ABSTRACT

By combining thermodynamic database mining with first principles density functional theory and phonon lattice dynamics calculations, a theoretical screening methodology to identify the most promising CO₂ sorbent candidates from the vast array of possible solid materials has been proposed and validated. The ab initio thermodynamic technique has the advantage of allowing identification of thermodynamic properties of CO₂ capture reactions without any experimental input beyond crystallographic structural information of the solid phases involved. For a given solid, the first step is to attempt to extract thermodynamic properties from thermodynamic databases and the available literatures. If the thermodynamic properties of the compound of interest are unknown, an ab initio thermodynamic approach is used to calculate them. These properties expressed conveniently as chemical potentials and heat of reactions, which obtained either from databases or from calculations, are further used for computing the thermodynamic reaction equilibrium properties of the CO₂ absorption/desorption cycles. Only those solid materials for which lower capture energy costs are predicted at the desired process conditions are selected as CO₂ sorbent candidates and are further considered for experimental validations. Solid sorbents containing alkali and alkaline earth metals have been reported in several previous studies to be good candidates for CO₂ sorbent applications due to their high CO₂ absorption capacity at moderate working temperatures. In addition to introducing our computational screening procedure, in this presentation we will summarize our results for solid systems composed by alkali and alkaline earth metal oxides, hydroxides, and carbonates/bicarbonates to validate our methodology. Additionally, applications of our computational method to mixed solid systems of Li₂O with SiO₂/ZrO₂ with different mixing ratios, our preliminary results showed that increasing the Li₂O/SiO₂ ratio in lithium silicates increases their corresponding turnover temperatures for CO₂ capture reactions. Overall these theoretical predictions are found to be in good agreement with available experimental findings.

1. Introduction

Carbon dioxide is one of the major combustion products which once released into the air can contribute to the global climate warming effects [1-3]. In order to mitigate the global climate change, we must stop emitting CO₂ into the atmosphere by separating and capturing CO₂ from coal combustion and gasification plants and sequestering the CO₂ underground. Current technologies for capturing CO₂ including solvent-based (amines) and CaO-based materials are still too energy intensive. Hence, there is critical need for new materials that can capture and release CO₂ reversibly with acceptable energy costs. Accordingly, solid sorbent materials have been proposed for capturing CO₂ through a reversible chemical transformation and most of them result in the formation of carbonate products. Solid sorbents containing alkali and alkaline earth metals have been reported in several previous studies to be good candidates for CO₂ sorbent applications due to their high CO₂ absorption capacity at moderate working temperatures [4-6].

To achieve such goals, one of these new methods considered at National Energy Technology Laboratory (NETL) is based on the use of regenerable solid sorbents. In this case sorbents such as alkaline earth metal oxides or hydroxides are used to absorb CO₂ at warm temperatures typically ranging from 100˚C - 300˚C [7,8]. The key phenomenon used in these processes is transformation of the oxide or hydroxide materials to a carbonate upon CO₂ absorption. Regeneration of the sorbent can be obtained, if necessary, in a subsequent step represented by the reverse transformation from the carbonate phase to the oxide or hydroxide phases. The efficiencies of these processes are highly dependent on identification of the optimum temperature and pressure conditions at which absorption, respectively regeneration are performed. In the case of high-performance sorbents, both these two mechanistic steps are optimized in order to achieve minimal energetic and operational costs.

Optimization of the sorbent material can be obtained starting from the analysis of their intrinsic atomistic structure and of their transformations upon interaction with CO₂. Particularly important is to identify the corresponding thermodynamic and kinetic characteristics of the sorbent material of interest. For this purpose scientists at NETL have developed a multi-step computational methodology based on combined use of first principles calculations combined with lattice phonon dynamics to describe the thermodynamic properties of CO₂ capture reactions by solid sorbents [4,9-15]. This methodology has been used to screen different classes of solid compounds and has as major objective identification of the optimum candidate materials that can be further subjected to experimental testing. The advantage of this proposed method is that it allows identification of the thermodynamic properties of the CO₂ capture reaction as a function of temperature and pressure conditions without any experimental input, excepting the crystallographic structural information of the solid phases involved. Such thermodynamics information is essential to guide experimental groups at NETL in development of highly optimized CO₂ sorbents. For a given database of solid materials, our screening scheme allows identification of a short list of promising candidates of CO₂ sorbents with optimal energy usages, which can be further evaluated by our experimental research groups.

In this work, we summarize our progress on development of novel screening scheme to indentify most promising candidates for CO₂ sorbents. The remainder of this report is organized as follows: In the second section we briefly describe the screening method we developed. In the third section, we provide validation results of our computational method for the case of alkali and alkaline metal compounds. Then, we present the preliminary results on CO₂ capture reactions by lithium related salts. The main conclusions are summarized in the last section.

2. Screening Methodology

2.1. Ab Initio Thermodynamics Approach

The complete description of the computational methodology can be found in our previous papers [4,9-15]. Here, we limit ourselves to provide only the main aspects relevant for the current study. The CO₂ capture reactions by solids in the presence of water vapors can be expressed generically in the form

(1)

where the terms given in [∙∙∙] are optional and n₁ and n₂ are the numbers of moles of CO₂ and H₂O involved in the capture reactions. We treat the gas phase species CO₂ and H₂O as ideal gases. By assuming that the difference between the chemical potentials (∆μº) of the solid phases of A, B (and C) can be approximated by the difference in their electronic energies (∆Eº), obtained directly from first-principles DFT calculations, and the vibrational free energy of the phonons and by ignoring the PV contribution terms for solids, the variation of the chemical potential (∆μ) for capture reaction with temperature and pressure can be written as

(2)

where ∆μ⁰(T) is the standard chemical potential changes between reactants and products. If these thermodynamiccal data are available in the thermodynamic database or literature, we can direct apply them into above equation. If these data are not available, they can be calculated using the ab initio thermodynamic approach based on the following approximation.

(3)

Here, ∆E_ZP is the zero point energy difference between the reactants and products and can be obtained directly from phonon calculations. The ∆F^PH is the phonon free energy change between the solids of products and reactants. If the capture reaction does not involve H₂O, then the P_H2O in above equations is set to P₀, which is the standard state reference pressure of 1 bar, and the G_H2O term is not present. The “+” and “−” signs correspond to the cases when H₂O is a product, respectively a reactant, in the general reaction. The free energies of CO₂ (G_CO2) and H₂O (G_H2O) can be obtained from standard statistical mechanics. The enthalpy change for the reaction (1), ∆H^cal(T), can be derived from above equations as

(4)

In Equation (3), ∆E^DFT is the total energy change of the reactants and products calculated by DFT. In this work, the Vienna Ab-initio Simulation Package (VASP) [16,17] was employed to calculate the electronic structures of the solid materials involved in this study. All calculations have been done using the projector augmented wave (PAW) pseudo-potentials and the PW91 exchange-correlation functional [18]. This computational level was shown to provide an accurate description of oxide systems [13-14,19]. Plane wave basis sets were used with a cutoff energy of 500 eV and a kinetic energy cutoff for augmentation charges of 605.4 eV. The k-point sampling grids of n₁ × n₂ × n₃, obtained using the Monkhorst-Pack method [20], were used for these bulk calculations, where n₁, n₂, and n₃ were determined consistent to a spacing of about 0.028 Å⁻¹ along the axes of the reciprocal unit cells. In Equations (3) and (4), the zero pointenergies (E_ZP), entropies (S_PH), and harmonic free energies (F^PH, excluding zero-point energy which was already counted into the term ∆E_ZP) of solids were calculated by the PHONON software package [21] in which the direct method is applied following the formula derived by Parlinski et al. [22] to combine ab initio DFT with lattice phonon dynamics calculations.

As an optimal CO₂ solid sorbent, it should not only be easy to absorb CO₂ in the capture cycle but also be easy to release the CO₂ during regeneration cycle. The operating conditions for absorption/desorption processes depend on their use as in a preor a post-combustion application. The US Department of Energy (DOE) programmatic goal for post-combustion and oxy-combustion CO₂ capture is to capture at least 90% of the CO₂ produced by a plant with the cost in electricity increasing no more than 35%, whereas the goal in the case of pre-combustion CO₂ capture is to capture at least 90% of the CO₂ produced with the cost in electricity increasing no more than 10% [23-24]. Under pre-combustion conditions, after the water-gas shift reactor, the gas stream mainly contains CO₂, H₂O and H₂. The partial CO₂ pressure could be as high as 20 to 30 bar and the temperature

(T₁) is around 313 - 573 K. To minimize the energy consumption, the ideal sorbents should work in these ranges of pressure and temperature in order to separate CO₂ from H₂. For post-combustion conditions, the gas stream mainly contains CO₂ and N₂, the partial pressure of CO₂ is in the range 0.1 to 0.2 bar, and the temperature range (T₂) is quite different. Currently, in post-combustion CO₂ capture technology, the amine-based solvents, carbonand zeolite-based solid sorbents (including metal organic framework) capture CO₂ within a lower temperature range (<200˚C) [25], while oxides (such as CaO, Na₂O, etc.) and salts (such as Li₄SiO₄, Li₂ZrO₃, etc.) capture CO₂ usually within a higher temperature range (>400˚C) [9- 13]. Based on Equation (2), the working conditions of each solid capturing CO₂ can be evaluated and used for determining its suitability as CO₂ sorbent.

In this study, the thermodynamic database HSC Chemistry [26] and Factsage [27] packages were employed to search for the available thermodynamic properties of solids.

2.2. Screening Scheme

Figure 1 shows the schematic of our screening methodology. For a given solid databank, this methodology includes four main screening steps (or filters) which allow identification of the most promising candidates [13].

Step 1: For each solid in the data bank, we first conduct basic screening based on acquisition of general data, such as the wt% of absorbed CO₂ in the assumption of a complete reaction, the materials safety and cost, etc. We also include where available the thermodynamic data from literature and from general thermodynamic databases, such as HSC Chemistry, Factsage, etc. If the necessary data for evaluation of the thermodynamic properties exists, then the use of DFT calculations is not necessary and the optimal candidates can be obtained by minimizing their known free energies based on the operating conditions. Otherwise, if the material passes basic screening, but no thermodynamic data are available, then continue to the next step.

Step 2: Perform DFT calculations for all compounds in the candidate reaction with this solid. If |∆E^DFT − ∆E_ref|/n₁ < 20 kJ/mol, where n₁ is CO₂ molar number in capture reaction, and ∆E_ref is the DFT energy change for the reference capture reaction (e.g. CaO + CO₂ = CaCO₃), we add this compound to the list of good candidates. Otherwise, we go back to step 1 and pick another solid.

Step 3: Perform phonon calculations for reactant and product solids to obtain the corresponding zero point energies and the phonon free energies for the list of good candidates. Specify the target operating conditions (temperature, partial pressures of CO₂ and H₂O) and compute the change in chemical potential for the reaction, namely ∆m(T, P) from above equations. If ∆m(T, P) is close to zero (e.g. |∆m(T, P)| < 5 kJ/mol) at the operating conditions, then we select this reaction as a member of the “better” list. Only a short list of compounds will likely be left after application of step 3.

Step 4: Additional modeling could be performed to rank the remaining short list of better candidates both obtained from database searching and ab initio thermodynamic calculations as shown in figure 1. One is the kinetics of the capture reactions, which could be done by transport and diffusion calculations as well as using experimental measurements. Another necessary and doable modeling task is the behavior of the solid in the reactor, which can be done by computational fluid dynamics (CFD) methods based on finite element method (FEM) approach and process modeling to estimate the overall costs [28]. These simulations are currently underway. Application of these screening filters will ensure that only the most promising candidates will be identified for the final experimental testing.

This screening methodology provides a path for evaluating materials for which experimental thermodynamic data are unavailable. One area where this approach could be used to great advantage is in evaluating mixtures and doped materials, where thermodynamic data are generally not available but for which the crystallographic structure is known or can be easily determined. Based on the above screening methodology, we have screened hundreds of solid compounds and found some promising candidates for CO₂ sorbents. Here, in this work we summarize the results obtained by applying the screening methodology to several classes of solid materials.

3. Results and Discussions

3.1. Applications to Alkali and Alkaline Earth Metal Oxides and Hydroxides [4,12-14]

The thermodynamic data for these oxides, hydroxides and corresponding carbonates and bicarbonates are available in thermodynamic databases, in order to validate our theoretical approach, we also made the ab initio thermodynamic calculations for these known crystals. Table 1 shows the calculated thermodynamic properties of these reactions accompanying with experimental data obtained from HSC Chemistry database [27].

As an example, Figure 2 shows the heats of reactions for alkali and alkaline earth metal oxides capture CO₂. From it, one can see that, except for BeO + CO₂ à BeCO₃ reaction, overall, the calculated results are in good agreement with HSC experimental data. These findings indicate that our theoretical approach can predict the right thermodynamic properties of various solid reacting with CO₂ if the right crystal structure of solids is known or is easy to be determined. The larger discrepancy observed for BeO/BeCO₃ system is due to lack of the crystal structure information of BeCO₃. As the only one input property of the solid in the ab initio thermodynamics calculations, this indicates that in order to obtain reliable results the crystal structure must be known or can be easily predicted correctly.

Table 1 listed the calculated DFT energy changes and

thermodynamic properties of reactions of these oxides and hydroxides capture CO₂. Among the 25 CO₂ capture reactions indicated in this table, after applying the first filter (steps 1 and 2), only 10 reactions satisfied our selection criteria and are worth to be considered for third screening step (filter two). After applying the second filter on these 10 reactions, as summarized in Figure 3, we found that only MgO(Mg(OH)₂)/MgCO₃, Na₂CO₃/ NaHCO₃, K₂CO₃/KHCO₃ are promising candidates for CO₂ sorbents in either post-combustion or pre-combustion CO₂ capture technologies [7,8,10]. These results are in good agreement with the experimental facts, which means our screening methodology is reliable and could be used to identify promising solid CO₂ sorbents by predicting the thermodynamic properties of solids reacting with CO₂ [14].

Based on Equation (2), Figure 4 gives the calculated relationships of the chemical potential ∆m(T,P) with temperature and CO₂ pressure for reactions M₂CO₃ + CO₂ + H₂O = 2MHCO₃ (M = Na, K), MgO + CO₂ = MgCO₃, and Mg(OH)₂ + CO₂ = MgCO₃ + H₂O. From Figure 4, one can see that Na₂CO₃/NaHCO₃ and K₂CO₃/KHCO₃

can capture CO₂ at low temperature range (400 - 500 K) when CO₂ pressure is around 0.1 bar (post-combustion) or 20 - 30 bar (pre-combustion) [10, 14]. We have examined the effect of H₂O on the reaction thermodynamics and have found that our modeling approach can be used to account for partial pressures of CO₂ and H₂O and the temperature. We found that formation of bicarbonates from the alkali metal oxides results in a lower sorbent regeneration temperature and that formation of bicarbonate from the carbonates, by addition of CO₂ and H₂O, reduces the CO₂ capturing temperature even further. Indeed, as shown in Figure 4, we predict that Na₂CO₃ and K₂CO₃ have turnover temperatures for CO₂ capture through bicarbonate formation that are suitable for operation under both preand post-combustion conditions. When the steam pressure (P_H2O) increases as shown in Figure 4, at the same temperature, the P_CO2 is decreased because both CO₂ and H₂O are on the reactant sides.

As one can see from Figure 4, our results show that MgO could be used for both preand post-combustion capture technologies due to its low regenerating temperature (T₂ = 540 K for post-combustion conditions and T₁ = 690 K for pre-combustion conditions) which are close to experimental findings. However, Mg(OH)₂ can only be used for post-combustion capture technologies with a turnover T₂ = 600 K because its turnover temperature (T₁) is very high, outside the temperature range of interest for pre-combustion applications.

Among the list of alkaline-earth metal oxides and hydroxides analyzed in Table 1, comparing with CaO, only MgO and Mg(OH)₂ are found to be good sorbents for CO₂ capture. Upon absorption of CO₂ both of MgO and Mg(OH)₂ can form MgCO₃. However, the regeneration conditions of the original systems can take place at different conditions as indicated in Figure 4. In this case we present the calculated phase diagram of MgO-Mg(OH)₂- MgCO₃ system at different CO₂ pressures and at two fixed P_H2O values (0.1 and 1.0 bar). From Figure 4 it can be seen that when H₂O is present and at low temperatures, MgCO₃ can release CO₂ to form Mg(OH)₂ instead of forming MgO. For example, at P_H2O = 0.1 bar, only for temperatures under the transition temperature (T_tr) 460 K, MgCO₃ can be regenerated to form Mg(OH)₂. By the increase in the H₂O pressure, the transition temperature is increased. As shown in Figure 4, when P_H2O is increased to 1.0 bar from 0.1 bar, the corresponding T_tr = 520 K. Above T_tr, MgCO₃ is regenerated to MgO. Therefore, when water is present in the sorption/desorption cycle, no matter whether the initial sorbent is MgO or Mg(OH)₂, and for temperatures below T_tr, the CO₂ capture reaction is dominated by the process Mg(OH)₂ + CO₂ ↔ MgCO₃ + H₂O(g), whereas above T_tr the CO₂ capture reaction is given by MgO + CO₂ ↔ MgCO_3. The reason is that between MgO and Mg(OH)₂, there is a phase transition reaction MgO + H₂O(g) = Mg(OH)₂ happening at the transition temperature T_tr. Obviously, by controlling the H₂O pressure as shown in Figure 4, the CO₂ capture temperature (T swing) can be adjusted because the CO₂ is a reactant while H₂O is a product. However, adding more water in the sorbent system will require more energy due to its sensible heat. These results are in good agreement with the experimental measurements [8].

3.2. Applications to Mixture of Solids [9-11,15]

Lithium silicate (Li₄SiO₄) and zirconate (Li₂ZrO₃) have been proposed experimentally as promising high-temperature CO₂ sorbents [29-35]. And our previous theoretical studies confirmed these findings [9-11]. However, with different ratios of Li₂O/SiO₂ and Li₂O/ZrO₂, one can get different lithium salt compounds as shown in Table 2. We performed first filter (steps 1 and 2) on these lithium salts. The absorbed CO₂ molar and weight

percentages as well as the calculated DFT energy differrences for the capture reactions are also listed in Table 2.

Figure 5 shows the free energy changes of CO₂ capture reactions by some lithium silicates as obtained from HSC Chemistry database. From Table 2 and Figure 5, one can see that comparing with Li₂O, Li₄SiO₄, and Li₂ZrO₃, the Li₂SiO₃, Li₂Si₂O₅, and Li₂Si₂O₇ are better CO₂ solid sorbent candidates because they require less free energy to reverse the CO₂ capture reactions and have lower regenerating temperatures. Our calculations show

that although pure Li₂O can absorb CO₂ efficiently, it is not a good solid sorbent for CO₂ capture because the reverse reaction, corresponding to Li₂CO₃ releasing CO₂, can only occur at very low CO₂ pressure and/or at very high temperature [12]. SiO₂ does not interact with CO₂ at normal conditions. Therefore, it can be concluded that when a lithium silicate compound with the ratio of Li₂O/SiO₂ is less or equal to 1.0, it could have better CO₂ capture performance than Li₄SiO₄, because its regeneration can occur at low temperature and hence require less regeneration heat. Further calculations (steps 3 and 4) and analysis on these lithium silicates capture CO₂ properties are underway.

Figure 6(a) summarizes our calculated heats of reactions (ΔH) for four alkali metal silicate and zirconates [9-11]. From Figure 6(a) and Table 2, one can see that the K₂ZrO₃ capture CO₂ has a larger ΔH than the other three solids. Li₄SiO₄ has a relative small ΔH while along a large temperature range the Li₂ZrO₃ and Na₂ZrO₃ have similar ΔH. Therefore, K₂ZrO₃ is not a good candidate as CO₂ sorbent because it needs more heat to regenerate. Among these four solids, Li₄SiO₄ is the best choice. These results are in good agreement with available experimental measurements [29-35].

According to Equation (2), the calculated relationships of Δµ with CO₂ pressure and temperature for these four solids are shown in Figure 6(b). The line in Figure 6(b) indicates that for each reaction, ∆µ(T, P) is approaching zero. The region close to the line is favorable for the absorption and desorption because of the minimal energy costs at a given temperature and pressure. Above the line, the solid (Li₄SiO₄, M₂ZrO₃ (M = Li, Na, K)) is favorable to absorb CO₂ and to form Li₂CO₃, while below the line the Li₂CO₃ is favorable to release CO₂ and to regenerate lithium silicate solids. The calculated thermodynamic

properties of these solids are also summarized in Table 3.

From Figure 6(b) and Table 3 one can see that these solids capture CO₂ up to higher temperatures (T₁ > 1000 K) compared with desired pre-combustion condition (313 - 573 K). Therefore, they are not good sorbents for capturing CO₂ in pre-combustion technology. However, some of them could be used for high-temperature postcombustion CO₂ capture technology with T₂ = 1285 K, 925 K, 780 K, 880 K, and 770 K for K₂ZrO₃, Na₂ZrO₃, Li₂ZrO₃ and Li₄SiO₄ respectively. Obviously, compared

to CaO, the T₂ of K₂ZrO₃ is still too high to be used for post-combustion technology. This may be part of the reason that there is no experimental work found in the literature for pure K₂ZrO₃ capturing CO₂. Therefore, Li₄SiO₄, Na₂ZrO_3, and Li₂ZrO₃ are good candidates for CO₂ sorbents working at high temperature.

Although Li₄SiO₄ and Li₂ZrO₃ have similar turnover temperature T₂ as shown in Table 3, from Figure 6(a) one can see that the reaction heat of Li₂ZrO₃ capture CO₂ is about 20 kJ/mol lower than that of Li₄SiO₄. This indicates that more heat is needed for regenerating Li₂ZrO₃ from Li₂CO₃ and ZrO₂. Therefore, as a CO₂ sorbent, the Li₄SiO₄ is thermodynamically better than Li₂ZrO₃ despite they may have different kinetics behaviours [36].

4. Conclusions

By combining thermodynamic database searching with first principles density functional theory and phonon lattice dynamics calculations, from vast of solid materials, we proposed a theoretical screening methodology to identify most promising candidates for CO₂ sorbents. The thermodynamic properties of solid materials are obtained and used for computing the thermodynamic reaction equilibrium properties of CO₂ absorption/desorption cycle based on the chemical potential and heat of reaction analysis. According to the preand post-combustion technologies and conditions in power-plants, based on our calculated thermodynamic properties of reactions for each solid capturing CO₂ varying with temperatures and pressures, only those solid materials, which result in lower energy cost in the capture and regeneration process and could work at desired conditions of CO₂ pressure and temperature, will be selected as promised candidates of CO₂ sorbents and further be considered for experimental validations. Compared to experimental thermodynamic data for known systems, our results show that this screening methodology can predict the thermodynamic properties for sorbents capture CO₂ reactions and therefore can be used for screening out good CO₂ solid sorbents from vast of solid materials which thermodynamic data are unknown.

5. Acknowledgements

One of us (YD) thanks Drs. D. C. Sorescu, J. K. Johnson, B. Zhang, Y. Soong, R. Siriwardane and G. Richards for fruitful discussions.

REFERENCES

NOTES

^*The original manuscript of this paper was initially included in the Proceedings of 28th Annual International Pittsburgh Coal Conference, September 12-15, 2011, Pittsburgh, PA.