Water resource management involves numerical simulations in order to study contamination of groundwater by chemical species. Not only do the aqueous components move due to physical advection and dispersion processes, but they also react together and with fixed components. Therefore the mass balance couples transport and chemistry, and reactive transport models are PDEs coupled with nonlinear algebraic equations. In this paper, we present a global method based on the method of lines and DAE solvers. At each time step, nonlinear systems are solved by a Newton- LU method. We use this method to carry out numerical simulations for the reactive transport benchmark proposed by the MoMas research group. Although we study only 1D computations with a specific geochemical system, several difficulties arise. Numerical experiments show that our method can solve quite difficult problems, get accurate results and capture sharp fronts.