Can convolution and deconvolution be used as tools for modelling multi component, mixing-limited reaction networks?

Transfer functions (i.e., convolutions) have been powerful tools for both forward modeling and reconstructing past states of transport systems in a wide range of subsurface flow problems. The advantage of the transfer function is that it is a simple alternative to complicated, distributed parameter models of flow and transport, but the majority of applications of transfer functions in hydrology have been limited to relatively simple cases, like passive tracers or first-order decay. The central question evaluated in this note is whether or not multicomponent mixing-limited reactive transport can be represented within a transfer function framework. Our examples consider forward-in-time predictions and backward-in-time reconstructions of a carbonate system that represents the intrusion of seawater into a freshwater aquifer. The main result is that accurate forward-in-time and backward-in-time models are developed by posing the problem in terms of conservative components. As with all convolution-based methods, the results are sensitive to errors and/or noise in the input functions, but we show that smoothed approximations of the requisite functions provide good representations of transport. Given the vast unknowns in any subsurface transport problem, such generalized, reactive transfer function models may have yet unexplored advantages when the trade-offs between overall computational cost, accuracy, and uncertainty are explored in more detail.