Introduction

Characterizing organic-rich shales can be challenging as these rocks vary in lithological behavior. Horizontal drilling and hydraulic stimulation have made hydrocarbon production from organic-rich shales economically viable. Identification of zones to drill a horizontal well and to initiate or contain hydraulic fractures requires use of elastic and mechanical properties.

The rock mechanical properties like Poisson’s ratio, Young’s modulus and brittleness of the rock play an important role to decide the completion type and fracture intervals and productivity. These two components (Poisson’s ratio and Young’s modulus) together are the reflection of the rocks ability to fail under stress and fracture. Brittle oil/gas shale’s are more likely to get fractured and will respond better to hydraulic fracturing treatment. Quantification of brittleness index (BI) combined Poisson’s ratio and Young’s modulus of rock mechanical properties in shale is necessary in identification of favorable zones for hydro fracturing.

Gamma ray, neutron porosity and resistivity logs are useful to characterize the reservoir. This additional information can come from the integration of specialized logging tools and core laboratory measurements. The availability of seismic data (P-impedance), X-ray diffraction (XRD) data, Fourier transform infrared spectroscopy (FTIR) data and dipole sonic, density logs enable characterization of a shale gas reservoir in terms of its mineral content and elastic properties.

Background Geology

Cambay Basin is a narrow, NNW–SSE trending intracratonic rift basin, formed at the end of cretaceous which is located on western margin of the Indian shield (Fig. 1). The basin, around 425 km long with an average width of about 138 km, extends from Luni river in the north to Tapti river in the south having five tectonic blocks (Fig. 1). The Cambay Basin covers an area of about 59,000 sq km. It lies between the west and northwestern margin of Indian shield between latitudes 21°N to 25°N and longitudes 71°15′E to 73°30′E in the states of Gujarat and Rajasthan.

Fig. 1
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Location map of the study area shows the five drilled well locations, total depth, Cambay shale top and bottom depth within the study area

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The Cambay shale formation (henceforth CSF) unconformably overlies the Olpad formation from lower to middle Eocene. The thickness of the formation varies widely from 50–70 m in the northern part over the Mehsana horst to more than 500–2500 in Hazira, Broach, Tarapur and Patan depressions. The CSF has been divided into two units—the lower (older) Cambay shale and the upper (younger) Cambay shale on the basis of a log marker (neck marker)—separated by an erosional unconformity. The Lower Cambay shale is dark gray, thin-bedded, fissile, carbonaceous and slightly calcareous with rare occurrences of pyrite, whereas the upper Cambay shale is from black, massive and soft to moderately hard, fissile, silty, pyritic, non-calcareous and carbonaceous (Sarraf et al. 2000; Chowdhary 2004; Sharma et al. 2004; Mishra and Patel 2011).

The study area is situated in Narmada tectonic block of south Cambay Basin. The area of study covers 160 sq km in which CSF varies in thickness from 25 m in east to 700 m in west (Fig. 1). The top of Cambay shale occurs at 1100 m–2200 m. The lithology of the CSF is mainly carbonaceous shale, clay stone with intercalations of siltstones.

Methodology

Four wells (namely well no 1, 2, 3 and 4) were drilled through CSF are considered for the study. Sonic logs, DTC and DTS recorded in all the four wells are used for estimating rock mechanical properties. Mineralogical study was done with the help of petrographic observation of the drill cuttings (rock chips) as well as from the XRD and FTIR analyses carried on the powder samples of the drill cuttings from well no. 2 and 3. Poisson ratio and Young’s modulus are calculated from the sonic log measurements in 4 (well no. 1, 2, 3, 4) wells in the study area from Eqs. 1–3 (Gassmann 1951; Fig. 2) and converted dynamic Young’s modulus to static Young’s modulus from E static = 0.83 E dynamic (Neville 1997; Salman 2006).

Fig. 2
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Graphical representation Young’s modulus, Poisson’s ratio and brittleness average from logs in well #1. The encircled depths indicate highly brittle areas

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$$\text{Poisson's ratio}\,\left( V \right) = \frac{{V_{p}^{2} - 2V_{s}^{2} }}{{2\left( {V_{p}^{2} - V_{s}^{2} } \right)}}$$
(1)
$$\text{Shear modulus}\,\left( G \right) = \frac{\rho b}{{T_{s}^{2} }}$$
(2)
$$\text{Young's modulus }\;\left( E \right) = 2G\left( {1 + V} \right)$$
(3)

Brittleness

When a rock is subjected to increasing stress, it passes through three successive stages of deformation: elastic, ductile and brittle. Based on these behaviors, it is possible to classify the rocks into two classes: ductile and brittle. If the rock has a smaller region of elastic behavior and a larger region of ductile behavior, absorbing much energy before failure, it is considered ductile. In contrast, if the material under stress has a larger region of elastic behavior but only a smaller region of ductile behavior, the rock is considered brittle.

Brittle average (BA) from logs

The term brittleness average was proposed by Grieser and Bray (2007) as an empirical relationship between Poisson’s ratio and Young’s modulus to differentiate ductile from brittle regions. They hypothesize that ductile rocks exhibit low Young’s modulus and high Poisson’s ratio, while brittle rocks exhibit moderate to high Young’s modulus and low Poisson’s ratio (Perez and Marfurt 2013, 2014; Salman 2006). Young’s modulus and Poisson’s ratio (for brittleness) are derived from Eqs. 4,  5, and using the calculated values normalized brittleness average was derived from Eq. 6.

$$\text{Young's modulus}\_{\text{brittlenes}} = \frac{E - E_{\text{min} }}{E_{\text{max} } - E_{\text{min} } }$$
(4)
$$\text{Poisson's ratio}\_ {\text{brittleness }} = \frac{V - V _{ \text{max} } }{V _{ \text{min} } - V _{ \text{max}}}$$
(5)
$${\text{Brittleness average }}\left( {\text{BA}} \right) = \frac{{\left( {E _{\text{Brittleness}} + V _{\text{Brittleness}} } \right)}}{2}$$
(6)

where E is Young’s modulus, and E min and E max are the minimum and maximum Young’s modulus measured in the logged formation, and where V is Poisson’s ratio, and V max and V min are the maximum and minimum values of Poisson’s ratio logged in the formation. Finally, they define a brittleness average (BA) shown Fig. 2. The Calculation of BI is extended to all the wells shown Fig. 3.

Fig. 3
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Graphical representation of BA, PR and static YM in from well logs in the study wells #1, 2 and 3

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Brittleness index (BI) from mineralogy

XRD is a techniques used to examine the chemical composition of rocks. In this technique a rock sample is powdered and irradiated with X-rays of a fixed wavelength. Intensity of the reflected radiation is recorded using a goniometer and gives the composition of the rock.

X-ray diffraction analyses of the samples were performed using a X’Pert PRO, Ultima IV automated powder diffractometer equipped with a copper X-ray source (45 kV, 40 mA) and a scintillation X-ray detector. The 10 rock samples were analyzed over an angular range of five to eighty degrees (5–80) two theta.

The semiquantitative determinations based on intensity of the major peaks preset in the sample (Fig. 4). The quartz grains have been seen in all the samples to be the main framework grain type. The quartz content ranges from 30 to 69% of the total rock. Kaolinite, pyrite, calcite and ilmenite are considered to be the second most abundant constituent detrital grains in all the samples, ranging from 1 to 10%. Presence of calcite and halite minerals has also been observed. As per the XRD results, kaolinite is the main clay followed by illite. Among all the clay minerals, kaolinite is consistently present in all the samples. The sample graphical representation of well no 2 is given in Fig. 5, and all the samples correlated each other giving the similar signatures indicate the same type of mineralogy is present in all the samples in well no 2 and well 3 in the study area Figs. 5 and 6 (Srodoi et al. 2001; Nadeau et al. 1984; Morkel et al. 2006; Nayak and Singh 2007).

Fig. 4
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A representative XRD data analysis and mineral identification from well #2 in the study area

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Fig. 5
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A representative XRD data analysis and mineral identification from well #2 from 5 samples in the study area

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Fig. 6
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A representative XRD data analysis and mineral identification from well #3 from 13 samples in the study area

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Fourier transform infrared spectroscopy (FTIR)

Spectroscopy is a technique for determining qualitative mineral identification. Mineral identification is possible because minerals have characteristic absorption bands in the mid-range of the infrared (4000–400 cm−1). The concentration of a mineral in a sample can be extracted from the FTIR spectrum because the absorbance of the mixture is proportional to the concentration of each mineral. The infrared spectra of well #2 and 3 of Cambay shale samples, presented in Figs. 7 and 8, exhibited OH stretching at bands 3620 and 3693 cm−1 and C-H stretching at bands 1411 and 1417 cm−1, and the OH deformation bands were observed at 911 and 911.5 cm−1. Bands associated with SiO stretching were 692, 994 and 695 cm−1; 753 and 754 cm−1; and 791, 795 and 796 cm−1, whereas SiO deformation bands were 1004, 1032 and 1033 cm−1 (Fig. 9). The same sample in petrography thin sections also showing the quartz and organic matter presence conforms to the sample containing clay minerals, organic matter and quartz. (Adamu 2010; Djomgoue and Njopwouo 2013).

Fig. 7
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A representative FTIR data analysis and mineral identification from well #3 in the study area

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Fig. 8
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A representative FTIR data analysis and mineral identification from well #2 in the study area

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Fig. 9
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Thin section showing the presence of organic matter, quartz and clay mineral in the sample of well #3

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Jarvie (2007) proposed BI definitions based on the mineral composition of the rock, dividing the most brittle minerals by the sum of the constituent minerals in the rock sample, considering quartz as the more brittle minerals; after Jarvie, some equations, Perez and Marfurt (2013), Nayak and Singh (2007), Altindag (2003), also used the following equation for BI calculation.

$$\text{Brittleness index }\left( {\text{BI}} \right)\,{\text{Jarvie }}\left( {2007} \right) = \frac{\text{Qtz}}{{{\text{Qtz}} + {\text{Ca}} + {\text{Cly}}}}$$
(7)

where Qtz is the fractional quartz content, Ca the calcite content and Cly is clay content by weight in the rock. In the study area the dolomite is absent. The main observed mineralogy is quartz, kaolinite, pyrite, siderite and calcite (Fig. 4). The main mineralogy is given in Table 1.

Table 1 Mineralogical composition and mineral-derived BI in the well #3
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After calculating BI from mineralogy, the log-derived brittleness average (BA) was correlated with BI from XRD data and the brittleness average converted to BI by established Eq. 8 is shown Fig. 10.

Fig. 10
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BI from mineralogy versus BA log cross-plot in well #3

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$$Y = 1.087X - 0.007\quad \left( { Y = BI, X = BA} \right)$$
(8)

Seismic inversion

Pre-stack simultaneous inversion estimates P-wave impedance, S-wave impedance and density, which is useful for predicting the lithology and geomechanical behavior of the shale reservoir. Acoustic impedance inversion transforms the seismic reflection data to a acoustic impedance model.

This P-impedance volume is then optimized by modifying the low-frequency trend and enforcing compliance with any additional constraints. P-impedance volume is used as a secondary input in distributing different properties in modeling (Fig. 11; Perez and Marfurt 2014; Harial and Tandon 2012; Angus et al. 2011).

Fig. 11
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P-impedance volume cross section along well #2 and well #3 in study area

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Modeling

A time–depth relationship was established leading to P-impedance. The cross-plot between BI from logs and P-impedance gives 72.8% correlation index (Fig. 12).

Fig. 12
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Cross-plots of P-impedance volume and log-derived BI for establishing the relation the correlation is 72.8%

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The established equation from cross-plot helped in modeling the brittleness and identifying high BI areas in the study area (Fig. 13).

Fig. 13
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P-impedance volume and log-derived BI showing in the section

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$${\text{BI}} = 0.000104773 \times {\text{P imp}} - 0.272992$$
(9)

Results

The sonic log data of 4 wells, both compressional and shear, were used to compute Poisson’s ratio (g API), Young’s modulus (GPa) and brittleness average (BA) in Table 2. BA was finally converted to BI values using the derived equation no 1, 2 and 3 (Table 3).

Table 2 Log-derived results in different wells in the study area in Cambay shale section
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Table 3 Log-derived BI in well #3
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After calculating BI from logs and mineralogy, rocks are classified into four categories based on Perez and Marfurt (2014) which are (a) high ductile, (b) less ductile, (c) less brittle and (d) high brittle. The ternary plot shows high quartz content and more brittle area from the XRD data (Fig. 14 and Table 4).

Fig. 14
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Ternary diagram results in the study area

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Table 4 Rock type classification based on the brittleness index in study area
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Figures 15 and 16 shows a log correlation in the study area, differentiating brittle and ductile areas in the well section. Log-derived BI was validated by comparing with XRD-derived value. A relationship between BI log and P-impedance was established, and a brittleness model was prepared in the study area for Cambay shale formation.

Fig. 15
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The Brittleness Index correlation in the study area wells; the red is indicating high brittleness and blue is indicating ductile area in well#1 and well#2

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Fig. 16
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The Brittleness Index modeling output along the study wells in the study area in Cambay shale section

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Conclusions

Brittleness is considered to be one of the important mechanical properties of shale rocks for hydraulic fracturing. In this study, sonic data were used for calculating BI of Cambay shale section.

In the Cambay shale zones, Young’s modulus static (YME) varies between 1.4 and 7.54 GPa, whereas the Poisson’s ratio (PR) ranges from 0.10 to 0.43 g API. The BI range is 0.44–0.75 in the study area. The well data results were transformed into seismic study by using the VSP check-shot data. This resulted in establishing a relation between seismic P-impedance and BI logs and established relation equation.

The complete study area was modeled by using Eq. 9, and areas of high brittleness were identified in the Cambay shale section. The brittleness derived from logs and brittleness from the model show very good correlation index (Fig. 17).

Fig. 17
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Relation between the BI logs and BI model; the correlation is 94%

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The information about the BI shell is useful for effective stimulation and leading to better production. Analysis shows that the northeastern part of the study area is ductile shale as compared to northwestern part of the study area.