Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

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Journal of Rock Mechanics and

Geotechnical Engineering
journal homepage: www.jrmge.cn

Full Length Article

Machine learning and data-driven prediction of pore pressure from

geophysical logs: A case study for the Mangahewa gas field, New Zealand
Ahmed E. Radwan a, b, *, David A. Wood c, Ahmed A. Radwan d
a
Faculty of Geography and Geology, Institute of Geological Sciences, Jagiellonian University, Kraków, 30-387, Poland
b
Exploration Department, Gulf of Suez Petroleum Company, Cairo, Egypt
c
DWA Energy Limited, Lincoln, UK
d
Department of Geology, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, 71524, Egypt

a r t i c l e i n f o a b s t r a c t

Article history: Pore pressure is an essential parameter for establishing reservoir conditions, geological interpretation
Received 16 July 2021 and drilling programs. Pore pressure prediction depends on information from various geophysical logs,
Received in revised form seismic, and direct down-hole pressure measurements. However, a level of uncertainty accompanies the
22 December 2021
prediction of pore pressure because insufficient information is usually recorded in many wells. Applying
Accepted 20 January 2022
Available online 25 March 2022
machine learning (ML) algorithms can decrease the level of uncertainty of pore pressure prediction
uncertainty in cases where available information is limited. In this research, several ML techniques are
applied to predict pore pressure through the over-pressured Eocene reservoir section penetrated by four
Keywords:
Machine learning (ML)
wells in the Mangahewa gas field, New Zealand. Their predictions substantially outperform, in terms of
Pore pressure prediction performance, those generated using a multiple linear regression (MLR) model. The
Overburden geophysical logs used as input variables are sonic, temperature and density logs, and some direct pore
Well-log derived predictions pressure measurements were available at the reservoir level to calibrate the predictions. A total of 25,935
Overpressure data records involving six well-log input variables were evaluated across the four wells. All ML methods
achieved credible levels of pore pressure prediction performance. The most accurate models for pre-
dicting pore pressure in individual wells on a supervised basis are decision tree (DT), adaboost (ADA),
random forest (RF) and transparent open box (TOB). The DT achieved root mean square error (RMSE)
ranging from 0.25 psi to 14.71 psi for the four wells. The trained models were less accurate when
deployed on a semi-supervised basis to predict pore pressure in the other wellbores. For two wells
(Mangahewa-03 and Mangahewa-06), semi-supervised prediction achieved acceptable prediction per-
formance of RMSE of 130e140 psi; while for the other wells, semi-supervised prediction performance
was reduced to RMSE > 300 psi. The results suggest that these models can be used to predict pore
pressure in nearby locations, i.e. similar geology at corresponding depths within a field, but they become
less reliable as the step-out distance increases and geological conditions change significantly. In com-
parison to other approaches to predict pore pressures, this study has identified that application of several
ML algorithms involving a large number of data records can lead to more accurate prediction results.
Ó 2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by
Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
licenses/by-nc-nd/4.0/).

1. Introduction essential for successful exploitation of conventional and uncon-

ventional oil and gas reservoirs. Historically, despite decades of
Pore pressure is a useful parameter in geomechanical and study, it remains difficult to predict pore pressure of strata buried in
resource analysis, and determining its variations with depth is sedimentary basins (e.g. Ramdhan and Goulty, 2010, 2011; Zhang,
2011; Radwan et al., 2019, 2021a; Abdelghany et al., 2021;
Flemings, 2021; Radwan, 2021). Pore pressure is usually estimated
from well-logs, assisted with available seismic data. However, this
* Corresponding author. Faculty of Geography and Geology, Institute of Geolog- method only provides estimates of pore pressure in the immediate
ical Sciences, Jagiellonian University, Kraków, 30-387, Poland
vicinity around the borehole. In addition, it requires substantial
E-mail address: radwanae@yahoo.com (A.E. Radwan).
Peer review under responsibility of Institute of Rock and Soil Mechanics, Chi- time, effort and cost to generate pore pressure estimates while
nese Academy of Sciences. drilling, and sometimes the data required cannot be reliably

https://doi.org/10.1016/j.jrmge.2022.01.012
1674-7755 Ó 2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-
NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1800 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

Fig. 1. Mangahewa field location map showing its position in relation to the main structural features of the northeastern Taranaki basin (western New Zealand), as well as the
positions and relative locations of the four wells drilled (New Zealand Petroleum and Minerals, 2014).

recorded due to bad hole conditions. Therefore, it is beneficial to maximum of five ML techniques considering a limited number of
develop a workflow, aided by machine learning (ML), which can data records and input variables. In this research, we propose a new
effectively predict pore pressure versus depth profiles for wells pore pressure prediction method using ML techniques based on a
without taking frequent direct formation pressure measurements. very large dataset. Nine ML techniques are applied and tested, and
Moreover, it is useful to be able to reliably extrapolate pore pressure their results are compared to identify the most accurate pre-
estimates away from the wellbore into the undrilled portions of dictions. Additionally, the results and prediction performance
formations. Not only do such workflows aid the optimization and achieved are compared with previously published pore pressure
reliability of pore pressure estimates, but they also enable those predictions.
estimates to provide useful inputs to various geomechanical cal- The major focus of this study is the Eocene Mangahewa gas
culations (e.g. stresses and related metrics), and improve reservoir- reservoir of Mangahewa gas field, New Zealand (Fig. 1). The field is
wide modeling. located north of the Taranaki basin, and is made up of a Cretaceous
ML techniques are widely applied to solve numerous problems to recent sedimentary accumulation up to 9000 m thick (King and
in geoscience and subsurface engineering. Indeed, advancement Thrasher, 1996; Radwan et al., 2021b, 2022). The Mangahewa
and sophistication of technology and ML algorithms are driving a reservoir is a non-marine to marginal marine sequence including
revolution throughout the energy sector. In the oil and gas sector, quartz-rich sandstones, carbonaceous siltstones and silty clay-
this is impacting commercial production and resource recovery by stones with some embedded thin coal seams (King and Thrasher,
solving industry problems more precisely with decreasing time and 1996).
effort. ML techniques have been successfully applied to many This research attempts to: (1) bridge the gap in estimating the
geosciences and subsurface engineering disciplines including spatial and temporal variability of pore pressure by adopting a ML
geophysical data, petrophysical properties, lithology, reservoir approach; (2) demonstrate the potential of high prediction per-
zonation, and organic richness (i.e. Poulton, 2002; Silversides et al., formance of shear-velocity in hydrocarbon-bearing and water-
2015; Shi et al., 2016; Xie et al., 2018; Saikia et al., 2020). Conse- filled intervals in the studied reservoir interval; (3) show that a
quently, applications and diversity of ML continue to grow affecting supervised and potentially semi-supervised learning approach can
most branches of geoscience and petroleum engineering (e.g. provide alternative innovative tools for pore pressure prediction;
Anifowose et al., 2011; Ahmadi et al., 2013, 2014; Schmidhuber, (4) develop a framework to boost the reliability of characterization
2015). Some recent studies have used ML to predict pore pressure and prediction of the geomechanical properties in the studied area
using different algorithms and input variables (Ahmed et al., 2019; using novel, fast and effective ML approaches; and (5) evaluate the
Paglia et al., 2019; Yu et al., 2020; Booncharoen et al., 2021; Farsi application of ML, and how such tools can be utilized to create data-
et al., 2021; Wei et al., 2021). The previous studies have used a driven solutions more generically to geomechanical problems.
 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809 1801

2. Material and methods where Z is the depth, RHOB is the bulk density log value, and g is the
gravitational acceleration.
2.1. Well-log dataset in the Mangahewa gas field The pore pressure values in the Mckee and Mangahewa sand-
stone reservoirs were directly recorded in the formations with a
The drilling and well-log data for the four wells drilled in the repeat formation tester (RFT) wireline tool in all four wells.
Mangahewa gas field (Mangahewa-02, Mangahewa-03, Man-
gahewa-04 and Mangahewa-06) form the core information used for
the ML evaluations. The available data include a high-resolution 2.3. Pore pressure prediction using several ML methods
geophysical well-log suite consisting of gamma ray (GR), formation
bulk density (RHOB), photoelectric absorption factor (PEF), The dataset is evaluated using nine established and widely
compressional- (DC) and shear-wave (DS) sonic travel times and applied ML models: Adaboost (ADA, a boosted decision tree (DT)
temperature (T) logs, which constitute the input variables consid- model), DT, extreme learning machine (ELM), multi-layer percep-
ered. A total of 25,935 data records were compiled for the four wells tron (MLP), multi-linear regression (MLR, with gradient descent
(6074 for Mangahewa-02, 5964 for Mangahewa-03, 6726 for optimizer), optimizer formula (OF, polynomial equation fit with
Mangahewa-04, and 7171 for Mangahewa-06). Statistical details of optimizer), random forest (RF), support vector regression (SVR),
the data distributions for the six well-logs (input variables) and pore and transparent open box (TOB).
pressure (dependent variable) are provided for the 25,935 data re- The methodologies associated with these ML techniques are
cords in Table 1. Correlations among the variables taking into account documented elsewhere with most previously employed for multi-
all data records for the four wells are also listed in Table 2. variate pore pressure prediction (e.g. Yu et al., 2020) and geo-
According to the results shown in Table 2, it is apparent that depth mechanical analysis: ADA (Salehin et al., 2020); DT (Bruno, 2001);
and temperature show good positive correlations with the pore ELM (Song et al., 2015); MLP (Najibi et al., 2017); RF (Zhou et al.,
pressure, as should be expected. Of the other recorded well-logs, GR 2019); SVR (Bagheripour et al., 2015); and TOB (Wood, 2020).
and PEF show moderate negative correlations with the pore pressure, Two (OF and TOB) of the nine ML models applied provide more
whereas RHOB, DTC and DTS show poor negative correlations with transparency for each prediction they make as regressions are not
the pore pressure. Fig. 2 displays the pore pressure measurements involved. The other ML models generate their predictions in a much
versus depth trends for the Eocene Mckee and Mangahewa forma- less transparent way by formulating and exploiting hidden
tions in the four wells studied. It is apparent from Fig. 2 that wells regression relationships. The transparent methods are of more
Mangahewa-02 and Mangahewa-04 follow similar pore pressure practical value in data mining applications aiming to consider the
versus depth trends, with wells Mangahewa-03 and Mangahewa-06 relationships between individual data records.
(a directional well sidetracked from the Mangahewa-03 location, A consistent workflow is used to apply each of these ML
Fig. 1) following their own distinct pore pressure versus depth trends. methods in this study. It involves selecting a training subset of data
As the pore pressure versus depth trend can vary from location and optimizing the hyper/control parameters for each method. The
to location across the field, the depth has not been included in input trained models are then applied to a testing subset of data records
well-log variable set for predicting pore pressure. This means that that are not involved in the model training process. Trial and error
generated pore pressure predictions are not influenced by the evaluations identified that for the large number of data records
depth of each data record. associated with each well, a split of 80% training subset and 20%
testing subset provided reliable and reproducible results for the ML
methods considered. Each model is evaluated multiple times and
2.2. Overburden and pore pressures modeling
the prediction performance results presented are based on the
average of those achieved by multiple runs. Table 3 lists the hyper/
The weight of the overlying sedimentary column forming the
control parameters applied to each of the ML methods with the
overburden is expressed quantitatively as vertical stress (sv) or
selections based on trial and error testing of each model. We have
overburden (Plumb et al., 1991; Zhang 2011; Radwan et al., 2019,
selected the parameters that generate minimum prediction errors.
2020, 2021a,b; Kassem et al., 2021; Radwan, 2021; Radwan and
Sen, 2021a, b, c, d). The composite density profile can be used to
calculate the overburden using available bulk density and depth
2.4. Statistical measures of prediction performance used to assess
information (Radwan et al., 2020). The vertical stress gradient
pore pressure predictions
(OBG) can be calculated applying the Amoco method as
The statistical measures of prediction performance used to
ZZ
assess and compare the pore pressure prediction performance of
OBG ¼ RHOBðZÞgdZ (1)
the nine ML methods applied are those defined as follows:
0

Table 1
Statistical details of the variable distributions considering all 25,935 data records from the four Mangahewa field wells evaluated. Values of the pore pressure measurements
are also listed.

Variable Symbol Unit Minimum Maximum Mean Standard deviation Percentile P25 Percentile P50 Percentile P75

Depth m 3291.5 5099.5 4104.4 424.2 3791.3 4095.8 4365.8

Bulk density RHOB g/cm3 1.205 2.852 2.522 0.113 2.48 2.52 2.587
Compressional-wave travel time DTC ms/ft 47.3 230.2 68.3 7.5 64.3 67 71.6
Shear-wave travel time DTS ms/ft 73.5 972.5 114.6 20.8 104.7 110.6 121.5
Gamma ray GR API 7.89 127.94 52.03 19.18 37.14 49.11 64.43
Photoelectric absorption factor PEF Barns/electron 0.143 12.062 3.713 1.169 2.783 3.559 4.372
o
Temperature T C 100.1 139.6 119.4 9.6 113.3 119.5 126.8
Pore pressure PP psi 4686.2 7682.6 6714.7 575 6285.6 6754.7 7171.4
1802 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

Table 2 Note that RMSE is used as the objective function to minimize

Correlations among well-log variables considering all 25,935 data records from the errors in each ML algorithm.
four Mangahewa field wells evaluated.

Variable Correlation coefficient (R) among well-log variables (3) Mean absolute error (MAE):
Depth RHOB DTC DTS GR PEF T PP
1X n
MAE ¼ jX  Yi j (4)
Depth 1 0.0533 0.0212 0.0196 0.1 0.2860 0.8809 0.6163 n i¼1 i
RHOB 1 0.3329 0.0152 0.2472 0.0468 0.0023 0.1337
DTC 1 0.6162 0.0205 0.1384 0.0203 0.0838
DTS 1 0.0294 0.1193 0.0437 0.1149
GR 1 0.3746 0.0846 0.3024 (4) Percent deviation between measured and predicted values
PEF 1 0.2834 0.2636 for the ith dataset record (PDi):
T 1 0.5803
PP 1 Xi  Yi
PDi ¼  100% (5)
Xi

(1) Mean square error (MSE): (5) Average percent deviation (APD):
Pn
i¼1 PDi
APD ¼ (6)
1X n
n
MSE ¼ ðX  Yi Þ2 (2)
n i¼1 i
APD combines both positive and negative percent deviations
where n is the number of data points; and Xi and Yi specify the and is expressed in percentage terms.
measured and the ML predicted values for the ith data record in the
subset evaluated, respectively. (6) Absolute average percent deviation (AAPD):
Pn
(2) Root mean square error (RMSE): i¼1 jPDi j
AAPD ¼ (7)
n
pffiffiffiffiffiffiffiffiffiffi AAPD combines the absolute values of the percent deviations
RMSE ¼ MSE (3) and is also expressed in percentage terms.

(7) Standard deviation (SD):

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pn 2
i¼1 ðDi  Dimean Þ
SD ¼ (8)
n1

where Di ¼ Xi e Yi stands for the ith data record of a dataset, and

Dimean is the mean of the Di values of all the data records in a
dataset:

Table 3
Control specifications applied to nine ML models used for pore pressure predictions
from the Mangahewa gas field well-log data.

Algorithm Software Model Control Parameter Values Applied

ADA Python Scikit- Number of estimators ¼ 300; learning rate ¼ 2;

learn base estimator is DT with depth ¼ 6; splitter ¼ best
DT Python Scikit- Maximum depth ¼ 100; splitter ¼ best
learn
ELM Python DWA Hidden_units ¼ 150; activation
function ¼ leaky_relu
MLP Python Scikit- 3 hidden layers with 100, 50 and 10 neurons; ReLU
learn (rectified linear unit) activation function; Adam
solver; alpha ¼ 0.00001; maximum
iterations ¼ 1500
MLR Python DWA Gradient descent optimizer, iterations ¼ 10000;
alpha ¼ 0.5
OF Excel/ DWA Generalized Reduced Gradient (GRG) optimizer to
VBA select polynomial equation coefficients
RF Python Scikit- Number of estimators ¼ 1000; maximum
learn depth ¼ 1000
SVR Python Scikit- Kernel ¼ rbf; C ¼ 1000; gamma ¼ 0.05;
learn epsilon ¼ 0.1
TOB Excel/ DWA Maximum number of data record matches
VBA (Q) ¼ 10; weights vary between 0 and 1; firefly
Fig. 2. Pore pressure measurements versus depth trends for the Eocene Mckee and
optimizer
Mangahewa in the four studied wells from the Mangahewa gas field.
 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809 1803

pore pressure and overburden pressure dataset of the Manghewa

1X n
gas field are documented in Table 4.
Dimean ¼ ðX  Yi Þ (9)
n i¼1 i

3.2. Pore pressure prediction using ML models

(8) Correlation coefficient (R) between variables Xi and Yi:
Pn Fig. 4 compares the predicted and measured pore pressure values
i¼1 ðXi  Xmean Þ ðYi  Ymean Þ
R ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pn (10) for the Mangahewa-06 well for the best performing DT model and
2 Pn 2
i¼1 ðXi  Xmean Þ i¼1 ðYi  Ymean Þ the least accurate MLR model. The details of the pore pressure pre-
diction accuracies achieved by the nine ML models applied individ-
where R is expressed on a scale of 1 to 1. ually to the well-log datasets of each of the four wells in the
Mangahewa gas field as well as the average are shown in the Ap-
(9) Coefficient of determination, R2 (between 0 and 1). pendix (Tables A1eA5). The individual well prediction accuracies are
illustrated graphically in terms of RMSE and APD in Figs. 5e8. Our
Each of these prediction measures carries distinct information results document that all ML models provide credible pore pressure
about prediction performance. Although the indications of pre- predictions across the entire depth intervals considered for each
diction performance provided by some of these measures tend to well. However, the MLR model outperforms all other ML methods for
be highly correlated, it is useful to consider and compare mul- this dataset in terms of pore pressure predictions in all four wells
tiple measures of prediction performance when assessing the considered. The best performing models in terms of all of the sta-
prediction performance of ML algorithms. The details are pro- tistical measures of prediction performance are DT, ADA, RF and TOB,
vided in the Appendix (Tables A1eA4) individually for each well in that order. SVR, ELM, OF, MLP and MLR generate substantially less
in terms of six prediction performance measures with respect to accurate predictions than the top four algorithms.
the ML algorithms evaluated. Furthermore, the mean of all The Mangahewa-06 well provides the best prediction perfor-
studied wells are also provided in the Appendix (Table A5) in mance of the four wells considered. The Mangahewa-02 and
terms of six prediction performance measures with respect to the Mangahewa-03 wells provide slightly better pore pressure pre-
ML algorithms evaluated. On the other hand, the results are diction performance than the Mangahewa-04 well. The slightly
illustrated with reference specifically to two of these prediction inferior pore pressure prediction performance for the Mangahewa-
performance measures (RMSE and APD), the results of which are 04 well may be due to its more complex pore pressure versus depth
not highly correlated. trend (Fig. 2) incorporating an upper normally pressured section
above the predominant overpressure zones. The TOB model that
uses data matching generates the most accurate pore pressure
3. Results predictions for the Mangahewa-04 well, with RF outperforming DT
and ADA in that well.
In this study, more than 17 km of cumulative well log data has An explanation for the differences in the pore pressure prediction
been evaluated from the four available well bores drilled in the performance between the four wells can also be explained with
Mangahewa gas field (Fig. 1). The penetrated sediments encompass reference to Fig. 2. In the Mangahewa-02 well, the depth interval
Eocene to Paleocene age formations. adheres more closely to a linear trend. On the other hand, for the
Mangahewa-04 well, there is a substantial pore pressure versus
3.1. Overburden and pore pressure modeling depth offset near the top of the section evaluated. The algorithms
therefore have more difficulty in predicting pore pressure in the
The Eocene Mckee and Mangahewa in the four Mangahewa Mangahewa-04 well. Also, the pore pressure offset section in the
gas field wells are dominant with sandstones, with intercalated Mangahewa-06 well covers a greater depth range than in
siltstone, clay, and minor coal streaks (King and Thrasher, 1996). Mangahewa-03 well, providing the algorithms with more data re-
The offset wells are used to calculate field-wide hydrostatic cords to predict that distinctive zone in the Mangahewa-06 well.
pressure of 8.33 ppg equivalent mud weight (EMW). Average
overburden or vertical stress ranges between 18.6 ppg and 21.5 Table 4
ppg (EMW) in the four studied wells (Table 4). The maximum The pore pressure and overburden pressure model values in the four studied wells of
vertical stress of 21.5 ppg (EMW) is reached in the Mangahewa- the Mangahewa gas field.
02 well, while the lowest vertical stresses are associated with the Well Formation Average pressure (ppg) Pressure regime
Mangahewa-04 well. The wireline signatures of the sonic and
Overburden Pore
density logs display clear reversals from the middle Otaraoa pressure pressure
formation downwards, which is an indication of the prevailing
Mangahewa- Mckee 18.6 10.41 Overpressurized
overpressure zone (Fig. 3). In the Mangahewa formation, 04
repeated formation test (RFT) measurements collected at the Mangahewa 18.8 10.41
Mangahewa-04 and Mangahewa-06 wells recorded an average Mangahewa- Mckee 21.46 10.44 Overpressurized
pore pressure of 10.41 ppg (EMW). This pressure is consistent 02
Mangahewa 21.4 10.44
with and close to the Mangahewa reservoir virgin pressure in-
Mangahewa- Mckee 21.5 10.3 Overpressurized
terval recorded in the Mangahewa field. The aforementioned 03
pore pressure measurements show overpressure conditions Mangahewa 21.49 10.3
throughout the Mangahewa reservoir. The recorded pore pres- Mangahewa- Mckee 21.15 10.41 Overpressurized
sures are 10.44 ppg (EMW) in the Mangahewa-02 well, while it 06
Mangahewa 21.2 10.41
shows 10.3 ppg (EMW) in the Mangahewa-03 well. The current
1804 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

Fig. 3. Log curves versus depth for Mangahewa-04 highlighting the presence of overpressure zones in the Otaraoa formation and deeper formations.

4. Discussion The ability to use pore pressure prediction models trained using
data from one well to predict, on a semi-supervised basis, pore
4.1. Application of ML models in the case study pressure from the well-log data of another Mangahewa well has
also been evaluated with mixed results. Making such semi-
Our study confirms that various ML methods can successfully supervised predictions on well bores in different parts of the field
predict pore pressure on a supervised base from a suite of well-log is much more challenging because the pore pressure trends with
data from individual wells, without consideration of well depth as depth differ for each well (Fig. 4). The best results for such semi-
one of the input variables. Displaying the average of the pore supervised pore pressure predictions were achieved using models
pressure prediction errors achieved for each well (Fig. 9) reveals trained using data from Mangahewa-03 and using those trained
that the DT model (RMSE ¼ 5.2 psi) generates a slightly lower error models to predict well Mangahewa-06 and vice versa. The RF
than the RF model (RMSE ¼ 5.5 psi). Those two models are closely model achieved prediction performance of RMSE ¼ 131 psi for the
followed in terms of statistical measures of prediction performance Mangahewa-06 well in a semi-supervised manner using the model
(averaged over the four wells) by the TOB model (RMSE ¼ 7.7 psi) trained with Mangahewa-03 data. This slightly outperformed the
and ADA model (RMSE ¼ 8.3 psi). The superior prediction perfor- ADA and DT models that both achieved semi-supervised statistical
mance of ML models (i.e. DT, RF, TOB and ADA models) is apparent measures of prediction performance of RMSE of 138 psi for that
from Figs. 5e8 (and Tables A1 eA5 in the Appendix), but is made purpose. Similar prediction performance accuracies were achieved
clearer in Fig. 10 by displaying the prediction accuracies for all wells by those models predicting pore pressure in Mangahewa-03 using
into one graphic. For geomechanical modeling purposes, the ability models trained with Mangahewa-06 data. These two wells are
to apply such prediction models to extrapolate pore pressure across located close to each other (Fig. 2), which undoubtedly has an in-
entire wellbore sections from relatively few formation test pressure fluence on the pore pressure prediction performance of these semi-
results is clearly of benefit. supervised models. However, attempts to predict pore pressure in
 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809 1805

Fig. 4. Comparison of pore pressure prediction performance by (a) the best performing DT model and (b) the least accurate MLR model applied to the Mangahewa-06 well data.

Mangahewa-02 and Mangahewa-04 wells using models trained in 2020; Booncharoen et al., 2021; Farsi et al., 2021; Wei et al.,
other wells were less successful with prediction accuracies of RMSE 2021). Yu et al. (2020) proposed a ML technique for pore pres-
> 300 psi for all ML models. sure prediction in a mixed lithology domain, exploiting specific
According to these results, we infer that using ML to predict pore well-log curve inputs (sonic velocity, porosity, and shale volume).
pressure from well-logs on a semi-supervised basis in other well- They combined the petrophysical properties with theoretical
bore in a field may require models trained on data from multiple effective stress in their training dataset in the normally pressured
wells to provide reliable prediction performance. This approach is sequences. On the other hand, they used the Bowers’ unloading
more likely to achieve high pore pressure prediction performance relationship in the overpressure zones. They evaluated four ML
in adjacent wells in similar structural and stratigraphic locations algorithms: gradient boosting, MLP neural network, RF, and sup-
within a field than for wells located at substantial distances in port vector machine (SVM). The results of their evaluations
distinctive geological settings or pressure compartments from the revealed good agreement between pore pressure measurements
trained datasets. and predictions, with the RF algorithm outperforming other ML
algorithms. Moreover, Yu et al. (2020) pointed out that their RF
4.2. Comparison with other studies model was able to detect the onset of overpressure more effec-
tively than the other three models they evaluated.
There are relatively few studies focusing on the prediction of Farsi et al. (2021) used nine petrophysical input variables
pore pressure considering multiple ML techniques. Here, we extracted from 1972 data records from a carbonate reservoir to
discuss some other techniques developed recently (i.e. Yu et al., predict pore pressure. They applied feature selection and

Fig. 5. Mangahewa-02 pore pressure prediction error analysis in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.
1806 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

Fig. 6. Mangahewa-03 pore pressure prediction error analysis in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.

developed and compared three-hybrid ML optimization models. and R2 to evaluate the prediction performance of the model. Their
Their analysis indicated that a multi-layer ELM (MELM) model findings indicated that the GRU and LSTM models performed much
optimized with a particle swarm (PSO) algorithm provided the better for pore pressure prediction than their MLP model.
most accurate pore pressure predictions. They applied their models Booncharoen et al. (2021) considered drilling parameters and
to three different wells in an Iranian oil field, and their results reservoir characteristics as input variables for predicting pore
illustrated that the trained model could be used reliably for pre- pressure in a Thailand oil and gas field using a model involving
dicting pore pressure across the entire studied field. three regression-based algorithms: quantile, ridge and extreme
Wei et al. (2021) compared the performance of deep learning gradient boosting (XGBoost). The RMSE achieved by their model for
recurrent neural networks (RNN), specifically long short-term data from 12 wells drilled in the Pattani basin ranged from 1.2 ppg
memory (LSTM) and gated recurrent units (GRU) with the MLP and 1.5 ppg. Ahmed et al. (2019) developed five ML models to
for pore pressure prediction in soil. In their model, they used RMSE predict the pore pressure from actual field measurements such as

Fig. 7. Mangahewa-04 pore pressure prediction error analysis in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.
 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809 1807

Fig. 8. Mangahewa-06 pore pressure prediction error analysis in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.

Fig. 9. Mean pore pressure prediction error analysis in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.

drilling parameters and well-logs. Their five models were artificial overcome pore pressure prediction constraints where there is a lack
neural network (ANN), radial basis function (RBF), fuzzy logic (FL), of detailed regional data available for pore pressure prediction.
SVM, and a functional network (FN). Comparative evaluations Such advantages make these ML models innovative tools for sub-
revealed that their SVM model delivered the best pore pressure surface pore pressure analysis and prediction for drilling and field
prediction performance achieving an average percentage error of development applications. The results presented in this study
0.14%. indicate that applying several ML algorithms to large datasets tends
In comparison with previous studies, the models evaluated here to generate to better predictions.
assess a much larger number of data records (5064e7171).
Furthermore, this study evaluates a greater number of ML tech- 5. Conclusions
niques employing quite distinct algorithms on a supervised
learning basis, which has not been conducted previously. The best The result of this research demonstrates the usefulness of
performing ML models developed have advantageous attributes applying ML tools to predict subsurface pore pressure from a
providing rapid and reliable predictions of pore pressure in normal limited range of well-log input variables. Furthermore, it compares
and overpressured conditions. Such models can be used to their prediction performance and identifies the best performing
1808 A.E. Radwan et al. / Journal of Rock Mechanics and Geotechnical Engineering 14 (2022) 1799e1809

Fig. 10. Comparison of pore pressure prediction error analysis for four Mangahewa wells in terms of RMSE (Eq. (3)) and APD (Eq. (6)) for the nine ML algorithms evaluated.

models in terms of their prediction performance. A total of 25,935 Acknowledgments

data records distributed over four wells in the Mangahewa gas
field, New Zealand, involving data from six well-log variables Authors are grateful to the GNS Science and the New Zealand
(gamma ray, formation bulk density, photoelectric absorption fac- Petroleum and Minerals (Ministry of Business, Innovation and
tor, compressional- and shear-wave sonic travel times, and tem- Employment) for providing the data and permission to publish.
perature), are used to predict pore pressure through the over-
pressured Mangahewa Eocene reservoir. The four wellbore sec-
tions evaluated show distinctive pore pressure versus depth trends. Nomenclature
Nine ML methods were evaluated with each providing good to ppg Pound per gallon
excellent levels of pore pressure prediction performance on a su- OBG Overburden pressure gradient (ppg or psi)
pervised learning basis (training and testing on individual wellbore sv Vertical stress (psi)
datasets). The DT model was found to be the most accurate, RHOB Bulk density log value (g/cm3)
achieving RMSE ranging from 0.25 psi to 14.71 psi for the four wells. g Gravitational acceleration (m/s2)
On the other hand, the MLR model was found to be the least ac- EMW Equivalent mud weight (ppg)
curate, achieving RMSE of 106e218 psi for the four wells. RFT Repeated formation test (ppg or psi)
When deployed on a semi-supervised basis, trained models r(H) Bulk density of the overlying rock, represented as
from one well were less successful in predicting pore pressure in function of depth H (g/cm3)
the other wells. However, the DT model did generate semi- rw Density of water column (taken as 1.02 g/cm3)
supervised prediction performance of RMSE of 130e140 psi for PP Pore pressure (psi)
predictions of Mangahewa-03 and Mangahewa-06 well datasets. RNN Recurrent neural network
The results suggest that the models are suitable for predicting pore LSTM Long short-term memory
pressure on a semi-supervised basis for planning wellbores at close GRU Gated recurrent unit
step-out locations within fields (i.e. similar structural positions and
geology) but are less reliable for larger step-out distances in Appendix A. Supplementary data
distinctive geological sections. The best performing ML models
developed have advantageous attributes that provide rapid and Supplementary data to this article can be found online at
reliable predictions of pore pressure in normal and over-pressured https://doi.org/10.1016/j.jrmge.2022.01.012.
conditions. The study illustrates how ML algorithms can be used to
create accurate data-driven solutions for predicting subsurface
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Radwan, A.E., 2021. Modeling pore pressure and fracture pressure using integrated
well logging, drilling based interpretations and reservoir data in the Giant El
Morgan oil Field, Gulf of Suez, Egypt. J. Afr. Earth Sci. 178, 104165. Dr. Ahmed E. Radwan is a research associate at the
Radwan, A., Sen, S., 2021a. Stress path analysis for characterization of in situ stress Institute of Geological Sciences of the Jagiellonian Uni-
state and effect of reservoir depletion on present-day stress magnitudes: versity (Poland). Dr. Radwan has the academic and in-
reservoir geomechanical modeling in the Gulf of Suez rift basin, Egypt. Nat. dustrial experience, since he obtained his PhD degree in
Resour. Res. 30, 463e478. geophysics at Sohag University, Egypt, besides his profi-
Radwan, A.E., Sen, S., 2021b. Characterization of in-situ stresses and its implications cient work as a geomechanics specialist and petroleum
for production and reservoir stability in the depleted El Morgan hydrocarbon system department head at the exploration department of
field, Gulf of Suez rift basin, Egypt. J. Struct. Geol. 148, 104355. the Gulf of Suez Petroleum Company (Gupco), Egypt. In
Radwan, A.E., Sen, S., 2021c. Stress path analysis of the depleted Miocene clastic 2019, he attended the Innsbruck University (Austria) as a
reservoirs in the El Morgan oil field, offshore Egypt. In: 55th US Rock Me- post-doctoral research scientist. In 2020, he joined the
chanics/Geomechanics Symposium. American Rock Mechanics Association Jagiellonian University (Poland). Despite his youth, he
(ARMA), Alexandria, USA. was awarded many prizes from international organiza-
Radwan, A.E., Sen, S., 2021d. Stress path analysis of the depleted middle Miocene tions (e.g. International Union of Geological Sciences
clastic reservoirs in the Badri field, Gulf of Suez rift basin, Egypt. In: SPE Annual (IUGS), Geochemical Society (GS), Clay Minerals Society
Technical Conference and Exhibition. https://doi.org/10.2118/205900-MS. (CMS), Österreichische Forschungsgemeinschaft (ÖFG), Narodowa Agencja Wymiany
Dubai, UAE. Akademickiej (NAWA), Austrian Federal Ministry of Education, and Science and
Radwan, A.E., Abudeif, A.M., Attia, M.M., Mohammed, M.A., 2019. Pore and fracture Research (BMBWF)), and petroleum companies. Dr. Radwan has authored more than
pressure modeling using direct and indirect methods in Badri Field, Gulf of 40 papers in highly indexed international peer-reviewed Journals, published 4 book
Suez, Egypt. J. Afr. Earth Sci. 156, 133e143. chapters, and presented lectures at numerous international conferences. Besides his
Radwan, A.E., Abudeif, A.M., Attia, M.M., Elkhawaga, M.A., Abdelghany, W.K., role as Editor for Asian Earth Sciences, he is currently a member of the editorial boards
Kasem, A.A., 2020. Geopressure evaluation using integrated basin modelling, of Asian Earth Sciences, Petroleum Sciences and Engineering, Petroleum Exploration and
well-logging and reservoir data analysis in the northern part of the Badri oil Production Technology, and Petroleum Research. His research interests focus on multidis-
field, Gulf of Suez, Egypt. J. Afr. Earth Sci. 162, 103743. ciplinary research integrating geosciences, petroleum engineering and reservoir engi-
Radwan, A.E., Abdelghany, W.K., Elkhawaga, M.A., 2021a. Present-day in-situ neering as follows: petroleum geology, reservoir characterization, carbonate and
stresses in Southern Gulf of Suez, Egypt: insights for stress rotation in an siliciclastic sedimentology, depositional environment, diagenesis, paleo-environment
extensional rift basin. J. Struct. Geol. 147, 104334. interpretations, basin analysis, unconventional and conventional resources and geolog-
Radwan, A.A., Nabawy, B.S., Abdelmaksoud, A., Lashin, A., 2021b. Integrated sedi- ical interpretations, petroleum geomechanics, reservoir geology and geophysics, reser-
mentological and petrophysical characterization for clastic reservoirs: a case voir damage, production optimization, water flooding, stimulations, fluids flow,
study from New Zealand. J. Nat. Gas Sci. Eng. 88, 103797. enhanced recovery, machine learning, formation evaluation, petrophysics, borehole
Radwan, A.A., Nabawy, B.S., Shihata, M., Leila, M., 2022. Seismic interpretation, geophysics, rock typing, basin modeling, petroleum system, isotope analysis, and ma-
reservoir characterization, gas origin and entrapment of the Miocene-Pliocene chine learning application in the petroleum industry.