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Artificial Intelligence techniques have been used in petroleum engineering to predict various reservoir properties such as porosity, permeability, water saturation, lithofacie and wellbore stability. The most extensively used of these techniques is Artificial Neural Networks (ANN). More recent techniques such as Support Vector Machines (SVM) have featured in the literature with better performance indices. However, SVM has not been widely embraced in petroleum engineering as a possibly better alternative to ANN. ANN has been reported to have a lot of limitations such as its lack of global optima. On the other hand, SVM has been introduced as a generalization of the Tikhonov Regularization procedure that ensures its global optima and offers ease of training.
This paper presents a comparative study of the application of ANN and SVM models in the prediction of porosity and permeability of oil and gas reservoirs with carbonate platforms. Six datasets obtained from oil and gas reservoirs in two different geographical locations were used for the training, testing and validation of the models using the stratified sampling approach rather than the conventional static method of data division.
The results showed that the SVM model performed better than the popularly used Feed forward Back propagation ANN with higher correlation coefficients and lower root mean squared errors. The SVM was also faster in terms of execution time.
Hence, this work presents SVM as a possible alternative to ANN, especially, in the characterization of oil and gas reservoir properties. The new SVM model will assist petroleum exploration engineers to estimate various reservoir properties with better accuracy, leading to reduced exploration time and increased production.
1. Introduction
Petrophysical properties such as porosity and permeability are two important properties of oil and gas reservoirs that relate to the amount of fluid in them and their ability to flow. These properties have significant impact on petroleum field operations and reservoir management. They both serve as standard indicators of reservoir quality in the oil and gas industry (Jong-Se, 2005).
Porosity is the percentage of voids and open spaces in a rock or sedimentary deposit. The greater the porosity of a rock, the greater its ability to hold water and other materials, such as oil. It is an important consideration when attempting to evaluate the potential volume of hydrocarbons contained in a reservoir (Schlumberger, 2007a). Permeability is the ease with which fluid is transmitted through a rock's pore space. It is a measure of how interconnected the individual pore spaces are in a rock or sediment (Schlumberger, 2007b). It is a key parameter associated with the characterization of any hydrocarbon reservoir. In fact, many Petroleum Engineering problems cannot be solved without having an accurate permeability value.
Many reports such as Ali (1994) and Mohagheh (1994) have featured the successful application of Artificial Neural Networks (ANN) as the pioneer Artificial Intelligence (AI) technique in oil and gas reservoir characterization over the years. Despite this, ANN has been reported to have some drawbacks (Petrus et al., 1995). The recent introduction of Support Vector Machines (SVM) that is based on the concepts of Tikhonov Regularization and Structural Risk Minimization (SRM) was introduced to overcome some of the limitations of ANN. Many reports such as such as Anifowose and Abdulraheem (2010); and Helmy et al. (2010) have presented SVM as a promising predictive technique in a good number of applications.
This paper focuses on the study and analysis of the comparative performance of ANN and SVM in the prediction of porosity and permeability of some Middle East and American oil and gas reservoirs. To achieve this aim, Section 2 presents a succinct survey of ANN and SVM. Section 3 describes the experimental methodology, structure of datasets and the evaluation criteria for the study. Section 4 presents the results of the study with a detailed discussion while conclusion is presented in Section 5.

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... The AI prediction methods include gray system theory, artificial neural network (ANN), time series analysis, SVM, and a combination of various prediction methods [30][31][32]. Among them, SVM is based on the principle of minimizing structural risk and can effectively solve the problems with small samples, high dimensions, and nonlinearity, such as the works of Zhao et al. [33] and Anifowose et al. [34]. Zhao et al. [33] trained a ε-insensitive SVM to regress the water saturation from seismic data. ...

... Zhao et al. [33] trained a ε-insensitive SVM to regress the water saturation from seismic data. Anifowose et al. [34] predicted the porosity and permeability of an oil and gas reservoir by using SVM. In this article, we adopted the SVM to predict the maximum stress of the offcenter casing under non-uniform ground stress. ...

... vector and y R i is the target output, we can transform the SVR problem with the insensitive loss function ε into the dual quadratic problem [34]: ...

The situation of an off-center casing under non-uniform ground stress can occur in the process of drilling a salt-gypsum formation, and the related casing stress calculation has not yet been solved analytically. In addition, the experimental equipment in many cases cannot meet the actual conditions and the experimental cost is very high. These comprehensive factors cause the existing casing design to not meet the actual conditions and cause casing deformation, affecting the drilling operation in Tarim oil field. The finite element method is the only effective method to solve this problem at present, but the re-modelling process is time-consuming because of the changes in the parameters, such as the cement properties, casing centrality, and the casing size. In this article, an artificial intelligence method based on support vector machine (SVM) to predict the maximum stress of an off-center casing under non-uniform ground stress has been proposed. After a program based on a radial basis function (RBF)-support vector regression (SVR) (ε-SVR) model was established and validated, we constructed a data sample with a capacity of 120 by using the finite element method, which could meet the demand of the nine-factor ε-SVR model to predict the maximum stress of the casing. The results showed that the artificial intelligence prediction method proposed in this manuscript had satisfactory prediction accuracy and could be effectively used to predict the maximum stress of an off-center casing under complex downhole conditions.
Electronic supplementary material:
Supplementary material is available for this article at 10.1007/s11431-019-1694-4 and is accessible for authorized users.

... Artificial Intelligence (AI) techniques has become very common in the most of petroleum engineering applications recently, for example, drilling engineering, reservoir engineering, production engineering, petrophysics, rock mechanics and exploration, Abdulraheem et al.(2007) [1], Ebrahimi and Sajedian(2010) [2], Al-Shammari(2011) [3], and Anifowose et al.(2012) [4]etc. Chase (1987) [5] presented a dimensionless IPR curves which involved prediction of the current and future performance for unfractured and fractured gas wells with the skin effect. ...

... Artificial Intelligence (AI) techniques has become very common in the most of petroleum engineering applications recently, for example, drilling engineering, reservoir engineering, production engineering, petrophysics, rock mechanics and exploration, Abdulraheem et al.(2007) [1], Ebrahimi and Sajedian(2010) [2], Al-Shammari(2011) [3], and Anifowose et al.(2012) [4]etc. Chase (1987) [5] presented a dimensionless IPR curves which involved prediction of the current and future performance for unfractured and fractured gas wells with the skin effect. ...

The Inflow Performance relationship is considered one of the diagnostic tools used by Petroleum engineers to evaluate the performance of a flowing well. An accurate prediction of well IPR is very important to determine the optimum production scheme, design production equipment, and artificial lift systems. For these reasons, there is a need for a quick and reliable method for predicting the well IPR in gas reservoirs.
This study presents back propagation network (BPN) and fuzzy logic (FL) techniques for predicting IPR for a gas reservoir. These models involved 489 data points from published literature papers and conventional PVT reports.
Statistical analysis was performed to see which of these methods are more reliable and accurate method for predicting the inflow performance relationship for the gas reservoir. The FL model outperformed the artificial neural network (ANN) model with least average absolute error, least standard deviation and highest correlation coefficient. The proposed fuzzy logic well inflow performance relationship model achieved an average absolute error of 4.303%%, standard deviation of 18.891% and the correlation coefficient of 0.995.
The developed technique will help the production and reservoir engineers to better manage the production operation without the need for any additional equipment. This technique will reduce the overall cost of the operation and increase the revenue.

... Artificial intelligence methods like artificial neural network (ANN) and support vector machine (SVM) have shown superior capability in classification and regression tasks. Usage of these methods reduces obstacles associated with costs and the generalization of the developed models for the prediction of permeability (Baziar et al., 2014;Al Anazi et al., 2009;Al Bulushi et al., 2007;Amari and Wu, 1999;Aminian and Ameri 2005;Aminian et al., 2001;Anifowose and Abdulraheem, 2010;Anifowose et al., 2011;Asadisaghandi and Tahmasebi, 2011;Bhatt, 2002;Carrasquilla et al., 2008;Chang et al., 1997;Goda et al., 2007;Huang et al., 1996;Ibrahim and Potter, 2004;Karimpouli et al.,2010;Mollajan and Memarian, 2013;Saffarzadeh and Shadizadeh, 2012;Shokir 2004;Sun et al., 2001;Wiener et al., 1995;Wong et al., 1995;Wong et al., 2000). Furthermore, Anifowose et al., in a comprehensive study, employed adaptive neuro-fuzzy inference system hybrid models to predict reservoir properties including Klinkenberg permeability. ...

Klinkenberg permeability is an important parameter in tight gas reservoirs. There are conventional methods for determining it, but these methods depend on core permeability. Cores are few in number, but well logs are usually accessible for all wells and provide continuous information. In this regard, regression methods have been used to achieve reliable relations between log readings and Klinkenberg permeability. In this work, multiple linear regression, tree boost, general regression neural network, and support vector machines have been used to predict the Klinkenberg permeability of Mesaverde tight gas sandstones located in Washakie basin. The results show that all the four methods have the acceptable capability to predict Klinkenberg permeability, but support vector machine models exhibit better results. The errors of models were measured by calculating three error indexes, namely the correlation coefficient, the average absolute error, and the standard error of the mean. The analyses of errors show that support vector machine models perform better than the other models, but there are some exceptions. Support vector machine is a relatively new intelligence method with great capabilities in regression and classification tasks. Herein, support vector machine was used to predict the Klinkenberg permeability of a tight gas reservoir and the performances of four regression techniques were compared.

... Oil rates have also been measured in the pipe line using ANN for varying pressures and temperatures [35]. Various applications of LSSVM include porosity and permeability determination [36][37][38][39], water conning in horizontal wells [40,41], well placement [40], gas-oil relative permeability curves [42], phase equilibrium calculations of hydrates [43], oil flow rate predictions [44], and temperature-pressure relationship in natural gas production and processing [45]. Wide applications of artificial intelligence in improved oil recovery were recently described by researchers [46][47][48][49]. ...

Artificial intelligence (AI) methods and applications have recently gained a great deal of attention in many areas, including fields of mathematics, neuroscience, economics, engineering, linguistics, gaming, and many others. This is due to the surge of innovative and sophisticated AI techniques applications to highly complex problems as well as the powerful new developments in high speed computing. Various applications of AI in everyday life include machine learning, pattern recognition, robotics, data processing and analysis, etc. The oil and gas industry is not behind either, in fact, AI techniques have recently been applied to estimate PVT properties, optimize production, predict recoverable hydrocarbons, optimize well placement using pattern recognition, optimize hydraulic fracture design, and to aid in reservoir characterization efforts. In this study, three different AI models are trained and used to forecast hydrocarbon production from hydraulically fractured wells. Two vastly used artificial intelligence methods, namely the Least Square Support Vector Machine (LSSVM) and the Artificial Neural Networks (ANN), are compared to a traditional curve fitting method known as Response Surface Model (RSM) using second order polynomial equations to determine production from shales. The objective of this work is to further explore the potential of AI in the oil and gas industry. Eight parameters are considered as input factors to build the model: reservoir permeability, initial dissolved gas-oil ratio, rock compressibility, gas relative permeability, slope of gas oil ratio, initial reservoir pressure, flowing bottom hole pressure, and hydraulic fracture spacing. The range of values used for these parameters resemble real field scenarios from prolific shale plays such as the Eagle Ford, Bakken, and the Niobrara in the United States. Production data consists of oil recovery factor and produced gas-oil ratio (GOR) generated from a generic hydraulically fractured reservoir model using a commercial simulator. The Box-Behnken experiment design was used to minimize the number of simulations for this study. Five time-based models (for production periods of 90 days, 1 year, 5 years, 10 years, and 15 years) and one rate-based model (when oil rate drops to 5 bbl/day/fracture) were considered. Particle Swarm Optimization (PSO) routine is used in all three surrogate models to obtain the associated model parameters. Models were trained using 80% of all data generated through simulation while 20% was used for testing of the models. All models were evaluated by measuring the goodness of fit through the coefficient of determination (R2) and the Normalized Root Mean Square Error (NRMSE). Results show that RSM and LSSVM have very accurate oil recovery forecasting capabilities while LSSVM shows the best performance for complex GOR behavior. Furthermore, all surrogate models are shown to serve as reliable proxy reservoir models useful for fast fluid recovery forecasts and sensitivity analyses.

... Machine learning methods were utilized expansively in the majority of petroleum engineering purposes, such as, drilling, reservoir, production and engineering, as well as petrophysics, rock mechanics and exploration [2]. One of such is the Response Surface Model which is utilized in numerous facets of reservoir engineering such as history matching [3,4], determining the initial uncertainty of hydrocarbons [5], locating spots for well placement [6] and estimating initial hydrocarbon uncertainty. ...

Machine Learning techniques and applications have lately gained a lot of interest in many areas, including spheres of arithmetic, finances, engineering, dialectology, and a lot more. This is owing to the upwelling of groundbreaking and sophisticated machine learning procedures to exceedingly multifaceted complications along with the prevailing advances in high speed computing. Numerous usages of Machine learning in daily life include pattern recognition, automation, data processing and analysis, and so on. The Petroleum industry is not lagging behind also. On the contrary, machine learning approaches have lately been applied to enhance production, forecast recoverable hydrocarbons, augment well placement by means of pattern recognition, optimize hydraulic fracture design, and to help in reservoir characterization. In this paper, three different machine learning models were trained and utilized to explore the feasibility of forecasting pore pressure of a well. The machine learning algorithms include, Simple Linear Regression, Decision Stump and Multilayer Perceptron (ANN). The predictive accuracies of the algorithm was analyzed using statistical measures. Five (5) parameters were utilized as input variables in the models: hydrostatic pressure, overburden pressure, observed and normal sonic velocities and pore pressure. 80% of the data was used in training while the remaining 20% was used for testing of the models. A sensitivity analysis of the five variable was conducted so as to identify correlations of the variables. Results of the sensitivity analysis revealed that both hydrostatic and overburden pressures appear to have the strongest correlation with pore pressure (0.766) and closely followed by normal compacted sonic velocity (0.753). Meanwhile, observed sonic velocity has the least correlation (0.046). The models were appraised by determining their Relative Absolute Errors. Results indicate that Multilayer Perceptron has the best prediction and least Relative Absolute Error of 5.77%. While the Decision Stump model had a Relative absolute error of 54.41%. The Simple Linear Regression had a relative absolute error of 67.93%. By and large, all three models appear to be suitable for modeling pore pressure but the Multilayer Perceptron is the most accurate.

... Recently, Artificial Intelligence (AI) techniques such as Artificial Neural Network (ANN), Fuzzy Logic (FL), and Functional Networks (FN) are being widely used for most of the petroleum engineering applications such as estimation of permeability [1], prediction two-phase inflow performance [2], prediction of pressure drop in two-phase vertical flow systems [3], calculation of oil and gas properties [4], estimation inflow performance relationship for vertical oil well in solution gas derive reservoirs [5], and calculation of inflow performance relationship of a gas field using [6] . ...

... 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., 2013Ahmadi et al., , 2014Schmidhuber, 2015). Some recent studies have used ML to predict pore pressure using different algorithms and input variables Paglia et al., 2019;Yu et al., 2020;Booncharoen et al., 2021;Farsi et al., 2021;Wei et al., 2021). ...

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.© 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/).

... Recently, artificial intelligence (AI) techniques such as artificial neural network (ANN), fuzzy logic (FL), and functional networks (FN) are being widely used for most of the petroleum engineering applications such as estimation of reservoir fluid properties [1] and [2], prediction of choke size in volatile and black oil reservoirs [3],calculation of oil and gas properties [4],estimation IPR for vertical oil well in solution gas derive reservoirs [5], and calculation of inflow performance relationship of a gas field using [6] . A artificial intelligence w w w . ...

Reservoir fluid properties such as crude oil viscosity, oil formation volume factor, bubble point pressure, solution gas oil ratio, gas formation volume factor, isothermal compressibility and crude oil density are very important in reservoir engineering computations. An accurate description of reservoir fluid properties of crude oils is necessary for solving many of reservoir engineering and surface operational problems. Most of the empirical Pressure-Volume-Temperature (PVT) correlations for any type of crude oil are functions of commonly available field data. The derived PVT correlations for crude oil are function of bubble point pressure, solution gas oil ratio, specific oil gravity, specific gas gravity, and temperature. Till date, no specific correlation has been developed for estimating PVT properties of crude oil using its chemical composition.
This study presents radial basis functions networks (RBF) and fuzzy logic (FL) techniques for predicting the crude oil density, gas specific gravity and the molecular weight of a gas mixture using chemical composition of crude oil. The presented models here were established using 1500 data points, collected from mainly unpublished sources. Statistical analysis was conducted to see which of the Artificial Intelligence techniques (AI) were more reliable and accurate for predicting the reservoir fluid properties. The new radial basis functions networks (RBF) models outperformed most of the fuzzy logic (FL) models. The presented models provide good estimation for crude oil density, gas specific gravity and the molecular weight of a gas mixture with correlation coefficient (R2) of 0.989, 0.997 and 0.998, respectively.

... SVM has gained popularity in petroleum engineering studies and have been used for prediction of reservoir and petrophysical properties [30, 37, [66][67][68][69][70][71][72][73][74][75][76]. There are some studies focusing on prediction of water saturation by using SVM [38,77]. ...

Reservoir water saturation is an important property of tight gas reservoirs. Improper calculation of water saturation leads to remarkable errors in following studies for development and production from reservoir. There are conventional methods to determine water saturation, but these methods suffer from poor generalization and cannot be applicable for various conditions of reservoirs. These methods also depend on core measurements. On the other hand, well log data are usually accessible for all the wells and provide continuous information across the well. Customary techniques are not fully capable to prepare meaningful results for predicting petrophysical properties, especially in presence of small data sets. In this regard, soft computing approaches have been used here. In this research, Support Vector Machine, Multilayer Perceptron Neural Network, Decision Tree Forest and Tree Boost methods have been employed to predict water saturation of Mesaverde tight gas sandstones located in Uinta Basin. Tree Boost and Decision Tree Forest are powerful predictors which have been applied in many research fields. Multilayer Perceptron is the most common neural network, and Support Vector Machine has been used in many petrophysical and reservoir studies. In this research, by using a small data set, the ability of these methods in predicting water saturation has been studied. Based on the data from four wells, two data set patterns were designed to evaluate training and generalization capabilities of methods. In each pattern, different combinations of well data were used. Three error indexes including correlation coefficient, average absolute error and root-mean-square error were used to compare the methods results. Results show that Support Vector Machine models perform better than other models across data sets, but there are some exceptions exhibiting better performance of Multilayer Perceptron Neural Network and Decision Tree Forest models. Correlation coefficient values vary from 0.6 to 0.8 for support vector machine, which exhibits better performance in comparison with other methods.

... Recently, artificial intelligence(AI) techniques have been used comprehensively in the petroleum engineering applications, such as; drilling, reservoir, production, petrophysics, rock mechanics and exploration (Abdulraheem 2007, Ebrahimi and Sajedian 2010, Al-Shammari 2011, and Anifowose 2012. ...

It is very important to determine or predict the bubble point pressure (BPP) with high accuracy in petroleum industry. Laboratory measurement of the BPP requires collecting actual samples from the bottom of the wellbore and simulates the reservoir conditions at the lab. This operation takes long time and high cost. To overcome this issue, many empirical correlations were developed to predict the BPP with wide range of average percent error.
In this research, we will use artificial intelligent (AI) techniques to predict the bubble point pressure using published data (760 data sets). Two different AI techniques will be used, artificial neural network (ANN) (back propagation network (BPN) and radial basis functions networks (RBF)), and fuzzy logic tool (FL) to develop the model. The obtained results will be compared with the available correlations in the literature.
The results obtained showed that all AI models were able to predict the bubble point pressure with a high accuracy. The new fuzzy logic (FL) model outperforms all the artificial neural network models and the most common published empirical correlations. BPN, RBF and FL models provide predictions of bubble point pressure with correlation coefficient of 0.9926, 0.9969, and 0.9995, respectively.

... It is a set of related supervised learning techniques that has been applied in various classification, pattern recognition, and regression problems [60]. Generally, SVM works based on the characteristics of the optimal hyperplane that maximizes the distance to training examples in a high dimensional feature space [61]. SVM's advantage over ANN is that it does not possess multi-local minimal and overfitting [62]. ...

Comprehensive experimental investigation and accurate predictive models are
required to understand the dynamics in Ionic liquid (IL) properties. Examples of
these predictive models are empirical correlations, Quantitative structure–activity
relationship (QSPR) and machine learning (ML). In this study, we reported the
application of various ML models for predicting thermo-physical properties of
ILs. Our study showed that these ML models could be categorized into
conventional and hybrid models. These conventional models include artificial
neural networks (ANN), least square support vector machine (LSSVM) and
adaptive neuro-fuzzy inference system (ANFIS). Meanwhile, the hybrid models
consist of random forest, gradient boosting, and group method of data handling.
We provided an overview of these ML models and optimization methods such as
genetic algorithm, particle swarm algorithm, and coupled simulated annealing
(CSA) algorithm, and their applications in IL studies. We observed that ANN,
LSSVM and ANFIS represent the three most frequently used ML approaches in
predicting the various properties of ILs among the models discussed. The
investigation revealed that the ANN approach is most widely used, while the
studies involving the solubility of gases (H2S and CO2) represent the mostcommon problems related to ML application in IL studies. However, the
combination of conventional ML and optimization algorithms such as LSSVMCSA gives better accuracy compared to ANN in most applications. It is noteworthy
that system parameters (temperature and pressure) and critical properties (critical
temperature and critical pressure) are the key thermo-physical that depicts the
phase behavior of any ILs. Finally, to generalize MLs methods to certain ILs based
on similarity in cations and anions, it is important to represent the molecular
descriptions of the liquid as one of the property predictors.

... Support Vector Regressions (SVRs) methodology involves a group of related supervised learning methods employed for regression problems. They fall in the category of generalized linear classifiers (Anifowose et al., 2011). In SVRs, a maximal hyperplane is constructed to separate a high dimensional space of input vectors mapped with the feature space. ...

Application of artificial intelligence in the accurate prediction of the rate of penetration (ROP), an important measure of drilling performance, has lately gained significant interest in oil and gas well drilling operations. Consequently, several computational intelligence techniques (CITs) for the prediction of ROP have been explored in the literature. This study explores the predictive capabilities of four commonly used CITs in the prediction of ROP and experimentally compare their predictive performance. The CIT algorithm utilizes predictors which are easily accessible continuous drilling data that have physical but complex relationship with ROP based on hydro-mechanical specific energy ROP model. The four CITs compared are the artificial neural network (ANN), extreme learning machine, support vector Regression and least-square support vector regression (LS-SVR). Two experiments were carried out; the first experiment investigates the comparative performance of the CITs while the second investigates the effect of reduced number of predictors on the performance of the models. The results show that all the CITs perform within acceptable accuracy with testing root mean square error range (RMSE) of 18.27–28.84 and testing correlation coefficient (CC) range of 0.71–0.94. LS-SVR has the best predictive performance in terms of accuracy with RMSE of 18.27 and CC of 0.94 while ANN has the best testing execution time at 0.03 s. Also utilizing the specific energy concept in chosen drilling parameters to be included among the predictors shows improved performance with five drilling parameters showing an improvement of 3%–9% in RMSE for LS-SVR in the two well studied. The utilization of the specific energy concept in the selection of the predictors in this study has demonstrated that the easily accessible drilling parameters have immense value to provide acceptable performance in the development of ROP model with CITs.

... The OPR depicts pressure drop that should be loosed when the fluid flow through tubing and pipeline into gas-oil separator while IPR is a correlation reflects reservoir ability to supply production well with fluid. Artificial Intelligence (AI) techniques has become very common in most of petroleum engineering application recently, for example, drilling engineering, reservoir engineering, production engineering, petrophysics, rock mechanics and exploration [1][2][3][4]. This study covered both conventional methods and artificial intelligence techniques for estimating inflow performance relationship of gas and oil reservoirs. ...

The Inflow Performance relationship (a Cartesian plot of bottom-hole flowing pressure versus surface flow rate) is considered one of the diagnostic tools used by petroleum engineers to evaluate the performance of a flowing well. The plot is used to determine whether any well under consideration is performing as expected or not. If it is not, then remedial action may be necessary. The equation that describes this curve is the Inflow Performance Relationship. This equation can be determined both theoretically and empirically. This study presents both conventional methods and artificial intelligence techniques for predicting the inflow performance relationship for a dry gas reservoir. The data used in this study was collected from conventional PVT reports for a Yemeni dry gas reservoir. Statistical analysis was performed to see which of these methods are a more reliable and accurate method for predicting the inflow performance relationship for the dry gas reservoir. The pseudo pressure approach is the lowest Average Absolute Relative Error (AARE) of all the three conventional methods with AARE (13.282%). The artificial intelligence techniques provide a better estimation of the inflow performance relationship than conventional methods with an average absolute relative error of 0.029% and 0.0001% for artificial neural network and fuzzy logic respectively.

... Recently, artificial intelligence(AI) techniques have been used comprehensively in the petroleum engineering applications, such as; drilling, reservoir, production, petrophysics, rock mechanics and exploration (Abdulraheem 2007, Ebrahimi and Sajedian 2010, Al-Shammari 2011, and Anifowose 2012. ...

... ML techniques can help to improve petrophysical properties prediction, log interpretation, to optimize core analysis planning and logging service, and to reduce the cost of laboratory measurements. As a result, there has been extensive research regarding the application of artificial intelligence (AI) techniques in well log interpretation [7], shear sonic log prediction [8], and prediction of various reservoir properties such as porosity, permeability, water saturation, lithofacies, and wellbore stability [9][10][11][12][13][14][15]. ...

Intelligent predictive methods have the power to reliably estimate water saturation (Sw) compared to conventional experimental methods commonly performed by petrphysicists. However, due to nonlinearity and uncertainty in the data set, the prediction might not be accurate. There exist new machine learning (ML) algorithms such as gradient boosting techniques that have shown significant success in other disciplines yet have not been examined for Sw prediction or other reservoir or rock properties in the petroleum industry. To bridge the literature gap, in this study, for the first time, a total of five ML code programs that belong to the family of Super Learner along with boosting algorithms: XGBoost, LightGBM, CatBoost, AdaBoost, are developed to predict water saturation without relying on the resistivity log data. This is important since conventional methods of water saturation prediction that rely on resistivity log can become problematic in particular formations such as shale or tight carbonates. Thus, to do so, two datasets were constructed by collecting several types of well logs (Gamma, density, neutron, sonic, PEF, and without PEF) to evaluate the robustness and accuracy of the models by comparing the results with laboratory-measured data. It was found that Super Learner and XGBoost produced the highest accurate output (R2: 0.999 and 0.993, respectively), and with considerable distance, Catboost and LightGBM were ranked third and fourth, respectively. Ultimately, both XGBoost and Super Learner produced negligible errors but the latest is considered as the best amongst all.

... Different methods such as published correlations and laboratory experiments and Artificial Intelligence (AI) techniques have been proposed to determine PVT parameters. However, laboratory experiments that required generating the correlations are expensive and time-consuming so it is not applicable to carry out these experiments for each field [1]- [4]. ...

PVT empirical correlations and Artificial Intelligence (AI) techniques become the best alternative when laboratory PVT analysis is not ready or very expensive to obtain. The objective of this paper is to determine the most frequently used oil viscosity (µ o ), formation volume factor (βo), and gas solubility (Rs) PVT properties of Yemeni reservoirs using the bottom hole fluid samples from different wells such as Well-BSWS-1, Well-BSWS-2, Well-BSWS-3, and Well-BSWS-4. Both Fuzzy Logic (FL) technique and a set of statistical error analysis were used to validate and compare the performance and accuracy of the generated reservoir fluid properties correlations. A total of 200 data sets of different crude oils from Yemeni reservoirs were used. The accuracy of the new Fuzzy Logic (FL) was compared with existing real measured bottom hole fluid samples data sets. The graphical plots showed that the predicted oil viscosity, formation volume factor, and gas solubility Fuzzy Logic curves have excellent matching with the experimental curves.

... While reservoir porosity has been estimated using empirical correlations (Ramamoorthy et al., 1995;Mukerji and Mavko, 1997;Goldberg and Gurevich, 1998;Darwin 2003;Saadat et al., 2011;Vargas et al., 2015;Mulyanto et al., 2019;Silva et al., 2019), statistical correlations (Xiao et al., 2011;Rafik and Kamel, 2017), and machine learning methods (Al-Anazi and Gates, 2010; Anifowose and Abdulraheem, 2010;Anifowose et al., 2011;Rafik and Kamel, 2017;Elkatatny et al., 2018;Shadrina and Shadrin, 2018;Lee et al., 2021;Gamal and Elkatatny, 2021), the need to obtain it in real time, ahead of wireline logging, is crucial and could help in making critical decisions and enable early assessment of reservoir quality. This work focuses only on mud gas data at this stage of our work to achieve a more objective and possible realtime porosity prediction. ...

Porosity, a critical property of petroleum reservoirs, is a key controlling factor of the reservoir storage capacity. It has been conventionally measured from core plugs. Empirical correlations, statistical, and machine learning methods have been employed for indirect estimation of porosity. The results obtained from these approaches are available only after acquiring drilling and wireline logs. Obtaining porosity estimates in real time, ahead of wireline logging, can help in making critical decisions and enabling early assessment of reservoir quality. We present the results of a machine learning approach to predicting porosity from advanced mud gas data. Datasets integrating advanced mud gas data with porosity were gathered from seven wells to prove this concept. The mud gas data includes light and heavy flare gas components. Optimized artificial neural network (ANN) models were applied to the datasets and multivariate linear regression (MLR) models were used as benchmarks. Each well dataset was split into training and validation subsets using a randomized sampling approach with the ratio of 70:30. A 100 ppm cut-off was applied to the total normalized gas. To evaluate the performance of the models, we use correlation coefficients (R) and mean squared error (MSE). The ANN models consistently outperformed the MLR models in all the datasets. The ANN models have training and validation correlation coefficients of up to 0.89 and 0.88, respectively, compared to an average of 0.79 and 0.77 for the MLR models. The training and validation MSEs for the ANN models are as low as 0.0135 and 0.021, respectively, compared to those of the MLR models in the range of 0.0007 and 0.03, respectively. These results indicate the nonlinearity of the relationship between porosity and the gas components. Furthermore, it can be deduced that the approach is feasible and better results are achievable. The randomized sampling ensures that each data point has an equal chance to be used for either training or validation without bias. The cut-off applied to the normalized total gas is a standard practice to eliminate the background gas effect in the mud gas data. This study provides an opportunity to utilize mud gas data beyond the traditional fluid typing and petrophysical correlation purposes. The presented approach has the capability to complement existing reservoir characterization approaches in providing reservoir quality assessments at the early stage of exploration. We plan to apply state-of-the-art machine learning models and perform sensitivity analysis on the gas components in the future to increase the accuracy.

Accurate prediction of permeability remains the key to the determination of oil and gas reservoir quality. A number of studies have been carried out to investigate the predictability of reservoir permeability from log measurements. More recent studies have attempted to predict permeability from seismic signals. Both log measurements and seismic signals have shown to provide rich information about the structure and texture of the subsurface and hence have jointly proven to be good predictors of permeability. However, previous studies on this subject were limited to the application of Artificial Neural Networks (ANN). With the persistent quest for more accurate predictions for more successful exploration and improved production, this paper investigates the effect of combining both seismic and log datasets with the application of more advanced Artificial Intelligence techniques on the accuracy of reservoir permeability predictions. Log measurements and seismic signals obtained from several wells in a giant oil and gas reservoir were used to train and evaluate the performance of Support Vector Machine (SVM) and Type-2 Fuzzy Logic (T2FL) models in the prediction of permeability. The log measurements were matched with the seismic signals of the exact corresponding wells taken from 10-, 20-, 30-and 40ms seismic zones. When compared with the long-existing ANN model, the SVM model gave the most accurate permeability predictions, with the highest correlation coefficient and the least error measures. The results also showed that a combination of seismic and log data has the potential to give more accurate permeability predictions than using either of them separately. A wider field application of the proposed techniques will give more insight, and is expected to save more time, effort and improve hydrocarbon recovery.

Development of high speed computing leads to major advancements in every field of science and engineering. Artificial intelligence (AI) method is emerging as new modern technology applied to machine learning, pattern recognition, processing and understanding data, robotics etc. Its application in oil and gas industry is new despite of the fact that it has huge potential to explore the knowledge regarding reservoir characterization, PVT properties estimation, maximize productions, locating sweet spot using pattern recognition, optimum design of fracturing job, calculation of recoverable hydrocarbon, well placement etc. The main objective of this study is to put AI such as LSSVM in perspective from reservoir engineering and encourage engineers and researchers to consider it as a valuable alternative tool in the petroleum industry. Factors most affecting the production from fractured low permeability reservoirs such as reservoir permeability, gas relative permeability exponent, rock compressibility, initial gas oil ratio, slope of gas oil ratio in PVT, initial pressure, flowing bottom hole pressure and fracture spacing, are studied. A wide range of values of each parameter based on real field data from Eagle Ford, Bakken and Niobrara in the USA are assigned. Two different kinds of mathematical surrogate models, polynomial response surface method (RSM) and least square support vector machine (LSSVM) are compared to seek the better surrogate models in terms of predictability. Data are generated from a generic reservoir model using commercial simulator. Various models of recovery factors and gas oil ratio are developed for different times (after 90 days, 1 year, 5 years, 10 years, 15 years and 20 years) and for a minimum economic rate (5 STB/ day). Multivariate regression was used to obtain coefficients for the second-order polynomial response surface models using 80% of the simulated results (144). The LSSVM models coupled with radial basis kernel function (RBF) are trained with 60% data. 20% of data is used to tune the regularization parameter and kernel parameter using genetic algorithm (GA) optimization routine. Rest 20% data is utilized for testing the models' predictability for future performance. Goodness of fit is statistically measured by calculating coefficient of determination (R2), normalized root mean square error (NRMSE) and average absolute relative error (AARE). LSSVM exhibits good predictability to forecast the production such as oil recovery, gas recovery as surrogate models. The developed models can be used with high accuracy to forecast the production of oil from ultra-low permeability reservoirs. Quick sensitivity analysis of oil recovery to any parameter used in this study can be performed. The models are also useful for uncertainty analysis of productions.

Reservoir fluid properties PVT such as oil bubble point pressure, oil formation volume factor, solution gas-oil ratio, gas formation volume factor, and gas and oil viscosities are very important in reservoir engineering computations. Perfectly, these properties should be obtained from actual laboratory measurements on samples collected from the bottom of the wellbore or at the surface. Quite often, however, these measurements are either not available, or very costly to obtain. For these reasons, there is the need for a quick and reliable method for predicting the reservoir fluid properties. Recently, Artificial Intelligence (AI) techniques were used comprehensively for this task. This study presents back propagation network (BPN), radial basis functions networks (RBF) and fuzzy logic (FL) techniques for predicting the formation volume factor, bubble point pressure, solution gas-oil ratio, the oil gravity, and the gas specific gravity. These models were developed using 760 data sets collected from published sources. Statistical analysis was performed to see which of these techniques are more reliable and accurate method for predicting the reservoir fluid properties. The new fuzzy logic (FL) models outperform all the previous artificial neural network models and the most common published empirical correlations. The present models provide predictions of the formation volume factor, bubble point pressure, solution gas-oil ratio, the oil gravity and the gas specific gravity with correlation coefficient of 0.9995, 0.9995, 0.9990, 0.9791 and 0.9782, respectively.

Reservoir fluid properties PVT such as oil bubble point pressure, oil formation volume factor, solution gas-oil ratio, gas formation volume factor, and gas and oil viscosities are very important in reservoir engineering computations. Perfectly, these properties should be obtained from actual laboratory measurements on samples collected from the bottom of the wellbore or at the surface. Quite often, however, these measurements are either not available, or very costly to obtain. For these reasons, there is the need for a quick and reliable method for predicting the reservoir fluid properties. Recently, Artificial Intelligence (AI) techniques were used comprehensively for this task. This study presents back propagation network (BPN), radial basis functions networks (RBF) and fuzzy logic (FL) techniques for predicting the formation volume factor, bubble point pressure, solution gas-oil ratio, the oil gravity, and the gas specific gravity. These models were developed using 760 data sets collected from published sources. Statistical analysis was performed to see which of these techniques are more reliable and accurate method for predicting the reservoir fluid properties. The new fuzzy logic (FL) models outperform all the previous artificial neural network models and the most common published empirical correlations. The present models provide predictions of the formation volume factor, bubble point pressure, solution gas-oil ratio, the oil gravity and the gas specific gravity with correlation coefficient of 0.9995, 0.9995, 0.9990, 0.9791 and 0.9782, respectively.

Artificial intelligence (AI) methods and applications have recently gained a great deal of attention in many areas, including fields of mathematics, neuroscience, economics, engineering, linguistics, gaming, and many others. This is due to the surge of innovative and sophisticated AI techniques applications to highly complex problems as well as the powerful new developments in high speed computing. Various applications of AI in everyday life include machine learning, pattern recognition, robotics, data processing and analysis, etc. The oil and gas industry is not behind either, in fact, AI techniques have recently been applied to estimate PVT properties, optimize production, predict recoverable hydrocarbons, optimize well placement using pattern recognition, optimize hydraulic fracture design, and to aid in reservoir characterization efforts. In this study, three different AI models are trained and used to forecast hydrocarbon production from hydraulically fractured wells. Two vastly used artificial intelligence methods, namely the Least Square Support Vector Machine (LSSVM) and the Artificial Neural Networks (ANN), are compared to a traditional curve fitting method known as Response Surface Model (RSM) using second order polynomial equations to determine production from shales. The objective of this work is to further explore the potential of AI in the oil and gas industry. Eight parameters are considered as input factors to build the model: reservoir permeability, initial dissolved gas-oil ratio, rock compressibility, gas relative permeability, slope of gas oil ratio, initial reservoir pressure, flowing bottom hole pressure, and hydraulic fracture spacing. The range of values used for these parameters resemble real field scenarios from prolific shale plays such as the Eagle Ford, Bakken, and the Niobrara in the United States. Production data consists of oil recovery factor and produced gas-oil ratio (GOR) generated from a generic hydraulically fractured reservoir model using a commercial simulator. The Box-Behnken experiment design was used to minimize the number of simulations for this study. Five time-based models (for production periods of 90 days, 1 year, 5 years, 10 years, and 15 years) and one rate-based model (when oil rate drops to 5 bbl/day/fracture) were considered. Particle Swarm Optimization (PSO) routine is used in all three surrogate models to obtain the associated model parameters. Models were trained using 80% of all data generated through simulation while 20% was used for testing of the models. All models were evaluated by measuring the goodness of fit through the coefficient of determination (R2) and the Normalized Root Mean Square Error (NRMSE). Results show that RSM and LSSVM have very accurate oil recovery forecasting capabilities while LSSVM shows the best performance for complex GOR behavior. Furthermore, all surrogate models are shown to serve as reliable proxy reservoir models useful for fast fluid recovery forecasts and sensitivity analyses.

In this paper, we introduce a novel semi-analytical production predictive tool for tight reservoirs. Due to the ultra-low permeabilities observed in unconventional resources such as shales, transient flow has become dominant during most of the productive life of unconventional wells. As a result, traditional reservoir performance analysis such as the conventional material balance have been rendered inapplicable. A new method based on application of material balance on a transient linear flow system is developed. There are several applications of this tool, ranging from production performance evaluation to prediction of hydrocarbon production. The main objective of this work is to clearly introduce a novel method for production evaluation, verify it and show its application using real field data. This method considers two important regions during transient production of oil reservoirs: the saturated region where gas evolves and flows with oil, and the undersaturated region where only oil flows. These regions evolve in extent as pressures diffuse from the fractures into the reservoir while production takes place. First, the proposed semi-analytical method and concept are introduced and validated using numerical simulations. After verification is done, the method is applied to a number of field cases including black and volatile oil examples where production prediction is highlighted. The performance of this novel method is discussed after simulation and field applications. We observed that application of this method on tight reservoirs around the U.S. shows very good forecasting capabilities. Weaknesses of this method are mostly related uncertainty regarding PVT data, relative permeability ratios, and average pressure estimations. There are several production analysis techniques aimed to asses and forecast production from hydraulically fractured tight formations. Most predictive tools in the literature are based on empirical methods that can overlook well frequent and/or prolonged well shut-ins. This method, however, is based on material balance application to several evolving flow zones during production and can accommodate for volatile bottom-hole pressures. We present a method simple enough for quick application on a spreadsheet, but comprehensive enough to capture important multiphase reservoir physics not present in most traditional production analysis.

The prediction of permeability from the information of a well log is a crucial and extensive task that is observed in the earth sciences. The permeability of a reservoir is greatly dependent on the pressure of a rock which is that trait of a rock that determines the ease of flow of fluids (gas or liquid) in that medium to percolate through rocks. When a single fluid totally saturates the porous media, the permeability is characterized as absolute. If the porous medium is occupied by more than one fluid, the permeability is described as effective. Over the recent years, many machine learning approaches have been used for the estimation of permeability of a reservoir which would match with the predefined range of permeability in a reservoir for an accurate and computationally faster result. These approaches involved the application of Genetic Algorithms (GR), Machine Learning Algorithms like Artificial Neural Networks (ANN), Multiple Variable Regression (MVR), Support Vector Machine (SVM), and some other Artificial Intelligence Techniques like Artificial Neuro-Fuzzy Inference System (ANFIS). A succinct review of many advanced machine learning algorithms such as MVR, ANN, SVM, or ANFIS and a few ensemble techniques will be conducted for a survey to predict the permeability of a reservoir over 12 years between 2008 and 2020. The second half of this review concludes that machine learning approaches provide better results, create robust models, and have much more room for improvement than traditional empirical, statistical and basic journal integration methods that are limited and computationally more expensive.

Static Poisson's ratio (1/2static) is a key factor in determine the in-situ stresses in the reservoir section. 1/2static is used to calculate the minimum horizontal stress which will affect the design of the optimum mud widow and the density of cement slurry while drilling. In addition, it also affects the design of the casing setting depth. 1/2static is very important for field development and the incorrect estimation of it may lead to heavy investment decisions. 1/2static can be measured in the lab using a real reservoir cores. The laboratory measurements of 1/2static will take long time and also will increase the overall cost. The goal of this study is to develop accurate models for predicting 1/2static for carbonate reservoirs based on wireline log data using artificial intelligence (AI) techniques. More than 610 core and log data points from carbonate reservoirs were used to train and validate the AI models. The more accurate AI model will be used to generate a new correlation for calculating the 1/2static. The developed artificial neural network (ANN) model yielded more accurate results for estimating 1/2static based on log data; sonic travel times and bulk density compared to adaptive neuro fuzzy inference system (ANFIS) and support vector machine (SVM) methods. The developed empirical equation for 1/2static gave a coefficient of determination (R2) of 0.97 and an average absolute percentage error (AAPE) of 1.13%. The developed technique will help geomechanical engineers to estimate a complete trend of 1/2static without the need for coring and laboratory work and hence will reduce the overall cost of the well.

Rate of penetration (ROP) is the main function that affects drilling operation economically and efficiently. Many theoretical models reported in the literature were produced to predict ROP based on different parameters. Most of these models used only drilling parameters to estimate ROP. Few models have considered the effects of drilling fluid on ROP using a simulated data or a few real field data. Some of the researchers used artificial intelligence to predict ROP by only one method.
The objective of this research is to predict ROP based on both drilling parameters and mud properties such as weight on bit (WOB), rotary speed (RPM), pump flow rate (Q), standpipe pressure (SPP), drilling torque (τ), mud density (MW), plastic viscosity (PV), funnel viscosity (FV), yield point (YP) and solid (%). More than 400 real field data in shale formation are used to predict ROP using support vector machine (SVM) which is a method of artificial intelligence (AI) and compare it with different mathematical models.
The result showed that support vector machine (SVM) technique outperformed all the theoretical equations of ROP by a high margin as shown by a very high correlation coefficient (CC) of 0.997 and a very low average absolute percentage error (AAPE) of 2.83%.

Drilling rate of penetration (ROP) prediction is an enormously important step to optimize drilling controllable parameters. Therefore, numerous efforts have been done in order to present a more precise estimator model that is still ongoing. The results of the literature review indicated that, between the two approaches followed for ROP modeling, namely physic-based models and data-driven methods, the use of the data-driven methods has grown significantly. The literature review made two points clear: (1) the geomechanical parameters were not considered adequately, and (2) no previous research had applied a combination of least-squares support-vector machines (LSSVM) with cuckoo optimization algorithm (COA), particle swarm optimization (PSO), and genetic algorithms (GA). This led us to use hybrid algorithms for ROP modeling at vertical wells drilled in the southwestern Iran. For this purpose, mud logging parameters (including depth (Depth), mud density (MD), torque (Tor), standpipe pressure (SPP), equivalent circulating density (ECD), weight on bit (WOB), revolutions per minute (RPM), flow rate (FR), and ROP) and geomechanical parameters (including gamma ray (GR), porosity (NPHI), density (RHOB), and uniaxial compressive strength (UCS)) were collected along the studied wells. Histogram analysis and pairwise evaluation of the studied features indicated the presence of outliers among the data points. Accordingly, the Tukey's method was used to omit the outliers. Subsequently, the most relevant features in the ROP prediction were selected using a combination of the non-dominated sorting genetic algorithm II (NSGA-II) with multilayer perceptron (MLP) neural network. The results showed that one could attenuate the modeling error by increasing the number of input parameters into the ROP estimation model. However, the improvement was very subtle when the number of input parameters exceeded six. Therefore, six parameters (UCS, FR, WOB, Depth, MD, and RPM) were used for ROP modeling using LSSVM-COA, LSSVM-PSO, and LSSVM-GA hybrid algorithms. Results of applying these hybrid algorithms indicated that the LSSVM-COA outperformed the other two algorithms in terms of accuracy and the coefficient of determination. In a next step, the LSSVM-COA was trained on both the outlier-omitted and raw datasets, indicating the important role of the outlier omission step in achieving a highly accurate and reliable model. Continuing with the work, in order to evaluate the performance of the LSSVM-COA hybrid model, the model was compared to support-vector regression (SVR)-COA, MLP-COA, Motahhari's, linear multivariate regression (LMR), and nonlinear multivariate regression (NLMR) models. The results confirmed superior accuracy of the LSSVM-COA model over the examined models. The small difference between the obtained levels of error in the training and testing stages with the LSSVM-COA model, as compared to the other models, revealed that the model can be used to predict the ROP at other wells across the field reliably and accurately provided the model be developed with larger sets of data across the field. Predicting ROP with high accuracy at the test Well clearly proved this claim.

A novel semi‐analytical production predictive tool for tight reservoirs based on the application of material balance on a transient linear flow system is developed in this paper. This method considers two important regions during transient production of oil reservoirs: the saturated region where gas evolves and flows with oil, and the undersaturated region where only oil flows. A zonal moving boundary approach is used to evolve the two regions as the reservoir pressure gradually decreases. A semi‐analytical method is used to calculate pressures in the various regions and volumetric expansions. For both black oil and volatile oil scenarios, calculations from this analytical framework are able to match reservoir pressures, oil and gas rates, and cumulative gas‐oil ratios determined using a reservoir simulator. The model was also applied to wells in tight reservoirs around the U.S. such as the Bakken (North Dakota) and the Eagle Ford (Texas) with reasonable success. This article is protected by copyright. All rights reserved.

Physical properties of pure components of oil such as critical compressibility, critical volume, critical temperature, critical pressure, molecular weight, specific gravity and standard boiling point are very important in compositional reservoir simulation. Perfectly, these properties should be obtained from actual laboratory measurements on samples collected from the bottom of the wellbore or at the surface. Quite often, however, these measurements are either not available, or very costly to obtain. For these reasons, there is a need for a quick and reliable method for predicting the physical properties of these components.
This study presents both back propagation network and fuzzy logic techniques for predicting critical compressibility, critical temperature, and critical pressure. The models were developed using 120 data sets collected from different published sources. These data were divided into two groups: the first was used to train the Artificial Intelligence models and the second was used to test the models to evaluate their accuracy and trend stability. Using the average percent relative error, average absolute percent relative error, minimum and maximum absolute percent relative error, root mean square error, and the correlation coefficient as criteria to evaluate the performance and accuracy of the new models. The present models provide predictions of the critical compressibility, critical temperature, and critical pressure with correlation coefficient of one for all models.

In the oil and natural gas industry, artificial intelligence (AI) technology has penetrated into all links from exploration and development to construction sites. This paper investigates the application of artificial intelligence in each link of oil reservoir. It is found in investigation that each algorithm plays a different and important role at each stage and every link of oil accumulation development cannot leave the cooperation of artificial intelligence. But, the application of AI is mostly scattered, forming a physical isolation, a lot of single information-island. This situation increases the communication cost of cross-departmental data cooperation and the repetitive screening and recognition work has seriously affected work efficiency. To address unsolved problems with the current application of AI, AI-based geo-engineering integration in unconventional oil and gas are proposed this article considers. Integrate data islands, and realize internal resource sharing, treat exploration and development as an organic whole, extend exploration to development. This article takes the well factory operation mode, meanwhile, the real-time synchronization and coordination of all links has been fully realized. This kind of integration of geology and engineering is helpful to realize coordination and cooperation at all levels, regions, and disciplines, effectively benefiting development of unconventional oil and gas reservoirs.

Lithologies are significant indicators to get deep insight of depositional and mineralogical properties of target formations, and the classic approach of achieving them is crossplot. Nonetheless, crossplot presents ineffectively when addressing classification of tight sandstone reservoirs, since most primary lithological components are characterized by similar logging responses. LightGBM (light gradient boosting machine) has been proved powerful to produce a remarkable classification, while its performance is seriously limited by the setting of hyper-parameters. LD-AFSA (linear decreasing-artificial fish swarm algorithm), an excellent solver for multi-objective optimization, then is introduced to modify the setting in a best circumstance. Besides, another integration for LightGBM is CRBM (continuous restricted Boltzmann machine), which specializes in generating less variables to speed up calculation. Consequently, a data-driven lithology predictor based on new ensemble learning is proposed, named CRBM-LD-AFSA-LightGBM. Data for validation of new predictor is cored by wells of Chang 4 + 5 member, Jiyuan Oilfield, Ordos Basin, and accordingly four experiments are designed to make a comprehensive evaluation. To highlight validating effect, SVM (support vector machine) and XGBoost (extreme gradient boosting) are adopted as competitors. Through comparison of experimental results, including prediction accuracy, F1-score, and AUC (area under curve), it is figured out that XGBoost-cored and LightGBM-cored predictors have capabilities to produce similar while more reliable results, meanwhile also exhibiting better generalization on prediction, but the computing time of latter predictor is only 1/25 shorter than that of the former. The results well demonstrate the proposed predictor plays a real high-efficient role in predicting lithologies and is deserved to receive a widespread employment in the field of logging interpretation because of its greater applicability.

Calculation of water influx into petroleum reservoir is a tedious evaluation with significant reservoir engineering applications. The classical approach developed by van Everdingen–Hurst (vEH) based on diffusivity equation solution had been the fulcrum for water influx calculation in both finite and infinite-acting aquifers. The vEH model for edge-water drive reservoirs was modified by Allard and Chen for bottom-water drive reservoirs. Regrettably, these models solution variables: dimensionless influx (WeD) and dimensionless pressure (PD) were presented in tabular form. In most cases, table look-up and interpolation between time entries are necessary to determine these variables, which makes the vEH approach tedious for water influx estimation. In this study, artificial neural network (ANN) models to predict the reservoir-aquifer variables WeD and PD was developed based on the vEH datasets for the edge- and bottom-water finite and infinite-acting aquifers. The overall performance of the developed ANN models correlation coefficients (R) was 0.99983 and 0.99978 for the edge- and bottom-water finite aquifer, while edge- and bottom-water infinite-acting aquifer was 0.99992 and 0.99997, respectively. With new datasets, the generalization capacities of the developed models were evaluated using statistical tools: coefficient of determination (R²), R, mean square error (MSE), root-mean-square error (RMSE) and absolute average relative error (AARE). Comparing the developed finite aquifer models predicted WeD with Lagrangian interpolation approach resulted in R², R, MSE, RMSE and AARE of 0.9984, 0.9992, 0.3496, 0.5913 and 0.2414 for edge-water drive and 0.9993, 0.9996, 0.1863, 0.4316 and 0.2215 for bottom-water drive. Also, infinite-acting aquifer models (Model-1) resulted in R², R, MSE, RMSE and AARE of 0.9999, 0.9999, 0.5447, 0.7380 and 0.2329 for edge-water drive, while bottom-water drive had 0.9999, 0.9999, 0.2299, 0.4795 and 0.1282. Again, the edge-water infinite-acting model predicted WeD and Edwardson et al. polynomial estimated WeD resulted in the R² value of 0.9996, R of 0.9998, MSE of 4.740 × 10–4, RMSE of 0.0218 and AARE of 0.0147. Furthermore, the developed ANN models generalization performance was compared with some models for estimating PD. The results obtained for finite aquifer model showed the statistical measures: R², R, MSE, RMSE and AARE of 0.9985, 0.9993, 0.0125, 0.1117 and 0.0678 with Chatas model and 0.9863, 0.9931, 0.1411, 0.3756 and 0.2310 with Fanchi equation. The infinite-acting aquifer model had 0.9999, 0.9999, 0.1750, 0.0133 and 7.333 × 10–3 with Edwardson et al. polynomial, then 0.9865, 09,933, 0.0143, 0.1194 and 0.0831 with Lee model and 0.9991, 0.9996, 1.079 × 10–3, 0.0328 and 0.0282 with Fanchi model. Therefore, the developed ANN models can predict WeD and PD for the various aquifer sizes provided by vEH datasets for water influx calculation.

In highly heterogeneous reservoirs classical characterization methods often fail to detect the location and orientation of the fractures. Recent applications of Artificial Intelligence to the area of reservoir characterization have made this challenge a possible practice. Such a practice consists of seeking the complex relationship between the fracture index and some geological and geomechanical drivers (facies, porosity, permeability, bed thickness, proximity to faults, slopes and curvatures of the structure) in order to obtain a fracture intensity map using Fuzzy Logic and Neural Network.

Reservoir characterization especially well log data analysis plays an important role in petroleum exploration. This is the process used to identify the potential for oil production at a given source. In recent years, support vector machines (SVMs) have gained much attention as a result of its strong theoretical background. SVM is based on statistical learning theory known as the Vapnik-Chervonenkis theory. The theory has a strong mathematical foundation for dependencies estimation and predictive learning from finite data sets. This paper presents investigation on the use of SVM in reservoir characterization. Initial results show that SVM can be an alternative intelligent technique for reservoir characterization.

This paper proposes unconstrained functional networks as a new classifier to deal with the pattern recognition problems. Both methodology and learning algorithm for this kind of computational intelligence classifier using the iterative least squares optimization criterion are derived. The performance of this new intelligent systems scheme is demonstrated and examined using real-world applications. A comparative study with the most common classification algorithms in both machine learning and statistics communities is carried out. The study was achieved with only sets of second-order linearly independent polynomial functions to approximate the neuron functions. The results show that this new framework classifier is reliable, flexible, stable, and achieves a high-quality performance

A hybrid computational intelligence model, integrating the least-squares fitting algorithm of Functional Networks with Type-2 Fuzzy Logic System, is presented. The hybrid model capitalizes on the capability of the least-squares fitting algorithm to reduce the dimensionality of input data while selecting the dominant variables. The model was evaluated with the prediction of porosity and permeability of oil and gas reservoirs. The model attempts to improve the performance of Type-2 Fuzzy Logic whose complexity is increased and performance degraded with increased dimensionality of input data. The Functional Networks block was used to select the dominant variables from the six core and log datasets. The dimensionally-reduced datasets were then divided into training and testing subsets using the stratified sampling approach. Hence, the Type-2 Fuzzy Logic block is trained and tested with the best and dimensionally-reduced variables from the input data. The results showed that the Functional Networks-Type-2 Fuzzy Logic hybrid model performed better in terms of training and testing with higher correlation coefficients, lower root mean square errors and reduced execution times than the original Type-2 Fuzzy Logic system. The success of this work has confirmed the bright prospect for the implementation of more hybrid models with better performance indices.

Petroleum reservoir characterization is a process for quantitatively describing various reservoir properties in spatial variability using all the available field data. Porosity and permeability are the two fundamental reservoir properties which relate to the amount of fluid contained in a reservoir and its ability to flow. These properties have a significant impact on petroleum fields operations and reservoir management. In un-cored intervals and well of heterogeneous formation, porosity and permeability estimation from conventional well logs has a difficult and complex problem to solve by statistical methods. This paper suggests an intelligent technique using fuzzy logic and neural network to determine reservoir properties from well logs. Fuzzy curve analysis based on fuzzy logic is used for selecting the best related well logs with core porosity and permeability data. Neural network is used as a nonlinear regression method to develop transformation between the selected well logs and core measurements. The technique is demonstrated with an application to the well data in offshore Korea. The results show that the technique can make more accurate and reliable reservoir properties estimation compared with conventional computing methods. This intelligent technique can be utilized as a powerful tool for reservoir properties estimation from well logs in oil and natural gas development projects.

Permeability is a key parameter associated with the characterization of any hydrocarbon reservoir. In fact, it is not possible to have accurate solutions to many petroleum engineering problems without having accurate permeability value. Attempts have been made to utilize artificial neural networks (ANNs) for identification of the relationship which may exist between the well log data and core permeability. Despite of the wide range of applications and flexibility of ANNs, there is still no general framework or procedure through which the appropriate network for a specific task can be designed. Design and structural optimization of neural networks is still strongly dependent upon the designer's experience. This is an obvious barrier to the wider applications of neural network. To mitigate this problem, a new method for the auto-design of neural networks was used, based on genetic algorithm (GA). The new proposed method was evaluated by a case study in South Pars gas field in Persian Gulf. Design of topology and parameters of the neural networks as decision variables was done first by trial and error, and then using genetic algorithms in order to improve the effectiveness of forecasting when ANN is applied to a permeability predicting problem from well logs.

Functional networks were recently introduced as an extension of artificial neural networks (ANNs). Unlike ANNs, they estimate unknown neuron functions from given functional families during the training process. Here, we applied two types of functional network models, separable and associativity functional networks, to forecast river flows for different lead-times. We compared them with a conventional artificial neural network model, an ARMA model and a simple baseline model in three catchments. Results show that functional networks are flexible and comparable in performance to artificial neural networks. In addition, they are easier and quicker to train and so are useful tools as an alternative to artificial neural networks. These results were obtained with only the simplest structures of functional networks and it is possible that a more detailed study with more complex forms of the model will improve even further on these results. Thus we recommend that the use of functional networks in discharge time series modelling and forecasting should be further investigated.

Petrographic data collected during thin section analysis can be invaluable for understanding the factors that control permeability distribution. Reliable prediction of permeability is important for reservoir characterization. The petrographic elements (mineralogy, porosity types, cements and clays, and pore morphology) interact with each other uniquely to generate a specific permeability distribution. It is difficult to quantify accurately this interaction and its consequent effect on permeability, emphasizing the non-linear nature of the process. To capture these non-linear interactions, neural networks were used to predict permeability from petrographic data. The neural net was used as a multivariate correlative tool because of its ability to learn the non-linear relationships between multiple input and output variables. The study was conducted on the upper Queen formation called the Shattuck Member (Permian age). The Shattuck Member is composed of very fine-grained arkosic sandstone. The core samples were available from the Sulimar Queen and South Lucky Lake fields located in Chaves County, New Mexico.

This paper introduces a new neural-fuzzy technique combined with genetic algorithms in the prediction of permeability in petroleum reservoirs. The methodology involves the use of neural networks to generate membership functions and to approximate permeability automatically from digitized data (well logs) obtained from oil wells. The trained networks are used as fuzzy rules and hyper-surface membership functions. The results of these rules are interpolated based on the membership grades and the parameters in the defuzzification operators which are optimized by genetic algorithms. The use of the integrated methodology is demonstrated via a case study in a petroleum reservoir in offshore Western Australia. The results show that the integrated neural-fuzzy-genetic-algorithm (INFUGA) gives the smallest error on the unseen data when compared to similar algorithms. The INFUGA algorithm is expected to provide a significant improvement when the unseen data come from a mixed or complex distribution.

Least squares support vector machine (LS-SVM) is a successful method for classification or regression problems, in which the margin and sum square errors (SSEs) on training samples are simultaneously minimized. However, LS-SVM only considers the SSEs of input variable. In this paper, a novel normal least squares support vector machine (NLS-SVM) is proposed, which effectively considers the noises on both input and response variables. It introduces a two-stage learning method to solve NLS-SVM. More importantly, a fast iterative updating algorithm is presented, which reaches the solution of NLS-SVM with lower computational complexity instead of directly adopting the two-stage learning method. Several experiments on artificial and real-world datasets are simulated, in which the results show that NLS-SVM outperforms LS-SVM.

The hybridization of two or more Computational Intelligence (CI) techniques to build a single model has increased in popularity over the recent years. Such models that combine the best properties of different Artificial Intelligence (AI) techniques in a single package are very much required in the process of reservoir characterization in petroleum engineering, where a high degree of prediction accuracy is essential for efficient exploration, and management of oil and gas resources. In this paper, we have successfully predicted, with higher accuracy, the porosity and permeability of oil and gas reservoirs through the hybridization of Type-2 Fuzzy Logic (FL), Support Vector Machines (SVM) and Functional Networks (FN), using several real-life well log data. While utilizing the capabilities of data mining and CI, two hybrid models (FFS and FSF) were built. In both models, FN, using its functional approximation capability with least-square fitting algorithm, was used to select the best of the predictor variables from the input data. In the FFS model, the selected predictor variables were passed to Type-2 FL to remove uncertainties in the data (if any), and then to SVM for training and making final predictions. In the FSF model, the best predictor variables from FN were passed to SVM to transform them to a feature space, and then passed to Type-2 FL to remove uncertainties (if any), extract inference rules and make final predictions. The results showed that the hybrid models, with their higher correlation coefficients, performed better than the individual techniques when used separately with the same datasets. An extended study, used as a benchmark, showed that the hybrid models also performed better than a hybridization of only two of the techniques viz. Type-2 FL and SVM, both in terms of higher correlation coefficients and lower execution times. This was attributed to the role of FN in selecting the best variables and reducing the dimensionality of input data in the FFS and FSF models.

As a new method, support vector machine (SVM) were applied for prediction of toxicity of different data sets compared with other two common methods, multiple linear regression (MLR) and RBFNN. Quantitative structure-activity relationships (QSAR) models based on calculated molecular descriptors have been clearly established. Among them, SVM model gave the highest q(2) and correlation coefficient R. It indicates that the SVM performed better generalization ability than the MLR and RBFNN methods, especially in the test set and the whole data set. This eventually leads to better generalization than neural networks, which implement the empirical risk minimization principle and may not converge to global solutions. We would expect SVM method as a powerful tool for the prediction of molecular properties.

How Small is a " Small " Data? Presented at the 2nd Saudi Conference on Oil and Gas Exploration and Production Technologies

- F Anifowose
- A Abdulraheem

Anifowose, F., and Abdulraheem, A. 2010b. How Small is a " Small " Data? Presented at the 2nd Saudi Conference on Oil and Gas
Exploration and Production Technologies (OGEP 2010), Dhahran, Saudi Arabia, 18-20 December.

Neural Networks: A New Tool for the Petroleum Industry. Paper SPE 27561 presented at the 1994 European Petroleum Computer Conference

- J K Ali

Ali, J.K. 1994. Neural Networks: A New Tool for the Petroleum Industry. Paper SPE 27561 presented at the 1994 European Petroleum
Computer Conference, Aberdeen, U.K., March 15-17.

Excellence in Educational Development Available online

- Schlumberger Glossary

Schlumberger Glossary. 2007a. Excellence in Educational Development, Science Lab Project, Available online,
http://www.seed.slb.com/en/scictr/lab/porosity/index.htm, Accessed on August 3, 2011.

Prediction of Crude Oil Viscosity and Gas/Oil Ratio Curves Using Recent Advances to Neural Networks. Paper SPE 125360-MS presented at the SPE/EAGE Reservoir Characterization and Simulation Conference

- M A Oloso
- A Khoukhi
- A Abdulraheem
- M Elshafei

Oloso, M.A., Khoukhi, A., Abdulraheem A., and Elshafei, M. 2010. Prediction of Crude Oil Viscosity and Gas/Oil Ratio Curves Using
Recent Advances to Neural Networks. Paper SPE 125360-MS presented at the SPE/EAGE Reservoir Characterization and Simulation
Conference, Abu Dhabi, UAE, 19–21 October.