Bentheim Sandstone (BS) is a sedimentary rock formed during the Lower Cretaceous in a shallow-marine environment in the western part of the Lower Saxony Basin. It takes its name after the German city Bad Bentheim, at the border with the Netherlands. Its main outcrop forms a 9-km-long east-west ridge centred on Bad Bentheim (Dubelaar & Nijland, 2016). Because of its well-sorted grain size, lateral continuity and homogeneity at the block scale (no bedding planes are visible in hand specimens), BS is considered a reference material in rock deformation experiments. In addition, BS is almost entirely composed of quartz crystals, and, because of its well-sorted grain size and a well-connected equant pore space (Benson et al., 2005), is both high porous and high permeable making it a perfect reservoir rock to study rock-fluid interactions and transport processes even a great depths (Fazio et al., 2021; Ma & Haimson, 2016; Peksa et al., 2015; Pimienta et al., 2017).
In fact, BS is a suitable deep, warm aquifer for potential low-cost geothermal energy in the Netherlands (de Groot et al., 2020), a case study rock for anhydrite cementification in georeservoirs (Wetzel et al., 2020) and one of the most important aquifers in the North German Basin (Kunkel & Agemar, 2019). The top of the BS formation is at a depth of about 1.5 km, but BS can be found at more than 2 km depth and has been buried as deep as 3.5 km (Parnell et al., 1996), so it is crucial to understand its properties at different depths.
While earlier studies focused mostly on geological and paleontological aspects of the BS, more recent ones, particularly in the last two decades, have experimentally investigated the physical, hydraulic, mechanical and chemical properties (Klein et al., 2001; Peksa et al., 2015; Schimmel et al., 2021). Permeability, in particular, is one of most important rock properties of porous materials and its indirect determination is quite difficult to achieve. In fact, while a relationship between porosity and permeability has been noted, a model applicable to all rocks does not exist, but it is rather specific for the investigated rocks under specific conditions (Benson et al., 2006; Guéguen & Palciauskas, 1994). Therefore, direct measurements of permeability and its evolution at different in-situ conditions are essential to characterize a georeservoir.
With increasing depth, an inverse relationship between lithostatic pressure and permeability has been observed in many rocks, both sedimentary and plutonic (Gavrilenko & Gueguen, 1989; Guéguen & Palciauskas, 1994; Pimienta et al., 2017), Nevertheless, the permeability of BS is unaffected by the increasing of effective pressure (\({\sigma }_{eff}=\sigma -{p}_{p}\)). In these experiments the pore pressure (pp) was kept constant, so that the increasing in effective pressure represented the increasing in lithostatic pressure, following Benson et al., (2005) and Pimienta et al., (2017).
This low pressure-sensitivity is due to the low structural and compositional anisotropy of BS, with no bedding layers visible to the naked eye, negligible permeability anisotropy affecting the fluid flow, and a well-connected network of equant (high aspect ratio) pores with little presence of microcracks (low aspect ratio). Low aspect ratio cracks tend to close more easily than high aspect ratio pores at increasing hydrostatic pressure, therefore the latter impede permeability reduction. In fact, over the investigated range 5–90 MPa, porosity of BS samples decreases by only 4%, compared to the 21% porosity reduction found in Crab Orchard sandstones (COS, less porous and permeable, with a mixture of cracks and pores). Over the same pressure range COS experiences a permeability reduction of more than 90%, in perfect agreement with the inverse relationship between lithostatic pressure and permeability (Benson et al., 2005).
A slight dependence of BS permeability on effective pressure has been observed in two recent studies. Benson et al. (2006) noted a small permeability decrease with increasing effective pressure, associated to the decrease of crack density. Although the equant-pores provide the largest contribution to the bulk permeability, the slight permeability reduction at higher pressure is mainly caused by change in microcrack permeability. Dautriat et al. (2009) also discovered a slight, non-linear change in BS permeability with applied pressure, with the parallel-to-bedding permeability decreasing more than the perpendicular-to-bedding permeability. In addition, Dautriat et al. (2009) demonstrated that end effects at the interface between sample and loading piston led to localized compaction damage at the sample surface, which caused significant permeability reduction. However, by measuring radial permeability and so bypassing the end surfaces, the measurement of permeability is not affected by end effects.
An increase in differential stress (\({\sigma }_{diff}={\sigma }_{1}-{\sigma }_{3}\)) typically leads to an initial compaction phase and permeability reduction, followed by a dilation phase and ultimately by sample failure, both causing permeability enhancement (Guéguen & Palciauskas, 1994). However, Dautriat et al. (2009) observed no permeability increase during the dilation phase. They did report a minor permeability increase at sample failure, but permeability still remained lower than at initial conditions. Overall, permeability decreased once the differential stress has been reduced to its initial value, implying that the permeability reduction due to compaction was greater than the increase during failure. This decrease, mostly perpendicular to the sample’s axis, has been associated to the formation of the shear band, followed by sliding and grain crushing along it. Although the fault gouge may not significantly affect the permeability of the whole sample (Wang et al., 2020), the permeability measured across a damage zone is highly reduced (Dautriat et al., 2009a; Eccles et al., 2005).
The role of strain in both plastic and ductile regimes has been investigated by Vajdova et al. (2004), where BS samples underwent significant axial strains up to 14%. Once failure or stress plateau occurred, BS either experienced strain-softening at low effective pressure or strain-hardening at high effective pressure with the formation of shear localization and compaction localization respectively. Similarly, to the case of differential stress, permeability continues to decrease by around one order of magnitude after formation of a fracture as more grain crushing is induced on the sample at elevated axial strain. In addition, when the sample does not fail, the formation of compaction bands in the plastic regime also impedes the fluid flow through the sample, causing permeability reduction by up to 3 orders of magnitude. This proves that even thin bands of low permeability can cause considerable decrease in bulk permeability when the flow intersect the low permeability band at high angle.
Mineral assembly also contributes to the evolution of permeability. In fact, the presence of clay minerals, reduces the permeability by clogging pore spaces when dislodged from their original positions at high flow rate, even with low clay concentrations as in BS (Tchistiakov, 1999).
With increasing depth, effective pressure, differential stress and lithostatic pressure are not the only variables that vary. Pore pressure change has contrasting effect on permeability compared to a change in effective pressure: while the latter tends to close pores and cracks, the former tends to open these. An increase in temperature may either induce thermal microcracking (leading to higher permeability), thermal expansion of the mineral matrix or dissolution and recrystallization reactions (both leading to lower permeability). Pressure conditions, rock microstructure and mineral assembly determine which mechanism eventually dominates (Gaunt et al., 2016; Guéguen & Palciauskas, 1994). In addition, rocks may undergo a complex stress history, with cycles of loading and unloading, which affects rock properties. Despite being a common benchmark material in geomechanics, the effects of all of these variables on permeability have yet to be investigated in BS, even while having been investigated on various other rocks (Coyner, 1984; Gaunt et al., 2016; Gehne & Benson, 2017; He et al., 2018).
Therefore, the objective of this study aims at closing the above-mentioned gaps, by performing laboratory experiments and studying both individually and collectively the variables affecting the permeability of Bentheim sandstone at increasing depths.