The Sherwood Sandstone Group is no obscure geological unit. It underlies large parts of the United Kingdom and serves as a regional aquifer for both groundwater supply and geothermal energy applications, including aquifer thermal energy storage systems that stash heat underground for later recovery. Accurate K values determine whether such schemes are feasible, how fast pollutants disperse after a spill, and how numerical groundwater-flow models behave. Yet the traditional way of measuring K, the pumping test, is time-consuming, costly and blind to local heterogeneity. A pumping test integrates flow across the entire open borehole section, producing a single bulk number for perhaps 70 metres of rock. It cannot tell you whether a thin clay-rich layer is quietly steering contaminants sideways or blocking heat flow.

BNMR logging promises something different: a noninvasive, high-resolution portrait of the pore space, measured at 0.01-metre depth intervals down the borehole. The physics is elegant. The logging tool’s permanent magnets align the hydrogen nuclei of water molecules in the pores surrounding the borehole. An oscillating magnetic field then perturbs that alignment, and as the nuclei relax back to equilibrium they emit a signal. The amplitude of that signal is proportional to the volume of water-filled porosity, while the rate of decay, characterised by the transverse relaxation time RT2, encodes the geometry of the pore space. Small pores with high surface area relax quickly; large pores relax slowly. Because a rock contains a distribution of pore sizes, the measured decay is a multiexponential sum, and inversion of the echo trains yields a full RT2 distribution at every depth.

From these relaxation data, two empirical equations dominate the industry. The Schlumberger-Doll Research (SDR) model estimates permeability from porosity raised to a power m, multiplied by the square of the logarithmic mean relaxation time RT2ML. The Timur-Coates (T-C) model instead splits the pore water into a free fluid index (FFI), the mobile water that can be extracted, and a bound volume index (BVI), the water held by capillary forces and clay interactions, and estimates permeability from porosity and the square of the FFI/BVI ratio. Both descend from the Kozeny-Carman relationship, which links permeability to porosity and the surface-area-to-volume ratio of the void space. Both were calibrated in laboratory studies of consolidated sandstone petroleum reservoirs, with a porosity exponent of 4 and a 33-millisecond cutoff time separating free from bound water.

That petroleum pedigree is precisely where the trouble begins. The team deployed the NMRSA BMR60 tool inside three boreholes completed on the Queen’s University Belfast campus, each cased through roughly 30 metres of glacial sands and till and left open through about 70 metres of the sandstone aquifer. Boreholes 1 and 2, drilled in 2004, sit about 30 metres apart; borehole 3, drilled in 2009, lies only 5 metres from borehole 1. Constant-rate pumping tests lasting 8 to 10 hours were run with one borehole pumping and the other two serving as observation wells, water levels logged every 10 seconds. Drawdown data were interpreted with the Cooper-Jacob and Theis recovery methods for a confined aquifer, and cross-checked with a Theis-Hantush partial-penetration solution. All three solutions produced transmissivity and K values within the same order of magnitude, consistent with published values for the Sherwood Sandstone in Northern Ireland.

When the standard petroleum constants were applied to the BNMR data, the mismatch was dramatic. The upscaled SDR estimates ranged from 3.48 x 10^-9 to 5.07 x 10^-8 metres per second, and the T-C estimates from 1.29 x 10^-8 to 7.5 x 10^-8 metres per second, both roughly 100 times lower than the pumping-test values. The reason is transferability. The empirical constants b, c and m were derived for deep reservoir rocks with different cementation, pore connectivity and diagenetic histories than near-surface groundwater systems. This echoes earlier groundwater studies: Dlubac and colleagues found in the High Plains Aquifer of Nebraska that petroleum-derived constants needed site-specific adjustment, and Knight’s team in Kansas confirmed reliable BNMR estimates in unconsolidated sediments only when near-surface calibration constants were used.

The fix was a semi-constrained least-squares calibration carried out in log space, because hydraulic conductivity spans several orders of magnitude. Before fitting, the depth-resolved SDR and T-C estimates were upscaled to the pumping-test scale using a weighted average based on porosity and RT2ML, giving greater influence to intervals with larger water-filled pore volumes and longer relaxation times, which are more likely to conduct groundwater. The optimisation minimised the root-mean-square error between the logarithms of the upscaled BNMR-derived and pumping-test K values, with the porosity exponent constrained to the 0.5 to 8.0 range reported in prior groundwater work. Sensitivity tests using a simple thickness-weighted arithmetic mean, and repeating the calibration without the problematic borehole 3, whose pump intake had skimmed only the uppermost saturated zone, showed the calibrated values remained broadly comparable, within the same order of magnitude across all tested cases.

After calibration, the new SDR and T-C estimates landed within an order of magnitude of the pumping-test K, a dramatic improvement over the two-order-of-magnitude gap. The calibrated profiles also revealed vertical variability with no consistent trend with depth. The T-C profiles showed sharper local variations than the smoother SDR profiles, reflecting the FFI/BVI ratio’s sensitivity to the balance between mobile and bound water. Natural gamma and resistivity logs provided independent lithological context: intervals with higher gamma counts and lower resistivity indicated finer, clay-rich material, and these commonly coincided with elevated BVI, marking zones of smaller pores and higher surface area where free fluid, and therefore flow, is reduced. The reduced porosity exponent after calibration suggests that in this heterogeneous sandstone, K depends not only on total pore volume but also on pore connectivity, grain-scale cementation, bedding planes and fractures.

The study delivers the first reported SDR and T-C constants for the Sherwood Sandstone Group, parameters that can now be used to estimate more reliable, high-resolution NMR-derived hydraulic conductivity wherever this formation is present in the United Kingdom and beyond, subject to lithological similarity and local validation data. The authors argue the calibrated constants could reduce uncertainty in groundwater-flow models and in feasibility and performance assessments of aquifer thermal energy storage systems. The workflow itself, pairing high-resolution BNMR logging with independent pumping-test constraints and calibrating in log space, is adaptable to other consolidated aquifers where hydraulic test data exist. For a discipline long dependent on expensive bulk tests, the message is clear: the pore-scale physics of NMR can map aquifer plumbing in unprecedented detail, but only when the empirical constants are re-tuned for the shallow world rather than borrowed from the deep petroleum realm.

Subject of Research: Hydrogeology

Article Title: Advancing hydraulic conductivity estimation in the Permo-Triassic Sherwood Sandstone Group using borehole NMR logging

Article References: Oguntade, S., Ofterdinger, U., Comte, J.-C., Gee, R., Kynaston, M., & Raine, R. (2026). Advancing hydraulic conductivity estimation in the Permo-Triassic Sherwood Sandstone Group using borehole NMR logging. Hydrogeology Journal. https://doi.org/10.1007/s10040-026-03192-2

Image Credits: AI Generated

DOI: 10.1007/s10040-026-03192-2

Keywords: borehole NMR logging, hydraulic conductivity, Sherwood Sandstone, groundwater, aquifer characterisation, SDR model, Timur-Coates model, pumping tests, geothermal energy, Northern Ireland, Advancing, hydraulic