Shale rock formed from small clay particles, and shale compaction is an essential factor to estimate shale reserves. The classical Athy’s model has been used to obtain the shale compaction curve to describe the relationship between porosity and depth, an essential input data for basin modelling. But recent studies revealed that burial time, among other factors, should be considered and that geological age is another important factor in some regions. This is because geological and lithological histories are crucially different among geological ages. This study employed the newest data of Thailand shales and confirmed that different geological ages (Cenozoic, Mesozoic, and Paleozoic ages) require different shale compaction curves by estimating numerical geological time with the relationship of velocity and depth in each geological age. We obtained empirical models of the shale compaction curve of each geological age by multi-linear regression. The standard curve of shale compaction with the relationship among porosity, depth, and time, proposed in a previous study, was also re-affirmed with the newly obtained models.
Shale is a clastic rock formed from muds and small clay particles. Shale compaction, a phenomenon in sedimentary basins (e.g. Mukherje and Kumar ), occurs through the mechanical, chemical and other compaction processes. Muds have higher initial porosity relative to coarser grains, which affects mechanical compaction more than other sediments such as sandstone and carbonate rocks . Thus, mechanical compaction, which is dominant at shallow depths, is the most significant process for shale dominances. The fluid absorbed by certain clay minerals in the shale is also affected by porosity, together with other factors such as pressure and the burial depth of sedimentary [3,4,5].
Shale compaction analysis has been considered to be important to estimate the potential quantity of shale (oil) reserve. Particularly in Asia-Paccific region, China, Australia, Pakistan, and India are known for their large shale potentials [6,7], and the US Energy Information Administration (EIA) also mentioned Thailand, Indonesia, and Mongolia for significant potentials of shale reserve [8,9]. In many parts of those countries, however, precise shale compaction analysis, which is the basis of shale reserve estimation, has been a due.
Conventionally, porosity-depth curves, which indicate the rate of mechanical compactions, are an essential tool to investigate shale compaction processes as input data for basin modeling . The most widely used model is the empirical relationship between porosity and depth. The classical Athy’s model  on the empirical equation of exponential porosity reduction with depth has been used in a large number of studies for shale compaction  and for other possible models on porosity-depth [12,13,14,15]. However, there are large variations in the porosity-depth curves of the mechanical compaction for shales [16,17,18], and several other factors including temperature, geological age, clay diagenesis, and overpressure may well affect porosity-depth relation, causing porosity-depth relation to often deviate from the classical Athy’s model [5,17,19,20,21,22]. Nowadays, various porosity-depth trends for shales  have been proposed based on empirical localisms. They are often based on the application of the standard model for sandstones to shale, but they are not so successfully robust.
Some advanced basin models employ the geological time factor, since the porosity at a place is heavily affected by sediment depositions, uplift sequence, and diagenetic effects, most of which occur over a long time . Early studies from Burst , who is a pioneer in studying the effect of the geological ages on shale compactions, concluded that the porosity of shales tends to reduce with increasing geological age. Puttiwongrak et al.  constructed porosity-depth models with different geological times using many different datasets in the world and clarified the effect of geological times. However, shales in different regions show different characteristics, and thus it is desirable to establish accurate compaction models of shales of specific regions, particularly in Asia-Pacific regions.
This study employed the new data of Thailand shale compactions integrated with published data, which were compiled in 2015 provided by Department of Mineral Fuel of Thailand (DMF) and constructed the compaction models of Thailand shales with geological age classification, Cenozoic, Mesozoic, and Paleozoic ages.
Geologically, Thailand is divided into several regions with different geological and lithological histories from the Precambrian period in the Paleozoic age to the Quaternary period in the Cenozoic age. Hydrocarbons in Thailand were discovered and produced from the Tertiary basins, which are groups of the Cenozoic age and pre-tertiary basins included Triassic in the Mesozoic age and in the Permian Period in the Paleozoic age. Tertiary basins are distributed in several parts of Thailand, both onshore (the north, the central, and the south regions) and offshore (the Gulf of Thailand and the Andaman Sea). Pre-tertiary basins are mainly located in the northeastern Thailand, which are made up of sedimentary rocks dating from the Carboniferous period of the Paleozoic age to the Tertiary period of Cenozoic age [25,26]. These geological and lithological histories influence compaction models, and thus this study constructed different compaction models of the relationship between porosity-depth curves and time according to geological ages. Specifically, this study employed the data from four Thailand local basins: Petchabun basins in the north Thailand, Mukdahan, Kuchinarai, and Phu Din basins in the northeastern Thailand.
The objective of this study is to clarify the time factor for shale compactions in Thailand shales. This study first confirms that the porosity-depth curves of shales of the targeted locations are well expressed with regard to different geological ages, Cenozoic, Mesozoic, and Paleozoic ages. Then, the new shale compaction models, the empirical relationships among porosity, depth, and time, of each age are proposed based on the methods in Puttiwongrak et al. . A model of standard compaction for Thailand shales is also discussed, compared to that in Puttiwongrak et al. .
2 Data collection and methods
The dataset of this study is composed of 176 data of shale formations from four areas in northeastern Thailand (Figure 1). Four study areas were selected based on the availability of porosity, burial depth, and geological age information for shale formations. They cover a broad range of ages and burial depth: from the Paleozoic to Cenozoic ages and between 280 and 1,432 m below the ground surface, based on well-logging data supplied by the Department of Mineral Fuel of Thailand (DMF).
Porosity data were calculated from the wireline density log (RHOB) using 2.762 g cm−3 as the matrix density and 1.000 g cm−3 as water density, and depth data are given in meter below the ground surface. However, the time data are in the geological ages, there are no numeric data of geological ages obtained from the DMF. Therefore, the numeric data of geological ages were estimated as discussed in the further section. The dataset is summarized in Table 1.
|Location||Porosity (%)||Depth (m)||Geological age||Total data||Estimation ages (Ma)|
3 Conventional porosity-depth plot
To quantify the compactional scatter of shale data from northeastern Thailand, the dataset was plotted by the porosity-depth plot as shown in Figure 2. The compaction of shales is defined by the porosity reduction during burial, and the shale mechanical compaction of porosity reduction is formulated as a mostly exponential function, a conventional model to represent the compaction curve of shales . The frequently used exponential function was proposed by Athy :
where c is a constant, generally known as the compaction coefficient, z is burial depth, ϕ is porosity in depth z, and ϕ o is the initial porosity (at the surface).
However, this function, equation (1), was not fit to the Thailand shale data (r-square = 0.0406) to obtain compaction curves. Figure 2 shows a trend of scattered data points at the entire depth, the porosity-depth curves at the same lithology and depth but from different areas have differences in the porosity of more than 20% .
4 Estimation of geological age data
In this study, new data is provided based on the different geological ages of the Paleozoic, Mesozoic, and Cenozoic ages. The numeric data of each geological age were not available, and a numeric estimation of geological ages was conducted by examining the relationship among velocity, depth, and geological age as suggested by Faust . The velocity data were calculated by the relationship between velocity (v) and depth (z.) using equations (2)–(4) for the Cenozoic, Mesozoic, and Paleozoic datasets, respectively, as shown in Figure 3. The modified plots from Faust  in Figure 3 give the relationship of the velocity and depth with the r-squares equal to 0.9414, 0.7701, and 0.6253 for each geological age (Cenozoic, Mesozoic, and Paleozoic, respectively) .
The equations for velocity as a function of depth in each geological age classification (Cenozoic, Mesozoic, and Paleozoic ages) are expressed below,
and the relationship of velocity, depth, and geological age in years is formulated as equation (5):
Where α is given presently the value of 46.55 and is numerically equal to velocity in meter per second when TZ = 1. With equation (5), the numerical geological age estimation is obtained with the depth data summarized in Table 1.
5 Analysis method
In this study, the compaction curve for shale, which is empirically determined by the porosity-depth plots, is made separately with regard to geological ages, considering the critical influence of time on shale compaction (Figure 4). The porosity-depth data in the Cenozoic age consist of the data of the age range from 65 million years ago to now, while the Mesozoic data consist of that of the age range from 250 to 65 million years ago. The data of the older ages are of the Paleozoic data. The empirical model was then constructed to fit the data among porosity, depth, and geological age for the Cenozoic, Mesozoic, and Paleozoic datasets, respectively.
The evaluation of the constructed model was conducted with the coefficient of the determination (r-square) calculated by equation (6):
where ϕ data designate the porosity data as shown in Table 1; ϕ model is the predicted porosity from the compaction model; and is the mean value of the statistical variable ϕ. The r-square is always comprised between 0 and 1. The larger its value is, the better the correlation between the observed and model data.
Our proposed models of the porosity-depth-time relations for northeastern Thailand shale are separately obtained for three geological age groups (the Cenozoic, Mesozoic, and Paleozoic ages), and they are finally reformulated as new compaction models where porosity is expressed as a function of depth and geological age.
6 Results and discussion
6.1 Effect of time on shale compaction
The distinctions among geological ages obviously contribute to a better fitting of the porosity-depth plots, as shown in Figure 4, compared to Athy’s model (see Figure 2). This result quantitatively supports the proposal of a previous study by Puttiwongrak et al. . The initial porosity (ϕ 0) for Athy’s trend is set as 40.11, 16.59, and 4.00% at the surface for the Cenozoic, Mesozoic, and Paleozoic ages, respectively. Relatively high r-square values (0.6572, 0.5100, 0.3612, respectively) support our age classification to obtain a better empirical relationship of geological ages and porosity-depth plots for each geological age group. This relationship is further used for the analysis of the empirical model among porosity, depth, and geological age in the next section.
6.2 Empirical model of geological age classification for Thailand shale compaction
The porosities plotted against burial depth for shales in northeastern Thailand were employed to obtain an empirical relationship of porosity, depth, and geological age with regard to the Cenozoic, Mesozoic, and Paleozoic ages separately. Each empirical model was re-fitted by multi-linear regression (Figure 5) instead of Athy’s model. The compaction models of each geological age are expressed:
Cenozoic Age (T < 65 M years ago):
Mesozoic Age (65 M < T < 250 M years ago):
Paleozoic Age (T > 250 M years ago):
Fitting equations (7)–(9) to the dataset based on the geological age classification give the relationship of the porosities as a function of depth and time with better accuracy (the r-squares are 0.7160, 0.7097, and 0.4006 for the Cenozoic, Mesozoic, and Paleozoic data, respectively (Figure 5a–c) than Athy’s model in all geological ages as shown obviously by the comparison of Figures 4 and 5. Older shales in ages, subject to long geological processes (deposition, diagenesis, erosion-uplift, etc.), will also contribute to lower initial porosities. Thus, our proposed model incorporates the influence of time on the shale compaction effectively.
6.3 Three-dimensional (3D) model of standard compaction for Thailand shales
The influence of geological ages on the shale compaction is explored explicitly in Figure 4, which makes it important to understand different geological ages more for the shale compaction analysis. As already pointed out in Figure 2, a popular model of Athy  fails to account for the porosity-depth variations, a new 3D model (porosity as a function of depth and geological age) of standard shale compaction is proposed. The 3D standard model for Thailand is based on the empirical equation (10):
Equation (10) fits the entire data well at r-square of 0.8372 (Figure 6). An earlier work by Puttiwongrak et al.  suggested that shale compaction analysis requires geological age data as a parameter of compaction data for better fitting, and the standard model of shale compaction in this study does support this suggestion. The initial porosity of the equation (10) gave 55.95%, which is very close to 55.9% from Puttiwongrak et al. , and the other model parameters are compared to the results in Puttiwongrak et al.  as shown in Table 2. The comparison result seems to be reasonable when the initial porosity and compaction coefficients are close to each other, except for the compaction coefficient of burial depth. It clearly means that the burial depth alone is not sufficient to describe the shape of the shale compaction curve.
|Parameter||The model proposed by this study||The model of Puttiwongrak et al. |
|Initial porosity, ϕ o||55.95%||55.9%|
|Compaction coefficient of burial depth||0.0012||0.4000|
|Compaction coefficient of geologic time||0.0066||0.0042|
The observed porosity and burial depth data were plotted with geological time data calculated using equation (5) in a three-dimensional (3D) plot as shown in Figure 7. The 3D curve fitting provides an initial porosity of 55.95% and its r-square is 0.8372, which is very similar to that given by equation (10) and Figure 6.
This study has explored and proposed the 3D empirical model in the relation among porosity, burial depth, and geological age in the shaly formation of northeastern Thailand from the analysis of the large datasets. The main conclusions of this study are:
The numeric data of geological age in a shaly formation may be difficult to obtain, but they are derived from the relationship of velocity, depth, and geological age proposed by Faust .
The conventional exponentially model of shale compaction from Athy  was not fitted to the data in order to obtain a compaction curve without an analysis of geological age classification.
The research findings of this study observed that the compaction trend of porosity reduction, especially in the shallow part, is different in each geological age for shales.
The significant relationship among porosity, burial depth, and geological age of the shaly formation throughout the study area provides a framework for the compaction curve of the effect of geological time.
The mathematical formalisms of the compaction model on shale data can be established by the 3D empirical analysis of the relationship among porosity, burial depth, and geological age.
The standard curve of the compaction data was found for northeastern Thailand shales using a 3D empirical model of the relationship among porosity, burial depth, and geological age, which is the most comprehensive state of the art of published work of Puttiwongrak et al. .
This study revealed the relation among porosity, burial depth, and geological age of northeastern Thailand on shale compaction, and the proposed new compaction model is better fitted to the data than the classical paradigm . On the other hand, the laboratory measurements of time effect on shale compaction have been rarely conducted due to the lack of sophisticated experimental procedures, and the effect of time on shale compaction at a laboratory scale needs future work.
The authors thank the Department of Mineral and Fuel of Thailand for provided the shale compaction data of northeastern Thailand.
Author contributions: AP; Conceptualization, writing-review & editing. SN; data collection, formal analysis, writing-original draft & editing. CC; data collection. PHG; supervision, resources. SV; writing-review & editing. TS; validation, resources. KH; editing & proofreading. All authors have read and agreed to the published version of the manuscript.
Conflict of interest: Authors state no conflict of interest.
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