Rate-Ratio Asymptotic Analysis of the Structure and Extinction

Paper # G37 Topic: Other

5th US Combustion Meeting Organized by the Western States Section of the Combustion Institute and Hosted by the University of California at San Diego March 25-28, 2007. Modeling Multicomponent Solid-Liquid Phase Equilibrium of Salts and Silicates in Biomass and Coal Thermal Conversion Processes

Bing Liu1, John L. Oscarson1, Larry L. Baxter1, and Reed M. Izatt2 1Department of Chemical Engineering, Brigham Young University, Provo, Utah 84602, USA 2Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah 84602, USA

A knowledge of the solid-liquid phase equilibrium of salts and silicates is important to understand ash deposition and slagging problems in biomas and coal thermal processing equipment. Computer codes simulating combustion/gasification processes require a good thermodynamic subprogram to describe the effect of slagging on the process. While ash deposits are generally not in equilibrium, thermochemical equilibrium represents the endpoint of their reaction and differences between current conditions and equilibrium conditions affect both chemical and physical (sintering, melting, vaporization) reaction rates. In the present work, a modified quasichemical model correlates the equilibrium phase diagrams of binary and ternary systems of significance to black liquor, biomass, and coal conversion equipment. Examples of NaCl-Na2CO3, Na2S-K2S, K2O-SiO2, and FeO- SiO2 systems validate the model and phase equilibrium algorithm by comparison with literature data. The model is discussed and a comparison of the model predictions and data is given.

1. Introduction

Biomass and coal thermal conversion equipment (combustors, gasifiers, pyrolyzers, etc.) represent the primary technologies based on ash-forming fuels for power generation. These technologies convert fuel, air/oxygen, and steam to lighter molecules such as water, carbon dioxide, hydrogen, carbon monoxide, and various pollutants. Depending on the technology and fuel, the systems typically operate at temperatures (T) from 600 to 2500 K and at pressures (P) from 0.1 to 50 atmospheres [1]. Due to their high energy conversion efficiency and improving environmental performance, these systems commonly represent large and long-term capital investments at the heart of power production or processing industries. However, converting the organic portion of the fuel to light gases generally impacts both design and operation of such technologies less than the behavior of inorganic compounds. These elements include Si, Al, Fe, Ca, Mg, Na, K, H, Ti, S, P, C, and O. These minerals and oxides form deposits and fly ash that often result in serious operational problems. If fixed beds or entrained beds are used, slagging may be even more serious. Despite the importance of inorganic transformation processes, the chemistry, , phase behavior, and other thermodynamic properties of these inorganic systems are poorly characterized, especially at high temperatures. The difficulty in constructing phase diagrams becomes even more pronounced as the number of components increases and the experiments necessary to obtain the required data become more time-consuming and costly. Models can, in principle, describe chemical equilibria in multicomponent systems. However, the

1 5th US Combustion Meeting – Paper # G37 Topic: Other complexity and non-ideality of condensed-phase equilibrium calculations thus far prove too great to yield to the comparatively simple models used to describe gas-phase phenomena In the present work, a modified quasi-chemical model is used to correlate properties of many molten salt and silicate systems of interest to these technologies. This model, together with a generalized phase equilibrium algorithm programmed at BYU, can be used to calculate the phase equilibria of many binary systems. As a subprogram in the BYU ash deposition project, the present model will be integrated into a software package to supplement existing and developing fouling/slagging models in thermal conversion equipment.

2. Modeling Approach

Salt and silicate properteies in liquid/solid phases depend only weakly on pressure. Therefore, the Gibbs energy (G) in most equation-of-state models for condensed salts and silicates are usually expressed as functions of concentration and temperature (T). However, the complexity of molten salts and silicates leads to phase diagram models involving molten salts and silicates at high temperatures that are usually system-dependent. Even for a given modeling approach, the equation forms and the number of modeling parameters used in the model vary with components. This variety increases the difficulty of developing a generalized model to correlate phase equilibria of multicomponent systems. In the present work, we used the modified quasichemical theory initially developed by Pelton and Blander [2, 3] and later further modified by Pelton et al. [4] to model binary liquid solutions. This model allows us to use one uniform approach to model various binary liquids. The model of Pelton et al. can be used to correlate many different types of binary systems. In this model, Pelton et al. used the “first-nearest-neighbor pairs” as the pair approximation. The atoms or molecules A and B are assumed to be distributed over the sites of a quasilattice. The interactions between different atoms/molecules can be obtained using the pair exchange reaction shown in Equation ,

(A- A) + (B - B) = 2(A - B) where (A−A), (B-B), and (A-B) represent the first-nearest-neighbor pairs of A-A, B-B, and A-B, respectively. The change in G for reaction , ∆gAB, accounts for the nonconfigurational change in G for the formation of two moles of (A−B) pairs, and is a function of T and mole fraction (x). The molar G value of the system is shown in Equation ,

o o config g=( xA g A + x B g B ) - T D s + ( n AB / 2) D g AB where g is the G value per mole of mixture for the binary system, xA and xB are the mole fractions o o of components A and B, respectively, gA and gB are the molar G values of the pure components A and B, respectively, and ∆sconfig is the configurational entropy change and is defined in Equation ,

config 骣 xAA x BB x AB Ds = - R( xA ln x A + x B ln x B ) - R琪 n AA ln2 + n BB ln 2 + n AB ln 桫 YA Y B2 Y A Y B where R is the gas constant, xAA, xBB, and xAB are the mole fractions of A-A, B-B, and A-B pairs, respectively, nAA, nBB, and nAB are the numbers of moles of A-A, B-B, and A-B pairs,

2 5th US Combustion Meeting – Paper # G37 Topic: Other

respectively, in one mole of solution, and YA and YB are the equivalent fractions of pairs containing components A and B, respectively. Equation defines the YA and YB terms. x x Y= x +AB and Y = x + AB A AA2 B BB 2

Most terms thus far discussed involve no explicit interactions. The ∆gAB term defined in Equation (2), which encapsulates the interactions, is usually divided into two terms: the enthalpy change due to mixing, ∆hAB, and the nonconfigurational entropy change, ∆sAB. Equation gives the expression for ∆gAB

DgAB = D h AB - T D s AB.

Both ∆hAB and ∆sAB in Equation are assumed to be independent of T and are usually expressed as polynomial functions of xA and xB, or functions of YA and YB, or functions of xAA and xBB, with the coefficients of each polynomial function determined from experimental data using a least- squares fitting method.

Solids may be modeled as pure minerals or solid solutions, depending on the crystal structures of the compounds in the solid phase. Some intermediate compounds may also exist in the solid phase. The thermodynamic properties of stable compounds can be found in thermodynamic databases [5, 6] or in published articles. Values for the thermodynamic properties of unstable or intermediate compounds result by fitting them to experimental. Solid solutions can also be modeled using the modified quasi-chemical approach. However, this approach is seldom used for solid solutions. Instead, the Bragg-Williams approach [7] with an ideal configurational entropy is often used and the excess G values are expressed as polynomial functions of mole fractions or equivalent fractions as shown in Equations through . Most solid solutions have more than one sublattice and require more complex models within the framework of the sublattice compound energy formalism.

n i DgAB = g i x A , i=0

n n i i DgAB = g 0 +邋 g i Y A + g jY B , i=1 j=1

n n i i DgAB = g 0 +邋 g i x AA + g j x BB i=1 j=1

When the liquid and solid phases have been modeled and the modeling parameters have been determined, optimizes their values. This analysis uses a program initially presented by Greenberg [7] and programmed at BYU for the minimization process. Many simpler algorithms either neglect ion formation or implicitly assume that activity scales with mole fraction, or both. A computation process diagram is shown in Figure 1.

Experimental data (thermochemical and phase diagram data)

Select thermodynamic models for each phase (e.g., modified quasi-chemical model for liquid phases, pure solid phases, etc.)

Optimize model parameters

Reproduce the phase diagrams of a given system Figure 1: Diagram of phase equilibrium computation

3. Modeling Results

Many binary salt and silicate phase diagrams have been modeled and are available from the ash deposition group at Brigham Young University [9]: NaCl-Na2CO3, KCl-K2CO3, NaCl-Na2SO4, KCl-K2SO4, K2CO3-KOH, KCl-MgCl2, Na2O-SiO2, CaO-SiO2, Al2O3-SiO2, FeO-SiO2, Na2S-K2S, etc. In this paper, phase diagrams of NaCl-Na2CO3, Na2S-K2S, K2O-SiO2, and FeO-SiO2 are shown and discussed.

Figure 2 illustrates the phase diagram of a liquid NaCl-Na2CO3 solution in equilibrium with pure solid NaCl and/or pure solid Na2CO3. The ∆sAB term in Equation was assumed to be zero in the modified quasi-chemical model. The coefficients in the ∆hAB polynomial expression were optimized and ∆hAB is expressed as a function of the mole fraction of NaCl-NaCl pairs as shown in Equation

2 Dh =238.384 + 85.7575 xAA + 96.6826 x AA , where xAA represents the mole fraction of NaCl-NaCl pairs. The results calculated using the model agree well with the measured values, and the calculated eutectic point (0.449, 633 ºC) is well within the reported eutectic point region (0.41−0.47, 632−645 ºC) [10-12].

900 850 NiggliAmadori /

e 800 Belyaev and Sholokhovich r u t

a 750 r e p 700 m e

T  C Liquid+Solid Na 2CO 3 650

600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole fraction Na 2CO3

Figure 2: T-x phase diagram of the Na2CO3-NaCl system. □ Amadori data [10], ♦ Niggli data [11], ● Belyaev and Sholokhovich data [12], (—) Results calculated using the model. Even though the ionic diameters of K+ and Na+ are rather different, it is quite common to find complete solid solutions over the whole composition range for binary salt systems with a common anion [13]. Thus, solid solutions containing Na2S and K2S may form. One such example is shown in Figure 3. Mäkipää and Backman [14] tentatively constructed the liquid-solid phase x 0.65 diagram of the K2S-Na2S system. A minimum solidus point at K2 O and T = 1009 K was reported [14] and is shown in Figure 3. With no further experimental data available, Lindberg et al. [13] pointed out that the binary liquid and solid Na2S-K2S systems can be modeled using the ideal solution and the regular solution approaches,Liquid respectively. The ideal mixing G equation for both phases (liquid and solid solutions) and the excess G equation for the solid solution used in the study of Lindberg et al. Liquid+Solidare shown NaCl in Equations and , respectively. Dgideal =2 RT ( x ln x + x ln x ) K2 SSolid K 2 S Na 2 S Na 2 S gex/(J� mol- 1 ) 26776 x x Na2 S K 2 S where ∆gideal and gex represent the ideal mixing and excess G values, respectively. There is a constant number “2” on the right side of Equation because each mole of Na2S or K2S contributes 2 moles of alkali cations.

In Figures 2 and 3, the pure-species G values used to compute the phase diagrams are based on the NASA thermodynamic database [6]. Liquid heat capacities were assumed constant at T values below the melting points because these heat capacities are nearly independent of T at conditions above the melting points.

1400 K /

e 1300 r u t

a 1200 r e p 1100 m e T 1000

900 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mole fraction of K 2S

Figure 3: Liquid-solid solution phase diagram of the K2S-Na2S system. The solidus line is calculated using the regular solution theory [13] and the liquidus line is calculated using the ideal solution assumption. ● Reported lowest solidus temperature point [14].

Many fuel deposits have large fractions of oxides and silicates. In Figure 4, a phase diagram of a binary oxide/silicate system (K2O-SiO2) is given.Liquid The solution parameters (L) in the liquid solution model were optimized using measured data [15] for liquid solutions in equilibrium with K2SiO3(s) and SiO2(s), respectively. The G valuesS+L of pure liquid species, pure solid K2SiO3, and pure solid SiO2 use the equations reported by Wu et al. [16]. The G value of pure K2Si2O5(s) was calculated from the measured data [15] of K2Si2O5(s) in equilibrium with the liquid solutionS+L (Equations and ). Equation shows the optimized Gibbs energy equationSolid solution of (S) K2Si2O5(s) used in the present work. K2 O(l )+ 2SiO 2 ( l ) = K 2 Si 2 O 5 ( s )

G( T )= u ( x , T ) + 2 u ( x , T ) K2 Si 2 O 5 (s ) K 2 O( l ) SiO 2 ( l )

G 11623 K2 Si 2 O 5 (s) =-2.549� 106 - 1068T - + 191.4 T ln( T ) 1.435 10 -6 T 3 J/mol T where u in Equation represents the chemical potential.

1600 Kracek et al. Cr

/ 1400

t 1200 a r

e 1046 C 9

O p Tr 977 C 5 4

1000 i O S 2 m 2 i

e 3 S K 2 T  C O i K

S Qu 800 2 767 C 770 C 729 C K 600 0.45 0.55 0.65 0.75 0.85 0.95 Mole Fraction SiO 2

Figure 4: T-x phase diagram of K2O-SiO2. ○ Kracek et al.[15]. Cr, Tr, and Qu represent the three forms of crystalline SiO2. (—) Results calculated using the model. Phase diagrams of silicate systems are more complex than those of salts (Figures 2 and 3). One possible reason is that silica is highly polymerized. When silica mixes with some other oxides, the structure of the mixture becomes highly networked resulting in large property changes. Another possible reason derives from the formation of many intermediate compounds during the mixing process. Depending on their stability, Liquidthese intermediate compounds may decompose or change into other compounds as T and x change. The high melting point (1046 ºC) of K2Si2O5(s) in Figure 4 relative to other intermediate compounds implies that solid K2Si2O5 is more stable at compositions 0.57~0.77 than other reported solid compounds (K2SiO3, K2Si4O9, etc.) [15].

Figure 5 illustrates a phase diagram involving iron and silicates (FeO-SiO2). The G values of pure components were calculated using the equations reported by Romero-Serrano and Pelton [17]. The parameters of the liquid solution model were optimized using the phase equilibrium data of liquid solution in equilibrium with FeSiO4(s), FeO(s), and SiO2(Tr). In the phase diagram for FeO-SiO2, only one intermediate compound, FeSiO4, has been reported [18]. The relatively x 0.33 small flat region around SiO2 implies that the association between SiO2 and FeO results in species of limited stability which can easily decompose as T increases or composition changes. An immiscible liquid region was found using the liquid solution model at xsio2 ≈ 0.6~0.99 and may partially account for the variety of mineral types in the slags.

Allen & Snow1928 ˚C 1900 Schuhmann & Ensio 2 Liquids

/ Bowen & Schairer

e 1700 Greig r u t Cr a

r Liquid

e 1500 p

i Tr e S 2 e T 1300  C F 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

Figure 5: T-x phase diagram of FeO-SiO2. Experimental data: □ Allen and Snow [19], ◊ Schuhmann and Ensio [20], Δ Bowen and Schairer [18], ○ Greig [21]. (—) Results calculated using the model.

4. Conclusions

A modified quasi-chemical model and a generalized Gibbs energy algorithm can calculate phase behavior of salt and silicate systems of importance to biomass and coal thermal process systems. The NaCl-Na2CO3, Na2S-K2S, K2O-SiO2, and FeO-SiO2 systems reported in this paper validate the model and phase diagram algorithm and provide evidence that the G models of the low-order phases can be used in extrapolations to multi-components in high-order phases once proper mixing rules are found.

References

[1] L.D. Smoot, P.J. Smith, Coal Combustion and Gasification, Plenum Press, New York, New York, N. Y., 1985. [2] A.D. Pelton, M. Blander, "Thermodynamic Analysis of Ordered Liquid Solutions by a Modified Quasi- Chemical Approach - Application to Silicate Slags," Metallurgical Transactions B-Process Metallurgy 17 (1986) 805-815. [3] M. Blander, A.D. Pelton, "Thermodynamic Analysis of Binary-Liquid Silicates and Prediction of Ternary Solution Properties by Modified Quasi-Chemical Equations," Geochimica et Cosmochimica Acta 51 (1987) 85-95. [4] A.D. Pelton, S.A. Degterov, G. Eriksson, C. Robelin, "The Modified Quasichemical Model I - Binary Solution," Metallurgical And Materials Transactions B-Process Metallurgy And Materials Processing Science 31 (2000) 651-659. [5] C. Bale, P. Chartrand, S.A. Degterov, G. Eriksson, K. Hack, R. Ben Mahfoud, J. Melancon, A.D. Pelton, S. Petersen, "FactSage Thermochemical Software and Database,". Calphad-Computer Coupling of Phase Diagrams and Thermochemistry 26 (2002) 189-228. [6] B. J. McBride, M.J. Zehe, S. Gordon, NASA Glenn Coefficients for Calculating Thermodynamic Properties of Individual Species, Glenn Research Center, Cleveland, Ohio, 2002. [7] W.L. Bragg, E.J. Williams, " Effect of thermal agitation on atomic arrangement in alloys," Proceedings of the Royal Society (London) A145 (1934) 699-730.

[8] J.P. Greenberg, The Design of Chemical Equilibrium Computation Algorithms and Investigations into the Modeling of Silicate Phase Equilibria, Ph. D. Dissertation, University of California, San Diego, San Diego, CA, 1986. [9] B. Liu, J. L. Oscarson, R. M. Izatt, Larry L. Baxter, Unpublished Data, Brigham Young University: Provo, UT, 2006. [10] M. Amadori, Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti 22 (1914) 366-372. [11] P. Niggli, "Carbonate and Chloride Melts" Zeitschrift Anorganische Allgemeine Chemie., 106 (1919) 126- 142. [12] I.N. Belyaev, M. L. Sholokhovich, "Reciprocal System of Sodium and Barium Chlorides and Carbonates," Sbornik Statei Obshchei Khimiya Akadamie Nauk S.S.S.R 1 (1953) 134-143. [13] D. Lindberg, R. Backman, M. Hupa, P. Chartrand, "Thermodynamic Evaluation and Optimization of the (Na+K+S) System" Journal of Chemical Thermodynamics 38 (2006) 900-915. [14] M. Mäkipää, R. Backman, "Corrosion of Floor Tubes in Reduced Kraft Smelts: Studies on the Effect of Chlorine and Potassium," in: 9th International Symposium on Corrosion in the Pulp and Paper Industry 1998. [15] F.C. Kracek, N.L. Bowen, G. W. Morey, "Equilibrium Relations and Factors Influencing Their Determination in the System K2SiO3-SiO2," Journal of Physical Chemistry 41 (1937) 1183-1193. [16] P. Wu, G. Eriksson, A.D. Pelton, "Optimization of the Thermodynamic Properties and Phase-Diagrams of the Na2O-SiO2 and K2O-SiO2 Systems," Journal of the American Ceramic Society 76 (1993) 2059-2064. [17] A. Romero-Serrano, A.D. Pelton, "Thermodynamic analysis of binary and ternary silicate systems by a structural model," Isij International, 39 (1999) 399-408.

[18] N. L. Bowen, J.F. Schairer, "The System: FeO-SiO2" American Journal of Science 24 (1932) 177-213. [19] W. C. Allen, R.B. Snow, "The Orthosilicate-Iron Oxide Portion of the System CaO-"FeO"-SiO2," Journal of the American Ceramic Society 38 (1955) 264-280. [20] R. Schuhmann, Jr., P.J. Ensio, "Thermodynamics of Iron Silicate Slags: Slags Saturated with γ Iron," Journal of Metals 3 (1951) 401-411. [21] J.W. Greig, "Liquid Immiscibility in the System: FeO-Fe2O3-Al2O3-SiO2," American Journal of Science 14 (1927) 473-484.