Reactive transport simulation of organic and inorganic carbon cycling following carbon dioxide sorption onto soil amendments in drylands

Terrestrial nature-based climate solutions (NbCS) for carbon dioxide removal (CDR) are critical for mitigating climate change. However, the arid climates characteristic of drylands (aridity index <0.65) often limit the effectiveness of many NbCS. At the same time, drylands cover approximately 45% of the global land area and are threatened by soil degradation, necessitating the deployment of CDR methods for drylands that also promote soil health. Soil amendments with high CO₂ sorption capacity, such as biochar, could provide CDR potential and soil health benefits in drylands provided they do not negatively impact the large inorganic carbon pools typical of dryland soils. The dynamics of soil CO₂ are therefore critical for assessing the response of dryland systems to sorbing amendments. To assess the soil response to CO₂ sorption, we developed a 1D reactive transport model of unsaturated soils in equilibrium with dissolved inorganic carbon and calcite under varying soil respiration rates and soil amendment application conditions. The simulations highlight how alteration of soil CO₂ due to sorption by biochar affects dissolved inorganic carbon, pH, Ca²⁺, and calcite. The transient conditions that emerge, including delayed emissions of respired CO₂, also emphasize the need to consider response times in monitoring campaigns based on CO₂ measurements. In scenarios where soil respiration is low, as is typical in drylands, sorption becomes increasingly important. Although the CDR potential of CO₂ sorption is variable and was modest relative to the overall CDR for a biochar deployment, the impacts of altered gas dynamics on soil inorganic carbon are important to consider as dryland soil amendments are developed.

1 Introduction

Nature-based climate solutions (NbCS) are considered essential to limit global warming as they represent one of the most mature carbon dioxide removal (CDR) methods, complementing the need for reductions in fossil fuel emissions (Griscom et al., 2017). NbCS rely on sustainable management of ecosystems to remove greenhouse gasses from the atmosphere while ideally addressing societal challenges associated with climate change (Chausson et al., 2020; Seddon et al., 2020). Early estimates suggest that sustainable management of forests, agricultural lands, grasslands, and wetlands could deliver over one third of the cost-effective climate mitigation needed to limit global warming to below 2°C above pre-industrial levels until 2030 (Griscom et al., 2017).

Drylands (aridity index <0.65) (Cherlet et al., 2018) should be important targets for NbCS because they occupy over 45% of the global land area (Dregne et al., 1991; Prăvălie, 2016; Berg and McColl, 2021) and play an important role in controlling atmospheric CO₂. Soil inorganic carbon (SIC) accumulates in drylands. The SIC is present as pedogenic carbonate and forms at depth from Ca²⁺ derived from a mixture of dust inputs and in situ weathering and CO₂ in percolating water (Chadwick et al., 1999). If Ca²⁺ is supplied by weathering of calcium silicates, this process constitutes a carbon sink (Monger et al., 2015; Lal et al., 2021). The SIC stock in the upper 1 m of soil is estimated to be around 940 Pg C, which mostly occurs in drylands and is larger than the C pool in the biosphere (Lal, 2020; Lal et al., 2021). This SIC has turnover rates of several thousand years (Monger and Gallegos, 2000). However, climate change could increase carbon sequestration via SIC or lead to SIC being a source of carbon (Lal et al., 2000; Naorem et al., 2022). Drylands are specifically vulnerable to changes in environmental conditions (Lal et al., 2021) and it has been estimated that over 57–70% of dryland soil is degraded or prone to degradation (Dregne et al., 1991; Lal, 2004; Reynolds et al., 2007). Another study estimated that grazing, especially in arid and semi-arid regions might account for half of global SOC loss over the last 12,000 years (Sanderman et al., 2017), which would also affect SIC storage. However, soil degradation is still difficult to quantify (Verstraete et al., 2011; Prince, 2016; Wang et al., 2022).

Many NbCS have limited applicability in drylands due to water requirements. NbCS that are currently considered as highly promising for CDR are enhanced weathering (EW), reforestation, and biochar. EW requires leaching of alkalinity, which is inefficient in drylands (Calabrese et al., 2022; Zhang S. et al., 2022; Lehmann et al., 2023). Similarly, net primary productivity is limited by water availability (Ferguson and Veizer, 2007) therefore placing limits on restoration of organic carbon (C) stocks and discouraging biochar application that seeks to enhance primary productivity. Estimates of CDR for the aforementioned NbCS often consider only agricultural and forest lands (Roe et al., 2021). However, agricultural and forest lands only constitute roughly 9 and 23% of the global land area, respectively, and thus the development of effective drylands CDR strategies presents an important avenue for increasing global CDR capacity.

Another challenge for CDR in drylands is that drylands are understudied (Verstraete et al., 2011) and predictions from other climatic conditions might not be applicable. Eddy-covariance measurement, which works well to determine C uptake in forests, has been insufficient to identify drylands as source or sink of atmospheric CO₂ (Schlesinger, 2017). This has been attributed partly to pressure pumping and carbonate dissolution in combination with transport to groundwater, although these abiotic processes are thought to be insufficient to explain discrepancies between analytical methods (Schlesinger, 2017). Diurnal soil CO₂ flux behavior can be explained by diurnal changes in moisture and temperature that drive gas dissolution in soil water, however these changes do not constrain long-term changes in carbon cycling (Sagi et al., 2021). Overall monitoring only soil CO₂ efflux does not give a complete picture of C cycling in dryland soils.

For water-scarce drylands, soil amendments with high CO₂ sorption capacity could provide CDR potential and soil health benefits. Carbon-based materials such as biochar, as well as inorganic materials such as zeolite, are suitable because of their low cost, abundance, benign nature and recalcitrance (Halliday and Hatton, 2021; Garbowski et al., 2023). Biochar is highly porous with variability in pore volume, pore structure, specific surface area and functional groups related to feedstock type and production conditions (Francis et al., 2023). It also constitutes an important CDR strategy (Lehmann et al., 2021). Minerals such as zeolites are porous materials with high sorption capacity, and they are tunable and can be functionalized (Halliday and Hatton, 2021). Both materials improve soil health under a range of conditions (Mondal et al., 2021; Nepal et al., 2023).

Predicting the soil response to biochar is highly uncertain but abiotic processes involving SIC could significantly contribute to the variability of soil CO₂ fluxes after biochar amendment (Liu et al., 2016; Mosa et al., 2023). There are unfortunately relatively few field trials of biochar that completely constrain the carbon dynamics. A field study conducted in temperate and summer monsoon climate found a decrease in SIC, an increase in SOC, and depletion of water-soluble Ca²⁺ and Mg²⁺ in response to biochar additions (Lu et al., 2021), with an accompanying study pointing toward leaching of cations (Zhang et al., 2020). A biochar field study that was conducted over a range of climatic conditions found an increase in SIC with decreasing precipitation, while soil type and hydrological processes were also correlated to accumulation of SIC (Zhang et al., 2020). Studies conducted under arid or semi-arid conditions generally found an increase in SIC and reasoned that there is precipitation of calcite at deeper depths (Wang et al., 2015; Dong et al., 2019). However, studies investigating how SIC reacts to biochar addition, especially in drylands, are still scarce.

In this paper we investigate CO₂ sorption on biochar applied as a soil amendment and explore how manipulation of soil CO₂ affects C cycling in dryland soils. We will briefly review sorption data and present a reactive transport model (RTM) to elucidate the coupling between geochemical reactions and gas transport. The RTM simulates gas diffusion, dissolved inorganic carbon (DIC) and weathering of calcite under different application conditions and soil respiration rates. Although the sorption of CO₂ is relatively low (around 2%) compared to the total C in the simulated biochar, the simulated interactions between organic and inorganic C cycling can inform application and monitoring of a range of CDR methods that affect soil C dynamics. We will discuss the limitations for application and the benefits for soil health.

2 Methods

2.1 Sorption isotherm models

The model parameters for CO₂ sorption on soil amendments were based on sorption isotherms fitted to dry sorption data collected under soil-relevant gas conditions without the presence of soil (Ringsby et al., 2024) (Figure 1 and Supplementary Table S1). Dry sorption experiments with sorbent were chosen because the presence of water and soil hinders comparability between studies and makes generalization difficult. However, it should be noted that water (Davidson et al., 2013) and soil (Kwon and Pignatello, 2005) can reduce the specific sorption capacity.

Figure 1

Figure 1. Langmuir CO₂ sorption isotherms from published data (Ringsby et al., 2024). Isotherms were fitted to data from dry sorption experiments under soil relevant conditions. Langmuir constants can be found in SI.

The sorbents were either not pre-treated before the sorption experiment (“as received”) or they were outgassed at 150°C before the sorption experiment (“outgassed”). This is an important distinction because pre-treatment has been identified as a major source of uncertainty (Figini-Albisetti et al., 2010). No outgassing or an outgassing temperature that is too low will likely underestimate sorption capacity while elevated temperatures applied to temperature-sensitive materials might irreversibly alter the sorbent behavior (Figini-Albisetti et al., 2010). However, the authors also noted that the outgassing temperature must be consistent with final application. During the large-scale application process of sorbents as soil amendment, elevated temperatures are not expected. Therefore, sorption isotherms “as received,” were assumed to be best in line with the intended application. The sorbent with the highest “as received” sorption capacity was Biochar 3 and was chosen for simulations, while the outgassed isotherm for Biochar 3 indicates the upper bounds likely for biochar sorbents (Ringsby et al., 2024).

A sorption isotherm model that is often used to describe experimental observations such as those above is the Langmuir model (Equations 1–3). The single site Langmuir model makes following assumptions: (1) there is a limited sorption capacity, (2) all sorption sites are equal, (3) one site sorbs one molecule of sorbent, and (4) all sites are energetically independent of the number of sorbed molecules (Limousin et al., 2007). The assumed reaction is:

$\begin{array}{ll}\left(q_m-q\right)+p{\mathrm{C}\mathrm{O}}_2\leftrightarrow q& (1)\end{array}$

Where $q$ is the surface complex, $q_m$ is the maximum sorption capacity, $q_m-q$ indicates free sites, and pCO₂ is partial pressure of CO₂. The conditional stability constant can be written as:

$\begin{array}{ll}K=\frac{\left[q\right]}{\left[q_m-q\right]\left[pC{O}_2\right]}& (2)\end{array}$

Where $K$ is the Langmuir constant. The equation can be rearranged to the typical Langmuir isotherm:

$\begin{array}{ll}q=\frac{q_{m}KpC{O}_2}{1+KpC{O}_2}& (3)\end{array}$

In many cases an improved description of experimental data can be achieved with a multisite Langmuir model (Equation 4):

$\begin{array}{ll}q={\displaystyle \sum }_{i=1}^p\frac{q_{m,i}{K}_{i}pC{O}_2}{1+K_{i}pC{O}_2}& (4)\end{array}$

Where $K_i$ and $q_{m,i}$ are Langmuir constant pairs $p$ for multiple sorption sites.

For inclusion in the reactive transport model, a multisite competitive Langmuir sorption model was adapted (Limousin et al., 2007). A reaction for a strong and a weak sorption site was implemented (Equations 5, 6):

$\begin{array}{ll}>{{\mathrm{S}}_{\mathrm{strong}}}^0+{\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)\leftrightarrow >{\mathrm{S}}_{\mathrm{strong}}{\mathrm{C}\mathrm{O}}_2^0& (5)\end{array}$

$\begin{array}{ll}>{{\mathrm{S}}_{\mathrm{weak}}}^0+{\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)\leftrightarrow >{\mathrm{S}}_{\mathrm{weak}}{\mathrm{C}\mathrm{O}}_2^0& (6)\end{array}$

Where >S_strong⁰ refers to a strong sorption site and > S_weak⁰ refers to a weak sorption site. The Langmuir constants $K_1$ and $K_2$ were implemented as the equilibrium constants for the two reactions. The maximum adsorption capacities $q_{m,1}$ and $q_{m,2}$ can be directly entered in the RTM. Physical properties necessary to simulate the sorbent mass were from the same published study (Supplementary Table S2). The Biochar 3 sample was obtained from Atlas Olive Oils, which produces biochar from olive tree byproducts, including pulp, pits, and branches. The chemical properties that were provided by the supplier are listed in Supplementary Table S3.

2.2 Reactive transport model

Simulations were conducted with the multi-component reactive transport code, CrunchFlow (Steefel et al., 2015). CrunchFlow allows simulation of variably saturated conditions at steady state, including gas diffusion as well as sorption of gas species. Gas diffusion was simulated via Fick’s law assuming a tortuosity correction via Millington (1958). A surface complexation model (SCM) capability in CrunchFlow simulates sorption. The SCM provides flexibility to simulate sorption mechanisms or empirical sorption reactions, e.g., via the Langmuir sorption model. Equilibrium between the gas and aqueous phase is governed by Henry’s law, and gas concentrations are simulated via the ideal gas law.

2.2.1 Model domain and gas transport

To simulate gas transport and C cycling in dry soil, we implemented a 1D model with 200 vertical cells representing a 2-meter soil profile. We assumed that there was no water flow, and that gas was transported only via diffusion with a free phase gas diffusion coefficient of 0.16 cm²/s¹ (Currie, 1960; Rolston and Moldrup, 2002). A Dirichlet boundary condition was specified at the top to ensure gas diffusion between air, fixed at atmospheric CO₂ levels, and soil. A no-flow or Neumann boundary condition was set at the bottom to simulate bedrock. Water saturation S_w was fixed to 0.4 over the whole column to simulate the presence of soil water. The value of S_w = 0.4 was chosen to simulate relatively dry conditions but above residual water saturation conditions (Jia et al., 2021). In the model, an increase of S_w caused an increase in pCO₂ due to lower air-filled porosity at a given CO₂ production rate. Pre-simulations showed that the same effect was achieved by varying CO₂ production. Therefore, only CO₂ production was varied to simplify interpretation of simulation outcomes.

2.2.2 Reaction network

The simulated reaction network with respect to C is shown in Figure 2. In total, eight primary and 14 secondary aqueous species were simulated including several major cations and anions that are not shown in Figure 2. Calcite was set to be in equilibrium with the aqueous phase due to its role as a pH buffer (Gaillardet et al., 1999; Wen et al., 2022; Pfeiffer et al., 2023). To simulate soil respiration a zero-order rate law assuming no inhibition or catalysis was chosen (Equation 7):

$\begin{array}{ll}R=A_s\cdot k_s& (7)\end{array}$

Figure 2

Figure 2. The simulated model domain (left) and the reaction network, including diffusive transport (right), are shown. When CO₂(g) dissolves in water, it becomes aqueous: CO₂(g) $\leftrightarrow$ CO₂(aq). The convention ${\mathrm{H}}_2{\mathrm{C}\mathrm{O}}_3^{*}={\mathrm{C}\mathrm{O}}_2\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{H}}_2{\mathrm{C}\mathrm{O}}_3$ has been adopted.

Where A_s is the solid component surface area and k_s is the intrinsic rate constant. The model parameters were set such that the solid component did not decrease over the simulation time, resulting in a constant production of CO₂ over time, which simulates CO₂ emissions from the soil to the atmosphere. To reproduce observed pCO₂ depth profiles, the CO₂ production rate was simulated to be faster in the top 25 cm compared to the remainder of the profile. This idealized representation was designed to facilitate examination of the resulting dynamics in the inorganic carbon pools.

Model parameterization of aqueous, and solid phases was based on literature values (Jia et al., 2021; Wen et al., 2022) (Supplementary Tables S4, S5). The calcite mineral volume fraction was set to 3 % over the entire model based on estimates for dry climates (Pfeiffer et al., 2023). For simplicity a constant distribution of calcite over depth was considered sufficient because sorbent was only applied in the top centimeters and rain events were not simulated. A more accurate distribution of calcite over depth would be necessary for different conditions. Thermodynamic constants are from the EQ3/EQ6 database (Wolery, 1992).

2.2.3 Model approach and simulation scenarios

Prior to adding the sorbent, simulations were run to steady state to both create a baseline and exclude transient features that confuse the analysis. Depending on the initial scenario, steady- state profiles were obtained after 60–100 days. To allow all scenarios to reach steady state, the spin-up period was set to 400 days, at which point sorbent was added, and the model was run until it reached steady state again. Simulation scenarios explored variations in (1) background CO₂ production rates, (2) application rates, (3) application density, (4) application depth, and (5) increased CO₂ production after application (Supplementary Table S6).

Three simulation scenarios with low, medium, or high CO₂ production over time were developed (Supplementary Figure S2) to simulate a range of observed pCO₂ profiles (Cerling, 1984; Amundson et al., 1998; Davidson et al., 2006; Wang et al., 2013; Chirinda et al., 2014; Winnick et al., 2020). Low CO₂ production resulted in low simulated pCO₂ and might represent soil respiration rates in drylands, although it should be noted that uncertainty of CO₂ production rates is high in drylands due to data scarcity (Oertel et al., 2016; Warner et al., 2019). Medium and high CO₂ production rates are more typical for temperate forests and croplands (Warner et al., 2019). The medium and high rates were included because those ecosystems also occur in drylands and because soil amendments such as biochar can increase soil respiration rates (El-Naggar et al., 2019).

Application rates were varied between 2 and 20 t/acre (Lehmann and Rondon, 2006; Thengane et al., 2021). The application density, which accounts for the importance of mixing and downward physical transport of biochar (Spokas et al., 2014) was varied by changing the application depth while holding the application rate constant.

A simulated increase in CO₂ production after soil amendment application in addition to sorption (Supplementary Figure S1) was intended to replicate increased soil respiration (positive priming) that sometimes occurs after amendment of biochar, specifically in soil with initially low fertility (El-Naggar et al., 2019). Although CO₂ sorption does not directly affect soil respiration rates, most soil amendments will fundamentally alter a range of soil properties and can change soil respiration rates. For biochar, positive and negative priming have been observed in field experiments (Mosa et al., 2023). Mechanisms previously implicated in changes of CO₂ emissions after biochar application are transport effects introduced by altered pore structure (Fan et al., 2020), increased water retention, increased SOC stock, promotion of CO₂-fixing bacteria, and CO₂ sorption (El-Naggar et al., 2019; Mosa et al., 2023). Mineral soil amendments also affect soil water retention, porosity, pH, and nutrient availability (Jarosz et al., 2022; Sha et al., 2022) and could thereby alter bacterial communities (Jarosz et al., 2022; Zeng et al., 2022) and increase microbial activity (Doni et al., 2021).

To describe the relative mobility of a chemical species, a retardation factor, R_f, is often used (Freeze and Cherry, 1979). Various methods for calculation have been developed and critically reviewed (Priddle and Jackson, 1991). The relationship between R_f and porosity, bulk density, and sorption coefficients is deduced from mass balance and verified with empirical data. However, transport and scale effects can lead to variations between theoretical and field measurements (Priddle and Jackson, 1991). Methods based on breakthrough curves and times have been shown to give better results for gas–solid systems and are often applied to laboratory and field data (Priddle and Jackson, 1991; Dou et al., 2016). Here, a simulation that mimics column experiments with a constant tracer gas injection is used to simulate the effects of sorption on migration of CO₂ after sorbent deposition. A simulation scenario where only sorbent was present as solid phase was compared to a scenario where only unreactive quartz was present as solid phase. To ensure comparable diffusion, the porosity was set to 0.7 for both simulations based on biochar porosity (Gray et al., 2014). In both cases CO₂ production within the column was set to zero. However, pCO₂ was set to 30,000 ppm at the lower boundary. This ensures CO₂ diffuses through the column. When sorbent is present there will be a delay in transport. In this set up the retardation factor R_f is related to the ratio of breakthrough time of the sorbed CO₂ and the CO₂ in the unreactive quartz column (Dou et al., 2016) (Equation 8):

$\begin{array}{ll}{R}_f=\frac{t_s}{t_u}& (8)\end{array}$

Where t is the time that it takes to reach half of the initial concentration in the column filled with sorbent (subscript s) and unreactive quartz (subscript u) respectively. The retardation factors were calculated from simulated concentrations at a depth of 0.75 cm. Breakthrough curves were constructed for pCO₂ at 0.5 depth.

A one-time reduction of CO₂ soil emissions was calculated as difference between simulated soil efflux without sorbent (i.e., the baseline or counterfactual) and with sorbent over the relaxation time (Equation 9):

$\begin{array}{ll}\%\mathit{removed}=\frac{{{\displaystyle \int }}_{t\_i}^{t}J{\left(t\right)}_{c}dt-{{\displaystyle \int }}_{t\_i}^{t}J{\left(t\right)}_{s}dt}{{{\displaystyle \int }}_{t\_i}^{t}J{\left(t\right)}_{c}dt}\cdot 100& (9)\end{array}$

Where J is the diffusive flux between soil and air, the subscript c indicates the counterfactual scenario, and the subscript s refers to scenarios with sorbent. Because flux J equals CO₂ production P under steady state conditions in the baseline scenario, Equation (9) can be rewritten as (Equation 10):

$\begin{array}{ll}\%\mathit{removed}=\frac{{{\displaystyle \int }}_{t\_i}^t{P}_{s}dt-{{\displaystyle \int }}_{t\_i}^{t}J{\left(t\right)}_{s}dt}{{{\displaystyle \int }}_{t\_i}^t{P}_{s}dt}\cdot 100& (10)\end{array}$

2.2.4 Model output analysis

For model verification and assessment, a time- and depth-integrated mass balance was developed (Equation 11):

$\begin{array}{l}\underset{t\_i}{\overset{t}{{\displaystyle \int }}}\frac{dC{O}_2}{dt}dt+\underset{t\_i}{\overset{t}{{\displaystyle \int }}}\frac{\mathit{dDIC}}{dt}dt+\underset{t\_i}{\overset{t}{{\displaystyle \int }}}\frac{\mathit{dCalcite}}{dt}dt=\underset{t\_i}{\overset{t}{{\displaystyle \int }}}Pdt-\underset{t\_i}{\overset{t}{{\displaystyle \int }}}\frac{dU}{dt}\\ -\underset{t\_i}{\overset{t}{{\displaystyle \int }}}J\left(t\right)dt\end{array}\text{ (11)}$

Where t represents time, carbon storage in the soil is calculated as the inventory of CO₂(g), DIC, and calcite, while U denotes CO₂ sorption. A detailed description of the mass balance can be found in supplemental information. The time elapsed between sorbent addition and the return of the system to steady state is the relaxation time.

3 Results

3.1 Baseline conditions under varying CO₂ production rates

Under baseline conditions with no sorbent present, simulated pCO₂ increased with depth and was higher in scenarios with higher CO₂ production (Figure 3A). The model adequately reproduced observed CO₂ trends for low, medium, and high CO₂ production where concentrations often rapidly increase to concentrations between 5,000 and 30,000 ppm over the first 50 cm (Cerling, 1984; Amundson et al., 1998; Davidson et al., 2006; Wang et al., 2013; Chirinda et al., 2014; Winnick et al., 2020). CO₂ gradients over depth (dCO₂/dz) were positive, meaning an efflux from the soil was simulated (Figure 3B). Simulated DIC increased, pH decreased and Ca²⁺ increased with depth and pCO₂ (Figures 3C–E). Depletion of the calcite mineral volume fraction was higher with higher pCO₂ (Figure 3F). As noted in the methods section, the calcite distribution over depth was simplified for model interpretation and will typically vary as a function of depth depending on climate (Pfeiffer et al., 2023).

Figure 3

Figure 3. Shown are baseline conditions under constantly low, medium, and high CO₂ production. Simulated depth profiles of (A) pCO₂, (B) concentration gradient [dCO₂(g)/dz], (C) DIC, (D) pH, (E) Ca²⁺, and (F) the calcite mineral volume fraction are presented.

3.2 Soil CO₂ response to sorbent addition

Sorption of CO₂ affected soil pCO₂ and soil CO₂ efflux (Figure 4). The simulated sorption capacity (sorbed CO₂/g sorbent) aligned with observed data that had been used to derive sorption isotherms (Figure 4A). Sorption increases with pCO₂, which in the simulations increased with depth and CO₂ production. The scenario with the highest CO₂ production reached almost 0.015 bar within the application depth of 25 cm, under which the sorption capacity was almost three times higher than at atmospheric pCO₂. Over the simulation time, the addition of the sorbent to the soil is visible in a decline of pCO₂ (Figure 4B). At a depth of 20.5 cm, the simulated pCO₂ was initially around 2,000 ppm for a scenario with low CO₂ production. At day 400 of the simulation, sorbent was added and pCO₂ decreased to almost 0 ppm. After several days the pCO₂ rose again and then slowly returned to steady state after around 50 days. The return to steady state was faster with higher CO₂ production. Sorption behavior was transient over depth because gas diffusion and production are not instantaneous (Figure 4C). Immediately after application, sorbed CO₂ over depth followed a u-shape with high sorption at the atmosphere-soil and the shallow-deep soil interface. The shape indicates that gas from the deeper soil and the atmosphere was diffusing in (Figure 4D). The sorption temporarily reduced CO₂ efflux and even caused CO₂ influx from the atmosphere (Figure 4B). The effect on efflux lasted longer when CO₂ production was lower.

Figure 4

Figure 4. Sorbed CO₂, pCO₂ and CO₂ efflux after sorbent addition. (A) Sorbed CO₂ (mol/g sorbent) as a function of pCO₂ simulated under high CO₂ production (red line) and observed values that were used to fit the Langmuir isotherm (Ringsby et al., 2024) (grey dots). Sorbent was present in model over the top 25 cm. (B) Simulated pCO₂ over time at a depth of 0.205 m for one scenario with low CO₂ production with sorbent addition at day 400. Simulated pCO₂ was at a steady state before sorbent addition and returned to steady state after roughly 50 days. (C) Transient depth profiles of sorbed CO₂ over the top 0.5 m under low CO₂ production. Shown are initial baseline conditions without sorbent (red), conditions at 0.1, 1, and 7 days after sorbent application, and final sorption (green) upon which all other simulated parameters return to baseline conditions. The grey area indicates the application depth. (D) CO₂ efflux at soil surface with low, medium, and high CO₂ production. A drop below zero indicates influx to the soil.

Total maximum sorption was higher with higher CO₂ production and higher total sorbent mass (Figure 5). Total sorption can be related to mean steady state pCO₂ over application depth (Supplementary Figure S3). A temporary reduction in efflux was related to CO₂ production and sorbent mass, as was expected (Figure 5B).

Figure 5

Figure 5. (A) Total sorbed CO₂ and (B) temporary reduction in CO₂ efflux, both as a function of total added sorbent mass and depending on CO₂ production.

Transport occurred in simulations only via diffusion, which is slow compared to advection and results in a notably delayed breakthrough and broadened breakthrough curve (Figure 6) compared with sorption studies that pump gas into columns (Kaur et al., 2019; Pal et al., 2019; Al Mesfer et al., 2020).

Figure 6

Figure 6. Simulated breakthrough curves for pCO₂ at 0.5 m depth when a 1 m column consists of either unreactive quartz or sorbent. Gas transport occurs only through diffusion resulting in a delay to reach steady state conditions without sorption.

3.3 Response of soil geochemical parameters

Depth profiles show that changes in pCO₂ through sorption affected all simulated parameters (Figure 7). Changes are particularly visible immediately after application and where sorbent had been applied (in the top 25 cm). Immediately after sorbent application, the pCO₂ reached almost zero over the application depth. The CO₂ gradients changed from positive to negative at the atmosphere-soil interface, indicating that there was CO₂ influx to the soil instead of efflux. The CO₂ gradients strongly increased where sorbent amended soil meets the unamended soil. Over the application depth, simulated DIC was reduced by over 90%, and pH increased from 7.5 to 8. The pH was increased because sorption of CO₂ that is in equilibrium with the aqueous phase removes bicarbonate ions and protons from solution via:

$\begin{array}{ll}{\mathrm{C}\mathrm{O}}_2\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}+{\mathrm{H}}^{+}& (12)\end{array}$

Figure 7

Figure 7. Simulated changes in soil geochemical parameters due to sorption on soil amendment and increased CO₂ production. (A) Simulated pCO₂ at depth 20.5 cm and over simulation time. Heatmaps over depth and simulation time for (B) sorbed CO₂, (C) pCO₂, (D) dpCO₂/dz., (E) DIC, (F) pH, (G) Ca²⁺, and (H) calcite volume fraction. Application rate of 9.86 t/acre and 25 cm application depth.

The simulated Ca²⁺ was around 50% lower and the calcite mineral volume fraction was slightly increased due to precipitation. The precipitation was temporary, and calcite redissolved. The transient change in calcite mineral volume fraction was larger with higher total sorption. Transient conditions lasted longer when CO₂ production was lower. Transient conditions lasted for 30–50 days when only sorption and no increased CO₂ production was simulated.

Assuming an increased CO₂ production after amendment application resulted in deviation of soil geochemical parameters after 20 days (Figure 7): higher pCO₂, higher dCO₂/dz, higher DIC, lower pH, higher Ca²⁺, and lower calcite volume fraction. This indicates that changes in CO₂ production – an empirical representation of soil respiration – have the potential to persistently change soil geochemistry.

A high retardation factor of $R_f=37.5$ was calculated in a simplified simulation scenario with either sorbent or unreactive quartz. The delay in diffusion due to sorption is clearly visible in pCO₂ heatmaps (Figure 7). In the column with quartz, pCO₂ increases rapidly in <1 day and is then at steady state. With sorbent, there is a slow increase over 30 days, after which steady state is reached.

4 Discussion

In the following we will discuss how manipulation of soil CO₂ affects inorganic C cycling in unsaturated soils and the importance of transient conditions. We present implications for application and monitoring of CDR that affects the soil response. Although simulations were focused on C cycling, there are additional benefits and limitations for soil amendment application in drylands, which we will also discuss.

4.1 Inorganic carbon cycling in dry soils

Figure 8 shows how carbonate alkalinity and Ca²⁺ concentrations are related to carbonate dissolution via acids in addition to other processes, e.g., degassing and sorption. The 1:1 line in Figure 8 indicates carbonate dissolution through carbonic acids (Semhi et al., 2000; Perrin et al., 2008):

$\begin{array}{ll}{\mathrm{CaCO}}_3+{\mathrm{C}\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\leftrightarrow 2{\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}+{\mathrm{C}\mathrm{a}}^{2+}& (13)\end{array}$

Figure 8

Figure 8. Carbonate alkalinity and Ca²⁺ and Mg²⁺ concentrations shown for steady state conditions at the soil-atmosphere interface (red square), transient conditions at the soil-atmosphere interface (blue dot), and steady state conditions at 1 m depth. The lower line depicts the 1:1 ratio expected for carbonate dissolution exclusively from carbonic acid. The upper line depicts 2:1 stoichiometry of calcite dissolution through other acids, e.g., in fertilizer impacted sites. The area above the 2:1 line represents conversion of bicarbonate to CO₂ through degassing.

And a possible reaction for the 2:1 line is (Zamanian et al., 2018):

$\begin{array}{ll}{\mathrm{CaCO}}_3+{\mathrm{N}\mathrm{H}}_3+{\mathrm{H}}_2\mathrm{O}+2{\mathrm{O}}_2\to {\mathrm{H}\mathrm{C}\mathrm{O}}_3^{-}+{\mathrm{C}\mathrm{a}}^{2+}+{\mathrm{NO}}_3^{-}+2{\mathrm{H}}_2\mathrm{O}& (14)\end{array}$

Equation 14 describes calcite dissolution after N fertilizer application. Acidification leads to increased calcite dissolution rates and cations are balanced by nitrate anions, as opposed to only bicarbonate (Zamanian et al., 2018). This reaction has been identified as a CO₂ source in agricultural areas that are either limed or where carbonates naturally occur (Semhi et al., 2000; Perrin et al., 2008; Zamanian et al., 2018). Transient conditions above the 2:1 line occurred in the simulations due only to sorption and degassing—contributing to lower bicarbonate concentrations but no cations. Some calcite precipitation occurred simultaneously resulting in a slight drop in cation concentrations.

Transient conditions in drylands are often driven by wetting events, which cause a complex biogeochemical soil response (Jarvis et al., 2007) including increased soil respiration, desorption (Sánchez-García et al., 2020), and dissolution and reprecipitation of carbonate minerals (Angert et al., 2015; Gallagher and Breecker, 2020). A short-term increase in CO₂ efflux is known as “Birch effect” and is mostly attributed to increased soil respiration although immediate release of CO₂ has been associated with desorption (Kemper et al., 1985; Sánchez-García et al., 2020) which strongly depends on OM content in soils (De Jonge and Mittelmeijer-Hazeleger, 1996). Carbonate dissolution increases with elevated pCO₂, which dampens the soil CO₂ efflux after wetting events and has been associated with underestimation of soil respiration rates when carbonates are present (Angert et al., 2015; Gallagher and Breecker, 2020). A second important source of transient conditions in drylands are daily, seasonal, and annual temperature changes. Increased temperature generally leads to increased soil respiration and desorption although concomitant changes in moisture can either amplify or reduce this response (Tang et al., 2003; Shen et al., 2009; Darrouzet-Nardi et al., 2015; Sagi et al., 2021).

Transient conditions lasted for varying time scales in the simulations, which has implications for monitoring (Figure 9). Increased calcite precipitation lasted only a few hours while the soil CO₂ efflux was affected over more than 10 days. Comparison to field observations shows similar variations in time scales. The Birch effect, which occurs on dryland soils, is most pronounced for a few hours or days after a wetting event (Jarvis et al., 2007; Unger et al., 2010). Seasonal variations in wet-dry cycles will lead to prolonged variation in carbonate dissolution and precipitation (Breecker et al., 2009; Gallagher and Breecker, 2020; Domínguez-villar et al., 2022).

Figure 9

Figure 9. Total concentration changes in sorbed CO₂, soil CO₂, DIC in porewater, and calcite over simulation time in comparison with CO₂ efflux from soil (right y-axis). The red area indicates the range of carbonate alkalinity flux in rivers in carbonate-dominated catchments (mol m⁻² s⁻¹) (data from Zhang S. et al., 2022).

Transient conditions are also important to for managing carbon cycling in drylands. In 5 h laboratory experiments, the peak after wetting composed almost 80% of the total CO₂ efflux (Sánchez-García et al., 2020). Transient conditions due to drying and rewetting—even when short-lived—were found to result in higher soil CO₂ emissions than constantly moist soils and gain relevance because of the spatial extent of drylands (Jarvis et al., 2007; Shen et al., 2009).

Shown as comparison to the simulated soil CO₂ efflux is the range of carbonate alkalinity fluxes in rivers in carbonate-dominated catchments (Zhang S. et al., 2022) (Figure 9). Carbonate alkalinity export to rivers derived from calcite correlates with hydrological conditions and carbonate precipitation under dry conditions leads to increased CO₂ soil efflux (Wen et al., 2022). Therein lies a potential benefit of increased gas sorption within carbonate containing soils. Sorption is reversible and desorption of CO₂ that occurs when water is present could aid export of carbonate alkalinity to rivers. How much of the desorbed CO₂ escapes to the atmosphere or is trapped in pore space depends on a myriad of environmental factors, such as water amount and soil properties (Sánchez-García et al., 2020).

4.2 Implications for application of soil amendments and monitoring of CDR

The simulated dynamics indicate both potential co-benefits and disadvantages for co-application of various soil amendments. Application of soil amendments that cause positive priming might be suitable to be combined with EW, because the increased production of CO₂ could drive mineral dissolution. However, soil amendments that induce negative priming associated with reduced CO₂ production could hinder EW. Biochar can cause positive or negative priming, but the underlying drivers are still poorly understood (El-Naggar et al., 2019). Thus, sites-specific evaluation of the response to biochar may be required.

The simulations have further implications for monitoring established or promising soil CDR methods. CDR via biochar currently only considers C that is contained in biochar, but biochar also affects native soil C. This is why recommendations for monitoring would be relevant for biochar if native soil C is regulated in the future. This is especially important because fragile drylands soils are more vulnerable to climate change (Lal, 2019). Key drivers for carbon cycling, such as temperature and precipitation, are currently changing at a regional scale, while the local response of SOC and SIC pools in drylands is uncertain (Shen et al., 2009; Wang et al., 2022). Depending on specific climatic and soil conditions in drylands, monitoring campaigns need to adequately capture transient conditions over different time scales. If degassing, (de)sorption, and soil gas displacement are expected to play a major role and should be investigated (Sánchez-García et al., 2020), monitoring needs to capture transient conditions that might last only a few hours or days. On the other hand, climates dominated by seasonal variations need to capture these variations over longer time scales and to avoid under-or overestimation of carbon fluxes.

Various monitoring methods need to be applied to distinguish different processes within the carbon cycle. There are a range of parameters that can help to monitor CDR by distinguishing between organic and inorganic carbon cycling. Carbon mass balance over depths, pCO₂ depth profiles, O₂ concentrations or depth profiles, and carbon isotope composition can help to distinguish biotic and abiotic process (Angert et al., 2015; Gallagher and Breecker, 2020). Monitoring major cations and anions is helpful to resolve if carbonate and silicate weathering consumes CO₂ or is driven by other acids (Perrin et al., 2008; Zamanian et al., 2018).

Simulated carbon dynamics are specifically relevant for monitoring of EW. Monitoring of all parameters that are affected by CDR methods like EW can be expensive, which is why monitoring schemes that provide reliable CDR estimates based on as little monitoring as possible are under development and there is no consensus yet on what constitutes a reliable method. Fuhr et al. (2023) also points out that highly dynamic natural background conditions need to be accounted to monitor EW fluxes reliably. Various methods to monitor or predict EW have been presented in the literature: (1) carbonate alkalinity and cation concentrations either in rivers (Knapp and Tipper, 2022; Zhang S. et al., 2022) or in soils (Holzer et al., 2023), (2) Ca, Mg and nitrate ions and rare earth elements (Kantola et al., 2023) (3) total alkalinity (Fuhr et al., 2023), (4) electrical conductivity (Rieder et al., 2023), and (5) simulations of varying complexity and spatial scale (Beerling et al., 2020; Cipolla et al., 2021; Kanzaki et al., 2023). An important process that was highlighted by simulations here and should be considered when monitoring EW is degassing, which resulted in additional removal of DIC from solution as well as short-lived calcite precipitation. Most streams are oversaturated with respect to CO₂ and degassing is prevalent (Stets et al., 2017). Estimates suggest up to 60% of CO₂ emissions from streams originate from DIC (Duvert et al., 2019; Winnick and Saccardi, 2024), and 30% of CO₂ originate from DOC (Khadka et al., 2014). Spatial and temporal patterns of pCO₂, degassing and sources of degassing depend on flow regimes, respiration, alkalinity, and groundwater inputs (Khadka et al., 2014; Winnick and Saccardi, 2024). A positive correlation between the pool of DIC and the contribution of DIC to degassing fluxes has been found (Winnick and Saccardi, 2024). In the simulations, degassing and removal of DIC also led to calcite precipitation. However many rivers are supersaturated with respect to calcite potentially due to inhibition (Knapp and Tipper, 2022).

4.3 Carbon sequestration potential

The simulations show that abiotic C-sinks such as CO₂ sorption gain importance as a C sink in soils when biological activity is low, which is the case in many dryland ecosystems (Warner et al., 2019; Sagi et al., 2021). The relative reduction in CO₂ efflux over relaxation time was higher with lower CO₂ production (Figure 5). Moreover, dryland soils with low organic matter content have the lowest sorption capacity of all naturally occurring soils and around 10 times lower sorption capacity than the simulated sorbents (De Jonge and Mittelmeijer-Hazeleger, 1996; Ravikovitch et al., 2005; Davidson et al., 2013). Although CDR through sorption is estimated to be relatively low for a single application (around 2% of total C for the simulated biochar as detailed in SI), soil amendments could be relevant for drylands due to the limitations of other methods and through provision of soil health benefits.

4.4 Additional considerations for soil amendments in drylands

Soil amendments have the co-benefit of alleviating soil degradation, specifically salinization. Soil salinity is a worldwide concern, with drylands, irrigated lands, and agricultural lands most at risk (Dregne et al., 1991; Ivushkin et al., 2019). Mechanisms that have been implicated in salinity amelioration with biochar are: release of Ca²⁺ and Mg²⁺, adsorption of Na⁺, proton release that promotes Na⁺ uptake in certain plant species, increased salt leaching through increased porosity (Akhtar et al., 2015; Amini et al., 2016), reduced EC (Lashari et al., 2015), and changes in evaporation dynamics (Liang et al., 2021; Lee et al., 2022). However, depending on biochar characteristics biochar could release Na⁺ (Saifullah Dahlawi et al., 2018) and some biochar studies have been criticized because salt stress was induced with NaCl (Akhtar et al., 2015).

Challenges for soil amendment application are health risks, transport emission and albedo changes. Although biochar feedstock can contain heavy metals and organic contaminants, the fraction that is bioavailable after pyrolysis tends to be small (Godlewska et al., 2021). Sorbent materials generally immobilize contaminants if the sorbent is immobile (Godlewska et al., 2021) suggesting positive health effects. Soil amendments can lead to reduced wind erosion long-term, which could be an important benefit for drylands (Şeker and Manirakiza, 2020; Pi et al., 2021).

Emissions from implementation, e.g., material preparation and transport will reduce the CDR potential. Transport emissions are a particular concern, because there is typically little infrastructure in drylands. Sources for biochar are scarce in drylands due to relatively lower above ground biomass (Cook-Patton et al., 2020), however, most of the global irrigated lands are situated on drylands (Dregne et al., 1991; Siebert et al., 2015) and could provide biomass sources, as could other organic wastes.

Albedo refers to surface albedo, which varies by land cover type, color, wetness and surface irregularities (Zhang X. et al., 2022). Albedo is highest in deserts (0.2–0.45) and dry soils (0.15–0.36) while increased water content (0.06–0.19) and vegetation cover reduce albedo (grasses 0.2, savannah 0.15–0.2) (Garratt, 1993). Biochar application was found to lead to albedo reduction of 0.05 on agricultural soil, which lowered the predicted climate change mitigation benefit by 13–22% (Meyer et al., 2012). The changes in soil albedo are less of a concern for vegetated grasslands and shrublands, which make up around two thirds of global drylands. Future work should assess albedo changes in field trials.

5 Summary

Reactive transport simulations were performed to investigate dynamics between organic and inorganic C pools in dryland soils and to predict CDR via CO₂ sorption on soil amendments. In the simulations, CDR via sorption gained importance when biological activity was low –transient conditions lasted longer and a larger percentage of CO₂ was prevented from efflux during those transient conditions. Simulations highlighted that CO₂ removal via sorption causes transient conditions affecting CO₂ efflux, pCO₂, DIC, pH, major cations and calcite. The simulated dynamics have implications for the application of a range of CDR methods, e.g., if the combined application of biochar and minerals for enhanced rock weathering will benefit CDR depends on soil priming effects. The transient conditions have implications for monitoring: the presence of carbonates, degassing, and desorption can affect the timing and magnitude of the soil CO₂ response, which needs to be considered in sampling schedules or sampling parameters. Future work should include evaluation of different sorbent designs, transport modes, and albedo changes. Considering that a high percentage of dryland soils are degraded and that other methods are limited by water availability, soil amendments with high sorption potential and soil health benefits could provide valuable CDR potential and aid restoration of dryland soils.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

SH: Conceptualization, Formal analysis, Methodology, Visualization, Writing – original draft, Writing – review & editing. AR: Data curation, Writing – review & editing. KM: Conceptualization, Funding acquisition, Methodology, Supervision, Writing – review & editing.

Funding

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. The authors gratefully acknowledge support from the Stanford Doerr School of Sustainability Accelerator Program. AJR acknowledges support from the National Science Foundation Graduate Research Fellowship Program under Award DGE-1656518.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fclim.2025.1505472/full#supplementary-material

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