The present disclosure is directed to measuring geomechanical properties of rock samples.
Mechanical properties are required inputs for any geomechanics analysis in the engineering activities in both the ground surface and underground environments, such as various operations in the life cycle of hydrocarbon exploration and production. For instance, accurate information of rock stiffness, for example, Young's modulus, is required to reliably predict the reservoir compaction and ground subsidence. In the drilling of a wellbore, the cohesive strength and frictional angle are necessary mechanical properties in the evaluation of the borehole breakout risk and safe mud weight design.
Common rock properties can be measured in a rock mechanics laboratories. For example, Young's modulus, Poisson's ration, cohesive strength, and frictional angle can be measured by performing uniaxial or triaxial compression tests. Tensile strength can be measured directly in direct tensile test, or a Brazilian test in which the tensile strength is determined by crushing a rock disk. Both compression and tensile tests require inch-sized cylindrical cores or discs. However, cores are often not available, especially for the overburden and seal rocks. On the other hand, small rock cuttings are circulated to the ground surface with mud in the drilling process. These cuttings carry the mineralogical and mechanical information of the original rocks from which they came.
An embodiment described herein provides a method for performing an indentation test on a rock sample. The method includes measuring load and displacement versus time on an indentation measurement unit, while preforming a multi-stage indentation test. The multi-stage indentation test includes indenting a saturated specimen to full load to generate a line segment 1, releasing the load on the saturated specimen to generate a line segment 2, indenting the saturated specimen to full load to generate a line segment 3, holding the loading until the displacement curve levels off to generate a line segment 4, and reducing the loading to zero to generate a line segment 5.
A technique is disclosed herein to measure multiple mechanical properties of rocks from their core samples or cuttings by performing a multi-step indentation test on small rock pieces. More specifically, the method allows for the measuring of two elastic properties, undrained and drained stiffness, and one hydraulic property, diffusivity or diffusion coefficient, of rock sample using a single-stage indentation on a saturated rock sample. Undrained stiffness is a critical parameter in calculating short-time deformation of rock mass in response to stress changes. Likewise, drained stiffness determines long-time deformation of rock mass caused by stress changes. Diffusivity characterizes the time scale of fluid flow from transient flow to steady state flow over a given distance.
In some embodiments, the specimen 104 is a rock sample collected during a well drilling process. For example, the specimen 104 may be collected from drilling cuttings, or a core sample, among others. In some embodiments, the specimen 104 is a rock sample collected at the surface, for example, over an oil sands field. The height (H) 106 and length (L) 108 of the specimen 104 are measured for use in the calculations described herein.
The indenter 102 is pushed into the specimen 104, or loaded, using pressure (P) 110 applied by the indentation measurement unit. In the loading process, both elastic and plastic deformation can take place, reflecting the elastoplastic response of the specimen. In the unloading process, the elastic deformation bounces back, or rebounds, so the stiffness can be extracted from unloading curve. Accordingly, after the pressure is released, the indentation has a height (h) that reflects the recovery after the elastic deformation has rebounded. After the rebound, the contact radius (RC) can be used to determine the amount of the indenter 102 that is still in contact with the specimen 104.
In equation 1, P is the applied vertical load, R is the radius of the spherical indenter, and δ is the vertical displacement at the center of spherical indenter. E* is an intermediate variable determined by the stiffness parameters of the material of the indenter and sample, for example, using the formula of equation 2:
In equation 2, Es and vs are Young's modulus and Poisson's ratio of the indented material and Ep and vp are Young's modulus and Poisson's ratio of the indenter.
If plastic deformation is induced, then only part of the deformation can be recovered after unloading. This is shown in the plot 200 of
In equation 3, the hardness (II) is defined as the ratio of the peak load (Pmax) to the projected contact area (Ac=πRC2, RC is the contact radius, as shown in
In equation 4, S is the slope of the unloading curve, and β is the geometry correction factor of the indentation tip. For example, β is 1 for spherical and cone tips, 1.034 for Berkovich and cubic corner tips, and 1.012 for Vickers and Knoop tips. Then, the stiffness of the indented material can be calculated using Eq. (2).
In more detail, in the first stage 302, at block 312, the saturated specimen is prepared. This may be performed by collecting a fresh drill cutting proximate to the wellbore being drilled, or by cutting a sample out of a core sample, among others. As noted, the technique described may be used to determine hydrocarbons in oil sand fields. In these environments, the saturated specimen may be collected at ground level. At block 314, the saturated sample is indented to the maximum load, Pmax, which is typically on the order of 100 mN in the indentation of rock materials. At block 316, the load and displacement are recorded in the time domain, generating line segment 1 of the plots of
In the second stage 304, at block 318, the load on the indenter is reduced to zero. At block 320, the load and displacement are recorded in the time domain, generating line segment 2 of the plots of
In the third stage 306, at block 322, the load on the indenter is increased to the maximum load, Pmax. At block 324, the load and displacement are recorded in the time domain, generating line segment three of the plots of
In the fourth stage 308, at block 326, the indenting load is held at the maximum load, Pmax. This allows the fluid in the specimen to fully dissipate. At block 328, load and displacement are recorded in the time domain, generating line segment 4 of the plots of
In the fifth stage 310, at block 332, the load on the indenter is reduced to zero. At block 334, the load and displacement are recorded in the time domain, generating line segment five of the plots of
Similar to the undrained stiffness, the drained stiffness (Ed*) is computed from the slope of line segment 5 of
H is the total height of the rock sample, and L is the total length of the rock sample, as discussed with respect to
An embodiment described herein provides a method for performing an indentation test on a rock sample. The method includes measuring load and displacement versus time on an indentation measurement unit, while preforming a multi-stage indentation test. The multi-stage indentation test includes indenting a saturated specimen to full load to generate a line segment 1, releasing the load on the saturated specimen to generate a line segment 2, indenting the saturated specimen to full load to generate a line segment 3, holding the loading until the displacement curve levels off to generate a line segment 4, and reducing the loading to zero to generate a line segment 5.
In an aspect, the method includes computing undrained stiffness based, at least in part, on the line segment 2. In an aspect, the method includes computing the undrained stiffness (Eu*) for a sample that does not show plastic deformation using the equations:
wherein ES is the Young's modulus of the indented material, νS is the Poisson's ratio of the indented material, EP is the Young's modulus of the indenter, and νP is the Poisson's ratio of the indenter. In an aspect, the method includes computing the undrained stiffness (Eu*) for a sample that shows plastic deformation using the equations:
wherein S is the slope of the unloading curve; β is the geometry correction factor of the indentation tip, and Ac is the projected contact area calculated as Ac=πRC2, wherein RC is the contact radius at peak load.
In an aspect, the method includes draining a portion of the rock sample by holding the loading until the displacement versus time levels off.
In an aspect, the method includes computing drained stiffness (Ed*) based, at least in part, on the line segment 5. In an aspect, the method includes computing the drained stiffness (Ed*) for a sample that does not show plastic deformation using the equations (1) and (2):
wherein ES is the Young's modulus of the indented material, νS is the Poisson's ratio of the indented material, EP is the Young's modulus of the indenter, and νP is the Poisson's ratio of the indenter. In an aspect, the method includes computing the drained stiffness (Ed*) for a sample that shows plastic deformation using the equation:
wherein S is the slope of the unloading curve; β is the geometry correction factor of the indentation tip, and Ac is the projected contact area calculated as Ac=πRC2, wherein RC is the contact radius at peak load.
In an aspect, the method includes measuring time from loading to level-off of the displacement versus time (tc) from line segment 4. In an aspect, the method includes calculating the diffusivity (c) by the equation c=Lc2/tc, where
and H is the total height of the rock sample, and L is the total length of the rock sample.
In an aspect, the method includes indenting the rock sample with a hemispherical tipped indenter. In an aspect, the method includes indenting the rock sample with a flat-tipped indenter. In an aspect, the method includes indenting the rock sample with a cone tipped indenter. In an aspect, the method includes indenting the rock sample with a Berkovich, cubic corner, Vickers, or Knoop tipped indenter.
In an aspect, the method includes obtaining the rock sample from cuttings resulting from a wellbore drilling process. In an aspect, the method includes obtaining the rock sample from a core sample.
Other implementations are also within the scope of the following claims.