# Determining Brittleness From Seismic Data

The key elements for shale resource evaluation are the mineral content - such as clay, quartz and calcite - the total organic carbon (TOC) content, the brittleness and some mechanical properties of the shale rocks. Geomechanical studies are necessary both for understanding wellbore environment stability and also interpreting well log data, by estimating the mechanical properties of the subsurface.

Simply stated, an accurate geomechanical model needs to be conceived, and its main features are the three principal elements - stresses, pore pressure and the rock strength. Availability of these parameters define a good geomechanical model, which help with the evaluation of wellbore stability, fracture permeability, drilling direction and others.

Highly brittle shale formations fracture better, and thus provide more fracture pathways for release of the hydrocarbons. The shale’s mineral content can be determined from the XRD analysis, or estimated from the wireline well log curves.

Similarly, brittleness and TOC can be estimated from the well log data - but this information is only available at the location of the wells.

In this article we focus on determination of brittleness of shale formations from seismic data - and demonstrate that brittleness is a relative term that has no standardization and needs to be carefully calibrated with the relevant data before it is used for interpretation.

Before we go ahead with that description, some common definitions of terms and elastic constants used in the discussion on brittleness are discussed first.

♦ When a slab of rock is acted upon by a force, it is expected to undergo a change in its dimensions.

For simplicity, let us consider the change along the length of the slab.

The force acting on a unit area of the rock is referred to as stress, and is commonly measured in Pascals (Pa) or pounds per square inch (psi). The resultant change in length of the rock or the rock’s deformation in response to the stress is measured as the change in length per unit length, and is called strain.

Being a ratio of two lengths, strain has no units.

Strain may be of three types, depending upon the change produced in the rock on the application of stress:

- Longitudinal strain is the change in length per unit length.
- Volumetric strain is the change in volume per unit volume.
- Shearing strain is the angle through which a face of the rock sample perpendicular to the fixed face is turned.

As a result of the tectonic activities that Earth experiences, subsurface rocks undergo two types of stresses - the stretching or extensional types of stresses, (or tensile stresses, implying the rock is under tension), and the compressive stresses.

The strains corresponding to these two types of stresses are referred to as tensile and compressive strains respectively.

♦ When the strain produced in a slab of rock is plotted against the applied stress, the graph shown is straight line, implying stress is proportional to strain - a result known as Hooke’s law. The gradient of the straight line is referred to as Young’s modulus, usually denoted as E.

Young’s modulus is a constant for a given material and is a measure of its stiffness. It is measured in Pascals (Pa) or pounds per square inch (psi). For the rocks that we commonly deal with, E turns out to be a large number, and thus larger units such as Mega Pascals (MPa) or Mega psi are commonly used.

Similarly, depending on the two other types of strain, we talk of two other moduli of elasticity - namely bulk modulus (𝜅), which corresponds to volume strain and is a measure of the rock’s incompressibilty, and shear modulus (μ), which corresponds to shearing strain and is a measure of the rock’s rigidity.

Besides these, there is another elastic constant, (λ), that is commonly employed in rock physics and is related to the bulk modulus. For this reason it is considered a proxy for incompressibility of the rock samples.

Both λ and μ are also known as Lame’s constants, named after the French mathematician, Gabriel Lamé.

♦ When a slab or rock is compressed in one direction, it tends to expand in the other two directions, perpendicular to the direction of compression. The ratio of the fractional expansion to the fractional compression of a rock is referred to as Poisson’s ratio (ν) - it is a measure of the rock’s strength, and its values for most rock types range from 0 to 0.5.

Thus there are different elastic constants (E, ν, 𝜅, μ, λ) that are used for characterizing reservoirs. Knowledge of any two of them allows the computation of the others.

The values of these constants are usually determined in the laboratory by making two distinct types of measurements on rock samples.

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