We study numerical methods for solving reactive transport problems in porous media that allow a separation of transport and chemistry at the software level, while keeping a tight numerical coupling between both subsystems. After recalling how each individual subsystem can be solved, we give a formulation that eliminates the local chemical concentrations, and keeps the total concentrations as unknowns. The block structure of the model is exploited both at the nonlinear level, by eliminating some unknowns, and at the linear level by using block Gauss-Seidel or block Jacobi preconditioning. The methods are applied to the easy 1D case of the MoMaS benchmark.