Baryte is of interest to nuclear waste disposal as the main scavenger of 226Ra, a long-lived nuclide playing a major role in the safety assessment of planned disposal sites. In specific repository setups, Ba and Ra released from the nuclear waste will react with sulphate-rich pore water, potentially leading to formation of Ra-bearing baryte. Baryte has a complex kinetic behaviour and its precipitation may strongly be inhibited. Because highly supersaturated solutions may persist metastably, it can be anticipated that the migration of Ra through the repository near-field will strongly depend on parameters related to nucleation and precipitation kinetics, so that thermodynamic equilibrium calculations will not be sufficient for a reliable prediction of 226Ra mobility. In this study, we implement Classical Nucleation Theory (CNT) and a saturation-state dependent precipitation rate equation into a Lattice-Boltzmann (LB) reactive transport code to model Ra-bearing baryte precipitation within a porous medium analogous to fragmented nuclear waste glass. In the simulations, baryte precipitation is induced by counter-diffusion of BaCl2 and Na2SO4 solutions. Radium co-precipitation is taken into account by assuming a fixed partition coefficient and constant Ra concentration at the BaCl2 injection boundary. Both homogeneous and heterogeneous growth were considered. Critical CNT parameters, particularly supersaturation-dependent induction times, were calibrated against independent turbidity and X-ray absorption experiments. The model allows exploring the influence of baryte nucleation/precipitation kinetics on the partitioning of Ra between aqueous phase and solid at the pore (micrometre) scale. Our results indicate that quantitative knowledge of kinetic and nucleation parameters is essential to predict radionuclide transport towards the geosphere in nuclear waste repository systems.