Semi-Empirical Modelling of Spray-Dry SO₂ Absorption Using Waste Black Ash and Raw Trona as Low-Cost Alternatives to Commercial Na₂CO₃

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Abstract
Sodium-based sorbents have received increasing attention for spray-dry flue gas desulphurisation (FGD). This study investigates waste black ash (a sodium-rich by-product of pulp and paper sludge incineration) and raw trona (a naturally occurring sodium sesquicarbonate mineral) as low-cost sorbents for spray dry SO₂ absorption, benchmarked against commercial-grade Na₂CO₃. Experiments were conducted in a laboratory-scale spray dryer at inlet gas temperatures of 140–200 °C, Na:S ratios of 0.5–2.0, and liquid-to-gas ratios of 0.0206 – 0.0274 L/m³, with a fixed inlet SO₂ concentration of 1000 ppm. The sorbents were characterised by X-ray diffraction (XRD) and Fourier transform infrared spectroscopy. A semi-empirical framework consisting of an exponential temperature model, a saturating exponential Na:S model, and a linear liquid-to-gas model was fitted independently for each sorbent and combined multiplicatively. The composite yielded R² values of 0.956, 0.915, and 0.962 for Botash, black ash, and trona, respectively, with RMSE values no greater than 0.031. At the reference condition of 140 °C, Na:S = 1, and L/G = 0.024 L/m³, SO₂ removal efficiencies were 73.0% for Botash, 66.8% for black ash, and 64.1% for trona. XRD-based calculations gave Na₂O-equivalent reactive contents of 58.5 wt.% for Botash, 57.8 wt.% for black ash, and 41.1 wt.% for trona. The corresponding theoretical SO₂ uptake capacities were 60.5, 59.3, and 42.5 g SO₂ per 100 g sorbent. This capacity, combined with the overall composite model across all the operating conditions, suggests that black ash is sufficient to meet FGD performance targets at Na:S ≥ 1 while reducing industrial landfill waste.

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