Machine learning and data-driven prediction of pore pressure from geophysical logs:A case study for the Mangahewa gas field,New Zealand

Ahme E.Rawan,Davi A.Woo,Ahme A.Rawan

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

Keywords:Machine learning (ML)Pore pressure Overburden Well-log derived predictions Overpressure

ABSTRACT Pore pressure is an essential parameter for establishing reservoir conditions,geological interpretation and drilling programs.Pore pressure prediction depends on information from various geophysical logs,seismic,and direct down-hole pressure measurements.However,a level of uncertainty accompanies the prediction of pore pressure because insufficient information is usually recorded in many wells.Applying 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 wells in the Mangahewa gas field,New Zealand.Their predictions substantially outperform,in terms of prediction performance,those generated using a multiple linear regression (MLR) model.The geophysical logs used as input variables are sonic,temperature and density logs,and some direct pore pressure measurements were available at the reservoir level to calibrate the predictions.A total of 25,935 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 predicting 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 performance of RMSE of 130-140 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 comparison 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.

1.Introduction

Pore pressure is a useful parameter in geomechanical and resource analysis,and determining its variations with depth is essential for successful exploitation of conventional and unconventional oil and gas reservoirs.Historically,despite decades of study,it remains difficult to predict pore pressure of strata buried in 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 method only provides estimates of pore pressure in the immediate vicinity around the borehole.In addition,it requires substantial time,effort and cost to generate pore pressure estimates while drilling,and sometimes the data required cannot be reliably recorded due to bad hole conditions.Therefore,it is beneficial to develop a workflow,aided by machine learning (ML),which can effectively predict pore pressure versus depth profiles for wells without taking frequent direct formation pressure measurements.Moreover,it is useful to be able to reliably extrapolate pore pressure estimates away from the wellbore into the undrilled portions of formations.Not only do such workflows aid the optimization and reliability of pore pressure estimates,but they also enable those estimates to provide useful inputs to various geomechanical calculations(e.g.stresses and related metrics),and improve reservoirwide modeling.

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).

ML techniques are widely applied to solve numerous problems in geoscience and subsurface engineering.Indeed,advancement and sophistication of technology and ML algorithms are driving a revolution throughout the energy sector.In the oil and gas sector,this is impacting commercial production and resource recovery by solving industry problems more precisely with decreasing time and effort.ML techniques have been successfully applied to many geosciences and subsurface engineering disciplines including geophysical data,petrophysical properties,lithology,reservoir zonation,and organic richness(i.e.Poulton,2002;Silversides et al.,2015; Shi et al.,2016; Xie et al.,2018; Saikia et al.,2020).Consequently,applications and diversity of ML continue to grow affecting most branches of geoscience and petroleum engineering (e.g.Anifowose et al.,2011; Ahmadi et al.,2013,2014; Schmidhuber,2015).Some recent studies have used ML to predict pore pressure using different algorithms and input variables(Ahmed et al.,2019;Paglia et al.,2019; Yu et al.,2020; Booncharoen et al.,2021; Farsi et al.,2021; Wei et al.,2021).The previous studies have used a maximum of five ML techniques considering a limited number of data records and input variables.In this research,we propose a new pore pressure prediction method using ML techniques based on a very large dataset.Nine ML techniques are applied and tested,and their results are compared to identify the most accurate predictions.Additionally,the results and prediction performance achieved are compared with previously published pore pressure predictions.

The major focus of this study is the Eocene Mangahewa gas reservoir of Mangahewa gas field,New Zealand(Fig.1).The field is located north of the Taranaki basin,and is made up of a Cretaceous to recent sedimentary accumulation up to 9000 m thick(King and Thrasher,1996; Radwan et al.,2021b,2022).The Mangahewa reservoir is a non-marine to marginal marine sequence including quartz-rich sandstones,carbonaceous siltstones and silty claystones with some embedded thin coal seams (King and Thrasher,1996).

This research attempts to: (1) bridge the gap in estimating the spatial and temporal variability of pore pressure by adopting a ML approach; (2) demonstrate the potential of high prediction performance of shear-velocity in hydrocarbon-bearing and waterfilled intervals in the studied reservoir interval; (3) show that a supervised and potentially semi-supervised learning approach can provide alternative innovative tools for pore pressure prediction;(4)develop a framework to boost the reliability of characterization and prediction of the geomechanical properties in the studied area using novel,fast and effective ML approaches;and(5)evaluate the application of ML,and how such tools can be utilized to create datadriven solutions more generically to geomechanical problems.

2.Material and methods

2.1.Well-log dataset in the Mangahewa gas field

The drilling and well-log data for the four wells drilled in the Mangahewa gas field (Mangahewa-02,Mangahewa-03,Mangahewa-04 and Mangahewa-06)form the core information used for the ML evaluations.The available data include a high-resolution geophysical well-log suite consisting of gamma ray (GR),formation bulk density (RHOB),photoelectric absorption factor (PEF),compressional-(DC) and shear-wave (DS) sonic travel times and temperature (T) logs,which constitute the input variables considered.A total of 25,935 data records were compiled for the four wells(6074 for Mangahewa-02,5964 for Mangahewa-03,6726 for Mangahewa-04,and 7171 for Mangahewa-06).Statistical details of the data distributions for the six well-logs(input variables)and pore pressure (dependent variable) are provided for the 25,935 data records in Table 1.Correlations among the variables taking into account all data records for the four wells are also listed in Table 2.

According to the results shown inTable 2,it is apparent that depth and temperature show good positive correlations with the pore pressure,as should be expected.Of the other recorded well-logs,GR and PEF show moderate negative correlations with the pore pressure,whereas RHOB,DTC and DTS show poor negative correlations with the pore pressure.Fig.2 displays the pore pressure measurements versus depth trends for the Eocene Mckee and Mangahewa formations in the four wells studied.It is apparent from Fig.2 that wells Mangahewa-02 and Mangahewa-04 follow similar pore pressure versus depth trends,with wells Mangahewa-03 and Mangahewa-06(a directional well sidetracked from the Mangahewa-03 location,Fig.1)following their own distinct pore pressure versus depth trends.

As the pore pressure versus depth trend can vary from location to location across the field,the depth has not been included in input well-log variable set for predicting pore pressure.This means that generated pore pressure predictions are not influenced by the depth of each data record.

2.2.Overburden and pore pressures modeling

The weight of the overlying sedimentary column forming the overburden is expressed quantitatively as vertical stress (σv) or overburden (Plumb et al.,1991; Zhang 2011; Radwan et al.,2019,2020,2021a,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 information (Radwan et al.,2020).The vertical stress gradient(OBG) can be calculated applying the Amoco method as

where Z is the depth,RHOB is the bulk density log value,and g is the gravitational acceleration.

The pore pressure values in the Mckee and Mangahewa sandstone reservoirs were directly recorded in the formations with a repeat formation tester(RFT) wireline tool in all four wells.

2.3.Pore pressure prediction using several ML methods

The dataset is evaluated using nine established and widely applied ML models: Adaboost (ADA,a boosted decision tree (DT)model),DT,extreme learning machine (ELM),multi-layer perceptron (MLP),multi-linear regression (MLR,with gradient descent optimizer),optimizer formula (OF,polynomial equation fit with optimizer),random forest (RF),support vector regression (SVR),and transparent open box (TOB).

The methodologies associated with these ML techniques are documented elsewhere with most previously employed for multivariate pore pressure prediction (e.g.Yu et al.,2020) and geomechanical analysis: ADA (Salehin et al.,2020); DT (Bruno,2001);ELM (Song et al.,2015); MLP (Najibi et al.,2017); RF (Zhou et al.,2019); SVR (Bagheripour et al.,2015); and TOB (Wood,2020).

Two(OF and TOB)of the nine ML models applied provide more transparency for each prediction they make as regressions are not involved.The other ML models generate their predictions in a much less transparent way by formulating and exploiting hidden regression relationships.The transparent methods are of more practical value in data mining applications aiming to consider the relationships between individual data records.

A consistent workflow is used to apply each of these ML methods in this study.It involves selecting a training subset of data and optimizing the hyper/control parameters for each method.The trained models are then applied to a testing subset of data records that are not involved in the model training process.Trial and error evaluations identified that for the large number of data records 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 the prediction performance results presented are based on the average of those achieved by multiple runs.Table 3 lists the hyper/control parameters applied to each of the ML methods with the selections based on trial and error testing of each model.We have selected the parameters that generate minimum prediction errors.

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.

Table 2 Correlations among well-log variables considering all 25,935 data records from the four Mangahewa field wells evaluated.

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

2.4.Statistical measures of prediction performance used to assess pore pressure predictions

The statistical measures of prediction performance used to assess and compare the pore pressure prediction performance of the nine ML methods applied are those defined as follows:

(1) Mean square error (MSE):

where n is the number of data points; and Xiand Yispecify the measured and the ML predicted values for the ith data record in the subset evaluated,respectively.

(2) Root mean square error (RMSE):

Fig.2.Pore pressure measurements versus depth trends for the Eocene Mckee and Mangahewa in the four studied wells from the Mangahewa gas field.

Note that RMSE is used as the objective function to minimize errors in each ML algorithm.

(3) Mean absolute error(MAE):

(4) Percent deviation between measured and predicted values for the ith dataset record(PDi):

(5) Average percent deviation (APD):

APD combines both positive and negative percent deviations and is expressed in percentage terms.

(6) Absolute average percent deviation (AAPD):

AAPD combines the absolute values of the percent deviations and is also expressed in percentage terms.

(7) Standard deviation (SD):

where Di=Xi-Yistands for the ith data record of a dataset,and Dimeanis the mean of the Divalues of all the data records in a dataset:

(8) Correlation coefficient (R) between variables Xiand Yi:

where R is expressed on a scale of-1 to 1.

(9) Coefficient of determination,R2(between 0 and 1).

Each of these prediction measures carries distinct information about prediction performance.Although the indications of prediction performance provided by some of these measures tend to be highly correlated,it is useful to consider and compare multiple measures of prediction performance when assessing the prediction performance of ML algorithms.The details are provided in the Appendix (Tables A1-A4) individually for each well in terms of six prediction performance measures with respect to the ML algorithms evaluated.Furthermore,the mean of all studied wells are also provided in the Appendix (Table A5) in terms of six prediction performance measures with respect to the ML algorithms evaluated.On the other hand,the results are illustrated with reference specifically to two of these prediction performance measures (RMSE and APD),the results of which are not highly correlated.

3.Results

In this study,more than 17 km of cumulative well log data has been evaluated from the four available well bores drilled in the Mangahewa gas field(Fig.1).The penetrated sediments encompass Eocene to Paleocene age formations.

3.1.Overburden and pore pressure modeling

The Eocene Mckee and Mangahewa in the four Mangahewa gas field wells are dominant with sandstones,with intercalated siltstone,clay,and minor coal streaks (King and Thrasher,1996).The offset wells are used to calculate field-wide hydrostatic pressure of 8.33 ppg equivalent mud weight (EMW).Average overburden or vertical stress ranges between 18.6 ppg and 21.5 ppg (EMW) in the four studied wells (Table 4).The maximum vertical stress of 21.5 ppg (EMW) is reached in the Mangahewa-02 well,while the lowest vertical stresses are associated with the Mangahewa-04 well.The wireline signatures of the sonic and density logs display clear reversals from the middle Otaraoa formation downwards,which is an indication of the prevailing overpressure zone (Fig.3).In the Mangahewa formation,repeated formation test (RFT) measurements collected at the Mangahewa-04 and Mangahewa-06 wells recorded an average pore pressure of 10.41 ppg (EMW).This pressure is consistent with and close to the Mangahewa reservoir virgin pressure interval recorded in the Mangahewa field.The aforementioned pore pressure measurements show overpressure conditions throughout the Mangahewa reservoir.The recorded pore pressures are 10.44 ppg (EMW) in the Mangahewa-02 well,while it shows 10.3 ppg (EMW) in the Mangahewa-03 well.The current pore pressure and overburden pressure dataset of the Manghewa gas field are documented in Table 4.

3.2.Pore pressure prediction using ML models

Fig.4 compares the predicted and measured pore pressure values for the Mangahewa-06 well for the best performing DT model and the least accurate MLR model.The details of the pore pressure prediction accuracies achieved by the nine ML models applied individually 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 Appendix(Tables A1-A5).The individual well prediction accuracies are illustrated graphically in terms of RMSE and APD in Figs.5-8.Our results document that all ML models provide credible pore pressure predictions across the entire depth intervals considered for each well.However,the MLR model outperforms all other ML methods for this dataset in terms of pore pressure predictions in all four wells considered.The best performing models in terms of all of the statistical measures of prediction performance are DT,ADA,RF and TOB,in that order.SVR,ELM,OF,MLP and MLR generate substantially less accurate predictions than the top four algorithms.

Table 4 The pore pressure and overburden pressure model values in the four studied wells of the Mangahewa gas field.

The Mangahewa-06 well provides the best prediction performance of the four wells considered.The Mangahewa-02 and Mangahewa-03 wells provide slightly better pore pressure prediction performance than the Mangahewa-04 well.The slightly inferior pore pressure prediction performance for the Mangahewa-04 well may be due to its more complex pore pressure versus depth 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 predictions for the Mangahewa-04 well,with RF outperforming DT and ADA in that well.

An explanation for the differences in the pore pressure prediction performance between the four wells can also be explained with reference to Fig.2.In the Mangahewa-02 well,the depth interval adheres more closely to a linear trend.On the other hand,for the Mangahewa-04 well,there is a substantial pore pressure versus depth offset near the top of the section evaluated.The algorithms therefore have more difficulty in predicting pore pressure in the Mangahewa-04 well.Also,the pore pressure offset section in the Mangahewa-06 well covers a greater depth range than in Mangahewa-03 well,providing the algorithms with more data records to predict that distinctive zone in the Mangahewa-06 well.

4.Discussion

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

4.1.Application of ML models in the case study

Our study confirms that various ML methods can successfully predict pore pressure on a supervised base from a suite of well-log data from individual wells,without consideration of well depth as one of the input variables.Displaying the average of the pore pressure prediction errors achieved for each well (Fig.9) reveals that the DT model(RMSE=5.2 psi)generates a slightly lower error than the RF model (RMSE=5.5 psi).Those two models are closely followed in terms of statistical measures of prediction performance(averaged over the four wells) by the TOB model (RMSE=7.7 psi)and ADA model (RMSE=8.3 psi).The superior prediction performance of ML models(i.e.DT,RF,TOB and ADA models)is apparent from Figs.5-8 (and Tables A1-A5 in the Appendix),but is made clearer in Fig.10 by displaying the prediction accuracies for all wells into one graphic.For geomechanical modeling purposes,the ability to apply such prediction models to extrapolate pore pressure across entire wellbore sections from relatively few formation test pressure results is clearly of benefit.

The ability to use pore pressure prediction models trained using data from one well to predict,on a semi-supervised basis,pore pressure from the well-log data of another Mangahewa well has also been evaluated with mixed results.Making such semisupervised predictions on well bores in different parts of the field is much more challenging because the pore pressure trends with depth differ for each well (Fig.4).The best results for such semisupervised pore pressure predictions were achieved using models trained using data from Mangahewa-03 and using those trained models to predict well Mangahewa-06 and vice versa.The RF model achieved prediction performance of RMSE=131 psi for the Mangahewa-06 well in a semi-supervised manner using the model trained with Mangahewa-03 data.This slightly outperformed the ADA and DT models that both achieved semi-supervised statistical measures of prediction performance of RMSE of 138 psi for that purpose.Similar prediction performance accuracies were achieved by those models predicting pore pressure in Mangahewa-03 using models trained with Mangahewa-06 data.These two wells are located close to each other (Fig.2),which undoubtedly has an influence on the pore pressure prediction performance of these semisupervised models.However,attempts to predict pore pressure in Mangahewa-02 and Mangahewa-04 wells using models trained in other wells were less successful with prediction accuracies of RMSE＞300 psi for all ML models.

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.

According to these results,we infer that using ML to predict pore pressure from well-logs on a semi-supervised basis in other wellbore in a field may require models trained on data from multiple wells to provide reliable prediction performance.This approach is more likely to achieve high pore pressure prediction performance in adjacent wells in similar structural and stratigraphic locations within a field than for wells located at substantial distances in distinctive geological settings or pressure compartments from the trained datasets.

4.2.Comparison with other studies

There are relatively few studies focusing on the prediction of pore pressure considering multiple ML techniques.Here,we discuss some other techniques developed recently (i.e.Yu et al.,2020; Booncharoen et al.,2021; Farsi et al.,2021; Wei et al.,2021).Yu et al.(2020) proposed a ML technique for pore pressure prediction in a mixed lithology domain,exploiting specific well-log curve inputs(sonic velocity,porosity,and shale volume).They combined the petrophysical properties with theoretical effective stress in their training dataset in the normally pressured sequences.On the other hand,they used the Bowers’ unloading relationship in the overpressure zones.They evaluated four ML algorithms: gradient boosting,MLP neural network,RF,and support vector machine (SVM).The results of their evaluations revealed good agreement between pore pressure measurements and predictions,with the RF algorithm outperforming other ML algorithms.Moreover,Yu et al.(2020) pointed out that their RF model was able to detect the onset of overpressure more effectively than the other three models they evaluated.

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.

Farsi et al.(2021) used nine petrophysical input variables extracted from 1972 data records from a carbonate reservoir to predict pore pressure.They applied feature selection and developed and compared three-hybrid ML optimization models.Their analysis indicated that a multi-layer ELM (MELM) model optimized with a particle swarm (PSO) algorithm provided the most accurate pore pressure predictions.They applied their models to three different wells in an Iranian oil field,and their results illustrated that the trained model could be used reliably for predicting pore pressure across the entire studied field.

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.

Wei et al.(2021) compared the performance of deep learning recurrent neural networks (RNN),specifically long short-term memory (LSTM) and gated recurrent units (GRU) with the MLP for pore pressure prediction in soil.In their model,they used RMSE and R2to evaluate the prediction performance of the model.Their findings indicated that the GRU and LSTM models performed much better for pore pressure prediction than their MLP model.

Booncharoen et al.(2021) considered drilling parameters and reservoir characteristics as input variables for predicting pore pressure in a Thailand oil and gas field using a model involving three regression-based algorithms: quantile,ridge and extreme gradient boosting(XGBoost).The RMSE achieved by their model for data from 12 wells drilled in the Pattani basin ranged from 1.2 ppg and 1.5 ppg.Ahmed et al.(2019) developed five ML models to predict the pore pressure from actual field measurements such as drilling parameters and well-logs.Their five models were artificial neural network(ANN),radial basis function (RBF),fuzzy logic (FL),SVM,and a functional network (FN).Comparative evaluations revealed that their SVM model delivered the best pore pressure prediction performance achieving an average percentage error of 0.14%.

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.

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.

In comparison with previous studies,the models evaluated here assess a much larger number of data records (5064-7171).Furthermore,this study evaluates a greater number of ML techniques employing quite distinct algorithms on a supervised learning basis,which has not been conducted previously.The best performing ML models developed have advantageous attributes providing rapid and reliable predictions of pore pressure in normal and overpressured conditions.Such models can be used to overcome pore pressure prediction constraints where there is a lack of detailed regional data available for pore pressure prediction.Such advantages make these ML models innovative tools for subsurface pore pressure analysis and prediction for drilling and field development applications.The results presented in this study indicate that applying several ML algorithms to large datasets tends to generate to better predictions.

5.Conclusions

The result of this research demonstrates the usefulness of applying ML tools to predict subsurface pore pressure from a limited range of well-log input variables.Furthermore,it compares their prediction performance and identifies the best performing models in terms of their prediction performance.A total of 25,935 data records distributed over four wells in the Mangahewa gas field,New Zealand,involving data from six well-log variables(gamma ray,formation bulk density,photoelectric absorption factor,compressional-and shear-wave sonic travel times,and temperature),are used to predict pore pressure through the overpressured Mangahewa Eocene reservoir.The four wellbore sections evaluated show distinctive pore pressure versus depth trends.

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.

Nine ML methods were evaluated with each providing good to excellent levels of pore pressure prediction performance on a supervised learning basis(training and testing on individual wellbore datasets).The DT model was found to be the most accurate,achieving RMSE ranging from 0.25 psi to 14.71 psi for the four wells.On the other hand,the MLR model was found to be the least accurate,achieving RMSE of 106-218 psi for the four wells.

When deployed on a semi-supervised basis,trained models from one well were less successful in predicting pore pressure in the other wells.However,the DT model did generate semisupervised prediction performance of RMSE of 130-140 psi for predictions of Mangahewa-03 and Mangahewa-06 well datasets.The results suggest that the models are suitable for predicting pore pressure on a semi-supervised basis for planning wellbores at close step-out locations within fields(i.e.similar structural positions and geology) but are less reliable for larger step-out distances in distinctive geological sections.The best performing ML models developed have advantageous attributes that provide rapid and reliable predictions of pore pressure in normal and over-pressured conditions.The study illustrates how ML algorithms can be used to create accurate data-driven solutions for predicting subsurface pore pressure using readily available well-log data from multiple wellbores.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

Authors are grateful to the GNS Science and the New Zealand Petroleum and Minerals (Ministry of Business,Innovation and Employment) for providing the data and permission to publish.

Nomenclature

ppg Pound per gallon

OBG Overburden pressure gradient (ppg or psi)

σvVertical stress (psi)

RHOB Bulk density log value (g/cm3)

g Gravitational acceleration (m/s2)

EMW Equivalent mud weight (ppg)

RFT Repeated formation test(ppg or psi)

ρ(H) Bulk density of the overlying rock,represented as function of depth H (g/cm3)

ρwDensity of water column(taken as 1.02 g/cm3)

PP Pore pressure(psi)

RNN Recurrent neural network

LSTM Long short-term memory

GRU Gated recurrent unit

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.jrmge.2022.01.012.