A portable triaxial cell for beamline imaging of rocks under triaxial state of stress

X-ray and neutron imaging beamlines are widely used in the field of material characterization and more recently of geomaterials. X-rays and neutrons provide complementary information, thus informing the nature of the material investigated [21]. While x-rays, especially from synchrotron sources, enable images of higher resolution to be captured, neutrons, on the other hand, are suitable for probing lighter elements such as hydrogen and can be used to investigate thicker sample materials. This properties of neutrons help the imaging of geomaterials containing hydrogen-rich fluids, such as water and oil. Furthermore, x-ray imaging of rock–fluid interactions requires the fluid to be doped with potassium iodide, especially if multiple fluids are present in the pore spaces, which can be avoided if neutron imaging is used.

With minor variations, imaging experiments consist of acquisition of 2D radiograms of the sample placed on a rotating table in the beamline. The attenuated radiation (I) can be computed using the sample of density, ρ, and thickness, x, the mass-attenuation coefficient µ/ρ (µ is the linear attenuation coefficient) and the incident radiation ($I_\mathrm{o}$) as [22]

$$\begin{equation} I = I_\mathrm{o}\exp\left[-(\mu/\rho)\rho x\right]. \end{equation} \tag{ 2 }$$

When the sample placed in the beamline is made of n different elements, equation (2) can be modified as

$$\begin{equation} \ln\left[\frac{I}{I_\mathrm{o}}\right] = -\sum_i^n \left(\frac{\mu}{\rho}\right)_i \rho_i x_i. \end{equation} \tag{ 3 }$$

The attenuation of four elements will be of interest in the current context of imaging rocks enclosed in a triaxial cell: aluminum in the various components of the triaxial cell, iron in the fixtures (e.g. bolts), silicon in the grains of rock and carbon if the pore space in rocks is saturated with organic materials such as hydrocarbons. For the purposes of comparison, the mass attenuation coefficient along with the specific densities are given in table 1 and will be used in the analysis of data later. It is to be noted that for the beamlines discussed here, the wavelength, λ is centered around 0.18 nm for BT2, the maximum flux at IMAT is around 0.26 nm and the coefficients reported in [22] correspond to approximately λ = 0.018 nm. For the design of x-ray and neutron transparent triaxial cells, it is vital to assess the mass attenuation coefficient of the system. Commercially available triaxial cells are either made of carbon fiber composites [10] or aluminum, with the latter being the cheaper alternative. Commercially available core holders are used to study pore-scale flow and non-localized deformation. An important aspect is that although carbon can be readily used as a sample holder for neutron imaging, carbon fiber composites are unsuitable due to the high hydrogen content of the epoxy resin used in the manufacture. A simple design of a x-ray transparent aluminum cell was detailed by Fussels et al [24]. Aluminum has a few distinct advantages over carbon in addition to favorable mass attenuation coefficients for neutrons. Aluminum alloys are cheaper, easy to machine and readily recyclable after their use, thus making them a sustainable option.

Most rocks used in the construction industry, as well as those investigated for oil and gas, such as sandstones, are consolidated and exhibit near-perfect elastic behavior with a brittle mode of fracture. However, with the interest in non-conventional hydrocarbon recovery, rocks with complex mechanical behavior, such as shales, are being studied with interest. Broadly, two types of minerals affect the degree of brittleness within the rocks: (a) quartz imparts brittleness in the rocks resulting in small elastic strain when loaded in compression prior to failure; and (b) clay imparts ductility, resulting in larger strains. Therefore, rocks containing these two minerals exhibit the behavior of dominating minerals, i.e. sandstones are brittle as the dominating mineral is quartz, whereas the mechanical behavior of shale depends on whether quartz or clay is the dominant mineral. Hence, the cell design needs to take into account the possible failure of the rocks that are intended to be tested.

The factor of safety (FoS) is included to ensure the equipment is safely operated. The FoS is often calculated as a ratio of the ultimate stress induced in the mechanical component and the working stress. However, other factors such as the presence of stress concentrations, exposure to extreme environments (temperature, pressure, corrosion, etc), frequency of maintenance or the operational setting are important factors to consider while designing the equipment. As the current triaxial cell is designed to be used in beamlines, the following aspects were considered while assigning an FoS: (a) the uncertainty in the strength of the rock; (b) the environment of the beamline, which is often confined spaces with a range of expensive and sensitive equipment; and (c) the requirement for the triaxial cell to be portable and transparent to the beamline.

The FoS for the current design is based on the ratio of the maximum stress induced in the cylindrical component (the main body) of the triaxial cell to the ultimate compressive strength of the rock. The uncertainty in the denominator is to be taken into consideration when deciding on the FoS. This design was used for experimentation at two beamlines: (a) IMAT at ISIS, a UK Science and Technology Facilities Council (STFC) facility in Harwell, Oxfordshire, UK; and (b) the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR), a US government facility in Gaithersburg, MD, USA. Details of the use and snapshots of the results are discussed in section 6.

The main body is the pressure-bearing component of the cell. It can be designed as a thick or thin walled cylinder, which in turn depends on the intensity of the imaging beam. The maximum attenuation can be calculated by knowing the exact composition of the aluminum alloy used, the chemical composition of the rock and the fluid in the pore space. Using mass attenuation data, the thickness of the main body spanning the length of the sample being imaged for acceptable attenuation of the beam can be determined.

The material selected for the cell is aluminum 6082-T6 alloy, as it has the highest strength (nearly 240 MPa–250 MPa of proof strength and 300 MPa of tensile strength) among 6000 alloys. Furthermore, the 6082 alloy has good corrosion resistance and is commonly used in applications involving stress-bearing components. One limitation of 6082 is the high manganese content, as Mn is strongly activated with neutrons releasing a strong beta radiation, making sample handling immediately after imaging quite challenging. To overcome this issue, aluminum 6061-T6 can be used. It is also noted that if strength is an absolute requirement—for instance, when testing extremely hard rocks—7075 alloy may be an option but would radiate a strong beta radiation field due to manganese. One noteworthy aspect is that the inclusion of other metals in the chosen alloy, for instance cobalt, would pose significant limitations in handling after the termination of the experiment due to the degree of activation.

The body of the triaxial cell is tubular with inside edges chamfered to house the collar that provides a seal with the rubber sleeve which in turn holds the rock sample in place (figure 3). The details of the other components are discussed later. A fluid entry and exit port that houses a 3.175 mm (one-eighth inch) National Pipe Thread (NPT) fitting is placed close to one end of the cell to facilitate the hydraulic pressure for confining stress ($\sigma_\mathrm{2}$). The hole is positioned to ensure that it is sufficiently away from the rock sample (as shown in figure 4) for two reasons: (a) it is designed to house a 3.175 mm (one-eighth inch) NPT stainless-steel male to 3.175 mm (one-eighth inch) female compression fitting (of Swagelok type), which will have higher attenuation and, if near the rock sample, it may affect the quality of the images acquired; and (b) if the images are truncated to contain only the rock sample and tubular part of the cell, the 3D reconstructions from those 2D radiograms are faster. The ends have a 46 mm × 2 mm threads to house the end caps.

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The critical load bearing part of the experimental test setup is the main body as it is subjected to the confining pressure of the fluid as well as stress resulting from the dilation of the sample during testing. Therefore, finite element analysis of the load bearing main body was undertaken. Apart from testing the structural integrity, the finite element analysis is expected to inform the FoS in the design.

Figure 5(a) depicts the 3D model of the main body created in SolidWorks software along with the imposed boundary conditions. The flat sides of the top and bottom of the cell were assumed to be fixed as these are held in place with near-zero allowable displacement during the test. In the real setup, the main body of the triaxial cell will also be subjected to axial tension due to the tightening of the bolts (shown by the number 5 in figure 2). The axial stress will, in fact, increase the burst pressure. However, for the current finite element modeling exercise, the axial stress is ignored, which results in a lower burst pressure and therefore a higher FoS. The threaded hole where the 3.175 mm (one-eighth inch) NPT to Swagelok fitting for confining pressure is housed (number 7 in figure 2) is fixed as the integrity of the fixture is ensured by selecting the correct fitting and appropriate depth of the thread. A uniform pressure was applied on the internal cylindrical surface, reflecting the application of confining pressure σ₃. The internal pressure applied on the main body of the cell is one of the design parameters and can be used to optimize the cell design, especially in terms of its thickness. Also note that the thickness of the cell/enclosure is an important parameter for synchrotron and non-synchrotron-based x-ray sources for imaging. However, the design is easily adaptable, as only the thickness of the main body needs to be altered to suit the energy in the imaging beamlines and phenomena of interest. In the current study, the cell was designed for an internal pressure of 10 MPa.

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Figure 5(b) depicts the finite element mesh. To enable discretization of all the features in the triaxial cell body, a free mesh was chosen and was optimized for convergence of displacement and stress.

Figure 5(c) shows the von Mises stress distribution within the main body of the triaxial cell and it can be noted that the maximum stress is near the hole that houses the 3.175 mm (one-eighth inch) NPT fitting, indicating the effects of concentration of stress due to the removal of material with slightly reduced thickness. The maximum stress induced due to the confining stress of 10 MPa was found to be 58 MPa. The FoS for the current design is 4.31, for a conservative yield strength of 6082 alloy as 250 MPa. Note that the thread recesses at both ends are chamfered and therefore do not contribute any stress to those areas.

Figure 5(d) shows the resultant solid displacement within the main body of the triaxial cell due to the applied internal pressure of 10 MPa. The shape of the distorted body is similar to other cylindrical vessels subjected to internal pressure.

The rock is held in place with a rubber sleeve (parts (h) and (c) respectively in figure 3). A SolidWorks model of the taper is shown in figure 6. The taper on the conical section of the collar is identical to that on the cell main body, which allows positioning of the sleeve so that it is compressed between the main body and the collar providing a surface seal. Note that the edges of the conical part must not be sharp to avoid any possible damage to the rubber sleeve. A fillet was applied to the edges to make it smooth. The taper angle must be selected to avoid sharp corners and retain the ability to slide the rubber sleeve on the collar for the assembly that provides the seal for the confining pressure. The sliding action of the conical element also enables the process of gradually settling up of rubber to provide a seal, as described in section 5 below.

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The end cap (figure 6) is designed to hold the collar and the sleeve in place. The end caps are threaded and are designed to match the thread on the body. In the current design 46 mm × 2 mm threads are machined on both of the end caps and on the main body of the cell. As shown in figure 3, the end cap thread on the main body and during the turning movement push the collar firmly into the main body, thereby forming a seal for the confining fluid (space is indicated by b in figure 3). The end caps also have eight equispaced holes at angle 45^∘ threaded to M6 to secure the platen (discussed in section 4.3 below).

Platens (plate-like structures with protrusions) have two functions in this cell:

• (a)  
  to impart load or to apply displacement boundary conditions; and
• (b)  
  to facilitate the flow of fluids through the rock sample (design was incorporated in the current setup but was not used in the demonstration).

There are two platens for the triaxial cell. First, there is a floating platen at the loading side of the cell (figures 3 and 6). It consists of a single cylindrical member with an extension at the end, primarily designed to limit the possible displacement, in case needed, and to enable the flow of fluids into and out of the rock. The extended portion has two ports each of depth 12 mm to house a 3.175 mm (one-eighth inch) NPT male connector to compression fitting (of Swagelok type). The length of the platen depends on the rock sample and estimated compression of the sample before failure. Two holes of diameter 3 mm run parallel to the longitudinal axis of the platen which can be used to inject fluids into the rock sample. The spacing between the holes can also be varied to suite specific experimental requirements. For the current design, the spacing between the ports was maximized and hence was set to 19 mm.

Figure 6 shows the fixed side platen. The cylindrical part of the platen is identical to the loading side platen but the cylindrical part ends in a flange, which is used to secure the platen to the end cap (figure 3). The flange has eight clear holes at 45^∘ as well to match the end cap. Depending on the load, only four bolts may be sufficient to secure the platens.

The plumbing of cells with ancillary equipment was carried out with 3.175 mm (one-eighth inch) stainless-steel tubing supplied by Swagelok. The fittings were of 316 stainless steel and are rated in accordance with the ASME Code for Pressure Piping B31.3. The pressure ratings for the fittings used are: maximum pressure of 68.9 MPa (male) and 44.7 MPa (female).

The load is applied using an RLS 100 hydraulic loading jack supplied by Powerteam. The maximum load that can be applied using an RLS 100 is 89 000 N (10 t). It is relatively lightweight, making the test setup very portable. It is housed in aluminum housing (figure 2). The RLS 100 has two holes which can be matched with the bottom platen using through bolts through the housing; spacing between the loading side end cap and the piston of RLS100 can be maintained. Before securing the bolts on the loading side end cap, it is advisable to ensure that there is enough space for the piston to travel so that the rock can be compressed to failure. A two-way valve is placed inline and can be used to isolate the cell once the desired axial load is applied to the rock sample. This isolation enables easy rotation of the cell along the longitudinal axis and hence makes it a convenient setup for use in fixed-source (x-ray or neutron) 3D tomography. A similar arrangement can also be used for confining stress ($\sigma_\mathrm{2}$).

Table 2 details the itemized cost (in British Pound Sterling) of the components used in the triaxial cell setup. It is to be noted that the prices include value-added tax (UK and EU, where applicable) and educational discounts (variable as it is in accordance with commercial negotiations between the university and individual suppliers) offered by suppliers to the University of Aberdeen. The total cost does not include the cost of manufacturing the equipment at the University of Aberdeen's workshop and subsequent modifications undertaken at the workshops at NIST and IMAT. Furthermore, the materials were procured at different times and therefore the costs in table 2 should be taken with caution.

The accuracy of the vertical load and confining stress will depend on the accuracy with which the pressure gauge can be read. In the case of the PGM-63 L-3000PSI/200BAR pressure gauge used in the current setup, the accuracy of the instrument is 1.6 % of span (200 bar). Parallax error is another source of error in the application of the load on the sample. The lowest count in this pressure gauge is 10 bar and hence the uncertainty in the measurement of applied pressure would be 10 bar. For experiments that require a high degree of precision in the application of loads, it is recommended that digital pressure transducers be used to monitor the pressure. Use of a pressure controller for the application of both confining stress and axial load could also be a viable option, especially if pressure-sensitive rocks are to be tested.

Figure 7 depicts the positioning of the cell on the IMAT beamline, ISIS facility, UK. The cell was 15 cm in front of the detector. The position of the cell with respect to the detector was adjusted using a laser mounted near the entrance of the beam in the experiment hall. An elbow connector, shown in figure 7(b), was used to minimize the distance the triaxial cell was positioned in front of the detector and enabled the triaxial cell to be isolated once axial stress was applied. The configuration of the elbow connector comprised a two-way valve and a Swagelok Miniature Quick-Connect connector, which enabled isolation of cell while maintaining axial stress. Figure 7(c) depicts one of the radiograms obtained for the water-saturated rock sample—a rock extremely rich in silicon from the side of Loch Aline in North West Argyll in Scotland [28]. Initial trials to image dry rock were unsuccessful due to very low attenuation of neutrons when passed through silicon-rich rock. It can be noted from figure 7(c) that a clear outline of the fractures appears to have propagated due to the application of the load. The voxel resolution obtained on IMAT was ≈ 120 µm.

Figure 8 depicts the variation of attenuation, $I/I_\mathrm{o}$, along the sections of the triaxial cell highlighted in figure 7(c) with A through to G. The reference r = 0 mm refers to the center of the triaxial cell. The following observations were made:

• Along A in figure 7, at r =−40 mm, the $I/I_\mathrm{o} = 0.38$ was measured from the beamline experiments, which was due to the high tensile strength of bolts of diameter 6 mm. With the density of material taken as 7.9 g cm⁻³, the mass attenuation coefficient, µ/ρ was found to be 0.2 cm² g⁻¹, which is in agreement with those reported in the literature for Fe [22].
• For the section indicated by line A and r = 0 mm, the attenuation of the beam is due to aluminum alone traveling through the 80 mm diameter of the top platen. Using the density of Al as 2.7 g cm⁻³, µ/ρ was found to be 0.047 cm² g⁻¹, which is comparable to results reported for Al in [22].
• The $I/I_\mathrm{o}$ measured along sections B, C and D can be used to confirm the presence of aluminum or iron (due to the bolts).
• At r = 0 mm in section E, the $I/I_\mathrm{o} = 0.09$ is a combination of beam attenuation due to Al in the cell body, Si in the grain and H in the pore space of the rock sample and in the Viton sleeve.
• At r = 0 mm in section G, the $I/I_\mathrm{o} = 0.448$, which is predominantly due to Al and H in the Viton sleeve.
• Although F is taken at the interface between rock and the Al of the loading side platen, the $I/I_\mathrm{0} = 0.236$ at r = 0 mm is less than those observed at G but greater than the H dominated attenuation at E. It suggests that the attenuation at r = 0 mm in section F is due to a combination of aluminium in the triaxial cell, hydrogen in the rock and Viton sleeve and silicon in rocks.
• The gradual change in attenuation at a few locations along all the sections can be noted, which is attributed to the combination of material and its thickness along the direction of the passing beam.

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In conclusion, it was noted that the design of the triaxial cell is suitable for its intended purpose of using it in a beamline for identification of specific characteristics of geomaterials subjected to triaxial state of stress and the attenuation of the beam at various spatial locations is largely as expected from the materials used in its manufacture.

Experiments were conducted at the BT2 beamline at NIST NCNR in Gaithersburg, MD, USA. The BT2 facility is equipped with an x-ray imaging facility in addition to a neutron-imaging facility, thereby enabling the collection of x-ray and neutron images simultaneously [27]. In BT2, due to the constraint of x-ray attenuation, the wall thickness needed to be reduced. The triaxial cell was therefore modified to remove the material on the cylindrical part of the cell body in order to have a wall thickness of 2 mm. Figure 9(a) depicts the modified cell with reduced wall thickness. Structural analysis of the 3D model was conducted to ensure that the design was safe under operating loads.

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Figures 9(b) and (c) depict the x-ray and neutron radiograms of Locharbriggs rock sample—a high porosity quartz rich (88%) red standstone of Permian origin, sourced from a quarry near Dumfries in south-west of Scotland [29]. The high neutron flux at BT2 and relatively low silicon content of Locharbriggs sandstone enabled imaging experiments to be carried out without saturating it with water.

The obtained voxel resolution for neutron imaging was ≈30 µm and for that of x-ray was ≈30 µm. It is to be noted that the Viton sleeve was not used in these experiments.

Figures 10 and 11 depict the attenuated neutron and x-ray beams through the triaxial cell. The following observations were made:

• Section A in figures 9(b) and (c) is composed mainly of aluminium. At r = 0 mm, the center of the triaxial cell, $I/I_\mathrm{o} = 0.65$ and therefore µ/ρ = 0.032 cm² g⁻¹, which is lower than those reported in [22]. However, for x-rays the attenuation ratio at the same location, $I/I_\mathrm{o} = 0.035$ and µ/ρ = 0.248 cm² g⁻¹, greater than those interpolated from the data from [23].
• For r = 0 mm in section C, which primarily consists of dry rock, i.e. silicon, $I/I_\mathrm{o} = 0.556$ for neutron beam and $I/I_\mathrm{o} = 0.1$ for x-ray. The attenuation is mainly due to the silicon in the rocks with contribution of aluminium and taking the density of silicon to be 2.33 g cm⁻³, the µ/ρ = 0.049 cm² g⁻¹ for neutrons and µ/ρ = 0.040 cm² g⁻¹ for x-rays, which is slightly lower than those reported by [23], with the variation attributed to the presence of aluminium and other metallic inclusions in the main body of the triaxial cell.

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The following are some of the identified limitations of the current design.

• The mechanical response of rock is sensitive to the rate of strain used in the triaxial test. The International Society of Rock Mechanics recommends a strain rate of 20 millistrain per hour. However, the current test setup only enables the application of instantaneous load. One suggestion would be to replace the manual hydraulic pump with a pressure controller that can enable application of axial displacement while maintaining a constant rate of strain. This would enable reproduction of identical laboratory triaxial conditions in the beamlines.
• The continued dilation of rock due to the increase in applied axial load would increase the radial displacement, which would in turn increase the pressure in the confining fluid chamber. Therefore, a further improvement would be to connect the confining pressure to a device that could control the confining stress during the experiment, for instance, a pressure controller. However, the plumbing needs to be carefully considered as it would be a major limiting factor for most beamlines that have rotating stages. One suggestion would be to investigate the use of multi-channel hydraulic or pneumatic rotary unions that would allow the rotation of the stage while maintaining pressure connectivity between the confining pressure chamber and the controller.