Article pubs.acs.org/EF
New CO2 Sorbent Synthesized with Nanoporous TiO(OH)2 and K2CO3 Abdulwahab Tuwati,† Maohong Fan,*,†,‡,§ Armistead G. Russell,§ Jianji Wang,∥ and Herbert F. M. Dacosta⊥ †
Department of Chemical and Petroleum Engineering, and ‡School of Energy Resources, University of Wyoming, Laramie, Wyoming 72071, United States § School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ∥ Henan Key Laboratory for Environmental Pollution Control, School of Chemistry and Environmental Science, Henan Normal University, Henan 453007, People’s Republic of China ⊥ Chem-Innovations, Post Office Box 3665, Peoria, Illinois 61612, United States ABSTRACT: The objective of this study is to develop a new cost-effective CO2 sorbent, K2CO3/TiO(OH)2 or KTi, with inexpensive and widely available K2CO3 and nanoporous TiO(OH)2 as supporting material. The performance of KTi CO2 capture was evaluated using a fixed-bed tubular reactor under different experimental conditions, including sorption temperature, flow rate, and moisture concentration of flue gas. Use of TiO(OH)2 as a support for K2CO3 leads to a significant increase of CO2 sorption capacity per unit of K2CO3 by about 37 times. The optimal K2CO3 loading on TiO(OH)2 is 30 wt %. The highest sorption capacity achieved with KTi is 1.69 mmol of CO2/g of KTi, whereas the theoretical sorption capacity of KTi with the prepared TiO(OH)2 could be as high as 3.32 mmol of CO2/g of KTi. The enthalpy change of the KTi-based CO2 sorption is −28.51 kcal/mol. Moreover, KTi is regenerable and stable. Therefore, KTi is a promising CO2 sorbent.
1. INTRODUCTION
because membranes have been considered to be only applicable to pre-combustion CO2 separation for a long period of time.16 People are increasingly interested in the use of chemisorption for the separation of CO2 from flue gas because the method has been widely considered to be able to reduce energy consumption needed for separation of CO2 from flue gas. Chemisorption can be classified into absorption and adsorption. Absorption mainly uses aqueous amine compounds [e.g., monoethanolamine (MEA)] as CO2 sorbents. MEA-based CO2 capture technologies are mature and very successful in the removal of CO2 in natural gas. However, the energy consumptions associated with the absorption method are relatively high because of the dilute CO2 characteristics of flue gas and need a large amount of water in an aqueous MEA absorbent. To considerably decrease the energy consumptions of chemisorption-based CO2 separation processes and, thus, make them economically viable for capture of CO2 from the flue gas, scientists are increasingly increased in the development of inorganic and organic solid chemisorbents.17,18 Significant progresses have been made in synthesizing new organic and inorganic solid CO2 sorbents in recent years.17−22 Organic solid sorbents are mainly based on amine compounds and new supporting materials. For example, Song’s group successfully developed a CO2 sorbent called “molecular basket sorbent (MBS)” by impregnating a nanoporous mobil composition of matter number 41 (MCM-41) with polyethylenimine. The CO2 sorption capacity of the MBS reaches 140 mg of CO2/g.19
Climate change is one of the most serious challenges people are currently facing. The amount of greenhouse gases emitted to the atmosphere has been substantially increased, and it will continue to increase in the foreseeable future.1−4 One of the major greenhouse gases is carbon dioxide (CO2) because of the use of fossil fuels (oil, natural gas, and coal), solid waste, trees and wood products, and also as a result of chemical manufacturing. The high demand for fossil fuel, which meets more than 98% of the world’s energy needs, is largely responsible for the increase in the CO2 concentration levels in the atmosphere. The atmospheric CO2 concentration has risen to ∼280−390 ppm,5−7 about a 35% increase compared to the level at beginning of the industrial revolution. It is projected that the atmospheric CO2 concentration will continue to increase unless effective CO2 emission control measures are taken. Capturing CO2 emitted from power station flue gas has been considered to be a potentially effective approach to control the atmospheric CO2 level. People have studied different methods for capturing CO2 in flue gas, such as cryogenic fractionation, solvent absorption, membrane separation, and chemisorptions. 8−11 Each method has its own advantages and disadvantages. For example, the cryogenic fractionation method can be used to produce pure liquid CO2, but its energy consumption is high because of the low concentration of CO2 in flue gas.12,13 Membrane separation has been considered a promising approach to CO2 separation, and many progresses have been made in many aspects of the technology, including syntheses of new membrane materials.14,15 The new membrane materials can be used for both pre-combustion and postcombustion CO2 separations, which is very encouraging © 2013 American Chemical Society
Received: July 17, 2013 Revised: October 29, 2013 Published: November 4, 2013 7628
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Eindhoven, Netherlands). Energy-dispersive X-ray spectroscopy (EDS) of the fresh and regenerated 30 wt % KTi sorbents was acquired using an Oxford Instruments X-Max EDS detector (model 51-XMX0005, Oxford Instruments America, Concord, MA). 2.3. CO2 Separation. The experimental setup used for CO2 separation tests is illustrated in Figure 1. The apparatus consists of
Inorganic CO 2 sorbents are inexpensive and easily available.23−32 Among them are metal oxides, such as CaO, which can directly react with CO2 under certain conditions, including relatively high temperatures. The metal oxides can be thermally regenerated for reuse through the decomposition of the salts, resulting from CO2 sorption at higher temperatures. However, the energy needed for regeneration of CaO is too high to be applicable to post-combustion CO2 capture. Two carbonates, Na2CO3 and K2CO3, are better choices for synthesis of inorganic sorbents. Potassium-based sorbents, such as K2CO3/activated carbon (AC), K2CO3/TiO2, K2CO3/ Al2O3, K2CO3/MgO, and K2CO3/zeolite, have been used for CO2 sorption. Some of them are regenerable and have shown high CO2 capture capacity. However, others, such as K2CO3/ Al2O3 and K2CO3/MgO, showed poor regeneration abilities.33 In other words, their CO2 sorption capacities decrease considerably after a few cycles of CO2 sorption and desorption, even at temperatures lower than 200 °C. Temperatures as high as 350−400 °C had to be used for complete CO2 desorption, however, doing so could destroy the structure of the original sorbents.33 The key to the success in developing carbonatebased CO2 sorbents is to find effective supporting materials for improvements of their CO2 sorption capacities and desorption kinetics. Accordingly, this research was designed to explore the feasibility of using nanoporous TiO(OH)2 as a supporting material and K2CO3 to synthesize a new CO2 sorbent, K2CO3/ TiO(OH)2 or KTi. The KTi-based CO2 separation mechanism can be described as follows: TiO(OH)2
K 2CO3 + H 2O + CO2 ←⎯⎯⎯⎯⎯⎯⎯→ 2KHCO3
Figure 1. Schematic diagram of CO2 separation setup: (1) CO2 cylinder, (2) N2 cylinder, (3′) CO2 flow meter, (3″) N2 flow meter, (3″′) gas leakage checking meter, (4) syringe pump, (5) heat tape temperature controller, (6) heat tape, (7) tube furnace temperature controller, (8) tube furnace, (9) quartz tube reactor, (10) quartz wool and notch block, (11) sorbent, (12) water removal unit, (13) multigas analyzer, and (14) data recording system.
(R1) three parts: gas preparation, CO2 sorption/desorption, and gas analysis. The first part includes a mixed CO2−N2 cylinder (1; 1 vol % CO2 and 99 vol % N2) for sorption tests, a N2 cylinder (2; ultrahighpurity N2) for CO2 desorption tests and apparatus cleaning and calibration, two flow meters (3′ and 3″; Matheson Trigas FM-1050) for control of the flow rates of the gases from the two cylinders, and a syringe pump (4; NE-300 Just Infusion, New Era Pump Systems), along with heat tape (6; Cole-Parmer Co., Vernon Hills, IL), whose temperature was adjusted by a controller (5; MiniTrol, Glas-Col, Inc.) whenever necessary. The gas cylinders were supplied by United States Welding, Inc. The syringe pump was employed to introduce water vapor at a predetermined rate into the CO2−N2 mixture to form simulated flue gas as the feed stream during CO2 sorption tests. The third flow meter (3″′) connected to the gas stream prior to the gas analyzer (13; ZRE, Fuji Electric System Co., Ltd.) was used for checking gas leakage. The CO2 sorption/desorption part consists of a furnace (8; Thermo Corporation, TF55030A-1) with a temperature controller (7; Yokogawa M&C Corporation, UT150) and a 3/8 in. quartz tube (9) containing sorbent or spent sorbent (11) with a notch at the top of the tube and quartz wool stoppers (10) as sorbent holders at the bottom of the quartz tube. The third part of the setup consists of a moisture removal unit (12; CaCl2 pellets), an infrared gas analyzer (13) for measurement of the CO2 concentration in outlet gas steam, and a data collecting unit (14; Monarch Instrument, Inc., Amherst, NH) for recording CO2 concentration profiles. To start CO2 sorption, 200 mg of KTi was loaded into a 3/8 in. quartz tube reactor (9) and then placed in the temperatureprogrammable furnace (8). The 1% CO2 and 1% H2O gas mixtures at a flow rate of 300 mL/min were used for CO2 sorption tests. The balance gas of the mixtures is balanced with N2. H2O was introduced into the inlet gas stream using the syringe pump, as shown in Figure 1. Sorption temperatures were set at 50 °C, unless otherwise specified. Each sorption test proceeded until the CO2 concentration in the outlet gas stream was equal to the inlet CO2 concentration. The same experimental setup was used for CO2 desorption tests. Pure N2 at the flow rate of 300 mL/min was used as a carrier gas for desorbed CO2.
2. EXPERIMENTAL SECTION 2.1. Sorbent Preparation. All reagents used in these experiments were of high analytical grades. Potassium carbonate (purity, 99.0%) was obtained from VWR International LLC (West Chester, PA). The supporting material TiO(OH)2 was prepared with Ti(OC2H5)4 (99 wt %, Acros) containing 33−35 wt % TiO2 using the procedure described below. Deionized (DI) water was used to prepare all of the sorbents tested in this research. The supporting material TiO(OH)2 was prepared from the starting material Ti(OC2H5)4 (99 wt %, Acros) containing 33−35 wt % TiO2. The first step was to add a predetermined amount of Ti(OC2H5)4 to DI water, with the molar ratio of H2O/Ti(OC2H5)4 being 26.3:1, followed by stirring the resultant mixture for 2 h. The precipitate TiO(OH)2 was then filtered, rinsed 3 times with DI water, and then dried at 120 °C for 3 h. The KTi sorbent was prepared by mixing predetermined amounts of anhydrous K2CO3 and TiO(OH) as well as 200 mL of DI water, followed by stirring the mixture for 5 h at room temperature, and then drying it in a rotary evaporator at 70 °C. The resulting powder was then ground and sieved to obtain KTi particles, with their diameters being less than 300 μm. The KTi samples containing different percentages of K2CO3 were prepared by varying the amounts of K2CO3 and TiO(OH)2. 2.2. TiO(OH)2 and KTi Characterization. K2CO3, TiO(OH)2, and fresh and regenerated 30 wt % KTi were characterized with different methods. Their Brunauer−Emmett−Teller (BET) surface areas and pore structures of K2CO3, TiO(OH)2, and fresh 30 wt % KTi were studied using a Micrometrics TriStar 3000 V6.04 BET analyzer. The powder X-ray diffraction (XRD) patterns of the fresh and regenerated 30 wt % KTi sorbents were collected by Scintag XDS 2000 (Scintag, Inc., Sunnyvale, CA) with Cu tube, Kα 1 line (1.5406 Å) being the radiation source. The morphological characteristics of the fresh and regenerated 30 wt % KTi sorbents were determined using Quanta FEG MK2 scanning electron microscopy (SEM; FEI, 7629
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3. RESULTS AND DISCUSSION 3.1. Characteristics of TiO(OH)2 and KTi. The BET surface areas, average pore sizes, and pore volumes of K2CO3, TiO(OH)2, and fresh KTi sorbent were listed in Table 1. It is
actual CO2 sorption capacity of KTi. Second, the CO2 sorption capacity of pure K2CO3 is rather low because of its low surface area and, thus, low accessibility of K2CO3 to CO2. Moreover, nanoporous TiO(OH)2 is an effective supporting material for K2CO3 because the CO2 sorption capacity of KTi is increased by more than 37 times. 3.2.2. K2CO3 Loading on TiO(OH)2. The loadings of alkali material loaded on the surfaces of porous supporting materials can profoundly affect the CO2 capture capacities of the synthesized sorbents.34 The relationship between the quantities of K2CO3 loaded on TiO(OH)2 and the resultant CO2 capacities of synthesized KTi is illustrated in Figure 3. It
Table 1. BET-Associated Characteristics of TiO(OH)2, K2CO3, and Fresh KTi Using BET Micrometrics TriStar 3000 V6.04 BET Analyzer sample
surface area (m2/g)
pore volume (cm3/g)
pore size (nm)
K2CO3 TiO(OH)2 KTi
0.76 519.16 15.76
0.0004 0.1745 0.0247
5.46 3.56 7.64
noted that the surface area, pore size, and volume of KTi are significantly smaller than those of TiO(OH)2 because of the loading of K2CO3 on TiO(OH)2 or blockage of the TiO(OH)2 pore structure because of the coating of K2CO3 on TiO(OH)2. More importantly, the surface area and pore volume of K2CO3 are 0.76 m2/g and 0.0004 cm3/g, respectively, while those of KTi, are 15.76 m2/g and 0.0247 cm3/g, respectively. The significant differences should be attributed to the use of a high surface area and large pore volume of TiO(OH)2, which play an important role in improving the CO2 capture capacity per unit of sorbent, as observed below. 3.2. Factors Affecting CO2 Sorption. 3.2.1. Use of Nanoporous TiO(OH)2. The porous structure of a supporting material plays a major role in the improvement of the capacity and selectivity of a given sorbent. A number of supporting materials, except for TiO(OH)2, have been tested for their performances on enhancing the CO2 sorption capacity of per mass unit of K2CO3.29−33 Thus, it was chosen as a support for K2CO3 to synthesize the new CO2 sorbent, KTi. The CO2 sorption profiles obtained under the same conditions with pure supporting material unsupported K2CO3, TiO(OH)2, and KTi are provided in Figure 2. The total CO2 sorption capacities of TiO(OH)2, K2CO3, and KTi sorbent were calculated using the integration method and found to be 0.004, 0.041, and 1.514 mmol/g of KTi, respectively. Several conclusions can be derived from the results. First, TiO(OH)2 as a supporting material has very low CO2 adsorption capacity, and thus, calculated CO2 sorption capacity of KTi should reflect the
Figure 3. Effect of the K2CO3 content in KTi on CO2 sorption efficiency (CO2 concentration, 1%; H2O concentration, 1%; gas flow rate, 300 mL/min; sorption temperature, 60 °C; and weight of KTi, 200 mg).
should be noted that the results were achieved with 200 mg of KTi at 60 °C within 300 mL/min flue gas stream containing 1 vol % CO2 and 1 vol % H2O. The CO2 sorption capacities increase with K2CO3 loading within the 20−30 wt % K2CO3 loading range and then decrease with K2CO3 loading within the 30−50 wt % K2CO3 loading range. The highest CO2 sorption capacity 1.28 mmol of CO2/g of KTi was achieved with 30 wt % KTi, which was about 60% of the theoretical CO2 sorption capacity of the sorbent. An increase in K2CO3 loading on the surface of TiO(OH)2 leads to the change in the accessibility of K2CO3 to CO2 per gram of KTi. Within the 20−30 wt % K2CO3 loading range, the accessibility increases with the loading of K2CO3. However, after K2CO3 loading reaches 30 wt %, the accessibility starts to decrease with the increase in K2CO3 loading, which results from the decrease in the surface area of KTi because of the increase in K2CO3 on the surface of TiO(OH)2, and thus generates negative impact on CO2 sorption. KTi (30 wt %) was the optimal loading for TiO(OH)2 prepared in this research and, therefore, chosen to be used for all of the other CO2 sorption tests conducted in this research. Assuming that CO2 can be adsorbed onto KTi in the form of a monolayer, the theoretical maximum K2CO3 loading of KTi, qK2CO3/KTi (mg of K2CO3/g of KTi), can be estimated using
Figure 2. Typical CO2 sorption curves of TiO(OH)2, K2CO3, and KTi (CO2 concentration, 1%; gas flow rate, 300 mL/min; H2O concentration, 1%; sorption temperature, 50 °C; and weight of KTi, 200 mg).
qK CO /KTi = 2
7630
3
SBET,TiO(OH)2 4ra2− e,K 2CO3
× NA
×
1000 × M K 2CO3 1+
M K2CO3 SBET,TiO(OH) 2 4ra2− e,K CO × NA 2 3
(E1)
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where SBET,TiO(OH)2 is the BET surface area of TiO(OH)2 (m2/g TiO(OH)2; 519.16 m2/g), ra−e,K2CO3 is the average effective molecular radius of K2CO3 (1.88 × 10−10 m),35 NA is the Avogadro constant (6.02 × 1023/mol), and MK2CO3 is the molar mass of K2CO3 (138 g/mol). According to E1 and the given values of the variables in E1, qK2CO3/KTi should be 458.88 mg of K2CO3/g of KTi or the ideal monolayer K2CO3 loading should be 45.88 wt %, while the optimal K2CO3 loading obtained in this research is ∼30 wt %, corresponding to 146.29 mg of CO2/ g of KTi (3.32 mmol of CO2/g of KTi) and 95.65 mg of CO2/g of KTi (2.17 mmol of CO2/g of KTi), respectively, calculated using the following relationship: qCO /KTi = qK CO /KTi 2
2
3
H2O/CO2 ratio is higher than 1, qCO2/KTi decreases with the increase of the moisture in gas. The changes of qCO2/KTi with moisture volume percentage or mole concentration in flue gas can be explained as follows. The difference between the chemical potentials of CO2 in gas (μCO2,g) and that in the quasi-liquid layer (μCO2,qll) is one of major factors affecting qCO2/KTi or qCO /KTi = f1 [(μCO ,g − μCO ,qll ), xi = 1,2,...]
(E3)
2
where xi represents other variables including sorption temperature (T) and qCO2/KTi increases with (μCO2,g − μCO2,qll). The values of μCO2,g and μCO2,qll are determined with the following relationships:
MCO2 M K 2CO3
2
2
(E2)
0 μCO ,g = μCO + RT ln pCO ,g ,g
(E4)
0 μCO ,qll = μCO + RT ln cCO2,qll ,qll
(E5)
2
where qCO2/KTi stands for the CO2 sorption capacity of KTi (mg of CO2/g of KTi) and MCO2 is the molar mass of CO2 (44 g/ mol). It should be noted that E2 was established on the basis of the stoichiometry of the sorption CO2 with K2CO3 presented in R1. However, the highest experimental CO2 sorption capacity was 1.69 mmol of CO2/g of KTi, as shown in one of the following figures, with about 77.9 and 50.9% of those theoretically achievable with the best KTi prepared in this research and the KTi ideally reachable with [TiO(OH)2] prepared with this research and K2CO3, respectively. Therefore, large rooms still exist for a significant increase in the CO2 sorption capacity of KTi by preparing more porous TiO(OH)2 and improving the dispersion of K2CO3 on the surface of TiO(OH)2. 3.2.3. Moisture. The effect of the moisture concentration in the simulated flue gas on the CO2 sorption separation performance of KTi was evaluated, and the results are presented in Figure 4. The CO2 sorption capacity of KTi, qCO2/KTi, initially increases with the H2O concentration and reaches its maximum value when the moisture concentration is 1 vol % or the mole ratio of H2O/CO2 is 1, which is determined by the stoichiometry of R1. However, when the
2
2
2
2
where pCO2,g is the partial pressure of CO2 in simulated flue gas and cCO2,qll is the mole concentration of CO2 in the quasi-liquid layer. To facilitate the following discussion, the H2O/CO2 mole (or volume) ratio of simulated flue gas is abbreviated as HCMR HCMR =
moles of H 2O in gas moles of CO2 in gas
(E6)
In the CO2-rich range (HCMR < 1), the increase in moisture or decrease in pCO2,g leads to the decreases in both μCO2,g and μCO2,qll. However, the drop of μCO2,g is smaller than that of μCO2,qll because pCO2,g is less affected than cCO2,qll in the range, where the moisture increase not only leads to the dilution of CO2 in the quasi-liquid layer but also the increase of CO2 consumption through CO2 hydration or HCO3− formation because of the fact that the increase in H2O moves the forward reaction of R2 from the left and right side and, thus, consumes more CO2, as shown below CO2 + H 2O ↔ H+ + HCO3−
(R2)
The net result is that qCO2/KTi increases with moisture in the CO2-rich range. The value of qCO2/KTi reaches its peak (1.514 mmol/g of KTi) when HCMR is equal to 1 (HCMRstoichiometry). In the CO2-lean range (HCMR > 1), cCO2,qll does not decrease as quickly as pCO2,g because H2O is overdosed and the threedimension distribution profile of the quasi-liquid layer determined by the hydrophilic characteristics of the sorbent on the surface of KTi does not change considerably, and thus, qCO2/KTi decreases with the increase of moisture. 3.2.4. Sorption Temperature. The sorbent capacities of KTi are considerably affected by the temperature (T) in the range of 40−80 °C, as demonstrated in Figure 5. The downhill trend in Figure 5 can be explained as follows. According to the rate law and reversible reaction theory, the kinetic model of R1 should be da KHCO3 /KTi dt
Figure 4. Effect of the H2O concentration on CO2 sorption capacities (CO2 concentration, 1%; gas flow rate, 300 mL/min; sorption temperature, 50 °C; weight of KTi, 200 mg; and K2CO3 content, 30 wt %).
n
n
n
n
KHCO3 O CO2 = k f a HH22O,qll aCO a K2CO3 − k ra KHCO 2 ,qll K 2CO3 /KTi 3 /KTi
(E7)
where ai and ni are the concentration and reaction order of the corresponding species i (KHCO3, H2O, CO2, and K2CO3), 7631
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KHCO3 {∂ln[(c KHCO /(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O 3 /KTi,e
× (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 × (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 )]/∂T } = ((c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O × (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 n
KHCO3 × (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 /c KHCO ) 3 /KTi,e
n
−1
KHCO3 {(nKHCO3c KHCO [(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O 3 /KTi,e
× (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 × (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] /[(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O Figure 5. Effect of the temperature on CO2 sorption capacity (CO2 concentration, 1%; H2O concentration, 1%; gas flow rate, 300 mL/ min; weight of KTi, 200 mg; and K2CO3 content, 30 wt %).
× (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 × (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] 2) + {([n H2O(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O − 1 × (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2
respectively, kf and kr are the rate constants of forward and reverse reactions of R1, respectively, and P represents the total pressure of the simulated flue gas. Assuming that the quasiliquid layer and the surface of KTi are in ideal states, then ai can be replaced with ci. Then, the above equation becomes dc KHCO3 /KTi dt
n
n
n
× (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] /[(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O × (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2
n
KHCO3 O CO2 = k f c HH22O,qll cCO c K2CO3 − k rc KHCO 2 ,qll K 2CO3 /KTi 3 /KTi
× (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] 2)
(E8)
+
At the equilibrium state, E8 is in the form of k K= f = kr
([(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O
nKHCO3 c KHCO 3 /KTi,e n CO3 n H2O nCO2 c H2O,qll,ecCO2,qll,ec KK22CO 3 /KTi,e
×nCO2(cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 − 1
KHCO3 = (c KHCO /(c H2O,qll,0 − c KHCO3 /KTi,e)nH2O 3 /KTi,e
× (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ]
× (cCO2,qll,0 − c KHCO3 /KTi,e)nCO2
/[ c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O
n
× (c K 2CO3 /KTi,0 − c KHCO3 /KTi,e)nKHCO3 )
(
× (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2
(E9)
× (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] 2)
where K is the equilibrium constant, cH2O,qll,0, cCO2,qll,0, cK2CO3/KTi,0, and cHCO3/KTi,0 are the initial concentrations of H2O, CO2, K2CO3, and KHCO3, respectively, while cH2O,qll,e, cCO2,qll,e, cK2CO3/KTi,e, and cKHCO3/KTi,e are the concentrations of H2O, CO2, K2CO3, and KHCO3 at the equilibrium state, respectively. According to the relationship between K and the enthalpy change (ΔH < 0) of R1, the following relationship should exist:
+ ([(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O × (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 − 1 × nKHCO3(c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 − 1] / [(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O
∂ln K nKHCO3 = {∂ln[(c KHCO 3 /KTi,e ∂T
×(cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 × (c K 2CO3 /KTi,0 − 0.5c KHCO3 /KTi,e)nKHCO3 ] 2)}×0.5
/(c H2O,qll,0 − 0.5c KHCO3 /KTi,e)nH2O × (cCO2,qll,0 − 0.5c KHCO3 /KTi,e)nCO2 × (c K 2CO3 /KTi,0
