In this talk we will focus on systems of advection-diffusion-reaction equations which arise when modeling the transport of chemical species in groundwater. In these equations, one can have kinetic and/or equilibrium reactions. Typically, the transport (advection-diffusion) is split from the reactions, thus one takes a transport step for each component, then combines all the components into a reaction step, which can be solved locally. This type of approach, while efficient, gives rise to time truncation errors. On the other hand, one can try to solve the system fully implicitly, which reduces the time truncation errors but gives rise to huge nonlinear systems. We will discuss various time-stepping approaches and examine the errors associated with each. Examples for both kinetic and equilibrium reactions will be discussed.