Coupled solute transport and reaction models are computationally demanding when multispecies, multidimensional simulations are considered. Split-operator methods approximate solutions to the reactive solute transport problem that are both relatively efficient to compute and to construct. The transport and reaction operators are split into two separate computational steps. Split-operator schemes are introduced in the context of single species sorption to the soil, with an emphasis on the splitting errors that are induced. For standard two- step methods, the splitting error is proportional to the temporal step size of the numerical scheme. The alternating split-operator scheme, in which the order of the operations is switched at succeeding time steps, apparently does not remove the splitting error for nonlinear reactions, whereas it is removed for linear cases. An alternative to the standard time discretisation approaches is presented. The transport step is assumed to be solved by any available groundwater transport code, while the reaction model is formulated as a system of coupled ordinary differential equations and solved using an ODE solver. Two variants of the standard two-step approach are presented. The efficiency of these latter schemes is compared with a standard split-operator approach.