SUGGESTED METHODS FOR UNIAXIAL‐STRAIN ... - ISRM · PDF fileSM UniaxComp Draft 13April2015...

SM UniaxComp Draft 13April2015

SUGGESTED METHODS FOR UNIAXIAL‐STRAIN COMPRESSIBILITY TESTING FOR RESERVOIR GEOMECHANICS (Draft to ISRM Commission on Testing, 13 April 2015)

1. Introduction

Rock bulk volume and pore volume compressibility are key parameters needed for an accurate understanding of the formation deformation response to pore pressure changes in rocks and sands. They can have a critical impact on both the economics and containment risks associated with fluid withdrawal or injection operations, particularly in the petroleum industry (where, e.g., reservoir compaction and subsidence impacts can be many millions of US$). It has been established that rock properties, including compressibilities, are often stress-path dependent. The uniaxial-strain (zero-lateral-strain) stress path is often considered the most representative stress path for many petroleum-related recovery processes, as it normally approximates the underground boundary conditions thought to be active during hydrocarbon recovery or fluid injection disposal operations. Figure 1 illustrates the deformation differences between hydrostatic, deviatoric, and uniaxial-strain compression on a homogeneous and isotropic material. The uniaxial-strain compressibility can vary over several orders of magnitude, and in addition it can be constant or highly variable with stress, all depending on the character of the material (Crawford et al 2011), which highlights the importance of accurately determining the compressibility. This document presents suggested methods (SM) for conducting uniaxial-strain compressibility measurements, for which no widely accepted Standard or SM is currently available. It has been developed by a group of petroleum geomechanics practitioners from industry and academia with experience in these measurements and a commitment to help improve their standardization and quality.

Figure 1. Deformation characteristics of hydrostatic (A), deviatoric (B) and uniaxial-strain (C) compression of a homogeneous and isotropic material.

2. Scope 2.1 Purpose

The SM provided here is primarily directed at formation compressibility measurements made to support reservoir geomechanics needs. They are not intended, for instance, for shallow soil consolidation or other (relatively) low stress testing. The objective is to provide information to help knowledgeable persons understand the requirements of equipment and measurement sensors needed to make the measurement, provide suggested testing protocols, detail how to determine the various compressibility parameters from the measured data, and decide what data and parameters to report. The apparatus


requirements for uniaxial-strain compressibility testing on cylindrical samples are described in Section 3, including important details on how to ensure accurate maintenance of the zero-lateral strain boundary conditions. Sample preparation for these and other geomechanical tests are provided in Section 4, consistent with other ISRM SM and ASTM standards in place at the time of publication. Section 5 details fluid-drained testing protocols that directly mimic the subsurface stress conditions with pressure depletion/inflation related to production/injection processes, and also those that simply mimic the effective stress path while maintaining a constant pore pressure. Analysis procedures for determining the various compressibility parameters that are measured in the different protocols are provided in Section 6, and the documentation required for reporting the sample and testing details and results is given in Section 7. Various other relevant notes, references and acknowledgements are provided in the remaining Sections.

2.2. Limitations

The SM presented is intended to provide guidance for those experienced in the equipment and materials associated with rock mechanical testing of reservoir core and other formation material. Discussion of the health, safety and environmental hazards of such testing, which are specific to the particular test equipment, material and test conditions, are beyond the scope of this document. Likewise, the effects of such things as cleaning methods, pore fluid, degree of saturation and temperature on the measured compressibility, while important, are not addressed here. The SM protocol conditions should simulate reservoir conditions as closely as can be practically achieved. Ideally, the stresses, pore pressure, stress path, sample orientation relative to the applied stresses, sample saturation, and temperature of the test protocol should match reservoir conditions. Conducting uniaxial-strain compressibility tests that deviate from reservoir conditions have the potential to generate results that are not representative of the reservoir in-situ rock mechanical behavior.

3. Apparatus

This section describes general characteristics of equipment suitable for uniaxial-strain compressibility measurements for petroleum geomechanics, and procedures for calibration of instrumental effects.

3.1 Equipment Capabilities and Guidelines 3.1.1 General Testing Equipment

A uniaxial-strain compressibility test can be performed using a typical triaxial load system that is capable of supplying, controlling, and monitoring confining pressure and axial load (Figure 2), with sufficiently accurate axial and radial deformation instrumentation. Some uniaxial-strain compressibility test protocols require pore pressure control. For a uniaxial-strain compressibility test with a horizontal or axial flow component, a continuous flow pump is necessary. All equipment shall be calibrated at suitable intervals, according to ASTM E4-14 and ASTM E2309/E2309M-05 or their equivalents.


Figure 2. Schematic view of a triaxial test apparatus (deformation instrumentation and other details are not shown).

3.1.2 Triaxial Loading Apparatus

A stiff (typically greater than 1 MN/mm) triaxial loading apparatus should be used that is able to withstand the confining pressure and axial load applied to the sample. The use of a computer and/or servo-controlled loading system is required. A thin impermeable malleable jacket should be placed around the sample in a manner that will seal out the confining fluid from the sample (discussed in greater detail in section 4.8).

3.1.3 Device for Applying Confining and Pore Pressure

A hydraulic pump or some other system of sufficient capacity and capable of fine regulation of the pressure to within ±0.1% of full scale shall be used.

3.1.4 Device for Applying Axial Load

A servo-controlled linear actuator of sufficient capacity and capable of fine regulation of the pressure to within ±0.1% of full scale shall be used. In-vessel measurement of axial load is shown in Figure 2 and is the preferred arrangement, although other arrangements may also be suitable.

3.1.5 Equipment for Measuring and Recording Loads, Pressures, Temperature, and Displacements

The axial and radial strains, axial load, confining pressure and other applicable measurements (including pore pressure, differential pressure, pore fluid temperature and injection rate) need to be monitored and/or controlled during each test. Suitable software should be used to read and record all necessary data. Axial and radial deformation should be monitored by either a strain gauge cantilever system, LVDT system, or other similar system.

Deformations should be recorded to an accuracy of ±0.03% full scale [this is ~12-bit accuracy] and a precision of ±0.001% [for ~16-bit systems] or ±0.01% [for ~12-bit systems]. In particular, for actively maintaining uniaxial-strain boundary conditions the radial deformation sensor(s) need to be free from any hysteresis effects. Internal axial strain measurements are preferred, but external measurement arrangements can be acceptable if the appropriate corrections for system deformation (see Section 3.2) can be made to sufficient accuracy. Pressures and loads should be recorded to an accuracy of ±0.1% of full scale. An internal


load cell is preferred, which eliminates the need to correct for load variations due to friction between the loading ram and any

associated pressure seals. Temperatures should be recorded to a precision of 0.1°C using a sensor accurate to within ±2.5 °C.

3.1.6 Loading Platens

End caps or loading platens should accommodate one of the most common sample diameters in use for petroleum geomechanical testing, 25.4 mm or 38 mm (1.0 inch and 1.5 inch), and should be made of a suitably stiff, hard material (e.g., hardened steel, titanium). Larger sample sizes such as 50.8 mm or 54.0 mm (2.0 inch and 2.125 inch – NX-size core) diameter are sometimes used in order to obtain sufficient representative volume, or to obtain larger pore volume. Surfaces of the end caps should be ground and polished, and their flatness should be ±0.005 mm (ISRM 2007, SM Triaxial Compression 2.3a). Samples should conform to the dimensions and shape described in Section 4.6 below.

3.1.7 Uniaxial-strain Condition Requirements

The accurate maintenance of the uniaxial-strain boundary conditions is of critical importance. The cross-sectional dimension(s) should be measured using either the circumferential strain or the average of two radial strains along orthogonal diameters, or the average of three radial displacements located at 120 degree spacing around the circumference, at the mid-height of the sample. This strain should be controlled to within ±0.0025% (i.e., ±25 microstrain).

3.2 Instrumental Effect Calibration Procedures

It is intended that all in-vessel sensors convert a measured physical value (displacement or force) into a proportional electrical voltage signal. Calibration processes are typically performed at ambient pressure. Therefore, in-vessel sensor output contains both the calibrated transducer linear output voltage and any pressure-induced voltage (either on the instrumentation itself, or on the rest of the system – i.e., sample jacketing material). Methods to calibrate and characterize these system pressure effects, as well as any other system effects on the measurements are essential before proceeding with any measurement.

One technique to calculate the confining pressure correction is to mount all in-vessel instrumentation to a sample with known elastic properties (such as aluminum 6061-T6) and vary hydrostatic stress (see Figure 1, A) to characterize the excess strain response of the system. In order to calculate excess system strain (as in the sample platens), a deviatoric (i.e., axial minus confining) stress correction can be calculated using a similar sample assembly and varying the deviatoric stress (see Figure 1, B).

Once all corrections are characterized, they can be integrated into the signal conditioning or control and data acquisition software to provide real-time correction for all sensors, which is necessary to provide accurate control, especially to maintain uniaxial-strain conditions. A suggested transducer corrected output "y" can be written as:

𝑦 = 𝑚𝑥 + 𝑏 + 𝛽𝑃𝑐 + 𝛾𝜎𝑑

Where “𝑚𝑥 + 𝑏” is the transducer calibration at ambient pressure and temperature,

“+ 𝛽𝑃𝑐” is the confining pressure correction coefficient 𝛽 and 𝑃𝑐 the confining pressure (one possible method for calculating the coefficient is described in 3.2.1), and

“+𝛾𝜎𝑑” is the deviatoric stress correction coefficient 𝛾 and 𝜎𝑑 the deviatoric stress (one possible method for calculating the coefficient is described in 3.2.2).

To verify accuracy of all instrumentation calibration and characterized corrections, a sample of known material properties (aluminum 6061-T6 or similar) can be loaded using non-simultaneous hydrostatic and deviatoric loading cycles, and the results compared to the known material properties (see Figure 3 and Figure 4 for example results from an aluminum 6061-T6 billet). An acceptable tolerance for such a comparison would normally be ±5% on Young’s and Bulk moduli, and ±10% on Poisson’s ratio. An additional verification can be to run a uniaxial loading path on an aluminum sample in order to check radial control.


Figure 3. Measured Young's modulus (left) and Poisson’s ratio (right) of an aluminum 6061-T6 billet during a deviatoric loading cycle. The results are within about 2% of expected values after incorporation of sensor deviatoric load corrections.

Figure 4. Measured bulk modulus of an aluminum 6061-T6 billet during a hydrostatic loading cycle. The results are within about 2% of expected value after incorporation of sensor pressure corrections.

3.2.1 Calculation of Pressure Correction Coefficient for Displacement

To calculate the pressure effects, a hydrostatic test is run on a reference billet at stress levels similar to the rock samples to be tested. The strains (axial, radial #1, radial #2 in this example) are plotted on the y-axis against the confining pressure on the x-axis. The slopes of these lines will be calculated and corrected so that they are equal to the theoretical slope of the reference billet material. Those corrections are then converted back to the calibrated displacement units. The theoretical slope of the material can be calculated as follows:

𝜖𝑣𝑜𝑙 = 𝜖𝑎 + 𝜖𝑟1 + 𝜖𝑟2

𝐾 = 𝐸3(1 − 2Q) = ∑ 𝜎𝑖𝑖3

13𝜖𝑣𝑜𝑙

𝐶 = 𝑑𝜖𝑣𝑜𝑙𝑑𝑃𝑐

= 1𝐾 = 3(1 − 2Q)

𝐸

𝑇𝐻𝐸𝑂𝑅𝐸𝑇𝐼𝐶𝐴𝐿 𝑆𝐿𝑂𝑃𝐸 = 𝜖𝑣𝑜𝑙∑ 𝜎𝑖𝑖3

1= 1

3 𝐶

Where 𝐾 is the Bulk Modulus,


𝜎𝑖𝑖 is the principal stress,

𝐸 is the Young’s Modulus,

𝜈 is the Poisson’s Ratio,

𝜖𝑣𝑜𝑙 is the volumetric strain,

𝜖𝑎 is the axial strain,

𝜖𝑟1 is the radial #1 strain,

𝜖𝑟2 is the radial #2 strain,

𝑃𝑐 is the confining pressure, and

𝐶 is the compressibility.

The theoretical slope as defined above is the slope of an individual strain. Since C is obtained from the volumetric strain, which is the axial strain (𝜖𝑎) + the two radial strains (𝜖𝑟1, 𝜖𝑟2) 𝐶 must be divided by 3 to obtain the slope for an individual strain. It is necessary to obtain a second order least squares polynomial curve fit for each strain versus the confining pressure. The curve fits for the measured and theoretical lines are given by:

𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑠𝑙𝑜𝑝𝑒 = 𝑏1𝑋 + 𝑏2𝑋2

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑠𝑙𝑜𝑝𝑒 = 𝑐1𝑋 + 𝑐2𝑋2

The theoretical curve is linear (𝑐2 = 0). The correction coefficients, 𝑎1and 𝑎2are obtained as follows:

𝑎1 = 𝑐1 − 𝑏1

𝑎2 = 𝑐2 − 𝑏2

There should now be two correction coefficients for each of the strain channels. These correction coefficients can now be applied to the test data. They are applied as follows:

𝐶𝑂𝑅𝑅𝐸𝐶𝑇𝐸𝐷 𝑆𝑇𝑅𝐴𝐼𝑁 = 𝑈𝑁𝐶𝑂𝑅𝑅𝐸𝐶𝑇𝐸𝐷 𝑆𝑇𝑅𝐴𝐼𝑁 + 𝑃𝑅𝐸𝑆𝑆𝑈𝑅𝐸 𝐸𝐹𝐹𝐸𝐶𝑇𝑆

𝐶𝑂𝑅𝑅𝐸𝐶𝑇𝐸𝐷 𝑆𝑇𝑅𝐴𝐼𝑁 = 𝑌 + 𝑎2𝑋2 + 𝑎1𝑋

where 𝑋 is the confining pressure,

𝑎2 is the second order correction coefficient,

𝑎1 is the first order correction coefficient, and

𝑌 is the uncorrected measured strain.

The corrected strain is then converted back to the displacement using the appropriate reference billet dimension. For example, the pressure corrected axial displacement measurement would be:

𝑦 = 𝑚𝑥 + 𝑏 + 𝛽𝑃𝑐 = 𝑌𝐿0 + (𝑎1𝑃𝑐 + 𝑎2𝑃𝑐2)𝐿0

where 𝐿0 is the reference billet length,


𝛽𝑃𝑐 is (in this example) a second-order pressure correction: 𝛽𝑃𝑐 = (𝑎1𝑃𝑐 + 𝑎2𝑃𝑐2)𝐿0

The radial displacement correction is done in an analogous way, using the diameter instead of the length.

Changes to the jacketing material, mounting platens, or mounting positions of individual sensors may alter the correction coefficients. It is necessary to keep the sample assembly geometry consistent with the geometry of the reference billet test.

Temperature may also alter the correction coefficients, so the billet test needs to be done at the approximate (± 5 °C) test temperature.

3.2.2 Calculation of Pressure Correction Coefficient for an Internal Load Sensor

Internal load sensors are preferred to eliminate issues with correcting external load measurements for friction between the loading ram and its associated seals in the pressure vessel. Such friction corrections are hysteretic with ram movement direction and normally more difficult to quantify and reliably correct for. Typical internal deviatoric load sensors, however, normally have a small, linear pressure effect that needs to be corrected for. This is easily accomplished by cycling the confining pressure in the vessel with no axial load applied (i.e., with a gap in the loading stack), and could be done simultaneously with the displacement sensor pressure correction coefficient determination. The negative of the slope of the measured load versus pressure provides the added load sensor pressure correction coefficient:

Ldcorr = Ldmeas + aLdPc

where Ldcorr is the corrected loading force,

Ldmeas is the measured loading force, and

aLdPc is a first-order pressure correction.

Figure 5 provides an example internal load cell pressure correction determination.

Figure 5. Example internal deviatoric load sensor pressure correction determination of aLd =0.025 KN/MPa (0.039 lbf/psi).

3.2.3 Calculation of Deviatoric Stress Correction Coefficient

A typical specimen stack may include both the sample specimen and mounting platens between the measuring devices for axial deformation. Therefore, the axial displacement measured by the sensors is measuring the displacement of the sample as well as the displacement of the mounting platens. To obtain the true axial displacement of the sample the displacement of the mounting platens must be subtracted out of the sensor measurement.


During testing there are three unknowns: the displacement from the strain of the sample, the ‘closure’ of the sample-platen interfaces, and the displacement from the strain of the mounting platens. The displacement of the sample will vary from test to test depending on the deformation properties of the sample, and the interface closure should be the same for similar sample end treatments, and should be negligible above a certain stress level. The effective modulus of the mounting platens is the same from test to test provided the material and geometry of the mounting platens remain the same. Therefore to determine the effective modulus of the mounting platens and therefore the platen strain, an unconfined compression test is run on a reference billet with a known Young’s Modulus (Aluminum 6061-T6 recommended) at stress levels similar to the rock samples to be tested. The true sample displacement is given by:

𝑠𝑎𝑚𝑝𝑙𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑎𝑥𝑖𝑎𝑙 𝑠𝑒𝑛𝑠𝑜𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 – 𝑚𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑝𝑙𝑎𝑡𝑒𝑛𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

Hooks law says that 𝐸 = 𝜎

𝜖

Therefore the displacement of a sample is:

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝜎𝜖 ∗ (𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑎𝑚𝑝𝑙𝑒)

This means that the true displacement of a sample can be expanded to the following equation:

𝜎𝐸 ∗ 𝐿0 = 𝑎𝑥𝑖𝑎𝑙 𝑠𝑒𝑛𝑠𝑜𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 − 𝜎

𝐸𝑚𝑝∗ 𝑙𝑚𝑝

where 𝜎 is the axial stress difference,

𝐸 is the Young’s Modulus of the reference billet (e.g., Al 6061-T6),

𝐿0 is the length of the reference billet,

𝐸𝑚𝑝 is the effective mounting platen modulus, and

𝑙𝑚𝑝 is the length of the mounting platens within the measurement device.

In the above equation all variables are known except 𝐸𝑚𝑝. The axial displacement and σ are recorded during testing, the different lengths are measured, and 𝐸 for aluminum 6061-T6 or other reference billet can be found in most metals handbooks.

To obtain 𝐸𝑚𝑝 it is necessary to find the slope of the line of the stress-strain curve of the mounting platens. This is given by:

𝜖𝑚𝑝 =𝑎𝑥𝑖𝑎𝑙 𝑠𝑒𝑛𝑠𝑜𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 − (𝜎

𝐸 ∗ 𝐿0)𝑙𝑚𝑝

where 𝜖𝑚𝑝 is the strain of the mounting platens. This equation shows how to get the strain in the mounting platens. To obtain the effective mounting platens modulus a linear regression must be taken with the deviatoric stress on the y-axis and the mounting platens strain on the x-axis. The slope should be taken for all the compression cycles. The effective mounting platen modulus is the average of these slopes. It is important to remember that the value will vary depending on the material and geometry of the mounting platens.

Once the effective mounting platen’s modulus is known we can return to the equation for true sample displacement:

𝑠𝑎𝑚𝑝𝑙𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑎𝑥𝑖𝑎𝑙 𝑠𝑒𝑛𝑠𝑜𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 – 𝑚𝑜𝑢𝑛𝑡𝑖𝑛𝑔 𝑝𝑙𝑎𝑡𝑒𝑛𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡

𝑠𝑎𝑚𝑝𝑙𝑒 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝑎𝑥𝑖𝑎𝑙 𝑠𝑒𝑛𝑠𝑜𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 − 𝜎 ∗ 𝑙𝑚𝑝𝐸𝑚𝑝


Therefore the fully pressure and load corrected displacement measurement would be:

𝑦 = 𝑚𝑥 + 𝑏 + (𝑎1𝑃𝑐 + 𝑎2𝑃𝑐2)𝐿0 − 𝜎 ∗ 𝑙𝑚𝑝𝐸𝑚𝑝

Again, changes to the jacketing material, mounting platens, or mounting positions of individual sensors may alter the effective mounting platen modulus. It is necessary to keep the sample assembly geometry consistent with the geometry of the reference billet test.

This correction for axial displacement is linear, and there can sometimes be some remaining non-linear displacement at low stress (e.g., Figure). If this amount of non-linear excess displacement is acceptable then no further correction is required. If, for the sample being tested, it is not acceptable, then an additional correction, non-linear with deviatoric stress, could be considered. However, this additional correction may detrimentally affect the sample data, depending on actual rock response. Alternatively, the operator should ensure that the displacement (and stress) ranges over which the samples will be tested are tightly bound by the load (and pressure) effect correction. In addition, the load cell should be chosen such that its sensitivity is appropriate to the anticipated sample response.

3.2.4 Temperature Considerations

Sensors may have a significant temperature effect on their operation, and therefore calibrations and pressure and load corrections should be done at the expected operating temperature. It is good practice to monitor the sample and/or equipment

temperature, and maintain it at a relatively constant value (e.g., ± 2°C). Calibrations and temperature corrections to allow accurately tracking of the deformation of a sample under significant temperature changes are beyond the scope of this document.

3.2.5 Hysteresis of Corrections

The necessary correction coefficients for increasing confining pressure may not be the same as for decreasing confining pressure. The same holds true for correction coefficients associated with increasing, vs. decreasing, deviatoric stress. In addition, the correction for the very first stress (or load) increase can sometimes be different than the correction for second and later increases. For example, sample jackets may compress differently the first time they feel an increasing confining stress, with some part of the deformation being permanent and not taking place upon unloading nor upon subsequent loading.

It is suggested practice to perform a minimum of three cycles of increasing then decreasing pressure (or deviatoric stress) on the sample of known properties, when determining correction coefficients. Generally, it is sufficient to average the responses of the last two cycles. The part(s) of the cycles used to obtain correction coefficients should correspond as closely as possible to the loading situation that will occur on the rock sample. For certain test protocols the rock deformations of interest take place during the very first loading, while for other test protocols (e.g., pore pressure depletion tests), the rock deformations of interest take place during a confining pressure decrease.

4. Sample Preparation

4.1 Purpose and Scope

This section describes the procedures to prepare rock core specimens for geomechanical tests, uniaxial-strain testing in particular. The intent is to implement steps to obtain oriented, cylindrical rock samples that will meet various specifications and recommendations such as those from ASTM, ISRM, government agencies, JIPs and the academia. Furthermore, all requirements necessary to conform to ASTM Standard D4543-08 are explicitly included in this implementing procedure. Besides those referenced explicitly in this section, other sources consulted for this section include ASTM D2938-71a, Deer and Miller 1966, Hoek and Brown 1980, Jaeger and Cook 1969, and Obert and Duvall 1967.


The following procedures include the topics of bulk rock or whole core orientation, drilling, parallel facing, checking dimensional tolerances and quality control. These guidelines are general enough and applicable not only for uniaxial-strain tests but also for a wide range of geomechanical testing such as (Brazilian) tensile strength, uniaxial compression, triaxial compression (including pore volume compressibility and isostatic compression), acoustic velocity (dynamic elastic properties) and creep tests. A well-prepared ideal homogeneous specimen should produce strains that are uniformly axisymmetric throughout the cylindrical test-sample. Note that this document does not address the safety aspects of preparing rock for geomechanical testing, which are left to the user’s responsibility.

Rock is a complex engineering material that can vary greatly as a function of lithology, stress history, weathering, moisture content and chemistry, and other natural geologic processes. As such, it is not always possible to obtain or prepare rock core specimens that satisfy the desirable tolerances given in this SM. Most commonly, this situation presents itself with weaker, more porous, and poorly cemented rock types and rock types containing significant or weak (or both) structural features. For these and other rock types which are difficult to prepare, all reasonable efforts shall be made to prepare a specimen in accordance with this SM and for the intended test procedure. However, when it has been determined by trial that this is not possible, prepare the rock specimen to the closest tolerances practicable and consider this to be the best effort (see Note 8.6) and report it as such and if allowable or necessary for the intended test.

4.2 Core Plug Dimensions

The rock sample should be a right circular cylinder having a height to diameter ratio of 2.0-2.5. The most common sample diameters in use for petroleum geomechanical testing are 25.4 mm (1.0 inch) and 38 mm (1.5 inch), but larger samples are also sometimes used. The minimum diameter varies with material characteristics, depending on grain-size and other fabric-related dimensions like laminations, clasts, inclusions, etc. For well-sorted clastics, the minimum diameter size is at least 10-times the largest mineral grain.

4.3 Core Plug Orientation

The vast majority of geomechanical testing samples are drilled perpendicular to sedimentary bedding. This is appropriate for compaction and subsidence measurements (although different orientations may be appropriate for other engineering applications). The bedding plane orientation may be determined visually or with other images like X-ray computed tomography (CT) scans. A discussion of rock orientation in preparation for drilling core plugs is examined considering the images in Figure 6. From the drawings in Figure 6, testable, cylindrical rock samples or core plugs should be obtained perpendicular to natural bedding (kV). In Drawing A, the massive depositional feature of the bulk rock or whole core indicates that the cylindrical plugs may be drilled parallel or perpendicular to the axis of the core, provided no in-situ orientation information may be utilized to definitively position the bulk sample along a true earth vertical axis. Drawing B shows two drilling orientations, one parallel to the axis of the whole core and a second orientation normal to in-situ bedding. Whole core obtained from deviated wells may display this sloped bedding feature, shown in Drawing B and C. In order to best apply vertical and horizontal stresses in the geomechanical testing apparatus, the vertical stresses should be applied normal to the depositional bedding plane. Core plugs should therefore be obtained normal to bedding. In Drawing D the core plug is first improperly oriented along the core axis. Second, the core plug should not be obtained at visual discontinuities (collect testable samples in massive features only – avoid shale streaks, deformation bands, cracks, vugs, etc.). CT scans may be utilized to avoid sampling sections of bulk rock or whole core containing discontinuities or flaws. Drawings E and F highlight vuggy or heterogeneous core for which small plugs are likely to be unrepresentative of bulk behavior.

If it is suspected that the sample has been cut with its axis not perpendicular to fabric or bedding, this should be clearly noted. For example, core size restrictions sometimes require that samples be cut parallel to the core axis, and this axis may not be perpendicular to fabric or bedding.


Figure 6. Diagram of core-plug orientation, where k is the core-plug axis. Geomechanical plugs are typically obtained normal to bedding. Drawing A shows horizontal (kH) and vertically (kV) oriented cylindrically drilled samples (test plugs) in a massive depositional feature. Drawings B and C show a laminated rock with test plugs drilled at normal to bedding (B and C) and normal to the core axis (B) orientations. In drawing D, the test plug has been obtained in a natural or man-made fracture - this plug may not be representative of testable bulk sediments. Drawings E and F show vuggy or heterogeneous core for which smaller plugs are also likely to be unrepresentative of bulk behavior (Drawings courtesy of Ove Wilson, Shell).

4.4 Core Plug Preparation Apparatus 4.4.1 Drill press or milling machine, and depending upon the size of the whole core section or bulk rock material,

extensions for additional vertical movement may be implemented. The drill press or milling machine may be modified with an actuated piston designed to place a small axial load on the rock within the core drill bit in order to minimize plug shearing or parting during drilling (Fjaer et al. 2004, pg. 255).

4.4.2 Hollow, diamond tipped coring bits specifically designed for stone materials are used for drilling core plugs. Drilling lubricants include air, nitrogen gas, refined oil, brine and liquid nitrogen (API 1998, and Fjaer et al. 2004). The reactivity or sensitivity of the rock mineralogy should be considered when choosing the drilling fluid or lubricant. The core bit diameter is chosen in order to achieve a core plug diameter that is a minimum of 10 times the diameter of the largest grains in the bulk rock (ASTM D4543-08).

4.4.3 Rock or Tile saw, preferably with diamond-tipped blades or carbide-tipped blades for softer rocks. 4.4.4 A high precision surface grinder (numerically controlled type or equivalent), or lathe with a grinding wheel

attachment should be used, with a sample holder suitable for the strength or weakness of the rock specimen being prepared. For highly cemented rock material or conglomerates, a surface grinder may be required to achieve an ASTM D4543-08 end-flatness.

4.4.5 Balance, dial gauges and calipers with digital indicators are preferred for measuring sample dimensions and weight.

4.5 Core Plug Drilling

The coring lubricants must be chemically compatible with the rock. Swelling clays prohibit the use of non-saline water (API 1998, pg. 2-11). In order to drill core plugs from unconsolidated or cohesionless rock, the bulk rock should be prepared through a sequence of chilled conditions. Assuming the bulk or whole core rock has been maintained in a frozen state, the


bulk material to be plugged must be placed on dry ice for a minimum of 4 hours, or until the bulk rock has assumed the temperature of frozen carbon dioxide (CO2). The plugs may then be obtained with a milling machine or drill press with liquid nitrogen (or cold gas from liquid nitrogen) serving as the lubricant (API 1998, pg. 3-5).

4.5.1 Once the proper orientation of the whole core or the bulk rock is determined, irregular shaped rocks should be slabbed or cut to a suitably uniform surface for the core drill bit.

4.5.2 Once the proper orientation of the whole core or the bulk rock is determined, the rock is clamped in a suitable vise. The vise prevents oscillation, tilting or shifting. Any axial loading of the bulk rock from within the hollow bit is applied. Rock selected for core-sampling should have minimal filtrate flushing, mud solids contamination or boring fluid invasion, unless it is deemed that this will not affect the deformation behavior.

4.5.3 Optimum drilling speeds vary with rock type and drill bit size. Drill bit speed frequently varies between 200 – 2000 rpm. Also, the drill bit should be checked and corrected for wobble prior to coring.

4.5.4 The right cylindrically drilled plugs should have a length to diameter ratio between 2.0 and 2.5, consistent with ISRM and ASTM standards for mechanical compression testing (ISRM 2007, ASTM D4543-08). This ratio renders the uniaxial compressive strength insensitive to minor deviations in the length/width ratio (Fjaer et al. 2004, pg. 256).

4.5.5 The core plug’s ends are then trimmed with a diamond- or carbide tipped rock-saw. 4.5.6 The ends of intact samples, and unconsolidated plugs, may be ground flat with a surface grinder, or lathe with a

grinding wheel attachment, down to a length/diameter ratio of 2.0 to 2.5 (please see Note 8.5). The plugs are first mounted in a suitably sized collet or sample-vise. Ensure that clamping forces to hold the sample in place do not unduly damage the rock itself. For unconsolidated samples, the plugs may be kept frozen or at liquid nitrogen temperatures during the grinding.

4.5.7 Fine grained, poorly cemented rocks may meet the dimensional tolerances of the next section after end-grinding with a lathe.

4.5.8 Depending upon the grain size, degree of cementation or conglomerates, the end faces of the core plug may require a surface ground polish.

Note that an alternative to drilling frozen samples may be the geotechnical procedure used for sampling soft sediments with thin wall tubes (i.e., socket punches or plunge cutters) (ASTM D1587-00). However, this technique can only be used with a limited range of materials, i.e. if the sediments have a certain minimal level of cohesion. It is not recommended for most materials outside this range, namely hard or significantly cemented material, conglomerates, or for highly unconsolidated or cohesionless materials. ASTM standard practice D 1587 “Thin-Walled Tube Sampling of Soils for Geotechnical Purposes” can be used as a reference guideline for the sampling operative procedures but it is not intended to this specific purpose, as it describes tubes with outside diameter greater than 2 in. Laboratory socket punches to obtain 1 in. and 1.5 in. diameter samples have length at least twice the diameter and can be designed by suitable downscaling the dimensions and tolerances reported in D 1587. Trial samples with a detailed microstructural examination to confirm minimal disturbance should be done before wholesale use of this technique.

4.6 Dimensional tolerances

The importance of parallel cylindrical end faces cannot be underestimated (see Vutukuri et al. 1974). In general, the specimen’s ends should be parallel to within 0.05 mm per 50 mm of sample length, and perpendicularity of the edges to within 0.25q. One possible apparatus for determining parallelism is shown in Figure 7. The core plug must meet the following ASTM D4543-08 standards for straightness, end face flatness and length tolerance:

4.6.1 The ends of the core plug shall be cut parallel to one another and at right angles to the cylindrical axis. Record end face flatness every 3 mm (1/8 in) increments along two 90 degree rotated diameters across both ends of the core plug. Calculate the difference between the maximum and minimum measurements of each diametrical line. The maximum and minimum measurement differences shall not exceed 0.1 mm per 25.4 mm of diameter (0.004 inch per inch of diameter).

4.6.2 The end face flatness (surface profile) of the core plug shall be smooth and free of abrupt irregularities. Record end face flatness every 3 mm (1/8 in) along three arbitrary diameters across the end of the core plug. The


flatness tolerance is met when the measured data is plotted with a best fit straight line, and the plotted data does not depart from the straight line by more than 25 μm (0.001 in). The sensitivity of the measurement system shall be 2.5 μm (0.0001 in).

4.6.3 The core plug shall be straight (parallel) along the cylindrical axis to a tolerance of 0.5 mm (0.02 in). The tolerance is defined as the difference between the maximum and minimum measurements along three cylindrical axis lines (requiring three plug rotations). The sensitivity of the measurement system shall be 25 μm (0.001 in).

4.6.4 For geomechanical measurement purposes, calculate the core plug diameter by averaging two diameters measured at right angles at approximately the top, the mid-height and the bottom of the core plug. The length of the core plug is determined by averaging the distance between the centers of the end faces. The measurements are made to a precision of 25 μm (0.001 in).

Figure 7. Assembly for determining straightness and perpendicularity of the cylindrical surface (from ASTM D4543-08)

4.7 Preparing surfaces for radial strain transducers

Surface preparation of the edges of the sample depends on the gage-types and instrumentation system. Popular transducer types are glued-on resistance-foil strain gage, reusable clamped LVDT circumferential chain, or reusable clamped full-bridge cantilevers. The latter is either circumferential or diametral. Instrumentation for radial displacements is of paramount importance in uniaxial-strain compaction tests because the lateral or radial strain is the main control in determining the confining pressure or radial stress. Therefore, utmost care is required when mounting the radial strain transducers (and the sensors must be free from any hysteresis, as discussed in the prior section). At mid-length, at the site of the transducer contact, the surface of the rock sample should be free of vugs, asperities and surface irregularities. The rock-surface coupling or mounting site should be flat to within 0.1% of its diameter.

Specific rock surface conditions should be considered in selecting the type of gage to be used. Foil-type bondable strain transducers or gages, if used, may be attached directly to the exposed sides of the specimen diameter, using vendor-recommended epoxy systems. Manufacturers have specific recommendations for their respective bondable strain gages. These include modulus-matching between the specimen and adhesive, surface preparation, void filling, curing agents and accelerators, curing time, and curing temperature, aging. Some rock conditions are not suitable for bonded strain gages, like friable and unconsolidated samples and frozen rock specimens.


4.8 Specimen Mounting

Specimen jacket or sleeve shall be made of an impervious, flexible, non-reactive membrane that will not restrain the rock from deforming, but can withstand strains beyond 5%. Preferable membranes are thin elastomeric sleeves; however metal or plastic based sleeves are normally required for elevated temperature tests.

A screen at each end of the specimen may be installed to prevent fine-particles from migrating and/or obstructing the flow of pore fluids. Similarly, for a test with a horizontal flow component, a specialized jacket with opposing flow ports is necessary. The effects of such screens/ports on the measured deformation should be known.

Reusable radial or lateral strain transducers, like cantilevers or chains may be attached directly to the sleeve or jacket, ensuring that the gages remain in-place, at sample mid-length, throughout the loading sequences. A preferred practice is to install dual radial strain transducers, at right angles to each other, to monitor the change in cross-sectional shape of the rock sample, in addition to the change in cross sectional area. Reusable axial strain transducers, like LVDTs and cantilevers may be attached directly to the loading platens at each end of the specimen. A minimum practice is to install a pair of axial strain transducers at 180-degrees from each other (or a device/arrangement that averages over multiple orientations such as a spreading cantilever bridge), in order to monitor uneven axial displacements. Refer to Section 3.1 for additional guidelines on instrumentation.

Ideally, a well prepared sample would be a true right-circular cylinder, i.e., surfaces are flat and at right angles or parallel. During the uniaxial-strain portion of the test, the sample would maintain its initial reference diameter and remain as a true right circular cylinder.

5. Testing Protocols

The Suggested Method for uniaxial-strain compressibility testing induces one-dimensional axial (vertical) deformation in a core plug by progressively increasing the axial (overburden) effective stress while simultaneously maintaining a zero radial (horizontal) strain boundary condition around the core plug circumference through computer feedback control between a radial strain measurement device and the confining pressure control system. Two separate experimental protocols for uniaxial-strain compressibility are recommended:

5.1 The Pore Pressure Depletion (PPD) Uniaxial-Strain Test: The core plug is first subjected to an external total axial stress, an external total confining pressure and an internal pore fluid pressure representing respectively, the initial, pre-production, in-situ total vertical overburden stress, in-situ total horizontal stress and in-situ reservoir fluid pressure magnitudes. Compressibilities (as defined below in Section 6) are determined by measuring bulk (and sometimes pore) volume strains associated with decreasing the pore pressure while holding total axial stress constant and simultaneously controlling total confining pressure such that core plug radial strain is maintained at zero, thus simulating one-dimensional vertical compaction. This is also referred to as a ‘delta-pore-pressure’ test since the pore pressure is the controlling parameter.

5.2 The Constant Pore Pressure (CPP) Uniaxial-Strain Test: The core plug is first subjected to a total axial stress, a total confining pressure and a pore pressure such that the applied mean effective stress and deviatoric stress magnitudes are equal to those calculated for the in-situ, pre-production, initial reservoir stress condition. The applied pore pressure magnitude is generally less than the in-situ reservoir pressure (for example, the pore fluid pressure could be equal to atmospheric pressure) and is maintained constant during subsequent compressibility measurement. Compressibility is determined by measuring bulk (and sometimes pore) volume strains associated with increasing the total axial stress over a constant pore pressure (such that simulated overburden effective stress increase substitutes for direct reservoir fluid pressure reduction) while simultaneously controlling total confining pressure such that core plug radial strain is maintained at zero, thus simulating one-dimensional vertical compaction. This is also referred to as a ‘delta-stress’ test since the external axial stress on the sample is the controlling parameter.

Both the PPD and CPP recommended testing protocols consist of four sequential stages (which may be modified from the SM in collaboration with the client):


5.3.1 Stage 1, Initial Loading: An initial nominal stress state is applied to the sample in order to seat the sample/loading platen stack, fully saturate the sample (if necessary) and allow for strain equilibration.

5.3.2 Stage 2, In-situ Stress Application: Laboratory stresses and pressures are raised in order to reproduce, in-situ, pre-production, initial reservoir stress conditions (IRSC) or effective IRSC.

5.3.3 Stage 3, Simulated Depletion: One-dimensional sample compaction is induced by increasing the axial (vertical) effective stress under a zero radial (horizontal) strain boundary condition. This is most often done at a constant rate, but can also be done (particularly in unconsolidated materials, see e.g. Dudley et al. 1998) in a series of equal stress increments and hold periods.

5.3.4 Stage 4, Measurement of creep at maximum stresses and unloading under continued uniaxial-strain conditions back to (effective) IRSC to quantify inelastic strain.

For the Initial Loading Stage (5.3.1) sample loading the recommended procedure as detailed below is the same for both PPD and CPP uniaxial-strain compressibility testing protocols:

5.4.1 A vertical core plug that has been jacketed and screened according to preferred sample preparation guidelines shall be instrumented and installed in the triaxial compression apparatus.

5.4.2 Initialize data acquisition such that a complete record of axial load, confining pressure, pore pressure, axial strain, radial strain and pore volume change is logged at an appropriate rate (sampling at 60 second intervals or faster is recommended) throughout the duration of the test.

5.4.3 Increase hydrostatic confining pressure at 2.5 MPa/min (5 psi/sec) to a nominal magnitude in the range 1.0-3.0 MPa (150-450 psi).

5.4.4 Ramp axial displacement at 25 μm /sec (0.001in/sec) until a nominal deviatoric stress (axial stress minus confining pressure) of approximately 0.5 MPa (75 psi) is achieved and maintain constant throughout initial loading phase.

5.4.5 Vacuum-saturate the sample with required pore fluid (such as inert mineral oil or artificial formation brine). For consolidated material this can be done prior to mounting in the cell. Following evacuation isolate the vacuum pump and connect the sample to an appropriate pore pressure control apparatus. Flow saturating fluid against a back-pressure of ½ the current confining pressure to ensure 100% saturation.

5.4.6 Hold pore pressure at ½ the current confining pressure and increase hydrostatic confining pressure at a constant rate (recommended range 0.5-2.5 MPa/min (1-5 psi/sec)) to a nominal effective confinement (confining pressure minus pore pressure) magnitude in the range 1.5-3.0 MPa (200-450 psi) and hold under pressure control for sample strain equilibration.

For subsequent Stage 2 In-situ Stress Application (5.3.2), a conventional, triaxial compressive stress path is recommended for attainment of initial reservoir stress conditions (IRSC) prior to the Stage 3 Simulated Depletion (5.3.3). Alternatively, a stress path associated with axial one-dimensional consolidation (radial uniaxial-strain boundary condition) from an appropriate stress condition near IRSC can also be used. While either triaxial or uniaxial loading to IRSC is permissible for both PPD and CPP testing protocols such that four possible Stage 2 plus Stage 3 combinations exist, we detail just two recommended procedures below as illustrative examples.

For Stage 2 triaxial compression to IRSC followed by Stage 3 PPD simulated depletion the recommended procedure for uniaxial-strain compressibility testing is given here and an example illustrated in Figure 8:

5.5.1 Hold the constant Stage 1 deviatoric stress of 0.5 MPa (75 psi) and increase the confining pressure at the recommended rate until the effective confining pressure (confining pressure minus pore pressure) has reached the initial reservoir effective horizontal stress conditions.

5.5.2 Hold confining pressure constant and increase deviatoric stress at recommended rate until the deviatoric stress reaches the value at IRSC. Sample is now at initial reservoir effective stress conditions.

5.5.3 Hold deviatoric stress constant and increase pore pressure and hydrostatic confining pressure synchronously at the recommended constant rate until pore pressure reaches the in-situ reservoir fluid pressure magnitude. Grain compressibility (Cg) can be determined during this constant effective stress loading phase, although accuracy can


be compromised if strain corrections are not specifically applicable to this loading sequence and range. The sample has attained IRSC.

5.5.4 Hold sample at IRSC conditions for a time period sufficient for sample equilibrium. 5.5.5 Holding pore pressure and deviatoric stress constant at the in-situ target values, cycle confining pressure down

2.0-3.5 MPa (300-500 psi) and then back up to IRSC at recommended rate. This cycle will provide data to determine the bulk compressibility at constant pore pressure (Cbc) at IRSC. Cbc and Cg can be used to calculate the isotropic Biot’s effective stress coefficient D at IRSC, as per section 6.4.2below.

5.5.6 Holding confining pressure and deviatoric stress constant at the in-situ target values, cycle pore pressure up 2.0-3.5 MPa (300-500 psi) and then back down to IRSC at recommended rate. This cycle will provide data to determine the bulk compressibility at constant confining pressure (Cbp) at IRSC. The difference between Cbc and Cbp provide a check on the measured Cg, as per section 6.4.2 below.

5.5.7 Switch to uniaxial-strain boundary conditions at IRSC where both radial strain and total axial stress are maintained constant such that any supplementary horizontal deformation is prevented and hold for a pre-determined time period prior to simulated depletion. The hold at IRSC can be just sufficient for equipment and sample stabilization or extended in order to quantify time-dependent creep effects. Extended holds can affect the deformations during the immediately-subsequent loading (see, e.g., Dudley et al. 1998).

5.5.8 Hold constant uniaxial-strain boundary conditions and decrease pore pressure at the recommended constant rate (or step-and-hold sequence, see 5.7.1) to a pre-determined target value, typically representing the in-situ reservoir abandonment pressure. Confining pressure will decrease as pore pressure is reduced in order to maintain zero radial deformation during simulated depletion.

5.5.9 Hold constant uniaxial-strain boundary conditions at depleted conditions briefly or for an extended period in order to quantify time-dependent creep effects.

5.5.10 Hold constant uniaxial-strain boundary conditions and increase pore pressure at the recommended constant rate back to the IRSC value. This can provide unloading compressibility information and quantify the inelastic or unrecoverable strain.

5.5.11 Return to independent confining pressure and axial stress control. Reduce deviatoric stress to nominal value or entirely to zero, then simultaneously ramp pore pressure and confining pressures back to zero.

Figure 8. Example test protocol for ramping to IRSC, followed by a uniaxial-strain PPD ramp stage. The specific protocol steps are indicated on the plot by the numbers within the vertical lines.


For Stage 2 uniaxial consolidation to IRSC followed by Stage 3 CPP simulated depletion the recommended procedure for uniaxial-strain compressibility testing is given here and illustrated in Figure 9 and Figure 10:

5.6.1 Hold the constant Stage 1 deviatoric stress of 0.5 MPa (75 psi) and increase the confining pressure at the recommended rate until the applied mean effective stress reaches a target value that is in the general range of one-half to two-thirds of the calculated in-situ initial reservoir mean effective stress.

5.6.2 Hold the deviatoric stress and target effective confinement pressure constant and increase pore pressure and hydrostatic confining pressure synchronously at the recommended constant rate until pore pressure reaches a specified target value that is generally less than the in-situ reservoir pressure. Pore pressure will be maintained constant at this target value for the uniaxial-strain portion of the test. Grain compressibility (Cg) can be determined during this hydrostatic loading phase, although accuracy can be compromised if strain corrections are not specifically applicable to this loading sequence and range.

5.6.3 Holding pore pressure and deviatoric stress constant at their target values, cycle confining pressure down 2.0-3.5 MPa (300-500 psi) and then back up to the target value at recommended rate. This cycle will provide data to determine the bulk compressibility at constant pore pressure (Cbc). Cbc and Cg can be used to calculate the isotropic Biot’s effective stress coefficient D, as per section 6.4.1 below.

5.6.4 Holding confining pressure and deviatoric stress constant at their target values, cycle pore pressure up 2.0-3.5 MPa (300-500 psi) and then back down to the target value at recommended rate. This cycle will provide data to determine the bulk compressibility at constant confining pressure (Cbp). The difference between Cbc and Cbp provide a check on the measured Cg, as per section 6.4.1 below.

5.6.5 Switch to uniaxial-strain boundary conditions and perform a uniaxial "probe" by increasing axial stress at the recommended constant rate until the deviatoric stress (axial stress minus confining pressure) reaches a target value that is in the general range of one-half to two-thirds of the calculated in-situ initial reservoir stress difference (overburden stress minus horizontal stress).

5.6.6 Unload under uniaxial-strain boundary conditions back to the initial Stage 1 deviatoric stress 0.5 MPa (75 psi) and hold axial stress and confining pressure constant. Use the slope of the uniaxial "probe" to calculate a mean effective stress "launch point" such that subsequent uniaxial loading will intersect IRSC (in-situ initial reservoir mean effective stress and deviatoric stress magnitudes).

5.6.7 Holding a constant Stage 1 deviatoric stress of 0.5 MPa (75 psi) increase hydrostatic confining pressure at the recommended constant rate to a target effective confinement value equivalent to the uniaxial "launch point".

5.6.8 Switch to uniaxial-strain boundary conditions at the target "launch point" where radial strain is maintained constant such that any supplementary horizontal deformation is prevented and increase axial stress at the recommended constant rate to intersect the effective IRSC.

5.6.9 Hold for a pre-determined time period at effective IRSC prior to simulated depletion. This hold can be just sufficient for sample equilibration or extended in order to quantify time-dependent creep effects. Extended holds can affect the deformations during the immediately-subsequent loading (see, e.g., Dudley et al. 1998).

5.6.10 Increase axial stress at the recommended constant rate over a constant pore pressure, such that simulated overburden effective stress increase substitutes for reservoir fluid pressure reduction, to the pre-determined target value, typically representing the in-situ reservoir abandonment pressure. Confining pressure will increase as axial stress is increased over a constant pore fluid pressure in order to maintain zero radial deformation during simulated depletion. Step-hold increases of axial stress can be used in lieu of a constant loading rate (see 5.7.1).

5.6.11 Hold constant uniaxial-strain boundary conditions at simulated depleted conditions briefly or for an extended period in order to quantify time-dependent creep effects.

5.6.12 Hold constant uniaxial-strain boundary conditions and decrease axial stress at the recommended constant rate back to the effective IRSC value. This can provide unloading compressibility information and quantify the in-elastic or unrecoverable strain.

5.6.13 Return to independent confining pressure and axial stress control. Reduce deviatoric stress to nominal value or entirely to zero, then simultaneously ramp pore pressure and confining pressures back to zero.


Figure 9. Example CPP test protocol for ramping to effective IRSC under uniaxial-strain stage at 2 MPa pore pressure. The specific protocol steps are indicated on the plot by the numbers within the vertical lines.

Figure 10. Example CPP test protocol (full test) for ramping through effective IRSC under uniaxial-strain stage at 2 MPa pore pressure. The specific protocol steps are indicated on the plot by the numbers within the vertical lines.


5.7 Testing Protocol Notes: 5.7.1 Step & Hold Testing Protocols: The Stage 3 effective stress change ramps of the above protocols can be replaced

by a series of incremental stress (CPP) or pore pressure (PPD) changes followed by a fixed hold period. In this case all the effective stress increments should be the same magnitude and hold periods the same duration. When using this protocol the compressibility and other parameters are calculated using the stress and strain data at the start of the first step, and the end of this and the subsequent step hold periods. This has been reported to provide a time-scaled compressibility (Dudley et al. 1998) that is independent of the particular effective stress increment and hold period chosen.

5.7.2 Recommended Loading Rates: Unless specifically stated otherwise in the testing protocols, the recommended rate for increasing or decreasing pore pressure, confining pressure and axial or deviatoric stress is generally in the range 0.5-10.0 MPa/hr (70-1450 psi/hr). This order of magnitude range is deemed sufficient to ensure the sample is maintained in a drained condition without the development of an excess pore pressure, and also minimizes the potential for excessive adiabatic heating or cooling. For Step & Hold protocols, the recommended loading rates are the effective rate averaged over the combined stress change and hold period. That is, a 3.5 MPa increase over 10 minutes followed by a 50 minute hold period is an effective loading rate of 3.5 MPa/hr (510 psi/hr), within the recommended range. Note that even slower rates may be required for very low permeability samples. Faster rates may be acceptable on very high permeability samples from a pore pressure drainage standpoint, but could very well be too fast for acceptable control stability (e.g., accurately maintaining the uniaxial-strain conditions).

5.7.3 Loading Rate Dependence: Time periods (holds) for maintaining constant initial reservoir stress conditions can be extended, and the rate of simulated depletion can be changed during a single loading cycle in order to investigate time-dependent effects and calibrate rate-type compaction (de Waal and Smits 1988, Smits et al 1988) or other creep models. Note that, in a rate-dependent material, long holds will affect deformations measured during the immediately-subsequent loading, as shown in the previous references, and is the reason Step & Hold protocols (5.7.1) need to have equal duration hold periods.

5.7.4 Re-pressurization: Additional loading and unloading cycles can be conducted during Stage 3 simulated depletion (pore pressure decrease then increase for PPD, total stress increase then decrease for CPP) in order to replicate reservoir re-pressurization and to determine how elastic the compaction is.

5.7.5 Additional Measurements: In addition to uniaxial compressibility, supplemental measurements such as ultrasonic (P-wave and S-wave) velocities and/or permeability can be determined at IRSC and during simulated depletion to assess stress-dependency of these parameters.

5.7.6 Pre-conditioning Stress Cycles: Pre-cycling (pre-conditioning) is not mandated by this SM, but is sometimes performed prior to the measurement portion of the test. This is performed for two reasons: 1) to seat the jacket and end caps on the sample (5.3.1) and 2) to bring the sample as close as possible back to its in-situ condition. For the latter purpose, the intent for well-consolidated rocks is to close any microcracks that may have formed due to the core retrieval, handling and sampling process. For unconsolidated sands the goal is more generally to push the grains back together in a close approximation to their in-situ state, or from a strain perspective, to get the sample dimensions back to their in-situ state. Note that if grain shifting has occurred it is not possible to get the sample back to its in-situ state. Pre-cycling or pre-conditioning involves loading the sample up to some pre-determined effective stress level, unloading down to some low effective stress level, and then reloading. Multiple cycles can be performed, but often after just one load-unload cycle the sample is then loaded either to IRSC or to a stress state below IRSC that is used as a starting point for uniaxial-strain loading. For convenience, pre-cycling is usually performed using hydrostatic stress, but it can also be performed with the presence of a deviatoric stress, and would be incorporated into the start of Stage 2 (5.3.2) of the above protocols. If the goal is only to better seat the jacket and end caps, an effective stress of 3 to 7 MPa is usually sufficient. If the goal is also to erase core damage or core expansion then usually the sample will be loaded up to the value of the minimum effective reservoir stress. For certain rocks it may be necessary to load beyond the minimum stress, for example up to the mean effective reservoir stress. However, this should be done with caution, especially with weak rocks. If the sample is overstressed (brought to a porosity which is lower than its in-situ porosity) then the sample may exhibit a falsely low compressibility for the first part of the compressibility


test (essentially, part of the compressibility test has been accidentally already performed). For certain classes of rocks, a cap-model approach can be used to determine safe loading levels for pre-conditioning, considering the effective stresses present in-situ as well as the stress changes during core retrieval.

6. Calculation of measured parameters

This section presents the equations and calculations necessary to derive homogeneous and isotropic elastic and poroelastic parameters from uniaxial-strain test data. The majority of this material has been published previously elsewhere. Besides those referenced explicitly in this section, other sources consulted for this section include Geertsma 1957 and Newman and Martin 1977.

6.1 Notations and definitions

Notation

6.1.1 L0, D0 original length and diameter 6.1.2 L, D current length and diameter 6.1.3 VB, VP current bulk and pore volumes 6.1.4 VB0, VP0 original bulk and pore volumes, zero stress 6.1.5 VBi, VPi volumes at initial reservoir effective stress (or chosen reference state) 6.1.6 VBj, VBk bulk volume at points j and k during test 6.1.7 VPj, VPk pore volume at points j and k during test 6.1.8 'L = L0 – L delta length, positive for length reduction 6.1.9 'D = D0 – D delta diameter, positive for diameter reduction 6.1.10 Vax, Vc total axial stress and total confining (lateral) stress 6.1.11 Vm = (Vax + 2Vc)/3 mean total stress 6.1.12 Pp pore pressure 6.1.13 I = VP/VB current porosity 6.1.14 E Isotropic Young’s modulus 6.1.15 Q Isotropic Poisson’s ratio 6.1.16 D� Isotropic Biot's coefficient

L0, D0 and VB0 are from caliper measurements, VP0 is calculated from VB0 and initial sample porosity. The initial sample porosity can be obtained from standard liquid or gas porosimetry measurement techniques, which may be done at nominal confining pressure (1-2 MPa/150-300 psi) to eliminate the effect of microcracks. 'L and 'D are direct from the test measurement system (however 'L and 'D usually must be modified to exclude apparent deformations that occur from the first few MPa of loading).

Compressibility Definitions

The definitions follow those of Zimmerman et al. 1986 and Zimmerman 2000.

6.1.17 𝐶𝑏𝑐 = − 1𝑉𝐵

( 𝜕𝑉𝐵𝜕𝜎𝑚

)𝑃𝑝=𝑐𝑜𝑛𝑠𝑡

6.1.18 𝐶𝑏𝑝 = 1𝑉𝐵

(𝜕𝑉𝐵𝜕𝑃𝑝

)𝜎𝑚=𝑐𝑜𝑛𝑠𝑡

6.1.19 𝐶𝑝𝑐 = − 1𝑉𝑃

( 𝜕𝑉𝑃𝜕𝜎𝑚

)𝑃𝑝=𝑐𝑜𝑛𝑠𝑡

6.1.20 𝐶𝑝𝑝 = 1𝑉𝑃

(𝜕𝑉𝑃𝜕𝑃𝑝

)𝜎𝑚=𝑐𝑜𝑛𝑠𝑡

6.1.21 𝐶𝑏𝑐,𝑢𝑛𝑖 = − 1𝑉𝐵

( 𝜕𝑉𝐵𝜕𝜎𝑎𝑥

)𝑃𝑝 𝑎𝑛𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 =𝑐𝑜𝑛𝑠𝑡


6.1.22 𝐶𝑏𝑝,𝑢𝑛𝑖 = 1𝑉𝐵

(𝜕𝑉𝐵𝜕𝑃𝑝

)𝜎𝑎𝑥 𝑎𝑛𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 =𝑐𝑜𝑛𝑠𝑡

6.1.23 𝐶𝑝𝑐,𝑢𝑛𝑖 = − 1𝑉𝑃

( 𝜕𝑉𝑃𝜕𝜎𝑎𝑥

)𝑃𝑝 𝑎𝑛𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 =𝑐𝑜𝑛𝑠𝑡

6.1.24 𝐶𝑝𝑝,𝑢𝑛𝑖 = 1𝑉𝑃

(𝜕𝑉𝑃𝜕𝑃𝑝

)𝜎𝑎𝑥 𝑎𝑛𝑑 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟=𝑐𝑜𝑛𝑠𝑡

6.1.25 Cg = grain compressibility

Note the denominators in the compressibility expressions (VB, VP) are current volume and are not original volume or reference volume. All compressibilities are positive numbers for volume reduction. The negative signs are necessary in this differential notation because all volumes, pressures and stresses are positive-valued. In the remainder of this section the sign convention will be maintained, but the definition of ‘delta-volume’ will be positive for volume reduction (however, delta-volume quantities will not be used directly for compressibility calculation).

Also note that grain compressibility Cg is the key parameter for the derivations of nearly all the poroelastic parameters described herein. Grain compressibility is assumed constant during all stages of uniaxial-strain CPP and PPD tests. It can be determined during the initial loading stage in the PPD test. During this stage, pore pressure and hydrostatic confining stress are simultaneously increased to the target pore pressure (section 5.5.3 above). The bulk volume strain measured divided by the applied pressure change provides the grain compressibility. Grain compressibility cannot be estimated during the CPP test unless a similar stage is used (section 5.6.2 above). Strain corrections (due to changing confining stress, for example) must be extremely accurate for the given loading sequence and stress range, in order to obtain accurate Cg.

Another commonly used uniaxial-strain compressibility is the uniaxial compaction coefficient Cm defined by Geertsma 1973 as

6.1.26 𝐶𝑚 = − 1𝐿 ( 𝜕𝐿

𝜕𝜎𝑎𝑥)

𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 =𝑐𝑜𝑛𝑠𝑡

This compressibility is equivalent to Cbc,uni (eq. 6.1.21) or Cbp,uni (eq.6.1.22), depending on the source of effective stress change, because the bulk volume strain w�VB/VB and axial strain w�L/L are identical under uniaxial-strain conditions. Those explicitly interested in Cmc or Cmp need only substitute Cbc,uni or Cbp,uni, respectively, from the calculations below.

6.2 Calculations to be performed at every ‘data line’ or at least at every state of interest

Data analysis should be done with sufficient resolution to identify significant nonlinear behavior in the compressibility. For a very linear stress-strain response this need only be a limited number of points over each stress path segment. For highly non-linear behavior a much finer resolution is required, but still with sufficient spacing to maintain accurate derivative calculations. In the case of stress-increment-and-hold test protocols, the data values at the start of the uniaxial-strain portion and the end of each subsequent stress-increment-hold step should be used for the analysis (Dudley et al. 1998).

'VB = (S/4)['LD02 + (L0-'L)(2D0'D – 'D2)]

This expression is positive for volume reduction. For compressible rocks this exact calculation can be significantly different than summing the three principal strains (which ignores second-order terms). Note that this calculation assumes that the cylindrical shape of the sample is maintained throughout the test. At large axial deformations this shape may significantly deviate from cylindrical due to bulging, shearing, localized compaction, developing ellipticity, which can be variable along the height of the sample.

VB = VB0 – 'VB

'VP = 'VB – Cg(VB0Vm – VP0Pp)

VP = VP0 - 'VP

Further notes on 'VP:


- The purpose of this expression is to subtract grain compression from bulk volume compression, to arrive at pore volume compression.

- This expression is not the exact integration since it uses VB0�and VP0 (original volumes), but it is usually accurate enough. This expression becomes inaccurate in the case of large changes in pore volume. Chertov and Suarez-Rivera 2014 provides a procedure to evaluate the quality of this approximation.

An alternative method to obtain VP at each step of interest is to accumulate small incremental changes in VP, by using the above equations modified to use incremental changes of VB, Vm and Pp, as follows:

dVP = dVB – Cg(VBdVm – VPdPp)

VP = VP0 - 6dVP

I = VP/VB (note that this is the current porosity)

Further notes on 'VP:

- 'VP calculated from 'VB can be compared to direct measurements of 'VP obtained from fluid expulsion. Direct measurements of expulsed fluid volume are generally less accurate in the case of small changes of pore volume. In the case of large pore volume changes, direct measurements can be more reliable than the approximations above.

- Incremental or single step calculations of pore volume changes are applicable to microhomogeneous materials (most sandstones), which do not have large local contrasts in compressibility of load carrying grains. This expression is inapplicable to materials with large local contrasts of grain compressibility (e.g., some organic rich mudstones). For the latter, direct measurement of pore volume is the only reliable option (Chertov and Suarez-Rivera 2014).

In summary, the following parameters are required for each data line or for each state of interest:

� Vax, Vc, Vm, Pp, VB, VP, I

Note that VB, VP and I will all decrease with increasing effective stress (i.e., increasing total stresses and/or decreasing pore pressure). Calculation of compressibility and pore volume multipliers (normalized pore volume) are based on these parameters. Explicit calculation of I is not always required for compressibility calculations, but is a useful quantity to have. It also provides a check to make sure that 'VP is not greater than 'VB.

6.3 Calculation of Compressibilities, Directly From Test Data

This section provides equations for the compressibility terms that can be calculated directly from the parameters listed above. These compressibilities will be different for a CPP (i.e., delta-stress) test versus a PPD (i.e., delta-pore-pressure) test. The section immediately following provides mathematical expressions for obtaining the missing compressibilities, utilizing isotropic poroelastic relationships.

6.3.1 Exact Form (logarithmic expression)

For the equations in the remainder of this section, all can be changed to use an exact form instead of the step-to-step form. The general form of the exact expression is:

C = (lnVk – lnVj)/(Sk – Sj)

Where V represents pore volume or bulk volume and S represents stress or pressure. This equation is easily derived by integrating the compressibility definition. Note that the exact expression can be approximated very closely by the step-to-step forms presented below, as long as Vk and Vj are not very different.

6.3.2 Compressibilities Directly From a CPP Test


Cbc, uni = (-1/VB)(VBk – VBj)/(Vaxk – Vaxj)

This is the compressibility for state j to state k in the test. Note that state j can be chosen to be the initial reservoir conditions or chosen reference state (state i), if desired. However, if state k represents a significant amount of deformation relative to state i, then it is best to use the exact logarithmic form to ensure accuracy.

Similarly, additional compressibilities can be calculated as

Cpc, uni = (-1/VP)(VPk – VPj)/(Vaxk – Vaxj)

Cbc = (-1/VB)(VBk – VBj)/(Vmk – Vmj)

Cpc = (-1/VP)(VPk – VPj)/(Vmk – Vmj)

Current values of bulk volume and pore volume are defined as follows:

VB = (VBk + VBj)/2, or = VBj for k close to j

VP = (VPk + VPj)/2, or = VPj for k close to j

One should also consider the formulation of the reservoir simulator of interest. For example, the simulator may use compressibility to calculate a new pore volume at state k using the pore volume at state j as a starting point. In this case the current pore volume should be set to VPj and not the average of VPj and VPk.

6.3.3 Compressibilities Directly From a PPD Test

Cbp, uni = (1/VB)(VBk – VBj)/(Ppk – Ppj)

Cpp, uni = (1/VP)(VPk – VPj)/(Ppk – Ppj)

This is the compressibility for state j to state k in the test. Note that state j can be chosen to be the initial reservoir conditions or chosen reference state (state i), if desired. However, if state k represents a significant amount of deformation relative to state i, then it is best to use the exact logarithmic form to ensure accuracy.

Current values VB and VP are determined as described above for a delta-stress test. No other compressibility terms can be determined directly from the test data for a delta-pore-pressure test. However, Cpp, uni is what is needed for reservoir simulation. The next section provides poroelastic equations for computing the remaining compressibilities.

6.4 Derived Compressibilities and Moduli

This section describes the calculation of the remaining bulk and pore volume compressibilities, isotropic elastic parameters and Biot's coefficient that are not directly determined in the particular test type run.

6.4.1 Additional Parameters from a CPP Test

The bulk compressibilities with respect to changing pore pressure and changing mean stress are related by:

Cbp = Cbc – Cg

Also, Cbp = ICpc , which can be used as a check.

Cpp = Cpc – Cg

Alternately, Cpp = [Cbc – (1+I)Cg]/I�, which can also be used as a check. The isotropic Biot's alpha coefficient is


D = 1 – (Cg/Cbc)

Note this is not constant, because Cbc varies. The effective Poisson’s ratio is

Q = (dVc/dVax)/(1+ dVc/dVax)

This also is not constant. It should be calculated for each stress step of interest (e.g., state j to state k)

Cbp, uni = Cbp [(1+Q)/[3(1-Q�@�

Alternately, Cbp, uni = ICpc, uni , which can also be used as a check. The relationship between the uniaxial-strain pore volume compressibility under PPD and CPP is

Cpp, uni = Cpc, uni – Cg + Cg[2(1-2Q�D]/[3(1-Q�I@�

The first two terms of this expression are similar to those for equivalent isotropic pore compressibility (subtracting grain compressibility). The last term is a consequence of the stress path being different for a PPD versus a CPP test; therefore the change in mean stress is different. Note that Cpp, uni > Cpc, uni is possible and does not signify an error. The effective Young’s modulus is

E = [(1+Q)(1-2Q)]/[(1-Q�Cbc, uni@�

This completes the calculation of all eight bulk and pore compressibilities, two isotropic elastic constants and the isotropic Biot’s coefficient.

6.4.2 Additional Parameters from a PPD Test

The bulk compressibility under isotropic stress change (Cbc) and uniaxial-strain pore pressure change (Cbp, uni) are related by:

Cbc = (Cbp, uni + Cg)/(1-O�

Where O = (Vmk – Vmj) / (Ppk – Ppj). This relationship follows from O = D {1-(1+Q)/[3(1-Q�@` in the case of uniaxial-strain PPD test.

As in the previous section, the bulk compressibilities with respect to changing pore pressure and changing mean stress and isotropic Biot’s alpha coefficient are

Cbp = Cbc - Cg

D = 1 – (Cg/Cbc)

Again, note that alpha is not constant, because Cbc varies. The remaining compressibilities and elastic parameters are then calculated via:

Cbc,uni = Cbp, uni/D

Cpc = Cbp/I

Cpp = (Cbp/I� - Cg

Cpc,uni = Cbp, uni/I

Q = (3Cbp, uni - Cbp) / (3Cbp, uni + Cbp)

E = [(1+Q)(1-2Q)]/[(1-Q�Cbc, uni@


This completes the calculation of all eight bulk and pore compressibilities, two isotropic elastic constants and the isotropic Biot’s coefficient.

Note that poroelastic deformation can be described with a single fluid-solid coupling parameter such as Biot’s D�coefficient only in the case of micro-homogeneous materials (Detournay and Cheng 1993). Otherwise, more than one fluid-solid coupling parameter is required. Therefore, for non-microhomogeneous materials (this could be materials with large contrasts in compressibility of load carrying grains, e.g., some mudstones), it is not possible to calculate the full suite of poroelastic parameters from either CPP or PPD tests. Such materials require direct measurement of pore volume changes via tracking the volume of the expulsed fluid. Only the subset of compressibilities can be estimated from each test that can be directly inferred from the recorded increments of stress and strain. For example, Cpp,uni can be defined from a PPD test, but not from a CPP test (Chertov and Suarez-Rivera 2014).

6.5 Pore Volume Multipliers (Normalized Pore Volume)

Certain reservoir simulators use pore volume multipliers, which are just pore volume normalized to the pore volume at initial reservoir conditions (or some reference state). These are easily calculated as:

PVMk = (VPk/VPi)

Where PVM is the pore volume multiplier (normalized pore volume) and state ‘i’ is the chosen reference state, which will typically be the initial reservoir effective stress conditions. For a PPD test this provides a value compatible with reservoir operations (changing pore pressure). However, for a CPP test it provides a normalized pore volume due to changing stress (not due to changing pore pressure). The only way to accurately calculate PVM values for changing pore pressure, from a CPP test, is to calculate the pore volume compressibility under changing pore pressure conditions, such as Cpp or Cpp, uni, and then use those compressibility values to compute changes in pore volume, and then to calculate the pore volume multipliers from the computed pore volumes.

7. Reporting of Results

The report shall include at least the following: (a) Source of specimen, including (if known by testing organization) appropriate designation of geographic location, true

and measured depth, azimuth and inclination of the core if recovered in-situ and orientation of the sample itself. If downhole sidewall core, specify if acquired with rotary or percussion system (note that in general percussion sidewall samples are not suitable for geomechanical testing due to damage incurred during acquisition). If possible a map showing the sampling point (surface sample) or a wellbore schematic (core sample) should be included.

(b) Lithological description of the specimen including grain size. (c) Details of the methods used for the test specimen preparation, also the history and environment of test specimen

storage, including temperature, humidity, and method of preservation, if any. (d) Orientation of the loading axis with respect to specimen anisotropy, bedding planes, etc. (e) Sample height, diameter, and weight, – as-received and at the time of testing. (f) Sample porosity at unstressed condition, and at (effective) IRSC, and method of porosity determination. (g) Oil and/or water saturation condition, if known, and if performed, any procedures used to clean and

resaturate/restore core. (h) Description of testing equipment (loading device, triaxial cell, device for applying and measuring confining pressure,

strain and load measurement instrumentation type and configuration). (i) Date of testing. (j) Test duration and stress/displacement rates. Include a description of the methodology for applying axial and

confining stresses, pore pressure and temperature and include a plot of all applied boundary conditions with time (e.g., Figure 8 or Figure 10).

(k) Document specific method for applying boundary stress and/or strain boundary conditions as well as pore pressure. (l) Document equations for calculating any reported compressibility or other parameter.


(m) Provide plots of the stresses and strains during the complete test (Figure 11), and also specifically over the uniaxial-strain portion of the test. Provide plots of any compressibility or other parameters calculated as a function of stress (or other variable), and also linear-fit plots of any constant compressibility or other parameters calculated over the specific stress (or other variable) range (e.g., Figure 12).

Figure 11. Example plot of stress and strain data over complete PPD test. Note this test lacks the Cbc and Cbp cycles at IRSC.

Figure 12. Example constant (left) and variable (right) compressibility plots.

(n) Tabulate sample identifier, true or measured depth and datum, relevant axial and confining pressure data in accordance with specific testing protocols (CPP, PPD) and compressibility information. Compressibility information includes bulk compressibility, pore volume compressibility, porosity, and simulated depletion rate. Report compressibility to three significant figures.

(o) Provide pre- and post-test photographs of the sample, and document any relevant observations on any mode of eventual sample failure.

(p) Any other observations, e.g., density, citing the method of determination of each, including any ISRM SM or ASTM standard followed.


(q) If test protocol contains varying loading rates or creep segments designed to calibrate a specific constitutive model provided to the testing organization, then include the necessary information or data plots necessary to calibrate the model parameters.

(r) All reported information should at least be provided in a suitable digital format.

8. Notes and Recommendations 8.1 Note on Viscosity for Test Protocols which Include Axial or Horizontal Flow for the Calculation of Permeability: Pore

fluids should have well characterized relationships between temperature, pressure, and viscosity. While some fluids may have rigorous published values, others may require specific laboratory measurements prior to use.

8.2 An accurate pore volume measurement is required to compute the pore volume compressibility, which generally requires cleaning and resaturating the pore volume. However, cleaning carries a high risk of altering the mechanical deformation and strength properties of the sample. A conservative best practice is to perform the uniaxial-strain compressibility test on an uncleaned sample, and estimate the pore volume using the porosity measured on a twin plug. If the compressibility sample is cleaned, it must be done using a methodology known not to alter the mechanical properties of the material. It is beyond the scope of this document to prescribe such cleaning methods, as they will vary depending on (at least) sample lithology, consolidation, porosity, permeability, and pore contents.

8.3 It is important to consider the flexibility and thickness of the membrane relative to the material being tested, particularly when the membrane itself is in the radial deformation measurement path. Elastomer-based membranes, such as thin heat-shrink fluorocarbon (e.g., Viton©), are significantly softer and more flexible than polyolefin or polytetrafluoroethylene (e.g., Teflon©), and therefore better suited to testing highly compressible materials like unconsolidated sands or pore-collapsing carbonates.

8.4 It is recognized that in some cases for some materials it may be desired to test specimens under different saturation conditions. Such conditions should be noted in the test report – as well as the history of the saturation processes, including the type of fluid (water, brine, oil, etc.) used to re-condition the sample.

8.5 Should it be necessary in some instances to test specimens that do not comply with the above specifications these facts should be clearly noted in the test report. In particular, it is sometimes difficult to obtain samples that meet the L/D equal 2.0 to 2.5 criteria. The origin of this requirement for rock mechanical tests comes from the impact of friction between the sample and the end caps or loading platens on the uniform deformation and measured compressive strength and post-yield behavior of the sample. During uniaxial-strain compaction, however, the diameter of the sample should not be changing and therefore there is little to no relative movement between the sample and end platens. For this reason strict adherence to the L/D =2.0 to 2.5 requirement is not as critical as in compressive strength testing, and tests on shorter samples may give acceptable results.

8.6 For some materials to be tested it is not possible to prepare a core specimen to the tolerances specified in Section 4. In these cases prepare the rock specimen to the closest tolerances practicable and consider this to be the ‘Best Effort.’ Best Effort in surface preparation refers to the use of a well-maintained surface grinder, lathe or lapping machine by an experienced operator in which a reasonable number of attempts has been made to meet the tolerances required in this SM.

9. Acknowledgements

This SM has been prepared by an ISRM Working Group (WG) established jointly under the Commission on Petroleum Geomechanics and the Commission on Testing Methods. The WG was coordinated by J.W. Dudley (Shell), with members A.S. Abou-Sayed (Advantek International), M. Brignoli (ENI), B.R. Crawford (ExxonMobil), R.T. Ewy (Chevron), D. Jiao (Core Laboratories), G. Li (Anadarko), D.K. Love (Shell), J.D. McLennan (Univ. Utah), G.G. Ramos (ConocoPhillips), J.L. Shafer (Consultant), M. Sharf-Aldin (Metarock Laboratories), E. Siebrits (Schlumberger), and J.F. Stenebraten (SINTEF). The following additional people are thanked for their contributions to and/or review of the SM: J. Boyer and M.A. Chertov (Schlumberger), and P.N. Hagin and M.L. Shalz (Chevron). The WG thanks our respective employers for supporting our involvement, and we appreciate the encouragement and support of the ISRM Commissions, and our fellow colleagues working in petroleum geomechanics and rock mechanics.


10. References

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