Models to determine first-order rate coefficients from single-well push-pull tests

Push-pull tests (PPTs) have been successfully employed to quantify various microbially mediated processes in the subsurface. Current models for determining first-order rate coefficients (k) from PPTs assume complete and instantaneous mixing of injected test solution in the portion of the aquifer investigated by the test, i.e., the system is treated like a well-mixed reactor. Here we present two alternative models to estimate k that are based on different mixing assumptions, i.e., plug-flow and variably mixed reactor models. Rate coefficients estimated by the models were compared using a sensitivity analysis and numerical simulations of PPTs. Results indicated that all models yielded reasonably accurate k estimates (errors < 13%), while best accuracy (errors < 1%) was obtained using the variably mixed reactor model. The well-mixed reactor model generally overestimated true (simulation input) k values, whereas true k values were consistently underestimated by the plug-flow reactor model. However, estimates of k obtained with the latter models bracketed true k values in all cases. As the variably mixed reactor model is more difficult to apply, we suggest using the well-mixed and plug-flow reactor models to obtain intervals for k estimates that will encompass true k values with high certainty. In an example application, we used all models to reanalyze a published PPT data set to obtain k estimates for nitrate consumption in a petroleum-contaminated aquifer. Similar results were obtained for all three models (relative differences < 10% between k estimates), indicating that all three models are robust tools for estimating k values from PPT experimental data.