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Including multiple mineral precipitation in anaerobic digestion models is important to accurately assess the quantity of phosphates (PO_4-P) in the liquid phase of digested sludge that can be recovered as a fertilizer in struvite precipitation reactors or by emerging processes such as ion exchange membranes. However, the performance of such processes is highly impacted by the presence of potassium (K⁺) or calcium (Ca²⁺) ions, which are most often neglected when validating precipitation models. The novelty of this work was to provide a calibration procedure of an anaerobic digestion model with multiple mineral precipitation that can be used for different case studies and do not focus only on PO₄-P but also on K⁺, Ca²⁺ Mg²⁺. To draw this calibration procedure, data from two anaerobic digesters located near Lyon (France) and in the Navarra region (Spain), treating sludge with different biodegradability and concentration ranges of phosphorus (P), calcium (Ca), magnesium (Mg), potassium (K) and soluble inorganic carbon (SIC), have been used. This procedure includes the calibration of the inert COD fraction (f_XI,COD) and kinetic precipitation constants (K_r) using Bayesian Monte Carlo techniques. However, a unique parameter set for both anaerobic digesters cannot be identified, leading to site-specific parameters for f_XI,COD (0.30 and 0.43), K_r,MgCO3 (274 and 0.4), K_r,CaCO3 (21 and 0.12) and K_r,ACP (270 and 58). The calibrated model was able to estimate PO₄-P, Ca²⁺, Mg²⁺ and K⁺ concentration in digested sludge with a relative error below 10 %.