Estimation of shear wave velocity in an Iranian oil reservoir using machine learning methods

https://doi.org/10.1016/j.petrol.2021.109841Get rights and content

Highlights

  • Five methods are implemented for predicting shear wave velocity (Vs) using petrophysical logs.

  • ANN can predict the Vs with high accuracy (R2 Test = 0.9898).

  • A sensitivity analysis performed on the significance of input variables on the Vs using the results of MGGP.

  • A correlation is introduced for forecasting the Vs.

  • Investigate the effects of Vs prediction by ANN on the geomechanical modelling.

Abstract

Shear wave velocity is considered as one of the most important rock physical parameters which can be measured by dipole sonic imager (DSI) tool. This parameter is applied to evaluate porosity and permeability, rock mechanical parameters, lithology, fracture assessment, etc. On the other hand, this data is not available in all wells and hence, an accurate and reliable estimation of this parameter with the least uncertainty is of great importance in reservoir characterization. In this study, regression, multi-layer perceptron artificial neural network (MLP-ANN), adaptive neuro-fuzzy inference system (ANFIS) and multi-gene genetic programming (MGGP) methods are utilized to estimate the shear wave velocity using well log data. Also, the reported empirical correlations in the literature are also investigated in the studied field. The input data include depth, effective porosity, Vp, gamma ray logs (natural and spectral), neutron log, density log and caliper log from the Bangestan Group Formation in one of the fields in southwestern Iran. In this study, all the expressed methods are compared based on the best coefficient of determination (R2), root mean square error (RMSE), mean squared error (MSE), average absolute relative error (AARE), and average relative error (ARE). Among the used methods, MGGP was developed for using the useful features of this method including sensitivity analysis and correlation. Sensitivity analysis is performed on the input data using the MLP-ANN and MGGP method. Also, a correlation is suggested based on the MGGP method which is able to predict the shear wave velocity using the mentioned input parameters. The results show that the MLP-ANN method is more accurate, reliable and efficient compared to other methods studied in this paper. R2 for the train, validation, and test phase are 0.9973, 0.9901 and 0.9898, respectively. The results of sensitivity analysis imply that compressional wave velocity has the highest impact on the shear wave velocity. Finally, Young Dynamic Modulus and Poisson Dynamic Ratio are computed using both real and predicted shear wave velocities. The results indicate that these two parameters can be calculated with high accuracy using predicted shear wave velocity.

Introduction

Shear wave velocity has many applications in geophysical and petrophysical studies especially in calculating geomechanical parameters. Unlike the compressional wave, shear wave cannot propagate throughout the liquids. Therefore, these data help to identify the properties of rock, including fluid in the pores and lithology. Also, knowing the relationship between lithology, pore distribution, and shear wave velocity provides useful information about the reservoir (Khatibi and Aghajanpour, 2020). This parameter can be used in construction and creation of the mechanical earth model which is one of the main goals of geomechanical studies. The mechanical earth model is a numerical determination of the mechanical properties and stress state of the rock. A mechanical earth model includes deep profiles of elastoplastic and/or elastic parameters, rock strength, and earth stresses(Plumb et al., 2000). Geomechanics by considering the mechanical behaviors of rock, plays an important role in planning related to exploration, drilling, reservoir engineering and even well completion and operation operations. Understanding the hazards of ground stress is of particular importance, especially for safe and effective drilling, and requires the development of geomechanical models. These models implement a vital role in the study of wellbore stability through calculating the stresses (Grandi et al., 2002; Ramjohn et al., 2018), hydraulic fracture (Suppachoknirun and Tutuncu, 2017; Zhang et al., 2019), drilling mud window (Najibi et al., 2017; Finisha et al., 2018), reservoir compaction and subsidence (Ranjbar and Kuenzel, 2017), and reactivation of faults due to gas injection (Figueiredo et al., 2015). In fact, geomechanics involves a wide variety of operations from exploration to field abandonment (Plumb et al., 2004). The main algorithm of geomechanical studies is the processing of existing data to predict the elastic properties of rock, pore pressures, and in situ stresses (Shukla and Solanki, 2020). Obviously, the reservoir complexity and the lack of reliable information may cause an inaccurate estimation of geomechanical parameters. Shear wave velocity is estimated using well log data in the wells without data (Shukla and Solanki, 2020). Empirical correlations and machine learning methods are the two main methods for predicting this parameter.

Various researchers used the empirical correlations to estimate shear velocity (Pickett, 1963, Carroll, 1969, Castagna and Backus, 1993; Eskandari et al., 2003, Behnia et al., 2017). However, there is not an exact correlation for calculating the shear wave velocity utilized for all types of reservoirs (Olayiwola and Sanuade, 2020). The reported correlations have some disadvantages including (Heidari et al., 2010; Adjei et al., 2020, Olayiwola and Sanuade, 2020):

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    Most of these correlations calculate the shear wave velocity based on the compressional wave velocity, while many parameters can affect this parameter.

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    The proposed models are mathematical relationships, and the data used to correlate them are related to a specific formation/lithology.

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    Using these correlations to estimate the shear wave velocity in other reservoirs may include errors. Therefore, they need calibration to be valid.

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    Most of the presented correlations are related to sand formations and it is not possible to use them for other rock types.

Machine learning methods and optimization algorithms can predict the shear wave velocity (Vs) using petrophysical data. Various researchers have studied and used such methods to estimate the shear wave. Eskandari et al., (2003) used multiple regression analysis and artificial neural network (ANN) to forecast Vs from petrophysical log data. Rezaei et al. (Rezaee et al., 2007) applied ANN, neuro-fuzzy and fuzzy logic to estimate Vs using well log data in the Carnau reservoir. Rajabi et al., (2010) estimated compressional (Vp), Stoneley (Vst) and shear wave (Vs) velocities using petrophysical data by neuro-fuzzy logic and genetic algorithms in one of the Iranian carbonated reservoirs. Zoveidavianpoor et al., (2013) estimated Vp using linear regression and adaptive neuro-fuzzy inference system (ANFIS). Asoodeh and Bagheripour (Asoodeh and Bagheripour, 2013) used NF, ANN and FL to predict Vs, Vp and Vst. Nourafkan and Kadkhodai-Ilkhchi (Nourafkan and Kadkhodaie-Ilkhchi, 2015) predicted the Vs from petrophysical data using the hybrid ant colony–fuzzy inference system. Nygaard (Hadi and Nygaard, 2018) performed ANN and regression analysis to estimate Vs using well log data in a well in southern Iraq. Anemangely et al., (2019) applied a combination of least square support vector machine (LSSVM), particle swarm optimization (PSO), Cuckoo optimization algorithm (COA) and genetic algorithm (GA) to predict Vs in Ahvaz oil field in southwestern Iran. Behnia et al., (2017) presented models for predicting Vs in limestone using data sets of several Iranian reservoirs with gene expression programming (GEP) and ANFIS methods. Olayiwola et al. (Olayiwola and Sanuade, 2020) used ANN, ANFIS and LSSVM. Their results showed that LSSVM can predict shear wave velocity with high accuracy. Table 1 presents the studies performed in the field of shear wave velocity estimation as well as the best proposed method of each study.

Some researchers addressed the uncertainty analysis during the prediction of shear wave velocity using the well logs. In these cases, an interval of the well without the relevant log data were selected. First, the well logs in the selected intervals were predicted using machine learning methods. After prediction, an uncertainty analysis was conducted on the prediction results which could provide additional information and increase the reliability of the prediction results. More information is available on Feng et al. studies(Feng et al., 2021a; b).

Fig. 1 demonstrates the procedure of this research. In this study, shear wave velocity is estimated using empirical correlations and machine learning methods using log data as well as some petrophysical properties of one of the fractured carbonate reservoirs in southwestern Iran. At first, the common empirical correlations are applied to predict the Vs. Then, simple and stepwise linear regression methods are used. The most efficient intelligent machine learning methods are then utilized to predict this parameter include MLP-ANN, ANFIS and multi-gene genetic programming (MGGP). These methods were selected based on the extensive and comprehensive study of previous research. It must be noted that depth, effective porosity, Vp, gamma ray logs (natural and spectral), neutron log, density log, and caliper log were selected to predict Vs. The results show that the MLP-ANN has the best performance in predicting this parameter in comparison with other methods. Also, a correlation is presented for predicting Vs based on input parameters. Then, sensitivity analysis is performed on the input parameters based on the results of the MLP-ANN and MGGP due to their higher accuracy in comparison to other methods. Based on the results of this sensitivity analysis, the most important and effective parameters on the Vs prediction are reported. Finally, the dynamic elastic parameters, which are the parameters of the geomechanical model, are calculated using Vs and Vp. The calculations are performed using both real and predicted data and the results are then compared.

This study provides accurate and precise models for predicting the shear wave velocity using well log data of an Iranian oil field. The main priority of this study is the comprehensive comparison of different well-known machine learning methods as well as traditional empirical correlations and regression models in shear wave velocity. In this study, the incapability of the traditional empirical correlations and regression models were shown. Moreover, the correlation of predicting shear wave velocity and the comprehensive sensitivity analysis on the input parameters have been done for the first time in this paper as the best of authors’ knowledge. Additionally, the proposed correlation can predict the shear wave velocity by the R squared more than 0.8.

Section snippets

Empirical correlations

Many researchers such as Pickett, (1963), Carrol (Carroll, 1969), Castagna et al. (Castagna and Backus, 1993), Eskandari et al., (2003) and Brocher, (2005) have proposed different empirical models for estimating Vs using Vp in different rocks. The well-known correlations are presented in Table 2. It should be noted that in the case of Castagna et al., The coefficients used are specific to dolomite rocks and thus have different values in sandstones.

Regression

Regression analysis is used to match a model to

Data Gathering

In this paper, the data set of one of the oil reservoirs in southwestern Iran has been studied. This reservoir faces with high gas oil ratio situation which has been studied by Izadpanahi et al., (2020) The reservoir formations of this field are Ilam and Sarvak formations. Reservoir rock in this field is highly fractured carbonate. This reservoir has an asymmetric structure and east-west trend and its slope in the north and south is 22 and 14°, respectively. The average altitude in the study

Empirical models performance

As stated in the theory section, many empirical correlations have been proposed by researchers to predict the shear wave. The most important challenge encountered in these models is that most of them are not comprehensive and usually these correlations are limited to the reservoir rock and the specific conditions of each reservoir. According to the data studied in this paper, only three of the correlations represent acceptable results. The results of shear wave estimation using each of the

Conclusions

This paper investigates the estimation of shear wave velocity based on machine learning methods and petrophysical logs. The estimation methods in the literature are studied in detail and three efficient and useful machine learning methods are selected. These methods are used to predict shear wave velocity in one of the Iranian carbonate oil reservoirs. According to the results of this study, several important conclusions are elaborated as follow:

  • Pickett correlation for predicting shear wave

Author contribution section

Arash Ebrahimi: Results Preparation, Draft Preparation, Analysis of Results. Amin Izadpanahi: Data Gathering, Analysis of Results, Idea, Conceptualization, Code Prepration, Draft Preparation, Editing Manuscript, Supervision. Parirokh Ebarhimi: Draft Preparation, Results Preparation. Ali Ranjbar: Idea, Conceptualization, Methodology, Editing.

Declaration of competing interest

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

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