Theoretical evaluation on CO2 removal potential of enhanced weathering based on shrinking core model

The discrepancy between current CO2 emission trend and the targeted 1.5 °C warming requires the implementation of carbon dioxide removal (CDR) technologies. Among the engineered CDRs, enhanced weathering (EW) is expected to exhibit substantial potential for CO2 removal, owing to the availability of abundant reserves of ultramafic rocks and demonstration of worldwide liming practice. While the shrinking core model (SCM) has been commonly adopted in previous theoretical and experimental studies, there still lacks a comprehensive assessment on the impacts of model parameters, such as rock particle size, size distribution, weathering rate and time length on the weathering kinetics and the resultant CDR potential. Herein, this study incorporates particle size distribution of rock powder into the surface reaction-controlled SCM, and conducts sensitivity analysis on EW’s CDR potential quantitatively. Even fully powered by low-carbon energy in the optimistic case, the application of EW with olivine only achieves maximum CDR per unit of rock and energy consumption of 0.01 kg CO2 per kg rock and 19 g per kWh at size of 8 and 22 μm respectively, indicating the limitations of EW. The derived optimal application parameters with olivine powers within 3.7–79 μm provide valuable insights into the practical real-world applications to achieve net CO2 removal.


Introduction
Enhanced weathering (EW) is widely regarded as one of the candidate carbon dioxide removal (CDR) technologies with significant potential [1].It involves spreading finely ground minerals in warm and humid environment to promote mineral weathering and CO 2 drawdown by reacting CO 2 with rock to form carbonate minerals (CaCO 3 ).In experimental and theoretical studies of CDR through EW, surface reaction-controlled shrinking core model (SCM) is often adopted to describe the kinetics of mineral weathering.The solid reactant continues shrinking down as the reaction with the surrounding fluid proceeds [2][3][4][5][6].The derived mathematical model can be used to fit experimental data for kinetic parameters [4,5] and to theoretically estimate the CDR potential of long-term and large-scale applications [3,6].
In theoretical studies, extremely fine rock powders with a single uniform size was assumed to achieve a large weathering extent in a short period of time, e.g.diameter less than 30 µm for 100% of weathering [7][8][9].However, this assumption is not in line with particle size distribution (PSD) of ground rock powders in real-world applications.Although some theoretical studies have attempted to incorporate PSD into their models, they typically rely on fixed distributions that neglect the impact of comminution methods and rock strength on the shape and range of the PSD [2,3].The impact of PSD of rock powders on the weathering extent and CO 2 removal potential has received limited attention in previous research.In reality, intensive grinding of rock powders leads to an increasing proportion of fine particles and creation of new surface area, which notably accelerates weathering rate (W r ) [10,11].However, a corresponding rise in grinding energy will cause additional CO 2 emissions that can counteract the CO 2 sequestration achieved via weathering [12].The double-edged effect of rock sizes must be taken into consideration for the evaluation of the net CO 2 removal potential.Currently, there is still a lack of comprehensive investigation into the impacts of model parameters, such as rock particle size, size distribution, weathering rate and weathering time length, on the weathering kinetics and the CO 2 removal potential when the overall emissions is taken into consideration as well.
Herein, this work introduced the PSD of rock powders into the surface reaction-controlled SCM and analyzed the impact of application parameters of EW on the weathering extent within a period of time.Sensitivity analysis on rock and energy types was also conducted regarding to energy consumption and CO 2 emissions during the application processes, i.e. mining, transportation, grinding, and spreading.Since the implementation of EW is energy and resourceintensive, figure of merits from the perspectives of energy and rock consumption was provided to gauge the real-world practical application.

Method
The dissolution of cations in minerals is affected by various factors, including the intrinsic physicochemical properties of minerals, solution chemistry, and environmental factors.In the field studies, sluggish dissolution kinetics on the mineral surface typically control the weathering process at ambient temperature and pressure [13,14].Therefore, surface-controlled SCM was adopted here to describe the overall weathering extent of rocks (φ) and carbonation process for CO 2 uptake.The relationship between the weathering extent of particles (X) with a certain size (D, unit: m) and time (t, unit: s) is expressed by: where V m denotes the molar volume of the minerals (unit: m 3 mol −1 ), W r stands for the weathering rate (unit: mol m −2 s −1 ).The full names and corresponding abbreviations of all parameters are listed in table 1.
The mathematical model further incorporated PSD of rock power represented by a bivariate function of Rosin-Rammler distribution, which is commonly used to fit the PSD of fine particles obtained from intensive grinding (see supplementary note 1 and 2) [15,16].For better understanding, the characteristic value of p80 size and the coefficient of variance (CV) were introduced as characteristic parameters of Rosin-Rammler distribution to provide granular information about the PSD statistically.The p80 size refers to the particle size at which 80% of the particles will pass when screened and the CV is the ratio of the standard deviation to the mean particle size.A large CV value indicates a high proportion of small particles in the distribution.Each set of p80 and CV values corresponds to a particular PSD.
It is assumed that the formation of pedogenic carbonates occurs within the soil, primarily relying on soil-retained water with limited capillary, percolating, and evaporating water.In the absence of a continuous water flushing into the soil, additional driving forces for percolating through aggregated particles, flushing off weathering-inhibiting surficial silica, and continuously removing carbonate and/or bicarbonates through soil drainage is mitigated.The precipitation of secondary carbonate is the major weathering product [17], which involves fixing one mole of CO 2 through the dissolution of each mole of magnesium or calcium ions from minerals expressed by equation (2).The maximum CO 2 removal potential of rocks (R CO2 in tons CO 2 per ton of rocks [18]) is therefore calculated to be 0.3 tons of CO 2 per ton of basalts (based on real-world basalt compositions [19]) and 0.63 tons of CO 2 per ton of pure forsterite (based on chemical formula Mg 2 SiO 4 ) as the base and optimistic cases.The influence of temperature and hydrology on the weathering kinetics and CO 2 uptake is discussed in supplementary note 4 and 5 ( The energy consumption for mining, transportation and spreading per unit mass of rock, denoted as E i , was collected from literature [18] (table S1) while grinding energy was calculated using the proposed size-energy relationship (see supplementary note 3) [20].Figure of merits, representing the CDR capability per unit of rock and energy consumption, was proposed as M CO2,M and M CO2,E (equations (3) and ( 4)) for sensitivity analysis of the influencing factors on CDR potentials, including rock types, energy intensity and carbon intensity of energy usage (EF i ) via use of fossil fuel (FF) and low carbon energy (LCE) as base and optimistic cases.Detailed parameters of sensitivity analysis are shown in table S1

Results and discussion
The impact of particle size on the CDR capability, regarding to both total energy consumption and CO 2 emissions, was initially investigated without considering the kinetic constraints of weathering, which means that the rock powders of all sizes undergo complete weathering, i.e. φ = 100% in equations ( 3) and (4).In this case, M CO2,M and M CO2,E represent the maximum net CDR capability that can be achieved for different rock types and energy usage scenarios at a specific particle size.The curves of net CO 2 removal for two different rock components, from realistic basalt to idealized pure forsterite, are distributed in two distinct  areas marked as the blue and gray shaded areas representing R CO2 = 0.3 and 0.63 tons of CO 2 per ton of rocks, respectively (figure 1).Curves within each area depict different energy usage scenarios.With increasing particle sizes, the intrinsic CO 2 capture removal determined by rock components dominates the net CDR amount.However, as the characteristic particle size decreases, the increase in energy consumption and carbon emissions gradually reduces the net CDR amount per unit rock, moving away from the intrinsic values.Consequently, the influence of energy usage (energy consumption and carbon intensity of energy) becomes the dominates factor.The intersection of these curves with M CO2,M = 0 and M CO2,E = 0 corresponds to the lower bound of particle size to avoid net emissions.In the base case which is energy-intensive and dependent on FFs, even if the forsterite with the maximum intrinsic capability is applied and completely weathered, CO 2 emissions during EW application cannot be totally removed when the particle size is less than 3 µm.By contrast, in the optimistic energy scenario, net CO 2 removal can be achieved with 100% weathering and any particle size.
In figure 1(a), two groups of curves with different R CO2 values overlap at particle sizes below 5 µm, whereas the overlap in figure 1(b) occurs at particle size below 10 µm.The intersection of the curves indicates that, for rocks with lower intrinsic CO 2 removal capabilities, optimizing energy usage through low-carbon energy and improving mechanical energy efficiency can lead to higher net CO 2 removal than olivine of the same size.Notably, it can be found that the overlap between the two rock-component areas in net unit-energycost CDR appears with relatively larger particle sizes (figure 1(b)) compared to the net unit-rock CDR curves (figure 1(a)), suggesting the impact on CO 2 offset due to particle size reduction is greater than that of energy consumption increment.Similarly, the size-dependent relative magnitude between the LCEbased curve with Bond work index (W) of 26 kWh/t and that based on FF with W of 12 kWh/t (figure 1(b)) is observed from their intersection points in the same rock component area (within the shaded area).As the particle size decreases, the change in the impact of particle size indicates a shift in the dominant factors affecting net CO 2 removal between CO 2 emissions offset and extra energy consumption.When particle size is greater than 10 µms which is more realistic in application, the nearly negligible influence of the CO 2 offset from auxiliary operations further emphasizes the significance of subsequent analysis on other influencing factors on net CDR potential.
In order to further incorporate the limitation of weathering kinetics into the evaluation of CDR potential, we extended our analysis to investigate the effects of particle size, size distribution, and weathering rate on rock weathering extent, considering the two boundary cases: basalts with R CO2 = 0.3 tons of CO 2 per ton of rocks in the base energy scenario, and ideal pure forsterite with R CO2 = 0.63 tons of CO 2 per ton of rocks in the optimistic energy scenario.Besides, the potential influence of parameter selection and underestimation of auxiliary energy cost in the theoretical model on the CDR potential was studies as well.

Impact of the selection of the minimum particle size in the mathematical model
In the mathematical model describing the surfacecontrolled shrinking core weathering kinetics, the minimum particle size of the rock powders in the PSD needs to be defined to calculate the weathering extent.The structure and properties of internal mineral crystals in rocks hinders the complete decomposition of all crystals into individual atoms even with highly intensive grinding in real-world mining practice [20].Therefore, we selected 1 nm, 50 nm, and 100 nm as the minimum particle size for theoretical calculations to investigate the quantitative relationship between oneyear weathering extent on particle size and W r .
Figure 2 illustrates the weathering extent of the rock within one year under different weathering rates and PSD characterized by size p80 and CV.p80 is depicted as the vertical axis of the plots, and each horizontal line corresponds to a specific set of PSD and distribution features determined by p80 and CV values.CV of 0.5 indicates a relatively even distribution of large and small particles in the rock powders (figure 2(a)-(c)).When CV is equals to 0.5, the selected minimum particle size of 1, 50, and 100 nm has almost no effect on the distribution of weathering extent contour lines.When CV is equal to 1.5, the peak of PSD shifts towards smaller particle sizes, and the proportion of fine particles in the rock powders increases.As the selected minimum particle size increases, the contour lines corresponding to the same weathering extent gradually shift to the right (figures 2(d)-(f)), revealing that a faster weathering rate is required.The shift is more prominent for contour lines of lower weathering extent.For instance, when the minimum selected particle size is 1, 50, and 100 nm with p80 of 10 µm, weathering extent of 0.2% requires a corresponding W r of 10 −13.4 , 10 −12.7 , and 10 −12.5 mol m −2 s −1 , respectively, while weathering extent of 10% requires corresponding W r of 10 −11.1 , 10 −10.9 , and 10 −10.8 mol m −2 s , respectively.Thus, when fine particles dominate the size distribution, the selection of the minimum particle size greatly affects the theoretical calculation of weathering extent.
The trends observed above indicate that as the selected minimum particle size increases, the weathering extent of rock powders with the same PSD and W r gradually decreases within one year.The reason is that the larger the minimum particle size is selected, the greater part of fine particles with size smaller than the minimum size are not included in the calculation, leading to a decrease in the overall weathering extent, which is particularly noticeable when the proportion of fine particles is high with CV of 1.5.According to the SCM, as the W r slows down, the depth of the dissolution reaction on the particle surface decreases, and the weathering of fine particles contributes significantly to the overall weathering extent.This accounts for the observation that contours with smaller weathering extent (φ = 0.02%) shift more to the right.Therefore, the minimum particle size should be determined based on the composition of rocks and type of grinding tools used in practice to avoid large deviations in the simulation of weathering extent.
Sarimai et al obtained forsterite powders with an average particle size of 345 nm after 40 h of ball milling.The grain size of the particles decreased from 53.8 nm to 18.78 nm after 5 h and obvious aggregation was observed [21].In another similar study [22], 30 h of high-intensity ball milling gave forsterite powders with an average particle size of 147 nm and the proportion of particle size less than 50 nm was 25%.Besides, the reported grinding limit is in the range of 10-50 nm in the literature [20].Subsequent theoretical analysis will be based on mathematical calculation with the minimum particle size of 50 nm.Although the selection of minimum particle size may cause deviation in the theoretical modeling as stated above, the influence is acceptable considering the uncertainty of reported weathering rates in the range of two to three orders of magnitude [23], which greatly exceeds the deviation caused by the selection of minimum particle size (10 0.1 -10 0.7 ).
Laboratories studies with experimental setups mimicking the real world application of EW stills shows weathering extent with large discrepancy.An experimental study conducted with fast-weathering olivine in agitated seawater for 137 d showed an initial W r of 10 −9.72 mol m −2 s −1 with the PSD represented by p80 of 214 µm and CV of 0.5 approximately [4].From the original data in the experiment, the one-year weathering extent was estimated to be about 2% through linear extrapolation of initial dissolution.In figure 2(b), the intersection point between the reference lines of initial W r (the rate line labeled as 'initial') and the corresponding particle size gives a weathering extent of 1.8%, which is consistent with the experimental observation.However, this relatively fast W r cannot be sustained, and a plateau was reached after ca.one month due to the accumulation of dissolved mineral cations, where the corresponding W r and annual weathering extent is about 10 −11.36 mol m −2 s −1 and 0.04%, respectively.In figure 2(b), the W r reference line labeled as 'plateau' intersects with the particle size reference line at the point of approximately 0.045% of weathering in theoretical calculation, which agrees well with the experimental results as well.With the assumption of weathering with the retained water in soil, a W r of 10 −11.36 mol m −2 s −1 in the plateau region of the experiment due to local saturation can be used as a reference for following evaluation on CDR potential.
Apart from olivine modeled here, weathering extents of other minerals with specific weathering rate are in line with the modeling results here.For instance, in a 14 month soil-core experiments involving basalts [24], where particle sizes ranged from 125 to 250 µm, the observed weathering extent was derived to be approximately 0.04% within one year.In comparison, the yearly weathering rate of 0.32% for basalts was obtained in a 10 month experiment with similar setups but a water feeding rate 140 times higher [25].Particle size with a p80 value of 74 µm was employed for basalts.The reported weathering rate for basalts in the former study (around 10 −15.3 mol m −2 s −1 ) was approximately two times slower than that in the latter one (10 −12.8 -10 −13.4 mol m −2 s −1 ) due to different weathering environments and particle size.The corresponding magnitude and range of weathering extent align with the trend in figure 2. Applying EW with weatheringaccelerating factors, such as greater water feeding [26,27], acidified soil due to organic and inorganic root exudates [28] and the reduction of particle size of minerals [29] can jointly contribute to greater weathering extent.
However, in two biotic and basalt-treated mesocosm studies with durations of 120 and 99 d, relatively higher yearly weathering extent of 17% and 7.4% were reported for basalts with p80 sizes of about 1250 and 250 µm, respectively [26,27].Notably, these two weathering extent were derived from the same 1D reactive transport model due to the relatively shorter experimental duration.It is essential to emphasize that the modeling results fall outside the scope of the discussion and comparisons in this study concerning only findings from field investigations.

Impact the particle size, size distribution and weathering rate on CO 2 removal potential
In the previous section, the different trends for CV of 0.5 and 1.5 in figure 2 indicate the influence of PSD on the kinetics of weathering.Contour lines of rock weathering presented in figures 2(b) and (e) reveals that as the PSD of the rock powders narrows towards smaller particles, higher extent of one-year weathering is achieved under specific size and W r .The resultant influence of PSD on CDR potential is further investigated in terms of per unit mass of rocks and unit energy consumption.
The impact of PSD, W r , and energy usage scenario on the CDR potential shows different features within specific particle size and W r ranges (figure 3).The horizontal and vertical black dashed lines are the tangents of the net zero CDR contour lines, representing the lower limits of particle size (particle size limit) and W r (rate limit) required to achieve net CO 2 removal.Both the CO 2 offset from extra energy consumption and restriction of weathering extent determine that only rock powers with particle size and W r larger than the corresponding limit have the potential for net CO 2 sequestration.With an increasing CV, the expansion of net sequestration area confined by particle size and rate limit implies that a higher proportion of small particles favors effective carbon sequestration in a wider range of particle sizes and weathering rates, which in turn increases the feasibility and flexibility of EW application.
However, even under the PSD with CV of 1.5 (figures 3(c) and (f)), net emissions are observed from the area on the left of the rate limit line where W r is less than ca. 10 −10 mol m −2 s −1 and below the particle size limit line where particle size is less than ca.6 µm.When W r is less than 10 −10 mol m −2 s −1 , the weathering extent gradually increases as the rock particle size decreases.But with the limitation of W r weathering extent of less than 10% can only be achieved over one year (figure 2).In comparison, when W r is greater than 10 −10 mol m −2 s −1 , an initial increase in the net carbon sequestration is followed by a sharp decline with decreasing particle size.This suggests that the significant increase in energy consumption and CO 2 emissions for size reduction further counteracts the carbon sequestration from weathering.The acceleration of weathering via size reduction is the main influencing factor in large size area, while the offset from CO 2 emissions of intensive grinding becomes dominant in the small size area.This phenomenon implies that rocks with W r greater than 10 −10 mol m −2 s −1 have an optimal particle size that achieves the maximum carbon sequestration under specific W r .
According to the aforementioned W r of olivine in weathering experiments (10 −11.36 mol m −2 s −1 ), even under the condition of CV = 1.5 with a high proportion of small particle size, this rate fails to intersect with the contour line of net zero CO 2 removal, meaning net emissions under the constraint of W r over one-year weathering (figures 3(c) and (f)).Net CO 2 removal can only be achieved within the range of particle size and W r limit lines.These results can be used as a valuable reference for the practical application of EW technology, including the selection of suitable rock types based on their weathering rate and the optimal target particle size comminution.

Impact of underestimation of auxiliary energy cost on CO 2 removal potential
When CV is 1.5, the rock powders tend to have a relatively high proportion of fine particles.Taking the characteristic size of p80, which is typically used in the size-energy model [30], to calculate the grinding energy consumption can result in more than twofold underestimation of energy consumption [31].It arises particularly because p80 represents a relatively large size in the PSD and fail to account for the fine particles' size and proportion in the PSD.In order to investigate the potential underestimation of energy consumption, we calculated grinding energy using p50 as the characteristic size in the PSD defined by both CV and p80 for comparison.Since p50 is smaller than p80, the resultant grinding energy using p50 is higher, leading to a drop of CO 2 removal capability per unit-mass of rock and unit energy consumption (figures 4 and S1).As both p80 and p50 satisfy the PSD defined by CV and p80, the difference in CO 2 removal capability is solely determined by the energy scenario, which is independent of W r (figures S1(a), (c) and (e)).
In the comparative analysis of the CO 2 removal capabilities calculated with p80 and p50 as the characteristic size for energy consumption (figure 4), it is evident that the particle size limit lines respond differently to the changes of CV.The former is not sensitive to the changes while in the latter one, particle size limit lines gradually shift towards larger particle sizes as CV increases.The increase of CV, requiring prolonged grinding time and an increase in grinding energy, will lead to a reduction in carbon sequestration under the same particle size and W r .Consequently, the net carbon removal area slightly above the particle size limit in figures 4(a), (b), (d) and (e), will convert into net CO 2 emission with a CV of 1.5 (figures 4(c) and (f)).This trend is apparently rendered when calculated with p50.Meanwhile, the weathering rate limit lines in figures 3 and 4 demonstrate the same trend.When p50 is used to calculate grinding energy consumption and the PSD satisfies CV = 1.5 (figure 4(c)), net CO 2 removal can be achieved when the p80 of the PSD and the W r is greater than 21 µm and 10 −9.4 mol m −2 s −1 respectively.
The CO 2 removal capability per unit-mass of rock is significantly affected by the choice of characteristic size used for energy consumption calculations.Specifically, when p80 of the PSD is 1 µm and CV equates 0.5, 1, and 1.5, the difference in CO 2 removal capability per unit-mass of rock between the two approaches is 1.7, 4.9, and 9.5 tons of CO 2 per ton of rocks respectively.Moreover, the difference between the two approaches for CO 2 removal capability per unit energy consumption increases with the increase of CV values.These results indicate that using p50 as the characteristic size to calculate the grinding energy consumption is more suitable for cases where fine particles occupy a major proportion and require high-intensity grinding.Therefore, in the subsequent analysis of carbon sequestration potential, the calculation of grinding energy consumption will rely on the use of p50 as the characteristic size.

Impact of energy usage scenario on CO 2 removal potential
To improve the CO 2 removal capability of the base case, it is necessary to optimize and enhance weathering from the perspectives of energy usage and rock types.The most favorable condition is represented by the optimistic case where low carbon intensity and reduced energy intensity are achieved.
In the optimistic case, the additional CO 2 emissions caused by grinding are greatly reduced, mitigating the offsetting effect on carbon sequestration and further expanding the effective range of net carbon removal under particle size and W r .The intersection between the experimentally measured W r of olivine and the net zero CO 2 removal contour line indicates that using olivine powders with p80 in the range of 3.7-79 µm can achieve net CO 2 removal.The maximum CO 2 removal capability per unit mass of olivine and per unit energy consumption is 0.01 tons of CO 2 per ton of rocks with p80 values of 8 µm and 19 g kWh −1 with p80 values of 22 µm, respectively (figure 5).To place these findings into context, Current and projected global total final energy consumption (TFC) of 418 EJ [32] and 616 EJ along current trajectory in 2050.Approximate 13% and 4% decline of annual global energy demand have come with profound sociopolitical and economic devastation in World War II [33] and the outbreak of Covid-19 pandemics [34], respectively.With such TFC scales and unaffordable energy cost, the net annual CDR potential in the optimistic scenario is estimated to be only 0.3 and 0.4 Gt at the 'world war cost' and 0.09 and 0.1 Gt at the 'against pandemic cost' , respectively.This is far less than the approximately 12 Gt CO 2 emitted annually from hard-to-abate sectors [35].To be competitive with another promising CDR technology direct air capture, whose CO 2 removal potential is derived as 505-805 g kWh −1 from life-cycle analysis [36,37], weathering rate ranging from 10 −10 to 10 −8 mol m −2 s −1 is required for EW with suitable sizes.
Nonetheless, due to the inherent complexities associated with continuous monitoring and quantification, only a limited number of laboratory and field studies have delved deeper into the energy consumption and CO 2 offset from auxiliary operations.Consequently, apart from weathering extent, which can be readily derived from raw data, the annual and unit area of CO 2 removal capabilities reported in laboratory and field studies are overestimated, which makes it challenging to directly compare CO 2 removal capacity per unit-mass of rock and per unit of energy.
In a pot experiment, gross 0.013-0.18t CO 2 /t olivine was reported in the presence of perennial ryegrass and olivine powder with p50 size ranging from 2 and 50 µm during a 32 week growth and weathering period [38].This corresponds to a range of 0.021-0.29 t CO 2 /t olivine within a single year, extrapolated linearly.The variation in CO 2 removal potential per unit mass of rock arises from the different application rate of olivine powders.When considering the CO 2 offset from tertiary milling to ultrafine particles and taking the previously reported 174 g CO 2 emitted per kg of CO 2 sequestered into calculation, the lower boundary of the reported net removal potential aligns with our modeling results.
For comparison, notably smaller CO 2 removal potential, ranging from 0.105 to 0.223 kg CO 2 /t dunite (containing approximately 90% olivine) was observed [29].This difference may be attributed to the exclusion of secondary carbonates as weathering products.Given the complexities of isolating variables that impact the dissolution process in field studies [39,40], future evaluations will require models that incorporate climatic, hydrological, and geochemical influencing factors and their interactions on weathering for more precise assessments.
It should be emphasized that to attain the maximum carbon removal potential in the optimistic scenario, low-carbon energy must be employed during the entire process of EW application.Currently, the global mining industry consumed approximately 4% of global TFC, resulting in carbon emissions that account for around 10% of energy-related greenhouse gas emissions.Apart from the issue of high energy intensity, the release of nickel into soil and the possibility of silica dust may arise concerns regarding the potential impact on human health.Thus, it is imperative to put significant efforts into the development of ultra-EW technology and detailed environmental monitoring.

Conclusion
Based on the surface reaction-controlled shrinking core model, this study quantitatively investigated the impact of rock particle size, size distribution, and weathering rate on the weathering kinetics and CO 2 removal potentials of EW. (1) The optimal application parameters including particle size, size distribution and weathering rate that achieves the maximum carbon removal potential can be determined.(2) The selection of an appropriate characteristic size of rock powder for the calculation of grinding energy holds notable importance in mitigating the underestimation of energy consumption.The dominant factors influencing the figure of merits for energy and rock consumption were identified within specific ranges of application parameters, which can serve as a valuable reference for real-world implementation.
Even fully powered by low-carbon energy in the optimistic case, the application of EW with olivine only achieves maximum CDR per unit of rock and energy consumption of 0.01 tons of CO 2 per ton of rocks and 19 g kWh −1 at size of 8 and 22 µm respectively, indicating the limitations of EW.While there are still scientific and technical uncertainties to be addressed, it is necessary to achieve techno-economic breakthroughs to establish EW as alternative strategy for achieving substantial CDR and reversing the trend of global warming.

Figure 1 .
Figure 1.The relationship between CDR capability per unit of rock and energy consumption and rock size with complete weathering.(The x-axis is the characteristic size of p80 which represents the size distribution of rock powders.The right panel is partial enlargement of the left one.W represents work index (kWh/t) for the calculation of grinding energy.LCE and FF stand for low-carbon energy and fossil fuel energy, representing different energy scenarios.RCO2 represents the maximum CO2 removal potential of rocks (tons of CO2 per ton of rocks)).

Figure 3 .
Figure 3.The relationship between particle size, weathering rate and on CO2 removal potential for base cases.(a)-(c) CO2 removal potential per unit mass of rock and (d)-(f) per unit of energy consumption with CV = 0.5, 1 and 1.5, respectively.(The grinding energy is calculated with p80).

Figure 4 .
Figure 4. relationship between particle size, weathering rate and on CO2 removal potential for base cases.(a)-(c) CO2 removal potential per unit mass of rock and (d)-(f) per unit of energy consumption with CV = 0.5, 1 and 1.5, respectively.(The grinding energy is calculated with p50).

Figure 5 .
Figure 5.The relationship between particle size and weathering rate on CO2 removal potential for optimistic cases.(a) CO2 removal potential per unit mass of rock and (b) per unit of energy consumption with CV = 1.5 (the grinding energy is calculated with p50 and reference lines represent data from enhanced weathering experiment [4]).

Table 1 .
Abbreviations and their corresponding full forms.