Considering the utility of backward-in-time simulations of multi-component reactive transport in porous media

Indirect inversion has been the predominant method for matching models and data in geochemical systems, typically using observations of chemical concentrations as calibration targets. This reserves the data with the highest confidence (observed concentrations) for the final comparison but does little to constrain the initial state of the system on which the indirect inversion is based. An alternative approach to inverse modeling is to start with the observations to reconstruct a concentration field, but it is unclear if this is feasible for reactive transport in heterogeneous systems. The purpose of this article is to consider the applicability of backward-in-time (BIT) techniques as tools for simulating reactive transport in porous media. A multi-component reaction system is considered in a variety of systems of increasing complexity and we show that complex, non-linear systems can be simulated backward in time, given a sufficiently robust integration scheme. Recent advances in reactive random walk particle tracking are employed to investigate simple flow systems with spatially variable reactions, as well as 2-d heterogeneous flows, and we show that some level of time reversibility exists in both cases. Under a uniform injection scheme, the total masses generated in forward and backward simulations of the 2-d models were all within 3.5% of each other for all the species considered, indicating good overall agreement between the models. This suggests that BIT techniques may have yet unrealized applications to inverse modeling; however, further research on the sensitivity of the approach to measurement errors and on how to efficiently apply BIT methods to transient problems is needed.