Simulation Framework for Environmental Remediation: Monte Carlo Estimation of Mass Transfer in Nickel Bioadsorption

Introduction:Toxic metal contamination in water is a critical environmental issue, and adsorption has emerged as a promising remediation technique due to its simplicity, efficiency, and cost-effectiveness. Beyond removal efficiency, the use of agricultural residues as bioadsorbents supports circular-economy strategies by valorizing low-cost biomass and reducing waste generation. Nickel removal using Moringa oleifera residues is particularly attractive due to their availability, sustainability, and contribution to cleaner production frameworks. A key challenge in adsorption modeling is the estimation of the internal mass transfer coefficient (ks), which governs intraparticle diffusion and strongly influences process performance.

Methods: In this study, we developed a Monte Carlo (MC)-based simulation framework to estimate ks in nickel bioadsorption using Moringa oleifera residues. The system was represented as a lattice where adsorption and desorption events occur probabilistically according to kinetic parameters. Simulations were performed on a 50×50 grid for up to 10⁶ steps to ensure convergence. Surface coverage (θ) and mass transfer coefficients were obtained and compared with experimental values previously determined from fixed-bed column and batch experiments.

Results: The MC model successfully predicted an equilibrium surface coverage of θMC=0.5188, in close agreement with the experimental value θexp=0.508 (error: 1.34%). The estimated coefficient was ks,MC=0.0329, deviating by 17.48% from the experimental reference ks,exp=0.028, but remaining within the reported uncertainty. Simulations also revealed a decrease in adsorption efficiency with increasing temperature, consistent with the exothermic nature of the process. A cluster-based MC variant underestimated equilibrium coverage and overestimated ks, indicating that independent-site adsorption is the most suitable representation for this system.

Conclusions: The proposed MC framework constitutes a valuable computational tool for evaluating adsorption-based remediation processes. By integrating stochastic simulation with experimental validation, the model supports the assessment and management of bioadsorption technologies, reduces experimental demand, and contributes to the design of sustainable water treatment strategies under the principles of circular economy.