During geotechnical drilling operations (e.g. to access brine deposits), hydrocarbon and non-hydrocarbon fluid reservoirs, aquifers or geothermal fluids, a wellbore is drilled through the overlying rock units. As illustrated in Fig. 1, during drilling operations, a drill bit (which is attached to the end of a drill string) bores its way down through sediment and bedrock to create the wellbore.

Figure 1.

A schematic of the lower wellbore. Drilling fluid is pumped through the drill string and exits the drill bit through its head to lubricate/cool itself, and the return flow transports rock cuttings to the surface, where they are separated out. Credit: Provided by C. Sellick.

Drilling fluid is pumped through the drill string and exits through nozzles in the drill bit, which, in addition to lubricating and cooling the bit and transporting cuttings to the surface, plays an important role in maintaining wellbore stability and limiting fluid exchange with the surrounding formation (Caenn et al., Reference Caenn, Darley and Gray2011; Cook et al., Reference Cook, Growcock, Guo, Hodder and Van Oort2011; Civan, Reference Civan2015). Drilling fluids may be water-based, oil-based or synthetic oil-based, with water-based fluids now receiving increasing attention due to environmental considerations and advances in their formulation (Hale & Mody, Reference Hale and F.K1993; Friedheim et al., Reference Friedheim, Guo, Young and Gomez2011; Fink, Reference Fink2015).

Wellbore instability is a significant challenge during drilling operations (Cheatham, Reference J.B1984; van Oort, Reference van Oort2003; Anderson et al., Reference Anderson, Ratcliffe, Greenwell, Williams, Cliffe and Coveney2010; Caenn et al., Reference Caenn, Darley and Gray2011; Civan, Reference Civan2015; Chan et al., Reference Chan, Yadav and Mikulencak2019), and drilling through different types of rocks comes with new and specific challenges. Wellbore instabilities account for close to 10–20% of associated drilling costs, costing ∼1–6 billion USD per year worldwide across the oil and gas industry alone (Albukhari et al., Reference Albukhari, Beshish, Abouzbeda and Madi2018).

Shale is a type of sedimentary rock found in marine basins (Gholami et al., Reference Gholami, Elochukwu, Fakhari and Sarmadivaleh2018). It is a heterogeneous, argillaceous clay mineral-containing rock with low permeability and pronounced fissility parallel to bedding (Hawkes et al., Reference Hawkes, McLellan, Ruan, Maurer and Gahan2000; Nichols, Reference Nichols2009; Caenn et al., Reference Caenn, Darley and Gray2011; Wilson & Wilson, Reference Wilson and Wilson2014). In the context of this paper, the term ‘shale’ is per the industry definition: a fine-grained sedimentary rock primarily composed of silt and clay, broadly encompassing any mudrock (Nichols, Reference Nichols2009; Wilson & Wilson, Reference Wilson and Wilson2014). This dominant clay mineral composition has been identified as a significant cause of shale instability (O’Brien & Chenevert, Reference O’Brien and M.E1973; Wilson & Wilson, Reference Wilson and Wilson2014; van Oort et al., Reference van Oort, Hoxha, Hale, Aldin and Patterson2016), whereby there are two types of interaction: mechanical processes, which are independent of time and linked to the density of the drilling fluids; and physicochemical processes (Zeynali, Reference M.E2012; Gholami et al., Reference Gholami, Elochukwu, Fakhari and Sarmadivaleh2018), which are related to the shale–water-based fluid interaction over time. In oil and gas geotechnical drilling, shale formations encompass close to ∼75% of intervals penetrated. Problematic shales are the primary cause of wellbore instability and account for more than 90% of all instability (Steiger & Leung, Reference Steiger and P.K1992; van Oort et al., Reference van Oort, Hale, Mody and Roy1996; Wilson & Wilson, Reference Wilson and Wilson2014; Gholami et al., Reference Gholami, Elochukwu, Fakhari and Sarmadivaleh2018). The problem is also potentially very costly to operators, as in the last two decades it has been reported that shale instability has been responsible for additional costs of up to an estimated 1 billion USD per year (Zeynali, Reference M.E2012).

Shales dominated by smectitic minerals are highly reactive to aqueous fluids, with smectite clay-induced swelling a primary cause of shale instability. However, there are many non-smectitic formations (often illitic and mixed-layer clays) that experience dispersive-related instability instead of swelling (Wilson & Wilson, Reference Wilson and Wilson2014). Clay swelling reduces wellbore strength, which results in ‘stuck pipe’, wellbore closure (causing ‘tight hole’) and potential collapse and cave-ins; the hydration of drill cuttings, which enables them to adhere to the drill bit assembly (‘bit balling’) and so reduces penetration time; and, finally, clay dispersion, which results in damage to the wellbore wall (van Oort, Reference van Oort2003; Anderson et al., Reference Anderson, Ratcliffe, Greenwell, Williams, Cliffe and Coveney2010; Friedheim et al., Reference Friedheim, Guo, Young and Gomez2011; Gholami et al., Reference Gholami, Elochukwu, Fakhari and Sarmadivaleh2018; Chan et al., Reference Chan, Yadav and Mikulencak2019).

All the clay mineral types listed earlier adsorb water, but smectites (montmorillonite) assimilate more into their structure than the other classes during swelling. It is because of this that many academic and industrial experiments related to clay or shale swelling use sodium montmorillonite clays to monitor volume changes.

There are two well-acknowledged swelling mechanisms:

1. (1) Crystalline swelling (also referred to as ‘surface hydration’): this results from adsorption of sequential monomolecular layers of water onto the basal crystal surfaces on the external and internal (expanding lattice) layer. Exchangeable cations influence crystalline swelling because many of the cations are already hydrated and have high hydration enthalpy, and the cations charge-balance permanent and temporary charges at the clay mineral surface – except for Na⁺ and Li⁺, which lightly bond and often diffuse away.

2. (2) Osmotic swelling: this occurs when the concentration of cations between the layers is higher than the bulk aqueous solution (Caenn et al., Reference Caenn, Darley and Gray2011). Accordingly, the c-spacing (defining the interlayer separation) increases as water is drawn in between the layers, thereby allowing for the formation of the diffuse double layer (DDL).

Osmotic swelling usually results in a much more significant increase in vertical displacement (i.e. swelling) than that seen in crystalline swelling. However, the repulsive forces amid the layers reduce in the osmotic rather than the crystalline region. The interlayer cations within clay minerals charge-balance the negatively charged clay platelets and may be exchanged according to the Hofmeister series (Underwood et al., Reference Underwood, Erastova and Greenwell2016). Dissolved cations in fluids contacting the clay minerals, such as Na⁺ from NaCl brines, move through the macropores and solution to balance the ion concentration. However, this movement is restricted by negatively charged clay mineral surfaces, and the interplay between diffusive and electrostatic forces leads to an ion distribution next to the surface of the clay (Caenn et al., Reference Caenn, Darley and Gray2011; Civan, Reference Civan2015). This restricted movement and associated change between forces together are termed the ‘diffuse double layer’, or DDL. Wilson & Wilson (Reference Wilson and Wilson2014), through a review of the literature, postulated that the narrow pore channel sizes in compacted clay minerals and shales were in a similar size range to that of the DDL, and that hydration of this during water ingress would result in rapid repulsion forces pushing the pores apart, thereby resulting in swelling, even for non-smectite-containing, clay-rich shales.

Clay swelling has traditionally been measured using a ‘linear swelling test’, whereby a shale sample (either a core or compacted tablet) is positioned into a holder, pre-loaded with a particular mass and then submerged in the fluid of interest. The swelling is then measured as a change in height of the tablet (Lalji et al., Reference Lalji, Ali, Z.U.H and Jawed2021). The potential for clay swelling has also been assessed via the ‘capillary suction time’ test, whereby a slurry of clay and water is placed on a filter paper, and the time for the water to move across the filter paper is measured, giving a qualitative indication of swelling potential (Dhar et al., Reference Dhar, Beg, Saxena and Sharma2021). These methods, while simple to carry out, lack the ability to produce high-resolution, short-term results to indicate what might happen when a shale initially contacts the fluid of interest.

Although there is a comprehensive literature on clay swelling at equilibrium, there are relatively few studies examining the short-term kinetics of clay swelling, especially in systems containing both swelling and non-swelling minerals. Understanding this early-time behaviour is important because wellbore instability may initiate before equilibrium conditions are achieved, and existing swelling tests and data generally lack details on early-time swelling kinetics.

In this work, we specifically set out to investigate the short-term swelling of model shale pellets using a non-contact linear swell meter capable of high-resolution measurements during initial fluid uptake. By systematically varying quartz content, compaction conditions and fluid salinity (deionized water and NaCl brines), we evaluate the factors controlling early-stage swelling kinetics in compacted bentonite–quartz tablets and their implications for shale–fluid interactions.

Methodology

Materials

The clay mineral used in this study was montmorillonite (as Na-bentonite), and this powder (moisture content 9–11%) was combined with varying mass percentages (0%, 10%, 20% and 30%) of quartz with different grain sizes, giving a total powder mass for each tablet of 2.5 g.

The Wyoming Na-bentonite GDM was purchased from Steetley Bentonite & Absorbents Ltd, Retford, UK. The X-ray diffraction (XRD) trace of the bentonite used is as given in Erdogan et al. (Reference Erdogan, Whitford, Underwood, Sellick, Patel, Skipper and Greenwell2023), and previous combined modelling and experimental studies represented the montmorillonite fraction with a Wyoming montmorillonite composition with a cation-exchange capacity of 73.8 meq 100 g^–1 (Ratcliffe et al., Reference Ratcliffe, Williams, Anderson, Greenwell, Cliffe, Suter and Coveney2009). The same study reported a Brunauer–Emmett–Teller (BET) surface area of 30.3 m² g^–1 for the GDM bentonite. The electrolyte used in this study was sodium chloride (≥98%; VWR International), and the quartz was in the form of sand (pure, 40–100 mesh; Arcos Organics). Swelling tests were run using 200 mL deionized water (18.2 MΩ∙cm) and 0.5 M and 2 M NaCl brine solutions.

Particle sizing

The quartz was sized by sieve to obtain size fractions of 125–250, 250–300 and >300 µm. These sized fractions, along with a sample of dry, powdered Wyoming bentonite (PWB; used as received with no additional sizing), were then analysed using a Morphologi® G3 particle characterization system from Malvern® Instruments to characterize quartz and bentonite particle size and shape to a resolution of 0.2 µm up to several millimetres via image analysis. Morphologi® G3 is an automated optical image analysis system that determines particle size and shape from high-resolution particle images. Analysis of dry powdered bentonite and quartz particles measured 1000–10 000 individual particles.

In image analysis, the principal method to determine the size of a three-dimensional particle is to convert the image to a two-dimensional shape and measure its circle-equivalent (CE) diameter, as illustrated in Fig. 2.

Figure 2.

Schematic for the process used during image analysis. (a) A 3D image of a quartz particle used in this study with measurement parameters. (b) The 3D image is converted to a 2D shape with the same perimeter as the particle. (c) The 2D image is converted into a circle with the same area, where the diameter is representative of the particle size.

Convexity is the convex perimeter (Fig. 2a) of the particle exterior divided by a measured edge, and elongation is defined as 1 – aspect ratio (width divided by length). Circularity (Equation 1) is the measure for the overall form of an object, and it describes how close a particle is to a ‘true’ circle:

(1)\begin{equation}{\text{ }}C = \frac{{2\sqrt {{{\pi }}A} }}{P}{\text{ }}\end{equation}

where C is the circularity, A is the area and P is the perimeter. Equation 1 describes the circumference of the area of the two-dimensional particle, which has been converted to an equivalent-area circle and is divided by the actual perimeter of that particle. This measure is sensitive to surface roughness and the total shape.

The most used metrics when using particle-size distributions (PSDs) are D-values: D ₁₀, D ₅₀ and D ₉₀, which correspond to 10%, 50% and 90% of the cumulative mass, respectively.

Preparation of synthetic shale tablets

The simplified synthetic shale tablets were constructed using powdered Wyoming bentonite and quartz. The study investigated the effects of quartz content, quartz grain size, compaction pressure, compaction time and swelling solution composition on short-term swelling behaviour. The minerals were mixed using a vortex mixer at 3000 rpm for 5 min to homogenize the samples, using the compositions listed in Table 1 and the grain-size fractions detailed in Table 2. Following this, the well-mixed powder was poured into a Specac evacuable 20 mm pellet die assembly, placed into a Specac manual hydraulic press and pressurized to either 4 or 8 tonnes for either 5, 8, 10 or 30 min. The applied pressure was monitored, and the pressure was manually maintained at a constant value throughout the compaction duration. Once a tablet was made, it was placed into a desiccator for at least 30 min before running a swelling test, as the initial moisture content of the clay has been shown to have an effect on the swelling properties of compacted bentonite (Villar & Lloret, Reference Villar and Lloret2008; Ivanishin & He, Reference Ivanishin and He2025).

Table 1.

Mixtures of PWB and quartz used for the tests. For each pellet composition, the swelling tests were repeated with three grain sizes (125–250, 250–300 and >300 µm).

Table 1 Long description

The table lists four tablet compositions, each with a total powder mass of 2.5 g. PWB contains 2.50 g bentonite and no quartz (100 percent bentonite). PWB:10 contains 2.25 g bentonite and 0.25 g quartz (90 percent bentonite, 10 percent quartz). PWB:20 contains 2.00 g bentonite and 0.50 g quartz (80 and 20 percent). PWB:30 contains 1.75 g bentonite and 0.75 g quartz (70 and 30 percent). For each composition, the swelling tests were repeated with three quartz grain sizes: 125–250 µm, 250–300 µm and over 300 µm.

Table 2.

Particles used to produce quartz–clay tablets to run swelling experiments and their associated sizes and shapes measured using the Morphologi G3 particle characterization system. Values refer to D₉₀ values.

Table 2 Long description

D90 values measured with the Morphologi G3 particle characterisation system. Quartz 125–250 µm: length 10.34 µm, width 11.45 µm, CE diameter 17.29 µm, circularity 0.967, convexity 0.987, elongation 0.350. Quartz 250–300 µm: length 100.50 µm, width 75.02 µm, CE diameter 271.61 µm, circularity 0.964, convexity 0.995, elongation 0.541. Quartz over 300 µm: length 160.00 µm, width 150.11 µm, CE diameter 364.02 µm, circularity 0.890, convexity 0.993, elongation 0.433. Wyoming bentonite: length 16.32 µm, width 6.66 µm, CE diameter 8.27 µm, circularity 0.806, convexity 0.996, elongation 0.515. An ideal circle has circularity 1, convexity 1 and elongation 0; on this basis the two smaller quartz fractions are rounded to sub-rounded, the largest quartz fraction is relatively angular to sub-angular, and the bentonite particles are elongated, flat and ellipsoidal.

Swelling measurements

To measure the one-dimensional (i.e. vertical) displacement for short-term, linear swelling of (compacted) synthetic shale tablets (bentonite–quartz mixtures), a novel instrument was used: a ‘non-contact linear displacement meter’ (N-CLDM; Mathias et al., Reference Mathias, Greenwell, Withers, Erdogan, McElwaine and MacMinn2017; Erdogan et al., Reference Erdogan, Whitford, Underwood, Sellick, Patel, Skipper and Greenwell2023).

The N-CLDM (Fig. 3) uses four non-contact linear sensors to measure the distance between each sensor and a target. The sensor uses inductive technology, and the thin metal disc target influences the measurements. Therefore, before any tests, each sensor is calibrated using the N-CLDM software, which incorporates an analytical solution (Mathias et al., Reference Mathias, Greenwell, Withers, Erdogan, McElwaine and MacMinn2017) into the software. The N-CLDM software was set up in accordance with the desired time, the number of measurements to be taken per minute (high resolution of 90 readings per minute) and with the correct associated calibration before beginning a test.

Figure 3.

Schematic of (a) the N-CLDM, (b) the see-through plastic lid and (c) the sample holder with (1) sensor wires connecting to a computer with N-CLDM software, (2) a steel non-contact linear displacement sensor with thread, two nuts and a sensor at the base, (3) a target 1 mm steel disc placed on top of a pressed tablet and (4) a perforated metal sample support disc.

For each test, four identical synthetic shale tablets were made, placed on top of filter paper and placed into holders (Fig. 3c) within the N-CLDM. Sample holders were placed into locating recesses on the N-CLDM water bath shelf. The appropriate metal target disc for a specific sensor (Fig. 3c) was placed onto the pellet, and then the sensor was screwed securely into place.

A total of 200 mL of deionized water or NaCl solution was poured into the bath through a hole in the centre, whereby tablets were partially immersed, and the test was then started for the allocated time (short-term tests were run for 30 min), producing four independent sets of data (repeats). Individual tests were repeated if there were any inconsistencies (e.g. due to tablets cracking) to ensure sufficient reproducible datasets.

Tests were performed at atmospheric pressure and room temperature (∼21°C); no confining pressure(s) was applied to the experimental system, and humidity was not specifically controlled for in the present instrument prior to contact with the solutions.

Data analysis

Data produced were from 810 individual tests, producing 180 averaged datasets. To aid data analysis, two swelling parameters were considered: initial and final swelling rate. The initial swelling rate for each test was determined by calculating the average percentage displacement for each minute of the test and the displacement rate (% min^–1) for all times between 0 and 5 min, and then taking the maximum rate found between 0 and 5 min as the initial swelling rate. The final swelling rate was found by taking the averaged 24 min displacement away from the 29 min displacement (the 30 min displacement was not used as there was often few data points for this due to the test terminating at 30 min, so this point was often overly affected by noise) or, in the case in which the test was terminated before 30 min, taking the averaged percentage displacement at the sixth-to-final time measured away from the second-to-final time measured (i.e. the final 5 min excluding the final minute). The only exception to this was the test with compaction time = 10 min, compaction pressure = 8 tonnes, NaCl concentration = 2 M, quartz content = 30% and particle size >300 µm, for which the final rate was taken as the rate during the final minute of the test.

Analysis of variance

Analysis of variance (ANOVA) was conducted on both the initial and final displacement rates, with data grouped by each independent variable (compaction pressure, compaction time, particle size, percentage quartz and concentration). The analysis also included interaction terms between pairs of variables to assess combined effects (Ståhle & Wold, Reference Ståhle and Wold1989).

Linear regression

Linear regression was used to identify a linear relationship between the independent variable and the dependent variable. Linear regression is a best-fit estimate for the plotted data. This method can be extended for numerous variables by using a multiple linear regression model, as outlined by Montgomery et al. (Reference Montgomery, Peck and G.G2021). Interaction terms can also be included, allowing the model to account for combined effects between pairs of independent variables. This analysis was performed using the StatsModel library (version 0.14.4; Seabold & Perktold, Reference Seabold and Perktold2010).

Errors and assumptions

While processing data, the following exclusion criteria for tests (for each sensor repeat) were applied: if the range of vertical displacement from origin to the last point produced <20% total difference, then this test would be excluded. The excluded values amounted to only 5.5% of individual tests, but all but two of the tests yielded three or more valid sensor readings, with the final two yielding two valid readings. Similarly, for the purposes of presenting data, the average displacement data were taken across all sensors (those meeting the inclusion criteria) per minute of the experiment for each set of experimental conditions, and the 95% confidence interval for each using non-parametric bootstrapping (1000 resamples) was calculated. From this, the rate data and corresponding errors were calculated.

For statistical significance, a threshold of p-value of <0.05 was selected based upon current standard practice, representing a reasonable balance between Type I (false-positive) and Type II (false-negative) errors. The p-value is the likelihood that, based on the observed data, the null hypothesis is correct; 5% is low enough to reject the null hypothesis (i.e. no effect) and accept the alternative hypothesis (that there is an effect).

The necessary assumptions to proceed with an ANOVA were considered: (1) the assumption of ‘independence of observations’ was believed to hold given the nature of the experimental design (e.g. calibration, resetting equipment, cleaning); (2) the residuals of the data were distributed normally because the data measured real-world phenomena, which invariably follows a normal distribution; and (3) the equality of group variance was not expected to deviate sufficiently to preclude the ANOVA.

Results

Particle-size analysis

The particle-size D ₉₀ values obtained from the PSD analysis with the Malvern Morphologi G3 system are shown in Table 2.

An ideal circle has circularity = 1, convexity = 1 and elongation = 0. Therefore, the powdered bentonite and quartz particles used in this study are:

• • Wyoming bentonite: elongated, flat and ellipsoidal

• • Quartz: 125–250 and 250–300 µm, rounded to sub-rounded

• • Quartz: >300 µm, relatively angular to sub-angular

ANOVA

The initial and final swelling rates were calculated for all individual variables and pairs of variables and were assessed using ANOVA; full results can be found in Tables S1 & S2. The significant individual variables (where p < 0.05) for the initial swelling rate were found to be quartz content (p < 0.001) and NaCl concentration (p < 0.001). The significant paired variables were compaction time and pressure (p < 0.001), pressure and quartz content (p = 0.001) and quartz content and NaCl concentration (p < 0.001). Plots illustrating the variation of initial swelling rate with all of the individual variables are shown in Figs 4 & 5.

The significant variable for final swelling rate was found to be NaCl concentration (p < 0.001) only, with no significant paired variables found. However, the paired variables of compaction time and quartz content came close to the cut-off significance level (p = 0.07), so they may have a minor effect. Plots illustrating the variation of final swelling rate with all of the individual variables are shown in Figs 6 & 7.

Linear regression

The linear regression for the initial displacement rate (% min^–1) gives the following significant predictors:

• • Changing the quartz content from bentonite only to including 30% quartz increases the initial rate (p < 0.001).

• • Changing the NaCl concentration from 0 to 0.5 M or 2 M increases the initial rate (p < 0.001 for both).

Additionally, changing the compaction time from 5 to 8 min was found to be close to the level of significance regarding a decrease in the initial rate (p = 0.06). Full results can be found in Table S3.

Figure 4.

Plots illustrating the variation of the averaged initial swelling rate of the tablets under each set of experimental conditions (compaction pressure = 4 tonnes, compaction time = 5, 8 or 10 min, particle size = 125–250, 250–300 or >300 µm or bentonite only, quartz content = 0%, 10%, 20% or 30%, NaCl concentration = 0, 0.5 or 2 M). The shaded region around each line is the standard deviation of the tests.

Figure 4 Long description

A grid of 12 line plots: 3 rows are compaction times of 5, 8 and 10 minutes; 4 columns are particle sizes of 125–250 µm, 250–300 µm, over 300 µm, and bentonite-only (no quartz). Each panel plots initial swelling rate in percent per minute (y-axis, roughly 0–70) against NaCl concentration in molar (x-axis), at three levels –0, 0.5 and 2 M – joined by straight line segments, with shaded standard-deviation bands. Four lines per quartz-containing panel show quartz content of 0, 10, 20 and 30 percent (purple, blue, green, yellow); the bentonite-only column has just the 0 percent quartz line. In nearly every panel the rate increases with concentration; the 30 percent quartz line most often reaches the highest rate at 2 M (up to roughly 40–45 percent per minute), while the bentonite-only column shows the smallest overall range, roughly 5–35 percent per minute.

Figure 5.

Plots illustrating the variation of the averaged initial swelling rate of the tablets under each set of experimental conditions (compaction pressure = 8 tonnes, compaction time = 5, 8 or 10 min, particle size = 125–250, 250–300 or >300 µm or bentonite only, quartz content = 0%, 10%, 20% or 30%, NaCl concentration = 0, 0.5 or 2 M). The shaded region around each line is the standard deviation of the tests.

Figure 5 Long description

A grid of 12 line plots: 3 rows are compaction times of 5, 8 and 10 minutes; 4 columns are particle sizes of 125–250 µm, 250–300 µm, over 300 µm, and bentonite-only (no quartz). Each panel plots initial swelling rate in percent per minute (y-axis, roughly 0–55) against NaCl concentration in molar (x-axis), at three levels – 0, 0.5 and 2 M – joined by straight line segments, with shaded standard-deviation bands. Four lines per quartz-containing panel show quartz content of 0, 10, 20 and 30 percent (purple, blue, green, yellow); the bentonite-only column has just the 0 percent quartz line. Rate increases with concentration in almost every panel; 20 and 30 percent quartz (green, yellow) most often reach the highest rates at 2 M, up to roughly 50 percent per minute, while the bentonite-only column stays lowest, roughly 5–30 percent per minute.

Figure 6.

Plots illustrating the variation of the averaged final swelling rate of the tablets under each set of experimental conditions (compaction pressure = 4 tonnes, compaction time = 5, 8 or 10 min, particle size = 125–250, 250–300 or >300 µm or bentonite only, quartz content = 0%, 10%, 20% or 30%, NaCl concentration = 0, 0.5 or 2 M). The shaded region around each line is the standard deviation of the tests.

Figure 6 Long description

A grid of 12 line plots: 3 rows are compaction times of 5, 8 and 10 minutes; 4 columns are particle sizes of 125–250 µm, 250–300 µm, over 300 µm, and bentonite-only (no quartz). Each panel plots initial swelling rate in percent per minute (y-axis, roughly 0–55) against NaCl concentration in molar (x-axis), at three levels – 0, 0.5 and 2 M – joined by straight line segments, with shaded standard-deviation bands. Four lines per quartz-containing panel show quartz content of 0, 10, 20 and 30 percent (purple, blue, green, yellow); the bentonite-only column has just the 0 percent quartz line. Rate increases with concentration in almost every panel; 20 and 30 percent quartz (green, yellow) most often reach the highest rates at 2 M, up to roughly 50 percent per minute, while the bentonite-only column stays lowest, roughly 5–30 percent per minute.

Figure 7.

Plots illustrating the variation of the averaged final swelling rate of the tablets under each set of experimental conditions (compaction pressure = 8 tonnes, compaction time = 5, 8 or 10 min, particle size = 125–250, 250–300 or >300 µm or bentonite only, quartz content = 0%, 10%, 20% or 30%, NaCl concentration = 0, 0.5 or 2 M). The shaded region around each line is the standard deviation of the tests.

Figure 7 Long description

A grid of 12 line plots, laid out as in Figure 6 but for a compaction pressure of 8 tonnes: 3 rows are compaction times of 5, 8 and 10 minutes; 4 columns are particle sizes of 125–250 µm, 250–300 µm, over 300 µm, and bentonite-only (no quartz). Each panel plots final swelling rate in percent per minute (y-axis, roughly −1 to 4.5) against NaCl concentration in molar (x-axis), at three levels – 0, 0.5 and 2 M – joined by straight line segments, with shaded standard-deviation bands. Four lines per quartz-containing panel show quartz content of 0, 10, 20 and 30 percent (purple, blue, green, yellow). As at 4 tonnes, the rate typically peaks around 0.5 M – sometimes sharply, e.g. 20 percent quartz in the largest particle size – then falls back to near zero by 2 M.

The linear regression for the final displacement rate (% min^–1) gives the following significant predictors:

• • Changing the compaction time from 5 to 8 min increases the final rate (p = 0.006).

• • Changing the NaCl concentration from 0 to 0.5 M increases the final rate, but changing it from 0 to 2 M decreases the final rate (p < 0.001 for both).

All other predictors fell above the level of significance (p = 0.05) and hence were not deemed to be influential on either swelling rate. In particular, it was noted that the particle size did not appear to have any significant effect on the swelling rates. Full results can be found in Table S4.

Swelling profiles of mixed bentonite–quartz tablets

Full swelling curves are given in Figs S1–S7. Short-term swelling tests (30 min) of bentonite-only tablets produced displacement curves that usually had rapid initial swelling within the first 5 min of the experiment, after which the rate of change for displacement would either gradually reduce (<2 M NaCl) or plateau (i.e. no more swelling occurred; 2 M NaCl); this is also clear from Figs 6 & 7, where final swelling rates are lowest at 2 M for all tests carried out, indicating plateauing.

When quartz was included in the tablets, the general trends remained similar to that of the bentonite-only tablets. However, if the concentration of the swelling solution increases, ANOVA suggests quartz content has an effect upon initial vertical displacement rate. A systematic variation in the appearance of the tablets during recovery following swelling tests was observed for changing the quartz content and NaCl concentration, which is illustrated in Fig. 8.

Figure 8.

(a) Photographs of a pure bentonite pellet compacted at 4 tonnes for 5 min, swollen with 0.5 M NaCl: (1) dry (bentonite) tablet and (2) the swelling after a short-term (30 min) displacement. (b) The physical swelling properties for individual quartz–clay tablets representative of all compaction times/pressures, with quartz content (%) plotted against deionized water and NaCl solutions (0.5 and 2 M). The dashed sections indicates a wet–dry boundary.

Figure 8 Long description

Part (a) shows two photographs of a pure bentonite tablet compacted at 4 tonnes for 5 minutes: (1) the dry tablet, a smooth pale disc sitting in its holder, and (2) the same tablet after a 30-minute swelling test in 0.5 M NaCl, expanded well above the holder with a cracked, ruptured surface. Part (b) is a schematic diagram of characteristic tablet shapes after recovery. Columns are swelling solution (deionised water, 0.5 M NaCl, 2 M NaCl, left to right); rows are quartz content (bentonite only, 10 percent, 20-30 percent). An ‘increasing expansion’ arrow beneath the grid points from deionised water toward 2 M NaCl - expansion is greatest at the highest salinity, not in deionised water. Bentonite-only tablets grow taller with concentration (vertical displacement); quartz-containing tablets increasingly bulge sideways at higher concentration and quartz content (lateral displacement), with dashed lines marking a wet-dry boundary, and the most expanded combination labelled ‘slump’.

Discussion

Throughout all tests, the concentration of the NaCl solution used to induce swelling in the bentonite or bentonite–quartz tablets was seen to be the most influential factor, with p < 0.001 for both ANOVA and linear regression of both initial and final swelling rates. While higher-salinity brines are generally known to reduce clay swelling (e.g. Ye et al., Reference Ye, Zhang, Chen, Chen, Wang and Cui2014; Wang et al., Reference Wang, Yan, Su, Ye and Zhang2024), the observed increase in initial swelling rate with both 0.5 and 2 M NaCl compared to 0 M (deionized water) deviates from this expected trend. In particular, 2 M NaCl induces rapid initial swelling (high initial swelling rate), which very quickly plateaued (near-zero final swelling rate), and although the extent of the equilibrium swelling may be lower than that for deionized water, the high early displacement rate may have implications for shale stability in the short term. A similar pattern was observed for 0.5 M NaCl, where the initial swelling rate was elevated (though lower than at 2 M), but swelling continued at a higher rate than in deionized water over the 30 min test. These findings may be related to the critical salt concentration recently reported by Alkhaldi & Al-Bazali (Reference Alkhaldi and T.M2023), who reported that the swelling of two smectite-rich shales increased above 8% NaCl (1.5 M), whereas at a concentration of 4% or 8% NaCl, the swelling was supressed. These transiently increased swelling rates contrast with the well-established understanding that increased salinity reduces long-term equilibrium swelling, and they have implications for shale stability in the event of a short-term influx of brines, thus having implications for the re-injection of concentrated brines.

Considering initial swelling rate only, another factor found to be statistically significant was the quartz content of the tablets. Quartz content was not, however, found to be statistically significant when considering final swelling rate. The replacement of some of the bentonite content of the tablets with quartz, which, for the purposes of this study, can be thought of as a non-swelling inert mineral, leads to the loss of some of the tablet that can contribute to the swelling, and hence the equilibrium swelling (linear displacement) would be expected to be reduced (Saba et al., Reference Saba, Barnichon, Cui, Tang and Delage2014). However, in this study, the swelling kinetics are considered. It appears that the presence of quartz, especially at 30% (supported by the linear regression results), increases the initial swelling rate no matter the other experimental conditions. Indeed, the presence of a statistically significant interaction term between the NaCl concentration and the quartz content highlights the contribution of quartz to the rapid initial swelling rate, as shown in Fig. 9a. Conceptually, this could be understood by considering that the quartz grains provide a surface over which the solution chosen to induce swelling can rapidly spread. Bentonite particles in contact with the quartz grains will then come into contact with the solution spreading across the quartz surface and begin to swell. If the quartz grains are in close proximity (as in the case of 30% quartz), as the bentonite particles continue to swell and the solution spreads to the neighbouring bentonite particles it will then encounter a further quartz particle and continue to rapidly spread across the quartz surface. Given that quartz will not incorporate water into its structure in the same manner as bentonite, the presence of inert particles in the place of reactive swelling particles serves to increase the observed swelling rate.

Figure 9.

Interaction plots showing the interactions between initial swelling rate (y-axis) and (a) quartz content (x-axis) and NaCl concentration (green line = 0 M, orange line = 0.5 M, light blue line = 2 M), (b) quartz content (x-axis) and compaction pressure (red line = 4 tonnes, blue line = 8 tonnes) and (c) compaction time (x-axis) and compaction pressure (red line = 4 tonnes, blue line = 8 tonnes).

Figure 9 Long description

Three side-by-side line plots, each with initial swelling rate in percent per minute on the y-axis. (a) Rate against quartz content for 0 M (green), 0.5 M (orange) and 2 M NaCl (light blue). The 2 M line is highest and rises steeply with quartz content, the 0.5 M line is intermediate, and the 0 M line is lowest and nearly flat, showing that quartz amplifies the rapid initial swelling seen at high salinity. (b) Rate against quartz content (0 to 30 percent) for 4 tonnes (red) and 8 tonnes (blue). At 10 percent quartz the red line rises relative to bentonite alone while the blue line falls; at 20 and 30 percent quartz the lines converge and the effect of pressure becomes negligible. (c) Rate against compaction time (5, 8 and 10 minutes) for pressures of 4 tonnes (red) and 8 tonnes (blue). The red line starts highest at 5 minutes and falls with time, while the blue line starts lowest; the two converge by 10 minutes, indicating an interaction between time and pressure.

Considering further the effects of varying quartz content on swelling, Fig. 9b shows the interaction of the effects of compaction pressure and quartz content on initial swelling rate. Here it is seen that the addition of 10% quartz has a large effect on initial swelling rate compared to bentonite alone when looking at the effect that pressure has in combination with quartz content. The addition of 10% quartz when compacting at 4 tonnes causes the initial swelling rate to increase compared to bentonite alone, but when compacting at 8 tonnes the rate decreases compared to bentonite. However, at higher quartz loadings, the difference between the initial swelling rate when compacted at either 4 or 8 tonnes reduces, and the effect of the different pressures is negligible. These data would therefore suggest that it is important to ensure consistency in the compaction pressure applied throughout a series of tests. In addition, to ensure consistency for a series of tests, Fig. 9b suggests that variation of compaction time with pressure may have a large influence on the initial swelling rate of a bentonite–quartz tablet. The fact that a higher initial swelling rate is seen at low compaction time and pressure but a lower initial swelling rate is seen at high compaction time and pressure, as well as the difference between the initial swelling rates at high compaction times regardless of pressure is smaller, suggests homogenization of the tablet fabric. Commercial swelling tests recommend a compaction time of 1.5 h (Lalji et al., Reference Lalji, Ali, Z.U.H and Jawed2021); the data presented here suggest that longer compaction times should give a much more uniform and more consistent initial swelling rate.

The fact that a compaction time of 8 min was found to increase the final swelling rate (p = 0.006) but to contribute in only a minor way to decreasing the initial swelling rate (p = 0.06) is an interesting finding. It may imply that at low compaction times some level of arrangement of the tablet fabric is taking place, and that a compression time of 8 min represents a change in fabric from a disordered, anisotropic structure to a more ordered one. Given the industry standard of a 1.5 h compaction time and the general utilization of the swelling properties of bentonite being significant in applications where compression has taken place over an extended period, this finding is likely to have limited real-world application.

Only NaCl concentration was found to be significant during the ANOVA for final swelling rate, with an 8 min compaction time being shown to be a relevant variable to consider when looking at linear regression compared to a 5 min compaction time. The final swelling rate in this test gives an indication of the gradient of the swelling curve at 30 min after the tablet comes into contact with the solution chosen to induce swelling. It was seen that the deionized water’s final swelling rate was higher than the 2 M final swelling rate, but that the 0.5 M final swelling rate varied more, sometimes appearing higher than the deionized water’s final swelling rate and sometimes lower, but still always being higher than the 2 M final swelling rate. The 2 M final swelling rates are all near-zero, implying that the tablet had achieved its equilibrium swelling potential. However, the swelling in deionized water and 0.5 M NaCl solutions had not reached its equilibrium extent and would have continued past the end point of the test. This represents a limitation of this test procedure: having a cutoff at 30 min does not allow the equilibrium swelling extent to be probed in tests other than the 2 M NaCl tests.