Average Absolute Percent Relative Error Research Articles

Modeling liquid rate through wellhead chokes using machine learning techniques

Precise measurement and prediction of the fluid flow rates in production wells are crucial for anticipating the production volume and hydrocarbon recovery and creating a steady and controllable flow regime in such wells. This study suggests two approaches to predict the flow rate through wellhead chokes. The first is a data-driven approach using different methods, namely: Adaptive boosting support vector regression (Adaboost-SVR), multivariate adaptive regression spline (MARS), radial basis function (RBF), and multilayer perceptron (MLP) with three algorithms: Levenberg–Marquardt (LM), bayesian-regularization (BR), and scaled conjugate gradient (SCG). The second is a developed correlation that depends on wellhead pressure (Pwh), gas-to-liquid ratio (GLR), and choke size (Dc). A dataset of 565 data points is available for model development. The performance of the two suggested approaches is compared with earlier correlations. Results revealed that the proposed models outperform the existing ones, with the Adaboost-SVR model showing the best performance with an average absolute percent relative error (AAPRE) of 5.15% and a correlation coefficient of 0.9784. Additionally, the results indicated that the developed correlation resulted in better predictions compared to the earlier ones. Furthermore, a sensitivity analysis of the input variable was also investigated in this study and revealed that the choke size variable had the most significant effect, while the Pwh and GLR showed a slight effect on the liquid rate. Eventually, the leverage approach showed that only 2.1% of the data points were in the suspicious range.

Modeling apparent viscosity of waxy crude oils doped with polymers using tree-based models, radial basis function neural networks, and Gaussian process regression

The probability of wax precipitation increases as temperature decreases and this happens during the flow of crude oil from a high temperature reservoir to the cool surface facilities. The present work aims to evaluate the apparent viscosity of waxy crude oils in two conditions: without presence of polymers and doped with them. To reach this purpose, a comprehensive databank consists of 622 actual values of waxy crude oils’ apparent viscosity were gathered. Various intelligent networks including Radial Basis Function (RBF) coupled with three algorithms, namely Teaching-Learning Based Optimizer (TLBO), Marine Predators Algorithm (MPA), and Barnacles Mating Optimizer (BMO), Decision Tree (DT), Random Forest (RF), Extra Tree (ET), and Gaussian Process Regression (GPR) were trained to predict waxy crude oil viscosity values. According to the findings, the GPR model demonstrates exemplary performance and offers forecasts with the minimum average absolute percent relative error (AAPRE = 0.30 %), the highest coefficient of determination (R2 = 0.999), and the lowest standard deviation (SD = 0.011). The accuracy of the other models was also acceptable and overall, tree-based techniques (except ET) and GPR provided better results than RBF coupled with different optimizers. Ultimately, the Leverage method was applied to identify the suspected dataset utilizing outlier detection. The outlier discovery represented that majority of data points, which were used for modeling in this paper, are statistically valid and trustworthy.

On the Evaluation of Coal Strength Alteration Induced by CO2 Injection Using Advanced Black-Box and White-Box Machine Learning Algorithms

Summary The injection of carbon dioxide (CO2) into coal seams is a prominent technique that can provide carbon sequestration in addition to enhancing coalbed methane extraction. However, CO2 injection into the coal seams can alter the coal strength properties and their long-term integrity. In this work, the strength alteration of coals induced by CO2 exposure was modeled using 147 laboratory-measured unconfined compressive strength (UCS) data points and considering CO2 saturation pressure, CO2 interaction temperature, CO2 interaction time, and coal rank as input variables. Advanced white-box and black-box machine learning algorithms including Gaussian process regression (GPR) with rational quadratic kernel, extreme gradient boosting (XGBoost), categorical boosting (CatBoost), adaptive boosting decision tree (AdaBoost-DT), multivariate adaptive regression splines (MARS), K-nearest neighbor (KNN), gene expression programming (GEP), and group method of data handling (GMDH) were used in the modeling process. The results demonstrated that GPR-Rational Quadratic provided the most accurate estimates of UCS of coals having 3.53%, 3.62%, and 3.55% for the average absolute percent relative error (AAPRE) values of the train, test, and total data sets, respectively. Also, the overall determination coefficient (R2) value of 0.9979 was additional proof of the excellent accuracy of this model compared with other models. Moreover, the first mathematical correlations to estimate the change in coal strength induced by CO2 exposure were established in this work by the GMDH and GEP algorithms with acceptable accuracy. Sensitivity analysis revealed that the Spearman correlation coefficient shows the relative importance of the input parameters on the coal strength better than the Pearson correlation coefficient. Among the inputs, coal rank had the greatest influence on the coal strength (strong nonlinear relationship) based on the Spearman correlation coefficient. After that, CO2 interaction time and CO2 saturation pressure have shown relatively strong nonlinear relationships with model output, respectively. The CO2 interaction temperature had the smallest impact on coal strength alteration induced by CO2 exposure based on both Pearson and Spearman correlation coefficients. Finally, the leverage technique revealed that the laboratory database used for modeling CO2-induced strength alteration of coals was highly reliable, and the suggested GPR-Rational Quadratic model and GMDH correlation could be applied for predicting the UCS of coals exposed to CO2 with high statistical accuracy and reliability.

Employing ensemble machine learning techniques for predicting the thermohydraulic performance of double pipe heat exchanger with and without turbulators

In this study, advanced machine learning techniques were utilized to forecast the thermohydraulic performance of a double pipe heat exchanger (DPHE). Key variables, including friction factor (f), Nusselt number (Nu), effectiveness (ɛ), and number transfer units (NTU), were modeled as functions of Reynolds number (Re), the number of turbulators (N), and the length of turbulators (L). To predict the DPHE's thermohydraulic performance, datasets were gathered from real-time experiments (case-1 and case-2) and literature (case-3). For clarity and analytical purposes, case-1 and case-2 were dimensioned to match the specifications outlined in literature (case-3). Case-1 represented a conventional DPHE without turbulators, while case-2 involved a DPHE with a gear disc turbulator. Additionally, datasets for DPHE with dolphin ring turbulators (case-3) were obtained for validation from literature. Subsequently, two ensemble boosting algorithms (extreme gradient and categorical) and one bagging algorithm (random forest) were applied to the dataset. The results highlighted that the categorical boosting model exhibited the highest accuracy, achieving a coefficient of determination (R2) of 0.9987 and an average absolute percent relative error (AAPRE) of 0.1837%. Furthermore, a sensitivity analysis was conducted for the best model (Random Forest), revealing relationships between input and output parameters. The Leverage statistical technique was also employed to identify valid, outlier, and out-of-range data points.

Toward empirical correlations for estimating the specific heat capacity of nanofluids utilizing GRG, GP, GEP, and GMDH

When nanoparticles are dispersed and stabilized in a base-fluid, the resulting nanofluid undergoes considerable changes in its thermophysical properties, which can have a substantial influence on the performance of nanofluid-flow systems. With such necessity and importance, developing a set of mathematical correlations to identify these properties in various conditions can greatly eliminate costly and time-consuming experimental tests. Hence, the current study aims to develop innovative correlations for estimating the specific heat capacity of mono-nanofluids. The accurate estimation of this crucial property can result in the development of more efficient and effective thermal systems, such as heat exchangers, solar collectors, microchannel cooling systems, etc. In this regard, four powerful soft-computing techniques were considered, including Generalized Reduced Gradient (GRG), Genetic Programming (GP), Gene Expression Programming (GEP), and Group Method of Data Handling (GMDH). These techniques were implemented on 2084 experimental data-points, corresponding to ten different kinds of nanoparticles and six different kinds of base-fluids, collected from previous research sources. Eventually, four distinct correlations with high accuracy were provided, and their outputs were compared to three correlations that had previously been published by other researchers. These novel correlations are applicable to various oxide-based mono-nanofluids for a broad range of independent variable values. The superiority of newly developed correlations was proven through various statistical and graphical error analyses. The GMDH-based correlation revealed the best performance with an Average Absolute Percent Relative Error (AAPRE) of 2.4163% and a Coefficient of Determination (R2) of 0.9743. At last, a leverage statistical approach was employed to identify the GMDH technique’s application domain and outlier data, and also, a sensitivity analysis was carried out to clarify the degree of dependence between input and output variables.

Estimation of the flow rate of pyrolysis gasoline, ethylene, and propylene in an industrial olefin plant using machine learning approaches

Light olefins, as the backbone of the chemical and petrochemical industries, are produced mainly via steam cracking route. Prediction the of effects of operating variables on the product yield distribution through the mechanistic approaches is complex and requires long time. While increasing in the industrial automation and the availability of the high throughput data, the machine learning approaches have gained much attention due to the simplicity and less required computational efforts. In this study, the potential capability of four powerful machine learning models, i.e., Multilayer perceptron (MLP) neural network, adaptive boosting-support vector regression (AdaBoost-SVR), recurrent neural network (RNN), and deep belief network (DBN) was investigated to predict the product distribution of an olefin plant in industrial scale. In this regard, an extensive data set including 1184 actual data points were gathered during four successive years under various practical conditions. 24 varying independent parameters, including flow rates of different feedstock, numbers of active furnaces, and coil outlet temperatures, were chosen as the input variables of the models and the outputs were the flow rates of the main products, i.e., pyrolysis gasoline, ethylene, and propylene. The accuracy of the models was assessed by different statistical techniques. Based on the obtained results, the RNN model accurately predicted the main product flow rates with average absolute percent relative error (AAPRE) and determination coefficient (R2) values of 1.94% and 0.97, 1.29% and 0.99, 0.70% and 0.99 for pyrolysis gasoline, propylene, and ethylene, respectively. The influence of the various parameters on the products flow rate (estimated by the RNN model) was studied by the relevancy factor calculation. Accordingly, the number of furnaces in service and the flow rates of some feedstock had more positive impacts on the outputs. In addition, the effects of different operating conditions on the propylene/ethylene (P/E) ratio as a cracking severity factor were also discussed. This research proved that intelligent approaches, despite being simple and straightforward, can predict complex unit performance. Thus, they can be efficiently utilized to control and optimize different industrial-scale units.

Modeling of the Sintered Density in Cu-Al Alloy Using Machine Learning Approaches.

In powder metallurgy materials, sintered density in Cu-Al alloy plays a critical role in detecting mechanical properties. Experimental measurement of this property is costly and time-consuming. In this study, adaptive boosting decision tree, support vector regression, k-nearest neighbors, extreme gradient boosting, and four multilayer perceptron (MLP) models tuned by resilient backpropagation, Levenberg-Marquardt (LM), scaled conjugate gradient, and Bayesian regularization were employed for predicting powder densification through sintering. Yield strength, Young's modulus, volume variation caused by the phase transformation, hardness, liquid volume, liquidus temperature, the solubility ratio among the liquid phase and the solid phase, sintered temperature, solidus temperature, sintered atmosphere, holding time, compaction pressure, particle size, and specific shape factor were regarded as the input parameters of the suggested models. The cross plot, error distribution curve, and cumulative frequency diagram as graphical tools and average percent relative error (APRE), average absolute percent relative error (AAPRE), root mean square error (RMSE), standard deviation (SD), and coefficient of correlation (R) as the statistical evaluations were utilized to estimate the models' accuracy. All of the developed models were compared with preexisting approaches, and the results exhibited that the developed models in the present work are more precise and valid than the existing ones. The designed MLP-LM model was found to be the most precise approach with AAPRE = 1.292%, APRE = -0.032%, SD = 0.020, RMSE = 0.016, and R = 0.989. Lately, outlier detection was applied performing the leverage technique to detect the suspected data points. The outlier detection discovered that few points are located out of the applicability domain of the proposed MLP-LM model.

Insights into modeling refractive index of ionic liquids using chemical structure-based machine learning methods

Ionic liquids (ILs) have drawn much attention due to their extensive applications and environment-friendly nature. Refractive index prediction is valuable for ILs quality control and property characterization. This paper aims to predict refractive indices of pure ILs and identify factors influencing refractive index changes. Six chemical structure-based machine learning models called eXtreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Categorical Boosting (CatBoost), Convolutional Neural Network (CNN), Adaptive Boosting-Decision Tree (Ada-DT), and Adaptive Boosting-Support Vector Machine (Ada-SVM) were developed to achieve this goal. An enormous dataset containing 6098 data points of 483 different ILs was exploited to train the machine learning models. Each data point’s chemical substructures, temperature, and wavelength were considered for the models’ inputs. Including wavelength as input is unprecedented among predictions done by machine learning methods. The results show that the best model was CatBoost, followed by XGBoost, LightGBM, Ada-DT, CNN, and Ada-SVM. The R2 and average absolute percent relative error (AAPRE) of the best model were 0.9973 and 0.0545, respectively. Comparing this study’s models with the literature shows two advantages regarding the dataset’s abundance and prediction accuracy. This study also reveals that the presence of the –F substructure in an ionic liquid has the most influence on its refractive index among all inputs. It was also found that the refractive index of imidazolium-based ILs increases with increasing alkyl chain length. In conclusion, chemical structure-based machine learning methods provide promising insights into predicting the refractive index of ILs in terms of accuracy and comprehensiveness.

Pore structure evolution of Qingshankou shale (kerogen type I) during artificial maturation via hydrous and anhydrous pyrolysis: Experimental study and intelligent modeling

In this study, alterations in the pore structure of the Qingshankou shale during hydrous and anhydrous pyrolysis (HP and AHP) over wide ranges of temperature (300–450 °C) were studied to elucidate the role of water. Mineralogy of the original shale sample along with geochemical properties and pore structure after each step of artificial thermal maturation were analyzed using X-ray diffraction (XRD), Rock-Eval pyrolysis, and N2 adsorption, respectively. Complexity of pore structure was assessed via fractal dimension analysis followed by delineating different pore families in the samples' PSD curves. Next, four common artificial neural networks (ANNs) models were implemented along with Bayesian regularization (BR) and Levenberg-Marquardt (LM) optimization algorithms to model the N2 adsorption/desorption volume as thermal maturity progressed. Results showed that all samples represent Type IV hysteresis loop while the amount of N2 adsorption during HP was much higher than that of the AHP revealing the importance of water. Overall, the complexity of AHP samples’ pore structure was less than that of the HP since the count of pores with smaller pore width was reduced more during thermal progression. Deconvolution analysis showed that the original sample has eight pore families (7 in mesopore and 1 in the macropore range), while pore families with larger mean pore width were formed and expanded and pore families with smaller mean pore width were eliminated as thermal maturation progressed in both HP and AHP. Moreover, the average absolute percent relative error (AAPRE) of 3.74% for the entire data inferred that generalized regression neural network (GRNN) model was superior for the estimation of N2 volume adsorbed and desorbed. Finally, sensitivity analysis revealed that the relative pressure and pyrolysis method (AHP or HP) respectively had the strongest linear and non-linear relationships with the N2 adsorption/desorption volume. Collectively, this case confirmed the role that water plays in the evolution of pore structures throughout thermal maturation, which could be even more significant than temperature.

Compositional modeling of gas-condensate viscosity using ensemble approach

In gas-condensate reservoirs, liquid dropout occurs by reducing the pressure below the dew point pressure in the area near the wellbore. Estimation of production rate in these reservoirs is important. This goal is possible if the amount of viscosity of the liquids released below the dew point is available. In this study, the most comprehensive database related to the viscosity of gas condensate, including 1370 laboratory data was used. Several intelligent techniques, including Ensemble methods, support vector regression (SVR), K-nearest neighbors (KNN), Radial basis function (RBF), and Multilayer Perceptron (MLP) optimized by Bayesian Regularization and Levenberg–Marquardt were applied for modeling. In models presented in the literature, one of the input parameters for the development of the models is solution gas oil ratio (Rs). Measuring Rs in wellhead requires special equipment and is somewhat difficult. Also, measuring this parameter in the laboratory requires spending time and money. According to the mentioned cases, in this research, unlike the research done in the literature, Rs parameter was not used to develop the models. The input parameters for the development of the models presented in this research were temperature, pressure and condensate composition. The data used includes a wide range of temperature and pressure, and the models presented in this research are the most accurate models to date for predicting the condensate viscosity. Using the mentioned intelligent approaches, precise compositional models were presented to predict the viscosity of gas/condensate at different temperatures and pressures for different gas components. Ensemble method with an average absolute percent relative error (AAPRE) of 4.83% was obtained as the most accurate model. Moreover, the AAPRE values for SVR, KNN, MLP-BR, MLP-LM, and RBF models developed in this study are 4.95%, 5.45%, 6.56%, 7.89%, and 10.9%, respectively. Then, the effect of input parameters on the viscosity of the condensate was determined by the relevancy factor using the results of the Ensemble methods. The most negative and positive effects of parameters on the gas condensate viscosity were related to the reservoir temperature and the mole fraction of C11, respectively. Finally, suspicious laboratory data were determined and reported using the leverage technique.

Modeling of H2S solubility in ionic liquids: comparison of white-box machine learning, deep learning and ensemble learning approaches

In the context of gas processing and carbon sequestration, an adequate understanding of the solubility of acid gases in ionic liquids (ILs) under various thermodynamic circumstances is crucial. A poisonous, combustible, and acidic gas that can cause environmental damage is hydrogen sulfide (H2S). ILs are good choices for appropriate solvents in gas separation procedures. In this work, a variety of machine learning techniques, such as white-box machine learning, deep learning, and ensemble learning, were established to determine the solubility of H2S in ILs. The white-box models are group method of data handling (GMDH) and genetic programming (GP), the deep learning approach is deep belief network (DBN) and extreme gradient boosting (XGBoost) was selected as an ensemble approach. The models were established utilizing an extensive database with 1516 data points on the H2S solubility in 37 ILs throughout an extensive pressure and temperature range. Seven input variables, including temperature (T), pressure (P), two critical variables such as temperature (Tc) and pressure (Pc), acentric factor (ω), boiling temperature (Tb), and molecular weight (Mw), were used in these models; the output was the solubility of H2S. The findings show that the XGBoost model, with statistical parameters such as an average absolute percent relative error (AAPRE) of 1.14%, root mean square error (RMSE) of 0.002, standard deviation (SD) of 0.01, and a determination coefficient (R2) of 0.99, provides more precise calculations for H2S solubility in ILs. The sensitivity assessment demonstrated that temperature and pressure had the highest negative and highest positive affect on the H2S solubility in ILs, respectively. The Taylor diagram, cumulative frequency plot, cross-plot, and error bar all demonstrated the high effectiveness, accuracy, and reality of the XGBoost approach for predicting the H2S solubility in various ILs. The leverage analysis shows that the majority of the data points are experimentally reliable and just a small number of data points are found beyond the application domain of the XGBoost paradigm. Beyond these statistical results, some chemical structure effects were evaluated. First, it was shown that the lengthening of the cation alkyl chain enhances the H2S solubility in ILs. As another chemical structure effect, it was shown that higher fluorine content in anion leads to higher solubility in ILs. These phenomena were confirmed by experimental data and the model results. Connecting solubility data to the chemical structure of ILs, the results of this study can further assist to find appropriate ILs for specialized processes (based on the process conditions) as solvents for H2S.

Modeling Viscosity of CO2-N2 Gaseous Mixtures Using Robust Tree-Based Techniques: Extra Tree, Random Forest, GBoost, and LightGBM.

Carbon dioxide (CO2) has an essential role in most enhanced oil recovery (EOR) methods in the oil industry. Oil swelling and viscosity reduction are the dominant mechanisms in an immiscible CO2-EOR process. Besides numerous CO2 applications in EOR, most oil reservoirs do not have access to natural CO2, and capturing it from flue gas and other sources is costly. Flue gases are available in huge quantities at a significantly lower price and can be considered economically viable agents for EOR operations. In this work, four powerful machine learning algorithms, namely, extra tree (ET), random forest (RF), gradient boosting (GBoost), and light gradient boosted machine (LightGBM) were utilized to accurately estimate the viscosity of CO2-N2 mixtures. To this aim, a databank was employed, containing 3036 data points over wide ranges of pressures and temperatures. Temperature, pressure, and CO2 mole fraction were applied as input parameters, and the viscosity of the CO2-N2 mixture was the output. The RF smart model had the highest precision with the lowest average absolute percent relative error (AAPRE) of 1.58%, root mean square error (RMSE) of 2.221, and determination coefficient (R 2) of 0.9993. The trend analysis showed that the RF model could precisely predict the real physical behavior of the CO2-N2 viscosity variation. Finally, the outlier detection was performed using the leverage approach to demonstrate the validity of the utilized databank and the applicability area of the developed RF model. Accordingly, nearly 96% of the data points seemed to be dependable and valid, and the rest of them were located in the suspected and out-of-leverage data zones.

Employing ensemble learning techniques for modeling nanofluids' specific heat capacity

Accurate investigation of nanofluids' specific heat capacity as an effective thermophysical parameter in applications of heat transfer-based equipment and solar-based systems can play a crucial role in improving their performance and efficiency. The current study utilized advanced machine learning techniques to predict nanofluids' specific heat capacity. This target variable was considered as a function of average nanoparticle size, particle volume fraction, temperature, specific heat of nanoparticles, and specific heat of the base-fluids. In order to predict the specific heat values of different nanofluids, 2084 experimental data related to 10 types of nanoparticles and 6 types of base-fluids were extracted from the literature. In the next step, (i) artificial neural network models such as Multi-Layer Perceptron (by employing different training algorithms) and Radial Basis Function, and (ii) advanced ensemble learning techniques including Categorical Boosting, Decision Tree, Light Gradient Boosting Machine, and Random Forest were implemented on the dataset. Results indicated that the Random Forest model with an Average Absolute Percent Relative Error (AAPRE) of 0.1928% and a Coefficient of Determination (R2) of 0.9995 had the highest accuracy compared to the other ones. Moreover, for the best model (i.e., Random Forest model), sensitivity analysis was performed to determine the relationships between the input and output parameters, and the Leverage statistical technique was applied to find the valid, outlier, and out-of-range data-points.

Modeling wax deposition of crude oils using cascade forward and generalized regression neural networks: Application to crude oil production

Crude oil is made of different compositions and materials, namely hydrocarbons, oxygen, nitrogen, sulfur, and various metals. Deposition of heavy components can lead to a restriction of flow paths and decrease the oil production rate during production processes. Deposition of wax is a crucial issue that appears in the transfer equipment and surface facilities and decreases the inner diameter of pipelines. Wax deposition leads to loss of effective diameter and an increase in roughness, which will increase the pressure drop in the oil reservoir. Deposition of wax particles appears in low temperatures which can lead to a blockage of pipelines. When the oil's temperature is less than the wax appearance temperature (WAT), which is called the cold flow regime, oil composition changes because wax crystals precipitate. This research generally focuses on developing accurate intelligent models to predict wax deposition using the pour point temperature and °API of the crude oil sample as input variables. Various smart networks, including multilayer perceptron (MLP), radial basis function (RBF), cascade forward neural network (CFNN), and generalized regression neural network (GRNN) are utilized for this purpose. Four optimization algorithms, namely Broyden–Fletcher–Goldfarb–Shanno quasi-Newton backpropagation (BFGS), Levenberg-Marquardt (LM), Scaled Conjugate Gradient (SCG), and Bayesian Regularization (BR) are used for training the models. The results showed that the developed GRNN smart model could obtain a superior performance providing predictions for the amount of wax deposited with a root mean squared error (RMSE) of 0.845, an average absolute percent relative error (AAPRE) of 10.36%, and a coefficient of determination (R2) of 0.975. The trend analysis indicated that increasing pour point temperature leads to a wax deposition increase. Oppositely, increasing oil °API gravity reduces wax deposition. Lately, outlier detection was carried out by applying the Leverage approach to identify the outlier data points in a data bank. It detected only 4 data points (out of 173) as outliers.

Evolution of porosity in kerogen type I during hydrous and anhydrous pyrolysis: Experimental study, mechanistic understanding, and model development

In this study, to clarify the role of water during thermal maturation on organic porosity evolution, pore structure characteristics of the Qingshankou shale (type I kerogen) were studied during anhydrous and hydrous pyrolysis (AHP and HP) over wide a range of temperature (300–450 °C). Following each step of thermal maturation, geochemical properties, and pore structure were analyzed with Rock Eval and low-pressure N2 adsorption, respectively. Furthermore, the deconvolution technique was applied to the pore size distribution curves to investigate different pore families and their complexity was assessed using fractal dimension analysis. Next, the volume of N2 adsorbed/desorbed was modeled using several intelligent models. It was found that organic matter displayed Type IV isotherm with hysteresis loops and mesopores stood out as the prevailing type of pores within the samples. Moreover, total surface area and pore volume were found less for AHP samples than the HP samples at all temperatures, which revealed the role of water in the evolution of organic porosity. Pore diameter in AHP samples was larger compared to HP ones, while the diameter of pores increased with the progress of thermal advance in both scenarios. The original sample exhibited five mesopore and two macropore families, while with rising temperature pore families with smaller average pore widths were decreased, and pore families with larger average pore widths were created and expanded. Furthermore, heterogeneity of the pores with maturation was more evident in AHP samples due to the decrease in the number of pores with smaller pore widths. The role of water in the creation of fractures within pyrobitumen was remarkable since it caused a substantial increase in the total pore volume of the organic matter during the gas window. Finally, modeling outcomes showed that cascade forward neural network (CFNN) outperformed other models in predictions of N2 volume adsorbed/desorbed with an average absolute percent relative error (AAPRE) of 2.48 %. It was understood that relative pressure followed by pyrolysis method (AHP or HP) were the most important variables in the estimation of N2 adsorbed/desorbed volumes based on sensitivity analysis. Collectively, the role of water on organic porosity evolution was confirmed based on distinct discrepancies in the two groups of samples pore structure details.

Neural Network Model for Permeability Prediction from Reservoir Well Logs

The estimation of the formation permeability is considered a vital process in assessing reservoir deliverability. The prediction of such a rock property with the use of the minimum number of inputs is mandatory. In general, porosity and permeability are independent rock petrophysical properties. Despite these observations, theoretical relationships have been proposed, such as that by the Kozeny–Carmen theory. This theory, however, treats a highly complex porous medium in a very simple manner. Hence, this study proposes a comprehensive ANN model based on the back propagation learning algorithm using the FORTRAN language to predict the formation permeability from available well logs. The proposed ANN model uses a weight visualization curve technique to optimize the number of hidden neurons and layers. Approximately 500 core data points were collected to generate the model. These data, including gamma ray, sonic travel time, and bulk density, were collected from numerous wells drilled in the Western Desert and Gulf areas of Egypt. The results show that in order to predict the permeability accurately, the data set must be divided into 60% for training, 20% for testing, and 20% for validation with 25 neurons. The results yielded a correlation coefficient (R2) of 98% for the training and 96.5% for the testing, with an average absolute percent relative error (AAPRE) of 2.4%. To validate the ANN model, two published correlations (i.e., the dual water and Timur’s models) for calculating permeability were used to achieve the target. In addition, the results show that the ANN model had the lowest mean square error (MSE) of 0.035 and AAPRE of 0.024, while the dual water model yielded the highest MSE of 0.84 and APPRE of 0.645 compared to the core data. These results indicate that the proposed ANN model is robust and has strong capability of predicting the rock permeability using the minimum number of wireline log data.

Prediction of critical total drawdown in sand production from gas wells: Machine learning approach

AbstractSand production is a critical issue in petroleum wells. The critical total drawdown (CTD) is an essential indicator of the onset of sand production. Although some models are available for CTD prediction, most of them are proven to lack accuracy or use commercial software. Furthermore, the previous correlations have not studied the trend analysis to verify the correct relationships between the parameters. Therefore, this study aims to build accurate and robust models for predicting CTD using response surface methodology (RSM) and support vector machine (SVM). The RSM is utilized to obtain the equation without using any software. The SVM model is an alternative method to predict the CTD with higher accuracy. This study used 23 datasets to develop the proposed models. The CTD is a strong function of the total vertical depth, cohesive strength, effective overburden vertical stress, and transit time with correlation coefficients (R) of 0.968, 0.963, 0.918, and −0.813. Different statistical methods, that is, analysis of variance (ANOVA), F‐statistics test, fit statistics, and diagnostics plots, have shown that the RSM correlation has high accuracy and is more robust than correlations reported in the literature. Moreover, trend analysis has proven that the proposed models ideally follow the correct trend. The RSM correlation decreased the average absolute percent relative error (AAPRE) by 12.7% compared to all published correlations' AAPRE of 22.6%–30.4%. The SVM model has shown the lowest AAPRE of 6.1%, with the highest R of 0.995. The effects of all independent variables on the CTD are displayed in three‐dimensional plots and showed significant interactions.

Novel Correlation for Calculating Water Saturation in Shaly Sandstone Reservoirs Using Artificial Intelligence: Case Study from Egyptian Oil Fields

The accurate determination of water saturation in shaly sandstone reservoirs has a significant impact on hydrocarbons in place estimation and selection of possible hydrocarbon zones. The available numerical equations for water saturation estimation are unreliable and depend on laboratory core analysis. Therefore, this paper attempts to use artificial intelligence methods in developing an artificial neural network model (ANN) for water saturation (Sw) prediction. The ANN model is developed and validated by using 2700 core measured points from the fields located in the Gulf of Suez, Nile Delta, and Western Desert of Egypt, with inputs including the formation depth, the caliper size, the sonic time, gamma rays (GRs), shallow resistivity (Rxo), neutron porosity (NPHI), the photoelectric effect (PEF), bulk density, and deep resistivity (Rt). The study results show that the optimization process for the ANN model is achieved by distributing the collected data as follows: 80% for training and 20% for testing processes, with an R2 of 0.973 and a mean square error (MSE) of 0.048. In addition, a mathematical equation is extracted out of the ANN model that is used to estimate the formation water saturation in a simple and direct approach. The developed equation can be used incorporating with the existing well logs commercial software to increase the accuracy of water saturation prediction. A comparison study is executed using published correlations (Waxman and Smits, dual water, and effective models) to show the robustness of the presented ANN model and the extracted equation. The results show that the proposed correlation and the ANN model achieved outstanding performance and better accuracy than the existing empirical models for calculating the formation water saturation with a high correlation coefficient (R2) of 0.973, lowest mean-square error (MSE) of 0.048, lowest average absolute percent relative error (AAPRE) of 0.042, and standard deviation (SD) of 0.24. To the best of our knowledge, the current study and the proposed ANN model establish a novel base in the estimation of formation water saturation.

Modeling of Brine/CO2/Mineral Wettability Using Gene Expression Programming (GEP): Application to Carbon Geo-Sequestration

Carbon geo-sequestration (CGS), as a well-known procedure, is employed to reduce/store greenhouse gases. Wettability behavior is one of the important parameters in the geological CO2 sequestration process. Few models have been reported for characterizing the contact angle of the brine/CO2/mineral system at different environmental conditions. In this study, a smart machine learning model, namely Gene Expression Programming (GEP), was implemented to model the wettability behavior in a ternary system of CO2, brine, and mineral under different operating conditions, including salinity, pressure, and temperature. The presented models provided an accurate estimation for the receding, static, and advancing contact angles of brine/CO2 on various minerals, such as calcite, feldspar, mica, and quartz. A total of 630 experimental data points were utilized for establishing the correlations. Both statistical evaluation and graphical analyses were performed to show the reliability and performance of the developed models. The results showed that the implemented GEP model accurately predicted the wettability behavior under various operating conditions and a few data points were detected as probably doubtful. The average absolute percent relative error (AAPRE) of the models proposed for calcite, feldspar, mica, and quartz were obtained as 5.66%, 1.56%, 14.44%, and 13.93%, respectively, which confirm the accurate performance of the GEP algorithm. Finally, the investigation of sensitivity analysis indicated that salinity and pressure had the utmost influence on contact angles of brine/CO2 on a range of different minerals. In addition, the effect of the accurate estimation of wettability on CO2 column height for CO2 sequestration was illustrated. According to the impact of wettability on the residual and structural trapping mechanisms during the geo-sequestration of the carbon process, the outcomes of the GEP model can be beneficial for the precise prediction of the capacity of these mechanisms.

Determination of the Gas-Oil Ratio below the Bubble Point Pressure Using the Adaptive Neuro-Fuzzy Inference System (ANFIS).

Determining the solution gas–oil ratio (Rs) below the bubble point is a vital requirement that aids in multiple production engineering and reservoir analysis issues. Currently, there are some models available for the determination of the solution gas–oil ratio under the bubble point. However, they still may prove unreliable due to the applied assumptions and their specification to operate only under a particular range of data. In this study, the neuro-fuzzy, i.e., the adaptive neuro-fuzzy inference system (ANFIS) approach, is utilized to develop an accurate and dependable model for determining the Rs below the bubble point pressure. A total of 376 pressure–volume–temperature datasets from Sudanese oil fields were used to establish the proposed ANFIS model. The trend analysis was applied to affirm the proper relationships between the inputs and outputs. Furthermore, using different statistical error analyses, the developed model was benchmarked against widely used empirical methods to evaluate the proposed method’s performance in predicting the Rs at pressures below the bubble point. The proposed ANFIS model performs with an average absolute percent relative error of 10.60% and a correlation coefficient of 99.04%, surpassing the previously studied correlations.