PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering

Stanford University, Stanford, California, February 24-26, 2014

SGP-TR-202

1

Strain Measurement of Geological Samples Subjected to Triaxial Stresses Experienced

During Hydraulic Loading

Yarom Polsky, Lawrence Anovitz, Ke An and Luc Dessieux

Oak Ridge National Laboratory

1 Bethel Valley Rd

Oak Ridge, TN, 37831 U.S.A

e-mail: polskyy@ornl.gov

Keywords: hydraulic fracture, strain measurement, rock mechanics testing, triaxial testing

ABSTRACT

Understanding stress, strain and material failure relationships, and having the ability to predict these quantities for known load

conditions, is crucial to all geomechanics and, in some instances, reservoir flow applications. The constitutive equations governing

the deformation of geological materials are typically adequate for bulk or large scale deformation and stress analyses. However,

these rules are generally less precise in their ability to make accurate predictions in physical processes where highly localized

material heterogeneity exists or where the presence of geometric irregularities such as micro-cracks may be present. This is

especially relevant to EGS where hydraulic fracture propagation models are needed to develop optimal reservoir creation strategies

and where fracture permeability is significantly influenced by regional stress states and may affect reservoir operation strategies.

The deficiencies of the models used to describe these physical processes are a practical reality necessitated by the manner in which

rock properties must be obtained. Conventional rock mechanics tests subject samples to controlled load conditions and measure

bulk deformations of the sample or more localized deformations only on exposed surfaces of the sample. They are currently unable

to comprehensively map the deformation state within the sample. For processes such as fracture, however, the state of a particular

region within the rock drives the overall failure behavior of the sample.

The authors believe that developing a means to measure strains within samples subjected to hydraulic fracture loading conditions

will provide a useful tool for understanding the localized effects not captured by conventional techniques and may serve as a

method for improving hydraulic fracture models. An ongoing effort at Oak Ridge National Laboratory endeavors to develop a

neutron diffraction based strain measurement capability to interrogate the strain state of a geological sample, at arbitrary internal

locations, subjected to a triaxial stress state. The basis of the method and initial results for simple load conditions were reported at

last year’s Stanford Geothermal Workshop. This work will report results from recent neutron diffraction strain measurement

experiments in which marble samples were subjected to load conditions more representative of hydraulic fracturing operations

within a pressure cell specially designed for the reported strain measurement technique.

1. INTRODUCTION

Understanding and modeling hydraulic fracture propagation has been an active area of research since it became a viable practice for

enhancing production in Oil & Gas applications in the early 1950’s. A variety of models have been developed over the years to

describe the hydraulic fracture propagation process including the PKN, KGD, and assorted 3-D models. They are generally based

on linear elastic fracture mechanics and posit that fracture initiation occurs when a critical stress intensity factor is exceeded. This

factor is generally related to the presence of a crack in the material which produces a region of elevated stress near the crack tip.

For the simple 2D case of a mode 1 crack developing radially from a hole in a plate, the regional stress is given as (Rice, 1968)

[

]

√

[

]

(1)

where are the stresses near the crack tip, KI is the stress intensity factor, and r and θ are cylindrical coordinates for a reference

frame with origin at the tip of the crack.

Conventional methods, such as strain gauges, are generally unable to measure the strain corresponding to this stress unless the

crack extends to an exposed surface. This is a significant limitation for bulk samples because it prevents comprehensive

characterization of the material stress state and relationship of this state to material failure. Appropriate failure criteria for rocks are

therefore arguably best determined using conventional rock mechanics testing and measurement methods by statistically comparing

the predictions of various criteria developed over the years to numerous experiments (Colmenares and Zoback, 2002). While this

empirical technique may be practical and statistically effective, it does not provide insight into the fundamental mechanisms and

structural features that drive failure.

There have also been a relatively large number of experimental efforts in recent years studying hydraulic fracture at the laboratory

scale. Much of this work has focused on using techniques such as acoustic emissions to better understand fracture event onset,

location, evolution and propagation dynamics (Stroisz et al, 2013and Damani et al, 2013). It is often accompanied by post-mortem

examination of the specimens using inspection methods such as X-Ray computed tomography or scanning electron microscopy. It

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has also often involved comparison of experimental results to simplified fracture initiation pressure models such as the Hubert and

Willis model:

(PC-Po)=T+3σh-σH

(2)

There is generally significant scatter in the data produced during these experiments indicating that a number of factors such as

material heterogeneity, grain boundary effects or the presence of stress rising features may have a significant influence on fracture

onset. The current lack of means to perform measurements internal to the sample is a significant limitation to further understanding

of this variability.

This work is part of a long term effort to adapt neutron diffraction based strain measurement techniques to geological applications.

The highly penetrating nature of the neutron permits the use of such techniques even when otherwise opaque structures such as

pressure vessels surround the measured specimen. Successful development of the method will permit strain mapping of the internal

regions of core samples subjected to triaxial stress conditions while undergoing hydraulic loading. This enabling capability can be

used to study many critical factors affecting or driving the hydraulic fracture process including, but not limited to, residual strains in

specimens prior to loading, localized strain variations within otherwise symmetrically loaded samples and the association of these

states with stress raising features or material variability, and strain redistribution within specimens during loading. This quantitative

tool can in turn be used to develop better models of the fracture initiation process and/or validate existing models.

The path to developing the methodology for implementing this capability is admittedly challenging. The sample environment and

experimental setup must be carefully designed for use with neutron diffraction instruments, the scattering characteristics of the

experimental setup and sample must be well understood in order to ensure that sufficient scattering statistics are accumulated to

enable accurate calculation of lattice parameters, and processing of the acquired neutron intensity data must be carefully performed

and related to calibration experiments in order to accurately calculate strain of the interrogated sample volumes. This paper will

describe the most recent efforts completed in this pursuit.

2. EXPERIMENTAL DESCRIPTION

A detailed description of the geothermal pressure cell was provided in a paper published at last year’s Stanford Geothermal

Workshop (Polsky et al, 2013). The cell design permits independent pressurization of the core surfaces in the axial and radial

direction to produce compressive loads representing confining stresses similar to conventional triaxial test methods. The core

specimen dimensions for the cell are 38.1 mm diameter by 152.4 mm length. Carthage Marble specimens were used in the

experiments described in this publication. A 75 mm long, 6.35 mm diameter hole was drilled through the center of one end of the

sample. Fluid pressure was to be simultaneously applied through the sample axial surface and this hole to create a fracture inducing

stress, resembling a stress on a borehole wall, with equivalent axial confining pressure.

Hydraulic fracture for this configuration is only achievable if the pressure applied to the hole exceeds the radial confining pressure.

It was discovered that this was not possible during trials performed prior to the neutron experiments because the pressures were not

adequately isolated from each other. This configuration uses an o-ring seal between the rock surface and axial flow component of

the pressure cell. Measurements performed after initial test failure indicated that the axial faces of all samples were between 5 and

10 degrees misaligned with the cylindrical axis of the sample. This sealing surface misalignment prevented the o-ring from

performing its sealing function, allowing the bypassed fluid to act on the sleeve delivering radial confining pressure. This sleeve is

unable to resist outward radial pressure and failed repeatedly during the staging of the experiment.

There was insufficient time for re-machining of the samples to meet alignment specifications prior to the neutron experiment so the

decision was made to epoxy a stainless steel tube in the hole to deliver fracture pressure. The tube was inserted to a depth of

approximately 25 mm. This sample configuration is depicted in the left of the Figure 1 below and only permits application of radial

confining pressure in addition to internal pressurization of the hole in the sample. This method was then successfully demonstrated

for initiating hydraulic fracture in the laboratory.

Neutron diffraction lattice spacing measurements were made through the pressure cell at 2 axial locations within the core sample at

each load step. The axial locations were 25 mm above the hole bottom and 30 mm above the hole bottom. Four points with gage

volume dimensions 2 mm x 2 mm x 12 mm were measured at roughly 2 mm from the hole wall for a total of 8 measurement points

per load step (see Figure 1 left for reference). The 12 mm dimension corresponds to the axial direction of the sample.

Lattice strain measurement was done at the VULCAN engineering diffractometer at the Spallation Neutron Source, Oak Ridge

National Laboratory (An et al, 2011). Lattice plane measurements were performed per the load schedule shown below in table 1.

The internal pressure level in load step 2 was meant to be sufficiently far from the expected failure load to ensure that fracture

initiation did not occur before the sample was placed in the beam. If rock failure occurs before the sample is placed in the beam

then measurements must be repeated over the entire load history for a new specimen to capture the strain evolution with load.

Future experiments will perform laboratory characterization of the fracture initiation pressure for multiple samples to identify an

appropriate peak internal pressure value that is closer to the fracture initiation pressure. Adjustment of the internal pressure

following neutron measurements produced fracture of the Carthage Marble sample at approximately 31 MPa. A photo of the

sample following fracture is shown in the right of Figure 1 below. This tensile failure in the plane perpendicular to the axial

direction is a result of the lack of compressive confining pressure in the axial direction. Future modification of the experimental

setup will ensure that the minimal principal stress is in the radial direction in order to produce fracture directions more

representative of subsurface conditions.

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Figure 1: Sample configuration and measurement points (left), Pressure cell with sample in Vulcan Neutron Instrument

(center) and Post fracture core sample (right)

Confining Pressure Internal Pressure

Baseline 0 MPa 0 MPa

Load Step 1 14.5 MPa 0 MPa

Load Step 2 14.5 MPa 17.25 MPa

Table 1: Confining and internal pressures for measurement steps.

3. RESULTS

3.1 Lattice Strain Measurements

Strains associated with lattice deformations were calculated in the standard manner by evaluating peak shifts associated with

particular crystallographic planes using the relation

(3)

where is the measured lattice plane spacing at a load measurement point and is the lattice plane spacing with no external

loading. Lattice values at the 0 MPa load state were taken for the of each measured location for the strain mapping

measurement in the pressure cell experiments. This provides a strain value relative to the baseline condition, which may contain

residual stresses, however it does not necessarily provide a strain value of the rock relative to a stress free state. More representative

stress free values are typically obtained from powder diffraction samples. Such data was not obtained in time for this

publication but is planned in the near future.

Accurate strain calculation using this technique is a meticulous process requiring extensive instrument calibration and

understanding of the scattering characteristics of the system exposed to the beam. The data reduction procedures must also be

carefully performed to ensure that the neutron intensity data collected during the experiment is sufficient and accurately related to

lattice spacing values. The first two sets of experiments performed at the Spallation Neutron Source Vulcan beam line have been

learning experiences on the path to establishing the validity of the approach. The first set of experiments performed as part of this

effort in December of 2012 focused on lattice strain measurement of geological specimens during uniaxial compression tests to

develop diffraction specific elastic constants. For relatively isotropic, texture free materials (materials without preferred grain

orientations), macroscopic stresses can then be related to lattice plane family strains using the constitutive relation (Hutchings et al,

2005):

[

] (4)

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The uniaxial load tests verified that strains can be reliably and accurately measured for geological specimens. The stress-strain

curves obtained for the Carthage Marble calcite crystal lattice planes are shown below in Figure 2. The elastic moduli for the

different planes are consistent with literature values as reported last year (Polsky et al, 2013). A cubic polynomial fit for the

measured macroscopic stress versus lattice strain is also shown in each graph.

Figure 2: Stress vs strain curves for calcite lattice planes measured for uniaxial compressive load tests

The fidelity of the data calculated in the triaxial loading experiments was in general poor. The 8 measurement points, 4 lattice

planes per point (006, 018, 104 and 113) and two load steps evaluated during the experiment result in 64 possible lattice strain

measurement points. The selection criteria typically used for a good fit of the neutron intensity data are the chi-squared statistic and

the number of raw neutron counts measured in the fitting region. The latter was particularly low for the experiments performed and

is attributed to scattering and attenuation by the titanium pressure cell, whose scattering tendencies were not adequately

characterized prior to the measurements. Improved statistics could have been achieved with increased counting time or selection of

a pressure cell material with better scattering characteristics, such as Aluminum. The poorer quality of the data is illustrated by

comparing a representative fit from the uniaxial load tests, which did not require the pressure cell, with a representative fit from the

pressure cell experiments as shown in the figure below.

Figure 3: Peak fits uniaxial load test (left) and pressure cell test (right)

A small set of the total, 18 of 64 points, were considered to have reasonable d0 and d values to justify lattice strain calculations. It is

important to note that both the initial and shifted lattice plane must be accurate in order to calculate an accurate strain value. With

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respect to threshold measurement counts for selection, the bank 1 and bank 2 detectors of the instrument showed different

sensitivities so different selection criteria were used for the data produced from each bank. Bank 1 measured peaks were fitted if

their intensities exceeded 1000 counts and bank 2 peaks were fitted if their intensities exceeded 300 counts. Peak fits were accepted

for strain calculation only with chi-squared values below 1.5. Additionally, it was noticed when initially using the peak fitting

algorithm that peak identified by the algorithm sometimes varied based on the initial values set by the user. Sensitivity analysis was

performed on all candidate peaks by evaluating the output produced by a range of initial lattice spacing and peak width values and

only peaks with less than 0.001% variation were accepted.

The lattice strains, d values and chi-squared values calculated from reasonable data points are shown are shown below in Table 1

for illustrative purposes. It is reiterated that although these values in principal seem reasonable, the data fidelity would be much

improved with better neutron counting statistics. Also for reference, the measurement point locations within the sample and strain

measurement directions of the instrument are shown from the plan view below in Figure 4. Understanding this orientation is

necessary for relating the strain measured by the instrument to a more convenient cylindrical coordinate system with origin at the

center of the sample. Bank 2, for example, measures radial strain in the sample cylindrical coordinate system while bank 1

measures circumferential strain.

Point Load # Bank Plane d0 d Lattice Strain Chi Squared

2 1 1 104 3.019956 3.019235 -238.7452003 1.36

2 1 1 006 2.830121 2.829467 -231.085526 0.90799999

5 1 1 104 3.019252 3.018724 -174.8777512 1.17

7 1 2 018 1.915553 1.915275 -145.1278038 1.12

5 2 1 104 3.019252 3.018763 -161.9606446 1.17

4 2 2 113 2.28942 2.289328 -40.18485031 1.05

4 2 2 104 3.045671 3.045507 -53.84691912 1.16

7 2 2 018 1.915553 1.915471 -42.8074817 1.12 Table 1: d0, d , lattice strain and Chi-squared values for select measurement points

Figure 4: Measured strain directions and locations of measurement points in r,θ plane of sample

3.2 Comparison to Finite Element Results

Finite element analysis (FEA) of the sample load cases was performed with COMSOL software for comparison to lattice strain

measurement results. Figures 5 and 6 below show radial and circumferential stresses versus the distance from the hole surface to

the outer diameter of the core sample. The length unit on the x-axis is inches. The strain values measured in the experiment

represent lattice strains and are not equivalent to macroscopic strains. They must be related to macroscopic stresses using

diffraction elastic constants as defined in equation (4). This is not feasible for the performed experiments because the complete

strain state was not captured due to the limited data available as explained above. All load case 1 strain values for example are

circumferential strains. Because the radial strains near the borehole wall are low for this load case it is nonetheless possible to

estimate the macroscopic stresses from the stress-strain curves shown in Figure 2.

Estimates of macroscopic stresses were made for applicable data points using this method. Only points for the 018 plane were not

estimated because there were no lattice stress-stain curves for this plane available from the uniaxial load tests. It is also noted that

the estimated stresses correspond to average stresses within the gage volume of measurement as opposed to element stresses as

typically obtained from FEA. Accurate relation of the measured stresses to simulated stresses requires averaging of the simulated

stresses over the measurement gauge volume. The average circumferential and radial stresses for load case 1 are 24 MPa and 5 MPa

respectively. The load case 2 values are 13 MPa in the circumferential direction and 16 MPa in the radial direction. Results of the

stresses as determined from the lattice strains are displayed in Table 2. Most of the stresses are in reasonable agreement

demonstrating the fundamental viability of the strain measurement technique.

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Figure 5: Radial (left) and Circumferential (right) stresses from hole surface to sample outer diameter for 14.5 MPa

confining pressure, 0 MPa internal pressure (x-axis is distance in inches from the hole surface)

Figure 6: Radial (left) and Circumferential (right) stresses from borehole wall to sample outer diameter for 14.5 MPa

confining pressure, 17.25 MPa internal pressure

Point Load # Bank Plane Lattice Strain Macroscopic Stress Stress Direction

2 1 1 104 -238.7452003 25 θ

2 1 1 006 -231.085526 22 θ

5 1 1 104 -174.8777512 17 θ

7 1 2 018 -145.1278038 N/A θ

5 2 1 104 -161.9606446 14 R

4 2 2 113 -40.18485031 3 θ

4 2 2 104 -53.84691912 5 θ

7 2 2 018 -42.8074817 N/A θ Table 2: Estimated macroscopic stress corresponding to measured lattice strain for select points and load steps

CONCLUSION

Significant progress has been made demonstrating the applicability of neutron diffraction based strain measurement methods to

rock mechanics applications. This publication reported lattice strain measurements of the interior of a Carthage Marble sample

subjected to a hydraulically-induced triaxial stress state. The evolution of this effort has been a learning experience made difficult

by the structural complexity of geological samples, which complicates acquisition and interpretation of neutron measurements, and

the interactions of the pressure cell with the neutron beam. Processing of the acquired neutron intensity data has also been a

challenge, but it is believed that a reasonable methodology has been developed for reducing data to strain values and it is believed

that these strain values can be reliably related to macroscopic stresses.

Further advancement of this technique holds great promise for geological applications, including geothermal energy extraction, and

the rock mechanics community in general. The ability to measure the strain experienced in the interior volume of a sample at

arbitrary locations in a high pressure environment is a unique and valuable tool. The authors are aware of no other method for

making measurements of the strain state within bulk samples. It is believed that these techniques, once developed, will enable

otherwise difficult or impossible insights into critical subsurface applications such as hydraulic fracturing and will serve as both a

means for improving theory and understanding of such processes as well as a means for validating simulation tools.

Future experimental efforts will focus on improving the neutron scattering characteristics of the pressure cell and honing the

procedure for determining when adequate counting statistics have been acquired. An Aluminum pressure vessel has been

constructed to address the former concern and is expected to provide a 3-4 time reduction in beam attenuation and scattering.

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Consideration will also be given to redesigning the mating interface between the pressure vessel and the axial core sample face to

eliminate the sealing issue experienced during the reported experimental work.

ACKNOWLEDGEMENT

Research supported by the Geothermal Technologies Office, Office of Energy Efficiency and Renewable Energy, U.S. Department

of Energy under contract DE-AC05-00OR22725, Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC.

The 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 would also like to thank Mr. Harley Skorpenske and Mr. Dunji Yu for their support during the neutron diffraction

experiment.

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