## 3 Methodology
### Instrumentation and Experimental Procedures  
For the ICP analysis, the instruments used were Spectro Arcos ICP-OES and Perkin Elmer NexION 300 ICP-MS, whereas for the XRF the instruments used were an electric fusion machine (TheOx from Claisse) and a wavelength-dispersive XRF spectrometer (MagiX PRO from Malvern Panalytical). The CHNS analysis was carried out using a Flash 2000 CHNS Elemental analyser from Thermofisher Scientific.  
The ICP-MS, ICP-OES, and XRF tests were done at the Spectra analytical facility, University of Johannesburg, at the C-LES lab. The CHNS test was done in the chemical sciences department.  
The tests carried out in this study were induced coupled plasma optical emission spectroscopy (ICP-OES), induced coupled plasma mass spectroscopy (ICP-MS), X-ray Fluorescence spectroscopy (XRF), and Carbon Hydrogen, Nitrogen, and Sulphur (CHNS) analysis. The ICP-OES test was carried out for both ash samples (A and B) to determine the element presents within the ash samples using an emission spectroscopy technique whereas the ICP-MS was also used to determine the ash elements present based on their overall percentage mass in the coal ash samples.  
The XRF test was carried out for both coal ash samples (A and B) to determine the chemical composition by mass of the elements present within the ash samples in an oxidised atmosphere using a non-destructive bombardment X-ray emission technique by directing emitted X-ray beam through a boron fusion disc.  
The CHNS analytical test was used to determine the major elements present [carbon (C), hydrogen (H), Nitrogen (N), Sulphur (S)] by mass percentage within the raw mine bituminous coal. An approximate mass of about 1.75-1.85 g of coal sample (C) was placed into a universal soft tin cup, the cup folded using tweezers to a barrel shape, and then placed into an autosampler. Using a Flash 2000 CHNS Elemental analyser from Thermofisher Scientific, the folded sample was fed by pushing it into a quartz reactor in the instrument furnace at a temperature of 950 \({}^{\circ}\)C for flash combustion with the aid of oxygen. The gaseous combustion products N\({}_{2}\), NO, H\({}_{2}\)O, SO\({}_{2}\), O\({}_{2}\) and CO\({}_{2}\) were carried away by the helium gas through a column filled with copper oxide (CuO) to a Copper (Cu) column where the nitrogen oxides are reduced to elementary nitrogen and oxygen to copper oxide (CuO). Water is then absorbed in another column. The remaining gasses are then introduced into a TPD (Temperature Programmed Desorption) column where the nitrogen gas enters right through, and the other gases are bound to the column. With a programmed temperature rise in the column, the gases are released separately flowing along a thermal conductivity detector (TCD) which produces an electrical signal proportional to the concentration (in %) of Nitrogen, Carbon, Hydrogen, and Sulphur present within the coal sample.  
The ash samples were prepared and analysed using a precision form of instrument repeatability for the ICP-OES and ICP-MS. The common instrumental error estimation for the ICP-OES and ICP-MS analysis is less than 5% in the equipment's analytical region and a 10% error at the detection limit.  
The estimated lower limit of detection for the ICP-OES analysed data is 0.05 mg/kg. The estimated assumed safe limit of detection for the ICP-MS analysis is 0.1 ug/L (0.0001 mg/Kg) for most elements and 0.01 ug/L (0.00001 mg/Kg) for Hg and Cd.  
For the XRF chemical composition analysis, the standard error estimation for the concentrated analysed major elemental composition (i.e., Al\({}_{2}\)O3 and SiO\({}_{2}\)) is 2%. The error/uncertainty tends to be higher for minor elements concentration (i.e., CaO, TiO\({}_{2}\), Fe\({}_{2}\)O\({}_{3}\), MgO etc.).  
The limit of detection for the analysed XRF results is approximately 0.05 mass (%) (500 mg/Kg).