A., Perez, L., Hidalgo, J. J., and Dentz, M.: Upscaling of pore-scale mixing and reaction through effective dispersion coefficients, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-15090,, 2021.

Georgina C. Kalogerakis, Hardiljeet K. Boparai, and Brent E. Sleep

Remediation of groundwater contaminated by organic compounds in porous and fractured media is a persistent and not well understood challenge. In situ chemical oxidation (ISCO) is a remediation technology that delivers oxidants to the subsurface to transform contaminants into benign products. The reactions take place in the aqueous phase where the oxidant comes in contact with the dissolved phase of the contaminant. In this work, we report on the impact of by-product formation on the effectiveness of ISCO. We conducted a series of batch experiments to identify by-products and increase our understanding for time scales required for complete mineralization of petroleum hydrocarbons. This was coupled with micro-CT imaging of column experiments and imaging in a glass fractured rock replica to track the formation of gaseous and solid by-products and determine their effect on flow, transport, and mass transfer. The final aim of this study is to propose novel strategies for improved remediation efficiency.


How to cite: Kalogerakis, G. C., Boparai, H. K., and Sleep, B. E.: Underlying Mechanisms in Groundwater Remediation via In Situ Chemical Oxidation, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-3098,, 2021.

Marco Dentz, Alexandre Puyguiraud, and Philippe Gouze

Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. 

How to cite: Dentz, M., Puyguiraud, A., and Gouze, P.: Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-13655,, 2021.

Block 3
Riccardo Sprocati and Massimo Rolle

Electrokinetic (EK) remediation is one of the few in-situ remediation technologies that can effectively remove contaminants from low-permeability porous media. Process-based modeling, including the complex multiphysics and biogeochemical processes occurring during electrokinetic remediation, is instrumental to describe EK systems and to assist in their design. In this work we use NP-Phreeqc-EK [1], a multidimensional, multiphysics code which couples a flow and transport simulator (COMSOL Multiphysics) with a geochemical code (PhreeqcRM) through a MATLAB LiveLink interface. The model allows the simulation of coupled fluid flow, solute transport, charge interactions and biogeochemical reactions during electrokinetics in saturated porous media. The process-based code is applied for the modeling of electrokinetic delivery of amendments to enhance bioremediation (EK-Bio) of chlorinated compounds at a pilot test site [2]. We simulate both conservative and reactive transport scenarios and we compute and show the Nernst-Planck fluxes and the velocities of the different species (such as lactate, chlorinated ethenes and degrading microorganisms). To compare remediation performances and model outcomes we define different metrics quantifying the spatial distribution of the delivered reactants and the mass of the organic contaminants in the system. The process-based model allowed the simulation of the key processes occurring during EK-Bio, including 1) multidimensional electrokinetic transport such as electromigration of charged species and electroosmosis, 2) Coulombic interactions between ions in solution, 3) kinetics of contaminant biodegradation, 4) dynamics of microbial populations, 5) mass transfer limitations and 6) geochemical reactions.


[1] Sprocati, R., Masi, M., Muniruzzaman, M., & Rolle, M. (2019). Modeling electrokinetic transport and biogeochemical reactions in porous media: A multidimensional Nernst–Planck–Poisson approach with PHREEQC coupling. Advances in Water Resources, 127, 134-147.

[2] Sprocati, R., Flyvbjerg, J., Tuxen, N., & Rolle, M. (2020). Process-based modeling of electrokinetic-enhanced bioremediation of chlorinated ethenes. Journal of Hazardous Materials, 397, 122787.

How to cite: Sprocati, R. and Rolle, M.: Modeling of coupled flow, transport and biogeochemical reactions during electrokinetic bioremediation: model development and application, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14376,, 2021.

Akash Ganesh, Romain Rescanieres, Carine Douarche, and Harold Auradou

We study the shear-induced migration of dilute suspensions of swimming bacteria (modelled as Active elongated Brownian Particles or ABPs) subject to plane Poiseuille flow in a confined channel. By incorporating very simple boundary conditions, we perform numerical simulations of the 3D equations of motion describing the change in position and orientation of the particles. We investigate the effects of confinement, of non-uniform shear and of aspect ratio of the particles on the overall dynamics of the ABPs population.

We particularly study the coupling between the local shear and the change in the orientation of the particles. We thus perform numerical simulations on both the case where the change in the orientation of the ABPs is purely diffusive (decoupled case) and the case where their orientation is coupled to the shear flow (coupled case). We observe that the decoupled case exhibits a Taylor dispersion i.e.  the effective dispersion coefficient of the ABPs along the direction of the flow is proportional to the square of the imposed shear at all shears. 

However, for all the coupled cases we observe a transition from a Taylor to an active-Taylor regime at a critical shear rate, indicating the effect of shear coupling on the orientation dynamics of the particles. This critical shear rate is directly correlated to the degree of confinement. The change in the dispersion coefficient along the direction of the flow as function of the shear rate is in qualitative agreement with previous studies[1]. 

To further understand these results, we also investigate the change in the dispersion coefficient in the other two directions along with the effect of the shape of the particles. We believe that this study should enhance our understanding of dispersion of bacteria through porous media, on surfaces etc. where shear flows are ubiquitous. 

[1] Sandeep Chilukuri, Cynthia H.Collins, and Patrick T. Underhill. Dispersionof flagellated swimming microorganisms in planar poiseuille flow.Physics offluids, 27, (031902):1 –17, 2015

How to cite: Ganesh, A., Rescanieres, R., Douarche, C., and Auradou, H.: Modelization of dispersion of swimming bacteria in Poiseuille flow, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-7183,, 2021.

Amir Golparvar, Matthias Kästner, and Martin Thullner

Organic carbon (C), either originated from soil organic carbon or introduced externally from anthropogenic sources, is the main pool for providing microorganisms with materials for biosynthesis (anabolism) and energy for catabolism. Routing the carbon source between catabolic and anabolic pathways eventually decides over the fate of C; either if it leaves the system as inorganic carbon (i.e. CO2) or, it stays in it due to anabolism and cell synthesis processes. The microbial carbon use efficiency (CUE) – and thus the proportion of the C that (potentially) remains in soil – depends on various factors.  Physio-chemical condition of the hosting environment, the composition and activity of the microbial community and in extreme cases, climatic changes can cause a high spatio-temporal variability in microbial activity and CUE. At microscale, also the pore-size distribution, pore connectivity and pore water-content can (directly or indirectly) alter the distribution of carbon and energy fluxes in soils. Across different soil types and conditions, the evolution of microbial community and of their CUE in the simultaneous presence of various factors are poorly understood.

In order to capture the in-situ dynamics of microbial activity and CUE in the dynamically changing environment of the vadose zone, we apply a pore-scale reactive transport modelling approach to disentangle the interplay of physio-chemical factors in the evolution of the soil carbon pool. Our modelling framework is capable providing a resolution of unsaturated water flow and solute transport at the microscale combined with capturing the underlying biogeochemical processes for tracking the evolution of microbial communities along with C pools in soil. Physical properties of the porous structure (such as pore geometry, pore size distribution and their connectivity) are accounted for via using digitized -CT images. Variable water flow and distribution is achieved by solving the Navier Stokes equation. A full set of advective-diffusive-reactive transport equation is solved for all chemical and microbial species to investigate their evolution in time and space. Model simulation cover various scenarios differing in properties of the solid matrix, imposed flow conditions and considered organic carbon substrates. Sensitivity simulations are performed to single out the effect of different bio-physio-chemical factors on evolution of microbial biomass and CUE.

How to cite: Golparvar, A., Kästner, M., and Thullner, M.: Quantification of key factors driving the microbial metabolism in the vadose zone – A microscale-modelling perspective, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9253,, 2021.

Ali Mahdavi Mazdeh and Stefan Wohnlich

Capillary fringe plays an important role in the fate and transport of infiltrated solutes from agricultural lands. In this study, flow patterns and the vertical distribution of the velocity and hydraulic gradient inside the capillary fringe were investigated using FEFLOW calibrated by experimental data. An experimental box along with a real sample of capillary fringe from the study area (Sand and clay pit Brüggen, Germany) was used for the experiments. The dimension of the filled part of the box was 0.75 m long, 0.55 m high, and 0.150 m wide. To maintain a constant hydraulic gradient throughout the experiments the upstream and downstream groundwater levels were fixed to 7 cm and 3 cm, respectively. The horizontal velocity at different points inside the capillary fringe and the vadose zone was measured by injecting the fluorescent dye tracer (Uranin). At the end of the experiments, the soil samples are collected from different parts of the box for water content measurement. The results indicate that FEFLOW successfully estimates water content, overall flow pattern, and more importantly horizontal movement inside the capillary fringe. The streamlines are parallel to the groundwater table in the middle part.  Based on both experimental and numerical results, while there is a downward movement near the outflow, an upward movement was seen near the inflow. In previous studies, the velocity profile inside the capillary fringe was estimated using Darcy’s law, unsaturated hydraulic conductivity, and constant hydraulic gradient. The detailed comparison of measured water content and velocity with numerical modeling results showed that the constant hydraulic gradient assumption above the water table in previous studies is not valid. The vertical hydraulic gradient profile calculated by FEFLOW showed that the hydraulic gradient at the middle part of the box changes from 0.042 to 0.03. Moreover, the shape of the vertical hydraulic gradient profile is a function of the location in the box and soil type.

Keywords: Solute transport, Unsaturated zone, Streamline, Pore velocity, Hydraulic conductivity, FEFLOW

How to cite: Mahdavi Mazdeh, A. and Wohnlich, S.: Numerical and experimental study of the vertical distribution of velocity and hydraulic gradient in the capillary fringe, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9143,, 2021.

Ishani Banerjee, Anneli Guthke, Kevin Mumford, and Wolfgang Nowak

Invasion-Percolation (IP) models are used to simulate multiphase flow in porous media across various scales (from pore-scale IP to Macro-IP). Numerous variations of IP models have emerged; here we are interested in simulating gas flow in a water-saturated porous medium. Gas flow in porous media occurs either as a continuous or as a discontinuous flow, depending on the rate of flow and the nature of the porous medium. A particular IP model version may be well suited for predictions in a specific gas flow regime, but not applicable to other regimes. Our research aims to compare various macro-scale versions of IP models existing in the literature and rank their performance in relevant gas flow regimes.

We test the performance of Macro-IP models on a range of gas-injection rates in water-saturated sand experiments, including both continuous and discontinuous flow regimes. The experimental data is obtained as a time series of images using the light transmission technique. To represent pore-scale heterogeneities of sand, we let each model version run on several random realizations of the initial entry pressure field. As a metric for ranking the models, we introduce a diffused version of the so-called Jaccard index (adapted from image analysis and object recognition). We average this metric over time and over all realizations per model version to evaluate each model’s overall performance. This metric may also be used to calibrate model parameters such as gas saturation. 

Our proposed approach evaluates the performance of competing IP model versions in different gas-flow regimes objectively and quantitatively, and thus provides guidance on their applicability under specific conditions. Moreover, our comparison method is not limited to gas-water phase systems in porous media but generalizes to any modelling situation accompanied by spatially and temporally highly resolved data.

How to cite: Banerjee, I., Guthke, A., Mumford, K., and Nowak, W.: Comparison of Competing Invasion-Percolation Models for Simulation of Multiphase Flow in Porous Media, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8826,, 2021.

Tomáš Princ and Michal Snehota

The research focused on the simulation of the previous experiment described by Princ et al. (2020). The relationship between entrapped air content (ω) and the corresponding satiated hydraulic conductivity (K) was investigated for two coarse sands, in the experiment. Additionally the amount and distribution of air bubbles were quantified by X-ray computed tomography.

The pore-network model based on OpenPNM platform (Gostick et al. 2016) was used to attempt simulation of a redistribution of the air bubbles after infiltration. Satiated hydraulic conductivity was determined to obtain the K(ω) relationship. The results from pore-network model were compared with the results from experiments.

Gostick et al. (2016). Computing in Science & Engineering. 18(4), p60-74.

Princ et al. (2020). Water. 12(2), p1-19.

How to cite: Princ, T. and Snehota, M.: The Pore-network Modelling of the Infiltration Experiments Performed on Unsaturated Coarse Sands, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-14147,, 2021.

Block 4
Chris Boeije, Pacelli Zitha, and Anne Pluymakers

Geothermal energy, the extraction of hot water from the subsurface (500 m to 5 km deep), is generally considered one of the key technologies to achieve the demands of the energy transition.  One of the main problems during production of geothermal waters is degassing. Many subsurface waters contain substantial amounts of dissolved gasses. As the hot water travels up the production well, the pressure and/or temperature drop will cause dissolved gas to come out of the solution. This causes several problems, such as corrosion of the facilities (due to pH changes and/or degassing-related precipitation) and in some cases even to blocking of the reservoir as the free gas limits the water flow.  To better understand under which conditions free gas nucleates, we need confirmation of theoretical bubble point pressure and temperature, and understand what controls the evolution of the bubble front:  i.e. what are the conditions under which free gas emerges from the solution and at what rate are bubbles created?

An experimental setup was designed in which the degassing process can be observed visually. The setup consists of a high-pressure visual cell which contains water saturated with dissolved gas at high-pressure. The pressure within the cell can be reduced in a reproducible manner using a back-pressure regulator at the outlet of the system. A high-speed camera paired with a uniform LED light source is used to record the degassing process. The pressure in the cell is monitored using a pressure transducer which is synchronized with the camera. The resulting images are then analysed using a MATLAB routine, which allows for determination of the bubble point pressure and rate of bubble formation.

The first two sets of experiments at ambient temperatures (~20 oC) were carried out using two different gases, N2 and CO2. Initial pressure was 70 and 30 bar for the N2 and CO2 experiments respectively. In these first experiments we determined the influence of the initial fluid used to pressurize the system. Using gas as the initial fluid causes a large amount of bubbles, whereas only a single bubble was observed for a system where degassed water is used as the initial fluid. An intermediate system where degassed water is pumped into a system full of air at ambient conditions and is subsequently pressurized yields a number of bubbles in between the two systems described previously. All three methods give reproducible bubble point pressures within 2 bar (i.e. pressure where the first free bubble is formed). There are clear differences in bubble point between N2 and CO2.

A series of follow-up experiments is planned that will investigate specific properties at more extreme conditions: at higher pressures (up to 500 bar) and temperatures (500 oC) and using high-salinity brines (2.5 M).

How to cite: Boeije, C., Zitha, P., and Pluymakers, A.: Experimental investigation of degassing properties of geothermal fluids, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-12311,, 2021.

Johanna Blöcher, Petr Mayer, and Michal Kuraz

An accurate representation of freezing and thawing in soil covers many applications including simulation of land surface processes, hydrology, and degrading permafrost. Freezing and thawing tightly couple water and heat flow, where temperature and temperature gradients influence the water flow and phase changes, and water content and flow influence the heat transport. In most porous media, the interface between liquid and frozen water is not sharp and a slushy zone is present. A common observation of freezing soil is water accumulation towards the freezing front due to Cryosuction. A mathematical model can be derived using the Clausius-Clapeyron equation, which allows the derivation of a soil freezing curve relating temperature to pressure head. This is based on the assumption that soil freezing is similar to soil drying.

Many models still lack features such as Cryosuction. We believe that this may be due to numerical issues that model developers face with their current solver and discretization setup. Implementing freezing soil accurately is not straight-forward. Using the Clausius-Clapeyron creates a discontinuity in the freezing rate and latent heat at the freezing point and little attention has been paid to the adequate description of their numerical treatment and computational challenges. Discretizing this discontinuous system with standard finite element methods (standard Galerkin type) can cause spurious oscillations because the standard finite element method uses continuous base/shape functions that are incapable of handling discontinuity of any kind within an element. Similarly, standard finite difference methods are also not capable of handling discontinuities. In this contribution, we present the application of regularization of the discontinuous term, which allows the use of the standard finite element method. We implemented the model in the open-source code base DRUtES ( We verify this approach on synthetic and various real freezing soil column experiments conducted by Jame (1977) and Mizoguchi (1990).

Jame, Y.-W., Norum, D.I., 1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resources Research 16, 811–819.

Mizoguchi, M., 1990. Water, heat and salt transport in freezing soil. sensible and latent heat flow in a partially frozen unsaturated soil. University of Tokyo.


How to cite: Blöcher, J., Mayer, P., and Kuraz, M.: Simple numerical strategies to model freezing in variably-saturated soil with the standard finite element method, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-873,, 2021.

Mamta Jotkar, Laurence Rongy, and Anne De Wit

We numerically study the effect of differential diffusion in chemically-driven convective dissolution that can occur upon the reaction of a dissolving species A in a host phase when the chemical reaction destabilizes an otherwise stable density stratification. For example, an A+B→C reaction is known to trigger such convection when, upon dissolution into the host solution, A reacts with B present in the solution to produce C if the difference between C and B in the contribution to the solution density is above a critical threshold. We show that differential diffusivities impact the convective dynamics substantially giving rise to additional convective effects below the reaction front, where C is generated. More specifically, we show that below the reaction front either double-diffusive or diffusive-layer convection can arise, modifying the local Rayleigh-Taylor instability. When B diffuses faster than C, a double-diffusive instability can develop below the reaction front, accelerating the convective dynamics and conversely, when B diffuses slower than C, diffusive-layer convection modes stabilize the dynamics compared to the equal diffusivity case. Our results are relevant for various geological applications or engineering set-ups that involve non-reactive stable density stratifications where transport can be enhanced by reaction-induced convection.

How to cite: Jotkar, M., Rongy, L., and De Wit, A.: Control of chemically-driven convective dissolution by differential diffusion effects, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-8718,, 2021.

Vittorio Di Federico, Alessandro Lenci, and Valentina Ciriello

Gravity-driven flow in porous and fractured media has been extensively investigated in recent years in connection with numerous environmental and industrial applications, including seawater intrusion, oil recovery, penetration of drilling fluids into reservoirs, contaminant migration such as NAPL spreading in shallow aquifers, and carbon dioxide sequestration in subsurface formations. The propagation of such currents is typically governed by the interplay between viscous and buoyancy forces, with negligible inertial effects. For long and thin currents, the spreading can be described by similarity solutions for a variety of geometries, with topographic controls often playing a crucial role. These solutions can be extended to gravity-driven flow in vertical narrow fractures or cracks via the well-known Hele-Shaw (HS) analogy between parallel plate and porous media flow, with the aperture b (distance between fracture walls) squared being the analogue of permeability k according to k = b2/12.  

Buoyancy-driven spreading in porous and fractured media is also influenced by spatial heterogeneity of medium properties; permeability, porosity, and aperture gradients affect the propagation distance and shape of gravity currents, with practical implications for remediation and storage. In this paper we are interested in the coupled effect of heterogeneity and a fixed edge draining the current at one end of a finite domain. Simultaneous permeability and porosity gradients parallel to the flow are considered: this is equivalent to a wedge-shaped fracture, as the Hele-Shaw analogy necessarily accounts for both permeability and porosity gradients.

A current of density ρ+Δρ advances horizontally in a fluid of density ρ under the sharp interface approximation, and is drained by an edge at a distance x = L from the origin; a no-flow boundary condition is considered at x = 0. We neglect vertical velocities for an elongated current; this implies vertical equilibrium, and in turn an hydrostatic pressure distribution within the advancing current. The final assumption is of vanishing height of the current at the draining edge after a relatively short adjustment time, favoured by the increase in permeability/porosity or aperture along the flow direction.

Under these assumptions, a semi-analytical solution is derived for the height of the current h(x, t) in a self-similar form, valid as a late-time approximation modelling the drainage phenomenon after the influence of the initial condition has vanished. This allows transforming the nonlinear PDE governing the flow into a nonlinear ODE amenable to a numerical solution. Knowledge of the current profile then yields the residual mass in the fracture and the drainage flowrate at the edge. A full sensitivity analysis to model parameters is performed, and the conditions required to avoid an unphysical or asymptotically invalid result are discussed. An extension to non-Newtonian rheology is then presented.

How to cite: Di Federico, V., Lenci, A., and Ciriello, V.: Drainage of viscous gravity currents from the edge of a porous or fractured domain with variable properties, EGU General Assembly 2021, online, 19–30 Apr 2021, EGU21-9130,, 2021.