Analysis of Compressive Strength of Anhydrite Binder Using Full Factorial Design

1. Introduction

Synthetic gypsum is produced as a by-product of an industrial process. Flue gas desulfurization (FGD) gypsum is one of the synthetic gypsum. In 2020, global FGD gypsum production reached an estimated 255 million tons, primarily in Asia (55%), followed by Europe (22%), North America (18%), and the rest of the world (5%) [1]. FGD gypsum is obtained from the desulphurization of combustion gases in fossil fuel power plants. The combustion of sulphureous fossil fuels, such as anthracite, bituminous coal, lignite, and oil produces sulphur dioxide (SO₂) which, if it is not removed in a flue gas desulphurization plant, escapes into the atmosphere with the flue gases [2]. Sulphur dioxide is one of the causes of atmosphere and environment pollution. Acid rain results when sulphur dioxide is emitted into the atmosphere. Sulphur dioxide contacts with water and oxygen in the atmosphere to form sulphuric acid [3]. Acid rain has negative impact on soil, aquatic ecosystem, forests trees, crop plants, lower plants, physiological activities of animals and human health. Uncontrolled emission of SO₂ within SO_x causes a wide range of diseases including destabilization of the heartbeat, skin cancer, asthma, cough, headache, throat and nose irritations [4]. It also effects on materials and buildings [5].

The most popular method to remove sulphur dioxide from flue gas is wet scrubbing method. The flue gas is countercurrent washed with aqueous suspensions of limestone (CaCO₃) or lime (Ca(OH)₂) producing calcium sulphite (CaSO₃) in aqueous suspension. Finally, calcium sulphite is further oxidized with atmospheric oxygen to calcium sulphate dihydrate (CaSO₄∙2H₂O) or gypsum – so called flue gas desulfurization gypsum (FGD gypsum) [2]. Usually, FGD gypsum has a higher purity (96-99 %) [6] and lower level of impurities than most natural gypsum (80-96 %) [7]. Because FGD gypsum is mainly composed of calcium sulphate dihydrate (CaSO₄·2H₂O), it can replace natural gypsum without further processing [8]. Therefore, manufacturing FGD gypsum has positive environmental and economic benefits.

FGD gypsum can be a product, which has many applications in different industries. It is used in agriculture [9,10], civil engineering [11,12], water treatment [13], sorption of phosphorus ions [14] and glass industry [2]. Also FGD gypsum can be used in construction industry. It is used as setting retarder in Portland cement [8,15,16,17], calcium sulphoaluminate cement [18], as high-strength building materials [19], as a component of gypsum plaster [20]. By adding Q phase (Quaternary phase (Q phase, Ca₂₀Al₁₃Si₃Mg₃O₆₈) [21] or cement and mineral powder [22] to FGD gypsum, it is possible to reduce the water solubility of FGD gypsum, softening coefficient, water absorption, increase comprehensive considerations of strength, speed-up hydration, and to improve microstructure.

FGD gypsum can be calcined to produce α-calcium sulphate hemihydrate (α-CaSO₄∙0.5H₂O), β-calcium sulphate hemihydrate (β-CaSO₄∙0.5H₂O) or calcium sulphate (anhydrite, CaSO₄). Manufacturing and utilization of α-CaSO₄∙0.5H₂O is widely investigated [23,24,25,26]. However, little works are focused on β-CaSO₄∙0.5H₂O [27] and CaSO₄ production. FGD gypsum was calcined at temperature range of 500-750 ^oC and soluble activators were used for the production of anhydrite binder with suitable physical-mechanical properties [28,29]. The FGD was calcined at 650 °C for 4 h and used in the mixture to produce self-leveling floors [30]. Anhydrite cement was obtained from FGD gypsum which was burnt together with activators such as glass and cupola dust at 800 and 900 ^oC [31].

The aim of this research is to investigate the impact of the factors, calcination temperature of FGD gypsum (500-800 ^oC), hydration time (3-28 days) and amount (0-2 %) of activators (K₂SO₄ and Na₂SO₄), on the compressive strength of anhydrite binder produced from FGD gypsum using a 2³ full factorial (DOE) design and develop a mathematical model using multiple linear regression to predict the compressive strength of anhydrite binder within the defined limits.

2. Materials and methods

2.1. Materials

The results of chemical composition (Table 1) showed that FGD gypsum was very purity, CaSO₄∙2H₂O was 96.22 %. The pH was 6.45. The specific surface area S_spec was less than 100 m²/kg.

The X-ray diffraction (XRD) analysis (Figure 1a) confirmed that gypsum CaSO₄∙2H₂O dominates in FGD gypsum. The results of simultaneous thermal analysis (STA) (Figure 1b) showed that gypsum dehydrated and water evaporated in temperature range of 105-190 ^oC. Insoluble anhydrite formed at temperatures between 340 ^oC to 370 ^oC.

K₂SO₄ and Na₂SO₄ were used as activators to accelerate the hydration and hardening of anhydrite binder. Either 1 % or 2 % of activator by the weight of anhydrite was added together with the gauging water.

2.2. Methods

X-ray fluorescence spectroscopy (XRF) was carried out with a Bruker X-ray S8 Tiger WD (Germany) spectrometer equipped with a Rh tube with the energy of up to 60 kV. The powder was passed through an 80 μm sieve and pressed to 5×40 mm cylindrical tablets. The samples were measured in He atmosphere. SPECTRAplus QUANT EXPRESS software was used to analyze the data.

X-ray diffraction analysis (XRD) was performed on a D8 Advance difractometer (Bruker AXS, Karlsruhe, Germany) with Bragg-Brentano geometry using Ni-filtered CuK_α radiation and graphite monochromator, operating at 40 kV and 45 mA. The measurement range was 3–70 °(2θ) in steps of 2θ = 0.02°.

Simultaneous thermal analysis (STA) was carried out on a LINSEIS STA PT 1000 (Germany) thermal analyzer with ceramic sample handlers and crucibles of Pt-Rh. The heating rate was set to 10 °C/min, the range of temperature was from 25 °C up to 945 °C under N atmosphere.

Scanning electron microscopy (SEM) was performed with OXSFORD ISIS LEO 440i using an accelerating voltage of 20 kV at working distance of 10 mm.

FGD gypsum was calcined at temperature range of 500-900 ^oC for 1 hour in a muffle furnace.

Density was measured with automatic gas pycnometer Quantachrome Instruments Ultrapyc 1200e (USA). The Blaine method was used to determine the specific surface area S_spec in accordance with the European Standard EN 196-6 [32].

Physical-mechanical properties of anhydrite binder were determined according to the European Standard EN 196-3, EN 196-1 [33,34]. Samples were hardened in 90 % relative humidity environment for 28 days and compressed by press ELE AutoTest.

Full factorial (DOE) design for three independent factors at two levels (2³) was used to study the effect of factors on a response. Calcination temperature of FGD gypsum, hydration time and amount of activators were chosen as independent factors. Compressive strength of anhydrite binder was chosen as response. Each factor had two levels, low and high, coded as (-1) and (+1). 8 experimental runs were performed with three independent factors [35].

Multiple linear regression as the statistical method was used in DOE data analysis [36]. It shows the relationship between multiple independent factors and a response. A general multiple linear regression model is [35,37]:

$$Y=b_0+{\sum }_{i=1}^k{b}_i{x}_i+{\sum }_{\begin{array}{c}i,j=1\\ i\ne j\end{array}}^k{b}_{ij}{x}_i{x}_j$$

(1)

where:

Y – a response,

x_i, x_j – an independent factor,

b₀ – an intercept,

b_i – a linear coefficient,

b_ij – an interaction coefficient.

The Student‘s t-test was used to evaluate the significance of coefficients in multiple regression. The sign of coefficient indicate whether the response increases (+) or decreases (-) as independent factor increases. The value of coefficient shows how much the mean of response changes when one independent factor increases by one unit while other factors are held constant [35]. Fisher’s test was used to evaluate the adequacy of model [38]. The calculations were done at 95 % confidence interval and a significance level α less than 0.05 [38]. The quality (suitability) of the multiple linear regression model fitness was expressed by the coefficients of determination (R²) and the mean absolute percentage error (MAPE). The model is a good fit for the data if R² value is in the range 0.8-1. The model is highly accurate if MAPE is less than 10 % [39].

3. Results and discussion

3.1. Calcination temperature

FGD gypsum was calcined at temperature range of 500-900 ^oC. The hydration, physical and mechanical properties of anhydrite binder was investigated. The size and surface of anhydrite particles have influence on the properties of anhydrite. To determine the impact of calcination temperature on the particles of anhydrite, the density was measured and SEM was performed. The results showed that the density of anhydrite calcined at different temperatures increases gradually (Figure 2). The relationship of density and calcination temperature can be described by a linear regression function. The coefficient of determination R² indicated perfect correlation (R²=1).

SEM analysis (Figure 3) confirmed that increased calcination temperature enabled to form the denser particles. Similar results were obtained by Kersten Elert et. Al [40].

In order to determine the effect of calcination temperature on the mechanical properties, the water (W) and anhydrite (A) ratio (W/A) and compressive strength were measured. The results showed that the water and anhydrite ratio (W/A) decreased from 0.47 to 0.35 as the calcination temperature increased (Figure 4). The Pearson’s correlation coefficient r (-0.96) indicated a very high negative linear relationship between W/A and calcination temperature. The coefficient of determination R² showed very high correlation (R²=0.927).

As the calcination temperature increased, the compressive strength of anhydrite binder decreased at its early age (up to 3 days) and increased after 28 days (Table 2). After 28 days, the compressive strength of anhydrite binder produced at 900 ^oC and 500 ^oC differed more than 6 times.

In summary, as the calcination temperature of FGD gypsum increased, the anhydrite particles became smaller and denser, for anhydrite binder needed smaller amount of gauging water and binder became stronger. The obtained results were similar to the results of Ludwig et. al. [28].

3.2. Activators and amount of activator

The influence of the activators (K₂SO₄ and Na₂SO₄) and amount of activator (1 % or 2 %) on the hydration of anhydrite binder produced at 500 ^oC and 800 ^oC was examined. The degree of hydration at different times of hydration was calculated and XRD analysis was performed.

The obtained results showed that anhydrite obtained at 500 ^oC (Figure 5a) hydrates faster than anhydrite obtained at 800 ^oC (Figure 5b).

Anhydrite obtained at a temperature of 500 ^oC was fully hydrated after 28 days (degree of hydration was 0.99), while the degree of hydration of anhydrite obtained at a temperature of 800 ^oC was only 0.73. Hydration of the anhydrite binder was influenced by the structure of the material. At a temperature of 500 ^oC, the water dispersed the gypsum crystals. Their surface was crannied (Figure 3b). Such material had a higher internal porosity and needed more gauging water (W/A=0.47, Figure 4). Anhydrite binded and hardened very quickly (Initial setting time was 2 minutes, Final setting time was 3 minutes), but gypsum stone was not very strong (compression strength after 3 days was 2.04 MPa, Table 2). At the temperature of 800 ^oC, the crystal lattice of the material became denser, less water was needed (W/A=0.37, Figure 4). Anhydrite set and hardened slowly (Initial setting time was 100 minutes, Final setting time was 135 minutes), and the compressive strength after 3 days of hydration was 0.51 MPa, Table 2). Activators were needed to accelerate hydration.

When using both K₂SO₄ (Figure 5a,b) and Na₂SO₄ (Figure 5c,d) as activators, hydration was significantly activated. After burning the smoke gypsum at a temperature of 500 ^oC and using K₂SO₄, after 1 day the degree of hydration already reached 0.95 (Figure 5a), which was more than two times faster than without using the additive (the degree of hydration was 0.42). When using Na₂SO₄, hydration was slower (Figure 5c) than when using K₂SO₄ (Figure 5a). However, using both one and the other additive, the degree of hydration reached 0.99 after 28 days.

Anhydrite obtained at the temperature of 800 ^oC and with the use of activators hydrated much faster compared to anhydrite without additives. After 3 days, the degree of hydration changed 8 times (Figure 5b,d).

When using K₂SO₄ and Na₂SO₄, complex salts were formed during hydration: syngenite K₂Ca(SO₄)₂·H₂O and glauberite Na₂Ca(SO₄)₂. Anhydrite hydrated according to reaction equations (2) – (5).

$${2\mathrm{K}}^{+}+{\mathrm{SO}}_4^{2-}+{\mathrm{CaSO}}_4+{\mathrm{H}}_2\mathrm{O}\text{→}{\mathrm{K}}_2{\mathrm{SO}}_4·{\mathrm{CaSO}}_4·{\mathrm{H}}_2\mathrm{O}$$

(2)

$${\mathrm{K}}_2\mathrm{S}{\mathrm{O}}_4·\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4·{\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{K}}^{+}+\mathrm{S}{\mathrm{O}}_4^{2-}+\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4·2{\mathrm{H}}_2\mathrm{O}$$

(3)

$$2\mathrm{N}{\mathrm{a}}^{+}+\mathrm{S}{\mathrm{O}}_4^{2-}+\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}\to \mathrm{N}{\mathrm{a}}_2\mathrm{S}{\mathrm{O}}_4·\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}$$

(4)

$$\mathrm{N}{\mathrm{a}}_2\mathrm{S}{\mathrm{O}}_4·\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{N}{\mathrm{a}}^{+}+\mathrm{S}{\mathrm{O}}_4^{2-}+\mathrm{C}\mathrm{a}\mathrm{S}{\mathrm{O}}_4·2{\mathrm{H}}_2\mathrm{O}$$

(5)

XRD analysis confirmed the formation of syngenite and glauberite. During hydration of anhydrite obtained at a temperature of 500 ^oC and using both 1 % and 2 % activator K₂SO₄, syngenite was recorded after 10 min (Figure 6a,b). Meanwhile, during hydration of the obtained anhydrite at 800 ^oC, syngenite was recorded after 1 day. Similar XRD results were obtained using Na₂SO₄, when glauberite was formed during hydration (Figure 7).

Thus, it is possible to state that K₂SO₄ and Na₂SO₄ made a large effect on the hydration of anhydrite binder at its early age (up to 3 day). After 28 days the amount (1 % or 2 %) of either K₂SO₄ or Na₂SO₄ almost no influence on the compressive strength was noticed.

3.3. Full factorial design and Statistical methods

The purpose of this part was to use full factorial design and statistical methods to investigate the impact of independent factors on the response and develop a mathematical model for predicting response values within the defined limits.

Three independent factors, calcination temperature of FGD gypsum (x₁), hydration time (x₂) and amount of activator (x₃), were chosen. The impact of these factors on the compressive strength of anhydrite binder using K₂SO₄ (Y₁) and Na₂SO₄ (Y₂) was investigated using a 2³ full factorial design. Three factors, two levels and the range were shown in Table 3.

The design matrix for three independent factors was presented in Table 4 for the 8 experimental runs using K₂SO₄ and Na₂SO₄.

The regression equation based on the first-order model with three factors and their interaction terms was given by the following expression [41]:

$$Y=b_0+b_1{x}_1+b_2{x}_2+b_3{x}_3+b_{12}{x}_{12}+b_{13}{x}_{13}{+b}_{23}{x}_{23}$$

(6)

where:

$Y$ – the response, the measured compressive strength of anhydrite binder using different activators,

x₁, x₂, x₃ – the independent factors, calcination temperature, hydration time and amount of activator,

x₁₂, x₁₃, x₂₃ – the interaction between independent factors,

b₀ – the intercept term,

b₁, b₂, b₃ – the linear coefficients for the main factors,

b₁₂, b₁₃, b₂₃ – the interaction coefficients for the interaction between corresponding factors.

The regression coefficients b₀-b₂₃ in Equation (6) were calculated and the significance of coefficients (Student‘s t-test) was determined. All coefficients were significant at 95 % confidence interval.

The regression equations describing relationship between the significant factors and the compressive strength of anhydrite binder using K₂SO₄ and Na₂SO₄ were presented in Equation (7) and Equation (8), respectively:

$${\mathrm{K}}_2{\mathrm{SO}}_4\hspace{1em}\hspace{1em}{{\widehat{Y}}_1=11.65+3.16x_1+7.32x_2+4.63x_3+4.96x_{12}-0.71x_{13}+1.66x}_{23}$$

(7)

$${\mathrm{Na}}_2{\mathrm{SO}}_4\hspace{1em}\hspace{1em}{{\widehat{Y}}_2=11.16+3.06x_1+7.29x_2+4.14x_3+4.93x_{12}-0.81x_{13}+1.63x}_{23}$$

(8)

where:

$\widehat{Y}$ – the response, the calculated compressive strength of anhydrite binder, MPa;

The results indicated that the calcination temperature (x₁), the hydration time (x₂), amount of activator (x₃) and the interaction between calcination temperature and hydration time (x₁₂) had a significant strong positive impact on the compressive strength of anhydrite binder using K₂SO₄ and Na₂SO₄. The positive impact means that as the mentioned factors and their interaction increase, the compressive strength also increases. The highest value of all coefficients in Equation (7) and Equation (8) had the coefficient for hydration time (b₂). The value of mentioned coefficient was +7.32 and +7.29, respectively. This coefficient (b₂) was bigger more than 2 times than the coefficient b₁ (+3.16 and +3.06, respectively) and more than 1.5 time than the coefficients b₃ (+4.63 and +4.14, respectively) and b₁₂ (+4.96 and +4.93, respectively). Thus, the hydration time (x₂) was the most significant factor than the mentioned main factors and their interaction.

The values of the coefficient for the amount of activator (b₃) also were similar in Equation (7) and Equation (8). It means that the effect of amount of activator to the compressive strength using above-mentioned activators was similar. However when K₂SO₄ was used, the influence of this variable was bigger compared with Na₂SO_4. This may be influenced by the higher activity of the potassium salt [42]. The coefficient for the calcination temperature (b₁) was similar in Equation (7) and Equation (8). It means that the impact of calcination temperature to the compressive strength using above-mentioned activators was similar, too. The values of the coefficient for interaction between calcination temperature and hydration time (b₁₂) were also positive and effect on the compressive strength was very strong when K₂SO₄ and Na₂SO₄ were used.

The coefficient for interaction between calcination temperature and amount of activator (b₁₃) was negative (-0.71 and -0.81). It indicated a negative and weak effect on the compressive strength using K₂SO₄ and Na₂SO₄.

According to regression analysis, it can be concluded that the hydration time (x₂) made the strongest influence on the compressive strength using K₂SO₄ and Na₂SO_4. The interaction between calcination temperature and hydration time (x₁₂) and the amount of activator (x₃) made less impact on the response but it was very significant compared with hydration time (x₂). Meanwhile, when K₂SO₄ was used, the amount of activator (x₃) indicated stronger effect on the compressive strength compared with Na₂SO₄.

The coefficients of determination (R²) and the mean absolute (MAPE) between experimental and calculated values of compressive strength were used to evaluate the obtained models suitability.

The coefficient of determination (R²) for Equation (7) and Equation (8) was found to be 0.9995 and 0.9996, respectively, and the mean absolute percentage error (MAPE) was calculated as 9.53 % and 8.48 %, respectively. Since the R² value was close to 1 and MAPE was less than 10 %, it is possible to state that regression Equation (7) and Equation (8) were reliable to forecast the relation between the significant factors, their interaction and the compressive strength of anhydrite binder.

3.4. Model Verification

The purpose of this part was to verify the obtained models. The compressive strength was calculated using the obtained Equation (7) and Equations (8) and measured under the same working conditions, using the anhydrite produced at 700 ^oC temperature and using 2 % of activator. The results were obtained after 3, 7 and 28 days. The experimental and calculated values of the compressive strength were presented in Figure 8. MAPE for the compressive strength of anhydrite binder using K₂SO₄ and Na₂SO₄ were 7.46 % and 9.39 %, respectively. It showed a good agreement between the experimental data and the calculation using obtained equations.

In summary, the mathematical models using multiple linear regression could be used to predict the compressive strength of anhydrite binder within the defined limits.

4. Conclusions

FGD gypsum was high purity and could be used to produce anhydrite binder. A 2³ full factorial design and statistical methods were used to investigate the impact of the main factors, calcination temperature of FGD gypsum (500-800 ^oC), hydration time (3-28 days) and amount (0-2 %) of activators (K₂SO₄ and Na₂SO₄), and their interactions on the compressive strength of anhydrite binder.

The statistical analysis showed that calcination temperature, hydration time, amount of activator and interaction between calcination temperature and hydration time had a significant strong positive impact on the compressive strength of anhydrite binder using K₂SO₄ and Na₂SO₄. The results indicated that the hydration time had the strongest positive effect on the response. K₂SO₄ made a greater influence on the compressive strength than Na₂SO₄.

The mathematical models using multiple linear regression were developed. The coefficients of determination (R² is close to 1) and the mean absolute percentage error (MAPE is less than 10 %) indicated that the obtained models were suitable to predict the compressive strength of anhydrite binder produced from FGD gypsum within the defined limits.