## 3 Methodology
### Fouling and Slagging Prediction Indices  
The application of successfully published ash deposition indices in predicting the severity of fouling and slagging deposits formed during the boiler operation would increase the boiler's operational efficiency [31]. The base acid ratio index expresses the relationship between the basic oxides (Fe\({}_{2}\)O\({}_{3}\), MgO, K\({}_{2}\)O, Na\({}_{2}\)O, CaO) and the acidic oxides (SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\) and TiO\({}_{2}\)) constituents in the ash samples. It is used to predict the slagging and fouling occurrence during the boiler operation, which can be evaluated using Equation (1) [46]. Higher acidic oxides indicate a higher melting point of the coal ash samples with a minimum fouling and slagging prediction during the boiler operation [45].  
\[\frac{B}{A}=\frac{(Fe_{2}O_{3}+MgO+K_{2}O+Na_{2}O+CaO)\%}{(SiO_{2}+Al_{2}O_{3} +TiO_{2})\%} \tag{1}\]  
The base acid ratio indices for samples A and B from the analysed results are 0.16 and 0.19, respectively. The base acid ratio of the coal ash sample with values between 0.4-0.7 indicates a low ash fusibility and a higher slagging potential during the boiler operation [21]. However, the base acid ratio of both ash samples in this study is less than 0.2 indicating high ash fusibility with a corresponding lower slagging potential prediction during Sasol boiler(s) operation. Ash deposition in the boiler furnace wall and heat transfer surfaces during the boiler operations is mainly caused by condensed alkaline vapours, thermophoretic aerosols/fume particles and the slagging/sintered passage formed by the molten basic components reacting with clay and quartz [47; 48; 49].  
The fouling potential (fu) during the boiler operations can be predicted based on the base acid ratio and the alkali (Na\({}_{2}\)O and K\({}_{2}\)O) chemical composition in the coal ash samples as expressed in Equation (2) [50].  
\[f_{u}=\frac{B}{A}(Na_{2}O+K_{2}O) \tag{2}\]  
An increase in the surface stickiness on the heat transfer tubes is caused by the condensation of potassium (K) in the fly ash particles. The major constituents that cause ash deposition problems on the boiler superheater tubes are K\({}_{2}\)O, SO\({}_{3}\) and CaO [20].  
[PERSON] (1996) proposed that the fouling potential during the boiler operation can also be predicted using an index based on the number of sodium oxides (Na\({}_{2}\)O) present within the coal ash samples within the low-grade bituminous coal [47].  
[PERSON] and [PERSON] developed a slagging prediction index (Rs) on the furnace wall during the boiler operation, this method is the product of the coal ash base acid ratio and the percentage of sulphur (S) contained within the raw coal samples as expressed in the Equation (3). This index is applicable for all types of coals [51].  
\[R_{s}=\frac{B}{A}\times S \tag{3}\]  
A predicted fouling tendency index during the boiler operation was also developed by evaluating the product of the base acid ratio and the number of sodium oxides (Na\({}_{2}\)O) present within the coal ash samples, as shown in Equation (4) [47; 51].  
\[R_{F}=\frac{B}{A}\times Na_{2}O \tag{4}\]  
Fouling during coal-fired boiler operation can also be evaluated using the alkali metals (K\({}_{2}\)O, Na\({}_{2}\)O) and silicate (SiO\({}_{2}\)) compounds present in the coal ash samples. The slag viscosity index (Sr) in Equation (5) is used to predict the slagging tendency in the boilerfurnace wall, since the furnace wall deposits are similar to the coal ash constituents that are made up of mostly silicate materials [52].  
\[S_{r}=\left(\frac{SiO_{2}}{SiO_{2}+CaO+MgO+Fe_{2}O_{3}}\right)\times 100 \tag{5}\]  
A higher slag viscosity index represents a high viscosity of the silica constituents inside the boiler furnace with a corresponding low slagging potential [34].