Pore Pressure Prediction for High-Pressure Tight Sandstone in the Huizhou Sag, Pearl River Mouth Basin, China: A Machine Learning-Based Approach

Abstract

A growing number of large data sets have created challenges for the oil and gas industry in predicting reservoir parameters and assessing well productivity through efficient and cost-effective techniques. The design of drilling plans for a high-pressure tight-sand reservoir requires accurate estimations of pore pressure (P_p) and reservoir parameters. The objective of this study is to predict and compare the P_p of Huizhou Sag, Pearl River Mouth Basin, China, using conventional techniques and machine learning (ML) algorithms. We investigated the characteristics of low-permeability reservoirs by observing well-logging data sets and cores and examining thin sections under a microscope. In the reservoir zone, the average hydrocarbon saturation is 55%, and the average effective porosity is 11%. The tight sandstone reservoirs consist of fine- to extremely fine-grained argillaceous feldspathic sandstone. The mean absolute error for reservoir property prediction is 1.3%, 2.2%, and 4.8%, respectively, for effective porosity, shale volume, and water saturation. Moreover, the ML algorithm was employed to cross-check the validity of the prediction of P_p. Combining conventional and ML techniques with the core data demonstrates a correlation coefficient (R²) of 0.9587, indicating that ML techniques are the most effective in testing well data. This study shows that ML can effectively predict P_p at subsequent depths in adjacent geologically similar locations. Compared to conventional methods, a substantial data set and ML algorithms improve the precision of P_p predictions.

1. Introduction

The challenges encountered during drilling under uncontrolled pressured conditions can result in well abandonment, incurring substantial costs for hydrocarbon production [1,2]. Companies have made significant efforts to improve pore pressure (P_p) prediction in drill planning to mitigate these risks [3]. The accurate prediction of P_p and assessment of fluid flow play a crucial role in developing hydrocarbon areas, particularly in the well-planning phase [4]. According to a survey conducted on 2520 wells completed in the Gulf of Mexico, problems with gas flow, shallow water flow, kicks, and lost circulation accounted for more than 24% of the entire drilling duration. These problems were primarily related to the fracture inclination and imprecise pore pressure estimation [5]. A robust modeling approach is required to precisely predict shear stress for the thixotropic fluids because these fluids have widespread use in the petroleum industry due to their prevalence in porous media and pipelines, and their complex rheological behavior [3]. It is crucial to accurately determine the minimum miscibility pressure of the reservoir fluid, rock, and thermal conditions to assess the gas injection process [6,7].

Well-logging data can offer an effective tool to obtain extensive details on subsurface formation and rock properties. Well logs provide such information as lithology information, formation resistivity, clay content, porosity, rock density, water saturation, rock physics, and flow capacity, which are very important for reservoir characterization [8,9,10,11]. Estimating P_p from borehole data has been accomplished through established theoretic techniques, which originated from the Terzaghi and Biot effective stress law [12,13,14,15], to accurately estimate P_p in formations, ensuring safe drilling operations and reducing the environmental effect. Drilling plans are guided by P_p, defined as the fluid pressures within pore spaces of permeable geological formations [4]. Substantial engineering catastrophes, such as seabed instability, formation destruction, well blowouts, etc., typically arise from errors in predicting P_p [16].

Hottmann and Johnson [17] introduced a typical theoretical approach for predicting P_p with shale character derived from sonic (DT) and gamma-ray (GR) logs. This method detected abnormal P_p by identifying deviations from the standard porosity style in the calculated results. Incorporating the average overburden stress gradient, normal fluid pressure gradient, depth, and two empirical constants, this model facilitated rapid P_p prediction. Eaton [15] proposed a renowned classical theoretical equation using Rt data and, later, in 1975, introduced a new empirical equation for P_p prediction utilizing DT data. In this new empirical Eaton model, the DT in the normal trend became a crucial parameter for calculating P_p [16]. Luo et al., 2021, presented a novel P_p model based on GR and resistivity logs’ data set, effective in formations with diverse lithologies and different tectonic compressions [18]. Like the DT-related equation, their empirical equation derived porosity from empirical expressions.

The prediction of P_p is a crucial factor in determining the effectiveness and cost-effectiveness of drilling operations and effectively managing the well. It is considered primary data for petroleum exploration and development strategies. This will aid in mitigating issues related to drilling operations and reducing the associated costs and risks [19,20]. The prediction of P_p has been performed through several traditional methods, which include analytical and numerical approaches. The empirical methods seldom consider the relationships between P_p and other well-log data, including sonic velocity, porosity, and resistivity logs, and the use of these methods makes them frequently utilized in the industry. The empirical methods are subject to some limitations, especially when the correlation is derived from a restricted data set as well as the geological context [20,21,22]. ML algorithms were employed to predict P_p and used risk identification for complex conditions. Nowadays, machines and deep learning-based methods have been developed to precisely predict P_p in cost-effective ways and reduce processing time [13,20].

As a critical region for petroleum production, the Huizhou Sag contains multiple significant hydrocarbon accumulations, especially natural gas reserves like HZ25-7, HZ21-1, LH11-1, and LF13-2. In this basin, grabens and half-grabens created by the Cenozoic extensional fault networks are typically filled with the source rocks [23]. This Cenozoic extension significantly impacts the integrity of fault seals and the preservation of traps [24]. Thus far, exploration efforts have largely penetrated the petroleum targets in the shallower sediments. It has been concluded from a literature review that minimal work was performed on P_p prediction. This study aims to fill this gap by determining the P_p of the basin so that drilling operations can be facilitated.

This research primarily focuses on the tight sandstone reservoirs of the formations in the Huizhou Sag, Pearl River Mouth Basin (PRMB), China. It aims to investigate the reservoir properties and P_p to understand its potential for further exploration and production (E&P) activities. This study addresses the gap in estimating P_p and reservoir properties through conventional and ML approaches with core data calibration. The supervised ML approach offers an innovative alternative for precisely and effectively predicting P_p and characterizing reservoir properties. The random forest (RF) algorithm was employed for a petrophysical analysis, while gradient boost and ADA boost algorithms were utilized for P_p prediction. To facilitate and calibrate ML model results in core data, analyses such as thin-section observation, mineral identification, and porosity and pressure data analyses were performed to investigate the petroleum characteristics of the Wenchang Formation (WC 421).

This study provides valuable insights into predicting P_p through theoretical and ML models and reservoir characterization in the Huizhou Sag Field, utilizing lab-measured formation P_p and readily available conventional well-logging data from the Wenchang Formation. Current research outcomes contribute to a reliable and better understanding of tight reservoirs and enhance our knowledge about P_p prediction from the well log data set. Additionally, these insights provide crucial guidance for oil and gas E&P activities for safe drilling operations in the PRMB, China.

2. Geological Setting

Rift basins are prevalent geological features, among many of which have suffered multiple phases of tectonic activity, incorporating extension, strike-slip, or inversion deformation in various orientations [23,25]. Underneath conditions of extension, newly formed fault systems verge toward being oriented practically vertically to the orientation of the extension fault [18]. However, the resulting fault network becomes more intricate when two extension stages occur in separate directions. This can include curved, various sets of a strike, and intersecting faults, as demonstrated in sandbox analog models [26].

Normal faults are typically generated in large numbers in rift basins during the syn-rift phase. However, their movement is periodic and relatively too constant. These faults may originate in the initial stages of rifting, become inactive during certain sedimentary phases, and then become reactivated and increase due to extensional stresses during later sedimentary periods. Newly formed faults that initiate during the late deposition phase may generate downward, vertically linking with other initial-manufacture faults or developing separately [18,27].

As a result, newly generated faults connected to reactivated faults are less affected by older faults and may display variations in their direction and propagation. The PRMB is a vast offshore sedimentary basin that spans around 175,000 square kilometers along the South China Continental border. That includes a sedimentary sequence of up to 17 km in depth, composed of Cenozoic and Mesozoic fluvial to marine deposits, including carbonate and clastic strata. The basin exhibits a complicated structural configuration, with different uplifted regions split by dual bowl shape geometry running in a NEE-SWW orientation (as shown in Figure 1). The northern depression zone comprises the Zhu 1 and Zhu 3 depressions. Comparatively, the southern depression was formed by the Zhu 2 and Chaoshan depressions. The Zhu 1 depression, located at the heart of the Huizhou Sag, extends over 11,719 sq. kilometers with a depth of around 10,000 m. Given the significance of this region, it is crucial to identify additional petroleum geometry within the basin, reduce exploration uncertainties, and establish dependable geological models for the fault systems in the area.

The literature survey of the study area suggested that the limited exploration data set of the Wenchang Formation is available to establish relationships between sedimentary facies and key formation evaluation parameters for reservoir characterization and enhance drilling operations. The significant post-depositional erosional events, including tectonic inversion and shifts in tectonic patterns, have impacted the Wenchang Formation (Target Formation) composition, and made it heterogeneous, while it was initially deposited in a deeper lake environment [26,28,29,30]. The reservoir formation presented in the study area exhibits distinct facies-controlled characteristics that make the assessment and prediction of reservoir quality viable [31,32]. It has been witnessed that previous studies performed on the Wenchang Formation have primarily focused on examining the structure, resource potential assessment, and source rock evaluation through seismic, well logs, and core data sets, and no study has been reported to predict pore pressure (P_p) of this formation [26,28]. Core measurement is the most reliable method to access reservoir properties and P_p. Still, it is expensive, and limited interval availability makes it challenging to assess the whole reservoir unit potential. To overcome this, the prediction of reservoir quality, P_p, and the potential presence of hydrocarbon in wells can be achieved by well-logging data without core data. Nevertheless, little work has been reported in the study area regarding the comprehension of P_p and a petrophysical analysis through machine learning (ML) methods.

PRMB in the South China Sea, with its two-kilometer-thick layer of Eocene sediments, has emerged as a hotspot for oil exploration. Recent discoveries, like the HZ25-7 field in the Wenchang Formation, have fueled this interest [28]. PRMB, a Cenozoic rift basin stretching northeastward along the continental margin, is crisscrossed by three fault systems: NE-EW normal faults, NW shear faults, and WNW oblique-slip faults [33]. The Huizhou Sag, a shallow area on the continental shelf, has been studied previously. These studies classified the Cenozoic sediments in the Huizhou Sag into syn-rift and post-rift mega-sequences. The syn-rift sequence comprises the Wenchang and Enping formations, divided by the T70 breakup unconformity. The post-rift sequence includes the Zhuhai, Zhujiang, Hanjiang, Yuehai, and Wanshan formations. Figure 2 illustrates Huizhou Sag’s stratigraphy with details on petroleum potential, lithology, and sedimentary facies.

3. Material and Methodology

The present research used data from HZ-26-A in China for reservoir characterization and pore pressure prediction. The log is used for the calculation of parameters. The target zone for the reservoir and pore pressure prediction for HZ-26-A is 3820.15 m to 3837.98 m, and the overall thickness of the zone is 17.83 m. The lithological identification was performed through thin sections (using a German Leica polarizing microscope), and logging equipment was widely used in the geoscience of well HZ-26-A. The sampling and analysis were carried out in strict accordance with the requirements of geological design and on-site geological supervision to identify thin lithology sections in this well, as demonstrated in Figure 3. Present studies employed different types of techniques involving conventional and machine learning approaches.

3.1. Conventional Method

With the help of a traditional linear technique, the volume of shale is estimated, as shown in Equation (1) [35].

$$I_{GR}=\frac{G{R}_{\log }-G{R}_{\mathrm{cln}}}{G{R}_{shl}-G{R}_{\mathrm{cln}}}$$

(1)

$$VS{H}_{Clavier}=1.7-\sqrt{3.38-{(I_{GR}+0.7)}^2}$$

(2)

$$VS{H}_{Stieber}=\frac{I_{GR}}{3-2I_{GR}}$$

(3)

where $I_{GR}$ is an Index Gamma Ray, GR_log is a log curve value obtained from the gamma-ray log, GR_cln is the average minimum value of GR, and GR_shl is the maximum value of GR_log. After the calculation of the $I_{GR}$, the Clavier and Steiber correction was estimated with the help of Equations (2) and (3) [36,37]. The estimation of shale volume through the linear approach, which is not based on geographical features (gamma-ray index), leads to the over-estimation of shale volume values. To reduce this, non-linear approaches have been developed that are more optimistic and reliable [33]. Clevier’s and Steiber’s non-linear approaches rely on geographical features or formation age to improve the accuracy and reliability of shale volume estimation in shaly sand reservoirs [38]. A literature survey revealed that the best estimation of shale volume is obtained using a gamma-ray log with the Stieber non-linear approach, which is calibrated with XRD in the tight reservoir [8]. Therefore, in the current study, we use Steiber’s approach to compute shale volume.

The next step was the calculation of the effective porosity. Effective porosity is the sum of all interconnected pores within the reservoir. The formula for the calculation of effective porosity is shown in Equation (4) [39].

$$PHIE=PHIA\times (1-VSH)$$

(4)

In the above equation, PHIE represents the effective porosity, PHIA represents the average porosity, and VSH shows the volume of shale. The last step of petrophysics is the calculation of water saturation; for that, Archie’s equation was used, as shown in Equation (5) [40].

$$S{W}_{Archie}={\left[\frac{a{R}_w}{PHI{E}^m{R}_t}\right]}^{\frac{1}{n}}$$

(5)

In $S{W}_{Archie}$, the saturation of water is calculated using Archie’s equation. R_w is the resistivity of the water, and R_t is the deep resistivity.

Vertical stress (σv) or overburden is the quantitative weight of the sedimentary column that creates the overburden [4,41,42]. Based on the information that is accessible, bulk density and depth data, the overburden can be computed [43]. Equation (6) [44], which shows how to apply the Amoco method to calculate the vertical stress gradient (OBG), uses Z as the depth, RHOB as the bulk density log value, and g as the gravitational acceleration.

$$OBG={\displaystyle \underset{0}{\overset{z}{\int }}RHOB(Z)gdZ}$$

(6)

The effective stress rule of Terzaghi and Biot [45] serves as the foundation for predicting pore pressure. The framework of this theory states that total and vertical effective stress are functions of fluid pore pressure. Equations (7)–(12) were adopted from [15,46] and express the connection between these terms:

Approximation of the normal compaction trend line (NCT).

$$P_{pg}=\sigma {\upsilon }_g-(\sigma {\upsilon }_g-P_{hg}){\left(\frac{\mathsf{\Delta }{t}_n}{\mathsf{\Delta }t}\right)}^m$$

(7)

$$\mathsf{\Delta }{t}_n=\mathsf{\Delta }{t}_m-(\mathsf{\Delta }{t}_{ml}-\mathsf{\Delta }{t}_m)e^{-cz}$$

(8)

(1)

Calculation of lithostatic pressure.

$$\sigma {\upsilon }_g=\frac{\left(P_{sea}+{\displaystyle {\int }_0^Z{\rho }_b(Z)gdZ}\right)-P_{sea}}{Z}=\frac{{\displaystyle {\int }_0^Z\rho b(Z)gdZ}}{Z}g$$

(9)

(2)

Calculation of hydrostatic pressure.

$$P_{hg}=\frac{\left(P_{sea}+{\rho }_{w}gZ\right)-P_{sea}}{Z}={\rho }_{w}g$$

(10)

(3)

Estimation of pore pressure using Eaton’s equation.

$$P_{pg}=\sigma {\nu }_g-(\sigma {\nu }_g-P_{hg}){\left(\frac{\mathsf{\Delta }{t}_n}{\mathsf{\Delta }t}\right)}^m$$

(11)

$$P_f=P_{sea}+P_{pg}Z$$

(12)

Δt_m is the transit time in the shale matrix, Δt_ml is the transit time at the mudline (Z = 0), (Z is the true vertical depth below the mudline, (c is the compaction parameter, σe is the effective stress [46], p_f is the pore pressure, p_pg is the pore pressure gradient, σv_gσ is the overburden pressure, p_hg is the hydrostatic pressure gradient, and P_pg is the formation pore pressure gradient [16,47].

3.2. ML Method

In conventional techniques, different log curves are predicted with the help of a regression analysis. The random forest ML technique was used for the prediction of petrophysical calculation. The detailed methodology of the ML techniques is shown in the flow chart in Figure 4.

In ML techniques, the first step is frequency distribution, which assists in a better understanding of the parameters present in our selected reservoir formation. The frequency distribution chart was developed for petrophysics’ input and output parameters. The plot’s x-axis represents the original scale, and the y-axis represents the frequency distribution, illustrating the frequency range in which different data sets are present, as shown in Figure 5. A pair plot is shown in Figure 6 before the outlier is removed. Note that the outliers were removed by applying the absolute square method. The standard equation available literature was used to calculate the error parameters. The error was calculated by using Equations (13)–(15). A command was given to the code to generate the error parameters.

$$RMSE=\sqrt{\frac{1}{n_{samples}}{{\displaystyle \sum }}_{i=0}^{n_{samples}-1}{(y_{measured,i}-y_{predicted,i})}^2}$$

(13)

$$RMSE=\sqrt{\frac{1}{n_{samples}}{{\displaystyle \sum }}_{i=0}^{n_{samples}-1}{(y_{measured,i}-y_{predicted,i})}^2}$$

(14)

$$MSE=\frac{1}{n_{samples}}{{\displaystyle \sum }}_{i=0}^{n_{samples}-1}{(y_{measured,i}-y_{predicted,i})}^2$$

(15)

3.3. Pore Pressure Prediction Using Sonic Log

Pore pressure prediction using a sonic log was performed on the ML algorithm using a sonic log. The input log is shown in Figure 7, along with their calculated parameters like porosity. The blue line shows the sonic log, and the black line represents the GR log. The two shades are marked on the GR log, which shows the shale and sand. Yellow represents the sand facies, and grey demonstrates the shale facies. Figure 8 illustrates the normal compensation line drawn on the sonic log and shown in red. The black scatter plot shows the travel time.

P_p was predicted with the help of gradient boost and ADA boost algorithms. Gradient boosting, being a mean algorithm, might promptly overfit a training data set. Regularization methods, penalizing various algorithm aspects, can enhance performance by controlling overfitting. AdaBoost, also called Adaptive Boosting, is a group ML method that may be used for multiple regression and classification tasks. A supervised learning technique classifies data by combining many weak or base learners (like decision trees) into a robust learner. ADA boosting gives training data set instances weights determined by how well previous classifications performed.

4. Results and Discussions

In recent decades, ML models have been used to predict petrophysical properties more precisely and efficiently because petrophysical properties are industry practice to evaluate the reservoir formation hydrocarbon potential and are further utilized to predict rock physics attributes [47]. The primary reservoir parameters porosity and permeability prediction have been achieved using ML and statistical regression tools in recent years. The use of conventional well-log data with the calibration of core measurements has become particularly effective. ML tools are widely used to accurately estimate reservoir properties, particularly permeability and porosity [48]. To create sophisticated predictive ML models for P_p prediction using petrophysical data [49]. The primary focus of the current study is on the best way to design and use ML models for petrophysical parameter estimation because they are further used to predict P_p.

4.1. Conventional Technique

Tight sandstone reservoir assessment is challenging due to their complex diagenesis and considerable heterogeneity in accessing porosity and permeability values. It is a crucial factor that serves as the foundation for creating geological models for the precise estimation of oil and gas reserves and the formulation of sensible development strategies. These days, several mathematical regression and ML techniques on petrophysical data are the primary methodologies for high-precision porosity and permeability prediction. Thin-section petrography and geometric analyses are very helpful in examining the pore structure properties of tight sandstone reservoirs [31,50]. The details of the lithological thin-section identification results of well HZ26-A (drilling coring) are shown in

Table 1. Lithological thin-section identification results of Well HZ26-6-4Sa (sample-type drilling cores).

Serial Number	Depth (m)	Rock Naming	Lithological Description
1	3820.00	Asphaltene very-fine-grained feldspathic quartz sandstone	Very-fine-grained structure; the debris is mainly composed of quartz + feldspar + rock debris. The quartz is well rounded; the surface of the feldspar is dirty, mainly alkaline feldspar, and partially completely clayized; and the rock debris is sandstone debris. The interstitial materials are mainly asphaltene and some mud. The asphaltene contains more feldspar + quartz microchips.
2	3821.00	Argillaceous fine-grained feldspathic quartz sandstone	Fine-grained structure: The rock fell off during grinding. The debris is mainly composed of quartz + feldspar + rock debris. The quartz is well rounded. The feldspar is mainly alkaline feldspar and plagioclase. It is heavily clayed with a small amount of carbonation. The rock debris is siltstone + a small amount of mudstone crumbs. The gap filler is mainly mud.
3	3822.00	Asphaltene very-fine-grained feldspathic quartz sandstone	Very-fine-grained structure. The debris is mainly composed of quartz + feldspar + rock debris. The quartz is well rounded, the feldspar is seriously clayed, and a small amount of mica is also found. The rock debris is siltstone + mudstone debris. The gap filler is mainly asphaltene + some mud iron.
4	3823.00	Argilly medium sandy fine-grained feldspathic quartz sandstone	The rock has a medium sandy fine-grained structure, and it has fallen off during grinding. The debris is mainly composed of quartz + feldspar + rock debris. The maximum particle size of quartz is about 0.53 mm. The feldspar is mainly alkaline feldspar and plagioclase. It is partially completely clayized. The rock debris is sandstone + a small amount of acid rock debris. The gap filler is mainly mud, and the mud contains more feldspar + quartz microchips.
5	3824.00	Argillaceous coarse sandy medium-grained feldspathic quartz sandstone	Coarse sandy medium-grained texture, same as above.
6	3825.00	Conglomerate (andesite)	The rock is andesite gravel and is heavily muddied. The composition consists of phenocrysts and matrix. The phenocrysts are composed of short columnar neutral plagioclase, a small amount of feldspar, and heavy mudification. The matrix is composed of volcanic glass and cryptocrystalline and fine acicular plagioclase. The acicular plagioclase is distributed in a directional or semi-directional manner. Volcanic glass is distributed between the feldspar grains, and chlorite metasomatism is found for plagioclase.
7	3826.00	Argilly medium sandy fine-grained feldspathic quartz sandstone	The rock has a medium sandy fine-grained structure, and it has fallen off during grinding. The debris is mainly composed of quartz + feldspar + rock debris. The quartz is well rounded; the feldspar is mainly alkaline feldspar and plagioclase, which is completely clayized in parts; and the rock debris is fine sandstone + a small amount of granite debris. The gap filler is mainly mud, and the mud contains more feldspar + quartz microchips.
8	3827.00	Asphalt-containing argillaceous fine-grained feldspathic quartz sandstone	Fine-grained structure, same as above.
9	3828.00	Asphaltic coarse sandy medium-grained feldspathic quartz sandstone	Coarse sandy medium-grained structure. The debris is mainly composed of quartz + feldspar + rock debris. The feldspar is mainly alkali feldspar, followed by plagioclase. The surface is dirty and partially zoisitized. The rock debris is sandstone + a small amount of mudstone. The interstitial material is mainly asphaltene and partially contains mud.
10	3829.00	Asphaltene very-fine-grained feldspathic quartz sandstone	Very-fine-grained structure; the debris is mainly composed of quartz + feldspar; the quartz particle size is small and well rounded; the surface of the feldspar is dirty, mainly alkaline feldspar, and partially completely clayized; and the debris is sandstone debris. The gap filler is mainly asphaltene + mud iron, with an asphaltene content of about 40%. The asphaltene contains more feldspar + quartz microchips.
11	3830.00	Asphaltene siltstone	Silty sand structure, the debris is mainly quartz + alkali feldspar, the interstitial material is mainly asphaltene, and the asphaltene content is about 45%.
12	3831.00	Asphaltene very-fine-grained feldspathic quartz sandstone	Very-fine-grained structure, the debris is mainly composed of quartz + feldspar, the quartz particle size is small and well rounded, and the surface of the feldspar is dirty, mainly alkaline feldspar, and partially fully clayized (also see mica); the rock debris is sandstone cuttings. The interstitial materials are mainly asphaltene and some mud. The asphaltene contains more feldspar + quartz microchips.
13	3832.00	Asphalt-containing argillaceous fine-grained feldspathic quartz sandstone	Fine-grained structure, the debris is mainly composed of quartz + feldspar + rock debris, the quartz is well rounded, the feldspar is mainly alkaline feldspar and plagioclase, the weathering degree is average, there is a small amount of carbonation, and the rock debris is siltstone + a small amount of mudstone debris. The gap filler is mainly mud + a small amount of asphaltene.
14	3833.00	Argilly medium sandy fine-grained feldspathic quartz sandstone	Medium sandy fine-grained texture, same as above.
15	3834.00	Argillaceous fine-grained feldspathic quartz sandstone	Fine-grained structure; the rock has fallen off during grinding. The debris is mainly composed of quartz + feldspar + rock debris. The quartz is well rounded. The feldspar is mainly alkaline feldspar and plagioclase. It is heavily clayed with a small amount of carbonation. The rock debris is siltstone + a small amount of mudstone crumbs. The gap filler is mainly mud.
16	3835.00	Tuffaceous fine-grained feldspathic quartz sandstone	It has a fine-grained structure. The debris is mainly composed of quartz + feldspar + rock debris. The feldspar is mainly alkaline feldspar and plagioclase. It is locally heavily clayed with a small amount of mica. The debris is sandstone + a small amount of tuff. The interstitial material is mainly tuffaceous, and the tuffaceous material contains more feldspar + quartz microchips.
17	3836.00	Mud-bearing asphaltene fine-grained feldspathic quartz sandstone	Fine-grained structure; the debris is mainly composed of quartz + feldspar + rock debris. The feldspar is mainly alkaline feldspar and plagioclase. It has general weathering, heavy clayification locally, and a small amount of mica. The debris is siltstone and fine sandstone. The gap filler is mainly asphaltene + mud.
18	3837.00	Argilly medium sandy fine-grained feldspathic quartz sandstone	Medium sandy fine-grained structure; the rock has fallen off during grinding. The debris is mainly composed of quartz + feldspar + rock debris. The maximum particle size of quartz is about 0.53 mm. The feldspar is mainly alkaline feldspar and plagioclase. It is partially completely clayized. The rock debris is sandstone + a small amount of acid rock debris. The gap filler is mainly mud, and the mud contains more feldspar + quartz microchips.
19	3838.00	Argilly medium sandy fine-grained feldspathic quartz sandstone	Same as above.

to access the tight sandstone reservoirs. The detailed petrophysical analysis result is shown in Figure 9. The correlation track represents the gamma ray with red and SP log with green, and the resistivity track shows the resistivity log, a deep resistivity log curve in a cyan color. The porosity track shows the sonic log curve, and DTR stands for delay time from the receiver. Tracks 5 to 10 show the calculated results. The detailed result of the reservoir formation is shown in Figure 9 and

Table 2. Petrophysics result of the WC 421 formation, where SH stands for saturation of hydrocarbons.

Depth (m)	Thickness (m)	VSH_GR (%)	VSH_C (%)	VSH_S (%)	PHIE (%)	SW (%)	SH (%)
3820–3837	17	39	24	20	11	45	55

.

Many clay minerals, including kaolinite, illite, and chlorite, were found in tight sandstone reservoirs, and their presence significantly impacts the quality of the reservoir. The type of clay minerals was determined using a spectral gamma-ray (SGR) log [51,52]. The precise assessment of mineral composition is crucial for enhanced reservoir characterization. However, it presents significant difficulties in shale and tight units because of the intricate mineralogical structure, minimal porosity, and extremely low permeability. Lab measurements can be accessed more precisely [53]. The conventional practice used for the assessment of porosity is lab-based measurement of rock samples as well as traditional logging methods, which encounter constraints related to cost, and time. To address this limitation, a machine learning-based method has been employed for estimating porosity based on drilling data [47,54]. Figure 10 shows the cross plot between the potassium and thorium, representing the amount of minerals present in the reservoir formation.

4.2. ML Techniques

The detailed result of the ML technique is shown in Figure 11, Figure 12 and Figure 13, while

Table 3. Detailed statistical analysis of selected well-log curves.

	Depth	Sonic	Shear	GR	SP	PHIE	SW	Pp
count	1090	1090	1090	1090	1090	1090	1090	1090
mean	3861.4	49.97	72.53	92.00	1.77	0.04	62.00	6046.28
std	31.48	16.13	28.56	23.71	1.05	0.02	26.34	48.23
min	3807.0	33.60	47.04	55.38	2.79	0.00	0.18	−2315.2
0.25	3834.2	38.40	53.76	77.08	1.67	0.02	45.00	567.25
0.50	3861.4	43.20	60.48	87.26	1.96	0.04	23.00	2708.00
0.75	3888.6	55.71	80.36	103.14	2.25	0.06	125.0	4586.20
max	3915.9	153.29	273.388	149.3	3.20	0.093	0.80	7126.25

demonstrates the detailed statistics of the log curve. Figure 11, Figure 12 and Figure 13 represent the correlation between the input parameters of shale volume, PHIE, and saturation and the calculated parameter.

Table 4. Error results of the Random Forest.

Error	PHIE	VSH_S	SW
Mean Absolute Error (MAE)	0.013	0.022	0.048
Mean Square Error (MSE)	0.015	1.13	0.054
Root Mean Square Error (RMSE)	0.018	0.034	0.065

describes the error result of the calculated parameter. Figure 11, Figure 12 and Figure 13 show the prediction result based on random forest algorithms. The testing and training results vary from the estimated curve data. Figure 11, Figure 12 and Figure 13 show the results of PHIE, SW, and VSH_S, respectively; the testing and training results are green and blue in color, respectively, and the regression line is orange. Most data points lie near the regression line, representing a good testing and training result. The x-axis shows the actual parameters, and the y-axis represents the predicted parameters. The curve is made by each parameter, which represents the actual and predicted parameters corresponding to their depth.

4.3. Pore Pressure Prediction Result

Figure 14 shows the prediction of the P_p by using the conventional method. Five different tracks are present, which represent the different log curves. The P_p is shown in green in the last column, and overburden pressure is shown in red while hydrostatic pressure (HP) is blue. If the HP is greater than the P_p, it is overpressure. Figure 15 shows P_p prediction using ML by the sonic log. The first two tracks represent the input parameters for predicting P_p and the last two tracks represent the P_p prediction result. Different curves are plotted on these tracks; the red in the last track represents the P_p, the blue color demonstrates the lithostatic pressure, and the green color shows the HP. Generally, if the lithostatic pressure is less than the P_p, it is considered an overpressure zone. In contrast, it is regarded as an under-pressure zone if it exceeds the P_p.

Figure 14 and Figure 15 show the P_p prediction of the interested formation in HZ-26-A. The output of Figure 14 is generated with the help of conventional software, while Python algorithms calculate the output of Figure 15. The initial track shows the input parameter for the pressure prediction, and the last two tracks represent the P_p result. The grey color in track 4 shows the sonic log, and the red represents the normal compensate trend line. Track 5 shows the pore pressure prediction in which the blue line represents the hydrostatic pressure, and the green color shows the P_p. If the P_p is greater than the hydrostatic pressure, it represents the overpressure. If hydrostatic pressure is greater than the pore pressure, it shows under-pressure. The machine learning results are better than those of conventional techniques. Figure 16 demonstrates the heat map in which the correlation between different parameters and P_p is defined, showing a correlation of 84% between the sonic log and P_p.

Figure 17 and Figure 18 represent the P_p prediction using gradient boost and ADA boost regression algorithms. Both algorithms give the best prediction of P_p and the best match of correlation between the training and testing data. The green color shows the predicted pressure, while the red color shows the actual pressure. Figure 19 shows the core and predicted pressure using ML and conventional techniques. The R² calculated by the traditional method is 0.85, while the R² from the ML method is 0.95 in the testing well. The result of R² shows that the P_p prediction of machine learning is excellent as compared to a conventional technique. Figure 20 shows the testing of the P_p in blind well HZ-26-B. The first three tracks show the training well parameter and tracks 4 to 6 show the testing well parameter. The prediction is made on the blind well with the R² of 0.98. Track 7 shows the result of both the training and the blind well. The grey color represents the prediction made on the blind well, and the red color represents the actual training curve. Figure 21 demonstrates the cross plot of predicted versus actual pore pressure with the square regression of 0.98 on the blind well.

It has been inferred based on the literature survey that studies on the prediction of P_p taking into account various ML models are minimal and obtain popularity due to better performance than conventional theoretical models (e.g., Eaton’s method) in geosciences to enhance drilling operations to overcome well failure [22,55]. A heterogeneous lithology presented ML models for P_p prediction that take advantage of well-log curve inputs (sonic velocity, porosity, and shale volume) and depend on geological formation composition [56,57,58]. The following ML techniques were assessed: a support vector machine (SVM), gradient boosting, MLP neural network, and RF were employed to predict P_p as input of petrophysical logs computed from well-log data sets. To precisely estimate P_p, a set of petrophysical data sets is required through a multivariate prediction model. However, in heterogeneous lithologies, the parametric multivariate models with assumptions on lithology require a calibration procedure [59]. Yu et al.’s [57] findings suggested that P_p measurements and predictions obtain better results with the RF method surpassing other ML techniques. Zhao et al. [60] applied different ML models. They concluded that ML models perform better than theoretical models in predicting pore pressure and obtained much better results through decision trees in high-temperature and high-pressure geological formations.

To predict P_p hybrid ML approaches, improve estimation accuracy by designating the optimal specific parameters of procedures. Moreover, P_p prediction by a combination approach is more efficient and offers a limited measured direct P_p data set availability [57,61]. Das and Maiti [62] performed a study to predict P_p through ML models in New Zealand. It is inferred that predicting the P_p trend in complicated geological provinces can be difficult because various intricate geo-processes can influence P_p. In complex geological provinces, conventional classical empirical techniques combined with advanced ML models can tackle these challenges. The stages of model establishment and data pre-processing make up the empirical method for PP prediction. The theoretical framework was developed from well-log data. The decision tree regression (DTR) algorithm provided the best results in the limited data set. Its performance is evaluated with the model to estimate the P_p and locate the overpressure zone.

By employing deep learning, Wei et al. [56] estimated pore water pressure and suggested that recurrent neural network results are much better than traditional methods. Precise pore pressure prediction was achieved by combining a mix of a random forest and least-square support vector machines with an optimization technique. Drilling data are less valuable than conventional well logs for machine learning-based formation pressure estimation. In our study, we employed different ML algorithms and performed validation with core measure P_p and found the best results to match predicted vs. actual P_p with the help of the ADA boost algorithm on the blind well with a correlation of 0.98.

5. Conclusions

This study investigates the efficacy of machine learning tools in predicting subsurface pore pressure, particularly when pore pressure data from core samples and well-log variables are limited. The capability of these ML models to accurately predict P_p was evaluated by comparing their performance with that of traditional theoretical methods.

(1)

The current study aimed to assess whether machine learning tools could mitigate uncertainty in pore pressure prediction compared to conventional theoretical methods and identify the most effective predictive models by comparing the predictions made by machine learning and those made by traditional methods. The results were validated by comparing the predicted pore pressure values derived from conventional and ML techniques with the actual values derived from core sample measurement.

(2)

It has been inferred that the Stieber correction provided the best results for the shale volume based on the analysis results with a correction efficiency of approximately 20%. Therefore, this technique can significantly enhance the accuracy and reliability of our predictions of pore pressure.

(3)

In a nutshell, it has been concluded that machine learning techniques provide superior prediction accuracy by comparing machine learning methods with conventional theoretical approaches. The ADA boost algorithm produces the best results on the blind well to predict pore pressure with correlation values of 0.98. It is evident from this study’s outcomes that ML models have the potential to improve the accuracy of subsurface P_p predictions with good performance.

6. Future Studies and Implications

It is suggested that to improve the predictive capabilities of machine learning models for estimating pore pressure, additional geophysical and geological data parameters should be incorporated. This is because the theoretical models used for pore pressure estimation depend on the geological features of the formation. Factors such as lithology, rock properties, and other geological features could potentially increase the accuracy and robustness of the predictive models. Furthermore, combining multiple ML models to make predictions could also prove to be beneficial. This method can be applied globally in areas with similar geological settings.