Constraint mapping
As a first step in assessing the technical suitability, constraints in the region that rule out the placement and operation of MAR systems were filtered out. This was done using Boolean logic, similar to the approaches by Kallali et al. (
2007) and Rahman et al. (
2012). The prerequisites are summarised in Table
1. For placement, MAR requires suitable land where infiltration and abstraction wells can be installed and operated continuously (Brown et al.
2005; Ghayoumian et al.
2007). Therefore, the protected Sundarbans mangrove area and the often-inundated aquaculture ponds and tidal river floodplains were filtered out, using a landcover map constructed from supervised classification of Landsat imagery (Naus et al.
2019b).
Table 1
Criteria and associated data used for the constraint mapping
Study area | Administrative boundaries | Satkhira, Khulna, Bagerhat districts: 1. Other districts: 0 |
Inundation likely or protected land | Supervised classification of cloudless imagery from Landsat 8 (17 and 24 March 2015, paths 137 and 138, row 44), calibrated with observations from aerial images and field observations | Treed village, one season rice, multiple season rice: 1. Water, (tidal) rivers, aquaculture, Sundarbans: 0 |
Aquifer | Thickness greater than 9.1 m (30 ft) within the first 60 m | Thickness greater than 9.1 m (30 ft): 1. Thickness less than 9.1 m (30 ft): 0 |
For operation, MAR requires a sandy aquifer where water can be injected and stored, with the storage capacity, the infiltration capacity and the transmissivity of the aquifer primarily controlling the potential capacity of MAR systems (Ghayoumian et al.
2007; Brown et al.
2005; Chowdhury et al.
2009). The target aquifer was stipulated to have to be present within manual drilling range of up to 60 m deep, to keep the costs of installation acceptable (Acacia Water
2014a).
For the geological constraints, 875 borehole descriptions from the DPHE, BWDB, the UNICEF MAR project, Naus et al. (
2019a,
b) and Ayers et al. (
2016) were collected. Many of the borehole descriptions were collected by drilling using the ‘sludger’ or ‘hand-flapper’ method (Horneman et al.
2004) and therefore lack details on storage capacity, infiltration capacity or aquifer transmissivity. To determine whether a sufficiently thick aquifer is present, any material described as sand was assumed to be suitable for the MAR systems, but that such a layer had to be thicker than 9.1 m (30 ft) to obtain sufficient storage, corresponding to the thickness used as a requirement for the pilot MAR systems (Acacia Water
2014a). The thickness of the aquifer was determined within the first 60 m for each borehole log, subsequently followed by spatial interpolation using Kriging, for which the same configuration as for the water quality data was used.
The performance of an MAR system that uses injection and abstraction wells is commonly assessed using the recovery efficiency (RE), defined as the percentage of infiltrated water that can be recovered while maintaining sufficient water quality (Bakker
2010; Maliva et al.
2006; Ward et al.
2009). The RE can be limited when the quality of the stored water is deteriorated by ambient water, which can occur due to lateral flow, diffusive/dispersive mixing and density-driven flow (Bakker
2010; Lowry and Anderson
2006; Maliva et al.
2006; Ward et al.
2009; Zuurbier et al.
2013).
Lateral flow is caused by the natural hydraulic gradient and leads to the infiltrated freshwater flowing away from the abstraction well. In southwestern Bangladesh, lateral flow was anticipated to be negligible at this time scale (Worland et al.
2015), as the hydraulic gradient in the region was expected to be low because elevation differences are small, and the infiltration rates are low due to the very thick confining clay layer (Naus et al.
2019a; Ayers et al.
2016). Diffusive/dispersive mixing occurs whenever there is a concentration gradient and due to aquifer anisotropy and heterogeneity during lateral flow, density-driven flow and enhanced flow from the injection wells towards the abstraction wells (Ward et al.
2009). In practice, it is difficult to predict diffusive/dispersive mixing (Ward et al.
2009), especially in southwestern Bangladesh, where data on the anisotropy or heterogeneity of the lithology are sparse. Density-driven flow is caused by density differences between the injected water and the native groundwater. The more saline the surrounding groundwater, the larger the difference in density is, and the larger the buoyant force is from the saline water on the freshwater. The interface between fresh and saline water will consequently be located higher in the aquifer, closer to the filter, making it more likely that upconing of native, saline groundwater will reach the bottom of the abstraction well. Additionally, a larger buoyant force causes injected freshwater to be pushed to the top of the aquifer and consequently to flow away laterally from the abstraction well (Bakker
2010; Ward et al.
2009).
Whenever native groundwater ends up in the well by any of the aforementioned processes or any unforeseen processes, the quality of the abstracted water will decrease, as the primary reason for installing an MAR system in southwestern Bangladesh is that the native groundwater present is not suitable for drinking. Groundwater salinity and arsenic concentration are the two dominant concerns and the vulnerability of an MAR system has been assessed using the groundwater salinity and arsenic database.
The expected technical performance of MAR was assessed by estimating the expected effect of density-driven flow and by estimating the vulnerability to any of the mixing processes. These two variables were combined into one technical suitability index.
The spatial varying magnitude of density-driven flow on the performance of MAR systems was estimated using the method of Bakker (
2010). Bakker (
2010) describes that the effect of density-driven flow on the RE for an MAR system, typically composed of one joint injection and abstraction well, depends on the duration of the injection period relative to the duration of the storage and abstraction period, and on a dimensionless parameter D which governs the flow in the MAR system. There are some important differences between the MAR systems for which the D value was developed and the MAR systems in southwestern Bangladesh in terms of their design and operation. Firstly, a single well that penetrates the entire aquifer is used for injection and abstraction in the MAR systems of Bakker (
2010), whereas the MAR systems in Bangladesh typically have 4–6 infiltration wells with a screen length of 9.1 m (30 ft) situated around one separate abstraction well with 3 m (10 ft) screen length of which the lower ends are placed approximately 3 m (10 ft) higher in the aquifer (Acacia Water
2014a). Secondly, the MAR systems in Bangladesh do not have clearly demarcated injection and abstraction periods. Their continuous injection and abstraction could lead to some of the water having a relatively short storage time, although on average there is a higher injection rate in the wet season and there is a higher abstraction rate in the water-stressed dry season, resulting in net storage from the wet season into the dry season. Despite these differences, the ‘D value’ developed by Bakker (
2010), as previously used for MAR site selection by Zuurbier et al. (
2013), was used as a best estimate of the spatially varying magnitude of density-driven flow on the performance of MAR systems throughout the region:
$$ D=\frac{Q}{k\alpha {H}^2} $$
(1)
with
D being the D value,
Q being the infiltration and abstraction rate during the days that infiltration or abstraction occurs (m
3/day),
k being the hydraulic conductivity,
H being the thickness of the aquifer and
α being the density difference ratio, calculated by:
$$ \alpha =\frac{\left({\rho}_{\mathrm{s}}-{\rho}_{\mathrm{f}}\right)}{\rho_{\mathrm{f}}} $$
(2)
with
ρs being the density of the native saline groundwater and
ρf being the density of the injected freshwater. The higher the D value is, the higher the RE. The density of the native groundwater varies spatially and was calculated based on the electrical conductivity of the shallow groundwater (<60 m), using the 1980 UNESCO state equation typically used for ocean water (for the full documentation, see Fofonoff and Millard
1983). Post (
2012) showed these equations to be useable for calculating the density of coastal groundwater. Exact information on the hydraulic conductivity (
k) was not available throughout the region, so the value of
k was based on the median value of 10.9 m/day (
σ: 5.68) obtained from 10 pumping tests performed by Acacia Water (
2014b). The other parameters,
H and
Q, are based on the design and capacity of the pilot MAR.
H was put at 9.1 m (30 ft), similar to the length of the filter of the injection wells used in the pilot MAR systems (Acacia Water
2014a), and similar to the minimum required thickness of the aquifer, although the total thickness of the aquifer can be different than
H.
Q was given a value of 5 m
3/day, which is slightly less than the median injection capacity (5.9 m
3/8 h) of the pilot MAR systems but higher than the median of the averaged actual infiltration rates per day (3.1 m
3/day; Acacia Water
2014b).
To interpret an associated RE from the D value, the design, injection, storage, and recovery periods, and the amount of cycles are important (Bakker
2010). Bakker formulated how to translate
D into RE for his typical design in which the injection period is of similar duration to the recovery period. Zuurbier et al. (
2013), who also applied Bakker’s method to assess MAR suitability, used a D value of 14.3 as criterion for well-functioning MAR systems with injection, storage and recovery periods of equal durations, related to an RE of 60% after five cycles. Due to the aforementioned differences in design and operation between the pilot MAR systems and the MAR systems of Bakker (
2010) and Zuurbier et al. (
2013), the same criterion could not be used. The Bangladesh MAR systems are likely to be less susceptible to density-driven flow than the MAR systems of Bakker (
2010) and Zuurbier et al. (
2013) because more upconing is needed for the native groundwater to reach the bottom of the separately installed abstraction well with a screen at shallower depth than the screens for the injection wells (Maliva et al.
2006; Zuurbier et al.
2014). Additionally, the simultaneous injection and abstraction in the MAR systems is likely to result in much shorter average storage times than in the MAR systems of Zuurbier et al. (
2013), which will result in less time for density-driven flow and an associated higher RE for similar D values.
In view of the foregoing, the design and operation differences were expected to likely lead to a higher RE for similar D values. As a best guess, a D value of 5 was chosen as the approximate criterion for well-functioning MAR systems, corresponding with an approximate EC of 3.1 mS/cm. In areas with a lower D value, density-driven flow is interpreted to noticeably reduce the efficiency of the MAR system. The D value instead of an associated RE value was decided to be reported, as the associated RE value is subject to MAR design choices and interpretation whereas the D value is closer to a subsurface property. For guidance, a D value above 5 is expected to likely lead to an RE higher than 60% and a D value below 1 is expected to likely lead to an RE of approximately 25% in the unmodified pilot MAR design.
The vulnerability to water quality deterioration due to mixing was expressed by calculating the fraction of native water that would result in the water quality being below the water quality standards of the Bangladesh government (Ayers et al.
2016). The maximum fraction of native water (
fi) in the abstracted water before a certain compound
i deteriorates the abstracted water was calculated as follows:
$$ {f}_{\mathrm{i}}=\frac{i_{\mathrm{c}}-{i}_{\mathrm{i}}}{i_{\mathrm{n}}-{i}_{\mathrm{i}}} $$
(3)
with
ic being the concentration criterion according the drinking-water-quality standards,
ii being the concentration of the compound in the injected water, and
in being the concentration of the compound in the native groundwater. The smaller the fraction, the less water is needed to deteriorate the water quality of the extracted water and the higher the vulnerability to any of the aforementioned processes. Vulnerability to deterioration was calculated for EC and arsenic, with the lowest value for these two determining when the water quality would be considered as deteriorated. For the quality of the native groundwater, data points for groundwater down to approximately 60 m deep from the water quality database were used, as described earlier.
To summarise the technical suitability of the region for MAR, the expected density-driven flow in the form of the calculated D value and the vulnerability to the mixing processes were combined in one technical suitability index. For this, a weighted linear combination (WLC) was used, similarly to Saraf and Choudhury (
1998) and Rahman et al. (
2012):
$$ \mathrm{WLC},\kern0.5em S\left({x}_{\mathrm{i}}\right)=\sum {w}_{\mathrm{i}}\cdotp {s}_{\mathrm{i}}\left({x}_{\mathrm{i}}\right) $$
(4)
in which
wi is the weight of each criterion, the sum of the weights is 1, and
si (
xi) are the standardised criteria. Equal weights were used for the expected density-driven flow and for the permitted fraction of native groundwater, i.e.,
wi = 0.5.
The D value and the permitted fraction of native groundwater were standardised so that they both had the same scale of 0 (no suitability) to 1 (high suitability). For standardisation of the D value, areas with a D value below 5 were interpreted as likely to be influenced by density-driven flow, corresponding to a standardised value of 1, which decreases linearly to 0 when the D value is 0. For the permitted mixing fraction, the standardisation was based on the scenarios described by Ward et al. (
2009), which regularly have mixing of up to 20% native water. The vulnerability was standardised linearly from 0 at 0% native water needed to deteriorate the water quality, to a vulnerability of 1 when more than 30% native water is needed to deteriorate the water quality. The resulting technical suitability index is not absolute but relative. Areas with a high index are more likely to have a technical well-functioning MAR system, but areas with a low index are not guaranteed to have nonfunctional MAR systems.