### A Modified Shrinking Core Model for Leaching of Aluminum from Sludge Solid Waste of Drinking Water Treatment

*Agus Mirwan, Susianto Susianto, Ali Altway, Renanto Handogo*

**Abstract**: The kinetics of aluminum

leaching from sludge solid waste (SSW) using hydrochloric acid at different

leaching temperatures (30-90°C) was studied. A mathematical model was developed based on a

shrinking core model by assuming first-order kinetics mechanisms for leaching

and an equilibrium linear at the solid-liquid

interface. The proposed model is suited to fit experimental data with three

fitting parameters and to simulate the leaching of aluminum from SSW, which was

validated with the mass transfer coefficient (

*k*, cm/s),

_{c}diffusion coefficient (

*D*,

_{e}cm

^{2}/s), and reaction rate constants (

*k*, cm/s). The evaluated

*k*,

_{c}*D*, and

_{e}*k*are expected to follow an increasing

trend with increasing temperature. The correlation coefficient ≥ 0.9795, the

root mean square error ≤ 0.399, the mean relative deviation modulus ≤ 6.415%,

and the value of activation energy is 13.27 kJmol

^{-1}. The proposed model could describe the kinetics of

aluminum leaching from the SSW DWT in accordance with test parameters and

relevant statistical criteria. Valuable information on the results of this work

can be given for the purposes of the simulation, optimization, scaling-up, and

design of the leaching

process.

**Keywords**: Aluminum; Leaching; Recovery; Shrinking core model; Sludge solid waste

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