<div className="">
    <a className="inline-flex items-center text-gray-500 bg-transparent border border-solid border-gray-500 hover:bg-gray-100 hover:text-white active:bg-gray-600 font-bold uppercase text-sm px-6 py-3 rounded-full outline-none focus:outline-none mr-1 mb-1" href="https://ogata.amphos21.com/" target="_blank">Launch Experiment</a>
</div>

Background
=========

Numerical modelling is nowadays the reference tool to simulate and predict the behaviour of hydrogeological systems. This fact, however, has not stopped the research and the continuous development of analytical solutions for the different porous media equations. Analytical solutions are still useful tools today for  system understanding and fast prediction scenarios.

At Amphos21, we also use analytical solutions to verify code developments. They are valuable resources to validate numerical implementations and explore the numerical method limits for handling certain physics (for example advection predominant problems when using FEM). 

In the last years, we have been involved in the development of different reactive transport codes. For their verification, we have been using intensively the analyitical solution **Differential Equation of Longitudinal Dispersion in Porous Media** provided by Akio Ogata and R. B. Banks (1961). This solution does not involve chemical reactions, we use it mainly to verify that the conservative tracers are handled correctly. This way we have fast feedback to determine if possible differences in reactive species are caused or not by errors or wrong settings in the solute transport equation resolution. 

See this use on one of the <a href="/technology/interface-comsol-phreeqc">iCP</a> verification problems (**Figure 1**). The chloride, which is a conservative species in this case, fits to the analytical solution.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/ogata_and_banks_image_2_4396a8693e.png" alt=""/>
  <figcaption><b>Figure 1</b>. Comparison between iCP, Phreeqc and a numerical solution (for Cl) for the cation exchange (example 11) problem extracted from the Phreeqc Manual.</figcaption>
</figure>

Ogata and Banks 1961
==================
Ogata and Banks analytical solution dates from 1961 and can be found in the following <a href="https://pubs.usgs.gov/pp/0411a/report.pdf">USGS report</a>. 

It solves the ADE  equation for a *Continuous Source of Infinite Duration* and a 1D domain:

$$
R \frac{\partial c}{\partial t} = - u \frac{ \partial c}{\partial x} + D\frac{ \partial ^2 c}{\partial x}  
$$

with the following boundary and initial conditions:

$$
\begin{aligned}
c(0, t) = c_o; t \geq 0 \\
c(\infty, t) = 0; t \geq 0 \\
c(x, 0) = 0; x \geq 0 \\
\end{aligned}
$$

where $c$ is the concentration $[ML^{- 3}]$, $x$ is the distance $[L]$, $R$ is the retardation factor $[-]$, $D$ the effective dispersion/difusion $[L^2 T^{- 1}]$, $u$ the flow velocity $[LT^{-1}]$ and $c_o$ the concentration at the upstream boundary $[ML^{- 3}]$.

The analytical solution is:

$$
\begin{aligned}
c(x, t) = \frac{c_o}{2} \left[ \text{erfc} \left(
\frac{x-ut}{2 \sqrt{Dt/R} }
\right)
+\text{exp} \left(
\frac{ux}{D/R }
\right)
\text{erfc} \left(
\frac{x+ut}{2 \sqrt{Dt/R} }
\right)
\right]
\end{aligned}
$$

Experiment
==========
We have implemented the Ogata and Banks solution in a <a href="https://ogata.amphos21.com">web application</a> to predict quickly the arrival concentrations at a distance $x$. We use it to have first estimations of tracer arrival times and the role that play different parameters on modifying the arrival curve shape.

Just set your simulation parameters and play **Add Curve** to get your results. We hope you enjoyed it!

<a href="https://ogata.amphos21.com">
<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/ogata_and_banks_image_1_1e2c757c6d.png" alt=""/>

</figure>
</a>

References
==========
*Ogata, A., & Banks, R. B.* (1961). **A solution of the differential equation of longitudinal dispersion in porous media: fluid movement in earth materials.** US Government Printing Office.


large_ogata_and_banks_image_2.png

medium_ogata_and_banks_image_2.png

small_ogata_and_banks_image_2.png

thumbnail_ogata_and_banks_image_2.png

ogata_and_banks_image_2.png

A Solution of the Differential Equation of Longitudinal Dispersion in Porous Media

Ogata and Banks Analytical Solution

The safety of Deep Geological Repositories (DGR) for spent nuclear fuel is a highly important issue, and should be assessed using the Best Available Technology (BAT). With this motivation in mind, Amphos 21 has recently developed a numerical tool, denoted as iDP (interface between DarcyTools and PFLOTRAN; Molinero et al., 2016), which provides aJuqueen unique High Performance Computing(HPC)-based framework for the simulation of multicomponent reactive transport problems in fractured crystalline media. iDP combines two powerful state-of-the-art software: DarcyTools (Svensson and Ferry, 2014), which is used to compute groundwater flow in sparsely fractured rocks using a stochastic continuum approach, and the massively parallel reactive transport code PFLOTRAN (Hammond and Lichtner, 2010). iDP has been tested during the JUQUEEN Extreme Scaling Workshop 2016 (Brömmel et al., 2016) showing excellent scalability up to 131,072 processes (8 racks).

<figure className="image">
  <StrapiImage  src="/uploads/HPC_Blog_Post_1_c4a1155a9d.png" alt=""/>
  <figcaption> </figcaption>
</figure>

<div className="grid grid-cols-5 gap-4">
  <div className="col-span-2">
    <StrapiImage  className="" src="/uploads/HPC_Blog_Post_2_9212e50e5d.jpg"/>
</div>

  <div className="col-span-3">
In cooperation with the Forschungszentrum Jülich and the Swedish Nuclear Fuel and Waste Management Company (SKB), Amphos 21 has used iDP to carry out two challenging reactive transport simulations. The first set of calculations has focused on evaluating the potential ingress of oxygenated glacial-meltwater into initially anoxic fractured media. This is an issue of concern for the safety of deep geological Pocos de Caldasrepositories for spent nuclear fuel as oxidizing conditions would increase the solubility and mobility of many radionuclides and O2-rich waters would corrode canister materials containing the nuclear waste.
</div>
</div>

<div className="grid grid-cols-7 gap-4">

  <div className="col-span-5">
The reactive transport models have pointed out the strong buffering capacity of a typical crystalline medium (e.g. Forsmark in Sweden), with the infiltration of oxygen being limited to few highly transmissive deformation zones. These findings are in agreement with data from the natural analogue site of Poços de Caldas (Brazil) (Nordstrom et al., 1992). For more details about these reactive transport simulations, the reader is referred to a paper recently published in Journal of Contaminant Hydrology (Trinchero et al, 2017a).
</div>
  <div className="col-span-2">
    <StrapiImage  className="" src="/uploads/HPC_Blog_Post_4_7e2c2e6e88.jpg"/>
</div>
</div>



Another important issue for the safety of a DGR is related to the potential of the host rock to retain those radionuclides that are released due to a possible failure of the engineered barriers.Total CS This potential, in turn, depends on two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces of the available reactive minerals. A typical modelling assumption is to use an equivalent (homogeneous) description of sorption sites. This assumption is here assessed using a very detailed micro-scale model of the rock matrix, which is built upon a numerical grid consisting of more than 50 million elements. The results of the calculations, in which the distribution of sorption sites is described at the grain scale, show that mineralogical heterogeneity has a significant impact on the retention of radionuclides, namely cesium. Not considering that sorption sites are sparse and unevenly distributed results in an important overestimation of the rock retention capacity. Further details can be found in a paper recently published in Transport in Porous Media (Trinchero et al., 2017b).

<figure className="image">
  <StrapiImage  src="/uploads/HPC_Blog_Post_5_7a7da1df76.png" alt=""/>
  <figcaption> </figcaption>
</figure>


Acknowledgement
==============
This work has been funded by the Swedish Nuclear Fuel and Waste Management Company (SKB). The authors gratefully acknowledge the computing time granted by the JARA-HPC Vergabegremium and provided on the JARA-HPC Partition part of the supercomputer JUQUEEN at Forschungszentrum Jülich. The authors also thank Ignasi Puigdomenech, Björn Gylling, Guido Deissmann, Urban Svensson, Glenn Hammond, Peter Lichtner and the PFLOTRAN development group for their help and valuable suggestions during the project.

References
=========
*Brömmel, D., Wylie, B. J., Frings, W.*, 2016.** JUQUEEN extreme scaling workshop 2016. **Tech. Rep. FZJ-JSC-IB-2016-01, Jülich Supercomputing Centre.

*Hammond, G. E., Lichtner, P. C.*, 2010. **Field-scale model for the natural attenuation of uranium at the Hanford 300 area using high-performance computing. **Water Resources Research 46 (9), W09527, 131.

*Molinero, J., Trinchero, P., Ebrahimi, H., de Vries, L., Luna, M., Svensson, U., Lichtner, P. *2016. **The BRIDGE project: development, testing and application of a High Performance Computing framework for reactive transport modelling in crystalline roks (iDP)**. R-15-17, Svensk Kärnbränslehantering AB, Stockholm, Sweden.

*Nordstrom, D., McNutt, R., Puigdomènech, I., Smellie, J. A., Wolf, M. *1992. **Ground water chemistry and geochemical modeling of water-rock interactions at the Osamu Utsumi mine and the Morro do Ferro analogue study sites,** Poços de Caldas, Minas Gerais, Brazil. Journal of Geochemical Exploration 45 (1-3), 249-287

*Svensson, U., Ferry, M., *2014. **Darcytools: A computer code for hydrogeological analysis of nuclear waste repositories in fractured rock. **Journal of Applied Mathematics and Physics 2 (06), 365.

*Trinchero, P., Molinero, J., Deissmann, G., Svensson, U., Gylling, B., Ebrahimi, H., Hammond, G., Bosbach, D., Puigdomenech, I.*, 2017b.** Implications of grain-scale mineralogical heterogeneity for radionuclide transport in fractured media.** Transport in Porous Media 116: 73. doi:10.1007/s11242-016-0765-0

*Trinchero, P., Puigdomenech, I., Molinero, J., Ebrahimi, H., Gylling, B., Svensson, U., Bosbach, D., Deissmann, G.*, 2017a. **Continuum-based DFN-consistent numerical framework for the simulation of oxygen infiltration into fractured crystalline rocks. **Journal of Contaminant Hydrology DOI: 10.1016/j.jconhyd.2017.04.001

large_HPC_BlogPost_1.png

medium_HPC_BlogPost_1.png

small_HPC_BlogPost_1.png

thumbnail_HPC_BlogPost_1.png

HPC_BlogPost_1.png

The safety of Deep Geological Repositories (DGR) for spent nuclear fuel is a highly important issue, and should be assessed using the Best Available Technology (BAT)

High Performance Computing as a prognostic tool for Deep Geological Repositories for spent nuclear fuel

The Challenge
===========

Physical transport in a heterogeneous porous media and non-uniform distributions of chemical and biological species in the natural subsurface environment exert scaling behavior of reactive transport processes. In most cases the fully characterization of the system is impossible because of the inherent random distribution of the material properties. This has led to the development of reactive transport models across a wide range of spatial scales. Continuum scale models (e.g. Darcy equation for flow) and spatial averaging, smooth out any heterogeneity of a scale comparable or smaller than the representative elementary volume (grid-spacing). The advances in both computational power and the development of new numerical algorithms, have made possible pore-scale calculations including advection and diffusion of reactant in a solid matrix with a complex topology. Pore-scale models are capable of simulating complex interplay and non-linear coupling between surface reactions, flow and diffusive transport as well as ability to solve for the distribution of reactant inside pores. One of such numerical paradigm is the lattice Boltzmann method (LBM) that was developed as an extension to cellular automata models for fluid flows [1,2,3].

Lattice Boltzmann Method
===================
The LBM approaches mass and momentum conservation equations from a kinetic theory standpoint, where the macroscopic variables of interest, the local density (or pressure with an equation of state) and momentum of the fluid are retrieved from the statistical moments of particle distribution functions that follow the evolution of a discrete set of Boltzmann kinetic equations (<b>Figure 1</b>).

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Lattice_Boltzmann_Phreeqc_1_6e78b3f9e4.png" alt=""/>
  <figcaption><b>Figure 1</b>. Lattice topologies and lattice velocity indexing for the D2Q9 (a) and D2Q5 (b). (c) Schematic illustration of the bounce-back boundary condition at fluid–solid interfaces. The real and effective (numerical) boundaries are shifted by half a node for a straight interface (1st order accuracy) lattices. (d) Phase-field approach to surface reactions. Interface fluid nodes are considered for precipitation and interface solid nodes for dissolution. We use two flag variables, the first one is which corresponds to the type of nodes (solid or fluid dominated) and the second ζ which is null for all site but interface nodes where they can be   -1 depending on there location with respect to the fluid–solid interface [2].</figcaption>
</figure>

A pore-scale reactive transport model based on LBM has been previously developed to study heterogeneous dissolution-precipitation and sorption reactions in a complex porous media [1,2] (<b>Figure 2</b>). The model was successfully validated with analytical solutions of various 1D and 2D reactive transport problems. It uses recent advances in the development of optimal advection-diffusion solvers within the lattice Boltzmann method framework. Another novelty of the model is that the treatment of surface reaction is independent of the fluid-rock interface topology and orientation.

<figure className="image">
<iframe width="560" height="315" src="https://www.youtube.com/embed/aDrscAjmYO8" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>
  <figcaption><b>Figure 2</b>. Simulating arsenic sorption on various iron minerals (i.e. ferrihydrite, goethite and magnetite). Panel (a) depicts 2D distribution of disolved arsenic in the pore space while panels (b), (c) and (d) illustrates adsorbed arsenic concentrations on ferrihydrite, goethite and magnetite, respectively. Concentrations have been normalized with respect to their inital values.</figcaption>
</figure>

The new coupled LBM-PhreeqcRM model (LAMP) uses flow and transport solver based on the Lattice Boltzmann method with the chemistry solver PhreeqcRM in the pore-scale system. PhreeqcRM is a newly-developed geochemical reaction module designed specifically to perform equilibrium and kinetic reaction calculations for reactive transport simulators that use an operator-splitting approach [4]. It comprises methods to transfer concentrations and other model properties, and retrieve selected outputs. Coupling with PhreeqcRM enables the existing multicomponent pore-scale transport model to be extended to simulate wide range of geochemical reactions.

The coupling procedure includes: initialization of the domain for initial and boundary conditions with PHREEQC; transferring the data to the LBM-based flow and transport solver; performing transport step; transferring the data to PHREEQC and performing the reactions; and update porous media (if dissolution-precipitations occurs) and sending back to transport model until the final convergence and time step is reached.

Results and Discussion
==================
To test the accuracy of the coupling procedure, two verification problems were solved using LAMP: 1) chloride tracer test and 2) ion-exchange. Both scenarios were run in a 2D micro channel and results were compared with the ones obtained from a 1D Darcy-scale PHREEQC model. In the first example a boundary water with a chloride concentration of 0.001 mol/kgw is injected at the inlet of the domain, progressively displacing the initial water with zero concentration of chloride (<b>Figure 3</b>). The cross-section chloride concentration profile resembles the classis parabolic velocity profile in a 2D channel i.e. higher Cl concentration along the centerline of the channel while decreasing as it approaches to the walls. As water continues infiltrating from the inlet, peak of the profile approaches to Cl concentration of 0.001 mol/kgw and once it reaches to the maximum value, the sharp parabolic front flattens as Cl concentrations gradually increase towards the vicinity of the walls.

In the second example, similar physical setup is used while it is assumed that ion-exchange reactions take place along the walls of the channel (<b>Figure 3a</b>). Initially the medium contains an equilibrated potassium-sodium-nitrate solution with cation exchanger. The initial water, then is flushed with boundary water composed of calcium-chloride solution. In order to assess the effect of cation exchanger on the composition of the effluent, two points along the cross section of the channel is chosen: one in the middle of the cross section of the channel and the other in the vicinity of boundary wall. Close to the longitudinal boundary, results show that sodium initially present in the column exchanges with the incoming calcium and its concentration reaches to a fixed value as long as the exchanger contains sodium. In the centerline point, however, sodium is flushed out of the system as cation exchange reaction doesn’t take place. Potassium, close to the wall, is released after sodium because of larger K value in the exchange reaction and reaches a constant concentration after an initial increase. Similar to sodium, potassium is completely displaced by the boundary water along the centerline.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Lattice_Boltzmann_Phreeqc_3_2db7e086d6.png" alt=""/>
  <figcaption><b>Figure 3</b>.  (a) Micro-channel geometry used for chloride transport and cation-exchange scenarios. In the cation-exchange problem it was assumed that exchanger exists along the longitudinal boundary walls. (b) Chloride front at the cross section of the channel (shown with the red line).</figcaption>
</figure>

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Lattice_Boltzmann_Phreeqc_4_699a1424c8.png" alt=""/>
  <figcaption><b>Figure 4</b>. Temporal evolution of the aqueous species concentrations at points close to the boundary walls (where cation exchangers exist) and at the centerline.</figcaption>
</figure>

Acknowledgments
==================
The LBM transport solver was developed at Georgia Institute of Technology in collaboration with Dr. Christian Huber, and Dr. Andrea Parmigiani. Their contributions are gratefully acknowledged.

References:
==================
[1] Shafei, B., Huber, C., Parmigiani, A., 2013. Pore-scale simulation of calcite dissolution and precipitation using lattice Boltzmann method. Mineralogical Magezine 77 (5).

 [2] Huber, C., Shafei, B., Parmigiani, A., 2014. A new pore-scale model for linear and non-linear heterogeneous dissolution and precipitation. Geochimica et Cosmochimica Acta 124, 109-130.

[3] Kang, Q.J., Chen, L., Valocchi, A.J., Viswanathan, H.S., 2014. Pore-scale study of dissolution-induced changes in permeability and porosity of porous media. Journal of Hydrology 517, 1049-1055.

 [4] Parkhurst, D., Wissmeier, L., 2015. PhreeqcRM: A reaction module for transport simulators based on the geochemical model PHREEQC. Advances in Water Resources 83, 176-189.

large_Lattice_Boltzmann_Phreeqc_1.png

medium_Lattice_Boltzmann_Phreeqc_1.png

small_Lattice_Boltzmann_Phreeqc_1.png

thumbnail_Lattice_Boltzmann_Phreeqc_1.png

Lattice_Boltzmann_Phreeqc_1.png

In this post, Reza Gooya (University of Copenhagen), Babak Shafei and Fidel Grandia, blog about a recently-developed coupled pore-scale lattice Boltzmann method with PhreeqcRM (LAMP).

A new coupled pore-scale LAttice Boltzmann Method with PhreeqcRM (LAMP)

Model description
===============
 
A simple 2D domain has been used to explore the methodology for implementing the water age calculation.
 

Figure 1 shows the geometry, parameters and boundary conditions of the example. It can be seen that groundwater will enter the domain by the upper left part (left red segment) and discharge through the upper right part (right red segment).

 

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_1_6dbbff6e87.png" alt=""/>
  <figcaption>Figure 1. Sketch of the model.</figcaption>
</figure>



 
Mode 1: Transient simulation
=====================
Equation solved
------------------
 

For this model, a simple transport equation of an instant pulse of tracer (entering the domain) must be solved. Then, the equation that must be solved to computed groundwater age was proposed by Goode D.J.,1996:

 
$$
A=\frac{\int_{0}^\tau c(t) t dt}{\int_{0}^\tau c(t) dt}
$$


Where *A* is the “Water age”, *t* is the time, *C* is the concentration of tracer and $\tau$ is the total duration of the tracer pulse.

 
Implementation in Comsol
-----------------------------------
The transport boundary condition is a prescribed concentration on the recharge zone (hydraulic head=1), and open boundary in the discharge zone (hydraulic head=0). No flux is prescribed in the rest of the boundaries.

The required instant pulse of tracer was implemented by using the Comsol capability to create a time function associated to the boundary condition. This step function could be used as time function “step(t)” in the solute transport physics. A prescribed concentration boundary condition, associated to the time function “step(t)” was used to generate the pulse, as shown in Figure 2 and 3.

 <figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_2_df8d64e13a.png" alt=""/>
  <figcaption>Figure 2. Example of step function in Comsol.</figcaption>
</figure>

The model is then solved in a transient mode until all tracer concentration exits the model domain. 
 
 <figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_3_09a6ce429f.png" alt=""/>
  <figcaption>Figure 3. Implementing the step function in the transpor boundary conditions.</figcaption>
</figure>


The time integration equation is implemented in the results section using the function timeint(from,to,variable) where from and to are t=0 and the time when all tracer exits the domain, respectively. In this case the expression needed is:

 

**timeint(t0,T,c*t)/timeint(t0,T,c)**

 

Where t<sub>0</sub> and *T* is the initial and final time respectively for the integral and *c* is the solute concentration.

The result of use this expression is a surface showing the computed water age, as shown in Figure 4.

 <figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_4_cb683ddc94.png" alt=""/>
  <figcaption>Figure 4. Results of transient method. Time in days.</figcaption>
</figure>
 

Mode 2: Steady state
==================
Equation solved
----------------
 

The equation solved for steady state method is:

 $$
\frac{\partial A}{\partial t}= 1 - \nabla \cdot A \frac{\mathbf{q}}{\theta} + \nabla \mathbf{D}  \nabla A + \frac{F}{\theta \rho}
$$


Where A is the water age (seconds), q is the Darcy flux (m/s), D is the dispersion tensor (m2/s), (Theta) is the porosity, ρ is the density (kg/m3) and F is the source term (equal to 0 in the conceptual model). In steady state the temporal term dA/dt is equal to 0.

Implementation in Comsol
-------------------------------
 

In this method the transport boundary conditions are open boundary for zones with prescribed hydraulic head and no flux for the rest of boundaries. Also a source term in all domain is needed to obtain the water age, the value of the source term is equal to one in the equation, if we use Darcy flux (q) and effective diffusion coefficient the source term must be the porosity, as shown in Figure 5.

 
 <figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_5_64d35d5069.png" alt=""/>
  <figcaption>Figure 5. Solute source condition with a value equal to porosity.</figcaption>
</figure>




 

The computed water age is shown in Figure 6. It can be seen that computed results with the steady-state methodology is almost identical to what was computed at the transient approach (Figure 4).

 


 <figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/groundwater_age_figure_6_d2ad378405.png" alt=""/>
  <figcaption>Figure 6.Results of steady-state method. Time in days.</figcaption>
</figure>


 

Summary and conclusions
=====================

Two different approaches have been implemented in Comsol Multiphysics for calculating the water age in an aquifer. The steady-state methodology is easier, more accurate and much faster than the transient approach.

Acknowledgements   
===============

My more sincere thanks to Elena Abarca by her guidance and good advices and to Paolo Trinchero by his help to solve the steady state approach.

 

References
==========

*Goode D J,* (1996). **Direct simulation of groundwater age. **Water resources research, vol 32.n No.12, pages 289-296

medium_groundwater_age_figure_6.png

small_groundwater_age_figure_6.png

thumbnail_groundwater_age_figure_6.png

groundwater_age_figure_6.png

This post is intended to illustrate how to calculate the water age in a volume (3D model) or surface (2D model) based in the methodology proposed by Goode D.J. (1996).

Computing groundwater age in Comsol Multiphysics: implementation of transient and steady-state methodologies

Scope and objectives
==================
In the framework of safety assessment studies for depth geological disposal of nuclear waste, important scientific efforts are needed in order to understand the feasibility of the planned repositories. This is precisely the case of Olkiluoto in Finland, where the land uplift, related to the withdrawal of ice from the last glacial Age, plays a pivotal role in the hydrogeological patterns of the site. It is thus very important to improve the knowledge about the past evolution of the hydrogeological and geochemical conditions. In fact, as a result of land uplift, the infiltration of meteoric water could have triggered weathering processes, which, in turn, have impact on key parameters controlling the long-term stability of the planned repository (pH and redox conditions, availability of mineral buffers, etc). Furthermore, the presence of sulphate-rich waters along with bacterial communities and substrate might activate microbial mediated sulphate reduction processes with the related generation of, which is a detrimental agent for the copper canisters where the waste is placed.

<figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/coupled_palaehydrogeological_microbial_figure_1_4d26cbef8c.png" alt=""/>
  <figcaption>Geographical location of Olkiluoto Island and related fractured system object of simulations. It is shown the initial density field in depth.</figcaption>
</figure>

Numerical model
==============
In order to improve the understanding of the effect of the aforementioned events on the current hydrochemical conditions, we have developed a complex three-dimensional palaehydrogeological reactive transport model of the Olkiluoto site. The model consist of four hydrogeological zones of the Well Characterized Area (WCA), namely BFZ100, HZ19A, HZ19B and HZ19C. The Palaeohydrogelogical Reactive Transport (PRT) simulations, which spans 2000 years (from 0AD to present), aim at capturing the mutual interplay of different processes (i.e. land uplift, intrusion of meteoric water, weathering, mixing of waters etc.). The hydrogeological zones are simulated as two-dimensional planes within a three-dimensional domain. 

 <figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/coupled_palaehydrogeological_microbial_figure_2_d60154d447.png" alt=""/>
  <figcaption>Detail of the hydrogeological zones and FE grid</figcaption>
</figure>

The numerical model has been implemented using the Interface COMSOL-PHREEQC (iCP), which has been developed and validated by Amphos 21. To increase the reliability of the PRT simulations, groundwater flow parameters (i.e. residual pressures and density fields) are taken from an existing  palaeohydrogeological flow model (Löfman and Karvonen, 2012)

Some Results
===========
After some preliminary runs, different sets of three-dimensional PRT simulations have been carried out. In each of these simulations the geochemical complexity of the system has been progressively increased by including new processes (e.g. mineral equilibrium → mineral equilibrium and kinetics → mineral equilibrium, mineral kinetics and cation exchange). 

 
 <figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/coupled_palaehydrogeological_microbial_figure_3_0ff817dfc0.png" alt=""/>
  <figcaption>Detail of sulphide distribution in mol/L (x10-5) for 2000 AD</figcaption>
</figure>


 <figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/coupled_palaehydrogeological_microbial_figure_4_ba61628795.png" alt=""/>
  <figcaption>Detail of calcite distribution in mol/Kg for 2000 AD</figcaption>
</figure>

The results of the PRT simulations have been compared with the available field data and the general good agreement of the results has highlighted both the reliability of the model and its potential for the prediction of the  future evolution of the geochemical conditions at Olkiluoto.

 <figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/coupled_palaehydrogeological_microbial_figure_5_b154cae116.png" alt=""/>
  <figcaption>Sulphate distribution in depth for 2000 AD</figcaption>
</figure>

Acknowledgements
=================
This work has been funded by POSIVA. Amphos 21 wants to thank Petteri Pitkänen and Lasse Koskinen for their support and very helpful comments. Miguel Luna also wants to thank the coauthors of this work: Paolo Trinchero and Jorge Molinero.

medium_coupled_palaehydrogeological_microbial_figure_2.png

small_coupled_palaehydrogeological_microbial_figure_2.png

thumbnail_coupled_palaehydrogeological_microbial_figure_2.png

coupled_palaehydrogeological_microbial_figure_2.png

A large-scale, long-term simulation of the hydrogeochemical behaviour of fractured rocks is shown in this post. 

Coupled Palaehydrogeological Microbial and Geochemical Reactive Transport Model of the Olkiluoto Site (Finland)

The challenge
=============

The Swedish Organization for Radioactive Waste Management, SKB, plans the disposal of spent nuclear fuel in a deep geological repository. Bentonite clay is planned to be used around the cylindrical waste packages as buffer material due to its low permeability and high swelling properties. To assess alternative clay materials, SKB started a field experiment in 2006 [1] where packages of different types of compacted bentonite hollow cylinders were placed and heated (> 100 ºC) from the inside to target values during ~2.5yr (Figure 1). Post-mortem analysis indicated that initially contrasting cation-exchanger compositions between different bentonite blocks significantly homogenized already after 880 days (Figure 2). The question arose of whether these observations can be reasonably well described by our conventional tools and understanding of the underlying processes. 




<figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/modeling_bentonite_figure_01_902f919667.jpg" alt=""/>
  <figcaption>Installation of the package and conceptualization in Comsol model.  </figcaption>
</figure>

 

<figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/modeling_bentonite_figure_02_12c1723b4f.png" alt=""/>
  <figcaption>Initial (before) and final (after the experiment) exchanger composition in terms of unit fraction Na, Ca, Mg and K occupancy (empty: no data available).  </figcaption>
</figure>



 
Comsol: an ideal platform for simple tailored models
=======================================
 

To verify whether a simple reactive transport model coupling diffusion, cation-exchange and temperature evolution can explain the observed homogenisation of cation-exchanger composition, a simplistic geochemical model was implemented in Comsol and coupled to physical processes. The model considers different porewater compositions for each clay material assuming chemical equilibrium and only 5 ionic species: Na+, Ca2+, Mg2+, K+ and Cl-. Fickian diffusion (coupled to temperature evolution based on experimental data) is the only transport process while cation-exchange is the only type of chemical reactions implemented. The implementation of diffusion uses the “Solute Transport” Interface, while cation-exchange is set through a system of coupled non-linear algebraic equations. Transport-Chemistry coupling uses the approach proposed in [2] and solved using Operator Splitting. More details can be found in [3].

 

Results: when modeling meets real experiments
=====================================

In conjunction with a composite boundary type (Figure 3) based on fracture logging measurements, the simple model is capable of reproducing the experimental data with reasonably good accuracy, especially for the dominant cations (Ca and Na). A relatively poorer fit for Mg is observed in the top (although still unclear, it could be due to additional chemical reactions or altered groundwater composition). Thus, we see how a very simple model (Figure 4) can be very useful to gain insight in the experiment evolution and serve as a basis for discussion between experimentalists. The model independently showed that part of the homogenization is most probably due to the higher water renewal in the fractured zone of the deposition hole.

 


<figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/modeling_bentonite_figure_03_d0d83660ea.png" alt=""/>
  <figcaption>Left – schematic representation of the model domain and its boundaries (blue: no-flux, red: constant concentration). Right – final experimental and simulated exchanger compositions (after 880 days) across the package.</figcaption>
</figure>

 

<figure className="image">
  <StrapiImage  className="mx-auto"  src="/uploads/modeling_bentonite_figure_04_9c89975751.png" alt=""/>
  <figcaption>Time evolution of Ca unit fraction on the cation exchanger. From initial 
</figcaption>
</figure>
 

Acknowledgments
==============
This work was made possible by the financial support from SKB and has been conducted at Amphos 21 by Marek Pekala, Andrés Idiart, Albert Nardi, and David Arcos. Their contributions are gratefully acknowledged.

References
=========
[1] *Svensson D. et al.,* 2011. Alternative Buffer Material – **Status of the ongoing laboratory investigation of reference materials and test package **1. SKB TR-11-06.

[2] *Saaltink M. et al., *1998.** A mathematical formulation for reactive transport that eliminates mineral concentrations. **Water Resources Research, 34, 1649-1656.

[3] *Idiart AE, Pękala M, Nardi A, Arcos D,* 2012. **Reactive transport processes in compacted bentonite. Application to a prototype experiment of underground repository for nuclear waste. **Int. Meeting Clays in Natural & Engineered Barriers for Radioactive Waste Confinement, Montpellier, France.



large_modeling_bentonite_figure_04.png

medium_modeling_bentonite_figure_04.png

small_modeling_bentonite_figure_04.png

thumbnail_modeling_bentonite_figure_04.png

modeling_bentonite_figure_04.png

This post is about a recent application case of Comsol in the field of thermo-hydro-geochemical behavior of clayey materials 

Modeling reactive transport processes of an in-situ test in compacted bentonite

Background and motivation
======================

In performance assessment (PA) studies of nuclear waste repositories, numerical simulations are used to study the potential impact of the release and transport of radionuclides in the near and far field. These simulations are typically carried out using a lumped approach: the different and highly non-linear underlying radionuclide retention processes are represented by a single parameter, the distribution coefficient (Kd), which relates the radionuclide mass retained in the solid phase to its aqueous concentration.

Kd-based simulations, which are particularly appealing due to their numerical efficiency, are mathematically robust but usually rely on an important assumption: the Kd value of each radionuclide is constant in time. This assumption could be critical when geochemical conditions are changing dramatically (e.g. in the transition from temperate to glacial conditions), as distribution coefficients depend on the pH, redox conditions and major chemistry of the system.

We have recently developed and tested a framework (interface to Marfa - iFM) that constitutes a significant improvement over the traditional constant Kd-based models. The basic premise of this approach is that the “background” geochemistry (excluding radionuclides) is first be pre-calculated using a reactive transport code in order to generate a dataset of Kd values in space and time that are representative of the actual geochemical conditions in the considered spatial and temporal domain. This information is then used by the computer code Migration Analysis of Radionuclides in the Far Field (MARFA) [1,2] to calculate radionuclide transport based on these “intelligent” Kd values.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/smart_Kd_figure_1_bb6a5d7027.png" alt=""/>
  <figcaption>Sketch showing a typical radionuclide transport problem. Radionuclides, which are released at repository depth, move along a number of transport pathways and are discharged into the biosphere.</figcaption>
</figure>

The tool: iFM version 2.0
=====================
The figure below shows a workflow of iFM v2.0.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/smart_Kd_figure_2_2eeb82baaa.png" alt=""/>
  <figcaption>Functionality overview of iFM v2.0. </figcaption>
</figure>

The numerical tool consists of two sets of numerical calculations:

- FASTREACT [3] simulates transport and geochemical reactions along the same set of transport pathwasy used by MARFA. This simulation only accounts for the background geochemistry (without radionuclides).
- PHREEQC batch calculations. At each time step, the background geochemical composition computed along the pathways (previous step) and an arbitrarily low concentration of the considered radionuclide(s) are used to perform zero-dimensional calculations. These batch calculations use a mechanistic description of the relevant sorption processes (e.g. surface complexation, cation exchange, etc) and provide as output quantitative information about the distribution coefficients, Kd, of each radionuclide at each location and at the considered simulation times.
 

Testing the tool – a synthetic example
======================

To test the robustness of the tool, we have solved a “typical" radionuclide waste performance assessment (PA) problem: the simulation of the migration of radionuclides from a deep geological repository to the surface.

A snapshot of a groundwater velocity field has been taken from an existing regional-scale three-dimensional hydrogeological model. Using particle tracking simulations, a number of transport pathways have been delineated.

Radionuclides have been released during a small time interval compared to the time frame of the problem. Initially, glacial conditions are assumed to prevail in the whole domain. After around 20,000 years, a different and less diluted water, representative of new temperate conditions, enters the model domain from the release boundary and propagates undisturbed along the streamlines.

The numerical exercises have been solved using (1) iFM+MARFA (see Figure below) and (2) FASTREACT.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/smart_Kd_figure_3_11bb3789da.png" alt=""/>
  <figcaption>Sketch that shows the approach and the different processes included in the iFM+MARFA simulations.</figcaption>
</figure>



The strontium breakthrough curves computed using iFM+MARFA and FASTREACT are shown in the Figure below. When strontium is overtaken by the geochemical perturbation, it is mobilized and moves nearly unretarded. Both simulations capture this effect and their results closely match each other. Thus, the verification exercise can be considered successful.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/smart_Kd_figure_4_671d85dc4e.png" alt=""/>
  <figcaption>Calculated breakthrough curve for strontium (iFM+MARFA: blue solid line; FASTREACT: orange dashed line).</figcaption>
</figure>

Acknowledgements
===============
This work is a collaborative project between SKB and POSIVA, the organizations in charge of managing nuclear fuel and radioactive waste in Sweden and Finland, respectively. Amphos 21 and Scott Painter want to thank Lasse Koskinen (POSIVA) and Jan-Olof Selroos (SKB) for their support and very helpful comments.

Paolo Trinchero also wants to thank the coauthors of this work: Luis Manuel de Vries, Jorge Molinero and Scott Painter.

References
=========
[1] *Painter, S., V. Cvetkovic, J.-O. Selroos, and O. Pensado.* (2007). **Time domain particle tracking methods for simulating transport with retention and first-order transformation. **Water Resources Research 43(9), W01406.

[2] *Painter, S., and Mancillas, J. *(2013). **MARFA User’s manual: migration analysis of radionuclides in the far field, **Working Report 2013-01, Posiva Oy.

[3]* Trinchero, P., Molinero, J., Román-Ross, G.* (2013) **A streamline-based approach for the solution of multicomponent reactive transport problems,** SKB report R-10-45.

 



medium_smart_Kd_figure_1.png

small_smart_Kd_figure_1.png

thumbnail_smart_Kd_figure_1.png

smart_Kd_figure_1.png

Distribution coefficients, also known as Kd values, are lumped parameters that contain information about the radionuclude-soil/rock interaction processes

An “intelligent” Kd approach for the simulation of radionuclide transport in the geosphere - iFM version 2.0

<div className="">
    <a className="inline-flex items-center text-gray-500 bg-transparent border border-solid border-gray-500 hover:bg-gray-100 hover:text-white active:bg-gray-600 font-bold uppercase text-sm px-6 py-3 rounded-full outline-none focus:outline-none mr-1 mb-1" href="https://nitrate.amphos21.com/" target="_blank">Launch Experiment</a>
</div>



Motivation
=============
Understanding the behaviour of pollutants in aquifers is a common issue we have to face as hydrogeologists. Numerical models are useful tools that allow us to predict the displacement and evolution of the pollutants in the subsurface.  For this modelling task we usually use well-known software, but we find important **keeping simple approaches in mind since they can be useful for learning about numerics insights and physics understanding**. 

To this end, we have developed a simple python program to compute the Advection-Diffusion equation  (Bear, 1972) with first order decay and degradation chain [Eq.1] in 1 dimension using finite differences. This **has been applied to simulate the nitrification chain**, the degradation of ammonium generates nitrite and this specie when degrades produces nitrate. ($NH_4^+ \rightarrow NO_2^- \rightarrow NO_3^-$).

Description
=============
The system modelled is represented by the following partial differential equations:

$$
\tag*{[Eq. 1]}
\begin{cases}
\frac{\partial NH_4^+}{\partial t}=D\frac{\partial^2 NH_4^+}{\partial x^2}-\frac{\partial}{\partial x }(aNH_4^+)-\lambda_1 NH_4^+\\
\frac{\partial NO_2^-}{\partial t}=D\frac{\partial^2 NO_2^-}{\partial x^2}-\frac{\partial}{\partial x }(aNO_2^-)+\lambda_1 NH_4^+-\lambda_2 N0_2^-\\
\frac{\partial NO_3^-}{\partial t}=D\frac{\partial^2 NO_3^-}{\partial x^2}-\frac{\partial}{\partial x }(aNO_3^-)+\lambda_2 N0_2^--\lambda_3 N0_3^-\\
\end{cases}
$$

Here, $a$ is the fluid velocity (water in the studied case) (m/s), $D$ is the diffusion coefficient ($m^2/s$) and $\lambda_i$ is the half-time of the $i$ species where 1 refers to $NH_4^+$, 2 is $NO_2^-$ and 3 is $NO_3^+$.


Obtained results (Figure 1) have been validated by comparing with the analytical solutions reported by (Cho et al. 1971).

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/numerical_vs_analytical_282d15042c.png" alt=""/>
  <figcaption>Figure 1. Analytical solution from (Cho et al. 1971) (solid lines) vs numerical solution (dashed lines).</figcaption>
</figure>


Numerical solution
==============
Previous to the **finite differences** scheme development, it is useful to define some terms:

- $L$ = Length of the domain.
- $N$ = number of grid points.
- $· x = L/N$ spatial discretization.
- $i$ is the position at the domain being, therefore, $i*· x$ where $i \in [O,N-1]$ is the real position.
- $T$ = Total simulation time.
- $k$ refers to a determined timestep being $· t$= time step and $k*·t$ the real time.

As can be seen in [Eq. 1] the proposed equation has a diffusive and a convective term. Using a Crank-Nicolson scheme for the diffusive term:

$$
	\frac{-D}{2· x^2}u^{k+1}_{i-1}+(\frac{1}{· t}+\frac{D}{· x^2})u_i^{k+1}-\frac{D}{2 · x^2}u^{k+1}_{i+1}=\frac{D}{2· x^2}u^{k}_{i-1}+(\frac{1}{· t}-\frac{D}{· x^2})u_i^{k}+\frac{D}{2 · x^2}u^{k}_{i+1}
$$

Here, $k$ is the current time and $i$ is the cell in the domain.

And for the advection term:
$$
	\frac{\partial au}{\partial x} \approx \frac{a}{4· x}(U_{i+1}^k-U_{i-1}^k+U_{i+1}^{k+1}-U_{i+1}^{k+1})
$$

Combining this two expressions, we obtain the advection diffussion equation in a cell point (i) at a time (k):

$$
 	\frac{U_i^{k+1}-U_i^k}{· t}=\frac{D}{2· x^2}(U_{i+1}^k-2U_i^k+U_{i-1}^k+U_{i+1}^{k+1}-2U_i^{k+1}+U_{i-1}^{k+1})+ \\ 
\frac{a}{4· x}(U_{i+1}^k-U_{i-1}^k+U_{i+1}^{k+1}-U_{i-1}^{k+1})-\lambda U_i^k
$$

We define $\sigma = \frac{D· t}{2· x^2}$ and $\rho = \frac{a· t}{4 · x}$. Reordering the previous approximation:

$$
 (-\sigma +\rho)U_{i-1}^{k+1}+(1+2\sigma)_i^{k+1}-(\sigma +\rho)_{i+1}^{k+1}=(\sigma -\rho)U_{i-1}^k+(1-2\sigma)U_i^k+(\sigma + \rho)U^k_{i+1}+· t (-\lambda U^k_i),\\
  i=1,..,N-2.	
$$

This equation holds for all grid points containing in the domain $i\in [1,N-2]$. The expression in the borders (0 and N-1) is given by the boundary conditions. In this case, we assume Neumann conditions in both boundaries.

The resulting expression for $i$ equal to $0$ and $N-1$ is:

$$
	 j=0: (1+\sigma +\rho)U_0^{k+1}-(\sigma+\rho)U_i^{k+1}=(1-\sigma -\rho)U_0^{k}+(\sigma+\rho)U_i^{k+1}+· t \lambda(U_0^{k})
$$

$$
 	 j=N-1: (-\sigma +\rho)U_{N-2}^{k+1}+(1+\sigma -\rho)U_{N-1}^{k+1}=(+\sigma -\rho)U_{N-2}^{k}+(1-\sigma +\rho)U_{N-1}^{k}+· t \lambda(U_{N-1}^{k})
$$

 The previous expression can be written as a linear system in matrix notation:

$$
 	AU^{k+1}=BU^{k}-f^k
$$

 Where:
$$

 A[NxN]=
 \begin{bmatrix}
 1+\sigma +\rho & -\sigma+\rho & 0 & 0 & 0  & 0 & 0 & 0\\
 -\sigma-\rho & 1+2\sigma &  -\sigma+\rho   & 0 & 0 & 0 & 0 & 0\\
0 &   -\sigma-\rho & 1+2\sigma &  -\sigma+\rho   & 0 & 0 & 0 & 0\\
 ... & ... &  ... & ... & ... & ... & ... &...\\
 ... & ... & ... & ... & ... &  ... & ... & ...\\
 0 & 0 & 0 & 0 &    -\sigma-\rho & 1+2\sigma &  -\sigma+\rho  &0\\
   0 & 0 & 0& 0 & 0 &    -\sigma-\rho& 1+2\sigma&  -\sigma+\rho \\
    0 & 0 & 0  & 0 & 0 & 0 &   -\sigma-\rho & 1+\sigma-\rho
 \end{bmatrix}
$$

$$
 B[NxN]=
 \begin{bmatrix}
 1-\sigma -\rho & \sigma-\rho & 0 & 0 & 0  & 0 & 0 & 0\\
 \sigma+\rho & 1-2\sigma & \sigma-\rho & 0 & 0 & 0 & 0 & 0\\
 0 &  \sigma+\rho& 1-2\sigma &  \sigma-\rho & 0 & 0 & 0 & 0\\
... & ... &  ... & ...& ... & ... & ... & ...\\
 ...& ... & ...& ... &... &  ... & ... & ...\\
 0 & 0 & 0 & 0 &  \sigma+\rho & 1-2\sigma &  \sigma-\rho &0\\
 0 & 0 & 0& 0 & 0 &  \sigma+\rho & 1-2\sigma&  \sigma-\rho\\
 0 & 0 & 0  & 0 & 0 & 0 &  \sigma+\rho & 1-\sigma+\rho
 \end{bmatrix}
$$

 $U^{k+1}$ and $U^k$ are the solution at a given time k and k+1.

$f$ is the source term which in our case is a vector of length $N$ with the following expression:

$$
f[N]= U^k\begin{bmatrix}
 	-· t \lambda ,-· t \lambda,....,-· t \lambda
 \end{bmatrix}
$$


Conclusions
==============
The proposed numerical scheme and its implementation are able to reproduce the results of the analytical solution reported by (Cho et al. 1971). The model describes the dissolved species movement through advection, diffusion and takes into account the degradation by first order decay.

References
===============
- *Cho C. M.*, 1971. **Convective transport of ammonium with nitrification in soil.Canadian journal of soil science.**
- *Bear J.,* 1972. **Fluid dynamics in porous media.**

medium_numerical_vs_analytical.png

small_numerical_vs_analytical.png

thumbnail_numerical_vs_analytical.png

numerical_vs_analytical.png

The current experiment presents a Crank-Nicolson scheme to solve the advection-diffusion equations

Modelling Advection-Dispersion with Decay Chains

We are pleased to announce the release of version 2.0 of iCP! iCP 2.0 includes new capabilities such as adding extra dimensions and chemo-mechanical couplings and has been updated for compatibility with the latest releases of Comsol and PhreeqC. 

You can download iCP 2.0 [here](/static/downloads/iCP-v2.0.zip) and you can request license by filling in the [license form](/form/icp-license-request/).

The following list outlines all the new capabilities/improvements added in iCP 2.0: 
- **Extra dimensions** can now be added to your reactive transport models. Extra dimensions extend a standard geometry with additional spatial dimensions and can be used to represent a rock matrix in a fracture-matrix system. The developments carried out in the iCP code allow to include chemical reactions in both domains, the extra dimension representing the matrix and the fracture. The main benefit of this methodology is the possibility to include matrix diffusion in discrete fracture networks (DFNs) of thousands of fractures with complex intersections, see for instance the animation below. It can be challenging or impossible to mesh the fractures and rock matrix with such a complex geometry. In this context, the extra dimensions of COMSOL can be very handy when the matrix has low permeability and transport is diffusion dominated. An example (Example 3) has been added to the examples library to demonstrate how to set up a model with extra dimensions. 

<figure className="image">
      <StrapiImage
        src="/uploads/extradim_dcd8cc3c5a.gif"  className="mx-auto" alt=""
      />
</figure>

- **Mechanical modelling** performed in Comsol can now be coupled with reactive transport with iCP.  These capabilities can be used to model the chemical degradation of concrete and its impact on mechanical properties (see animation below) or to predict the swelling potential of bentonite under different geochemical conditions. Chemo-mechanical coupling is demonstrated with Example 4 in the examples library. 

<figure className="image">
      <StrapiImage
        src="/uploads/mechanics_gif_9d4abcd0ff.gif"  className="mx-auto" alt=""
      />
</figure>

- The amount of exchanger and surface complexes specified in PhreeqC can now be updated from Comsol. This can be used to model variations in number of sites or cation exchange capacity due to mineral dissolution/precipitation. 

- iCP 2.0 is compatible with the latest releases of Comsol: versions 5.4, 5.5 and 5.6. iCP 2.0 by runs Comsol in Standalone mode (without Comsol server) by default, which improves computational performance and memory handling. Note that this option is not available with Comsol 5.5. 

- iCP 2.0 is compatible with Comsol physics that include internal DOFs. This means that physics can now be run with the Compute boundary fluxes option enabled.

- The IPhreeqC library has been updated to the latest version, 3.7.0.

- The default water content used by iCP (when it is not coupled) is now the value specified in the input PhreeqC files. Note that in previous versions this value was overwritten by default by 1 kg of water. 

- Error logging has been improved in iCP 2.0. When an error occurs in the chemical step, iCP now specifies the coordinates at which the error occurred. Also, when an error occurs in the transport step the full error message given by Comsol is displayed.


icp20.png

We are pleased to announce the release of version 2.0 of iCP! iCP 2.0 includes new capabilities such as adding extra dimensions and chemo-mechanical couplings.

iCP v2.0 release

Since 2000, Amphos 21 has been deeply involved in the development and maintenance of ThermoChimie, the database managed by Andra (France), RWM (UK) and Ondraf/Niras (Belgium).

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Thermo_Chimie_Online_1_6d6999db56.png" alt=""/>
</figure>

Since the beginning of this month, a new database version (10d) is available on-line (<a href="http://www.thermochimie-tdb.com">http://www.thermochimie-tdb.com</a>). This new version includes:

- Thermodynamic data for two new elements, **beryllium and copper**, of interest in radioactive waste disposal.
- Some **updates for palladium, nickel and trivalent lanthanides and actinides**.
- A **non-extensive update for some organic species**.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Thermo_Chimie_Online_2_c85fa5300b.png" alt=""/>
</figure>

The new database version can be consulted and downloaded in different formats compatible with the geochemical codes PhreeqC, Geochemist’s Workbench, Spana, Chess, Crunch and Toughreact.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/Thermo_Chimie_Online_3_c004f0feee.jpg" alt=""/>
</figure>

Further updates for iron and radionuclides are expected to be published early next year. If you are interested in the new releases, please stay tuned to the website  <a href="http://www.thermochimie-tdb.com">http://www.thermochimie-tdb.com</a> or contact consortium-tc3-tech@thermochimie-tdb.com for additional information.

medium_ThermoChimie_Online_1.png

small_ThermoChimie_Online_1.png

thumbnail_ThermoChimie_Online_1.png

ThermoChimie_Online_1.png

Since the beginning of this month, a new database version (10d) is available on-line (http://www.thermochimie-tdb.com)

New ThermoChimie database version is on-line

Since 2000, Amphos 21 has been deeply involved in the development and maintenance of ThermoChimie, the database managed by Andra (France), Nuclear Waste Services (UK) and Ondraf/Niras (Belgium).

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/thermochimie_11_1_088c1c1dd8.png" alt=""/>
</figure>
The ThermoChimie database is under constant revision and development. After its public release in 2014 and further updates in 2015, 2018 and 2021, <b> a new database version (11a) </b> is now <b><a href="http://www.thermochimie-tdb.com"> available on-line</a></b>  .

ThermoChimie version 11 contains significant updates on <b> U, Np, Pu, Am/Cm, and Tc</b>  following the NEA-TDB update (Grenthe et al. 2020) and beyond. In addition, an exhaustive and accurate review of Fe thermodynamic properties has been carried out, using the NEA-TDB reviews (Lemire et al. 2013, 2020) and additional literature publications. Furthermore, <b> PFlotran</b>  extraction has been newly added to the list of geochemical compatible codes.

<figure className="image">
  <StrapiImage className="mx-auto"  src="/uploads/thermochimie_11_2_11c25fd05a.png" alt=""/>
</figure>
A new <b> XCheck</b>  tool to consult, filter, retrieve and export the information available in the latest database version is also now available for the user’s at <a href="https://register.thermochimie-ctool.com">https://register.thermochimie-ctool.com</a>.

Please stay tuned to the website  http://www.thermochimie-tdb.com/ or contact consortium-tc3-tech@thermochimie-tdb.com for additional information.



large_thermochimie_11_1.png

medium_thermochimie_11_1.png

small_thermochimie_11_1.png

thumbnail_thermochimie_11_1.png

thermochimie_11_1.png

After its public release in 2014 and further updates in 2015, 2018 and 2021, a new database version (11a) is now available on-line.

ThermoChimie database version 11a released!

<a href="/technology/interface-comsol-phreeqc/">iCP</a> is an interface that couples COMSOL Multiphysics and PHREEQC. It is a powerful and flexible tool for reactive transport modelling in porous and fractured media developed by Amphos 21. iCP is used for a wide range of geoscientific applications that include geochemistry, with prominent case studies about geological disposal of radioactive waste, carbon capture and storage, and mining. Complex thermo-hydro-mechanical processes can be flexibly coupled with geochemistry in a single modelling framework. 

Amphos 21 is happy to announce the 2024 **fully online iCP Training** course that will be held between 11th and 14th November 2024 from 9:00 to 13:15 Spanish Time (UTC/GMT +1 hour).

The **16 hours online course** give you the tools to get started in reactive transport modelling with iCP, covering the following topics:

* **1st day (9/11/2024):**

    * iCP overview and installation
    * Introduction to PHREEQC, a geochemical simulator from USGS (USA), with practical examples
    * Introduction to COMSOL Multiphysics, focusing on flow and solute transport in porous media, with practical examples

* **2nd day (10/11/2024):**
    * Introduction to Reactive Transport Modelling
    * First Hands-on iCP example: Cation exchange

* **3rd day (11/11/2024):**
    * Second Hands-on iCP example: Calcite dissolution

* **4th day (12/11/2024):**
    * Advanced hands-on iCP example: thermo-hydro-geochemical couplings
    * Advanced applications of iCP, case studies, and on-going developments

After the course, you will be able to:
* Understand the fundamentals of reactive transport modelling and how to implement them in iCP,
* Work independently with the most important features of model setup in iCP,
* Leverage many of the advanced features and powerful functionalities of COMSOL and how to use them in combination with iCP,
* Setup your own geochemical systems in PHREEQC, a powerful geochemical simulator,
* Implement practical examples of flow and solute transport in porous media using COMSOL Multiphysics.


The course will be held by experts in the use of COMSOL, PHREEQC and iCP, with vast experience in the application of reactive transport modelling in geosciences:

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
    <StrapiImage src="/uploads/Albert_Nardi_5bef2c7183.jpg"/>
  </div>
  <div className="col-span-6">
    <p>
<b>Albert Nardi</b> is is Project Manager and Senior Consultant in Hydroinformatics, Software and Data Science at the Department of Digital Solutions of Amphos 21. He holds an Industrial Engineering degree and a Master in Hydrogeology from UPC (Spain). He is an expert in numerical modelling and software development. He is in charge of the development team of <a href="/technology/interface-comsol-phreeqc/">iCP</a> and also <a href="https://gibbsstudio.io/">GibbsStudio</a>.
    </p>
  </div>
</div>


<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Elena_Abarca_342eaced61.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Elena Abarca</b> leads the Department of Water Resources and Environment at Amphos 21. She holds a PhD in Hydrogeology from the UPC – Barcelona Tech. Her work focusses in numerical modelling of groundwater flow and reactive transport of contaminants in porous and fractured media. Before joining Amphos 21, she was a Post-Doctoral Research Associate at the Auburn University (USA) and the Massachusetts Institute of Technology (MIT, USA).
</p>
</div>
</div>

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Andres_Idiart_d564c47f22.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Andrés Idiart</b> is the Director of Operations at Amphos 21. He holds Civil Engineer with a PhD in Civil Engineering and Solid Mechanics from the UPC – Barcelona Tech and a post-doc in reactive transport modelling as a Marie Curie Research Fellow from the EDF-spin-off company Oxand S.A., in France. His fields of expertise include geomechanics and the coupling between multiphysics and geochemistry.
</p>
</div>
</div>

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Emilie_Cohene_d489bf9505.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Emilie Coene</b> is a Senior Consultant and iCP developer at Amphos 21, with a Chemical Engineering degree and a Master in Modelling for Science and Engineering from the UAB, Spain. She is an expert in numerical model development and application using iCP. She has been involved in numerous projects related with reactive transport and multiphase-flow models for geological disposal of radioactive waste, carbon capture and storage, and mining.
</p>
</div>
</div>

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Marcelo_Lavina_afedebdcb0.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Marcelo Laviña</b> is a Senior Consultant at Amphos 21. He obtained his Civil Engineering degree and Master of Science degrees from the Technical University of Madrid (UPM, Spain). His research at the Hydraulics Department of UPM was related with the modelling of hydro-geomechanical processes in fractured media. At Amphos 21, he is an expert in the development and implementation of coupled hydro-chemo-mechanical models in porous media for geological disposal of radioactive waste applications. 
</p>
</div>
</div>

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Diego_Sampietro_f4f90d94ce.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Diego Sampietro</b> is a Senior Consultant at Amphos 21. He is a Geologist from the University of Zaragoza (Spain) with a post-graduate course in Hydrogeology from UPC (Spain) and a Master’s degree in mathematical modelling from UAB (Spain). He is an expert in reactive transport modelling in fractured systems with iCP. As a Senior Consultant, he has been involved in several projects related with geological disposal of radioactive waste studies in different countries, such as Sweden, Finland, Spain, or Japan.
</p>
</div>
</div>

<div className="grid grid-cols-8 gap-4">
  <div className="col-span-2">
<StrapiImage src="/uploads/Ersan_Demirer_26f1b8af25.png"/>
</div>
  <div className="col-span-6">
<p>
<b>Ersan Demirer</b> is a Senior Consultant at Amphos 21 since 2021. He has a PhD in Mechanical Engineering from the Georgia Institute of Technology, focusing on computational fluid dynamics and particularly constructing numerical models to capture fluid-structure interaction phenomena. He is an expert in numerical modelling of transport phenomena, as well as computational mechanics and optimization methods. As a consultant at Amphos 21, he has been involved in nuclear waste management and Oil and Gas projects involving numerical modelling of multiphase flow and reactive transport in porous media such as concrete, clay, or carbonate rocks.
</p>
</div>
</div>


The cost of the course is:
* 1,500€ Early Bird Registration (before 30th of September 2024) 
* 1,700€ Standard (after 30th of September 2024).

The course includes the lectures, lecture material and one permanent R&D license per participant.

Course registration form is open until October 27th 2024 or until the maximum of registered participants is attained.

[Go to course registration form](/form/icp-course-registration-request)

If you have recently acquired an iCP license, you qualify for a discount on the course. Contact us for more info.  

For any questions or doubts, please contact us at techlabs@amphos21.com. 

We look forward to seeing you in November!



Reactive-transport