5.1 Upper and lower bound of elastic properties
Sone and Zoback (2013a) and Trezciak et al. (2018) has interpreted variation in elastic properties of organic-rich shales in terms of a binary mixture model consisting of soft components, in the form of clay minerals and organic matter, and stiff components, represented by quartz, feldspar, pyrite, carbonate, and other stiff minerals. The elastic properties of these end-member components are approximated by Hill’s average of the elastic properties of each component derived from dynamic laboratory measurements (Mavko et al., 2020), resulting in 86.9 GPa for Estiff and 10.8 GPa for Esoft (Sone and Zoback, 2013a). The soft and stiff component end members are then used to calculate the theoretical upper and lower bound using Voigt and Reuss averages, respectively. It is important to point out that the simplified shale model assumes that the elastic properties do not explicitly consider the influence of porosity since the soft component properties are considered to already take into account pore compliance. The U.S. and Polish shale data (Sone and Zoback, 2013a; Trezciak et al., 2018) confirm the general validity of this model, where the upper and lower bounds limit the distribution of the elastic modulus. However, Sone and Zoback (2013a) observed that the measured static Young’s moduli are slightly lower than the predicted theoretical bounds and suggested that the discrepancy reflects the difference between static and dynamic measurements. Therefore, compared to the dynamic measurements subject to small strain and less inelastic deformation, the static moduli of soft components shall be lower than inferred from dynamic measurements. Lowering the soft components value to half of its reference value, i.e., 5.4 GPa, successfully captured the variations in the static Young’s modulus of U.S. shales (Sone and Zoback, 2013a).
The Young’s modulus data of the Indonesian shales are first compared against the theoretical upper and lower bounds calculated using the same end member elastic properties as the U.S. shales (Fig. 15). Results show that the static Young’s moduli for Indonesian shale samples, except for BAO1 and BAO2 samples, mostly fall within the bounds consistent with U.S. shale data (Fig. 15 black lines). However, Indonesian shale data distribute much lower than the U.S. shale data, especially for horizontal samples, which is relatively close to the lower limit. This lower distribution is problematic because horizontal samples should plot closer to the Voigt upper limit because the loading condition is closer to the iso-strain condition of a Voigt average than the iso-stress condition of a Reuss average. This distribution suggests that we need to lower the end member moduli to lower the theoretical bounds and achieve consistency with the laboratory-measured elastic moduli.
We notice that even if the soft-component modulus is lowered to zero, the moduli of the horizontal samples will plot closer to the Reuss lower bound rather than the Voigt upper bound. Therefore, since there is no specific reason to change the soft component modulus, we still use 5.4 GPa as the soft-component modulus for BLM and CSB samples. On the other hand, lowering the stiff component Young’s modulus helps to decrease the Voigt upper bound closer to the horizontal sample data. We reduce Young’s modulus of stiff components from its original value of 86.9 GPa used in Sone and Zoback (2013a) to 50 GPa as a rough first order guess. This reduction successfully shifts the bounds to better capture the laboratory-measured Young’s modulus of the Indonesian shale (Fig. 15 blue lines), except for the BAO1 and BAO2 samples of the Baong Formation.
The BAO1 and BAO2 samples of the Baong Formation show striking differences from other samples in terms of their elastic properties, brittle strength, and creep behavior. These samples also had much higher soft component contents (> 45%) as well as porosity (> 15%) compared to the U.S. shale and the other Indonesian samples. These physical properties result in the additional compliance of the BAO1 and BAO2 samples and their Young’s modulus being plotted below and outside the U.S. and Indonesian shale bounds. In search of a set of upper and lower bounds that is consistent with the Baong Formation samples, we first lower the soft-component modulus to 3.2 GPa, which is the lowest modulus observed for the BAO1 and BAO2 vertical samples. This is because the soft-component modulus marks the lower limit of Young’s modulus and thus must be no greater than 3.2 GPa. We then also lower the stiff-component Young’s modulus to 18 GPa to ensure that the BAO1 and BAO2 data lie below the Voigt upper bound. The upper and lower bounds drawn as such (Fig. 15 red line) roughly agrees with the BAO1 and BAO2 experimental data. The end-member moduli values found from this bound-matching exercise are summarized in Table 2.
Table 2
Summary of the Young modulus and Creep compliance of stiff and soft components for three different shales
| Esoft | Estiff | Ssoft | Sstiff |
U.S. Shales | 5.4 | 86.9 | 1.00E-04 | 1.50E-07 |
CSB and BLM Shales | 5.4 | 50.0 | 1.18E-04 | 2.59E-06 |
BAO1 and BAO2 Shales | 3.2 | 18.0 | 5.48E-04 | 5.36E-05 |
5.2 Creep properties
In terms of creep properties, Sone and Zoback (2013b) found that the tendency to creep (Screep) for each shale sample correlated well with the elastic Young’s modulus (E), as shown in Fig. 16. They explained the correlation through the internal stress partitioning between the soft and stiff components of the shale, as expressed in Eq. 2 below
$${S}_{creep}=\frac{{A}_{1}}{E}+{A}_{2}$$
2
Where \({A}_{1}=\frac{{E}_{stiff}{E}_{soft}}{{E}_{stiff}-{E}_{soft}}\left({S}_{soft}-{S}_{stiff}\right), {A}_{2}=\frac{{E}_{stiff}{S}_{stiff}-{E}_{soft}{S}_{soft}}{{E}_{stiff}-{E}_{soft}}\)
Estiff and Sstiff represent the Young’s modulus and 3-hr creep compliance of the stiff components, respectively. For the soft components, Esoft and Ssoft describe those parameters, respectively. Since there are no direct measurement of Sstiff and Ssoft, Sone and Zoback (2013b) inferred these values by comparing lab-measured properties of their stiffest and most compliant samples with their analytical equations on the relation between elastic and creep properties of the individual components. From such comparison, they determined that Ssoft and Sstiff for the studied U.S. shales are approximately 1x10− 4 and < 1x10− 7 MPa− 1, respectively.
Indonesia shales, however, have a lower elastic modulus than the U.S. shales. Since creep compliance is a function of Young’s modulus (Eq. 2), this suggests that Indonesian shale will follow a different relationship between creep and elastic properties. Here we utilize the same analytical equations from Sone and Zoback (2013b) and compare them with our data to obtain appropriate Sstiff and Ssoft for the Indonesian shales. For the case of CSB and BLM samples, the stiffest samples represented by the horizontal SKR1 sample had a Screep of 4.9x10− 6 MPa− 1, while the most compliant sample represented by the vertical PAP sample had a Screep of 4.32x10− 5 MPa− 1. Following the method suggested by Sone and Zoback (2013b), we estimated the Sstiff and Ssoft as 2.59x10− 6 MPa− 1 and 1.18x10− 4 MPa-1, respectively. For the case of BAO1 and BAO2 samples, we used data from BAO1 horizontal-2 having Screep of 2.10x10− 4 MPa− 1 as the stiffest sample and BAO1 vertical-2 with Screep of 5.48x10− 4 MPa− 1 as the most compliant sample. The resulting Sstiff and Ssoft were estimated as 5.36x10− 5 MPa− 1 and 5.48x10− 4 MPa− 1, respectively. We summarize the Sstiff and Ssoft values recovered from the different datasets in Table 2. New relations between Screep and E for CSB/BLM samples and BAO1/BAO2 samples are drawn in Fig. 16 using Eq. 2 and the values in Table 2.
As shown in Fig. 16, in general, the CSB and BLM samples (solid blue curve) closely follow the U.S. shales trend (black solid curve). In contrast, the BAO1 and BAO2 shale samples show a higher 3-hr creep compliance for a given Young’s modulus, by approximately a factor of 2, compared to the trend of the U.S., CSB, and BLM shale samples (solid red curve).
5.3 Relation between burial history and mechanical maturity
From the values in Table 2, we see that it is the low stiffness and high creep compliance of the stiff components that makes the mechanical properties of the Indonesian shales distinct from US shales. In this section, we discuss the cause of this distinct mechanical properties in relation to the burial history of the Indonesian shales. We also suggest to introduce the idea of mechanical maturity to describe how burial history influence the progression of diagenesis and the resulting evolution of shale mechanical properties.
Burial histories are an essential component of source rock evaluation, especially concerning the ability of the source rocks to produce oil and gas, commonly known as the thermal maturity. Burial history describes the change in depth of a formation after their deposition, which controls the stress and temperature that a rock experiences. Since diagenesis occurs as a result of stress and temperature increase, burial histories provide constraints in understanding the diagenetic state and thermal maturity of organic materials in sedimentary rocks. Meanwhile, compaction is a process that also occurs during diagenesis driven by stress and facilitated by physical processes such as frictional grain boundary sliding (Hagin, 2003; Karner, 2006) and pressure solution (Fowler and Yang, 1999). Laboratory data generally shows that a decrease in porosity leads to an increase in elastic modulus and decrease in creep compliance. Therefore, we expect a causal relationship between burial history and the mechanical properties of shale.
To delineate the impact of burial history on mechanical properties of organic-rich shales, we compare some example burial histories of U.S. and Indonesian shale reservoirs. Figure 17 shows the 1D burial history of a well at Fort Worth Basin, USA (Curtis, 2002) and North Sumatra Basin, Indonesia (Ascaria, 2010). The Barnett Formation is a Carboniferous Period (359 − 299 Ma) deposit, buried to a depth of about 9000 ft (2750 m), from the Pennsylvanian to Late Cretaceous Epoch (323 − 100 Ma), and uplifted to its present depth around 4000 ft (1200 m) from Late Cretaceous to Miocene Epoch (100 − 23 Ma). The burial to its deepest position coincides with the early generation of petroleum from Late Permian Period (260 Ma).
As a comparison, in NSB, the deposition of the Belumai Formation started at the early Miocene Epoch (23 Ma), followed by the lower Baong Formation at the middle Miocene Epoch (16 Ma), and the above formations until Pleistocene Epoch (Ascaria, 2010). In this presented example, which comes from a well drilled in a deeper area of the NSB compared to our study, the Belumai formation was buried to its present depth of about 2400 m from about 23 Ma to 5 Ma and started its oil expulsion from Pliocene Epoch (4 Ma). The well we studied likely has a slightly different burial history since it is located relatively near the Barisan mountains and hence affected by Barisan Orogeny (Ariyanto and Syarifuddin, 2018). Specifically, in addition to the general burial history shown in Fig. 17b, the formations penetrated by our studied well have also been experiencing uplift since about Pleistocene Epoch (2 Ma) to its present depth.
As seen in the comparison of the burial histories, the Belumai and Baong Formations are at slightly shallower depths compared to the Barnett Shale. Nevertheless, because of the higher heat flow in Indonesia, the Indonesian shales have experienced similar, or even higher, temperatures compared to the Barnett Shale. This higher heat flow leads to both U.S. and Indonesian shales having undergone early maturation and expulsion processes resulting in similar thermal maturity.
On the other hand, there is a significant difference in mechanical properties despite the only slight difference in burial depths. Extrapolation of the consolidation theory from soil mechanics (Mitchell and Soga, 2005) suggest that the consolidation state (i.e., porosity) of a sedimentary rock is determined by the maximum overburden stress experienced during the burial history. However, the overburden stresses at the maximum burial depth of the Barnett Shale and the Belumai Formation are approximately 69 MPa and 60 MPa, respectively, assuming average rock density of 2500 kg/m3, only slightly different from each other. Therefore, we suggest that the vast difference in the age of deposition is the cause of difference in mechanical properties. Age controls the duration that the formations experience the maximum load and the duration of the time-dependent diagenetic processes.
Although direct evidences are not available, time-dependent compaction of shales have been suggested to operate over geological time scales. Sone and Zoback (2014a, b) extrapolates the power-law creep behavior of gas shales observed in the lab to geological times to show that such extrapolation may help explain intra-reservoir stress heterogeneities and would not lead to unrealistic predictions of porosity loss over geological time. If so, porosity loss due to diagenesis is also a function of time and results in mechanical properties that vary due to difference in geological age. We propose to describe this progression of mechanical properties with age as the process of mechanical maturation, and the degree to which this maturation has progressed as mechanical maturity. Mechanical maturity is a function of stress magnitude and time, potentially some integration of the stress history with respect to time, because compaction is a time-dependent process driven by stress, as opposed to thermal maturity which is mainly dependent on maximum temperature.
The comparison of elastic moduli and creep compliance of the Indonesian shales with the U.S. shales has shown three distinct trends (Fig. 16): the U.S. trend, CSB/BLM trend, and BAO1/BAO2 trend. These trends mainly reflect the difference in the stiff component properties as shown in Table 2. Because the minerals composing the stiff components in the binary mixture model should not change significantly during mechanical maturation, we interpret that this reflects, to the first order, the inter-granular porosity that resides between stiff grains and closes with mechanical maturation by compaction. If we take the U.S. Shales as the mature reference, CSB/BLM will represent a relatively early-mature state, whereas the BAO1/BAO2 are notably immature mechanically due to the overpressure that reduces the maximum effective stress experienced by the formations. Note that in Baong formation, significant disequilibrium compaction is suggested to have occurred (Syaiful et al., 2020) in addition to hydrocarbon generation which should lead to residual intergranular porosity. Indonesian shales are thermally mature but mechanically early-mature to immature compared to U.S. shales because the significantly younger age has limited the time needed for mechanical maturation.
5.4 Influence of shale depositional environment on the mechanical properties
Shales deposit in very slow-moving water in various depositional environments ranging from terrestrial, transitional, to marine environments. Terrestrial environments include lacustrine, swamp, and river floodplains; transitional environments include marsh and delta; marine environments range from shallow to deep water. Shale can be found in various depositional ages, from Paleozoic to Cenozoic Era, and in extensive tectonic settings, from stable Craton to active convergent / divergent margins.
The success of the U.S. in extracting gas from their marine source rocks has attracted other countries to search for potential shale gas reservoirs in shale deposits from similar marine environments first, potentially subordinating shale deposits from the terrestrial and transitional settings. It is reasonable to expect that the type of organic material found in shales are dependent on the particular depositional environments as previously suggested by Tissot and Welte (1984). However, in the case of kerogen type, Vandenbrouck and Largeau (2007) have shown that type of kerogen does not have to be associated with any specific environment. In addition, as is known in conventional petroleum systems, gas can be produced from mature source rocks of kerogen type 2 and 3 or even from over-mature source rocks of kerogen type 1. Thus, depositional environment may not be a determining factor for mature organic-rich shales to produce gas.
Our laboratory analyses suggest no significant differences in the mechanical properties of shale deposited in the lacustrine (CSB samples) and marine environment (BLM samples), as both datasets lie within the same bounds and are described by the same binary mixture model. Even though our data in Table 1 show differences in composition between the two sample groups, where marine samples are more clay-rich, while lacustrine samples are more affluent in organic matters, treating their influence on mechanical properties to be equal by summing their volumes as the soft component volume appears to obscure the difference in composition (Fig. 3). Here, we treat their contribution as mutually complementary, although the specific contribution of each component in the shale is unknown and still requires further research. In addition, the relation between creep and elastic properties of CSB and NSB samples generally follow the same trend describing the progression of diagenesis, as shown in Fig. 16. Therefore, our data do not show the influence of the depositional environment on the mechanical properties of the shale.