Find the Complete PDF version of this series here: The Delicate Matter of Rock Brittleness
Her reputation is no less brittle than it is beautiful. (Jane Austen, Pride and Prejudice)
It should not surprise us that oil producers would appreciate quick measures such as ‘brittleness index’ to tell them where to drill, complete, and fracture to achieve better hydrocarbon production results in low-permeability formations such as unconventional plays . Recently, we have seen different forms of this index introduced to the industry though the definition of ‘brittleness’, as a mechanical property of rock, has still remained a controversial matter among the experts from different disciplines and with different perspectives towards rock mechanics. In its typical application for characterization of unconventional plays, brittleness index is expected to define the mechanical behaviour of rock during fracture propagation. A brittle rock is usually expected to allow a pressurized fracture to propagate the same way ‘a knife cuts through butter’. The opposite case is a ‘ductile’ rock that tends to blunt a propagating fracture. In addition, a brittle rock is expected to be a good host for the proppants filling the fractures without swallowing them as may happen during propping a ductile rock. This will let fractures to remain functionally open and perform their role as fluid conduits. Some experts would rather using the term ‘fracability’ instead to define this behaviour of rock probably because ‘brittleness’, as a technical term, has been reserved by mechanical engineers to define a more general behaviour of materials as will be discussed later in this post since a long time ago. Another main reason for using ‘fracability’ instead of ‘brittleness’ is to emphasize that the process of fracture propagation is not just a function of mechanical rock properties but it also depends on other parameters such as in-situ stresses, fracturing fluid ‘s type, rate, and pressure, existence of natural fractures, etc. This article intends to review the concept of rock brittleness from different perspectives such as rock mechanics, fracture mechanics, geophysics, and petrophysics.
Old Definitions, New Applications
Mechanical engineers, in general, have been traditionally using the two terms of ‘brittle’ and ‘ductile’ to define the behaviour of rock before its final failure. In response to excessive loading, a brittle material (e.g., a steel knife blade) breaks abruptly without a significant deformation while a ductile material (e.g., a copper wire) deforms significantly before it breaks apart. Figure 1 shows examples of stress/strain behaviours of ductile and brittle metallic materials during standard tensile strength tests. In reality, fracture propagation in rocks during hydraulic fracturing is a tensile failure (i.e., Mode I failure) process but, unfortunately, direct tensile tests similar to what shown in Figure 1 are not usually possible to be conducted for sedimentary rocks due to very small tensile strength of these rocks [i]. Therefore, in rock mechanics, brittle/ductile behaviour of rocks is usually studied under compressive loading instead of tensile loading. In this case, most likely, the sample will fail in a shear mode (i.e., Mode 2 failure).
Figure 1. Stress-strain diagram obtained from the standard tensile tests (a) ductile material (b) brittle material (Modified after Budynas and Nisbett, 2008).
During compressive loading (e.g., triaxial tests), rocks usually fail on shear failure surfaces (Figure 2). Rock behaviour in response to this type of loading is very similar to what the earth crust experiences under tectonic movements and, therefore, the results of such tests have been traditionally used to study rock brittleness/ductility in geological structures (e.g., geological folds are usually formed in ductile rock and faults are formed in brittle rocks, see Figure 3, for instance), earthquakes (brittle rocks are likely to induce larger earthquakes/seismic events than ductile rocks), and reservoir sealing integrity (comparing to ductile sealing, the brittle ones are more likely to act as conduits after being deformed by reservoir depletion).
Figure 2. Brittle-ductile behaviour of rocks under compressive loading (Source: Evans et al., 1990)
Figure 3. Effect of rock brittleness/ductility in forming geological structures (a) folds formed in ductile rocks (b) fractures developed in brittle rocks. (Sources: a: www.esci.umn.edu; b: www.geoscience.wisc.edu).
While the compressive tests are designed to study the rock’s behaviour when it fails under shear, some rock mechanics engineers believe that these results can also act as proxies for the behaviour of rock in response to fracture propagation during hydraulic fracturing. We know that failure criteria of rocks during compressive loading are distantly different from that of tensile loading. Therefore, if we really want to measure the actual rock behaviour during hydraulic fracturing, we need to develop more precise and comprehensive testing procedures to quantify rock’s response during tensile loading [iii]. Nevertheless, the compressive failure tests using triaxial apparatus are commonly used to verify rock brittleness and ductility in the laboratories. Based on the results of these tests, the magnitude of brittleness index may be quantified in different ways by using strains, rock strengths, or the work/energy during these tests. Figure 4 shows a list of different equations. Drilling, geotechnical, and mining engineers have also shown interest in the concept of rock brittleness as they believe it is one of the parameters that governs the penetration rate during drilling wells, mine shafts, and tunnels (this character is called drillability). Some of the relationships used in these fields calculate the rock brittleness index as a function of rock compressive strength (Sc) and tensile strength (St). These parameters have been usually used in different combinations to calculate rock brittleness (e.g., BI=Sc/St; BI=Sc x St/2; BI=(Sc – St)/(Sc + St)). Even some standard tests are used in these disciplines to measure rock brittleness.
Figure 4. Different types of brittleness indices defined based on compressive loading tests (modified after: Yang et al., 2013)
We need to remember that compressive loading (e.g., triaxial) tests are strongly influenced by testing condition such as in-situ stresses and ambient pressure and temperature. For instance, experiments show that these tests are strongly dependent on the magnitude of confining stress applied during testing. Rocks usually (though there are exceptions) show more brittle responses at lower confining stresses and, with increasing in this parameter, their responses become more ductile (Figure 5). The combined effect of confining pressure (i.e., in-situ stresses in here) and temperature on rock brittleness has been the main subject of investigation for ‘brittle-ductile transition zone‘ studies performed in plate tectonics, seismology, and earthquake engineering.
Triaxial measurements are costly and time-consuming and the scattered data found by them may not be enough for characterizing the rock behaviour in geological scales. This might be the motivating reason for some experts in the petroleum industry to use the abundantly available wireline log and seismic data for assessment of rock fracability and brittleness in geological formations as will be discussed in the other parts of this article.
Figure 5. Dependency of stress-strain behaviour to confining pressure. The numbers on the curves in the top figure are confining pressures and, in the lower figure, confining pressure is increased from a to d. (source: Paterson and Wong, 2006).
[i] Rock tensile strength is usually measured indirectly using a loading pattern that is not tensile by definition. The most common method is called Brazilian test that imposes a lateral edge loading on a cylindrical sample of rock until it breaks under stress. Point loading is another approach that applies a concentrated load on a planar piece of rock. 3-point bending is another approach that is less used in rock mechanics.
[ii] The terms ’brittle’ and ‘ductile’ in this sentence have been used in their most general forms.
[iii] Defining fracture toughness for quantifying the resistance against fracture propagation has been one of these efforts though the methodology implemented for its measurement can be argued for different reasons.