This paper presents a nonlinear predictive control (NMPC) framework using Richard's phenomenological model for heap leaching within a closed-loop system. It divides the leaching pile into control volumes modeled as leaching columns with separate sprinklers, allowing local regulation of saturation by adjusting irrigation rates. The NMPC framework includes an Identification Module for optimal parameter fitting and an Optimization Module for determining optimal irrigation trajectories, both formulated as dynamic optimization problems connected to partial differential algebraic equations. The objective is to improve leaching performance by maximizing bed homogeneity using real-time data, including moisture measurements obtained from Electrical Resistivity Tomography. The optimization problems were reformulated using orthogonal collocation within finite elements. Solutions were achieved through the interior point method with CasADi for gradient estimation via automatic differentiation. Numerical experiments assessed NMPC performance under partial model knowledge, analyzing two scenarios to determine moisture measurement impact on mitigating structural uncertainty. Results show that without moisture data, the NMPC improved leach bed homogeneity but failed to maintain set-point moisture levels. In contrast, with moisture measurements, the NMPC achieved both bed homogeneity and set-point saturation. Computational times were under 10 s, making the approach suitable for real-time applications. Incorporating real-time saturation data effectively addressed modeling uncertainties, demonstrating the NMPC's potential to enhance leach bed conditions and potentially improve copper recovery efficiency, laying the groundwork for future advancements in heap leach management.