Neutron scattering and neutron imaging have emerged as powerful methods for experimentally investigating material deformation and fluid flow in the interior of otherwise inaccessible or opaque structures. This paper describes the design and provides example uses of a pressure cell developed for investigating such behaviors within geological materials. The cell can accommodate cylindrical samples with diameters up to 38.1 mm and lengths up to 154 mm. Ports in the cell and a pressure isolating sleeve around the sample allow the independent application of confining pressure up to 69 MPa and axial pressure up to 34.5 MPa. Two material versions of the cell have been manufactured and used to date. An aluminum version is typically used for temperatures below 40 °C, because of its relative transparency to neutrons, while a titanium version, which is comparatively more neutron attenuating, is used for experiments requiring triaxial pressurization under conditions up to 350 °C. The pressure cells were commissioned at the VULCAN engineering diffractometer at the Oak Ridge National Laboratory (ORNL), Spallation Neutron Source, and have since been used at the ORNL high flux isotope reactor CG1-D imaging beamline, National Institute of Standard and Technology (NIST) BT-2, and NIST NG6 imaging beamlines.

Understanding the mechanical deformation of geological materials and fluid flow through porous and fractured geological media is of critical importance to a number of subsurface energy-related applications including oil and gas production, geothermal energy extraction, mining, and subsurface disposal of nuclear waste. Conventional methods for experimentally studying these processes can have significant shortcomings which limit their ability to provide the data needed to better understand fundamental mechanisms governing their behavior. For example, one of the primary shortcomings of conventional experimental methods applied to geological materials is the measurement of bulk or effective behavior and an inability to measure behavior within the sample.

In the case of rock deformation and failure modeling, conventional rock mechanics testing may involve uniaxial loading, triaxial loading, direct shear loading, or, in some cases, rate-dependent loading of the sample, while simultaneously measuring either the bulk deformation of the sample using a displacement sensor such as a linear variable displacement transducer (LVDT) or the deformation of an exposed surface using a strain gauge (Fossum and Brannon, 2006). The interior of the sample remains inaccessible to measurement using these conventional techniques. This can be a significant limitation for polymineralic materials or materials where grain size and orientation may vary. With respect to the former, micromechanics approaches are often used to develop constitutive models of material behavior (Zhu and Tang, 2004). Experimental calibration of micromechanical parameters is required in such approaches, but the process currently involves trial and error, varying different parameter values to match bulk behavior, since the behavior of constituent mineral phases cannot be directly measured in situ. However, because these bulk measurements fail to capture microstructural details of the rock deformation process, there is a significant risk that the calibrated micromechanics approach produces a quantitatively accurate model for a particular test, but a poor model of the material system, limiting its general applicability. With respect to factors such as preferred grain orientation or residual stress, conventional deformation measurement methods offer no direct means of quantitatively separating the contributions of these influences on the deformation process.

The inaccessibility of the interior of geological materials has, similarly, produced difficulties related to the experimental measurement of flow in porous and fractured materials. Techniques such as particle image velocimetry have proven to be capable of producing high-resolution spatial and temporal datasets that can be used to quantify the flow structure (Adrian, 2005). Unfortunately, the conventional implementation of this method cannot be applied to high-pressure environments or geological materials because it relies on the optical evaluation of the fluid medium (Fourar and Bories, 1995; Chen et al., 2004). Alternative methods for experimentally studying the flow in geological materials have also been investigated including x-ray computed tomography, nuclear magnetic resonance (NMR), and neutron radiography (Mees et al., 2003; Fukushima, 1999; and Deinart et al., 2002). X-ray methods remain limited in their application to fluid measurement, particularly for high-pressure experimental systems, because they interact weakly with the fluids of interest, such as oil and water, and are highly attenuated by typical pressure vessel materials. NMR does interact strongly with water but is subject to magnetic field distortion and tends to have very low resolution, limiting its quantitative applicability. Neutron radiography, by comparison, is highly suited to studying processes such as fluid flow because thermal and cold neutrons are highly attenuated by substances with hydrogen, such as water, and weakly attenuated by most rocks and high Z materials such as metals.

The highly penetrating nature of neutrons and their high contrast for water make neutron-based measurements a unique and powerful tool for investigating physical processes within geological materials (Polsky et al., 2013). A thorough review of the application of neutron diffraction to the study of the mechanical behavior of geological materials can be found in Covey-Crump and Schofield (2009). A wide range of work performed to better understand deformation in polymineralic and textured materials is covered in that review, including a brief overview of a pressure vessel designed to apply confining pressure to samples during uniaxial compression loading. A review of neutron imaging in geomaterials and engineered porous media can be found in Perfect et al. (2014). However, the overwhelming majority of imaging and strain studies using neutrons have been applied to materials under unconfined conditions. These have been instrumental in demonstrating the potential of neutron-based techniques to provide data related to physical processes occurring within the evaluated material but have yet to take full advantage of the penetrating nature of neutrons. Specifically, these advantages are based on the ability to perform experiments on samples contained in pressure-controlled and temperature-controlled environments that represent in situ conditions for geophysical applications. This evolution, and continued development of the sample environment, is critical to fully utilizing the advantages of neutron-based measurement techniques.

This paper describes the design considerations and applications of a pressure cell capable of performing neutron diffraction strain measurements and imaging of fluid flow in porous and fractured geological cores under triaxial stress conditions at elevated temperatures. An overview of the performance specifications of the pressure cell is first provided, followed by a detailed description of the mechanical design of the vessel. The remaining sections of the paper highlight special design considerations related to loading the sample and the types of experiments that have been performed to date. Early experiments with the vessel highlighted the need to evolve its design and associated sample loading hardware, as initially conceived, to enable or improve certain types of neutron-based measurements. Additional improvements were also made to the experimental setup to better control the application of physical conditions to the sample. This has been particularly critical for fracture flow experimentation using the vessel because fluid-flow entrance conditions can drastically change the flow field within the sample and affect the ability to achieve fully developed conditions.

It is hoped that this description of the vessel design and its use stimulate additional interest in the application of neutron imaging and strain measurement techniques for the geosciences. These are arguably unique tools available to geoscientists with the potential to provide powerful insights into physical processes occurring within geological media and material behaviors that are either difficult or impossible to study by other means. As is the case with most experimental efforts, careful design of the sample environment is required to ensure that the process being investigated can be accurately related to environmental conditions.

Figure 1 shows the completely assembled core test vessel attached to a mount used for precise alignment and positioning within the neutron beam. In Fig. 2, the same vessel is shown disassembled with the various components labeled.

FIG. 1.

The core test vessel in the assembled state, shown attached to a mount used for positioning within a neutron beam.

FIG. 1.

The core test vessel in the assembled state, shown attached to a mount used for positioning within a neutron beam.

Close modal
FIG. 2.

The core test vessel shown disassembled. Labels: (1) vessel body, (2) core sample, (3) Kapton tube, (4) fluid-flow stems, (5) stem cap, (6) stem cap fasteners, (7) seal-forming pins, (8) seal plate, (9) sealing fasteners, (11) compression ring, and (12) tapered Teflon gasket.

FIG. 2.

The core test vessel shown disassembled. Labels: (1) vessel body, (2) core sample, (3) Kapton tube, (4) fluid-flow stems, (5) stem cap, (6) stem cap fasteners, (7) seal-forming pins, (8) seal plate, (9) sealing fasteners, (11) compression ring, and (12) tapered Teflon gasket.

Close modal

An isometric view and a cross sectional view of the core test vessel are shown in Fig. 3. There are two separate pressure regions in the vessel. Inlet port “C” in Fig. 3 is used to deliver a pressurized fluid to the axial face of the cylindrical core sample (the exit port is not visible in the isometric view). A pressurized gas or liquid is introduced in the port labeled “B” to provide confining pressure. This fluid is not in direct contact with the sample. The annular pressure compresses a neutron-transparent Kapton tube (item 3 in Fig. 4) against the core sample (2) preventing the working fluid from preferentially flowing around the sample. The working fluid is limited to a pressure of ∼35 MPa (5000 psi), while the confining pressure is limited to ∼69 MPa (10 000 psi). These pressures are relevant for a number of subsurface applications such as oil and gas production and geothermal energy extraction, where average well depth is on the order of 3000 m, and are meaningful when studying mechanical and hydraulic processes in geological materials.

FIG. 3.

(Left) An isometric view of the assembled cell; (right) a cross sectional view of the cell (cutting plane labeled “A” in the isometric view). Labels: (A) Cutting plane used for the cross sectional view in Fig. 2, (B) annular pressure port, (C) inlet pressure port for the working fluid, (D) tapped holes for mounting fixtures, (1) vessel body, (2) core sample, (3) Kapton tube, (4) fluid-flow stems, (5) stem cap, (6) stem cap fasteners, (7) seal-forming pins, (8) seal plate, (9) sealing fasteners, and (10) seal region (shown in greater detail in Fig. 3).

FIG. 3.

(Left) An isometric view of the assembled cell; (right) a cross sectional view of the cell (cutting plane labeled “A” in the isometric view). Labels: (A) Cutting plane used for the cross sectional view in Fig. 2, (B) annular pressure port, (C) inlet pressure port for the working fluid, (D) tapped holes for mounting fixtures, (1) vessel body, (2) core sample, (3) Kapton tube, (4) fluid-flow stems, (5) stem cap, (6) stem cap fasteners, (7) seal-forming pins, (8) seal plate, (9) sealing fasteners, and (10) seal region (shown in greater detail in Fig. 3).

Close modal
FIG. 4.

Detailed view of the sealing region (labeled 10 in Fig. 3). Labels: (3) Kapton tube, (4) fluid-flow stem, (7) seal-forming pins, (11) compression ring, and (12) tapered Teflon gasket.

FIG. 4.

Detailed view of the sealing region (labeled 10 in Fig. 3). Labels: (3) Kapton tube, (4) fluid-flow stem, (7) seal-forming pins, (11) compression ring, and (12) tapered Teflon gasket.

Close modal

Two versions of the vessel body (item 1 in Fig. 3) have been constructed to date. One version is composed of a high-temperature alloy, Ti–6Al–4V Grade 5 titanium, to allow the use at temperatures up to 350 °C. A low temperature version composed of 7075-T651 aluminum alloy is used at temperatures below 40 °C because it has the required strength characteristics, but is more transparent to neutrons than titanium. The less attenuating cell body decreases the time required to obtain images by allowing more neutron flux through the sample and reduces measurement noise associated with neutrons scattered by the vessel body. Tapped holes “D” allow the cell to be mounted to various holding mechanisms to aid in positioning in the beam, as shown in Fig. 1.

A labeled cross sectional view of the cell is shown alongside the isometric view in Fig. 3 (cross section taken from the plane labeled “A” in Fig. 3). As mentioned, the vessel body (1) is either a titanium alloy or an aluminum alloy depending on the temperature of the study. A core sample (2) with a diameter of 38.1 mm (1.5 in.) and a height of up to 154 mm (6 in.) is inserted into a thin (∼0.1 mm wall) Kapton tube (3) that extends the length of the body (the Kapton tube is too thin to be visible in the figure). The pressurized working fluid enters through the fluid-flow stem (4), spreading across the face of the core sample through flow channels in the face of the flow stem visible in Fig. 3. An identical stem serves as the exit orifice on the opposite side of the cell. The fluid-flow stems are finely threaded into the stainless steel “stem cap” (5), allowing the height with respect to the core sample to be adjusted. The stem caps are fastened to the vessel body by using three high-strength bolts on each side of the cell (6); these fasteners must also carry the axial load resulting from the working pressure. To seal the annular pressure region around the Kapton tube from the working pressure region in the core sample, a Teflon gasket is compressed against the outer diameter of the Kapton tube, forcing the Kapton against the fluid-flow stem to create two isolated pressure regions. The seal region (10) is shown in greater detail in Fig. 4. The compression of this gasket is achieved by applying a force to a plate (8) containing several high-strength pins (7) that are inserted through the stem cap (5). The force is applied by using three fasteners on each end of the vessel (9).

A detailed view of the seal-forming region (labeled 10 in Fig. 3) is shown in Fig. 4. The high-strength steel seal-forming pins (7) come into contact with a precision-machined compression ring (11), made out of Ti, to ensure that the tight manufacturing tolerances are retained with thermal changes in order to prevent extrusion of the Teflon. The bottom of the compression ring is tapered and matches the taper on the Teflon gasket (12). These tapers force the gasket to extrude toward the Kapton liner (3). This makes a reliable seal between the gasket and the Kapton tube, as well as a seal between the Kapton tube and the Ti fluid-flow stem (4).

The operating stresses in the wall of the pressure vessel can be calculated analytically by solving the Lamé equations. For the general case of a pressure vessel of any given thickness subjected to both internal and external pressures, the component stresses are

σθ=poK2+piK21(popi)K2K21rir2,
(1)
σz=poK2+piK21,
(2)
σr=poK2+piK21+(popi)K2K21rir2,
(3)

where σθ, σz, and σr are the tangential, longitudinal, and radial stresses, respectively, ri is the inner radius, ro is the outer radius, K is the ratio ro/ri, pi is the inner pressure, po is the outer pressure, and r is the radial distance at which the stress is calculated (Manning and Labrow, 1971). With these component stresses calculated, the von Mises equivalent stress can be calculated using

σv=σ1σ22+σ2σ32+σ1σ322.
(4)

For an applied pressure of 68.9 MPa (10 000 psi) acting on a vessel with an inner radius of 19.2 mm and an outer radius of 26.2 mm, the tangential, longitudinal, and radial stresses were calculated to be 230.9 MPa, 81.0 MPa, and −69.0 MPa, respectively. The von Mises equivalent stress is then calculated to be ∼259.70 MPa. Assuming Ti–6Al–4V Grade 5 titanium alloy has a yield strength of ∼572 MPa at 350 °C, this results in a safety factor of ∼2.20. For 7075-T651 aluminum alloy with a room temperature yield strength of ∼503 MPa, the safety factor is ∼1.94. These low safety factors are justifiable since the stored energy in the vessel is minimal—the compressed gas volume is ∼1 mm3 in the annular region. Nevertheless, safety precautions should still be undertaken with the use of any pressurized system.

Finite element method (FEM) calculations were performed using the ABAQUSTM software package to validate the analytical approach and ensure that areas of higher stress are not present in the vessel. Figure 5 shows the stresses and deflections in the vessel body due to an applied pressure of 68.9 MPa. The FEM results agree well with the analytical results, showing a maximum stress of 255 MPa.

FIG. 5.

FEM simulation of the pressure cell body showing von Mises stresses (a) and radial deflection (b).

FIG. 5.

FEM simulation of the pressure cell body showing von Mises stresses (a) and radial deflection (b).

Close modal

The fluid-flow stem (item 4 in Figs. 2–4) is designed to be interchangeable depending on the core sample and experiment layout. The original fluid-flow stem [Fig. 6(a)] was designed to distribute the fluid over the axial surface of the core sample through a central passage for pore flow experiments. Computational fluid dynamics (CFD) analyses were performed to evaluate the suitability of the center hole design for fracture flow experiments. The idealized flow between parallel plate models is typically used to represent the flow in fractured geological systems based on the geometry of the opposing fracture faces. CFD simulation of the center hole stem piece [Fig. 7(a)] revealed a significant “jetting” effect where the velocity at the center of the fracture was many times higher than the velocity regions near the sample outer diameter. To mitigate this entrance effect, a new fluid-flow stem was designed to minimize the transverse velocity gradient on the surface of the core [Fig. 6(b)]. This stem was fabricated from heat treated 17-4 PH steel, with the exit of the stem fabricated from 7075-T651 aluminum alloy, again for its relative neutron transparency. The design of the stem using computational fluid dynamics and performance results are discussed in the reference (Polsky et al., 2015).

FIG. 6.

Isometric solid and transparent views of the original fluid-flow stem (a) and the modified flow stem (b).

FIG. 6.

Isometric solid and transparent views of the original fluid-flow stem (a) and the modified flow stem (b).

Close modal
FIG. 7.

Velocity field contour map and velocity profile at the inlet, 25 mm from the inlet, and 50 mm from the inlet for (a) the original flow stem design and (b) modified flow stem design.

FIG. 7.

Velocity field contour map and velocity profile at the inlet, 25 mm from the inlet, and 50 mm from the inlet for (a) the original flow stem design and (b) modified flow stem design.

Close modal

The process and instrumentation diagram (P&ID) for the fluid injection and confining pressure system is shown in Fig. 8. The upper portion of the figure (enclosed in a red dashed line) is the annular pressure circuit for a gas pressurization setup. It utilizes a gas bottle, booster pump, and various safety components, gauges, and regulators. Alternatively, confining pressure can be applied using a high-pressure liquid syringe pump provided that a fluid with a low neutron scattering cross section is used. The bottom portion of the figure (enclosed in a blue dashed line) is the core pressure circuit. Fluid is delivered to the cell by using a high-pressure piston pump P2. A needle bubbler connected to a computer-controlled syringe pump (P3) is used to introduce a neutronic contrast agent (discussed in Sec. V) into the circuit before entering the vessel inlet. The needle bubbler is made using high-pressure tubing with an outer diameter of ∼1.59 mm (1/16 in.) and an inner diameter of 0.15 mm, inserted midway into the primary fluid line through a tee. The pump injection flow rates can be controlled from 0.01 ml/min to 30 ml/min. In the present configuration, the exiting fluid is pumped into a fluid collection tank T1.

FIG. 8.

Process and instrumentation diagram (P&ID) for the geothermal pressure vessel. The upper portion (enclosed in a red dashed line) is the annular pressure circuit, while the lower portion (enclosed in a blue dashed line) is the core pressure circuit. GB1: gas bottle; P1: gas booster pump; V1, V2, and V3: high-pressure valves; PT1, PT2: pressure transducers; AC1: high-pressure accumulator; RV1, RV2, and RV3: rupture disks; PRV1, PRV2: high-pressure regulators; P2: fluid pump; T1: fluid collection tank; and PV: pressure vessel.

FIG. 8.

Process and instrumentation diagram (P&ID) for the geothermal pressure vessel. The upper portion (enclosed in a red dashed line) is the annular pressure circuit, while the lower portion (enclosed in a blue dashed line) is the core pressure circuit. GB1: gas bottle; P1: gas booster pump; V1, V2, and V3: high-pressure valves; PT1, PT2: pressure transducers; AC1: high-pressure accumulator; RV1, RV2, and RV3: rupture disks; PRV1, PRV2: high-pressure regulators; P2: fluid pump; T1: fluid collection tank; and PV: pressure vessel.

Close modal

The cell is heated using a 5 kW induction heating system (Ameritherm EasyHeat 5060 LI) driven in the range of 150 kHz–300 kHz. The RF transmitter is coupled to a water-cooled ¼ in. copper pipe that is wrapped around the cell in a way to ensure suitable inductive coupling to the system, while not obstructing the incident neutron beam or regions between the cell and the scattering detectors (see Fig. 9). Due to the only slightly lower electrical resistivity of titanium as compared to that of steel, as well as the cell geometry, the power coupling is very efficient, only utilizing a fraction (<30%) of the 5 kW power output when operating at 200 °C in open air.

FIG. 9.

Titanium pressure cell with an inductive heating coil.

FIG. 9.

Titanium pressure cell with an inductive heating coil.

Close modal

Control of the heating power is facilitated via a Eurotherm PID controller which is feedback controlled using the temperature reading from a type-K thermocouple affixed to the surface of the cell using the Kapton tape. The controller was tuned to specifically control this system, and thus, the temperature stability is within ±1°.

The following examples are intended to highlight the unique insights that can be gathered with the experimental setup described in the previous sections when employed with neutron-based measurement techniques. Representative flow imaging experiments will include characterizations of multiple constituent immiscible or multiple phase flows and single-constituent flows within porous media and flow channels. Neutron diffraction experiments will highlight the ability to perform measurements of lattice deformations that can be correlated with engineering stresses under triaxial loading conditions.

Neutron radiography can be used to measure the movement of phase and fluid boundaries in real-time provided that there is a sufficient contrast difference between the fluids at the boundary. Implementation considerations include radiograph exposure time, capture rate, total attenuation of the neutron beam through the sample, and symmetry of the flow field. Exposure time limits the ability to resolve dynamic changes of the flow field. If the exposure time required to produce a clear image is significantly larger than the time that it takes the feature of interest to move 1 pixel in the field of view, then the structural characteristics of the flow will be averaged over the image field.

Figure 10 shows an example of a 38.4 mm diameter by 152.4 mm long cylindrical granite sample prepared for a fracture flow experiment. The sample is bisected along the axis, and the two flat faces are offset using spacer shims to create a flow channel representing a fracture. Figure 11 shows a sequence of radiographs of the sample as it is being filled with water inside the pressure cell at a rate of ∼1 l/min. The fracture was initially filled with air, and a 10 ms exposure time was used for each image. The average velocity of the water in this fill sequence is ∼30 cm/s, based on the volumetric flow rate of the water and aperture dimensions of the fracture (31.25 × 1.6 mm2), so the water front moves a distance of ∼0.3 cm over the course of each exposure. Therefore, while the image resolution of the radiograph is technically 300 µm, the motion of the front is effectively smeared over 10 pixels. The motion of the air/water boundary can, nonetheless, be seen in the sequence of images (water is represented with brighter pixels in this set of images) as well as in an air bubble near the flow front. Higher resolution measurement of the flow front and bubble geometry would require a shorter exposure time. Thus, the exposure time required to capture the flow dynamics must be balanced against the time required to capture an image of sufficient contrast. Similar considerations must be applied to the image capture rate. A high capture rate is required to resolve rapid variations in the field of view, but this is at the expense of larger data storage requirements.

FIG. 10.

Engineered granite sample.

FIG. 10.

Engineered granite sample.

Close modal
FIG. 11.

Image sequence of water (brighter pixels) filling an initially air-filled engineered fracture in a granite sample inside the pressure cell.

FIG. 11.

Image sequence of water (brighter pixels) filling an initially air-filled engineered fracture in a granite sample inside the pressure cell.

Close modal

An example of a two-constituent immiscible flow through porous media experiment is shown in Fig. 12. The sample in this experiment was a porous sandstone that was initially saturated with hexadecane (C16 H34), a proxy for oil in an enhanced oil recovery experiment. The hexadecane is displaced by supercritical CO2 under conditions representative of in situ subsurface conditions. The image sequence captures the spatial and temporal dynamics of the displacement in a manner that cannot be obtained by other experimental methods (to the authors’ knowledge). Unlike the previous example, where the fluid was contained in a planar fracture and the thickness of the fluid through which the neutron beam passes along the width of the image was constant, the thickness of the fluid through which the beam passes in this experiment was greatest in the center and diminished toward the edges because it was approximately homogeneously distributed through the cylindrical sample. Thus, the images obtained require correction to account for the additional attenuation of the beam through the center, without which the results give the impression that the distribution of hexane remaining at the center is larger than that at the edges. Asymmetries in the displacement of the hexadecane by the CO2 are, nonetheless, visible in the image sequence.

FIG. 12.

Image sequence of supercritical CO2 displacing hexadecane in a sandstone sample in the pressure cell.

FIG. 12.

Image sequence of supercritical CO2 displacing hexadecane in a sandstone sample in the pressure cell.

Close modal

Measuring the velocity and direction of a single-constituent fluid within the cell requires injection of a contrast agent in order to implement particle image velocimetry methods (Polsky et al., 2015). Applications of this approach to date have included the measurement of the fluid flow within both engineered and naturally fractured geological samples. In the case of engineered fractures, for example, samples have been fabricated with different surface roughnesses in order to quantify flow fields and visualize the onset of laminar to turbulent flow transitions as a function of surface characteristics.

Initial efforts developing these techniques employed an injection system that delivered large slugs of contrast agent into the primary fluid flow. Figure 13 shows representative results of water flow experiments using a fluorocarbon-based liquid (FluorinertTM) as the contrast agent for the granite sample configuration shown in Fig. 10 above. It is evident that the seeding of the flow field with the contrast agent was highly nonuniform using this approach. Because the contrast agent and primary flow fluid have different viscosities and densities, this distorts the flow field from its natural condition and precludes accurate quantification of the flow structure (Fig. 14).

FIG. 13.

Contrast slug injection through the fracture flow sample shown in Fig. 10. Fluorinert is the contrast agent and water is the primary flow fluid.

FIG. 13.

Contrast slug injection through the fracture flow sample shown in Fig. 10. Fluorinert is the contrast agent and water is the primary flow fluid.

Close modal
FIG. 14.

Needle bubbler contrast injection through the fracture flow sample shown in Fig. 10. Fluorinert is the contrast agent and water is the primary flow fluid.

FIG. 14.

Needle bubbler contrast injection through the fracture flow sample shown in Fig. 10. Fluorinert is the contrast agent and water is the primary flow fluid.

Close modal

An improved injection scheme was, therefore, developed using high-pressure capillary tubing, as described in Sec. III. This produced sparsely distributed bubbles of the contrast agent in the flow field with controllable dimensions that could be tracked and correlated with the speed and direction of the flow field. Image processing tracking algorithms have been developed to quantify flow field characteristics. The individual bubbles are segmented in the image, and their positional changes in image sequences are used to calculate their velocity. An example quiver plot of bubble velocities for a contrast injection sequence is provided in Fig. 15. The length of each arrow corresponds to the bubble speed.

FIG. 15.

Quiver plots of contrast agent bubble trajectories and speeds from the fracture flow experiment of the granite sample in the test vessel.

FIG. 15.

Quiver plots of contrast agent bubble trajectories and speeds from the fracture flow experiment of the granite sample in the test vessel.

Close modal

Strain measurement using neutron diffraction is performed by irradiating the sample within the test cell with a collimated neutron beam that is either monochromatic or white (with energy separation as a function of time) and measuring the intensity of the reflected beam as a function of either diffraction angle or neutron wavelength. This produces a diffraction pattern from which peaks can be quantified and related through Bragg’s law to the lattice–plane spacing (an example diffraction pattern is shown in Fig. 16).

FIG. 16.

Example diffraction pattern of Carthage Marble sample with 113 and 104 lattice planes marked.

FIG. 16.

Example diffraction pattern of Carthage Marble sample with 113 and 104 lattice planes marked.

Close modal

Bragg’s law is given by the expression = 2dhkl sin(θ), where λ is the neutron wavelength, dhkl is the lattice plane spacing, and θ is the angle between the incident and reflected beams. The relative strain of the sample is determined by measuring the lattice plane spacing of the sample before and after successive load steps using

εhkl=dhkldhkl0dhkl0,
(5)

where εhkl is the lattice–plane strain and dhkl and dhkl0 are the final and initial measured lattice–plane spacings.

Lattice strains can be related to macroscopic stresses through the use of diffraction-specific elastic constants. The stress–strain relationships for a macroscopically isotropic material without preferred crystal orientations, commonly referred to as texture, are

σij=Ehkl1+υhklεijhkl+υhkl12υhklεkkhklδij
(6)

and

εijhkl=1Ehkl1+υhklσijυhklσkkδij,
(7)

where σij are the macroscopic stresses and Ehkl and υhkl are diffraction-specific elastic constants for assumed isotropic material behavior (Hutchings et al., 2005).

To illustrate the ability of neutron diffraction to perform internal-strain measurements within samples using the high-pressure test vessel, a 38.1 × 154 mm2 cylindrical Carthage Marble sample was installed and subjected to a confining stress of 27.6 MPa. Neutron diffraction measurements of the lattice plane spacings within the sample were measured at three points on a plane perpendicular to the sample axis, as depicted in Fig. 17, with and without a confining load. Point 1 was located at the center of the sample, point 2 was located 5 mm from the center of the axis in the x-direction, and point 3 was located 5 mm from the center in the y-direction. The measurements were performed at the VULCAN beamline at the Spallation Neutron Source at the Oak Ridge National Laboratory. The layout of the instrument is shown in Fig. 18. The point locations were selected such that the measured sample strains correspond to either circumferential or radial strains based on the beam and detector orientations. The axial symmetry of the load and the sample geometry produce circumferential and radial strains that should be equal throughout the sample for an isotropic material.

FIG. 17.

Measured point locations within the sample.

FIG. 17.

Measured point locations within the sample.

Close modal
FIG. 18.

VULCAN instrument layout. Labels: (1) incident neutron beam, (2) diffracted beams, (3) sample, (4) measured strain component directions, (5) ±90° neutron detectors.

FIG. 18.

VULCAN instrument layout. Labels: (1) incident neutron beam, (2) diffracted beams, (3) sample, (4) measured strain component directions, (5) ±90° neutron detectors.

Close modal

Carthage Marble is a nominally isotropic material largely composed of calcite. Table I shows the measured strain values within the sample for the (104) and (113) calcite lattice planes. These peaks were chosen for evaluation because they produced the lowest numerical fitting errors among the high-intensity calcite peaks. The error of the diffraction peak fitting for these measurements corresponds to accuracies on the order of 10s of microstrain, so the radial and circumferential strains are nominally equivalent when considering the measurement error. This matches the expectation for the load case, sample symmetry, and isotropic elastic material behavior.

TABLE I.

Measured radial and circumferential strains in microstrain units within the Carthage Marble sample at three points within the sample, as depicted in Fig. 17.

ϵrϵθ
Lattice planeLattice plane
(104)(113)(104)(113)
Point 1 208 195 209 183 
Point 2 238 208 225 216 
Point 3 221 195 241 228 
ϵrϵθ
Lattice planeLattice plane
(104)(113)(104)(113)
Point 1 208 195 209 183 
Point 2 238 208 225 216 
Point 3 221 195 241 228 

Further assessment of the lattice strains, their expected values, and their relationship with macroscopic linear elastic isotropic material behavior can be evaluated using Eq. (7). This first requires determination of the diffraction elastic constants. A set of uniaxial compression tests using a different Carthage Marble sample was performed for this purpose. Figures 19 and 20 show the measured (104) and (113) plane lattice strains in the load and transverse load directions for six uniaxial compression tests measured at three different locations within the sample. The average diffraction Young’s moduli for these measurements are 80 GPa and 86 GPa, and the average Poisson ratio values are 0.34 and 0.34 for the (104) and (113) planes, respectively.

FIG. 19.

Results for six uniaxial compression stress vs strain tests for the calcite (104) lattice plane and linear regression fits through data.

FIG. 19.

Results for six uniaxial compression stress vs strain tests for the calcite (104) lattice plane and linear regression fits through data.

Close modal
FIG. 20.

Results for six uniaxial compression stress vs strain tests for the calcite (113) lattice plane and linear regression fits through data.

FIG. 20.

Results for six uniaxial compression stress vs strain tests for the calcite (113) lattice plane and linear regression fits through data.

Close modal

Substitution of the diffraction elastic modulus and Poisson ratio into Eq. (7) produces expected circumferential and radial strain values of 228 microstrain and 212 microstrain for the (104) and (113) planes, respectively. These calculated values are within 1.5%–8.8% of the measured values shown in Table I. Substitution of the measured diffraction elastic constants and Table I lattice strains into Eq. (6) produces the computed radial and circumferential macroscopic stress values shown in Table II. Measured strain and calculated macroscopic stress values in general compare very well with the values expected for the load condition and measured material properties affirming the usefulness of the experimental method.

TABLE II.

Computed radial and circumferential stresses within the Carthage Marble sample using Eq. (6) with measured radial and circumferential lattice strains.

σrσθ
Lattice planeLattice plane
(104)(113)(104)(113)
Point 1 25.2 25.0 25.3 24.2 
Point 2 28.4 27.4 27.6 27.9 
Point 3 27.4 26.5 28.6 28.6 
σrσθ
Lattice planeLattice plane
(104)(113)(104)(113)
Point 1 25.2 25.0 25.3 24.2 
Point 2 28.4 27.4 27.6 27.9 
Point 3 27.4 26.5 28.6 28.6 

It is noted that the applications described in this section represent distinct strain or flow measurement experiments. This is because the measurement of the lattice plane strain and neutron imaging involve distinct techniques (diffractometry vs radiography), and high-resolution neutron instruments are currently configured to perform one measurement type or the other. There are many geological processes for which simultaneous investigation of flow and rock deformation are of interest. While current neutron instruments are not configured for performing simultaneous flow and strain measurements, there are emerging methods, such as Bragg edge imaging, and spectral imaging instruments, such as the VENUS beamline currently under construction at the Spallation Neutron Source at the ORNL, that may enable this capability in the future (Chen et al., 2004; Fourar and Bories, 1995; Hutchings et al., 2005; Manning and Labrow, 1971; and Polsky et al., 2013).

This paper describes in detail the design of a high-pressure, high-temperature test vessel for performing neutron irradiation experiments on geological materials and demonstrates the ability of neutron imaging and neutron diffraction to quantify flow behavior and mineral strain within geological samples subjected to triaxial loading conditions. The ability to perform measurements within materials at in situ stress and temperature levels reflecting conditions within the crust of the earth represents a powerful and arguably unique tool. The presented proof-of-principle examples are relevant to a broad range of geotechnical applications and represent only a subset of the potential uses for the test cell for neutron imaging and diffraction measurements. These methods can be used to inform our fundamental understanding of flow through porous and fractured geological media, mineral deformation in geological materials, and can be used to improve our understanding and practice of geotechnical engineering.

J.R.C. and Y.P. contributed equally to this work.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This manuscript has been authored by UT-Battelle, LLC, Contract No. DE-AC05-00OR22725, with the U.S. Department of Energy (DOE). The U.S. government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

Research was supported by the Geothermal Technologies Office, Office of Energy Efficiency and Renewable Energy, U.S. Department of Energy under Contract No. DE-AC05-00OR22725, Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.

Research at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.

The authors also acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work.

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