Numerical evaluation of the performance of injection/extraction well pair operation strategies with temporally variable injection/pumping rates

Highlights

• A recirculation well system with an injection/extraction pair was evaluated.

• Injection/pumping rates were subjected to sinusoidal temporal variation.

• The sinusoidal variation strategy performed better than the traditional system.

Abstract

In general, in situ remediation techniques require that treatment agents come into contact with contaminants to facilitate the treatment process. Greater contact causes more in situ mixing of the two compounds and greater contaminant reduction. In a recirculation well system featuring an injection/extraction well pair, delivery controls the remedial and economic efficiency of decontamination, and is therefore a key consideration for successful in situ remediation. In this study, we numerically evaluated the remedial and economic efficiency of a recirculation well system with sinusoidal temporally varying pumping and injection rates for enhancing remediation; the results were compared with those of a traditional recirculation well system with constant injection/extraction rates. We performed sensitivity analyses to determine the optimal values of four operational parameters associated with the effects of temporally variable pumping or injection rates on the cumulative swept area of injected chemical amendment for a given operation time or cumulative injected volume, which are good measures of remediation and economic efficiency. The findings of this study provide insight into the mechanical process of plume spreading in response to injection/pumping operational strategies, and demonstrate that enhanced plume spreading is a key requirement for achieving sufficient contact between chemical amendments and contaminants.

Introduction

In recent decades, groundwater quality has deteriorated worldwide due to rapid industrialization and inappropriate handling of hazardous chemicals. Most contaminated sites cannot feasibly be cleaned using conventional pump-and-treat technology within in a reasonable time frame and appropriate cost, especially when chlorinated solvents are present (Mackay and Cherry, 1989, Haley et al., 1991). To overcome the disadvantages of pump-and-treat methods, various remedial technologies have recently been developed such as surfactant enhanced aquifer remediation (SEAR), in situ chemical oxidation (ISCO), and in situ bioremediation (ISB), which includes biostimulation and bioaugmentation. All of these in situ groundwater remediation technologies involve the injection of treatment solutions containing chemical amendments such as electron donors or nutrients, oxidants, or surfactants into an aquifer, and require that these chemical amendments come into contact with the contaminants. To efficiently achieve in situ mixing of contaminants and remedial compounds, these technologies conventionally employ single or multiple injection/extraction well pairs, also known as recirculation wells. In these systems, contaminated water is extracted from a downgradient extraction well, amendments that promote biological or chemical contaminant degradation (i.e., ISB and ISCO, respectively) or enhance the effective aqueous solubility of non-aqueous phase liquid (NAPL) constituents (i.e., SEAR) are mixed with the extracted contaminated water, and then the extracted water containing the amendments is reinjected from an upgradient injection well (McCarty et al., 1998, Lang et al., 1997, Christ et al., 1999, Gandhi et al., 2002a, Cunningham et al., 2004, North et al., 2012). In these recirculation wells, a portion of the reinjected water is recaptured by the extraction well, while the remainder escapes the recirculation zone to flow along the gradient. The proportion of recirculated water to escaped water and the fluid residence time within the recirculation zone depends on various factors such as the pumping rate; aquifer properties such as hydraulic conductivity, anisotropy, and thickness; well separation distance; and regional groundwater flow rate. Several analytical and numerical models have been developed for hydraulic analysis of an injection–extraction well pair (Strack, 1989, Shan, 1999, Zhan, 1999, Christ et al., 1999, Huang and Goltz, 2005, Luo et al., 2007). Christ et al. (1999) presented a semianalytical scheme using complex potential theory to evaluate the recirculation ratio of flow within recirculation zones in injection–extraction well systems with an arbitrary orientation relative to the hydraulic gradient. Cunningham and Reinhard (2002) compared capture zone widths of injection–extraction well pairs oriented perpendicular to the regional flow and permeable reactive barriers by using the hydraulic potential and stream function. Cunningham et al. (2004) calculated the fraction of captured water and the travel time distribution in the recirculated zone in recirculating well pairs based on the previous solutions of Cunningham and Reinhard (2002). Zhan (1999) presented a closed-form analytical solution based on complex potential theory for capture times in an injection–extraction well pair and compared the result with numerical solutions obtained using particle tracking. In addition, Luo and Kitanidis (2004) presented several analytical solutions for the fluid residence times within the recirculation zone created by an extraction-injection well pair for several types of flow fields. Huang and Goltz (2005) developed a three-dimensional analytical solution for steady flow using the Fourier cosine transform and calculated capture zone width and interflow, in conjunction with numerical particle tracking in recirculating wells. Wu et al. (2008) provided site managers with user-friendly curves to evaluate overall treatment efficiencies, capture zone width, and recirculation fractions in injection–extraction wells or tandem recirculating wells based on an analytical solution developed using complex potential theory. Bica et al. (2019) proposed a semi-analytical solution based on complex potential theory to delineate capture zones, in conjunction with the particle tracking approach on a large number of arbitrarily positioned injection/pumping wells with different rates.

Cirpka and Kitanidis (2001) developed a numerical model based on the travel-time approach for modeling reactive transport in a flow field caused by recirculating wells. Gandhi et al. (2002b) developed a reactive transport finite-element model to simulate a complex bioremediation field demonstration in the recirculating wells at Edwards Air Force Base in southern California. Chen et al. (2010) developed a Laplace-transform finite difference model to provide an effective tool for designing enhanced groundwater remediation in an anisotropic aquifer using the vertical circulation well. Chen et al. (2011) employed the Laplace-transform finite difference model developed by Chen et al. (2010) to investigate the effect of transverse dispersion on solute transport in a vertical dipole flow test with a tracer. Recently, Xia et al. (2019) simulated hydraulic zones of a vertical circulation well using the particle tracking approach and superposition principle. However, unfortunately, the aforementioned analytical and numerical models are limited to steady groundwater flow with constant pumping or injection rates. Furthermore, these models are mainly limited to analysis of capture zone, recirculation ratio, and average residence time related to hydrodynamics and do not account for the transient spreading behavior of plume migration in a transient flow field created by temporally variable injection/pumping rates, which greatly affect the mixing controlling remediation efficiency.

Recirculation well system operation strategies that can increase the areal extent of the recirculation zone can achieve the remediation of contaminated water over larger contaminant zones with longer fluid residence times. Increasing the proportion of recirculated water to escaped water or the proportion of recirculation cell size to the amount of injected chemical amendments would improve the economic efficiency of the operation strategy. Accordingly, the delivery efficiency of a recirculation well system consisting of an injection/extraction well pair can be evaluated by calculating the evolution of the recirculation cell size over time and analyzing the relationship between the recirculation cell size and the amount of injected chemical amendment, which can be used as proxies for remedial and economic efficiency, respectively. Previous studies have performed capture zone analysis of the recirculating cell within the recirculation well system through numerical and analytical investigations; however, these studies considered only pumping or injection rates that were constant in time. Periodic pumping or injection that produces frequent pathline reorientation can induce chaotic advection under dipole flow within a recirculation well (Sposito, 2006); this chaotic advection enhances plume spreading, leading to significant solute mixing through stretching and folding the fluid interface between the injected treatment solution and contaminated groundwater, ultimately enhancing remediation. Because groundwater flows are chaotic, solute pathlines completely fill the spatial domain of the flow in a manner similar to stretching material filaments, with asymptotic exponential growth over long periods (Ottino, 1989). Trefry et al., 2012, Zhang et al., 2009 reported that an oscillating well increased the plume interface length, i.e., enhanced plume spreading, compared with a non-oscillating well with constant pumping and injection rates. In chaotic advection, the extent and size of the recirculation cell changes over time, which is in contrast to the traditional recirculation well system with constant injection and extraction rates. Accordingly, in spatially and temporally varying flows with chaotic advection, the swept area also changes with time after chemical amendment injection. Therefore, in spatially and temporally varying flow, remediation efficiency is better characterized by the cumulative swept area for a given operation time, rather than by a snapshot of the area of the recirculation at specific time. Similarly, in chaotic flow systems, economic efficiency is better characterized by the cumulative swept area for a given cumulative injected volume of chemical amendment, rather than by a snapshot of the area of the recirculation zone at a specific time for a given cumulative amount of injected chemical amendments. Cumulative swept areas can be determined by accumulating all areas swept by particles of the injected remedial reagent transported within recirculation cells that evolve over time. These cumulative swept areas can be used to evaluate remediation efficiency, as larger cumulative swept areas have greater contact between the remedial agent and contaminants, leading to more significant reduction of groundwater contaminants.

Although previous studies have provided conceptual theories about the fundamental mechanism of chaotic advection for groundwater remediation, to our knowledge, none have examined the effects of sinusoidal temporal variation in pumping and injection rates in a recirculation well pair system. Such a system is expected to create a periodic flow field with frequent pathline reorientation, thereby inducing chaotic advection. Only a few researchers have used the sinusoidal pumping rate test to estimate aquifer properties such as transmissivity and storativity (Black and Kipp, 1981, Rasmussen et al., 2003, Young et al., 2002), but they did not apply it to aquifer remediation. Rasmussen et al. (2003) designed field test equipment to perform sinusoidal pumping at the Savannah River site. In this sinusoidal aquifer test, a variable frequency drive (VFD, model Redi-Flo, Grundfos Pumps Corp., Clovis, CA) was used to control the sine wave pumpings rate. The advantage of the pumping control equipment is its ability to specify the flux at the borehole wall rather than at the pump itself (Young et al., 2002). The dynamic head loss and borehole storage can be monitored according to the change in groundwater level, and the pumping rate can be adjusted to provide a specified flux at the borehole wall (Young et al., 2002). Thus, although the groundwater table can fluctuate greatly due to the sinusoidal pumping rates, desired target pumping rates programmed with sinusoidal pumping rates can be achieved by monitoring borehole storage from water level changes in the borehole and using a flow meter to account for the dynamic head loss.

Therefore, in the present study, we performed sensitivity analyses to determine the effects of operational parameters associated with temporal sinusoidal variable pumping or injection rates on important design factors such as the cumulative swept area for injected chemical amendment for a given operation time and the relationship between the cumulative swept area and the cumulative injected volume of the chemical amendment. We also performed numerical experiments to determine which operation strategies of sinusoidal temporally varying pumping and injection wells would achieve better remediation performance in terms of both remediation and economic efficiency. We assumed that the pumping and injection rates in the recirculation well system were a sinusoidal harmonic function of time under a homogenous confined aquifer. Accordingly, the pumping and injection rates were assumed to be characterized by the frequency and phase lag of a sinusoidal function. We also assumed that the pumping and injection rates had the same frequency. We performed numerical simulations for various scenarios including constant pumping and injection rates, and calculated the cumulative swept area of the recirculation cell for each scenario as a function of the frequency and phase lag. The results of each scenario were then compared to determine which showed the best remedial performance in terms of the cumulative swept area and its relationship to cumulative injected volume. Although geological heterogeneity significantly affects delivery efficiency, which can limit remedial and economic efficiency, in this study, our analysis was limited to a homogeneous aquifer.