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Rock strength from log parameters
An understanding of rock strength is important for designing recovery plans for a reservoir and for developing an appropriate reservoir simulation. A detailed discussion of rock failure can be found in Rock failure relationships and Compressive strength of rocks. But the data needed for these methods may not be readily available, so there is a desire to use data available from well logs that are available.
Relationships based on velocity
Several techniques have been proposed for deriving rock strength from well log parameters. Coates and Denoo calculated stresses induced around a borehole and estimated failure from assumed linear envelopes with strength parameters derived from shear and compressional velocities. They relied on the work of Deere and Miller to provide estimates of compressive strength from dynamic measurements. Simplified forms of these relations are:
where C0 is uniaxial compressive strength and E is dynamic Young’s modulus (see Stress strain relationships in rocks). Alternatively, we can include an empirical dependence of the internal friction angle, α, or the porosity, Φ.
Relationships based on velocity, lithology and density
Eqs. 4 and 5 provide a way to derive strengths assuming a linear envelope, and provided that compressional and shear velocity, lithology (e.g., gamma ray or SP), and density logs are available. If there is no shear log, one can be derived from the compressional velocity log and Vp-Vs relationships previously shown in Table 1.
The strength-porosity trend shown in Eq. 3 and modulus-porosity trends in Stress strain relationships in rocks imply a correlation between strength and shear modulus for sandstone:
This leads to a velocity transform if the bulk density is known:
If we presume a simple relationship between compressional velocity of brine-saturated sandstones and shear velocity as developed by Castagna et al., we get
The shear modulus (or velocity) should be the most sensitive measure of strength, and shear properties are little affected by fluid saturations. Whenever possible, shear wave data should be collected and used in this analysis. If only compressional data is available, care must be used in translating the information into effective gas- or brine-saturated values (see Stress strain relationships in rocks). This is particularly true for partial oil saturations.
C0 was first determined from porosity. The influence of clay content was examined separately. The velocity-strength relationships above were derived from the porosity dependence, but clays are handled only indirectly through their effects on velocities. Strength parameters can be calculated directly from porosity (Eq. 8), but clays must then be included, as in Eq. 9. Calculated strengths based directly on porosity and clay content are shown in Fig. 1. These types of logs can be very valuable in detecting weak zones and units susceptible to failure. If at all possible, these kinds of logs should be calibrated with strength measurements directly on core samples.
Fig. 1 – Strength analysis applied to a Gulf of Mexico suite of logs. Sand/shale fraction is derived from gamma ray and SP logs (left track). Porosity is extracted from the density log (see previous sections). Uniaxial compressive strength is derived from using Eq. 13.153. Weaker sands can be identified and failure predicted based on in-situ stresses around a borehole and a particular production scenario (red zones).
|C0||=||uniaxial or unconfined compressive strength, GPa or MPa|
|E||=||Young’s modulus, GPa or MPa|
|G||=||shear modulus, GPa or MPa|
|m||=||Hoek-Brown strength coefficient|
|Vp||=||compressional velocity, m/s|
|Vs||=||shear velocity, m/s|
|α||=||failure envelope slope|
|ρ||=||density, kg/m3 or g/cm3|
- Coates, G.R. and Denoo, S.A. 1981. Mechanical properties program using borehole analysis and Mohr’s circle. Presented at the 1981 SPWLA 22nd Annual Logging Symposium, Houston, 23–26 June. Paper DD.
- Deere, D.U. and Miller, R.P. 1966. Engineering classification and index properties for intact rock. Report AFWL-TR-67-144, U.S. Air Force Weapons Lab, Kirtland AFB, New Mexico (December 1966).
- Castagna, J.P., Batzle, M.L., and Eastwood, R.L. 1985. Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks. Geophysics 50 (4): 571–581. http://dx.doi.org/10.1190/1.1441933.
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