Introduction

Ground basalt added to agricultural fertilizer captures atmospheric carbon dioxide (CO2), raises the soil pH, reduces ocean acidification and supplies important nutrients such as magnesium, potassium, calcium, iron and phosphorus. Ground silicate rock has been used as mineral fertilizer since the early thirties (Hilf 1938; de Villiers 1961; Gillman et al. 2002; van Straaten 2006; Anda et al. 2009). More recently, CO2 sequestration by silicate rock has been investigated by incubation and infiltration experiments, which had reaction periods in the range of 3–12 months (ten Berge et al. 2012; Dietzen et al. 2018; Kelland et al. 2020; Amann et al. 2020). These experiments exploited only a minute fraction of the CO2 sequestration potential. However, reactive-transport modelling with the TOUHGHREACT software is capable of covering the full lifetime of a basalt reactor. The design of models with various environmental parameters is the subject of this paper.

The weathering of silicate rock involves the reaction with dissolved carbon species, the activities of which are controlled by the thermodynamic equilibrium between CO2 gas in the atmosphere and soil, on one hand, and liquid CO2, on the other hand. This is a natural process, which controls the CO2 level of the atmosphere on the geological time scale. The only way to enhance this natural process is to increase the reactive surface area of the silicate rock by grinding.

In terms of CO2 sequestration potential, basalt is unique. Basalt is both a highly reactive and wide-spread silicate rock. Basaltic volcanic and subvolcanic rock occupies 5.6 × 106 km2 or 3.5% of the land surface of the Earth (Fig. 1; Hartmann and Moosdorf 2012). Important occurrences are located in South Africa, Russia, Brazil, Ethiopia, India, the USA, Iceland, Australia, and some neighbouring countries.

Fig. 1
figure 1

Occurrences of basaltic volcanic and subvolcanic rock (Hartmann and Moodorf 2012). Equal-area Mollweide projection

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The capture of CO2 from the atmosphere via chemical reaction with ground basalt rock added to agricultural fertiliser implies additional costs. These are investment costs rather than operational costs because of the long lifetime of a basalt reactor. Basalt amendment typically would constitute less than one third of the price of high-yielding agricultural land under favourable transport conditions (transport by lorry, train and/or ship). Combining the benefits of high yield induced by basalt amendment and income from CO2 emission certificates may lead to an economically viable situation.

Basalt amendment shares the high environmental costs of climate neutrality with other techniques such as storage of electrical energy or hydrogen production. These environmental costs arise from the mining of immense amount of rock and minerals needed for the setup-up of the emission-reducing installations.

The purpose of this research is to predict the performance of the basalt reactor as a function of reactive surface area, CO2 partial pressure and rainwater infiltration. The research is meant to guide decision-makers in a more reliable way than previous studies with a more general approach (Taylor et al. 2015; Taylor et al. 2017; Strefler et al. 2018; Lefebvre et al. 2019; Beerling et al. 2020a).

Materials and methods

TOUGHREACT computer code

All models have been calculated with TOUGHREACT version 3. This a numerical simulation programme for chemically reactive flows of multi-phase fluids in porous and fractured media (Xu et al. 2014a). Interactions between mineral assemblages and fluids can occur under local equilibrium or via kinetic rates. The reaction rate is a function of the mineral saturation ratio and is calculated with the rate expression of Lasaga et al. (1994). This is a chemical inhibition term, which slows the dissolution/precipitation rate as the chemical state of the fluid approaches chemical equilibrium with respect to the dissolving/precipitating mineral phase.

Flow model

Base case

A structured orthogonal model mesh with three elements and horizontal dimensions of 1 × 1 m is used (Table 1). The top and bottom elements have a volume of 1052 m3. Thus, Dirichlet conditions are imposed, i.e., the thermodynamic conditions of the top and bottom element do not change at all. The intermediate element has a volume that represents 100 tonnes of ground basalt distributed over an area of 1 hectare (0.005 m3). The total pressure at the top element is 105 Pa, and the partial pressure of CO2 gas is set at 41.1 Pa, which is actual atmospheric partial pressure at standard conditions (105 Pa, 25° C). The bottom element has a total pressure of 0.999982 × 105, 0.999965 × 105 or 0.999947 × 105 Pa, which serves to maintain an infiltration rate of 400, 800 or 1200 mm/a, respectively. These infiltration rates characterize mid-latitude, subtropical and tropical climate conditions.

Table 1 Flow model setup
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The rock grain density has the typical value of Columbia River basalt, US.A. (2.8 g/cm3; DOE 1982). The remaining material parameters are taken from a CO2 sequestration test case of Xu et al. (2014b).

Sensitivity cases

The sensitivity cases have the same setup as that of the base case but use soil CO2 partial pressure instead of atmospheric CO2 partial pressure. The lower limit (3 × 102 Pa) and upper limit (3 × 103 Pa) of the range given by Bohn et al. (2001) are applied.

Reactive transport model

Base case

The transport conditions are simulated for ground rock with a reactive surface area of 7.4 m2/g determined for a grind size P80 = 1250 μm (80% sieve passing size) for crushed basalt using the N2 adsorption method (Kelland et al. 2020) and calculated with the BET equation named after Brunauer, Emmett, and Teller who developed the theory. The initial and boundary water composition is that of rainwater collected in the tropical Pune area, India (Momin et al. 2005), supplemented with Fe and Si analyses of rainwater collected in the Panipat area, India (Bharti et al. 2017), and an Al analysis of rainwater collected in the Bandung area, Indonesia (Hasan et al. 2017) (Table 2). The temperature is 25 °C. The initial and boundary partial pressure of CO2 gas is set at 41.1 Pa, which is actual atmospheric partial pressure at standard conditions (105 Pa, 25 °C). This setup defines a total aqueous carbon concentration of 1.3 × 10–5 mol C per kg H2O (molal).

Table 2 Reactive transport model setup: initial composition of the liquid phase
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The glass fraction of the basalt is 0.25, which is a typical value for Columbia River basalt, USA, such as that used by Kelland et al. (2020). The proportion of the crystallised phases corresponds to the mineralogical composition of the basalt used by Pollyea and Rimstidt (2017) (Table 3). A volume fraction of 0.02, consisting of TiO2 and P2O5 components, is neglected, i.e., assumed to be non-reactive. A simplified set of reaction products is used (Pollyea and Rimstidt 2017): calcite, siderite, magnesite (i.e. carbonates representative of ankerite-dolomite solid solution; Reeder and Dollase 1989), amorphous SiO2, Ca-montmorillonite, Na-montmorillonite and illite (i.e. Al-silicates representative of mixed-layer minerals solid solution; Meunier and Velde 1989). There are no kinetic data for solid solutions; therefore, the available data for minerals with a fixed composition must be used. Basalt glass (Pollyea and Rimstidt 2017) can only dissolve. Siderite (Knauss et al. 2005) and the remaining components (Palandri and Kharaka 2004) dissolve and precipitate under kinetic constraints. Illite is assumed to have the same rate constants as montmorillonite. The precipitation rates equal dissolution rates. The initial volume fraction of all reaction products is zero.

Table 3 Reactive transport model setup: Initial volume fractions, reactive surface areas and kinetic properties
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The calculations are performed with the THERMODDEM thermodynamic database (Blanc et al. 2007), supplemented by data for basalt glass (Pollyea and Rimstidt 2017). All aqueous species of the elements shown in Table 2 were allowed to take part in the reactions.

Sensitivity cases

The sensitivity cases have the same setup as that of the base case but use the reactive surface area of the base case multiplied and divided by 2. The corresponding values are 15 and 3.7 m2/g, respectively.

Results

Base case

The performance of the basalt reactor is monitored by the efficiency ratio. This is the CO2/basalt weight ratio corresponding to the fraction of basalt that can be converted into carbonate minerals. The theoretical efficiency ratio is 0.211 but this value is not achievable under realistic assumptions, because basalt can react with water without the participation of aqueous carbon species.

Figure 2 shows that the efficiency ratio varies little with infiltration (0.161–0.165) at the end of the sequestration period. But the time spam for reaching the end of the sequestration period is strongly influenced by the infiltration rate. At tropical conditions (1200 mm/a), the end point is reached after 11.2 years. At mid-latitude conditions (400 mm/a), the end point is reached after 33.1 years.

Fig. 2
figure 2

Basalt reactors with 41.1 Pa CO2 partial pressure and various combinations of infiltration rate and reactive surface area. Efficiency ratio (CO2/basalt weight ratio; see text; black solid line; vertical scale text in black) and SmCO2 (total CO2 sequestered in mineral phases in kg/m3 medium; red interrupted line; vertical scale text in red) plotted versus time. Efficiency ratios obtained from infiltration experiments (red point symbols; see text) are shown for comparison

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The end point is reached when all basalt glass and forsterite have dissolved (Fig. 3). Although dissolution of plagioclase and pyroxene continue beyond the end point, the activities of aqueous Ca, Mg and Fe species remain too low for stabilizing previously precipitated carbonate minerals. The net effect is the reduction of the SmCO2 value (mass of CO2 sequestered in solid mineral phases). All previously precipitated carbonate minerals are completely dissolved after 36.5 years and 101.7 years in the 1200 mm/a and 400 mm/a scenarios, respectively.

Fig. 3
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Basalt reactor with a CO2 partial pressure of 41.1 Pa, reactive surface area of 7.4 m2 and infiltration rate of 800 mm/a. Fraction of dissolved mineral phases (forsterite, plagioclase and pyroxene) and glass plotted versus time

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It is implicitly assumed that CO2 originally sequestered via solid carbonate phases is not recycled to the atmosphere but stored in the geosphere and hydrosphere. Nevertheless, field studies that support such an assumption have not been conducted yet (Kelland et al. 2020).

Sensitivity cases

Multiplying the reactive surface area of the base case (7.4 m2/g) by 2 has hardly any positive effect on the efficiency ratio (Fig. 2). In contrast, dividing the base case value by 2 has a significant negative effect on the efficiency ratio especially when the infiltration rate is high. This implies that there is no point in finer grinding to achieve a reactive surface area > 7.4 m2/g. However, coarser grinding resulting in a reactive surface area < 7.4 m2/g risks to jeopardize the performance of the basalt reactor especially under tropical conditions with a high infiltration rate.

The variations of the CO2 partial pressure have little influence on the efficiency ratio at the end of the sequestration period (Fig. 4). But the time span for reaching the end of CO2 sequestration decreases significantly when the CO2 partial pressure is high. For example, the infiltration case with 400 mm/a has the end point at 28.2 years at 3000 Pa partial pressure; the corresponding value for a low partial pressure (41.1 Pa) is 33.1 years. The infiltration case with 1200 mm/a has the end point at 9.5 years; the corresponding value for a low partial pressure (41.1 Pa) is 11.4 years.

Fig. 4
figure 4

Basalt reactors with a reactive surface area of 7.4 m2 and various combinations of infiltration rate and CO2 partial pressure. Efficiency ratio (CO2/basalt weight ratio; see text; black solid line; vertical scale text in black) and SmCO2 (total CO2 sequestered in mineral phases in kg/m3 medium; red interrupted line; vertical scale text in red) plotted versus time. Efficiency ratios obtained from infiltration experiments (red point symbols; see text) are shown for comparison

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Comparison with experiments

The comparison of the TOUGHREACT model with experimental results is not straightforward because these are recorded in terms of release of Mg (± Ca) from dissolving ground rock but not in terms of precipitated solid carbonates. The duration, infiltration rate, type of media and ground rock loading of the experiments are

  1. 1.

    0.33-year infiltration (766 mm/a) into ground basalt mixed with soil containing cereal plants, the rock loading being 100 t/ha (Kelland et al. 2020)

  2. 2.

    0.61-year infiltration (213 mm/a) into forsterite-dominated olivine (the most reactive mineral component of basalt) mixed with soil containing ryegrass plants, the rock loading being 204 t/ha (ten Berge et al. 2012)

  3. 3.

    1-year infiltration (800 mm/a) into ground dunite (an ultrabasic plutonic rock mainly composed of olivine) mixed with soil containing cereal plants, the rock loading being 220 t/ha (Amann et al. 2020).

The efficiency ratio of the experiments is higher or lower than that of the TOUGHREACT model (Figs. 2 and 4, Table 4):

  1. 1.

    The modelled efficiency ratio after 0.33 year infiltration is in the range of 0.0018–0.0057, i.e., lower than the experimental value (0.013)

  2. 2.

    The modelled efficiency ratio after 0.61 year infiltration is in the range of 0.0031–0.011, the maximum value being slightly lower than the experimental value (0.013)

  3. 3.

    The modelled efficiency ratio after 1 year infiltration is in the range of 0.0051–0.018, i.e., the whole range is higher than the experimental value (0.0002).

Table 4 Comparison of experiments and models for direct air CO2 capture
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In summary, the experiments do neither confirm nor contradict the TOUGHREACT model.

Comparison with previous models

Two reactive-transport models with a simulation period that extends beyond that of the experiments with a basalt reactor have been published (1 year, Beerling et al. 2020b; 5 years, Kelland et al. 2020). Owing to the restriction of the software used (PHREEQC, Parkhurst and Appelo 2013), all precipitating phases react under equilibrium conditions. The result is a strongly non-linear relationship between efficiency ratio and time. This is in stark contrast to the near-linear relationship of the TOUGHREACT model with both dissolving and precipitating phases reacting under kinetic constraints. Preference should be given to the TOUGHREACT model, because the PHREEQC model relies on unphysical assumptions. All participating minerals precipitate under kinetic constraints with reaction rates that are at least as low as the dissolution rates (Palandri and Kharaka 2004, and references therein).

Conclusion

The modelling of the basalt reactor succeeded in predicting its efficiency ratio (0.153–0.165 tonne CO2 per tonne ground rock) and its lifetime (9.5–33.1a) as a function of the reactive surface area, CO2 partial pressure and infiltration rate. These results are useful for decision-makers. E.g., the combined production costs and 300 km transportation costs for ground basalt are $ 82 US per tonne for a grind size of 50 μm (Strefler et al. 2018). Accordingly, the costs for capturing one tonne of CO2 are in the range from $ 496 US to $ 536 US. These costs are considerably less than the costs of the alternative adsorption/absorption method of direct air CO2 capture if the obligatory CO2 underground injection is included. For the above-ground adsorption/absorption unit alone, Viebahn et al. (2019) quote $ 540 US per tonne of captured CO2 for both the Climeworks installation, Switzerland, and the Carbon Engineering installation, Canada, a recipient of the Gates Foundation. Including underground storage in Iceland basalt, Climeworks charges EURO 960 ($ 1100 US) per tonne CO2 compensation in 2021 (Niemann 2021).

The permanent and safe underground storage of CO2 is an expensive enterprise with considerable technical, geological and environmental problems. For underground CO2 injection on the large scale, there is no easy solution in sight. To date, there is no major on-land operation for injecting CO2 derived from an industrial source except for the petroleum industry. However, the petroleum industry is a very special case because CO2 is obtained as an unwanted by-product during gas or petroleum exploitation and is reinjected close to its original source.

The optimal underground target for injecting CO2 captured with a physical (non-reactive) method is basalt where CO2 is converted into solid carbonates (Schwartz 2020); whereas non-reactive target rocks such as sandstone imply the risk that injected CO2 may leak to a near-surface aquifer and pollute the groundwater (Schwartz 2014, and references therein).

Underground CO2 injection into basalt and mining of basalt for fertilizer production are likely to compete for space if conducted on a large scale. About 3.5% of the Earth’s surface is occupied by basalt but only a minor fraction has the transport infrastructure that allows a reasonably economic use of these basalt resources. In summary, the CO2 direct air capture is bound to encounter many obstacles. Nevertheless, modelling direct air capture is a useful comparative tool for demonstrating the advantages of reducing greenhouse gas emissions at the source.