# Numerical Study on the Effects of Regional Groundwater Flow on the Contaminant Migration through an Inactive Supply Well as a Preferential Flow Pathway

Authors: Xu Li; Shilin Su; Qiang Guo; Haitao Zhang; Qi Zhu; Hamza Jakada
Journal: Geofluids
 (2022)

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## Abstract

Preferential flow pathways connect upstream and downstream channels in abandoned mines or seasonally pumping areas. The inactive supply well facilitates contaminant migration between aquifers leading to water quality challenges; it is important to note that the impacts of regional groundwater flow on contaminant migration through pumping wells have not been well elucidated in literature. In the study, we developed a numerical model describing contaminant migration through an inactive supply well that is pumped seasonally influenced by the regional groundwater flow field. The model was developed using the finite-element COMSOL Multiphysics software to estimate the potential threats to water quality. Major findings showed that a larger regional groundwater velocity results in lower concentration of contaminant. In addition, during pumping, a smaller recovery ratio inside the wellbore facilitates the deterioration of water quality in the deep aquifer. Furthermore increasing pumping frequency can effectively prevent contamination and improve the water quality in the deep aquifer. Similarly, higher pumping rate leads to a larger capture zone, which can significantly improve the water quality in the deep aquifer. The general conclusion is that the regional groundwater flow has a negative impact on the quality of groundwater extracted by seasonally pumping well.


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## Body

## 1. Introduction

It is well established that preferential flow paths facilitate contaminants migration due to limited resistance. The inactive (or nonpumping) supply well with a long screen usually provides a preferential flow pathway [1–3], through which the upward or downward flow is usually considered as natural recharge or discharge in sedimentary aquifers. In addition, contaminant migration through inactive supply wells (denoted as ISW hereafter) can deteriorate groundwater quality unexpectedly, introducing environmentally hazardous constituents from neighboring aquifers. Mayo [4] found that extracted groundwater must not be used until acceptable water quality is established after a nonpumping phase has been observed from two long-screened well in alluvial aquifers (due to susceptibility to contaminant migration).ISWs include abandoned well and seasonally pumping wells (hereafter denoted as SPW, such as irrigation wells and municipal supply wells). During the cessation of pumping (or inactive phase) spanning months and years, a large amount of groundwater and contaminants can migrate into neighboring aquifers through the preferential pathways in the groundwater systems [5]. For example, many irrigation wells, which are pumped seasonally, are usually inactive during winter season. Hence, contaminants can leak downward in agriculture and farmland, especially for the nonpoint source nature of nitrate species [6, 7]. In addition, many municipal supply wells are inactive during low-demand period to save water. Therefore, the switchover between nonpumping and pumping conditions is common, causing the seasonal deterioration of water quality in the aquifers.It is important to note that, a regionally scattered distribution of ISWs results in the deterioration of water quality in groundwater systems [8]. During this process, a poorly designed and maintained well may provide potential preferential pathways for contaminant migration. Potentially preferential pathways of ISW can be summarily characterized as follows: (1) it is quite common that the wells become vertically preferential conduits because of long screens with short separation between slots; (2) if the gravel pack around wellbore extends the thickness of the screen, the wells will become conduits for flow and contaminant migration; (3) sealing failure and casing resulted from corrosion can make the wells act as vertically preferential conduits.Consequently, understanding the mechanism of flow and contaminant migration through ISWs is critical to the evaluation of the potential threats to groundwater environment [9–12]. Based on general groundwater flow, the vertical head gradients between neighboring aquifers can push the water flow through the wellbore during the well’s inactive phase. For example, in alluvial aquifers, the anisotropy of hydraulic conductivity (Kvertical/Khorizontal) is normally about 10−3~10−4, limiting vertical flow in a multiple-aquifer system [8]. However, effective pipe conductivities of well casings, screens, and gravel packs range from 104 to 106 cm/s [8, 10]. Therefore, even a little vertical head difference will lead to an increase in cross-aquifer flow inside the borehole. Based on the field data collected, Mayo [4] reported that vertical head difference of 0.1 m in the Closed Basin in south-central Colorado led to great volumes of water being transferred between aquifers through wells.Similar to the groundwater flow through vertical preferential flow pathway, contaminants can migrate through an ISW and result in groundwater deterioration in shallow aquifers with upward migration or deep aquifers with downward migration. For example, contaminants, such as nitrate, pesticides, and other agricultural chemicals, can migrate into the deep groundwater system from the shallow groundwater [13–16]. It takes only a short time for these contaminants to penetrate sediments facilitated by ISWs, resulting in significant contamination of deep aquifers [11, 17]. On the other hand, if the hydraulic head in deep aquifer is higher than in shallow aquifer, environmentally hazardous substances like arsenic, chloride, or hexavalent chromium in deep aquifers can be carried upwards into shallow aquifers [18, 19].To interpret the contaminant migration behavior explicitly, extensive theoretical models of flow and solute transport have been developed under various conditions. For example, Lacombe et al. [10] developed a numerical model to simulate the contaminant migration through a leaky borehole, indicating that contaminants can rapidly move deeply into the aquifer and creating widespread contamination. Konikow and Hornberger [20] simulated intraborehole solute transport for nonpumping vertical wells penetrating multiple layers. Their study used MODFLOW’s Multi-Node Well package, which was also employed to explore the effects of intraborehole flow on groundwater age [21]. In addition, in flow and transport models accounting for SPW with two long screens in alluvial aquifers, Yager and Heywood [22] quantified the effects of seasonally variable pumping rates on intraborehole flow and solute transport, indicating poor quality water in winter due to low pumping rates in public-supply wells.Due to seasonal pumping, the contaminants, which have migrated into other aquifers, may be extracted out many times by the SPWs. However, the rate of contamination of the aquifer can only be diminished and not totally eliminated. An important point in this regard is that regional groundwater flow drives contaminants away from the supply well during the inactive pumping phase. Although the regional groundwater flow velocity is relatively low (about order of 10−6 m/s) [23, 24], a long inactive phase facilitates the contaminants to move far away from the SPW downstream [25]. Hence, a portion of the contaminants may not be extracted from the aquifer despite a long pumping phase. This is because there is a dividing streamline during the pumping phase, which divides the flow into the capture zone and noncapture zone [26]. Li et al. [26] found that the contaminants which cannot migrate beyond the capture zone during the inactive phase can be extracted from the aquifer again. Therefore, understanding influencing mechanism of the capture zone on the contaminant migration contributes to the operation strategies of SPW to reduce its negative influences on aquifers. For example, a reasonable design of pumping frequency or pumping rate can provide a good strategy to protect groundwater environment. Overall, the presence of regional groundwater flow increases the challenge or difficulty of protecting groundwater quality.Therefore, in many cases, the risks are not fully understood due to limiting factors including information regarding well operations and local hydrogeology, especially for regional groundwater flow. Following a critical look at recent literature, the impacts of regional groundwater flow on contaminant migration through ISW, especially for SPW, have rarely been studied. Therefore, this study investigated the effects of regional groundwater flow on cross-aquifer deterioration of water quality considering a SPW. The finite-element COMSOL Multiphysics package is used to numerically simulate the contaminant migration through a SPW with steady-state, two-dimensional (2D) horizontal flow. Flow is assumed to be Darcian, and solute transport is characterized by the advection-dispersion equation in the model. This theoretical research can also be applied in there-dimensional (3D) groundwater flow model. Meanwhile specific attention is given to the effects of the regional groundwater velocity on contaminant migration [27–29]. For example, the model is developed in a sandy aquifer with regional groundwater flow. Secondly, the influence of regional groundwater velocity on the deterioration of water quality is quantitatively assessed. Thirdly, two approaches to reducing the effects of contamination are proposed. One is more frequent pumping, and the other is higher pumping rate.


## 2. Mathematical Model of the ISW with Presence of Regional Groundwater Flow

A case of vertical flow and contaminant migration through a SPW is investigated. As shown in Figure1(a), water and contaminant from upper aquifer can move into deeper aquifer through a vertical SPW during the inactive pumping phase and then spread out with the assistance of regional groundwater flow. Figure 1(b) shows the deterioration of water quality in deep aquifer during the pumping phase after contaminant migration through a SPW. To illustrate the effects of regional groundwater flow on the problem, the contaminant is assumed to be conservative. Also, the confined aquifer is assumed to be unbounded laterally, homogeneous, and horizontally isotropic. A fully penetrating well is used in the groundwater systems. The flow rate and concentration of the contaminant migrating through a SPW are assumed to be constant during the inactive pumping phase. Similarly, the pumping rate of the well in the pumping phase is assumed to be constant. During the inactive and pumping phases, the groundwater flow field results from the superposition of the flow fields generated by both the pumping well and the regional flow. A 2D schematic diagram of the model is depicted in Figure 2, where the origin of the coordinate system is located at the center of the test well bottom, and the x-axis points to the direction of regional groundwater flow.Figure 1
The schematic of well that acts as a preferential flow pathway: (a) vertical flow and contaminant migration through a well with regional groundwater flow in inactive phase; (b) deterioration of water quality in pumping phase with regional groundwater flow.
(a)(b)Figure 2
The schematic diagram of the flow system.S1, S2, S3, and S4 are the boundaries of the model, and S1 and S2 are constant-head boundaries; both S3 and S4 are no-flux boundaries.


### 2.1. Mathematical Model of Groundwater Flow

The groundwater flow during the inactive and pumping phases around a SPW is assumed to be steady-state. Also, the groundwater flow velocity of the aquifer can be expressed as the superposition of the flow components generated by both the supply well and the regional flow as follows:(1)v⟶=v⟶r+v⟶x,(2)v⟶r=Q2πθBre⟶r,(3)v⟶x=−KJθe⟶x=vdθe⟶x,(4)r=x2+y2,where the arrow over a symbol represents a vector. For example, v⟶r is the average radial pore velocity vector generated by the well (inactive or pumping phase) with a magnitude of vr [L/T]; e⟶r is a unit vector along the radial direction; v⟶x is the pore velocity vector of regional groundwater with a magnitude of vx [L/T], which has a Darcy form denoted as vd; e⟶x is a unit vector along the x-axis; v⟶ is the superposed groundwater flow velocity around the supply well [L/T]; B is the aquifer thickness [L]; Q is the flow rate (inactive or pumping phase) [L3/T], which is positive for the inactive phase and negative for pumping phase; K is the hydraulic conductivity in the aquifer [L/T]; J is the hydraulic gradient of regional flow in the aquifer [L/L]; θ is the effective porosity in the aquifer [dimensionless]; r is the radial distance [L] from the well; x and y indicate two directions parallel and perpendicular to the regional groundwater flow direction, respectively [L].


### 2.2. Mathematical Model of Solute Transport

The solute transport has been characterized by the advection-dispersion equation (ADE). The ADE of conservative solute in the aquifer without source/sink can be written as(5)∂C∂t=∇∙D∇C−∇∙v⟶C,0<r≤∞,t>0,where C is solute concentrations in the aquifer [M/L3]; t is the transport time [T]; D is the hydrodynamic dispersion [L2/T]; and ∇∙ and ∇ are the divergence operator and the gradient operator, respectively; the hydrodynamic dispersion is a velocity-dependent tensor depicted as
(6)Dxx=αLvx2v⟶+αTvy2v⟶+D0,(7)Dyy=αLvy2v⟶+αTvx2v⟶+D0,(8)Dxy=Dyx=αL−αTvxvyv⟶,(9)v=vx2+vy2,where Dxx, Dxy, and Dyy are the components of the hydrodynamic dispersion coefficient tensor [L2/T]; D0 is the molecular diffusion coefficient [L2/T]; αL is the longitudinal dispersivity [L], while αT is the transverse dispersivity [L]; the transverse dispersion effect is much smaller and αL=10αT is usually assumed [30]; vx and vy are pore velocities in the x and y direction, respectively.


## 2.1. Mathematical Model of Groundwater Flow

The groundwater flow during the inactive and pumping phases around a SPW is assumed to be steady-state. Also, the groundwater flow velocity of the aquifer can be expressed as the superposition of the flow components generated by both the supply well and the regional flow as follows:(1)v⟶=v⟶r+v⟶x,(2)v⟶r=Q2πθBre⟶r,(3)v⟶x=−KJθe⟶x=vdθe⟶x,(4)r=x2+y2,where the arrow over a symbol represents a vector. For example, v⟶r is the average radial pore velocity vector generated by the well (inactive or pumping phase) with a magnitude of vr [L/T]; e⟶r is a unit vector along the radial direction; v⟶x is the pore velocity vector of regional groundwater with a magnitude of vx [L/T], which has a Darcy form denoted as vd; e⟶x is a unit vector along the x-axis; v⟶ is the superposed groundwater flow velocity around the supply well [L/T]; B is the aquifer thickness [L]; Q is the flow rate (inactive or pumping phase) [L3/T], which is positive for the inactive phase and negative for pumping phase; K is the hydraulic conductivity in the aquifer [L/T]; J is the hydraulic gradient of regional flow in the aquifer [L/L]; θ is the effective porosity in the aquifer [dimensionless]; r is the radial distance [L] from the well; x and y indicate two directions parallel and perpendicular to the regional groundwater flow direction, respectively [L].


## 2.2. Mathematical Model of Solute Transport

The solute transport has been characterized by the advection-dispersion equation (ADE). The ADE of conservative solute in the aquifer without source/sink can be written as(5)∂C∂t=∇∙D∇C−∇∙v⟶C,0<r≤∞,t>0,where C is solute concentrations in the aquifer [M/L3]; t is the transport time [T]; D is the hydrodynamic dispersion [L2/T]; and ∇∙ and ∇ are the divergence operator and the gradient operator, respectively; the hydrodynamic dispersion is a velocity-dependent tensor depicted as
(6)Dxx=αLvx2v⟶+αTvy2v⟶+D0,(7)Dyy=αLvy2v⟶+αTvx2v⟶+D0,(8)Dxy=Dyx=αL−αTvxvyv⟶,(9)v=vx2+vy2,where Dxx, Dxy, and Dyy are the components of the hydrodynamic dispersion coefficient tensor [L2/T]; D0 is the molecular diffusion coefficient [L2/T]; αL is the longitudinal dispersivity [L], while αT is the transverse dispersivity [L]; the transverse dispersion effect is much smaller and αL=10αT is usually assumed [30]; vx and vy are pore velocities in the x and y direction, respectively.


## 3. Numerical Solution of the Model

In this study, a steady-state flow model of 2D horizontal plane was developed based on COMSOL Multiphysics as shown in Figure2. The model region was set according to the dimension 600m×600m, and the well having a radius of 0.1 m. In addition, B=5 m, K=8.0 m/d, and θ=0.3 in Table 1. According to Figure 2, the boundary conditions for the domain of concern can be expressed as
(10)Hx,ys1=H1,Hx,ys2=H2,(11)K∂H∂ns3=0,K∂H∂ns4=0,where S1, S2, S3, and S4 are the boundaries of the model; S1 and S2 are constant-head boundaries with prescribed total heads of H1and H2, respectively; both S3 and S4 are no-flux boundaries; n is the normal vector of the boundary (an outward pointing vector perpendicular to the boundary). Therefore, a constant regional flow field can be generated and one can obtain different values of vx by changing the head differences between H1 and H2. In this model, constant-head boundaries were prescribed, and the value of H2 was set to be 15 m; according to Equation (3), one can obtain different values of vx by changing the value of H1. In the model, a continuous mass flux of flow rate for inactive or pumping phase was assigned at r=rw, which can be expressed as
(12)N0=Qρ2πrwB,where N0 is the mass flux per unit thickness [M/L2/T] and ρ is the density of groundwater [M/L3].Table 1
The parameter values used in this numerical model.
Parameter nameSymbolsValuesAquifer thickness (m)B5Radius of well screen (m)rw0.1Density of groundwater(kg/m3)ρ1000Effective porosity of aquiferθ0.3Hydraulic conductivity of aquifer (m/d)K8Constant heads ofS1 (m)H115.22, 15.44, 15.65Constant head ofS2 (m)H215.0Regional groundwater Darcy velocities (m/s)vd5×10−7, 1×10−6, 1.5×10−6Longitudinal dispersivity of aquifer (m)αL0.1Rate (inactive or pumping phase) (m3/s)Q5.79×10−4Mass flux per unit area (kg/(m2·s))N00.1843Inactive period (day)tinact90,180Pumping period (day)tpump90,180For the solute transport model, the initial condition in the aquifer is(13)Cr,0=0,r≥rw.During the inactive phase, the boundary condition atr=rw can be described as
(14)C1r,t=C0,r=rw,tpumpi−1<t<tinacti,i=1,2⋯N,where C0 represents the concentration of the inactive phase [M/L3]; tpumpi−1 is the time of the i-1th pumping phase [T], and when i=1, tpump0= 0; tinacti is the time of the ith inactive phase [T]; t1 is the total duration of inactive phases [T], which can be expressed as
(15)t1=∑i=0ntinacti,i=1,2⋯N.During the pumping phase, the time-dependent concentration is calculated in the borehole, and the concentration of contaminant in the wellbore can be expressed as(16)C=Cr,t,r=rw,tinacti<t<tpumpi,i=1,2⋯N,where tpumpi is the time of the ith pumping phase [T]; t2 is the total duration of pumping phases [T], which can be expressed as
(17)t2=∑i=0ntpumpi,i=1,2⋯N.Furthermore, for simplicity, inactive and pumping periods are assumed to be same (tinact=tpump) in this study. Hence, the total durations of inactive and pumping are the same (t2=t1). A period is defined as P=tinact+tpump [1/T], where one year is assumed to be 360 days for convenience of numerical simulation, Hence, pumping frequency is fpump=360/P [1/T].Because the values of velocity and concentration are different around the perimeter of the borehole during pumping phase, it is necessary to use the weighted average method, which integrates the concentration around the borehole with the velocity as a reference index to the weighted average. Thus, a flux-averaged concentration at the well can be expressed as(18)C¯pump=∮lwvwCw∮lwvw,r=rw,tinacti<t2<tpumpi,i=1,2⋯N,where vw represents the velocity around the borehole during the pumping phase [L/T]; Cw represents the concentration around the well perimeter [M/L3]; C¯pump is the concentration inside the well [M/L3]; and lw is the perimeter of the wellbore [L]. It is notable that the simulation results at the end of each phase (inactive and pumping phases), including the hydraulic head and the contaminant concentration, were set to be the initial values for the simulation in the next phase.To quantitatively evaluate the influences of the regional groundwater velocity on the deterioration of water quality, we have computed the ratio of contaminant mass recovery at the end of each pumping phase, which is denoted asμ and can be written as
(19)μ=mpumpminact=∫0t2QpumpC¯pumpdtQinactt1C0,where minact is the mass of contaminant migrated into the deep aquifer during the inactive phase [M] and mpump is the mass of contaminant recovered from the deep aquifer during the pumping phase [M].The model domain was discretized into 24248 elements, and the mesh size was progressively refined near the well. Therefore, the selected mesh is regarded as sufficiently fine for the problem investigated here. To further check the accuracy of the numerical model, the numerical solution for a special case (without regional groundwater velocity) in a period was used to compare with the analytical solution of Huang et al. [31], which investigated a steady-state flow single-well push-pull (SWPP) test model with injection and pumping phases. The inactive and pumping phases for a SPW without regional groundwater flow in our proposed mathematical models are equivalent to the injection and pumping phases of Huang’s SWPP tests, respectively. Therefore, the analytical solution of Huang et al. [31] can be used as a benchmark solution to check the accuracy of this numerical model in Figure 3. The simulated time span of inactive (or injection) and pumping were 0.5 and 1 day, respectively. The other parameters were set as Qinact=5.79×10−4 m3/s, Qpump=−5.79×10−4 m3/s, B=10 m, αL=0.1 m, 0.5 m, 1 m, and θ=0.3. C0 at r=rw was set to be 1.0 mol/m3. The results showed that our numerical solution agreed perfectly with the analytical solution, which indicates that our numerical solution is reliable.Figure 3
Comparison between the numerical solutions of this study and the analytical solutions of Huang et al. [31].


## 4. Results and Discussions

### 4.1. The Effects of Regional Groundwater Velocity on Water Quality Produced by a SPW

To analyze the effects of regional groundwater velocity on the contaminant migration through a SPW, a parametric study over a wide range of regional groundwater velocities was conducted. During the 720-day simulation period, both inactive and pumping periods appear alternately with each lasting for 90 days (tinact=tpump=90 days) within every single period. Figure 4 shows the breakthrough curves (BTCs) inside the well for the contaminant during the entire pumping phases with varying regional groundwater velocities. The parameters are as follows: vd=0 m/s, 5×10−7 m/s, 1×10−6 m/s, and 1.5×10−6 m/s, Qinact=5.79×10−4 m3/s m3/s, and Qpump=−5.79×10−4 m3/s with the other parameters listed in Table 1. The results indicate that the regional groundwater velocity has great impacts on BTCs for each pumping phase. This implies that a greater regional groundwater velocity results in a lower contaminant concentration, similarly, a greater regional groundwater velocity results in less pumped contaminant. Therefore, contaminant migration through a SPW with the presence of a larger regional groundwater velocity may lead to more serious water deterioration. Additionally, it is notable that the value of contaminant concentration increases gradually at the end of each pumping phase when vd=0 m/s, which indicates a gradual contaminant enrichment at every switch point between inactive and pumping conditions. This finding also proves that water deterioration can only be diminished but cannot be totally eliminated [5].Figure 4
BTCs for different values ofvd inside the well in the pumping phase.To quantitatively evaluate the influences of the regional groundwater velocity on the deterioration of water quality, the recovery ratio of contaminant was computed at the end of each pumping phase with different regional groundwater velocities. Table2 represent the recovery ratio based on Equation (19) with different given values of regional velocities when tpump=90 and 180 days, respectively. It is apparent that a higher flow velocity leads to a smaller recovery ratio in the cases of tpump=90 and 180 days, which means a higher flow velocity results in a more serious water deterioration in the deep aquifer. For example, the recovery ratio decreases from 0.85 to 0.21when vd increases from 0 to 1.5×10−6 m/s in the case of tpump=90 days.Table 2
The recovery ratioμ of contaminant at the end of pumping phase.
vd0 m/s5×10−7 m/s1×10−6 m/s1.5×10−6 m/sμ (tpump=90d)0.850.600.360.21μ (tpump=180d)0.850.520.230.11Figure5 shows the superposed flow field generated by the pumping well and the regional flow. The results indicate that there exists a stagnation point (Sp) and a dividing streamline (Ds). At the Sp, all velocity components are zero, and several Ds may cross each other. Note that Ds divides the flow region into capture zone and noncapture zone. If the travelling contaminant cannot escape from the capture zone in the inactive phase, it may be extracted out from the aquifer during the pumping phase. To further elucidate this behavior, the concentration distributions of the contaminant in the 2D horizontal plane at t2=270 day with varying regional groundwater velocities are shown in Figure 6. The results indicate that higher regional groundwater velocity makes the contaminant mass move further away from the well. Besides, a higher regional groundwater velocity leads to a smaller distance from Sp to well, resulting in a smaller proportion of contaminant that can be extracted out during the pumping phase. Note that for the case where vd=0 m/s in Figure 6(a), nearly all the contaminant is distributed near well. Hence, almost all contaminant in principle can be extracted out from the well over time through pumping. Overall, a higher regional groundwater velocity causes a larger proportion of contaminant that drift beyond the Ds in the inactive phase, resulting in relatively lower contaminant concentration inside the wellbore and a lower recovery ratio during the pumping phase as shown in Figure 4 and Table 2, respectively.Figure 5
The schematic diagram of the flow system in the pumping phase.Figure 6
Concentration distributions in a 2D horizontal plane att2 = 270 day. (a) vd=0 m/s; (b) vd=5×10−7 m/s; (c) vd=1×10−6 m/s; (d) vd=1.5×10−6 m/s.
(a)(b)(c)(d)


### 4.2. The Effects of Pumping Frequency on Water Quality

For the purpose of alleviating the deterioration of groundwater quality, the optimization strategies for the management of wells should include better execution of regulations and more stringent design criteria. Moreover, changes in operational parameters can also provide positive influence, such as the implementation of intermittent pumping or increasing pumping frequency during the periods of low demand, which assists the inhibition of contaminant migration. Figure7 shows the BTCs inside the well for two kinds of pumping frequency, i.e., 180 days of pumping with another 180 days of rest (fpump=2/year) and 90 days of pumping with 90 days of rest (fpump=4/year) over a period of 720 days, respectively. The parameters were as follows: vd=1×10−6 m/s, Qinact=5.79×10−4 m3/s, and Qpump=−5.79×10−4 m3/s, and the other parameters are the same as those used in Table 1. Figure 7 represents that the concentration at the wellbore in the case of fpump=2/year is higher than that in the case of fpump=4/year. The results indicate that more frequent pumping yields more contaminant extracted when the total pumping time is fixed. Moreover, the recovery ratios at the end of pumping phases with two different pumping frequencies are shown in Table 2. For example, μ are 0.36 and 0.23 with fpump=2/year and 4/year, respectively, which indicates that a more frequent pumping leads to a greater recovery ratio with regional groundwater velocities. Therefore, an increasing pumping frequency can effectively improve water quality in a groundwater system involving such a SPW.Figure 7
BTCs inside the well with different pumping frequencies during the pumping phase.To further interpret this behavior, the concentration distributions in a 2D horizontal plane wheret2=360 days with fpump=2/year and 4/year are shown in Figure 8. The results indicate that large number of contaminants accumulate in the aquifer, and the contaminant distribution spreads along the downstream in the case where fpump=4/year days is larger than in the case where fpump=2/year. This supports the position that frequent pumping can effectively diminish contamination and improve water quality in deep aquifer.Figure 8
Concentration distributions in a 2D horizontal plane att2=360 day. (a) tpump=180 days, and (b) tpump=90days.
(a)(b)Furthermore, we evaluate the recovery ratios with more frequent pumping but without regional groundwater velocity, i.e.,vd=0 m/s. Figure 9 shows the BTCs induced by intermittent pumping with varying frequencies where fpump=2/year and 4/year in the case of vd=0 m/s; the other parameters are the same as those used in Table 1. It is worthy to note that the value of contaminant concentration increases gradually for different pumping frequencies at the end of each pumping phase. In addition, it can be observed that the value of contaminant concentration where fpump=4/year at the end of each pumping phase is larger than when fpump=2/year, suggesting that a more frequent pumping accelerates the contaminant accumulation in the vicinity of wellbore. To further estimate the proportion of contaminant migrating into the deep aquifer when vd=0 m/s, and equal recovery ratios of contaminant where fpump=2/year and 4/year are shown in Table 2. The results show that more frequent pumping cannot effectively improve water quality in a groundwater system. However, the recovery ratios are the highest when vd=0 m/s, indicating that frequent pumping has better performance with lower regional groundwater velocity in terms of water quality control. Therefore, the regional groundwater velocity is critical to pollution prevention with the SPW as a cross-aquifer conduit.Figure 9
BTCs inside the well with different pumping frequencies without regional groundwater velocity in the pumping phase.


### 4.3. The Effects of Pumping Rate on Improving Water Quality in Deep Aquifer

Figure10 shows the intermittent pumping induced BTCs of contaminant with different pumping rates. The pumping period tpump is set for 90 days. Besides these values where vd=1×10−6 m/s, Qinact=5.79×10−4 m3/s, Qpump=−2.31×10−4, −3.47×10−4, −4.63×10−4, and −5.79×10−4 m3/s, the other parameters are the same as those used in Table 1. The results indicate that a higher pumping rate leads to a higher contaminant concentration at later times in Figure 10. It is notable that a higher pumping rate results in a wider capture zone, resulting in greater contaminant extraction contaminant during the pumping phase. Consequently, the results in higher contaminant concentration of BTCs at later times. Hence, the recovery ratios of contaminant were computed for varying pumping rates for all pumping periods as shown in Table 3. The results indicate that a higher pumping rate results in a higher recovery ratio. Therefore, increasing the pumping rate has a positive effect for improving the water quality in the deep aquifer.Figure 10
BTCs inside the well with different pumping rates during the pumping phase. (a)Qpump=−2.31×10−4 m3/s; (b) Qpump=−3.47×10−4 m3/s; (c) Qpump=−4.62×10−4 m3/s; (d) vd=Qpump=−5.79×10−4 m3/s.Table 3
The recovery ratioμ of contaminant for different pumping rates.
Qpump2.31×10−4 m3/s3.47×10−4 m3/s4.62×10−4 m3/s5.79×10−4 m3/sμ0.150.220.300.36Besides, the contaminant concentration distributions in a 2D horizontal plane att2=270 day with different pumping rates are also shown in Figure 11. One can see that a higher pumping rate leads to a larger capture zone, i.e., the area enclosed by the dividing line expands with higher pumping rates, resulting in more extracted contaminants as shown in Figure 10. Furthermore, the results indicate that higher pumping rates lead to smaller contaminant plume at the switch point between inactive and pumping conditions. Therefore, we can increase the pumping rate for contaminant control; however, local water demand is seasonally variable, and more optimized water supply strategies are needed when employing an increasing pumping rate. For example, an effective method is to change the pump location inside the well, since Gailey [5] noted that about 29% of the extracted volume came from the deep aquifer in multilayer aquifers if pump location is shallow inside the well. However, the volume pumped was raised by about 48% in the case of a deeper pump location as our numerical simulation has also suggested. As such, a deeper pump in the wellbore leads to higher pumping volume, which yields a larger capture zone with regional groundwater flow as well as a higher recovery ratio of contaminant, thereby improving the water quality.Figure 11
The contaminant concentration distributions in a 2D horizontal plane att2=270 day with different pumping rates. (a) Qpump=−2.31×10−4 m3/s; (b) Qpump=−3.47×10−4 m3/s; (c) Qpump=−4.62×10−4 m3/s; (d) Qpump=−5.79×10−4 m3/s.
(a)
Qpump=−2.31×10−4 m3/s(b)
Qpump=−3.47×10−4 m3/s(c)
Qpump=−4.62×10−4 m3/s(d)
Qpump=−5.79×10−4 m3/s


## 4.1. The Effects of Regional Groundwater Velocity on Water Quality Produced by a SPW

To analyze the effects of regional groundwater velocity on the contaminant migration through a SPW, a parametric study over a wide range of regional groundwater velocities was conducted. During the 720-day simulation period, both inactive and pumping periods appear alternately with each lasting for 90 days (tinact=tpump=90 days) within every single period. Figure 4 shows the breakthrough curves (BTCs) inside the well for the contaminant during the entire pumping phases with varying regional groundwater velocities. The parameters are as follows: vd=0 m/s, 5×10−7 m/s, 1×10−6 m/s, and 1.5×10−6 m/s, Qinact=5.79×10−4 m3/s m3/s, and Qpump=−5.79×10−4 m3/s with the other parameters listed in Table 1. The results indicate that the regional groundwater velocity has great impacts on BTCs for each pumping phase. This implies that a greater regional groundwater velocity results in a lower contaminant concentration, similarly, a greater regional groundwater velocity results in less pumped contaminant. Therefore, contaminant migration through a SPW with the presence of a larger regional groundwater velocity may lead to more serious water deterioration. Additionally, it is notable that the value of contaminant concentration increases gradually at the end of each pumping phase when vd=0 m/s, which indicates a gradual contaminant enrichment at every switch point between inactive and pumping conditions. This finding also proves that water deterioration can only be diminished but cannot be totally eliminated [5].Figure 4
BTCs for different values ofvd inside the well in the pumping phase.To quantitatively evaluate the influences of the regional groundwater velocity on the deterioration of water quality, the recovery ratio of contaminant was computed at the end of each pumping phase with different regional groundwater velocities. Table2 represent the recovery ratio based on Equation (19) with different given values of regional velocities when tpump=90 and 180 days, respectively. It is apparent that a higher flow velocity leads to a smaller recovery ratio in the cases of tpump=90 and 180 days, which means a higher flow velocity results in a more serious water deterioration in the deep aquifer. For example, the recovery ratio decreases from 0.85 to 0.21when vd increases from 0 to 1.5×10−6 m/s in the case of tpump=90 days.Table 2
The recovery ratioμ of contaminant at the end of pumping phase.
vd0 m/s5×10−7 m/s1×10−6 m/s1.5×10−6 m/sμ (tpump=90d)0.850.600.360.21μ (tpump=180d)0.850.520.230.11Figure5 shows the superposed flow field generated by the pumping well and the regional flow. The results indicate that there exists a stagnation point (Sp) and a dividing streamline (Ds). At the Sp, all velocity components are zero, and several Ds may cross each other. Note that Ds divides the flow region into capture zone and noncapture zone. If the travelling contaminant cannot escape from the capture zone in the inactive phase, it may be extracted out from the aquifer during the pumping phase. To further elucidate this behavior, the concentration distributions of the contaminant in the 2D horizontal plane at t2=270 day with varying regional groundwater velocities are shown in Figure 6. The results indicate that higher regional groundwater velocity makes the contaminant mass move further away from the well. Besides, a higher regional groundwater velocity leads to a smaller distance from Sp to well, resulting in a smaller proportion of contaminant that can be extracted out during the pumping phase. Note that for the case where vd=0 m/s in Figure 6(a), nearly all the contaminant is distributed near well. Hence, almost all contaminant in principle can be extracted out from the well over time through pumping. Overall, a higher regional groundwater velocity causes a larger proportion of contaminant that drift beyond the Ds in the inactive phase, resulting in relatively lower contaminant concentration inside the wellbore and a lower recovery ratio during the pumping phase as shown in Figure 4 and Table 2, respectively.Figure 5
The schematic diagram of the flow system in the pumping phase.Figure 6
Concentration distributions in a 2D horizontal plane att2 = 270 day. (a) vd=0 m/s; (b) vd=5×10−7 m/s; (c) vd=1×10−6 m/s; (d) vd=1.5×10−6 m/s.
(a)(b)(c)(d)


## 4.2. The Effects of Pumping Frequency on Water Quality

For the purpose of alleviating the deterioration of groundwater quality, the optimization strategies for the management of wells should include better execution of regulations and more stringent design criteria. Moreover, changes in operational parameters can also provide positive influence, such as the implementation of intermittent pumping or increasing pumping frequency during the periods of low demand, which assists the inhibition of contaminant migration. Figure7 shows the BTCs inside the well for two kinds of pumping frequency, i.e., 180 days of pumping with another 180 days of rest (fpump=2/year) and 90 days of pumping with 90 days of rest (fpump=4/year) over a period of 720 days, respectively. The parameters were as follows: vd=1×10−6 m/s, Qinact=5.79×10−4 m3/s, and Qpump=−5.79×10−4 m3/s, and the other parameters are the same as those used in Table 1. Figure 7 represents that the concentration at the wellbore in the case of fpump=2/year is higher than that in the case of fpump=4/year. The results indicate that more frequent pumping yields more contaminant extracted when the total pumping time is fixed. Moreover, the recovery ratios at the end of pumping phases with two different pumping frequencies are shown in Table 2. For example, μ are 0.36 and 0.23 with fpump=2/year and 4/year, respectively, which indicates that a more frequent pumping leads to a greater recovery ratio with regional groundwater velocities. Therefore, an increasing pumping frequency can effectively improve water quality in a groundwater system involving such a SPW.Figure 7
BTCs inside the well with different pumping frequencies during the pumping phase.To further interpret this behavior, the concentration distributions in a 2D horizontal plane wheret2=360 days with fpump=2/year and 4/year are shown in Figure 8. The results indicate that large number of contaminants accumulate in the aquifer, and the contaminant distribution spreads along the downstream in the case where fpump=4/year days is larger than in the case where fpump=2/year. This supports the position that frequent pumping can effectively diminish contamination and improve water quality in deep aquifer.Figure 8
Concentration distributions in a 2D horizontal plane att2=360 day. (a) tpump=180 days, and (b) tpump=90days.
(a)(b)Furthermore, we evaluate the recovery ratios with more frequent pumping but without regional groundwater velocity, i.e.,vd=0 m/s. Figure 9 shows the BTCs induced by intermittent pumping with varying frequencies where fpump=2/year and 4/year in the case of vd=0 m/s; the other parameters are the same as those used in Table 1. It is worthy to note that the value of contaminant concentration increases gradually for different pumping frequencies at the end of each pumping phase. In addition, it can be observed that the value of contaminant concentration where fpump=4/year at the end of each pumping phase is larger than when fpump=2/year, suggesting that a more frequent pumping accelerates the contaminant accumulation in the vicinity of wellbore. To further estimate the proportion of contaminant migrating into the deep aquifer when vd=0 m/s, and equal recovery ratios of contaminant where fpump=2/year and 4/year are shown in Table 2. The results show that more frequent pumping cannot effectively improve water quality in a groundwater system. However, the recovery ratios are the highest when vd=0 m/s, indicating that frequent pumping has better performance with lower regional groundwater velocity in terms of water quality control. Therefore, the regional groundwater velocity is critical to pollution prevention with the SPW as a cross-aquifer conduit.Figure 9
BTCs inside the well with different pumping frequencies without regional groundwater velocity in the pumping phase.


## 4.3. The Effects of Pumping Rate on Improving Water Quality in Deep Aquifer

Figure10 shows the intermittent pumping induced BTCs of contaminant with different pumping rates. The pumping period tpump is set for 90 days. Besides these values where vd=1×10−6 m/s, Qinact=5.79×10−4 m3/s, Qpump=−2.31×10−4, −3.47×10−4, −4.63×10−4, and −5.79×10−4 m3/s, the other parameters are the same as those used in Table 1. The results indicate that a higher pumping rate leads to a higher contaminant concentration at later times in Figure 10. It is notable that a higher pumping rate results in a wider capture zone, resulting in greater contaminant extraction contaminant during the pumping phase. Consequently, the results in higher contaminant concentration of BTCs at later times. Hence, the recovery ratios of contaminant were computed for varying pumping rates for all pumping periods as shown in Table 3. The results indicate that a higher pumping rate results in a higher recovery ratio. Therefore, increasing the pumping rate has a positive effect for improving the water quality in the deep aquifer.Figure 10
BTCs inside the well with different pumping rates during the pumping phase. (a)Qpump=−2.31×10−4 m3/s; (b) Qpump=−3.47×10−4 m3/s; (c) Qpump=−4.62×10−4 m3/s; (d) vd=Qpump=−5.79×10−4 m3/s.Table 3
The recovery ratioμ of contaminant for different pumping rates.
Qpump2.31×10−4 m3/s3.47×10−4 m3/s4.62×10−4 m3/s5.79×10−4 m3/sμ0.150.220.300.36Besides, the contaminant concentration distributions in a 2D horizontal plane att2=270 day with different pumping rates are also shown in Figure 11. One can see that a higher pumping rate leads to a larger capture zone, i.e., the area enclosed by the dividing line expands with higher pumping rates, resulting in more extracted contaminants as shown in Figure 10. Furthermore, the results indicate that higher pumping rates lead to smaller contaminant plume at the switch point between inactive and pumping conditions. Therefore, we can increase the pumping rate for contaminant control; however, local water demand is seasonally variable, and more optimized water supply strategies are needed when employing an increasing pumping rate. For example, an effective method is to change the pump location inside the well, since Gailey [5] noted that about 29% of the extracted volume came from the deep aquifer in multilayer aquifers if pump location is shallow inside the well. However, the volume pumped was raised by about 48% in the case of a deeper pump location as our numerical simulation has also suggested. As such, a deeper pump in the wellbore leads to higher pumping volume, which yields a larger capture zone with regional groundwater flow as well as a higher recovery ratio of contaminant, thereby improving the water quality.Figure 11
The contaminant concentration distributions in a 2D horizontal plane att2=270 day with different pumping rates. (a) Qpump=−2.31×10−4 m3/s; (b) Qpump=−3.47×10−4 m3/s; (c) Qpump=−4.62×10−4 m3/s; (d) Qpump=−5.79×10−4 m3/s.
(a)
Qpump=−2.31×10−4 m3/s(b)
Qpump=−3.47×10−4 m3/s(c)
Qpump=−4.62×10−4 m3/s(d)
Qpump=−5.79×10−4 m3/s


## 5. Conclusion

In this study, a numerical model describing contaminant migration was developed and investigated based on a SPW with the presence of regional groundwater flow. By considering the SPW as a conduit for cross-aquifer contamination, the influences of the regional groundwater velocity on the deterioration of water quality were quantitatively assessed. Also, strategies were proposed to reduce the negative influences of regional groundwater flow considering seasonal water demand. The following conclusions were drawn:(1)
Regional groundwater velocity has significant effects on the deterioration of water quality. A higher regional groundwater velocity means a lower contaminant concentration. Similarly, during pumping, a smaller recovery ratio inside the wellbore facilitates the deterioration of water quality in the deep aquifer. The opposite is true in the case of a lower regional flow velocity(2)
Frequent pumping can increase the recovery ratio of contaminant in all pumping phases with the presence of regional groundwater flow. Thus, the method is effective for preventing such contamination in deep aquifer. However, it is worth noting that frequent pumping is not helpful for improving the water quality without the presence and action of regional groundwater velocity(3)
A higher pumping rate leads to a larger capture zone, resulting in a greater recovery ratio and improving effectively the water quality in deep aquifer. This method may be limited by seasonal requirement. As such, one can locate the pump at a deeper location inside the wellbore to increase the pumping volume from deep aquifer with long screens or multiple screens connecting multilayer aquifers. Besides, the modeling research fits a framework of Darcian flow and equivalent porous medium approach to sedimentary aquifers



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*Source: 5819518-2022-09-16.xml*