Methods for modelling and simulation of CO2

Methods for modelling and simulation of CO2 impurities and their reactive transport in geological storage reservoirs

Jan Lennard Wolf Federal Institute for Geosciences and Natural Resources (BGR) Stilleweg 2, 30655 Hannover [email protected], [email protected] Abstract: The consideration of CO2-stream impurities in numerical simulations of the reactive transport processes in saline aquifers as storage reservoirs is complex. Since the commonly applied modelling approaches “trace gas transport (TGT)” and “additional brine injection (ABI)” each suffer from specific inaccuracies and artefacts, an improved modelling approach using a mobile additional brine injection (mABI) was developed. This approach basically consists of a sequential computation of TOUGHREACT - MATLAB - TOUGHREACT simulation runs. It is currently limited to consideration of the geochemical impacts of SO2, NO2, O2, and H2. Yet it allows for the consideration of temporarily varying concentrations of these impurities in the injected CO2 stream. The presented work is part of the research project CLUSTER, in which the assessment of potential impacts of temporarily varying impurity concentrations is one of the main goals. The numerical results of simulations using the mABI approach reflect the dominant periods of varying impurity injection concentrations in the impurityinduced alteration of reservoir rock mineral composition. Hence, the presented modelling approach provides a promising tool for the geochemical evaluation of storage scenarios using impure CO2, if suffcient model validation on the basis of experimental data can be achieved in future work.

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Introduction

An important aspect for the technical realisation of a carbon capture and storage project (CCS) is the consideration of CO2-stream impurities and their impacts on capture, transport, and storage. Beside physical effects of impurities on, e.g., viscosity and density of the CO2-stream, some impurities such as SOx, H2S, NOx, H2 may cause significant chemical effects on pipeline material (corrosion) as well as on the rock material of a geological storage reservoir. A general concept for an economically feasible realisation of CCS projects could be the combination of several industrial CO2 sources with a common transport and storage infrastructure. With respect to CO2-stream impurities, this clustering would result in temporarily varying concentrations of individual impurities within the pipeline system, at the injection well, and subsequently within the storage reservoir. The qualitative and quantitative analysis of the impacts of this variability on the storage operation is the primary research goal of this study within the project CLUSTER. For the evaluation of the geochemical interactions of temporarily varying impurity concentrations with the reservoir rock material, reactive transport simulations have

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proven to provide valuable insides into the processes in the reservoir at in situ pressure, temperature, and salinity conditions (p – T – S) [GAUS et al., 2008]. While the injection of pure CO2 has been studied in reactive transport simulations for more than a decade, the consideration of impurities in these simulations can be realised only by indirect modelling approaches. For methodological reasons, the simulation programmes such as TOUGHREACT V3.0-OMP [XU et al., 2014] can handle only water (brine), CO2 (gas), and dissolved salt (NaCl in brine) as fluid components. Hence, in most simulation studies on this topic, the impurities of interest are injected by pre-equilibrating formation water (brine) with the CO2-impurity (gas) mixture. This impurity-loaded brine is then additionally injected with the CO2 stream. This modelling approach can be called additional brine injection (ABI). While this approach already leads to qualitatively reliable simulation results [W OLF et al., 2017b], it is faced with at least two modelling inaccuracies [W OLF et al., 2017a; W OLF et al., 2016a]. Firstly, the transport of impurities is restricted to the aqueous phase, which has a significantly lower mobility compared to the CO2 (gas) phase due to the higher viscosity of the transport medium. Secondly, in order to avoid artificial mineral precipitation under dynamically changing geochemical conditions near the injection well, the additionally injected brine needs to be undersaturated with respect to primary and secondary minerals of the reservoir, which inevitably leads to artificial mineral dissolution [ANDRÉ et al., 2015; W OLF et al., 2017a]. This holds at least in case of fast reacting minerals such as carbonates or sulfates. An alternative modelling approach has been implemented in commonly used simulation programmes such as TOUGHREACT V3.0 [XU et al., 2014] or STOMPCOMP [BACON et al., 2014] for a few years. In such simulation studies, CO2-stream impurities are implemented as trace gases within the CO2 phase [BACON et al., 2014; WOLF et al., 2016a; ZHANG et al., 2011]. In these simulations, the hydrodynamic transport properties of the CO2 phase are assumed to be unaffected by the presence of small amounts of impurities. This approach is called trace gas transport (TGT). However, in this approach impurities in the CO2 (gas) phase are treated to be at local equilibrium with the aqueous phase. Thus, the mass transfer of highly soluble impurities such as SO2 to the aqueous phase tends to be overestimated with respect to fast transport processes within the CO2 phase. In addition, chemical speciation reactions in the aqueous phase are computed using a system of equilibrium equations, leading to an infinitely fast formation of thermodynamically favoured products such as H2SO4 in case of SO2. Hence, the mass flux of the overall process (non-stoichiometrically exemplified for SO2)

is generally overestimated, if comparatively fast transport processes (e.g. in vicinity of the injection well) or the kinetically controlled formation of oxidation products are involved. In addition, this speciation of impurities as well as the subsequently induced dissolution of minerals lead to an increase in the total ion concentration and, hence,

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in an increased ionic strength as well. However, while running TOUGHREACT simulations, geochemical computations are restricted to grid cells with an ionic strength 1 lower than a chosen threshold, e.g. 6.0 mol/kg for NaCl dominated brines. Any further mineral dissolution and precipitation reactions are skipped once this threshold is exceeded. This leads to an incomplete computation of mineral alteration for regions (i.e. grid cells) of the storage reservoir, where high impurity dissolution occurs [W OLF et al., 2017a; W OLF et al., 2016a]. In consequence, no long-term mineral reactions, e.g. of silicate minerals, can be covered in these simulations. Hence, the numerical results of reactive transport simulations of impure CO2 injection using the TGT approach in TOUGHREACT V3.0, i.e. the spatial profiles of mineral alteration, are artificially distorted by the ionic strength limitation [W OLF et al., 2016a]. In order to avoid or minimise the disadvantages of both modelling approaches described above, a hybrid modelling approach, combining the advantages of the ABI and TGT approaches, was developed [W OLF et al., 2017a] and is presented in the following sections. It is based on a transport and kinetically controlled dissolution model for a more sophisticated two-phase time-dependent interaction representation. The model simulation is performed with a newly developed MATLAB programme. The derived space and time-dependent data of dissolved impurities are transferred into a TOUGHREACT simulation with local additional brine injection sources. As the dissolution front of impurities moves through the reservoir, the same holds for the local brine injection including individual impurities, which basically mimics the impurity transport in and the dissolution from the CO2 phase. Hence, this modelling approach can be described as mobile additional brine injection (mABI). Due to locally limited additional brine injection, any artificial impact on mineral alterations by this addition is minimised. In addition, this mABI approach is capable of including timedependent injection concentrations. However, as yet it is limited to a radial 1D grid structure so that gravity effects cannot be represented. The simulation procedure is able to deal with SO2, NO2, O2, and H2 as impurities. Note that the work presented here is focussed on acidic interactions only originating from SO2 and NO2.

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General simulation and solver procedure

The general procedure of an impure CO2 injection simulation based on the mABI approach follows the subsequently described steps. These steps and details of the MATLAB algorithm sequence are summarised in Figure 1. 1. As an initial step, a TOUGHREACT simulation run of a pure CO2 injection is performed. This simulation is based on the hydrodynamic properties of the storage reservoir and determines the temporal and spatial evolution of the CO2 propagation.

1

This holds for stoichiometric as well as true ionic strength.

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2. In case of a radial 1D simulation of a CO2 injection, the gas saturation 2 Sg depends only on the similarity variable ξ = R²/t with R being the radial distance and t being time [PRUESS & MÜLLER, 2009]. Thus Sg(R, t) = Sg(ξ) = f(R²/t) is derived as a piecewise linear function of ξ (four sections A, B, C, D, see figure 2). 3. This derived CO2 plume migration is re-created in MATLAB. Within this MATLAB algorithm an impurity dissolution and transport model is used (see sections 3 and 4), which is capable of including tabulated, time-dependent impurity concentrations during the injection. 4. After the completion of the full simulation run (here: run time one year), for technical reasons, the (huge) amount of dissolution rate data points is reduced by time-weighted averaging and application of cut-off values. 5. These edited dissolution rate data in [mol / s] are converted into water injection rates in [kg / s], which are needed for a use in TOUGHREACT. An injection source input file (GENER) is automatically generated, formatted for being read by TOUGHREACT. 6. The simulation of the CO2 injection is performed again in TOUGHREACT, now including the time and cell (=distance) -dependent injection of additional brine. This additional brine has a specified composition including the impurities. In this final step the reactive transport of impurities and their chemical interactions with rock material are simulated.

2.1. Simplifications Due to the sequential execution of the different steps in the simulation procedure, several simplifications of physical processes and properties had to be made within the newly developed MATLAB part and these are described in the following: • The density of the CO2 phase is considered to remain temporarily and spatially constant. Thus, the CO2 mass injection [kg / s] corresponds to volume injection [m³ / s] and volume flow. • The porosity of the saline aquifer is treated as being constant. Thus basically no feedback between mineral reactions, porosity change, and its impact on permeability can be considered in the MATLAB part. • While within the basic TOUGHREACT simulation (step 1) H2O transfer into the CO2 phase is included, its contribution to the phase volume changes cannot be rebuild in the MATLAB part (step 3). Here, volume changes of both fluid phases are fully treated to originate from flow processes. Thus the aqueous phase transport is slightly overestimated. 2

Defined as the fraction of the pore volume occupied by the CO2 phase, independently from the actual gaseous, liquid, or supercritical phase properties.

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• The whole impurity dissolution process is treated as a mass flux starting from the CO2 phase and ending in the aqueous phase as fully speciated impurity species. It is assumed that the impurity dissolution rate is initially determined by a fast physical uptake and subsequently controlled by kinetic chemical speciation reactions [HEDAYATI et al., 2017; WOLF et al., 2016b] until maximum solubility is achieved (see section 4).

Figure 1: Work flow of complete simulation procedure and details of the MATLAB algorithm sequence. The time step length within the MATLAB part is computed as a function of the gas saturation Sg of the smallest grid cell, i.e. with respect to the volume exchange of this cell.

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Figure 2: Profile of gas saturation Sg depending on similarity variable ξ = R² / t. Note the logarithmic scaling of the abscissa. The symbols A, B, C, D denote the four nearly linear sections.

2.2. Grid structure The grid used for the TOUGHREACT simulations has a 1D radial symmetric structure. The first cell symbolises the injection well with a radius of 7/2’’ (≈ 9 cm, i.e. a diameter of 18 cm, see figure 3). In this cell only pure CO2 is injected. Porosity is set to 1 and no mineral precipitation is allowed, i.e. this CO2 injection cell is completely unreactive. The main reservoir model is divided into 350 cells with exponentially increasing cell size. The lateral extent of the simulated reservoir comprises 30 km for proper computation of pressure dissipation. The outer boundary is treated as an unlimited open flow outlet. For injection of each impurity (e.g. SO2, NO2), each of the main reservoir cells is connected to an artificial injection cell (AIC). The injection of the impurity containing water takes place in the respective AIC. These AICs all have the same volume (0.05 m³) and the same interface area (1 m²) to their respective main cells. No other connection except to the corresponding main cell exists. Mineral reactions are not allowed in the AICs by using the same settings as for the injection well cell. The general scheme of the reservoir grid structure and the AICs is presented in figure 3.

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Figure 3: Schematic grid structure including artificial injection cells (AIC). The black AICs represent NO2(aq), light grey stands for SO2(aq) injection. ti and t*i symbolise the water injection rate data, which are tabulated for each cell and each impurity independently from all neighbouring cells.

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Transport

For a radial 1D grid simulation of pure CO2 injection, the evolution of the gas saturation Sg depends only on the similarity variable ξ = R² / t [PRUESS & MÜLLER, 2009]. The four linear parts of the spatial Sg(R, t) profile (marked as A, B, C, D in figure 2) are used in the MATLAB programme to compute the current gas saturation and thus the volume of the CO2 phase and its changes per each time step. These changes are used to approximate the volume flows V‘g, V‘l following the equation (exemplified for the ith grid cell, for list of variables see below)

These computed volume flows in both phases are used to simulate the transport in the CO2 (gas) phase

and in the aqueous phase:

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Both equations preserve mass balance within the numerical accuracy. Thereby the symbols denote the following variables:

4

Dissolution and chemistry

4.1. SO2 dissolution and chemistry Within the TOUGHREACT simulation, all dissolved impurity species with respect to a single element (e.g. H2S, SO2(aq), H2SO3, H2SO4 in case of sulfur) are treated as one dissolved primary component (i.e. SO2(aq)) with associated secondary species. To account for this merging of properties, the dissolution process in MATLAB is modelled by the following non-stoichiometric reactions:

The total simulated SO2(aq) concentration caq comprises the sum of all dissolved sulfur species. While this concentration is still below the maximum physical solubility cphys, a comparatively fast physical uptake (reaction 6) is modelled with its rate rphys being based on experimental data [AMSHOFF, 2017]. Once maximum physical solubility is achieved, further dissolution of SO2 may occur only if secondary speciation reactions such as oxidation or disproportionation (reaction 7) occur [W OLF et al., 2016b]. Thus the comparatively slow chemical speciation rate rchem is ratedetermining for the overall dissolution process at aqueous SO2 concentrations cphys ≤ caq ≤ cchem. An additional transport restriction is implemented in the simulation since, at maximum, only the total available amount of SO2(g) can be transferred to the aqueous phase for each grid cell and each time step (rt limitation, equation 10). A

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damping term (cchem – caq) / cchem is added in the rate equation in order to account for the net decrease of dissolution rate if the overall solubility equilibrium including chemical speciation cchem is approached. In summary, the dissolution rate rdiss of SO2(g) depending on the aqueous concentration caq is computed as follows:

The parameters used for the presented simulations are shown in table 1. Table 1: Used SO2 parameters parameter

value

unit

cphys

0.02

mol / L

cchem

0.1224

mol / L

comments

references

TOUGHREACT simulation without chemical

compare [XIA et al.,

speciation, y(SO2) = 400 ppm

1999] for pure SO2 gas

TOUGHREACT simulation with chemical speciation, gas phase mole fraction y(SO2) = 400 ppm

rphys

1.0E-5

mol / (L·s)

estimation based on experimental data

[AMSHOFF, 2017]

rchem

6.5E-9

mol / (L·s)

best fit value 3.25 · 10-7 s-1 multiplied by cphys

[HEDAYATI et al., 2017]

4.2. NO2 dissolution and chemistry The dissolution of NO2 proceeds via a similar, but slightly different mechanism compared to SO2. As an initiating step, NO2 molecules dimerise to establish an equilibrium with N2O4, which is the actually dissolving compound [KOMIYAMA & INOUE, 1980]. The addition of H2O to the dimer followed by an immediate decomposition forming HNO2 and HNO3 is the rate-determining step in the liquid phase. Thus the dissolution reactions of NO2 can be described as follows:

The rate law used for NO2 dissolution is of second order with respect to NO2(g) [KOMIYAMA & INOUE, 1980]:

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This equation gives the dissolution rate in mol / m²·s, i.e. per interface area. For TOUGHREACT simulations this rate needs to be converted with respect to the liquid volume, i.e. mol / L·s. Thus, the rate is multiplied with the surface-to-volume ratio ɣ in m² / L, which can be estimated as a function of gas saturation Sg using a cubic closepacking of equal spheres model for the porous structure of the solid phase. The spheric diameter of solid particles is set to 1000 µm, a typical value for coarse sand [MCCANN & MANCHEGO, 2015]. Thus, the dissolution rate of NO2 applying the respective parameters (table 2) can be computed as follows:

Table 2: Used NO2 parameters parameter

value

unit

comments

references

DN2O4

9.0E-10

m² / s

diffusion coeficcient

[KOMIYAMA & INOUE, 1980]

Kg1

0.4858

m³ / mol

equilibrium constant

[KOMIYAMA & INOUE, 1980]

k1

554

s-1

rate coefficient

[KOMIYAMA & INOUE, 1980]

κN2O4

48.2

1

distribution coefficient between g / l

[KOMIYAMA & INOUE, 1980]

r

500

µm

representative radius of coarse sand particles

[MCCANN & MANCHEGO,

between d = 630 µm and d = 2000 µm

2015] p105

cchem

0.174

mol / L

TOUGHREACT simulation with chemical speciation, y(NO2) = 400 ppm

sg0

0.93

1

gas saturation within the dry-out zone, depending on solid saturation of salt precipitation

Φ

0.26

1

porosity in a cubic close-packing of equal spheres

α

0.166

1

geometrical parameter

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Figure 4: MATLAB results: Exemplary distribution of dissolved impurities after 1 year of injection (upper panel SO2, lower panel NO2). The amount of injected impurity is plotted in each graph for comparison, scaled with respect to its propagation speed (mainly t1/2 dependence due to the radial grid structure).

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Results and conclusions

The basis of the here presented strategy of temporarily varying injection concentrations for the impurities SO2 and NO2 is a scenario developed within the CLUSTER project [KAHLKE & KATHER, 2017]. Figure 4 presents the spatial distribution of the amount of dissolved impurity relative to the rock volume after one year of injection simulation from the MATLAB part (step 3 in section 2). Two main observations can be made. Firstly, SO2 and NO2 exhibit different spatial extents of propagation within one year of injection in this scenario (approximately 42 m for SO2 and 47 m for NO2). This is due to the different amounts of injected impurity (on average 25 ppm for SO2, 44 ppm for NO2), while both impurities exhibit a similar total solubility (see cchem in tables 1 and 2). Secondly, sharp concentration changes and pronounced phases during the injection, e.g. a low SO2 concentration between the sixth and eigth month, which corresponds to 30 m and 35 m in Figure 4, are mirrored in the dissolution profile though a smearing and averaging effect of the impurity concentrations in the injected CO2 stream occurs through the simulated transport and mixing in each grid cell (see equation 4). This mirroring implies that the local impurity dissolution mass flux to a distinct rock volume is dominantly determined by the concentration in the injected CO2 stream. This holds at least if the duration of changes in the injection concentrations is signifcantly larger than the transport and dissolution time scale. This has to be confirmed later by using a more detailed grid structure with a higher spatial (and thus also temporal) resolution.

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The derived dissolution profiles are included in a TOUGHREACT simulation based on hydraulic and petrophysical rock properties of a generic storage scenario [RÜTTERS et al., 2016]. The mineralogy is based on an averaged representative mineral composition of Buntsandstein sandstone in the North German Basin, which was compiled within the COORAL project [WALDMANN et al., 2014]. The dominant simulated mineral alterations induced by SO2 and NO2 are presented in figure 5. Both acidifying impurities have induced calcite (CaCO3) dissolution resulting in pH buffering of the aqueous phase. This calcite dissolution results in reduced calcite volume fractions within the distance of the impurities’ impact (R ≤ 47 m), compared to the “CO2 only”, nearly unaffected background value at distances R ≥ 50 m. The dissolution of calcite results in a release of Ca2+, which directly leads to a precipitation of anhydrite (CaSO4) in the presence of sulfate i.e. at distances R ≤ 42 m. Hence, the different spatial extents of SO2 and NO2 propagation also cause different impacts on mineral alteration. With respect to the anhydrite background volume fraction (at approximately R ≈ 50 m), the spatial profile of additionally precipitated anhydrite looks very similar to the SO2 dissolution profile presented in figure 4. Thus the temporarily varying injection concentrations and the impurity dissolution profile are directly reflected in the mineral alterations. However, the total quantitative impact of the dissolved impurities on mineral alteration is rather limited due to the comparatively low injection concentrations.

Figure 5: TOUGHREACT results: Simulated spatial profiles of dominant Ca2+-containing minerals after one year of injection, based on temporarily varying injection concentrations of SO2 and NO2.

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Summary and outlook

In this study a newly developed modelling approach abbreviated as mABI (mobile additional brine injection) is presented. It deals with the dissolution and reactive transport of the CO2-stream impurities SO2 and NO2. This hybrid approach is capable of accounting for temporally varying injection concentrations of these impurities. These are directly mirrored in mineral alteration profiles. By this approach, simulation

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artefacts associated with so far used modelling approaches are minimised (1. TGT: skipped geochemical computations through ionic strength limitation; 2. ABI: artificial mineral dissolution near the injection well). The numerical results of this simulation, which is based on theoretical and empirical models, are plausible with respect to the temporal input data and to the (experimentally) well-known geochemical behaviour of pH sensitive, fast reacting carbonate minerals. However, it has to be stated, that this application is clearly oriented to studies on CO2 / impurity / rock interactions and it can be expected that this approach and the used modelling technique are presumably only restrictively transferable to other scenarios (e.g. H2 storage) and need significant, additional development and implementation efforts. In future work technical verification will be performed, e.g. by refining the grid structure and variation of selected input parameters, yielding a sensitivity analysis of the model and its implementation. It is intended to address the validation of the mABI model and the simulation procedure by comparison to existing modelling approaches (e.g. [XU et al., 2007] and experimental data [HEDAYATI et al., 2017]. As a next step different mineralogies, e.g. without prevailing carbonate phases (i.e. without any fast buffering capacity), will be addressed. An important improvement of the MATLAB part of the approach will be tested by inclusion of solid precipitation as a sink term for SO2, as this might strongly influence the overall SO2 dissolution capacity and hence the spatial distribution of this impurity within the storage reservoir.

Acknowledgements The work is funded by the German Federal Ministry of Economic Affairs and Energy based on the basis of a decision by the German Bundestag under grant agreement number 03ET7031A as part of the CLUSTER project. References Amshoff, P., Experimental data of SO2 physical dissolution into non-saline water at CLUSTER storage p-T conditions. - Personal Communication, 2017. André, L., Azaroual, M., Bernstone, C. & Wittek, A.: Modeling the geochemical impact of an injection of CO2 and associated reactive impurities (SO2 and O2) into a saline reservoir. – Transp. Porous Med., 108, (1): 185205, 2015. Bacon, D. H., Ramanathan, R., Schaef, H. T. & McGrail, B. P.: Simulating geologic co-sequestration of carbon dioxide and hydrogen sulfide in a basalt formation. – Int. J. Greenh. Gas Control, 21: 165-176, 2014. Gaus, I., Audigane, P., André, L., Lions, J., Jacquemet, N., Durst, P., Czernichowski-Lauriol, I. & Azaroual, M.: Geochemical and solute transport modelling for CO2 storage, what to expect from it? – Int. J. Greenh. Gas Con., 2: 605-625, 2008. Hedayati, M., Wingston, A., Wolf, J. L., Niemi, A. & Rebscher, D.: Impacts of SO2 gas impurity within the CO2 stream on reservoir rock of a CCS pilot site: An experimental and modelling approach. – Int. J. Greenh. Gas Control, in preparation: 2017. Komiyama, H. & Inoue, H.: Absorption of nitrogen oxides into water. – Chem. Eng. Sci., 35: 154-161, 1980. McCann, T. & Manchego, M. V.: Geologie im Gelände. – Berlin (Springer), 2015. Pruess, K. & Müller, N.: Formation dry-out from CO2 injection into saline aquifers: 1. Effects of solids precipitation and their mitigation. – Water Resour. Res., 45: W03402, 2009. Rütters, H., Bettge, D., Fischer, S., Schatzmann, S., Knauer, S., Engel, F., Pöllmann, H. & Schütz, S.: CLUSTER - Definition des Ausgangsszenarios. - B3.1/B50324-12/2016-0004/001, Bundesanstalt für Geowissenschaften und Rohstoffe, 2016.

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