2. Brittleness index (BI) and brittleness average (BA)

Brittleness of rock has been defined in different ways. Jarvie [2] defines the brittleness index (BI) as a fraction of the mineral composition of rock, while Grieser and Bray [3] define brittleness average (BA) as purely related to the elastic properties of the rock.

As mineral composition of rock defines its brittleness, the number of fractions of most brittle mineral impacts on the rock brittleness. Brittleness index (BI) is formulated as

$$\text{BI}\_{\text{Jarvi}} = \frac{\text{Qz}}{\text{Qz} + \text{Ca} + \text{Cl}\text{y}} \tag{1}$$

where Qz, Ca, and Cly are the fractional quartz content, calcite content, and clay content, respectively.

For wells that are located where the composition of mineral can be properly determined, the BI can be calculated. However, away from the well, the BI is difficult to be estimated due to the difficulties in predicting the mineral content distribution. Hence, it is still difficult to use this technique to estimate brittleness three-dimensionally, because of the challenge in estimating mineral content from seismic data.

Elastic-Based Brittleness Estimation from Seismic Inversion DOI: http://dx.doi.org/10.5772/intechopen.82047

Grieser and Bray [3] proposed the use of brittleness average (BA) to express the brittleness of the rock. Brittleness average is calculated based on elastic properties, i.e., normalized Poisson's ratio and Young's modulus. By using this relation, estimation of brittleness in a wider area is possible. Both Young's modulus and Poisson's ratio can be derived from seismic data through seismic inversion. Hence, using this technique the brittleness of rock in terms of BA can be estimated from seismic data.

Young's modulus (E), representing the stiffness of the rock, can be defined in terms of bulk modulus (κ) and Poisson's ratio (σ) as.

$$E = -\mathfrak{Z} \times (\mathfrak{1} - \mathfrak{2} \,\, \sigma) \tag{2}$$

On the other hand, Poisson's ratio can be derived from P-wave (Vp) and S-wave (Vs) velocities:

$$\sigma = \frac{\text{V}p^2 - \text{Vs}^2}{2\text{V}p^2 - 2\text{Vs}^2} \tag{3}$$

By substituting Eq. (3) in Eq. (2), the Young modulus is expressed as

$$E = \rho V s^2 \frac{\left(3Vp^2 - 4Vs^2\right)}{Vp^2 - Vs^2} \tag{4}$$

Hence, the brittleness average (BA) is expressed in Rick's relation [1]:

$$BA = \frac{1}{2} \left( \frac{E - E\_{\text{min}}}{E\_{\text{max}} - E\_{\text{min}}} + \frac{PR - PR\_{\text{max}}}{PR\_{\text{min}} - PR\_{\text{max}}} \right) \times 100\tag{5}$$

where Emin and Emax are the minimum and maximum Young's modulus and PRmin and PRmax are the minimum and maximum Poisson's ratio.

To evaluate the correlation between brittleness average and brittleness geomechanically, the brittleness average is tested against well logs of the domain and compared to geomechanical properties obtained from the formation microimager (FMI) log (Figures 1 and 2). Examples are taken from a fractured basement reservoir field located in Malaysian offshore. This field is located at a margin of the basin as permo-carboniferous metasediments and volcanic, cretaceous granites, or possibly cretaceous rift fill and mesozoic to carboniferous carbonates and mesozoic granites [4]. The lithology of the offshore basement for this area is described in Tjia et al. [5] based on well drilling distribution with pre-tertiary rock penetration.

Figure 1 shows the brittleness average logs which is calculated from normalized Poisson's ratio and Young's modulus logs and compared to the core of two different depth samples. The first sample (upper right) was taken from the depth where the brittleness average value is low. In this depth, the core sample showed that only a view number of fractures appear. The crack density of this core sample is low which is correlated with a low value of brittleness average. The second sample (bottom right) was taken from the depth where the brittleness average value is high. Many fractures appeared in this core sample. The core data is taken from a region where the rock is more brittle, which is also associated with a high value of brittleness average in the log. In other words, the intensity of fracture of the rock can be determined by the brittleness average log.

The feasibility study on well log data shows that the brittleness average has a good correlation with fracture density. A high fracture density area is associated Exploitation of Unconventional Oil and Gas Resources - Hydraulic Fracturing…

#### Figure 1.

Brittleness average log (left) compared to the FMI data (right). The high value of brittleness average associated with high crack density.

### Figure 2.

Lithology and fracture density logs (left) compared with brittleness average (right log).

with high brittleness average log. Because of the elastic properties, Young's modulus and Poisson's ratio can be extracted from seismic data through inversion result; therefore, the brittleness average, which is associated with fracture density also can be calculated from inversion result.
