  Calculating how long a coupled multi-species reactive-diffusive transport
process in a heterogeneous medium takes to effectively reach steady state is
important in many applications. In this paper, we show how the time required
for such processes to transition to within a small specified tolerance of
steady state can be calculated accurately without having to solve the governing
time-dependent model equations. Our approach is valid for general first-order
reaction networks and an arbitrary number of species. Three numerical examples
are presented to confirm the analysis and investigate the efficacy of the
approach. A key finding is that for sequential reactions our approach works
better provided the two smallest reaction rates are well separated. MATLAB code
implementing the methodology and reproducing the results in the paper is made
available.
