Thermodynamic Modeling of Condensed Salts and Silicates at High Temperatures Bing Liu, Larry L.
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Thermodynamic Modeling of Condensed Salts and Silicates at High Temperatures Bing Liu, Larry L. Baxter, John L. Oscarson, and Reed M. Izatt Departments of Chemical Engineering and Chemistry & Biochemistry Brigham Young University Ash Deposition • Thermal converter slagging/fouling strongly influences design and operation. • . Major Inorganic Compounds in Coals 1 4 13 22 55 26 Low Rank 1 12 Fusion temperature of ash varies with coal 1 24 31 Sulfides Halides Hydroxides Sulfates Phosphates Low Melting 16 Oxides and Hydroxides Oxides Carbonates Silicates High Melting Mineraloids 3 16 32 28 High Rank 0.5 44 0.5 24 61 8 Measuring phase equilibria of ash/slags is difficult and costly over a wide range of compositions and temperatures Thermodynamic Models Few ash deposits are in equilibrium, but equilibrium represents an important limiting behavior. Thermodynamic models help describe • Fusion temperatures • Deposition rates and mechanisms • Operating regime Objectives •Develop a thermodynamic model that can be used to correlate or predict phase behavior of coal-derived slag at high temperatures. •Given temperature (or total energy level) and overall concentrations, calculate numbers and types of phases and compositions in each phase at equilibrium •Provide a robust computer program with high computational efficiency and ease of incorporation into other simulation systems •Validate the model using available experimental data Pure Component Properties Are Needed 1800 1600 Tsaplin et al. Kracek Kracek Cracek Zaitsev et al. 1124 ˚C 1090 ˚C Na2SiO3 800 Na6Si2O7 1000 Liquid 875 ˚C Na6Si8O19 1200 Cr Na2Si2O5 1400 Na4SiO4 Temperature /C 1723 ˚C Tr Qu 600 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 Mole Fraction SiO 2 Na2O-SiO2 phase diagram. •The melting point of the mixture may lie several hundred degrees below pure component data •Intermediate compound properties may not have been measured or be available in a standard thermodynamic database Extrapolation is Unreliable 250 230 210 Extrapolated results using M&G Equation Values Used in the Present Research Cp /J/molK 190 170 150 • The overestimated heat capacity results may lead to errors in the phase diagram expectations. 130 110 90 70 50 200 300 400 500 600 700 800 900 1000 1100 1200 T/K Comparison of Liquid MgCl2 Heat Capacities Pure Component Properties (Cont.) • The FACTsage heat capacity equation form is used to calculate the heat capacities of pure components 5 c 10 d 6 2 9 3 Cp a b 103T e 10 T f 10 T 2 T T • Heat capacities at unstable conditions (supercooled/superheated) can be approximated using thermodynamic identities in the cases where no literature data exist trG tr H T tr S d 2 tr G CP CP,L CP,S T 0 2 dT • Properties of the intermediate compounds can be optimized based on other kinds of measured thermodynamic properties (e.g., phase diagram data) Liquids: Modified Quasi-chemical Model • In a binary system composed of components A and B, the mixing Gibbs energy change can be accounted for by a quasi-chemical reaction: (A-A) + (B-B) = 2 (A-B) ΔgAB • AA AA AA AA AA AA + BB BB BB BB BB BB The Total Gibbs energy of the system is: G ( xA gAo xB gBo ) T S config (nAB / 2)gAB AB A G: total Gibbs energy of the solution T: temperature AB A xi: mole fraction of the components AB A gio: Gibbs energy of the pure component ΔSconfig: configurational entropy accounting for mixing effect nAB: number of AB pairs in the solution ΔgAB: nonconfigurational gibbs energy change B B B Modified Quasi-chemical Model (Cont.) • ΔgAB is the nonconfigurational Gibbs energy change due to the reaction. n g AB gi xA i or i=0 n n g AB g 0 giYA + g jYB j or i i=1 j=1 n n g AB g 0 gi xAA + g j xBB j i i=1 j=1 • The coefficients (g0, gi, gj) of ΔgAB are optimized using available thermodynamic data (enthalpies, entropies, phase equilibrium data etc.) Binary Salt System Example I Liquid solution is in equilibrium with pure solids 900 Temperature/C 850 QC Model Literature 800 750 Liquid 700 Liquid+Solid Na 2SO 4 Liquid+Solid NaCl 650 Solid 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole fraction of Na 2SO4 T-x phase diagram of the Na2SO4-NaCl system. The dashed line is calculated using the smoothed data of Dessureault et al.’s Binary Salt System Example II Temperature/C 900 800 QC Model Literature 700 600 500 Liquid+Solid K 2CO 3(b) Liquid Liquid+KOH(c) 400 Liquid+Solid K 2CO 3(a) Solid 300 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole fraction of K 2CO 3 T-x phase diagram of the K2CO3-KOH system. The dashed line is calculated using the smoothed data of Dessureault et al. • Liquid solution is in equilibrium with pure solids (different crystals) • The minimum melting point of the system is near the KOH side resulting because of the relatively large absolute Gibbs energy value of K2CO3 Eutectic Point Comparisons •A eutectic or eutectic mixture is a mixture of two or more phases at a composition that has the lowest melting point. •Agreement of the eutectic points (calculated using the model and literature data) shows the ability of the model to correlate phase diagrams System (A−B) Model xB Literature xB Model Teu , ˚C Literature Teu, ˚C Reference NaCl-Na2CO3 0.449 0.41−0.47 632.96 632−645 8-10, 12, 13, 15-17 KCl-K2CO3 0.358 0.35−0.38 629.69 623−636 8, 11-13, 15, 16, 18 KCl-K2SO4 0.260 0.23−0.29 690.89 688−694 17, 19, 20 NaCl-Na2SO4 0.481 0.45−0.48 627.80 623−634 13, 17, 19 KOH-K2CO3 0.091 0.09−0.10 362.48 360-367 21-23 Binary Salt System Examples II Liquid solution is in equilibrium with solid solution 1040 Temperature/C Temperature/K 1400 1300 Liquid solution (L) 1200 S+L 1100 S+L 1000 Reisman Reisman Rolin and Recapet 960 880 Liquid Solution(L) 800 S+L S+L 720 Solid Solution(S) Solid solution (S) 900 640 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of K 2S Liquid-solid solution phase diagram of the K2S-Na2S system. ● from Mäkipää and Backman 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mole fraction of Na 2CO 3 Liquid-solid solution phase diagram of the K2CO3-Na2CO3 system. 1 K2O-SiO2 Phase Diagram 1800 •The equation of Gibbs energy of the K2Si2O5 is optimized using the equilibrium T~x data based on the following reaction: K2O(l ) 2SiO2 (l ) K2Si2O5 (s) 1600 Kracek et al. Cr 1400 Liquid 1200 600 0.45 767 C 0.55 K2Si4O9 K2Si2O5 1000 800 1046 C 977 C K2SiO3 Temperature /C •Properties of many intermediate silicates cannot be measured and must be optimized based on data in the regions where there is no formation of these compounds. 0.65 729 C 0.75 Tr 770 C 0.85 Mole Fraction SiO 2 GK2Si2O5 ( s) (T ) uK2O(l ) ( x, T ) 2uSiO2 (l ) ( x, T ) Qu 0.95 CaO-SiO2 Phase Diagram 2400 2200 2133 ˚C 2000 Davies Greig Tewhey and Hess Hageman et al. •The high melting temperature of pure CaO accounts for the high melting point in CaO-rich systems •The thermodynamic properties (e.g., Gibbs 1800 2 Liquids energy and melting point values) of the Cr 1540 ˚C 1600 Tr intermediate compounds 1400 are obtained by 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 optimizing the phase Mole Fraction SiO 2 equilibrium data 1895 ˚C CaSiO3 Ca3Si2O7 Ca2SiO4 Liquid Ca3SiO5 Temperature /C 2600 AlO1.5-SiO2 Phase Diagram 1950 1858 ˚C 1850 Klug et al. Aramaki & Roy Liquid 1750 Al6Si2O13 Temperature /C 2050 1650 1550 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction SiO 2 •More experiments are needed to better correlate the phase diagrams in the intermediate compounds regions •The intermediate compound Al6Si2O13 may account for the slow decrease of the melting point with increasing SiO2 concentrations FeO-SiO2 Phase Diagram Allen & Snow Schuhmann & Ensio Bowen & Schairer Greig 1900 1700 1500 1300 2 Liquids Cr Liquid Fe2SiO4 Temperature /C 1928 ˚C Tr 1205 ˚C 1100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole Fraction SiO 2 The relatively low melting point of Fe2SiO4 implies that the association between FeO and SiO2 is not as strong as those between many other metallic oxides (CaO, Al2O3 etc. ) and SiO2 Comparison of melting points of several associated compounds in silicate systems Component Calculated MP (˚C) Literature MP (˚C) K2SiO3 977 976-977 K2Si2O5 1046 1045-1046 K2Si4O9 770 769-771 Na2SiO3 1090 1090-1100 Na2Si2O5 875 875 Na4SiO4 1085 1085 Na6Si2O7 1124 1124 Ca3SiO4 - 1800-2149 Ca2SiO4 2133 2130-2145 CaSiO3 1540 1540-1544 Eutectic Points in Silicate Systems Type Calculated EP T (˚C) x(SiO2) Literature EP (˚C) T (˚C) x(SiO2) K2SiO3 + K2Si2O5 767 0.569 780-781 0.567 K2Si2O5 + K2Si4O9 729 0.767 743 0.764-0.766 K2Si4O9 + Quartz 770 0.807 770 0.805 Na4SiO4 + Na6Si2O7 1029 0.367 1002 0.361 Na6Si2O7 + Na2SiO3 1015 0.442 1016 0.455 Na2SiO3 + Na4SiO4 839 0.623 841-847 0.614-0.63 Na6Si8O19 + Quartz 804 0.747 794-799 0.742 Ca3SiO5-Ca2SiO4 2023 0.295 2057-2060 0.273-0.30 Ca3Si2O7-CaSiO3 1467 0.422 1450-1460 0.42-0.445 CaSiO3-SiO2 1441 0.615 1441-1444 0.61-0.635 Summary of Current Progress • A modified quasi-chemical model taken from the literature has been used to correlate phase diagrams of molten salts and silicates • The validity of the model has been tested and verified using many binary systems • Optimal modeling parameters of many binary systems potentially related to the coal ash components have been found for use in later multicomponent modeling • Thermodynamic properties of many pure compounds have been collected, approximated, or optimized.