Reactive transport with wellbore storages in a single-well push–pull test

Abstract

Abstract. Using the single-well push–pull (SWPP) test to determine the in situ biogeochemical reaction kinetics, a chase phase and a rest phase were recommended to increase the duration of reaction, besides the injection and extraction phases. In this study, we presented multi-species reactive models of the four-phase SWPP test considering the wellbore storages for both groundwater flow and solute transport and a finite aquifer hydraulic diffusivity, which were ignored in previous studies. The models of the wellbore storage for solute transport were proposed based on the mass balance, and the sensitivity analysis and uniqueness analysis were employed to investigate the assumptions used in previous studies on the parameter estimation. The results showed that ignoring it might produce great errors in the SWPP test. In the injection and chase phases, the influence of the wellbore storage increased with the decreasing aquifer hydraulic diffusivity. The peak values of the breakthrough curves (BTCs) increased with the increasing aquifer hydraulic diffusivity in the extraction phase, and the arrival time of the peak value became shorter with a greater aquifer hydraulic diffusivity. Meanwhile, the Robin condition performed well at the rest phase only when the chase concentration was zero and the solute in the injection phase was completely flushed out of the borehole into the aquifer. The Danckwerts condition was better than the Robin condition even when the chase concentration was not zero. The reaction parameters could be determined by directly best fitting the observed data when the nonlinear reactions were described by piece-wise linear functions, while such an approach might not work if one attempted to use nonlinear functions to describe such nonlinear reactions. The field application demonstrated that the new model of this study performed well in interpreting BTCs of a SWPP test.

New model of reactive transport in a single-well push–pull test with aquitard effect and wellbore storage

“…The Borden site of Canada (Sudicky, 1988) is one example of weak aquifer heterogeneity. Wang et al (2018) employed a stochastic modeling technique to test the assumption of homogeneity associated with the SWPP test and found that such an assumption could be used to approximate a heterogeneous aquifer when the variance of spatial hydraulic conductivity was small.…”

“…Similar to other aquifer tests, the SWPP test is a forcedgradient groundwater tracer test, and analytical solutions are often preferred to determine the in situ aquifer properties, due to the computational efficiency. Currently, many analytical models are available for various scenarios of the SWPP tests (Gelhar and Collins, 1971;Huang et al, 2010;Chen et al, 2017;Schroth and Istok, 2005;Wang et al, 2018). However, these studies are based on a common underlying assumption, i.e., that the studied aquifer was isolated from adjacent aquitards.…”

“…The examples of ignoring wellbore storage include Gelhar and Collins (1971), Chen (1985Chen ( , 1987, Moench (1989), Chen et al (2007Chen et al ( , 2012Chen et al ( , 2017, Schroth et al (2001), Tang and Babu (1979), Huang et al (2010) and Zhou et al (2017). Recently, Wang et al (2018) developed a two-phase (injection and extraction) model for the SWPP test with specific considerations of the wellbore storage. In many field applications, the chaser and rest phases are generally involved and the mixing effect also happens in these two phases in the SWPP test, which will be investigated in this study.…”

“…Besides the abovementioned issues in previous studies, another issue is that the advection-dispersion equation (ADE) was used to govern the reactive transport of SWPP tests (Gelhar and Collins, 1971;Wang et al, 2018;Jung and Pruess, 2012). The validity of ADE has been challenged by numerous laboratory and field experimental studies before, when using a single representative value of advection, dispersion and reaction to characterize the whole system.…”

“…It does not seem difficult to solve this model of this study using numerical packages like MODFLOW-MT3DMS, TOUGH and TOUGHREACT, and FEFLOW. However, the numerical solutions may cause errors in treating the wellbore storage, since the volume of water in the wellbore was assumed to be constant (Wang et al, 2018), while in reality it changes with time and well discharge. Meanwhile, the numerical errors (like numerical dispersion and numerical oscillation) have to be considered in solving the ADE equation, especially for advection-dominated transport.…”