In this scenario, rapid variations in liquid levels were monitored using time-lapse cross-borehole ERT. Conventional hydraulic level measurements in monitoring wells only provide information about the immediate vicinity of the borehole, whereas cross-hole ERT can yield estimated properties of the formation between the boreholes. An example of where this can be useful is the landfill context, where leachate levels in the waste mass may vary considerably between monitoring points and complex internal structure of the waste and engineered barriers may result in perched leachate tables.

In this scenario, rapid lateral transport of a conductive tracer fluid in a saturated medium was monitored using cross-hole ERT along a multi-borehole fence. This scenario can be regarded as a proxy for a wide variety of hydraulic processes, such as solute transport, contaminant migration or leachate recirculation.

3.1.2.1 Test cell 1

Cell 1 comprises a large pit with a depth of 2.25 m (void space approximately 10 m³), excavated into made ground and lined with plywood (Fig. 1). The surrounding material consists of reworked mudstones of the Cropwell Bishop Formation (Mercia Mudstone Group, [12]), which are rich in clay and of low permeability, thus providing a suitable natural barrier for the purposes of our experiments. Water inflow is provided through a slotted horizontal pipe at the base of the cell, which was installed in a bed of pea gravel to allow controlled water injection and abstraction from the cell base. Three simulated boreholes were installed in a central imaging plane, consisting of stainless steel electrodes mounted at 0.1 m separations on the outside of PVC pipes (34 mm diameter). This design is the scale equivalent of standard monitoring well completions typically used in landfill sites. Each well was equipped with 21 electrodes, resulting in a total of 63 electrodes useable for monitoring. Multicore cables were used to connect individual electrodes with the switching modules of the ALERT monitoring system located in the vicinity of the cell.

3.1.2.2 Test cell 2

Cell 2 was established in the vicinity of Cell 1 and comprises an unlined elongated trench (6.0 m × 1.5 m × 1.6 m, void space = 14.4 m³), which allows the creation of an approximately uniform horizontal flow field by imposing a hydraulic gradient on the saturated volume. A more complex layout with 19 simulated wells was chosen, facilitating the use of both 2D and 3D imaging configurations (Fig. 2). A central fence of 11 wells forms a central imaging plane in the trench, with a matrix of 3 × 4 wells creating a 3D imaging volume offset from the centre of the cell. Each well was equipped with 16 electrodes mounted at 0.1 m separations. Electrical connectivity was established in the same way as in Cell 1. Cell 2 was backfilled with the same type of sand as Cell 1, except that a finer grade was used (Chelford 52, average grain size 0.267 mm). This was done in order to achieve a suitably low horizontal flow rate through the trench, so as to avoid image blur during ERT acquisition. A system of pumps and level sensors was installed, providing precise control over the hydraulic gradient along the trench, which is an essential prerequisite for solute transport experiments. A number of wells in Cell 2 were equipped with multilevel sampler ports [6] made of thin PVC tubing to allow in situ sampling of pore water from the saturated zone across a range of depths. All wiring and services were routed to a nearby portacabin, which served as a field laboratory and permanent shelter. A prototype ALERT system was installed in the portacabin along with wireless communication in order to simulate remote conditions on a field site.

Initially, the cell was filled with tap water and the sand saturated to a level of “high water” approximately 0.5 m below ground level (bgl). A constant pumping rate was employed, which resulted in a rate of water level change in Cell 1 of around 0.35 m/h during both injection and abstraction. Using this constant pumping rate, the cell was first emptied to a level of “low water” of 1.9 m bgl, where submersible level sensors were set to switch off the abstraction pumps and activate injection, thus refilling the cell again at the same constant rate. A corresponding set of sensors at the “high water” level ensured that pumping was reversed again once the cell was fully saturated, thus completing a full pumping cycle. This alternating pumping regime was maintained over a period of at least 24 h, so that the cell was drained and refilled at least five times. One half-cycle (either falling or rising water levels) lasted approximately 4.5 h.

A key question in ERT monitoring is whether time-lapse images are able to resolve in sufficient detail the spatial property changes associated with the process monitored. In our experiment, the expected change related to the retreat or advance of the phreatic surface, which in practice takes the form of a capillary fringe (or tension-saturated zone) above a notional water table [8]. The degree of saturation of the capillary fringe decreases gradually from the water table upwards, implying a gradational change in electric properties [2]. The capillary forces and hence the extent of the rise are affected by the pore radius of the medium and the surface tension of the liquid. The Washburn equation describes capillary flow for the simplified case of cylindrical capillaries [26], but is found to be applicable to many porous media in general:

Here, ρ denotes the liquid density and g the gravitational acceleration. Assuming γ = 0.073 N/m for water, α = 0, ρ = 998 kg/m³ at 20 °C, g = 9.8 m/s² and r ≈ 0.2 d₁₀, the estimated maximum capillary rise for our experiment in Cell 1 is likely to be h ≈ 0.14 m. This compares favourably with the fundamental vertical resolution of cross-hole ERT monitoring in our experiments, which was expected to be of the order of the electrode spacing on the simulated wells (0.1 m). We therefore expected to be able to resolve a transition zone of 1–2 electrode spacings in the ERT images between the phreatic and vadose parts of the cell. The estimated timescale of capillary flow over this distance of 0.14 m according to Eq. (2) is approximately 5 s (η ≈ 10⁻³ Pa·s at 20 °C). This is negligible against the timescale of pumping (see above) and that of ERT measurements on a crosshole imaging plane. Consequently, time-lapse image blur due to capillary-delayed flow was deemed unlikely.

ERT measurements were made using cross-borehole configurations spanning all three simulated wells (W1, W2, W3, cf. Fig. 1). The imaging plane comprised two neighbouring inter-borehole panels (W1-2 and W2-3). In accordance with Zhou and Greenhalgh [30], we opted for the symmetrical bipole–bipole array as the preferred array geometry for all crosshole measurements. For this geometry, one current electrode and one potential electrode are placed in each of two wells. In order to keep acquisition time to a minimum, we considered only measurements where current and potential bipoles were approximately horizontal, i.e. C₁ and C₂ (as well as P₁ and P₂) were placed at similar depths (Fig. 3a). This was deemed adequate as previous studies had shown that 2D crosshole resistivity models could be sufficiently well constrained if measurements were made on horizontal bipoles only [5,15,27].

One important objective of this study was to assess the impact of using multiple panels for data acquisition on tomographic reconstruction and image quality. We devised two complementary measurement strategies in order to evaluate the effect of measurement sequences and timings on image blur during monitoring. The first strategy (referred to as panel-by-panel) aims to complete individual inter-borehole panels before moving to a neighbouring panel (Fig. 3b). With regard to the overall imaging plane, all measurements at a particular lateral position are therefore made at similar times. The second strategy gives priority to interleaved measurements across all neighbouring panels. Measurements at equal depths are therefore made at similar times (Fig. 3c). In both cases, resistance measurements commence at the bottom of a panel and current and potential dipoles are then moved up successively along the boreholes. For each current injection, the set of measurements with the shorter separation between current and potential dipoles (Fig. 3a, left-hand diagram) is carried out first; this is followed by the set with longer separations (Fig. 3a, right-hand diagram).

The ALERT system uses switched DC source signals with self-adapting current settings. Input currents between 4 and 112 mA were employed in Cell 1, depending on the local contact resistance, which is a function of saturation state. We found that comprehensive measurement schemes covering the complete imaging plane typically required 480 individual resistance measurements. Using current pulse widths of 800 ms and minimal stacking of two readings per measurement, these schemes took approximately 15–17 min to complete. Data acquisition was therefore scheduled every 20 min and automatically performed by the ALERT system. Individual datasets were transferred via telemetry to the data management system for processing. Datasets were screened for quality, but were found to require only moderate pre-processing owing to the tightly controlled experimental setup with favourable noise conditions. In almost all occasions, all individual measurements could be retained. Datasets were then inverted using a 2D crosshole least-squares smoothness-constrained algorithm (Res2dinv, [17]).

Fig. 4 shows a direct comparison between two images acquired with the panel-by-panel (Fig. 4a) and interleaved (Fig. 4b) measurement strategies. The tomograms cover the full imaging zone comprising both inter-borehole panels (W1-2 and W2-3). Both datasets were collected at identical water levels while the cell was being emptied. The resistivities range from around 20 Ωm (blue) to over 5500 Ωm (red), with intermediate resistivities (∼300–1000 Ωm) displayed as faint blue, white or faint red colours. The model discretisation we have chosen comprises 480 model cells in 40 layers (5 cm thickness) and 12 columns (10 cm width). The images show a very clear separation between the water-saturated sand at the bottom of the test cell (phreatic zone) and the dry or partially saturated sand at the top of the cell (vadose zone). The water table and overlying capillary fringe are represented by a sharp transition from low (blue) to high resistivities (red).

The two strategies give significantly different results and the image distortion caused by the panel-by-panel approach is clearly visible. During the time it took for an individual borehole panel to be measured (approximately 7–8 min), the water level in Cell 1 had changed by an estimated 0.05 m, given the average pumping rate of 0.35 m/h. Although this change is nominally smaller than the anticipated fundamental image resolution of 0.1 m, the impact on the inverted images is obvious. The result of the panel-by-panel acquisition is a skewed image, in which the transition zone is noticeably offset between the two neighbouring panels. For the interleaved scheme, the resulting image shows no distortion as the transition zone is traversed on both panels within a very short period of time. These results demonstrate the sensitivity of the bipole–bipole crosshole measurement scheme to variations in the sharp vertical contrast in electrical properties. All further measurements were therefore carried out with the interleaved strategy.

A sequence of inverted resistivity images for the full pumping cycle is presented in Fig. 5. Only the abstraction phase is shown, in which the water table falls from its maximum to its minimum level. The 63 electrode positions used for the experiment are superimposed on the images. The times shown refer to the elapsed time in hours/minutes relative to the beginning of the experiment. Iteration 5 is shown for each inverted model, with RMS misfit errors ranging between 3 and 8% throughout the sequence. In most of the images, the transition zone spans one or two rows of model cells, corresponding to a maximum thickness of around 10 cm. This result suggests that the extent of the capillary fringe in Cell 1 is limited, which confirms the relatively free-draining characteristics of the Chelford 16/30 sand discussed in Section 3.2.1.

Averaging over a large number of model cells allows the calculation of representative values for the bulk resistivities of (1) tap-water saturated and (2) partially saturated or dry sand in the test cell. For the dataset obtained after 1:40 h, the water table divides the model approximately in half. At that stage, the upper half of the cells has an average value of ∼1802 Ωm, the lower half of ∼89 Ωm, i.e. the resistivity contrast between phreatic and vadose zones is approximately 1:20. The fluid conductivity of the tap water was measured with a hand-held conductivity meter and showed average values of 650–700 μS/cm. This corresponds to fluid resistivities of 14.3–15.4 Ωm.

Conventionally measured water table data have been superimposed on the resistivity images in Fig. 5 as dashed lines. The sequence of images demonstrates that the ALERT methodology is able to track the falling water table with great accuracy (within the limits of the model discretisation). We found that, for each image in the sequence, the measured water table coincides with the lower edge of the transition zone observed by ERT.

Prior to the start of the experiment, Cell 2 was filled with tap water to a level just below the ground surface in order to pre-saturate the imaging zone and to flush out any potential residuals from the pore spaces. Level sensors at the injection and abstraction ends of the cell (Fig. 2) were then set so that a constant head difference (and thus a constant hydraulic gradient) of around 0.5 m (0.15 to 0.65 m bgl) was maintained across the cell throughout the experiment. This resulted in an approximately uniform horizontal flow field in the majority of the cell volume. The rate of flow was controlled by the hydraulic conductivity of the Chelford 52 sand (saturated value 2.29 × 10⁻⁴ m/s) and the hydraulic gradient (approximately 0.083) imposed by the pumping. With these values, horizontal flow rates along Cell 2 of approximately 4–5 m/d were expected. Tracer movement at this rate was deemed to be suitably slow for monitoring with ALERT.

ERT measurements were made on nine simulated wells aligned in a vertical plane along the centre of Cell 2 (W2 to W10, cf. Fig. 2). Consequently, the imaging zone now comprised eight neighbouring inter-borehole panels, resulting in a total of 144 electrodes used for this experiment. As in Cell 1, bipole–bipole configurations were used exclusively. A comparison of strategies analogous to that described under Section 3.2.2 showed that in the case of Cell 2, panel-by-panel data acquisition could help avoid horizontal distortion. As the aim of the second experiment was to image lateral movement (as opposed to vertical movement in Cell 1), a panel-by-panel strategy was preferred on this occasion in order to minimise image skew.

Due to the larger number of electrodes, longer measurement times were required. We found that schemes with approximately 1400 individual resistance measurements gave the best results in the shortest possible time. Using identical source parameters as in Cell 1, these schemes took approximately 35 min to complete on the nine-well fence. Data acquisition was therefore scheduled every 40 min and automatically performed by the ALERT system. Individual datasets were again transferred to the data management server for processing. Datasets were screened for quality, and only moderate pre-processing was found to be necessary. Typically around 94% of measurements were used for imaging. Datasets were inverted in the same way as for Cell 1. A baseline image prior to tracer injection is shown in Fig. 6, proving that the phreatic surface of the stationary flow in Cell 2 follows a drawdown curve caused by abstraction at the end of the cell.

Cooking salt (predominantly NaCl) dissolved in tap water at moderate concentrations is environmentally benign and was considered suitable for use as a tracer fluid in our test cells. The exact concentration is an important experimental design parameter as it controls not only the electrical conductivity of the tracer (and hence the contrast against the background medium), but also its density. As saline solution is denser than tap water, a saline plume injected into a freshwater-saturated porous medium will sink under gravity. In the context of our experiment, sufficiently high electrical contrast is desirable for successful resolution with ERT, but high-concentration tracers may sink at a faster rate than the horizontal flow rate, thus potentially missing the zone of greatest sensitivity.

Tracer design is discussed in some detail by Slater et al. [22], who point out that for a medium saturated with a stagnant fluid of density ρ₀, an estimate for the gravity-induced downward flow of a plume of fluid of density ρ₁ is described by

Pore water samples were obtained from Cell 2 at regular intervals during the tracer experiment, so that direct comparison was possible between fluid properties determined on the sample and those inferred from the electrical images. Using the multilevel sampler tubes and a peristaltic pump, small samples (∼30 ml) were extracted on several wells from a range of depths at regular intervals coincident with electrical data acquisition. Fluid conductivities were measured with a handheld conductivity meter.

Alternatively, fluid conductivities can be estimated from the bulk resistivities determined by ERT through application of petrophysical relationships. In our experimental setup, only clean unconsolidated sand is employed, which has a clay content of practically zero. It is therefore safe to assume that surface conduction is negligible and simple estimates of fluid properties can be made by applying Archie's Law, in which fluid conductivity σ_w is linked to bulk formation conductivity σ_t by an empirical formation factor [1]:

In our experiments, this formation factor F can be estimated from the observed bulk resistivity of tap-water-saturated sand, given that the pore water properties are well known. This bulk value was calculated as a resistivity average for the phreatic zone as detected in the baseline image (Fig. 6), and an approximate formation factor of F≈5.9 was obtained by calculating the ratio σt/σw.

The sequence of inverted resistivity images obtained during the tracer test is shown in Fig. 7. The time span required for the tracer to enter at the injection point, traverse the length of the imaging zone and disappear from the images is approximately 24 h. Given a minimum interval of 40 min required per imaging snapshot (see Section 3.3.2), a maximum number of 36 frames could be obtained over that period, highlighting the limitations in temporal resolution currently achievable with ERT monitoring. Each tomogram covers the full imaging zone comprising eight inter-borehole panels (W2–3 to W9–10, cf. Fig. 2). The simulated wells with the 144 electrode positions used for this experiment are superimposed on the first image in Fig. 7. The times shown refer to the elapsed time in hours/minutes relative to the beginning of the experiment. The resistivity colour scale ranges from 2.5 Ωm (blue) to 500 Ωm (red), with intermediate resistivities (∼19–50 Ωm) displayed as transitionary colours. The chosen model discretisation contains 1280 model cells in 32 layers (5 cm thickness) and 40 columns (10 cm width). Iteration 5 is shown for each inverted model, with RMS errors reaching around 4–6% throughout the sequence.

In addition to the water-saturated zone and the dry or partially saturated zone already evident from the baseline image (Fig. 6), the tracer plume can now be clearly distinguished in the images. As before, resistivities less than 20 Ωm are found to represent saturated sand with elevated salinities. The lowest bulk resistivities observed are around 1.3 Ωm, i.e. over five times the value of the tracer liquid at its original concentration. The first image in the sequence coincides with the start of tracer injection, showing a faint conductive spot at the injection point. The overall duration of tracer injection was approximately 1:30 h, hence injection was completed within the first three image frames. In the following images, the conductive plume then grows in size and can eventually be seen to move in the direction of the hydraulic gradient (towards the left of the image) after 2:40 h. The neighbouring borehole is reached after 3:20 h and parts of the plume begin to differentially move downwards under the influence of gravitational sinking. This is particularly evident from 6:00 h onwards. In the following images, the tracer plume assumes an increasingly elongated shape until its front reaches the downstream boundary of the imaging zone. In the wake of the plume, the saturated zone is found to quickly revert back to resistivity values comparable to those prior to injection. The plume has almost completely disappeared from the imaging zone after around 22:00 h. A downward loss of small amounts of tracer in the leftmost four wells (W2 to W5) is revealed in the images, manifested in increased conductivities along the borehole columns. This can be explained by the fact that W2 to W5 were amongst a group of wells that had been completed with slotted casing, thereby allowing the passing tracer front to penetrate the free water column inside the well.

A time-sequence of ERT images can act as a proxy for spatio-temporal sampling of tracer breakthrough [4]. For the purpose of comparison with the pore water samples, fluid conductivity estimates were obtained from the ERT results. Bulk resistivities were extracted from ERT model cells that corresponded to the locations at which direct samples had been obtained from MLS ports. By applying the empirically determined formation factor described in Section 3.3.4, fluid conductivities were estimated. Plotting both datasets along the same time axis (“breakthrough curves”) allowed us to study the evolution of pore water conductivity as seen by the two different methodologies. The results of this comparison are shown in Fig. 8. Both datasets show characteristic maxima at times when the tracer plume passes the sampling point. We observed excellent correspondence between both methodologies at the shallower sampling points. At greater depth however, the ERT-derived estimates are consistently lower than those obtained from direct sampling. We suspect that this may be either (1) an intrinsic effect of the smoothness constrained inversion algorithm or (2) a systematic error introduced by the physical sampling procedure, which may disturb the local flow regime by abstracting significant amounts of pore fluid. This effect is exacerbated at greater depths, where more vigorous pumping over longer periods of time is usually required to extract a viable pore water sample.