Abstarct: This study explores the synthesis and efficacy of a novel geopolymer aimed at mitigating manganese pollution in acidic wastewater generated by copper industries, alongside the numerical modeling of the reactive transport processes involved in manganese removal. To achieve these objectives, a geopolymer composed of fly ash modified with activated carbon was synthesized under varying laboratory conditions and subsequently employed as a permeable reactive barrier for manganese ion removal. The optimal synthesis parameters were identified as follows: a precursor mixture consisting of 40 wt% activated carbon and 60 wt% fly ash, a sodium hydroxide (NaOH) concentration of 12 M, a sodium silicate to sodium hydroxide (Na2SiO3/NaOH) ratio of 2.5, a curing temperature of 55 °C, a curing duration of 14 hours, a solid content of 30%, and ultrasound irradiation at a frequency of 37 kHz. Characterization of the synthesized adsorbent under these optimal conditions was conducted using various analytical techniques. Field Emission Scanning Electron Microscopy (FESEM) analysis revealed that the synthesized adsorbent possesses a porous structure with a heterogeneous surface and a broad particle size distribution. Fourier Transform Infrared Spectroscopy (FTIR) analysis provided compelling evidence for the successful formation of a geopolymer matrix, indicated by the presence of Si-O-Si bonds. Subsequently, the response surface statistical method (RSM-CCD) was employed to investigate the effects of various parameters on the removal efficiency of manganese ions by the geopolymer. The results demonstrated that under optimal conditions—specifically, pH ~ 2.3, an adsorbent dosage of approximately 0.2 g, a contaminated solution volume of 20 mL with an initial concentration of ~ 500 ppm, stirring speed of ~ 300 rpm, and a contact time of ~ 60 minutes—complete removal of manganese ions was achieved. Further analysis utilizing kinetic, isotherm, and thermodynamic models provided deeper insights into the adsorption mechanism. Kinetic data indicated that the phenomenological internal mass transfer (IMT) model exhibited the best fit with experimental results, with internal diffusion identified as the rate-controlling mechanism. Isotherm analysis confirmed multilxayer and homogeneous interactions between the adsorbent and manganese ions. Thermodynamic evaluations suggested that the adsorption process is spontaneous and endothermic, with Gibbs free energy values indicating physical adsorption phenomena. The performance of the geopolymer adsorbent was also assessed in a fixed bed column under varying operational conditions, including contaminant solution pH, initial manganese concentration, flow rate, and both diameter and height of the bed. Findings revealed that increasing bed diameter diminishes the mass transfer area while enhancing manganese removal efficiency. Notably, under optimal conditions, the modified geopolymer achieved a pollutant removal efficiency of 99.26%. Kinetic models such as Adams-Bohart, Yoon-Nelson, Thomas, and Bed Depth Service Time (BDST) were applied to predict breakthrough curves; nonlinear fit correlation coefficients (R²) indicated strong congruence between laboratory data and model predictions. Additionally, the MIN3P reactive transport code was utilized to simulate complex interactions between manganese effluent and the geopolymer adsorbent. The simulations corroborated laboratory findings and elucidated the intricate transport phenomena involved in the adsorption process.