Experimental and numerical investigation of Engineered Injection and Extraction (EIE) induced with three-dimensional flow field

Remediation of groundwater contamination is a major concern for water professionals from all over the world. Various technologies have been developed for remediating contaminated groundwater. Contaminated groundwater often defiles the porous media matrix in contact with it and vice versa. Hence, remediation of a contaminated aquifer should always address the treatment for both water and porous media matrix. In situ groundwater remediation techniques have gained much recognition in this context. It works by injecting a suitable reagent into the contaminated aquifer, thus remediating groundwater and the porous media matrix simultaneously. It is more convenient compared to ex situ technologies such as pump and treat where contaminated water is extracted, treated offsite and injected back. But, in most of the in situ treatment methods, the remediation remains incomplete owing to the laminar nature of groundwater flow causing a lack of intermixing between the treatment reagent and the contaminant (Zhang et al. 2009). The extent of spreading of reagent into the aquifer is a crucial factor in deciding the efficacy of any in situ remediation technique.

Studies on the spreading of reagents (for remediation) in aquifers are mainly of two broad categories. First is passive spreading which takes place as a result of inherent properties of the aquifer and natural flow field and the second is active spreading which takes place as a result of deliberately induced flow fields within the aquifer (Kapoor & Kitanidis 1996). Several numerical models that dealt with active spreading in porous media have been reported in the literature. Pulsed dipole by Jones & Aref (1988) was one among them. Stremler et al. (2004) experimented with the pulsed dipole model to create enhanced spreading in porous media, which was later applied for groundwater remediation by Sposito (2006). Similar approaches to pulsed dipole were oscillating well triplets by Bagtzoglou & Oates (2007) and rotated potential mixing (RPM) protocol by Trefry et al. (2012). All these methods were found to increase spreading in porous media in response to the unsteady flow fields created by using different active pumping protocols. A pulsed dipole has limitations when applied to real aquifers as complete mixing is difficult to achieve without proper reinjection rules (Radabaugh et al. 2009; Mays & Neupauer 2012). This method also causes clogging in pumps arising from the extraction of reagents and contaminants simultaneously (Li et al. 2009). Engineered Injection and Extraction (EIE) was introduced by Mays & Neupauer (2012), which overcomes the above-mentioned drawbacks.

EIE is an advanced in situ remediation technique in which a suitable treatment reagent is introduced into a contaminated aquifer and a series of injections and extraction of clean water is performed in an arrangement of surrounding wells that can generate chaotic advection(depending on the resulting velocity field). Chaotic advection creates velocity variations and complex particle trajectories in laminar flows (Ottino 1990). EIE is said to stretch and fold the reagent and contaminant plume thereby increasing mixing and thus improving contaminant degradation. Chaotic advection provides a theoretical framework for the stretching and folding of the treatment reagent and the contaminant plume in aquifers during EIE (Mays & Neupauer 2012). Several numerical investigations on enhanced spreading by chaotic advection generated in response to EIE have been found in the literature (Mays & Neupauer 2010, 2012; Piscopo et al. 2011, 2013; Neupauer & Mays 2015; Piscopo et al. 2015; Greene et al. 2017). The numerical investigations showed the potential of EIE in the enhancement of spreading and reaction under various scenarios.

Most of the studies related to EIE and chaotic advection dealt with two-dimensional analysis. Very few attempts have been made to develop EIE in three dimensions. Trefry et al. (2012), suggested developing a spherical equivalent of the active spreading protocol for inducing a truly three-dimensional spreading in aquifers. Asha et al. (2021) attempted the possibility of enhancing three-dimensional spreading by emplacement of partially screened wells in EIE. They used a three-dimensional homogeneous and confined aquifer model domain and simulated the behaviour of particle movement under EIE with partially screened wells. Enhancement in spreading was observed when EIE was attempted with partially screened wells. However, most of the numerical models describing EIE lack proper experimental validation. Conducting experiments to predict the transport processes in porous media and visualising the process is always a topic of utmost importance. A few experimental studies related to chaotic advection in porous media have been reported (Zhang et al. 2009; Nissan et al. 2017; Roth 2018; Cho et al. 2019). Zhang et al. (2009) conducted an experiment in a sand-packed flow cell using the oscillating well triplet reported by Bagtzoglou & Oates (2007). Nissan et al. (2017) conducted a tracer transport experiment for an unsteady flow through a column packed with sand and showed an increase in the spreading under such flow conditions. Roth (2018) conducted an experimental investigation of scalar spreading as a result of EIE in a homogeneous porous media by using a two-dimensional flow apparatus and showed that EIE could lead to enhanced spreading. A field-scale study of chaotic advection was reported by Cho et al. (2019) in which they employed an active pumping protocol (RPM) and studied the enhancement in plume spreading in an experimental lock gate created in a sand pit area. They employed fully screened wells for active pumping and hence, the active flow essentially remained two-dimensional in nature.

Large-scale field experiments provide a clear insight into the actual process, but managing and controlling various unforeseen processes is troublesome. Field tests also involve time-consuming procedures and are expensive; making them difficult to execute. Laboratory experiments are comparatively easier and give better control of the experimental conditions. Considering the ambiguity associated with porous media characteristics (such as conductivity, dispersivity, and porosity), every numerical model needs to be experimentally validated to get much refined and reliable numerical results. EIE in three dimensions employing partially screened wells was numerically simulated by Asha et al. (2021), and enhanced spreading in terms of particle trajectories was presented. The study showed enhanced spreading through flow modelling and did not include transport modelling. To get a complete insight into spreading in three dimensions by employing partially screened wells in EIE, the transport of the contaminant should also be considered. The findings based on transport should be experimentally validated before further investigations for optimising the spreading in three dimensions. Therefore, the current study aims to assess the efficacy of EIE in enhancing the three-dimensional spreading of a conservative tracer in laterite soil media, in response to a three-dimensional flow field (created by employing partially screened wells), through numerical simulation and experimental validation. To the best of our knowledge, this is the first attempt at experimental investigation of EIE (with partially screened wells) in three dimensions using natural porous media.

Laterite soil sample that passed through a 6 mm IS sieve was taken for the study. The soil was weighed and filled in layers with a fixed height of fall and lightly compacted equally in each layer to ensure uniform packing density. After filling, the soil was saturated by filling water in the outer water chambers and allowing ample time for saturation. The soil samples were tested for various transport and flow parameters prior to the experiment.

The permeability, porosity, grain size analysis, and dispersivity of the laterite soil sample were experimentally estimated. The permeability of the soil sample was determined by using the constant head permeability test (IS 2720 part 17). The soil sample was filled in the permeameter with the same density as that was filled in the experimental glass tank. The average permeability value was observed as 3.5 × 10⁻⁵ m/s. The porosity of the soil sample with the same density as that of the model was determined by using saturation of soil as described in the index properties determination by Matko (2003). The porosity of the soil was observed as 0.36. The particle size distribution of the sample was also determined by using sieve analysis and the particle size distribution chart was utilised during the design of the well screen in Section 2.2.

For the column experiment, the tracer solution was continuously introduced into a column filled with soil samples in the same density as filled in the glass tank. The breakthrough curve for the NaCl tracer was plotted and was fitted with a solution of one-dimensional advection-dispersion Equation (1) by Ogata (1970) to evaluate the dispersivity of soil. The breakthrough curve is shown in Supplementary material Appendix (Figure A1). The dispersivity was determined by following the method mentioned in Chapter 9, Freeze & Cherry (1979) and the value was obtained as 0.115 m. The range of dispersivity varies with different factors such as the length of the soil column, saturation, soil texture and flow velocity (Zhuang et al. 2021). Huang et al. (1996)) observed that the values of the dispersivity for the homogeneous sandy column ranged from 0.001 to 0.3 m, while those for heterogeneous columns were as high as 2 m. The empirically determined value of longitudinal dispersivity lies within the above-mentioned ranges. This value was assigned as the longitudinal dispersivity for the initial numerical simulation. During the calibration of the numerical model, the ratio of horizontal to vertical dispersivity was changed in a trial and error method to fix the final ratio.

To represent injection/extraction wells, perforated carbon fibre tubes of 8 mm inner diameter of 1 m length were placed at the required position. Perforations were designed based on the guidelines provided by Raghunath (2007). The grain size distribution of formation was considered while deciding the size of perforations such that the size of perforations lay between D40 and D70 of aquifer material. Four holes of 2.5 mm diameter were drilled along the circumference of the tube and these holes were provided at a distance of 8 mm c/c along the length. A gravel pack is required if the aquifer material is homogeneous with uniformity coefficient Cu or effective size < 0.25 mm. Gravel packing was not necessary as the experimentally observed values of uniformity coefficient and effective size of particles were 7.75 and 0.29 mm, respectively. However, a small thickness of gravel was packed around the perforated tubes to avoid extraction of very fine soil particles that are likely to clog the valves of syringe pumps. The gravel size was designed such that of gravel pack lay between four to six times of particles of the soil (Raghunath 2007).

For a passive experiment, one set of dual syringe pumps is used. Each syringe is connected to a dual check valve as shown in Figure 2 and they work together in dual mode to continuously inject the tracer at the given pumping rate. The injection tube is buried into the soil such that the tip of the tube is at the required depth (mid-depth). During one cycle, the master pump (M) injects the tracer solution into the injection well and simultaneously the secondary pump (S) withdraws the tracer solution from the reservoir as shown in scheme 1 in Figure 2. Once the master pump finishes injecting the volume assigned, the next cycle starts and the process gets reversed. i.e, the Master pump extracts solution from the reservoir and the secondary pump injects the tracer into an injection well. In either way, it is ensured that continuous tracer injection takes place at the injection well. The rate and volume of fluid for injection/extraction will be preset on the master pump.

Positive values in the graph (Figure 3) represent injection and negative values represent extraction. As per the pumping schedule, the first two steps are injection at the east and west wells. For this, the injection tube of one set of dual syringe pumps is carefully immersed into the west well up to mid-depth and injection according to the rate specified in the graph is performed. Meanwhile, the injection tube of the other set of dual pumps is kept immersed into the east well to start injection immediately after the injection at the west well stops. The same procedure is repeated for extraction using scheme 2. Only one set of dual syringe pumps operates at a time. Hence, the other set of pumps can be set for the upcoming withdrawal or pumping at the given rate according to the pumping schedule. The injection and extraction tubes are interchanged and immersed into the required wells as per the schedule. The extracted water from wells is stored in a surplus reservoir rather than a freshwater reservoir to monitor the concentration and make sure that no tracer solution is getting extracted.

Three sets of experiments were conducted in the experimental setup: one passive experiment and two active experiments. All the experiments were conducted for 195 min and the tracer concentrations were measured at observation points. The conservative tracer used in this study was NaCl. The concentration of NaCl can be measured in terms of EC as it forms an electrolyte solution when dissolved in water. The EC of the solution is directly proportional to the Na+ and Cl^– ions present in the water and thus represents the concentration of NaCl. Soil EC-meter (Groline, HI98331 Soil Test) as shown in Figure 1 was used in this study to measure EC of samples. It measures ionic concentration in soil and water in terms of EC. It contains a stainless steel penetration electrode which measures EC in the range 0.00–4.00 mS/cm. EC-meter was calibrated and a concentration vs. conductivity chart was created.

Six observation wells were selected for measuring tracer concentrations at different times. Samples were taken from two layers for the passive experiment and from three layers for the active experiment. The sampling points for passive and active experiments are shown in Appendix (Supplementary material, Figure A2). Samples were taken from different vertical levels using a thin suction rod and were measured for EC values. The time and EC values were recorded manually for each observation point. The observation values obtained were in mS/cm which was converted into mg/l with the help of calibration charts. Observations taken at different intervals were stored as observed concentration time series well data for calibration and validation.

Constant head boundary conditions with a head value of 0.8 m were provided on the eastern and western boundary of the model while no-flow boundary conditions were given for north and south boundaries. In the current study, head-dependent groundwater flow (initial groundwater flow) was kept at zero by providing equal heads on either side of the model. This helps in understanding the effect of advective transport created by using EIE alone. The initial head was also given as 0.8 m. Initial concentrations of 25 mg/l were assigned in all cells which was observed as the average concentration in observation wells prior to the experiment.

Pumping and extraction were incorporated into the model by using the pumping well boundary condition. Negative values of the pumping rate were used for extraction wells. A 12-step pumping schedule as shown in Figure 3, similar to that used in Asha et al. (2021) was used in this study. The pumping and extraction values were calculated based on non-dimensional numbers reported by Mays & Neupauer (2012) and then scaled down to a suitable value according to the size of the aquifer model and also to maintain a value less than the maximum pumping capacity of the syringe pump (viz. 100 ml/min). The pumping schedule is depicted in Figure 3 to have a better understanding and the positions of these wells are given in Figure 4.

The numerical simulation was conducted by using Visual MODFLOW Flex (version 7.1) which is a groundwater modelling software (Zheng & Wang 1999; Harbaugh et al. 2000). The numerical engines used to solve Equations (3) and (4) were MODFLOW (2005) and MT3DMS, respectively. For three-dimensional investigation, the model has been vertically discretized into 80 layers thereby keeping vertical discretisation equal to horizontal discretisation. The model was simulated in a transient state for 195 min divided into suitable stress periods for passive and active simulations.

An experimental investigation of EIE was conducted in this study by using a laboratory-scale tank model. Three sets of experiments and corresponding numerical simulations were carried out namely case: 1 (Passive simulation), case: 2 (active simulation with fully screened wells) and case 3(active simulation with partially screened wells). Numerical transport modelling was carried out in Visual MODFLOW flex by using the engine Modflow-2005 and MT3DMS. The experimental observations, calibration charts and numerical model results are explained in this section.

This study includes three sets of experiments – one passive set of experiments (case 1) and two active sets (case 2 and case 3) of experiments. The position of observation wells for all cases is shown in (Supplementary material, Figure A3).

It can also be seen that the final concentration at the end of the experiment in all wells lies at a lower level in case 3 than that in case 2. This concentration reduction indicates that EIE is more effective when flow fields are forced in vertical dimension by means of partially screened wells. It is to be noted that the difference in concentration reported in this section is just a representative value. The actual difference that is expected in the field is a multitude of this value, owing to the scale of the experiment. Hence, even a small difference or improvement observed in this experimental study is indicative of the large difference that could occur in the field.

It is essential to calibrate any numerical model either by experimental data or field data. The present study uses an experimental-scale model for this purpose. Almost all the parameters that are required for a numerical model were either measured or selected from the literature. The longitudinal dispersivity was kept at 0.115 m as obtained from the column experiment. The dispersivity ratios were calibrated by trial and error considering the observed concentration obtained during the experiment. During passive simulation, observations were taken from two layers closer to the injection layer. Spreading is much lower in the passive case, especially in the vertical direction and hence the ratio of horizontal to longitudinal dispersivity was calibrated by using this experiment. The vertical-to-longitudinal dispersivity ratio was calibrated using the observations taken at three layers in the active set of experiments. Final adjustments in ratios were carried out through trial and error such that a maximum correlation between numerical and experimental results was obtained. Horizontal to longitudinal dispersivity and vertical to longitudinal dispersivity ratio were calibrated as 0.2 and 0.09, respectively. The numerical results matched with experimental observations (omitting the outliers). Hence the model was calibrated and the calibrated value of dispersivity was used for the third set of simulations which showed a reasonable match with observed values. Thus the model was validated. The calibration charts are shown in Supplementary material, Figure A4–A6 and details of error analysis are tabulated in Table 2.

The correlation coefficient of greater than 0.98 and normalised RMS error of less than 10% were obtained for all three cases (Table 2). From the correlation coefficients, standard error estimate, RMS and normalised RMS, it is evident that the simulated results and experimental results match with reasonable accuracy. An exact match between simulated and observed results was not obtained owing to the fact that the numerical model is based on the assumption of homogeneity of porous media which is not the case with the experiment. Even though the soil has been filled carefully to ensure a uniform distribution of properties, 100% homogeneity cannot be expected.

The three-dimensional view of concentration contours at the end of the simulation indicates that spreading and dilution increase when EIE is introduced. The initial concentration injected was 1,500 mg/l of conservative tracer. It was observed that the maximum concentration decreased to approximately 419.29 mg/l in case 1 while that in case 2 to 211.73 mg/l and in case 3, to 163.58 mg/l. In case 1, the advective transport occurs during the tracer injection period (initial 15 min) and continues until the head created due to injection reduces to the initial head. The dilution occurs as a result of dispersion, anisotropy and advection caused by the injection head. The dilution because of dispersion and anisotropy continues even after the advection stops (as in case 1). In case 2, the spreading occurs mainly due to advective transport created by active EIE protocol along with dispersion and anisotropy. The advective transport causes more spreading and dilution of the plume compared to case 1. In case 3, advective transport in the vertical direction also takes place in addition to the spreading happening in case 2. The advective transport in the vertical direction further increases the spreading across layers and dilutes the plume. Hence, maximum dilution and more spread are observed in the case 3 where three-dimensional flow was induced by using partially screened wells.

At initial stress periods, the concentration contours show the pattern of a concentric circle in the horizontal view with maximum concentration at the injection point and an oval shape in the vertical view for all the cases. Major distinctions in plume dynamics cannot be made at this stage. At 75 min, there is no peculiar deviation from the circular dispersion of contour in case 1. This is because of the passive spreading nature, where the spreading takes place by virtue of dispersion and advection in response to the head created by injection; while in case 2 and case case 3 the shape of the contour shows a diamond shape in layer view (Figure 7(a) and 7(b)). More dilution is observed in case 3 than in case 2. In case 3, the elongation of contours also takes place diagonally owing to vertical flow in response to partially screened wells. Plume distortion is found in case 3 which is more evident in row view at 75 min (Figure 7(a)). This is due to the flow field created by diagonally opposite partially screened wells of an east-west pair of wells (at 75 min) and is evidence of enhanced plume extension in the vertical plane. Hence more dilution is observed in case 3. Similarly, the partially screened north–south wells tend to create plume distortion which can be seen in column view at 195 min (Figure 7(b)). These plume distortions in the vertical direction are the reason behind more dilution in case 3.

The practical difficulty in conducting experimental studies in EIE is high. In this context, a three-dimensional experimental simulation of tracer spreading in response to EIE is a step towards further improvement in this technology. This paper illustrates the effect of EIE on the transport of a conservative tracer in real porous media by using a three-dimensional experimental setup. The purpose of the experiment was to validate and improve numerical simulations of EIE available in the literature, particularly the effect of partially screened wells as reported by Asha et al. (2021). Screen depth variation and its effectiveness have been carefully formulated in this study and a comprehensive conclusion has been derived.

• Enhancement in the transport of tracer solution is observed when EIE is made in three dimensions by replacing the screen depth appropriately forcing the flow in three dimensions. This was proved both experimentally and numerically by properly validating the model with experimental data. With active screen depth emplaced at different vertical levels, the contours elongated diagonally causing plume stretching and dilution.

• The time series observation from the experiment indicates that case 3 (EIE with partially screened wells) shows consistently lower concentration when compared to case 2 (EIE with fully screened wells). This shows that partially screened wells work better than fully screened wells in diluting the plume keeping all other conditions the same. Here dilution can be attributed to the higher rate of dispersion of the plume, which indirectly shows that partially screened wells enhance the plume area available for reaction. Concentrations at observation wells show higher dilution in case 3 thus reinforcing the finding that partially screened wells give higher dilution within real porous media. During an in situ porous media treatment, the scenario mentioned above will increase the rate of reaction. Hence, just an emplacement can lead to better solute transport without any increase in the cost of treatment.

• The spread quantified in terms of solute mass attenuation also shows maximum spreading for case 3, which matches with the experimental results.

• The model validated in this study can be easily reproduced for further numerical simulations including flow-through models, continuous injection models or any complex models related to active spreading. The model can also be adapted for optimisation of different elements of EIE to maximise spreading in three dimensions which will render guidance to field application of EIE.

• The experimental setup can be further used for analysing the effect of EIE in under flow-through conditions and different patterns of pumping. It can also be reused for different types of soil and layered soil study.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.