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Historical single-borehole pumping test data from the studied wells have been re-analysed using the ESI AquiferWin32 V.5 software package to obtain reliable transmissivity values from single-borehole pumping tests from both the shallow aquifer (<150 m BGL; Bridge End Trial, Rottington Trial, West Cumbria ABH 1; all UK Environment Agency groundwater monitoring wells) and the deep aquifer beneath the Calder and Ormskirk Sandstone formations (150-1100 m BGL, conducted in deep Sellafield boreholes BH2 and BH3). Transmissivity values were converted into mean field-scale hydraulic conductivity by dividing by well-screen length; this assumes sub-horizontal flow. This assumption is reasonable given the layered nature of the aquifer (Kh>Kv at the field scale, Streetly et al. 2000).

Additionally, calliper and acoustic televiewer logs have been analysed in the five wells in the shallow aquifer to acquire information on fracturing pattern and lithology (similar information was obtained from the BGS archived core logs for the Sellafield deep wells). Step pumping tests in West Cumbria ABH1, Rottington Trial and Bridge End Trial wells have been analysed using the Eden and Hazel (1973) step-test analysis methodology, which determines transmissivity from single-borehole tests in confined aquifers. Step test analysis has been preferred to analysis of the available constant flow rate tests in Bridge and Trial, Rottington Trial and West

Cumbria ABH 1, since the former takes into account well-loss correction (Eden and Hazel, 1973; Clark, 1977; Mathias et al., 2008; 2010; Houben, 2015). However, aquifer transmissivities have also been computed using the Theis (1935) methodology where data relating to recovery phase (or pressure build-up) associated with constant flow-rate tests are available, as is the case for the deep Sellafield borehole well tests (BH2 l, BH2 s, BH3 l, BH3 s; the letters l and s stand for the long and short interval tests conducted in these wells, see Table 5.4 for details).

Acoustic televiewer logs (Advanced Logic Technology QL40 mk5), calliper and conductivity and temperature fluid logs (pumped conditions sampling fluid each centimetre) have been realised in the shallow St Bees Sandstone aquifer by European Geophysical Services Limited (Shrewsbury, UK) in Rottington Trial borehole. Flow velocity was logged in Rottington Trial borehole while pumping water from ~15 m below the water table at 72 m³/day, using an impeller flow-meter (Geovista mk2).

Flow-log analyses aimed to determine the hydraulic conductivity (ki) of each identified hydraulic layer i, with thickness (∆zi) from the computed partial transmissivity (Ti) using equation (1),

Ti = ki× ∆zi (1)

A quantitative methodology has been used to analyse flow meter data in the Rottington Trial borehole to determine partial transmissivity (Ti) by combining overall well transmissivity values derived from the Eden and Hazel (1973) analysis with fluid velocity logs. Day-Lewis et al. (2011) provides a computer program for the latter model, called “Flow-Log Analysis of Single Holes (FLASH)”. This program is based on the multi-layer Thiem (1906) equation (2), which describes confined radial flow in both ambient and stressed flow conditions,

Qi =^2πT_ln⁡(r^i(hw−hi)

0/rw) (2)

where Qi is the volumetric flow into or out of the well from layer i; hw and hi

are, respectively, the hydraulic head in the well (which has radius rw) and in the far-field at r0 (the radius of influence); Ti is the transmissivity of layer i. The FLASH program has an optimizing calibration method which minimize difference between data and model misfit. The model misfit is generated based on the differences (hw-hi) between the water level in the borehole (hw) under pumped and ambient conditions and the far-field heads (hi).

Drawdowns in the wells between pumped and ambient conditions are assumed to represent aquifer drawdowns; head losses between the well and the aquifer (skin effects, wells losses) are assumed to be small.

Additionally, the FLASH program requires information concerning well construction (top and bottom elevations of open section, well diameter), depth of the water table and an estimate of the radius of influence of pumping (ro=80 m, in the Rottington Trial borehole)⁴.

Core logs, calliper, gamma-ray, neutron porosity, pumping tests, fluid conductivity and temperature logs (pumped conditions, sampling fluid every 0.15 m) in the deep confined St Bees Sandstone intercepted by Sellafield BH2 and 3 were provided by the British Geological Survey; these data were originally acquired by Schlumberger during the 1990s.

4 Radius of influence for the entire pumped interval was found using the transient flow equation assuming a storativity value of 2x10^-4 (Allen et al., 1997) and water that has been pumped for a period of 40 minutes. Radius of influence 80 m in Rottington Trial, although the FLASH program is strongly insensitive to r0 since this parameter appears inside the logarithm of equation (2).

5.4.3 Upscaling hydraulic conductivity

Transmissivity values from short screen well tests (<25 m; BH2 s, BH3 s) from the deep St Bees Sandstone aquifer were compared with upscaled values derived from hydraulic conductivities from cored plugs from the same interval. The horizontal hydraulic conductivity from sandstone plugs was upscaled using the geometric mean of the plug values and the screen length to give screened interval transmissivity. Flow in this upscaling approach is assumed bed-parallel and sub-horizontal due to the shallow dip and layered nature of the aquifer (the dip of the beds is 17° and 8° for BH2 b and BH3 b, respectively). Geometric and harmonic means are typically used for upscaling of hydraulic conductivity in heterogeneous sandstone aquifers and hydrocarbon reservoirs (Chen et al., 2003; Jackson et al., 2003). We used the geometric mean in this work as it represents the sensitivity of bedding-parallel flow to layer permeability variation (Zheng et al., 2000).