#
Investigation of the K-Mg-Ca Sulfate System as Part of Monitoring Problematic Phase Formations in Renewable-Energy Power Plants^{ †}

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

## Abstract

**:**

_{2}SO

_{4}-(Mg,Ca)SO

_{4}system were reviewed and experimentally investigated. Based on the new and revised thermochemical data, binary phase diagrams of the K

_{2}SO

_{4}-CaSO

_{4}and K

_{2}SO

_{4}-MgSO

_{4}systems above 400 °C, which are of interest in the combustion processes of renewable-energy power plants, were optimized.

## 1. Introduction

_{2}Ca

_{2}(SO

_{4})

_{3}. For example, the composition of the slag can be KCl-NaCl-K

_{2}Ca

_{2}(SO

_{4})

_{3}[11]. SiO

_{2}, KCl, NaCl, CaSO

_{4}, CaCO

_{3}, K

_{2}Ca

_{2}(SO

_{4})

_{3}, K

_{2}CaMg(SO

_{4})

_{3}, and (Na,Ca)Al(Al,Si)

_{3}O

_{8}are reported to exist in some boiler ashes [12]. An example of the deposits build up on the heat exchangers is shown in Figure 1. Furthermore, Figure 1 depicts the three operational problems in combustion processes: fouling, slagging, and corrosion.

_{2}SO

_{4}and CaSO

_{4}[16]. In the present work, thermodynamic properties including solubility limits of some phases and thermal stabilities of double sulfates in the K

_{2}SO

_{4}-(Mg,Ca)SO

_{4}system were reviewed and experimentally investigated. Based on the revised and new thermochemical data, binary phase diagrams of K

_{2}SO

_{4}-CaSO

_{4}and K

_{2}SO

_{4}-MgSO

_{4}in the temperature range that would be of interest in the renewable-energy power plant processes were optimized. Recommended melt formation temperatures in the two studied systems have been compiled. All the thermodynamic calculations for the modeling were performed using the FactSage 7.1 software [17].

#### Thermochemical Data and Ash Deposits Prediction

## 2. Literature Data: Thermal Stabilities in the K_{2}SO_{4}-CaSO_{4}-MgSO_{4} System

_{2}SO

_{4}-MgSO

_{4}, and [12,13,14,15,16,23,24,25,26,27] the system K

_{2}SO

_{4}-CaSO

_{4}. Unlike simple sulfates such as K

_{2}SO

_{4}, the thermodynamic properties of the double sulfates have not been studied thoroughly. Consequently, the thermodynamic properties of intermediate phases in the K

_{2}SO

_{4}-CaSO

_{4}-MgSO

_{4}system are not well-defined. For instance, heat capacity measurements below 67 °C are the only available experimental thermodynamic data for K

_{2}Ca

_{2}(SO

_{4})

_{3}[15].

_{2}SO

_{4}-MgSO

_{4}system was modeled in the past by [14,19,22]. Dissolution of MgSO

_{4}in to K

_{2}SO

_{4}was considered only in Grahmann’s [22] phase diagram. The compound Mg

_{2}Ca

_{2}(SO

_{4})

_{3}was previously reported as Mg

_{3}Ca(SO

_{4})

_{4}[14,28] and was found to be a minor constituent of the ash from several conventional coal-fired power plants [29,30].

_{2}SO

_{4}-CaSO

_{4}system was modeled in the late 1960s by Rowe et al. [14] based on their and Bellanca’s [25] experimental observations. In the proposed phase diagram of K

_{2}SO

_{4}-CaSO

_{4}system, the high-temperature hexagonal K

_{2}SO

_{4}dissolves a considerable amount of CaSO

_{4}, and the low-temperature orthorhombic K

_{2}SO

_{4}may also dissolve minor amounts of CaSO

_{4}. K

_{2}Ca

_{2}(SO

_{4})

_{3}(calcium langbeinite) is the only intermediate stoichiometric phase to be identified in the system. Details on the thermodynamic properties of the double sulfates K

_{2}Ca

_{2}(SO

_{4})

_{3}for which we have conducted experiment is discussed in the subsequent sections.

## 3. Materials and Methods

#### 3.1. Materials

_{2}SO

_{4}delivered by Merck (Germany), and 99.0% pure powder of CaSO

_{4}∙2H

_{2}O delivered by Merck (Germany). The double sulfate K

_{2}Ca

_{2}(SO

_{4})

_{3}was synthesized by mixing fine powders of the pure K

_{2}SO

_{4}and CaSO

_{4}in to 1:2 molar ratio. The phase mixture was annealed for 4 days at 800 °C in a normally locked L51/SR muffle furnace (Nabertherm, Germany) with good heating control and a continuous flow of N

_{2}(gas). The synthesis took place according to Reaction (1):

_{4}+ K

_{2}SO

_{4}⇄ K

_{2}Ca

_{2}(SO

_{4})

_{3}.

#### 3.2. Methods

_{2}Ca

_{2}(SO

_{4})

_{3}was performed by applying the differential scanning calorimetry (DSC) and thermogravimetry (TGA) method using a NETZSCH STA 449 F1 Jupiter

^{®}—Simultaneous DSC-TGA equipment. The calorimeter was calibrated with the melting temperatures of high-purity metals, such as bismuth, tin, indium, zinc, aluminum and gold. The average temperature measurement accuracies were determined to be ±1 °C.

_{2}Ca

_{2}(SO

_{4})

_{3}. The initial weight of each sample was 60.4 mg in all the measurements. Before each experimental run the chamber was evacuated and then backfilled with high-purity Ar(gas) in three cycles. The Ar(gas) with the flow rate 39 mL/min was used as a protective gas in all runs. At the start of each experimental runs, the furnace was heated to 40 °C and kept at an isothermal condition for 10 min. Then, the furnace was heated to 1100 °C and cooled to 300 °C at a rate of 10 °C/min, in both heat cycles. Weight losses and heat flows were measured simultaneously during the linear heating and cooling.

## 4. Thermodynamic Optimization

_{p}is the temperature dependent heat capacity at constant pressure. $\Delta {H}_{298.15\text{}\mathrm{K}}^{o}$ is assumed to be 0 J/mol for elemental species stable at reference state T = 298.15 K and P = 1 atm. To calculate the Gibbs energy of compounds accurately the other thermodynamic parameters should be determined based on experimental data or well proven estimation. High-temperature C

_{p}values of pure phases, for which experimental data is not available in the literature or experimental data acquisition is challenging, were estimated by the summation method described in [31], i.e., for example, the C

_{p}(K

_{2}Ca

_{2}(SO

_{4})

_{3}) above 136 °C was estimated from the experimentally determined C

_{p}values of K

_{2}SO

_{4}and CaSO

_{4}according to the reaction in Equation (1). All the thermodynamic assessments and calculations in this work were performed using the FactSage 7.1 software [17].

## 5. Results and Discussion

_{2}Ca

_{2}(SO

_{4})

_{3}in the temperature range from 40 to 1260 °C are shown in Figure 3. The measured DSC and TGA curves for the five different samples were coinciding precisely. Due to the slight loss of mass (0.48 wt.%) above the peak temperature 1020.4 °C (Figure 3), replication of the measurement for the same starting sample through reheating were not considered. On the heating DSC vs. temperature curves, temperatures of phase transition and melting appeared as sharp endothermic peaks. As the TGA vs. temperature curves in Figure 3A show, weight losses of the samples during heating cycles up to the melting peaks were negligible (below 0.06 wt.%). The total weight loss up on heating to 1100 °C above the melting peak is 0.48 wt.%; thus, expected reflections of the peaks on the cooling DSC curves were observed, for example, as solidification temperatures in the case melting temperatures. From the integral between the onset and end temperatures of the peak (shaded areas in Figure 3B), the enthalpy of phase transition and melting were determined and compiled in Table 1 together with their corresponding phase transition and melting temperatures. Heat capacity (C

_{p}(T)) for K

_{2}Ca

_{2}(SO

_{4})

_{3}was determined from the stable DSC vs. T values that appear well before phase transition by comparing with the well-defined heat capacities of the reference, sapphire, as suggested by the manufacturer of a NETZSCH STA 449 F1 Jupiter

^{®}—Simultaneous DSC-TGA equipment.

#### 5.1. Thermochemical Data of Phases in the K_{2}SO_{4}-CaSO_{4}-MgSO_{4} System

_{2}Ca

_{2}(SO

_{4})

_{3}in this study from the onset temperatures of the three distinct peaks on the DSC vs. temperature curve are: 200 ± 1 °C, 914 ± 1 °C and 1010.6 ± 1 °C. The onset temperature 200 ± 1 °C corresponds very well with the phase transition temperature of K

_{2}Ca

_{2}(SO

_{4})

_{3}determined by Morey et al. [23], 200 ± 2 °C, and Cao et al. [15], 201.5 ± 0.1 °C. The phase transition temperature reported by Speer and Salje [32], 184 °C, is lower by about 16 °C than the result determined in this study and the result reported by [15,23].

_{melt}(K

_{2}Ca

_{2}(SO

_{4})

_{3}) = 1011 °C, is in excellent agreement with the onset temperature 1010.6 ± 1 °C determined in this work. The incongruent melting temperature range reported by [23], 1009–1013 °C, agrees very well with the determined value in this study. The incongruent melting temperature 1004 °C reported by [19] is lower by about 7 °C than the value determined for K

_{2}Ca

_{2}(SO

_{4})

_{3}in this study. A comparative summary of the phase transition and melting temperatures determined from the DSC-TGA vs. temperature measurements are compiled in Table 1 together with the available literature values.

_{2}Ca

_{2}(SO

_{4})

_{3}to be ∆

_{tr}H°

^{β}

^{→}

^{α}= 2.6 ± 0.1 kJ·mol

^{−1}and Δ

_{melt}H

^{α}

^{→L}= 37.1 ± 0.6 kJ·mol

^{−1}, respectively. The ∆

_{tr}H°

^{β}

^{→}

^{α}= 2.12 ± 0.02 kJ·mol

^{−1}determined at 201.5 ± 0.1 °C by Cao et al. [15] agrees with our result. A comparative summary of the phase transition and melting temperatures and the corresponding enthalpies determined from the DSC-TGA vs. temperature measurements are collected in Table 1 together with the available literature values.

#### Heat Capacity

_{p}functions for K

_{2}SO

_{4}and CaSO

_{4}were determined in our previous work [16]. The derived functions, Equations (5) and (6), for both substances agree with the values given in the handbook of Barin [36].

_{p}functions for K

_{2}Ca

_{2}(SO

_{4})

_{3}were calculated from the measured DSC vs. temperature values of the sample taking the well-defined C

_{p}values of sapphire as a reference. The experimental data below 130 °C were fitted by using the normal format C

_{p}-data fit of HSC Chemistry 6 [37]. Cao et al. [15] determined C

_{p}values for K

_{2}Ca

_{2}(SO

_{4})

_{3}up to 67 °C, based on results obtained with an adiabatic calorimeter. They reported the C

_{p}(K

_{2}Ca

_{2}(SO

_{4})

_{3}) value at 25 °C to be 343.6 ± 0.7 J·K

^{−1}·mol

^{−1}. Our calculation based on Equation (7) at the same temperature gives 331.4 ± 1 J·K

^{−1}·mol

^{−1}. C

_{p}(K

_{2}Ca

_{2}(SO

_{4})

_{3}) values that are calculated by adding C

_{p}values of the simple sulfates (Equations (5) and (6)) at 25 °C according to reaction in Equation (1), by the method described in [31], gave C

_{p}= 334.6 ± 1 J·K

^{−1}·mol

^{−1}. This value is in agreement with the experimentally determined value in this work. In the thermodynamic modeling of the phase diagram of the K

_{2}SO

_{4}-CaSO

_{4}system, we applied the experimental values determined in this study, and, for high-temperature phase regions, summations of the heat capacities of the simple sulfates method were applied. For K

_{2}Mg

_{2}(SO

_{4})

_{3,}the heat capacity and entropy data of Robie et al. [38] below 727 °C were applied together with the heat capacities estimated by adding heat capacities of the simple sulfates, K

_{2}SO

_{4}and MgSO

_{4}.

#### 5.2. The K_{2}SO_{4}-MgSO_{4} System

_{2}SO

_{4}-MgSO

_{4}system in Figure 4 was optimized using the FactSage 7.1 software package [17]. The available literature data [14,19,20,21,22] were used in the optimization. The first liquid phase in the system appears at the eutectic temperature 737 °C. This temperature is lower than the eutectic temperature 750 °C reported in the Rowe et al. [14] and Grahmann [22] phase diagrams. With regard to the solid solubility limit of MgSO

_{4}in K

_{2}SO

_{4}(maximum 3.6 mol.%), our optimization is in agreement with that of Grahmann [22]. The eutectic temperature Grahmann [22] reported for MgSO

_{4}+ K

_{2}Mg

_{2}(SO

_{4})

_{3}, at T = 884 °C, is lower by 9 °C than our optimized temperature.

_{2}Mg

_{2}(SO

_{4})

_{3}dissolves CaSO

_{4}to form a solid solution that melts as low as 885 °C compared to the melting temperature of the pure K

_{2}Mg

_{2}(SO

_{4})

_{3}, T = 930 °C. However, the melting point rises again in the presence of excess of CaSO

_{4}(>22 wt.%).

#### 5.3. The K_{2}SO_{4}-CaSO_{4} System

_{2}SO

_{4}-CaSO

_{4}system presented in Figure 6 is also optimized using the FactSage 7.1 software package [17]. Prior to this optimization, the latest phase diagram of the system was proposed by Rowe et al. [14], in the late 1960s, and revised by Arceo and Glasser [26], in 1990. Similar to the K

_{2}SO

_{4}-MgSO

_{4}system, it consists of a double sulfate K

_{2}Ca

_{2}(SO

_{4})

_{3}that melts congruently at 1010.6 °C. The optimized phase diagram of the system above 400 °C includes our experimental data presented in this work and in the previous paper from which this work has been extended of [16] as well as the literature data of [14,23,24,25,26,27].

_{2}SO

_{4}-MgSO

_{4}system, the K

_{2}SO

_{4}-CaSO

_{4}system constitutes the extensive solid solution of CaSO

_{4}in K

_{2}SO

_{4}(ss). The extent of the solid solution reported by [24,25,26] is in the range of the average value 24 ± 4 mol.% K

_{2}SO

_{4}reported by [27] and is considered in our revised phase diagram of the system. Melt-forming reactions and temperatures in the whole K

_{2}SO

_{4}-MgSO

_{4}-MgSO

_{4}system that are optimized in this work are collected to Table 2.

## 6. Conclusions

_{2}SO

_{4}-MgSO

_{4}and K

_{2}SO

_{4}-CaSO

_{4}systems in the temperature ranges which are of interest in the combustion processes of renewable-energy power plants were reviewed, experimentally studied and optimized using the FactSage software package. According to the literature data, the pure K

_{2}Mg

_{2}(SO

_{4})

_{3}phase melts at 930 °C. The optimization results in this work show that K

_{2}Mg

_{2}(SO

_{4})

_{3}coexisting with excess K

_{2}SO

_{4}(ss) melts at an eutectic temperature of 737 °C. This is lower by about 193 °C than the optimized melting temperature of the pure K

_{2}Mg

_{2}(SO

_{4})

_{3}due to the effect of excess K

_{2}SO

_{4}(ss). Moreover, CaSO

_{4}was reported to readily dissolve into K

_{2}Mg

_{2}(SO

_{4})

_{3}and lower its meting temperature by up to 52 °C. The thermal stability of K

_{2}Ca

_{2}(SO

_{4})

_{3}was experimentally studied by applying the DSC-TGA method. Based on the obtained results, its high-temperature phase transition and congruent melting temperatures were determined to be 914 ± 1 °C and 1010.6 ± 1 °C, respectively. We have also determined the C

_{p}values for K

_{2}Ca

_{2}(SO

_{4})

_{3}below 136 °C experimentally, which served as a basis for extrapolation to high-temperature C

_{p}values. The heat of fusion of K

_{2}Ca

_{2}(SO

_{4})

_{3}, Δ

_{melt}H

^{α}

^{→L}= 37.1 ± 0.6 kJ·mol

^{−1}, was also determined in this study for the first time. The results obtained were used to together with the literature data to optimize the K

_{2}SO

_{4}-CaSO

_{4}system. Generally, the phase diagrams optimized based on critically selected literature data and experimental observation in this work contribute to the development of a larger databases that can be used for simulating and controlling the ash deposition and build up in renewable-energy power plants.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematic diagram of a boiler with magnified images showing ash-related problems—slagging, fouling, and corrosion—on the surfaces of furnace walls and superheater tubes.

**Figure 2.**Schematic diagram showing novel concept for reliable prediction of deposition. The idea was adapted from [18] and modified.

**Figure 3.**Differential scanning calorimetry-thermogravimetry (DSC-TGA) curves for the synthesized K

_{2}Ca

_{2}(SO

_{4})

_{3}phase: (

**A**) phase transition temperatures, and (

**B**) highlighted areas of each peak for enthalpy of phase transition or melting calculations.

**Figure 4.**K

_{2}SO

_{4}-MgSO

_{4}system optimized using the FactSage software package. Compositions are in mole fraction; (ss) indicates solid solution.

**Figure 5.**Phase relations on the tie line K

_{2}Mg

_{2}(SO

_{4})

_{3}-CaSO

_{4}in the K

_{2}SO

_{4}-MgSO

_{4}-CaSO

_{4}system, modified from [14].

**Figure 6.**K

_{2}SO

_{4}-CaSO

_{4}system optimized using the FactSage software package. Compositions are in mole fraction.

**Table 1.**Comparative summary of temperatures and enthalpies of phase transitions and melting of single phases in the K

_{2}SO

_{4}-(Mg,Ca)SO

_{4}system.

Phase | T_{tra(1)}/°C | T_{tra(2)}/°C | ∆_{tr}H°/kJ·mol^{−1} | T_{melt}/°C | ∆_{melt}H°/kJ·mol^{−1} | Ref. |
---|---|---|---|---|---|---|

K_{2}SO_{4} | 586.1 ± 1 | None | 7.2 ± 0.1 | 1069.2 ± 1 | 21.12 ± 0.3 | [16] |

583 | - | 1069 | - | [14,33] | ||

581 | - | 1067 | - | [34] | ||

CaSO_{4} | 1201 ± 1 | None | 9.1 ± 0.1 | - | - | [16] |

1195 ± 2 | - | 1462 ± 4 | - | [14,24] | ||

1199 | 29.43 | - | - | [33] | ||

1193 | - | 1450 | 28.1 | [35] | ||

MgSO_{4} | - | None | - | 1136 ± 4 | - | [14] |

1110 | - | - | 1130 | 14.6 | [35] | |

1015 | - | 18.08 | - | - | [33] | |

K_{2}Ca_{2}(SO_{4})_{3} | 200.1 ± 1 | 914 ± 1 | 2.6 ± 0.1_{tra(1)} | 1010.6 ± 1 ^{1} | 37.1 ± 0.6 | This work |

201.5 ± 0.1 | - | 2.1 ± 0.02_{tra(1)} | - | - | [15] | |

184 | - | - | - | - | [33] | |

- | 936 | - | 1004 ^{1} | - | [19] | |

- | 940 | - | 1011 ^{1} | - | [14] | |

200 ± 2 | - | - | 1009–1013 ^{1} | - | [23] | |

K_{2}Mg_{2}(SO_{4})_{3} | - | - | - | 943 | - | [23] |

- | - | - | 930 | - | [19,20] |

^{1}Incongruent melting: K

_{2}Ca

_{2}(SO

_{4})

_{3}⇄ L + CaSO

_{4}.

**Table 2.**Summary of the optimized temperatures of melting and eutectic reactions in the K

_{2}SO

_{4}-(Mg, Ca)SO

_{4}system. Decimals are rounded to the nearest whole number and a cumulative error range is ±4 °C.

Reaction | T_{melt}/°C | Remark |
---|---|---|

K_{2}SO_{4} + MgSO_{4} ⇄ K_{2}SO_{4}(ss) + Liquid phase | 737–1069 | Melting of K_{2}SO_{4} with solid solution of up 3.6 mol.% MgSO_{4} |

K_{2}SO_{4} + CaSO_{4} ⇄ K_{2}SO_{4}(ss) + Liquid phase | 871–1069 | Melting of K_{2}SO_{4} with solid solution of up 24.1 mol.% CaSO_{4} |

MgSO_{4} ⇄ Liquid phase | 1130 | Congruent melting |

CaSO_{4} ⇄ Liquid phase | 1462 | Congruent melting |

K_{2}Mg_{2}(SO_{4})_{3} ⇄ Liquid phase | 930 | Congruent melting |

K_{2}Mg_{2}(SO_{4})_{3} + CaSO_{4} ⇄ K_{2}Mg_{2}(SO_{4})_{3}(ss) + Liquid phase | 885–930 | Melting of K_{2}Mg_{2}(SO_{4})_{3} with solid solution of up 18 mol.% CaSO_{4} |

K_{2}SO_{4}(ss) + K_{2}Mg_{2}(SO_{4})_{3} ⇄ Liquid phase | 737 | Eutectic melting |

MgSO_{4} + K_{2}Mg_{2}(SO_{4})_{3} ⇄ Liquid phase | 893 | Eutectic melting |

K_{2}Ca_{2}(SO_{4})_{3} ⇄ Liquid phase | 1011 | Congruent melting |

K_{2}SO_{4}(ss) + K_{2}Ca_{2}(SO_{4})_{3} ⇄ Liquid phase | 871 | Eutectic melting |

K_{2}Ca_{2}(SO_{4})_{3} + CaSO_{4} ⇄ Liquid phase + CaSO_{4} | 1011 | Congruent melting |

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**MDPI and ACS Style**

Tesfaye, F.; Lindberg, D.; Moroz, M.; Hupa, L.
Investigation of the K-Mg-Ca Sulfate System as Part of Monitoring Problematic Phase Formations in Renewable-Energy Power Plants. *Energies* **2020**, *13*, 5366.
https://doi.org/10.3390/en13205366

**AMA Style**

Tesfaye F, Lindberg D, Moroz M, Hupa L.
Investigation of the K-Mg-Ca Sulfate System as Part of Monitoring Problematic Phase Formations in Renewable-Energy Power Plants. *Energies*. 2020; 13(20):5366.
https://doi.org/10.3390/en13205366

**Chicago/Turabian Style**

Tesfaye, Fiseha, Daniel Lindberg, Mykola Moroz, and Leena Hupa.
2020. "Investigation of the K-Mg-Ca Sulfate System as Part of Monitoring Problematic Phase Formations in Renewable-Energy Power Plants" *Energies* 13, no. 20: 5366.
https://doi.org/10.3390/en13205366