# Aquifer Storage and Recovery in Layered Saline Aquifers: Importance of Layer-Arrangements

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{inj}[L

^{3}] is the volume of injected freshwater during a single ASR cycle, and V

_{rec}[L

^{3}] is the recovered volume of potable water during the same ASR cycle. RE is calculated after each ASR cycle. Each ASR cycle includes the injection, storage, and recovery phases. RE values are reported to range from 0 to 100% [19,20,21,22]. Extreme values close to 0 indicate that ASR is not feasible under local aquifer conditions and ASR practices.

^{−1}] is the hydraulic conductivity, B [L] is the confined aquifer thickness, Q [L

^{3}T

^{−1}] is the pumping rate, $\overline{\alpha}$ [-] is the density difference ratio, which equals to $({\rho}_{\mathrm{s}}-{\rho}_{\mathrm{f}})/{\rho}_{\mathrm{f}}$, ρ

_{s}[ML

^{−3}] is the density of the native saline groundwater, ρ

_{f}[ML

^{−3}] is the density of injected freshwater, θ [-] is the effective porosity, and t

_{i}[T] is the duration of the injection phase. A higher M value indicates a stronger intensity of density-driven convection and it leads to an earlier saline water breakthrough at the bottom of the ASR well during recovery phases, thereby reducing the RE [27].

_{z}

^{ave}(geometric mean of hydraulic conductivities of all stratum). In addition, a dimensionless Rayleigh number was introduced to characterize the relative contributions of density-driven convection versus dispersion (by neglecting diffusion) during the storage phase [28]:

_{L}[L] is the longitudinal dispersivity. The performance of ASR was found to be sensitive to the layering patterns. Since density-driven convection can be suppressed by the low permeability layer underlying the high permeability layer, a higher RE value was obtained for the scenario with greater hydraulic conductivity contrast between the neighboring layers. Ward et al. [28] also suggested that layered heterogeneity can be simplified to homogeneous anisotropy by taking the geometric mean and arithmetic mean (respectively) of the hydraulic conductivities of all stratum as the vertical and horizontal hydraulic conductivities for the whole domain. Although this method led to an overestimation of RE in early cycles, they found that the long-term ASR RE (i.e., after ten ASR cycles) was not overestimated [28].

## 2. Conceptual Model

_{s}[L

^{−1}]) of each cell by 2πr (where r [L] is taken as the distance between the axis of symmetry and the center of the cell) to account for the increased flow area and cell volume with radial distance from the well [30]. The conceptual model adopted in this study, as shown in Figure 1, is based on the model in Ward et al. [28]. We divided the model domain into five horizontal layers with equal thickness. However, the hydraulic conductivities of all layers are different (K

_{1}≠ K

_{2}≠ K

_{3}≠ K

_{4}≠ K

_{5}). We investigated 120 scenarios including all possible arrangements of layers. Note that the contrast of conductivities between two neighboring layers is not limited to a constant in each scenario in this study, which is different from the identical conductivity contrast assumed in [28].

^{6}m/d) with θ set to unity. During the injection and recovery phases, the pumping rate is specified to 500 m

^{3}/d (Q, indicated with blue arrows in Figure 1) and −500 m

^{3}/d (−Q, indicated with red arrows in Figure 1), respectively. The fluxes that enter/leave the aquifer through the well zone are distributed uniformly across the entire well depth (i.e., the entire aquifer thickness). During the storage phase, the well boundary is converted to a no-flow boundary and the pumping rate is zero. Such settings of the well boundary are used following Maliva et al. [7] and Kang et al. [31]. The solute concentration of the water entering the model by injection (left boundary) is specified as zero (i.e., C

_{i}= 0). The right side of the model domain is designated as a specified-head boundary with hydrostatic head distribution reflecting the density of the native saline water (i.e., h

_{0}= 100 m). Groundwater entering the model through the right boundary has a concentration of C

_{s}= 10 g/L, which is at the moderate range of that applied in previous ASR studies (2–28 g/L; e.g., [19,27,28]). At the start of the first ASR cycle, the aquifer is saturated with native saline water with a concentration of C

_{s}. The initial head is h

_{0}, which is larger than the aquifer thickness (B = 50 m) to guarantee the confined aquifer condition.

## 3. Numerical Modelling

#### 3.1. Governing Equations

^{−3}] is the fluid density, h [L] is the water head, t [T] is time, z [L] is the vertical coordinate directed upward, ρ

_{ss}[ML

^{−3}] is the source/sink density, and q

_{ss}[T

^{−1}] is the sink/source flow rate per unit volume of the aquifer.

^{−3}] is the solute concentration,

**D**[L

^{2}T

^{−1}] is the hydrodynamic dispersion coefficient tensor, and

**v**[LT

^{−1}] is the pore water velocity vector.

#### 3.2. Model Discretization and Solver Setup

_{L}(with α

_{L}equals 0.3 m), such that the numerical dispersion arising from truncation errors is avoided [34].

^{−4}m, and the flow convergence criterion was set to 10

^{−4}m

^{3}/d. For the transport equation, the generalized conjugate gradient (GCG) solver was used with the third-order total-variation-diminishing (TVD) scheme [37] to solve the advection term and for automatic timestep control (with courant number set to 0.9). TVD scheme is preferred here, because it is inherently mass conservative and does not introduce excessive numerical dispersion and artificial oscillation [34]. The concentration convergence criterion was set to 10

^{−9}g/L.

#### 3.3. Input Parameters and Scenarios

_{r}

^{ave}and K

_{z}

^{ave}respectively) are identical among the 120 scenarios, which are calculated as:

## 4. Results and Discussion

^{−3}). The boundary of this zone is slightly tilted at the end of the storage phase due to the density effect and its resulting free convection (Figure 2(b1)). At this phase, the Rayleigh number equals to 1.462, representing the fact that density effect and dispersion have a similar magnitude during storage. The tilt of the interface is magnified in the recovery phase as a result of a combined effect from pumping, free convection and time (Figure 2(c1)). The mixing zone between the freshwater and saline water can be visualized by the gradual color changes shown in Figure 2. The mixing zone is narrow during the injection and storage phases, yet it becomes much wider in the recovery phase. The difference between the injection and recovery phases can be explained by the different combination of the directions between longitudinal dispersion and advection. Whereas the direction of longitudinal dispersion is invariably pointing from saline water to freshwater (right to left in Figure 2), injection leads to the advection from left to right and extraction from right to left. The opposite directions between longitudinal dispersion and advection in injection phase results to the suppression of mixing zone extension. In contrast, the identical direction between longitudinal dispersion and advection during recovery enhanced the mixing between the freshwater and saline water. As a result of the coupled effect from density difference and dispersion, the saline water intrudes into the lower half of the well (see contour line of C = 0.3 g/L in Figure 2(c1)). This leads to a limited RE of 63%, significantly lower than 100%.

^{3}/d), flow from right to left in the lower aquifer leads to the salinization of the injected freshwater. Subsequently, it leads to the flow from left to right in the upper aquifer, resulting to a decrease in salinity. Such a flow condition is also reflected by the slight tilting of the fresh-saline interface shown in Figure 2(b1).

^{3}/d, much larger than that in the ‘Hom’ case. Such complex flow conditions formed in the heterogeneous cases result to remarkable salinity changes during the storage phase. In the ‘DEC’ case, salinity increases in the bottom four layers and decreases in the top one layer (Figure 3(b2)). Since the hydraulic conductivity is higher in the upper layer compared to the neighboring lower layer, the density effect is restricted by the lower layer and leads to a spreading of salinity at the bottom of each layer. In contrast, for the ‘INC’ case, salinity decreases in the top four layers and increases in the bottom one layer (Figure 3(c2)). Nevertheless, due to density effect, salinity always increases in the lower part of the aquifer and decreases in the upper part of the aquifer for all the homogeneous and heterogeneous cases.

_{r}and vertical flow q

_{z}at the vertical cross-section of r = 20 m in Figure 5. As shown by the red lines, q

_{z}varies significantly along the vertical direction and shows a relatively high value at the high permeable zones. Such a phenomenon is consistent with that shown in the storage phase (see Figure 3(a2,a3)), indicating complex flow conditions in the recovery phase for the two heterogeneous cases. Additionally, the q

_{r}values in the ‘EH’ layers are different between the two heterogeneous cases. The faster q

_{r}in the ‘INC’ case is the result of summation between forced and free convection, whereas the slower q

_{r}in the ‘DEC’ case is caused by the subtraction of flow velocity due to the density effect from forced convection.

_{r}

^{ave}and K

_{z}

^{ave}) overestimates the ASR RE under density-dependent conditions. Such an overestimation is reduced but still non-negligible after ten ASR cycles. Consistently, the absolute difference of RE values among different scenarios is up to 22% in the first cycle (shown as circles), but it reduces to a maximum absolute difference of 9% after ten ASR cycles (shown as crosses).

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Conceptual model of 2D axisymmetric flow and transport associated with ASR implemented in a confined five-layer aquifer.

**Figure 2.**Salinity distributions at the end of injection (

**a1**–

**a3**), storage (

**b1**–

**b3**), and recovery (

**c1**–

**c3**) phases for the first ASR cycle. Results shown are for the equivalent homogeneous anisotropic case (‘Hom’), the heterogeneous cases where isotropic hydraulic conductivity decreases from the aquifer top to the bottom (‘DEC’), and that increases from the aquifer top to the bottom (‘INC’). Salinity contours of C = 0.3 g/L are plotted as white lines on salinity plots at the end of recovery, with RE values listed.

**Figure 3.**Flow field distributions at the intermediate storage phase (i.e., after 82 days of storage;

**a1**–

**a3**) and the salinity changes during storage (i.e., concentration difference between the end and start of the storage phase;

**b1**–

**b3**) for the first ASR cycle. Results shown are for the equivalent homogeneous case ‘Hom’ (top), and the heterogeneous cases ‘DEC’ (middle) and ‘INC’ (bottom). The black lines represent the contour of C = 5 g/L, indicating the approximate location of the fresh-saline interface.

**Figure 4.**Flow vectors at the intermediate recovery phase (i.e., after 50 days of storage;

**a1**–

**a3**) and the salinity changes during storage (i.e., the difference between the concentration distribution at the end of the recovery phase and that at the start;

**b1**–

**b3**) for the first ASR cycle. Results shown are for the homogeneous anisotropic case ‘Hom’ (top), and the heterogeneous cases ‘DEC’ (middle) and ‘INC’ (bottom). The black lines represent the contour of C = 5 g/L, indicating the approximate location of the fresh-saline interface.

**Figure 5.**Flow in the horizontal direction q

_{r}(blue) and vertical direction q

_{z}(red), for the heterogeneous cases ‘DEC’ (solid lines) and ‘INC’ (dashed lines). Results are assessed at r = 20 m that is approximately the average location of the fresh-saline interface.

**Figure 6.**Salinity distributions at the end of injection (

**a1**–

**a3**), storage (

**b1**–

**b3**), and recovery (

**c1**–

**c3**) phases for the tenth ASR cycle. Results shown are for the homogeneous anisotropic case (‘Hom’), the heterogeneous cases where isotropic hydraulic conductivities decrease from the aquifer top to the bottom (‘DEC’), and that increase from the aquifer top to the bottom (‘INC’). Salinity contours of C = 0.3 g/L are plotted as white lines on salinity plots at the end of recovery, with RE values listed.

**Figure 7.**RE values calculated for ten ASR cycles for the homogenous (‘Hom’) and two heterogenous cases (‘DEC’ and ‘INC’).

**Figure 8.**RE values assessed at the first and tenth cycles, for heterogeneous cases of all possible arrangements of the five isotropic layers (‘Het’, scattered points) and the homogeneous anisotropic case (‘Hom’, lines).

**Figure 9.**Distributions of the RE values versus the sum of squared hydraulic conductivity difference between neighboring layers for the first (blue circles) and tenth (red crosses) ASR cycles. The straight lines are obtained by the first-order linear regression with 95% confidence.

Parameter | Symbol | Value | Unit |
---|---|---|---|

Model radius | R | 250 | m |

Model thickness | B | 50 | m |

Cell width | ∆r | 0.2 to 1 | m |

Cell thickness | ∆z | 0.5 | m |

Uniform thickness of each layer | b | 10 | m |

Isotropic hydraulic conductivities (for each layer) | K_{1} to K_{5} | 0.09 (EL), 0.36 (L), 0.82 (M), 1.46 (H), 2.27 (EH) | m/d |

Horizontal hydraulic conductivity (average) * | K_{r}^{ave} | 1 | m/d |

Vertical hydraulic conductivity (average) * | K_{z}^{ave} | 0.06 | m/d |

Longitudinal dispersivity | α_{L} | 0.3 | m |

Transverse dispersivity | α_{T} | 0.03 | m |

Molecular diffusion coefficient | D_{d} | 10^{−9} | m^{2}/s |

Specific storage | S_{s} | 10^{−4} | 1/m |

Initial head | h_{0} | 100 | m |

Injected water concentration | C_{i} | 0 | g/L |

Native saline water concentration | C_{s} | 10 | g/L |

Density difference ratio | $\overline{\alpha}$ | 7.143 × 10^{−3} | - |

Effective porosity | θ | 0.3 | - |

Injection/Recovery pumping rates | Q | 500 | m^{3}/d |

Injection duration | t_{i} | 100 | d |

Storage duration | t_{s} | 165 | d |

Recovery duration | t_{r} | 100 | d |

Mixed convection ratio | M | 8.772 × 10^{−3} | - |

Rayleigh number | Ra | 1.462 | - |

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**MDPI and ACS Style**

Li, H.; Ye, Y.; Lu, C. Aquifer Storage and Recovery in Layered Saline Aquifers: Importance of Layer-Arrangements. *Water* **2021**, *13*, 2595.
https://doi.org/10.3390/w13182595

**AMA Style**

Li H, Ye Y, Lu C. Aquifer Storage and Recovery in Layered Saline Aquifers: Importance of Layer-Arrangements. *Water*. 2021; 13(18):2595.
https://doi.org/10.3390/w13182595

**Chicago/Turabian Style**

Li, Hongkai, Yu Ye, and Chunhui Lu. 2021. "Aquifer Storage and Recovery in Layered Saline Aquifers: Importance of Layer-Arrangements" *Water* 13, no. 18: 2595.
https://doi.org/10.3390/w13182595