Pore structure–transport relationships in the Bowland Shale Open Access

Improved knowledge concerning shale rocks is important because of their involvement in oil and gas production, gas storage and carbon dioxide sequestration (Kim et al. 2017; Liu et al. 2019). Shale rocks can be hydrocarbon sources, reservoir rocks, or inter-layers and seals. The demand for oil and gas has continued to rise and there is currently a growing global energy demand which has led to the depletion in conventional oil and gas reserves. Renewable energy, however, is still in its formative years, particularly the ability to store energy generated outside of peak hours, so cannot be considered, as yet, a reliable source. At the time of writing, we are amidst a global energy transition, where unconventional natural oil and gas have become an invaluable resource to the bridge the gap from conventional to renewable energy production. Technology development has meant shale gas production has been commercially deployed, and, over the past 10 years, there has been a shale gas production boom in the USA (Barsotti et al. 2016; Yu et al. 2016). There is also the potential for shale gas production in the UK (Andrews 2013).

The gas-in-place in shale reservoirs exists as both bulk gas within the pore lumen, but also as adsorbed phase on the pore surface. The pore structure of shales is complex and multi-scale, with pores ranging in size from macroscopic faults and fractures down to atomic-scale gaps between clay layers. The nature of the pore network will determine producibility of the gas. However, many shales are poorly characterized. The pores are, generally, in the nanometre range and classified as micro-, meso- and macro-pores defined by the ranges <2 nm, 2–50 nm and >50 nm respectively (Thommes et al. 2015). Shales also contain larger-scale, complex fracture structures that are in the micrometre range. Pores can be further characterized as inter- or intra-particle pores (Li et al. 2016). The properties of shales (pore size, shape, connectivity, pore wall roughness, mineralogical composition), and their interaction with the key adsorbate properties (wettability, molecular size and polarity), influence the nature of the gas adsorption isotherm, yet a fully quantitative understanding has not been fully established (Barsotti et al. 2016). This multi-scale complexity presents a challenge to pore structure characterization which necessitates the development of new methodologies and/or techniques. In particular, it is necessary to know how pore structures on different length-scales relate to each other.

Hence, multi-scale methodologies, often utilizing two or more imaging modalities, that can bridge much of the requisite length-scale range have been proposed by workers such as Keller et al. (2013), Ma et al. (2016, 2017, 2019) and Saif et al. (2017). However, the multiscale imaging studies of Bowland shale samples have had shortest length-scale resolution limited to c. 1 nm and 2D, which misses the smaller microporosity and its 3D connectivity (Ma et al. 2021). It will be seen that pores of these smaller sizes are key to controlling the accessibility of the larger voids in the Bowland Shale samples studied here. In addition, given the limitations on field-of-view and sampled volume at the highest resolution, some sort of scale-up method is required. The determination of the appropriate sampling volume is often based purely on the volume fraction of different phases. This assumes that an unambiguous classification of different phases at a given length-scale is possible, and that phases so-identified as similar at one scale, are actually similar at smaller length-scales. The degree of heterogeneity in short length-scale properties, even for supposedly identical phases, over larger length-scales can be so large as to make statistically representative sampling via imaging impractical, and prevent simple scale-up methods. The void space properties (such as pore sizes, connectivity etc.) within grains of supposedly similar phase can be very different (Rigby 2018, 2020). Even with supercomputers it is currently not feasible to examine and reconstruct every grain of each phase in even a small sample volume. Indirect methods (such as gas sorption and mercury porosimetry) allow sampling of much greater volumes.

In contrast, gas overcondensation experiments are one of the very few techniques that can be used to study the pore structure of shales from micrometre length-scales down to the very smallest nanoscale (<2 nm) porosity, below the resolution limit of many imaging techniques, all in one experiment on a macroscopic sample (Rigby 2020). However, in previous work in the literature, the type of gas sorption experiment conducted, and data thereby obtained, typically consisted of a boundary adsorption isotherm only up to a restricted maximum pressure, followed by a pseudo-boundary desorption isotherm that is, actually, merely a descending scanning curve because complete pore-filling with liquid-like condensate was not achieved at the top (high-pressure end) of the adsorption isotherm. Therefore, conventional gas sorption alone cannot probe the complete pore size range up to large macropores. Hence, it cannot deliver information on the inter-relationship between pores from both ends of the wide length-scale range present in many shales, namely very large pore bodies (with radii >100 nm) and very narrow necks with sizes of a few nanometres or less, well below the resolution of many imaging methods. The upper cut-off in pore size that can be studied with conventional gas sorption is limited by the highest ultimate pressure obtained in the experiment. This is often truncated well before saturation to avoid flooding the apparatus with bulk condensate. However, the overcondensation method allows the full boundary desorption isotherm to be obtained even for samples where complete pore-filling is not achieved at the top of the adsorption isotherm during conventional experiments (Aukett and Jessop 1996; Murray et al. 1999). Hence, overcondensation can be used to study macroporosity without the concerns of potential crushing of samples arising with mercury porosimetry, and probe its inter-relationship with very small pores (Rigby et al. 2020; Pitcher et al. 2021). Previous studies of shales using only conventional gas sorption thus often miss out a large amount of the macroporosity entirely, or try to stitch-together data from mercury intrusion and gas sorption. This latter strategy is fraught with issues around using mutually consistent pressure-to-pore size conversions such that the pore size distributions (PSDs) are merged properly, even assuming that the correct branch of the sorption isotherm has been used to ensure consistency (i.e. desorption).

In addition to restrictions on the pressure range studied, conventional gas sorption experiments are also often limited to just the boundary curve isotherms. However, gas sorption is a much richer source of information on porous shale structures than just the boundary curves, since scanning loop experiments can also be performed (Barsotti et al. 2020; Rigby et al. 2020). Scanning loops consist of experiments where the direction of change of pressure steps on a boundary curve is itself changed at some chosen pressure point, and then proceeds in the new direction for a chosen pressure range before once more reversing the direction of pressure changes back to the original direction. Scanning loops can be used to probe the pore geometry and inter-connectedness of the pore network (Rigby et al. 2020). In this work, scanning loops will be used to probe the spatial pervasiveness of the very large pore bodies filled only by overcondensation, and the particular neck sizes that guard these pore bodies.

Gas sorption, even with just one adsorbate, is sensitive to many aspects of a surface of an adsorbent (Rigby 2020). The early stages of adsorption up to a monolayer are sensitive to the chemical nature of the surface through the heat of adsorption. The multi-layer region is sensitive to surface roughness through its effects on the numbers of adsorption sites possible in each successive layer of adsorbate. Different surfaces can often be distinguished by different combinations of these properties. Gas sorption can thus be used to probe the nature of the accessible porosity, and this capability will be used in this work. The combination of different adsorbate probes allows more of the complexity of the surface to be probed (Rigby et al. 2020). In this work both nitrogen and carbon dioxide will be used to probe the surface of the shale samples.

The extent of the penetration of carbon dioxide injected into shale rocks, and the production of methane from shale reservoirs, are, besides pore structure, also limited by the rate of mass transport within the rock. Mass transport is typically studied using gas uptake kinetics and permeability experiments. However, mass transport rates can also be inferred from adsorption calorimetry experiments (Auroux 2013), but this technique has rarely, if ever, been applied to shale rocks. The kinetic parameter from calorimetry is particularly related to the accessibility of the adsorption sites because the heat-flow arises from the heat of adsorption evolved when a molecule settles on an adsorption site. In this work adsorption calorimetry will be used to study mass transport in the different types of Bowland shale rocks. The kinetic parameter from calorimetry will be compared with the mass transfer rate from kinetic mass uptake experiments, and can, thereby, be used to mutually validate each method.

The complex structure and chemistry of shales means that sample preparation before some types of characterization is delicate as the sample can be very sensitive to preparation conditions (Holmes et al. 2017; Rigby 2020). The variability and heterogeneity of shale rocks make general prescriptions for sample pre-treatment difficult, and idiosyncratic approaches often need developing for each type of new material. It will be seen that some types of Bowland shale are very susceptible to giving rise to different results depending upon sample preparation, due to particular components of the rock.

This chapter first describes the materials and methods used in this work. Then the theory required to interpret the gas sorption and mass transfer experiments is described. This work will show how gas overcondensation and scanning loop experiments can deliver substantial additional information beyond that possible for conventional adsorption experiments even for macroporous samples inaccessible to mercury intrusion porosimetry. In addition, the novel method of adsorption calorimetry coupled with mass uptake experiments will be used to assess the accessibility of the void space and its sensitivity to saturation levels.

The three samples studied in this work were obtained from the British Geological Survey, Keyworth, UK. They were originally taken from the Preese Hall Well 1 in northwestern England, as shown in Table 1. The samples studied here are denoted Above Marine Band, Marine Band and Below Marine Band.

The Bowland Shale was deposited during the Carboniferous (Visean to Bashkirian) time period, and makes up a part of the Craven Group; it overlies the Pendeleside Formation and is overlain by the Millstone Grit. Data on the Bowland Shale are known from a combination of outcrop data and subsurface borehole data across the north of England, Isle of Man, parts of North Wales and the English Midlands.

During the depositional period for the Bowland Shale, sea-level fluctuations led to the sedimentary successions developing in a cyclical fashion with non-marine and marine shales. Marine shales make up the minor bands in the sequence and are associated with maximum flooding surfaces and the maximum rate of sea-level rise (Gross et al. 2015; Hough et al. 2014). There is significant interest in this cyclicity and the consequential variations in total organic carbon throughout the cycle because of where certain areas may be of a greater or lesser prospect for oil or gas production.

A Micromeritics 3Flex instrument was used for conventional sorption experiments, using nitrogen (at 77 K) and carbon dioxide (at 273.16 K) as adsorbates, over the relative pressure ranges 0–1.0, and 0–0.035, respectively, for shale chip samples of characteristic sizes of 3–5 mm. The nitrogen sorption technique is used to measure pore sizes in the range of 2–50 nm; although the analysis can provide data for larger pore sizes, it is not possible to be confident that complete filling of these pores has occurred. Hence, nitrogen overcondensation experiments were also performed on a Micromeritics ASAP 2020 physisorption analyser to probe the larger pore sizes and upper end of the hysteresis. In the overcondensation experiment, the pressure is increased above the standard vapour pressure of nitrogen, which should facilitate condensation such that even the largest pores are filled with liquid nitrogen at the start of the desorption isotherm. With the overcondensation adaptation to the standard gas adsorption technique, it is possible to analyse pores that are greater in size than c. 50 nm. Furthermore, the overcondensation experiment also incorporated scanning loops. The ascending branches of two scanning loops were initiated at relative pressures of 0.5 (henceforth denoted scanning loop 1, SL1) and 0.8 (SL2), respectively, on the overcondensation boundary desorption isotherm, and the descending branches of both loops were initiated at a relative pressure of 0.995. The pore radii corresponding to these relative pressures from the Broekhoff and de Boer (1967, 1968) method for hemispherical menisci are 2.6 (SL1), 6.4 (SL2) and c. 300 nm, respectively.

Secondary analysis was carried out on an Autosorb iQ – Chemisorption (& Physisorption) Gas Sorption Analyser (iQ-C/MP/Kr/MS) from Quantachrome Instruments coupled to an in-situ mass spectrometry and calorimetry system (Setaram SenSys EVO 3D TG-DSC) with carbon dioxide at 283.15 K over the relative pressure range of 0–0.027 (lower pressure reached due to increased temperature). The coupling of these systems provides the data to analyse the system kinetics and heat of adsorption at each pressure step.

As part of the analysis conditions, the degas and equilibration times were varied to investigate the effect of sample pre-treatment on the results. Experiments were conducted where the intensity of the thermal pre-treatment was varied in terms of temperature and time, and the equilibration time during the gas sorption experiment itself was also varied. In this way the impact of any degassing on the pore structure and its subsequent accessibility can be assessed. The primary aim is to investigate the pore properties and characterization of the samples, as opposed to measuring the impact of mineral swelling on potential production and storage uses.

Shale samples were pre-treated in a range of different ways before adsorption experiments. Samples were given either no thermal pretreatment at all (just evacuation to vacuum), or were degassed at 110°C for 16 h overnight, or degassed at 140°C for 3 h, or degassed at 140°C for 16 h, and then degassed at 140°C for a further 3 h after initial degassing and a nitrogen sorption experiment. Nitrogen sorption experiments were conducted with equilibration times of either 20 s or 60 s.

A Micromeritics AutoPore IV 9500 was used for low- and high-pressure mercury intrusion porosimetry at ambient temperature and constant volume. The low- and high- analysis ports take the sample from atmospheric pressure, to under vacuum, and then to 207 MPa (low-pressure) and 414 MPa (high-pressure). Mercury intrusion porosimetry enables the analysis of macropores, but only measures the throat size of the pore and not the body size (which gas adsorption does). The mercury is also only able to access pores that have throat sizes >4 nm, which can lead to very low intruded volumes in samples that are dominated by micro-pores or fine meso-pores.

SEM MLA was carried out on an FEI Quanta 600 (operated at 20 kV, working distance of 13 mm and spot size 7) equipped with mineral liberation analysis software. This enables the quantification of sample mineralogy by taking several energy dispersive X-ray (EDX) points that are associated with a specific dispersive X-ray spectra and can be matched to known minerals from a mineral database. The necessity of comprehensive mineralogical understanding is such that the adsorptive properties of the samples can be thoroughly understood and analysed.

The homotattic patch is based on the understanding that different materials will have different sorption behaviours based on their surface chemistry. Shales have a very heterogeneous surface formed of organic and inorganic minerals. In this work, the homotattic patch theory will be used to separate the contributions to adsorption from each of the organic and inorganic matter phases in the shale. The homotattic patch models used represented adsorption on the inorganic phase using the fractal BET equation, or the FHH isotherm, while the organic phase was represented by an empirical fit to an experimental isotherm for a pure kerogen sample extracted by acid-dissolution of the inorganic matrix from a similar shale.

The thermokinetic parameter is thought to characterize the accessibility of adsorption sites, since it is obtained from the heat evolved when molecules reach their adsorption sites (Auroux 2013). The LDF model is thought to particularly characterize the limitations arising from surface barriers (Rigby 2020).

As can be seen from Figure 1, the Bowland Shale samples analysed in this work are clay dominated with the presence of some silicates (predominantly quartz) and a variable quantity of carbonates (limestone). Considering the aforementioned depositional environment of the samples, the mineralogy supports the locations from which they were taken. The Below Marine Band represents a period of shallowing sea levels where the quantity of carbonates is increasing as the carbonate platform begins to form, although deposition is still dominated by the transport of mud sized particles. The Marine Band is a period of the lowest sea level where there was a greater carbonate platform and less input from mud sized particles in hemipelagic flows. The sea level then fluctuates again and increases moving towards a maximum flooding surface in the Above Marine Band sample, during this time there is a much greater input of sediment and results in a clay dominated sample with very little carbonate content.

Figures 2 to 4 show typical scanning electron microscopy (SEM) images of the three Bowland Shale samples. It can be seen that the texture is dominated by clay particles, but also with coarser quartz and calcite grains throughout the samples. With decreasing depth of origin of the shale, the coarseness of the quartz and calcite grains decreases, and they are more aligned with a particular direction (see Fig. 2). While visual inspection of the images suggests a similar incidence of total organic carbon (TOC) in the Below Marine and Marine Band samples, there is a much greater quantity of (visible) TOC in the Above Marine Band sample. The Above and Below Marine Band samples exhibit some suggestion of an ordering in the TOC distribution, where the long axis of particles is aligned in the same direction, but this is not seen in the Marine Band sample, where the distribution and direction of TOC is non-uniform. Additionally, with decreasing depth there is an increase in the quantity of pyrite within the samples, which indicates an excess quantity of iron and sulfides within an anoxic environment, as in the presence of oxygen iron oxides such as haematite would have preferentially formed.

At the resolution of these SEM images it is not clear whether there are any biogenic carbonate inputs from fossils or tracks, and it also appears that all carbonate inputs are as a result of sedimentary deposition and not precipitation. Consequently, it is likely that, in this particular area, a shallow marine environment may have not formed, or have had time to form, and lead to the preservation of any fossil evidence.

Nitrogen sorption isotherms were obtained at 77 K for samples of the Marine Band shale, that had previously been exposed to the atmosphere for 8 days, utilizing a variety of pre-treatment and experimental conditions, namely either no thermal pretreatment at all (just evacuation to vacuum) and equilibration time (ET) of 20 s (condition #1), or degassed at 140°C for 3 h and ET = 20 s (#2), or degassed at 140°C for 16 h and ET = 20 s (#3,), and then degassed at 140°C for a further 3 h after initial degassing and nitrogen sorption experiment before conducting a further nitrogen sorption experiment with ET = 60 s (#4,). From Figure 5, it can be seen that as the harshness of the thermal pre-treatment conditions increases through conditions sets 1–3, the degree of low-pressure hysteresis increased. However, for conditions set 4, the low-pressure hysteresis is lower. It is noted that the times for equilibration of the first data-point in each of the isotherms 1–4 in Figure 5, were 54, 119, 214 and 835 min, respectively. The micropore volumes from these initial datapoints were 0.046, 0.180, 0.282 and 0.497 μl g⁻¹, for isotherms 1–4, respectively. These findings suggest there is some phase, which if given minimal pre-treatment (#1) or gentle pre-treatment, probably keeps much of pre-adsorbed atmospheric moisture, which freezes at 77 K, thereby blocking access, and, thus, the phase is rendered inaccessible to nitrogen, and the nitrogen isotherm is reversible. If a progressively harsher (longer time at higher temperature) pre-treatment is applied then more water is released from this phase, and nitrogen can enter slowly, and not leave over experimental timescales, so there is increasing low-pressure hysteresis. However, this water loss or other process can be overcome with even longer outgassing and longer equilibration times (#4) but these are getting very long to be practicable for routine analysis. The narrowing of hysteresis between experimental conditions sets #3 and #4 suggests some stabilization of structure and equilibrating of isotherm can occur but these are very slow processes. Hence, in subsequent data discussed in this section a gentler pre-treatment data will be used, which means the gas sorption characterization is thus restricted to characterizing other non-swelling phases only. It is noted that the Marine Band shale sample was the least stable against varying thermal pre-treatment conditions, while the Above Marine Band (data not shown) was much more stable.

Figure 6 shows the conventional nitrogen sorption isotherms obtained for the three different shale samples, following degassing at 110°C for 16 h, and using equilibration times of 30 s for the micropore region and 20 s for the mesopore and above region. It is noted that this set of conditions results in little low-pressure hysteresis, especially compared with harsher outgassing conditions, as seen in Figure 5. It can be seen that each isotherm still has a steep step at low relative pressure associated with the filling of some microporosity, with the Above Marine Band having a larger step than the other two samples. Thereafter the adsorption isotherms increase slowly in a linear fashion. However, at higher relative pressures above c. 0.8, there is a significant rise in amount adsorbed. The top of all the conventional adsorption isotherms has a hyperbolic form suggesting that complete pore-filling has not been achieved at the ultimate pressure obtained in the conventional experiment. In all three cases, desorption commences immediately upon the reverse of the change in pressure and the top of the isotherms are reversible. However, all three isotherms show a widening of the hysteresis with decreasing pressure on the desorption branch. While the width of hysteresis remains narrow for the Marine Band and Below Marine Band shales, it widens into a large rhomboid-shape for the Above Marine Band sample. All three shale samples also have a sharp knee in the desorption at relative pressure of c. 0.45–0.5, but it is much steeper for the Above Marine Band shale.

Figure 7 shows a comparison of the nitrogen overcondensation desorption isotherm with the conventional sorption isotherms, all obtained with an equilibration time of 20 s, for all three shale samples. The sample preparation for the Marine Band sample was exposure to the atmosphere for 1 week followed by thermal pre-treatment at 110°C for 3 h. The other two samples were degassed at 140°C for 2 h. From Figure 7, it can be seen that, while SL2 crosses SL1 for the Below Marine Band shale, it does not for the Above Marine Band shale, where the ascending branch for the former merely touches the descending branch of the latter. From Figure 7, it can be seen that the height of the step at a relative pressure of c. 0.45–0.5 is increased in the overcondensation desorption isotherm, when compared to the conventional desorption isotherm, for the Above Marine Band shale. It is noted that the hysteresis width for the Marine Band shale is such that there is little gap between the desorption branch of the scanning loops and the overcondensation boundary desorption isotherm.

Figure 8 shows carbon dioxide isotherms obtained at 273.16 K for the three different shale samples, following degassing at 110°C for 16 h. It can be seen that uptake is highest for the Above and Below Marine Band samples over the pressure range obtained.

Figure 9 shows the raw mercury porosimetry data for the three shale samples. The initial steep rise in the intrusion curves for the Marine Band and Below Marine Band samples represents inter-particle intrusion. For all three samples the intra-particle intrusion at higher pressures (>1000 psi) is very small indeed. Hence, mercury intrusion seems unable to access the interior of the samples, thereby suggesting that pore openings on the exterior are all below c. 3.5 nm, which is the lower limit for the mercury porosimeter used in this work.

Figure 10 shows typical examples of raw datasets obtained from the carbon dioxide adsorption kinetics experiments to study mass transport in the shales. From Figure 10a, it can be seen that the heat-flow for a typical adsorption step, obtained by microcalorimetry, exhibits the ‘shark-fin’ like asymmetric peak form, as observed in previous studies of carbon monoxide adsorption on carbon materials (Auroux 2013). There is an initial relatively steep rise in heat released, followed by a slower decrease. It can be seen, from the good fit of equation (6) obtained to the trailing edge of the shark's fin, that it follows an exponential decay. The region fitted was well beyond the peak but stopped at the marked change in slope. In addition, from Figure 10b, it can be seen that the mass uptake response with time for the same typical adsorption step follows an exponential growth akin to the form of equation (7).

Figure 11 shows correlations of the characteristic mass transfer parameters obtained from the adsorption microcalorimetry (τ in equation 6) and mass uptake (k in equation 7) methods for the same adsorption step for a range of saturation levels of carbon dioxide during adsorption experiments on the three shale samples. The observed mass transfer coefficients k, as obtained from plots like Figure 10b, have been corrected for adsorption before plotting in Figure 11, but the correction factors were very close to unity due to low saturations in shales. It can be seen that for the lowest and medium-sized values of time constant, τ, there is a good fit to a straight line correlation with the reciprocal of the mass transfer coefficient, suggesting both methods are probing the same mass transfer process. However, there is some deviation from the linear fit for all shales at the highest values of 1/k, which correspond to the highest carbon dioxide saturation levels tested, where the time constant τ shows a tendency to plateau instead of continuing to increase.

Figure 12 shows the variation in mass transport coefficient parameter k with carbon dioxide saturation. From Figure 12 it can be seen that the rate of mass transfer declines steeply with increasing carbon dioxide saturation for all three shale samples.

It should be noted that in the calculation of carbon dioxide saturation used in this work, the determination of the Gurvitsch volume (specific pore volume from quantity of liquid adsorbate required to completely fill the void space) used nitrogen as the adsorbate. The result is that the pore volume probed could be different from that by carbon dioxide, and, when a sample has an especially low volume of pores larger than micro-pore sizes, then the Gurvitsch volume method will potentially underestimate the specific pore volume resulting in the ratio of quantity adsorbed between nitrogen and carbon dioxide to be skewed. Consequently, the trend of the data for the samples is more significant than the exact values that are derived from the analysis.

The nitrogen adsorption isotherms shown in Figure 6 were each fitted to separate fractal versions of the BET (equation 1) or FHH (equation 2) model isotherms over relative pressure ranges of 0.2–0.5 and 0.5–1.0 in order to obtain the surface fractal dimensions that applied over these two ranges, denoted D1 and D2, respectively. The cutoffs for these relative pressure ranges were selected as follows. The FHH model is only valid above monolayer coverage, where the surface film is complete, and so a lower relative pressure cutoff well above the initial knee (known as Point B (Gregg and Sing 1982) was selected. The cutoff relative pressure of 0.5 corresponds to the upper bound for cavitation effects for nitrogen (Rouquerol et al. 1999). Cavitation is associated with desorption from pore bodies shielded by very narrow necks (<4 nm diameter). The fits to the fractal BET and FHH models gave very similar results so only those for the FHH model are explicitly reported here.

Figure 13 shows the variation of surface fractal dimension D1, and the clay content, for the three shale samples. It can be seen that there is a correlation between D1 and the clay content. This might be anticipated because the fitting range for D1 corresponds to the small mesopore sizes expected in clay materials.

It was found that there was no correlation between the values of D1 and D2 for each shale, suggesting that the structures over larger length-scales are different to those for shorter length-scales, which might be expected if the origins of the porosity over these length-scales was different. Figure 14 shows that D2 correlated well with the carbonate and silicate content in the shale samples.

The Barrett–Joyner–Halenda (BJH) (Barrett et al. 1951) PSDs were obtained from the conventional nitrogen adsorption isotherms in Figure 6, and are shown in Figure 15. It was assumed that the multi-layer build-up was described by the Harkins-Jura t-layer equation and capillary condensation occurred via a hemispherical meniscus (Rigby 2020). The range of pore sizes in the BJH PSD for the cumulative surface area and pore volume parameters discussed below was 0.7 to 320 nm. It can be seen that the Above Marine Band shale had substantially more mesoporosity than the other two shale samples, particularly at the lower end of the range. The amounts of microporosity were more similar in the range probed.

Figure 16 compares the variation of the fraction of the accessible void space surface occupied by organic carbon (kerogen), according to the homotattic patch model (equation 4), across the three different shale samples with the variation in the standard BET specific surface area, and the BJH cumulative surface area and pore volume for pores with diameters in the range 320–0.7 nm. It can be seen that the accessible kerogen surface fraction shows the same trend across the three shale samples as the total surface area and pore volume parameters.

The experimental carbon dioxide sorption data shown in Figure 8 were fitted to the Toth isotherm equation, and the resultant fitted isotherm parameters are shown in Table 2. From Table 2, it can be seen that the adsorption capacity parameter is highest for the Marine Band shale, followed by the Above Marine and then Below Marine Band shales. This is different to the trend in the corresponding nitrogen sorption data, which suggested the Above Marine Band had the highest capacity. It is noted that the exponent T increases from the Above Marine Band, through the Marine Band, to the Below Marine Band. Since a T value of unity is what is expected for a homogeneous surface, this suggests the degree of surface heterogeneity, as perceived by carbon dioxide, increases from below to above the Marine Band. The surface affinity parameter b peaks for the Marine Band, with the overall pattern of variation amongst the shale samples similar to that seen for the silicates in Figure 14 

It has been seen that Bowland Shale samples present several issues for the standard methods and data analysis techniques used for common pore structure characterization techniques, such as conventional gas sorption and mercury porosimetry. However, while very little mercury can intrude in from the surface of the shale samples, it is possible to probe the macroporosity of the shale samples, and other elements of the void space, using nitrogen overcondensation. Hence, this work demonstrates that overcondensation can probe very tight shale rocks that are impossible for mercury porosimetry. A comparison of the length-scale ranges that can be probed by each technique is shown schematically in Figure 17. Overcondensation also has the advantage that high pressures are not needed to conduct the experiment, as used in mercury intrusion, which risk crushing the sample.

However, careful sample preparation is necessary for gas sorption studies. The increase in the width of the low-pressure hysteresis with increasing equilibration time in the nitrogen sorption data is opposite to the direction of change expected if mass transport limitations were causing the hysteresis. The low temperature of the nitrogen experiments means that the nitrogen mass transport is slow. This low temperature often means that the nitrogen diffusivity is small and, thence, the allowed equilibration time can be too short to enable all of the desorbed nitrogen to leave the sample in the time permitted. The low-pressure hysteresis observed here for Bowland Shale samples is in marked contrast to the lack of, or very little, low-pressure hysteresis observed for Utica and Rempstone shales studied in previous work (Rigby et al. 2020; Pitcher et al. 2021).

The sharp step down at a relative pressure of c. 0.4–0.5 in desorption isotherms is generally considered to be due to cavitation associated with the evaporation of unstable condensate in larger pore bodies shielded by pore necks of small sizes less than c. 4 nm (Rouquerol et al. 1999). It is likely that it is these small necks that prevent access of mercury to the interior of the shale samples, as they are too narrow for mercury to intrude even at the highest pressures. For the Marine Band and Below Marine Band shales the size of the cavitation step remains shallow even in the overcondensation boundary desorption isotherms suggesting only a small fraction of the larger pore bodies are shielded by very small necks. The predominantly narrow hysteresis at the upper part of the isotherms for these two shales suggests relatively small differences between pore bodies and pore necks for the largest pore sizes in these shales.

The overall form of the nitrogen sorption isotherms for the Above Marine Band sample is very different to the form of the other two shale samples. The very wide rhomboid hysteresis loop of the Above Marine Band shale data suggests a much greater fraction of the large pore bodies in this shale are shielded by narrow necks below c. 4 nm in size, compared to the other shales. The higher overcondensation data suggest that the conventional adsorption experiment misses some very large pore bodies that are shielded by necks smaller than 4 nm.

It is noted that, for the Above Marine Band shale, the conventional desorption isotherm between relative pressures of c. 0.9 and c. 0.55 is tilted down at a similar angle to the overcondensation boundary desorption isotherm, while the ascending branch of SL1 is much flatter (horizontal). These findings suggest that a large fraction of the pores that empty on the overcondensation curve between these relative pressures are the large pore bodies that can fill in the conventional adsorption experiment and are shielded by necks that have radii over a wide range from 2.5 to 13 nm. A large fraction of the pores that are only filled by overcondensation, and are thus very large (radius >100 nm), are probably ultimately shielded by very narrow necks of sizes <c. 4 nm.

The gaps between the descending (desorption) branches of SL1, or SL2, and the overcondensation boundary desorption isotherm for the Above Marine Band shale suggest that seeded percolation of vapour phase penetration is occurring for the desorption on the scanning curves (Parlar and Yortsos 1988). This means that the very largest pores left unfilled with condensate at the top of SL1 and SL2, but are filled by overcondensation, are sufficiently well dispersed and pervasive to act as efficient seed sites for desorption to commence at higher pressures than on the overcondensation desorption boundary curve. In contrast, the adsorption and desorption branches of SL1 and SL2 for the Marine Band converge with the overcondensation desorption isotherm at the top of each, suggesting less residual vapour pockets exist then. This is also consistent with the relatively wide hysteresis of the SLs for the Marine Band sample such that the desorption branches are close to the boundary desorption isotherm. The narrowness of the equivalent gaps for the Below Marine Band sample also suggests few residual vapour pockets.

The ultimate amounts adsorbed at the tops of SL1 and SL2, at a relative pressure of 0.994, for the Above Marine Band shale both greatly exceed that at the top of the conventional adsorption boundary isotherm at a relative pressure of 0.995. This suggests that some of the additional very large pores filled by overcondensation still remained filled at the springing-off point of SL1, due to the very small necks shielding them. The relative flatness of the adsorption branch of SL1 between relative pressures of 0.55 and 0.9 suggests that the additional adsorption is not due to a swelling phase. It is also noted that, for the Above Marine Band shale, the difference in amount adsorbed, at a relative pressure of 0.8, between the adsorption branch of SL1 and the springing off point for SL2 on the overcondensation desorption boundary curve is larger than the difference in ultimate amount adsorbed at the tops of SL1 and SL2 at a relative pressure of 0.994. Hence, this ultimate relative pressure is insufficient to refill some pores that were empty at the springing-off point of SL1 (relative pressure of 0.55) but were still filled at the springing-off point for SL2 (relative pressure of 0.8). This suggests that the gap between the tops of SL1 and SL2 is due to very large pores that emptied between relative pressures of 0.8 and 0.55 on the overcondensation desorption boundary curve that can only be re-filled by overcondensation. Further, this means that this small volume of very large (>300 nm) pores (0.2 μl g⁻¹) is shielded by necks in the range 2.9 to 6.4 nm.

As has been seen, the characteristic time constants from adsorption calorimetry and mass uptake measurements of mass transfer rates in the shales are very well correlated up to the (relatively) longer time-scales associated with ingress at high existing carbon dioxide saturations. Thereafter the pattern of variation of the mass transport parameters diverges, with the calorimetry time constant τ showing signs of plateauing out at a more or less constant value. This suggests that at higher saturations the mass transfer processes probed by the two different experimental techniques are different. The foregoing pore structural characterization suggests that the void space of the shales consists, to an extent, of larger pore bodies shielded by very much narrower pore necks, in an hour-glass-type configuration. Dynamic mean-field density function theory simulations of the kinetics of adsorption into carbon pore networks, consisting of pore bodies surrounded and interspersed by pore necks, suggests that the early stages of adsorption are characterized by filling of the pore necks with plugs of adsorbate (Woo and Monson 2003; Desouza and Monson 2021). Thereafter, there is a slower filling process for the progressively more deeply buried pore bodies. Therefore, it is suggested, for the Bowland Shale, that adsorption proceeds as follows. The initial rapid adsorption at low saturation fills adsorption sites at narrow pore necks. However, as most of these necks become filled, access to the larger pore bodies becomes more restricted. The mechanism of adsorption then consists of the adsorbate initially adsorbing near a neck site, thereby releasing most of the heat of adsorption. However, this adsorption is metastable because a lower energy configuration of adsorbate involving more deeply buried adsorption sites is possible. Hence, there then follows a slower reconfiguration of the adsorbed phase to a more stable arrangement. This process releases much less heat of adsorption over a longer period than the initial adsorption, and so is harder to detect with calorimetry, but can be detected by mass uptake methods, as the re-arrangement of adsorbed phase makes more room for further uptake. If this model is correct then the saturation levels where the calorimetry time constant plateaus out for a given shale characterizes the accessibility of the pore network in the shale, and the degree of shielding provided by the aforementioned pore necks. The earlier plateauing of the time constant comparison plot in Figure 10, and the more rapid decline in k values with saturation, for the Above Marine Band shale suggest that the pore necks most severely restrict the accessibility of the interior void spaces in this shale, compared with the others. This is consistent with the higher cavitation step in the nitrogen desorption isotherm for the Above Marine Band shale. This also has implications for gas flow through this shale, and, thus, expected relative producibility.

It has been seen that gas overcondensation can be used to study macroporosity within shale samples impenetrable by mercury intrusion and unobtainable by conventional gas sorption. The overcondensation data and mass transfer studies both suggest the presence of ‘hour-glass’ type pore size configurations. There is a general decline in macroporosity and its accessibility from above to below the Marine Band in the Bowland shale samples studied here. In the Above Marine Band, in particular, some very large macropores are shielded by very narrow pore necks which significantly restrict mass transport. This is confirmed by the lack of penetration possible for mercury intrusion.

SPR, DJL and EP also thank the University of Nottingham for the award of a partial PhD studentship. The authors thank Martin Corfield and Elisabeth Steer (of the Nottingham nmRC) for assistance with acquiring the CXT and SEM data, respectively. We would also like to thank Schlumberger for the kind donation of a kerogen sample.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

EGP: data curation (equal), methodology (equal), writing – original draft (supporting), writing – review & editing (supporting); RSF: methodology (equal), writing – review & editing (equal); DJL: investigation (equal); SPR: conceptualization (equal), investigation (lead), methodology (equal), supervision (lead), writing – original draft (lead), writing – review & editing (lead).

This work was supported by the Natural Environment Research Council [grant number NE/M00578X/1].

The datasets generated during and/or analysed during the current study are not publicly available due to these data being part of an ongoing study and are thus currently unavailable, but are available from the corresponding author upon reasonable request.