- Email: [email protected]
Reservoir rock properties estimation based on conventional and NMR log data using ANN-Cuckoo: A case study in one of super fields in Iran southwest
Journal Pre-proof Reservoir rock properties estimation based on conventional and NMR log data using ANN-Cuckoo: A case study in one of super fields in Iran southwest Ghasem Zargar, Abbas Ayatizadeh Tanha, Amirhossein Parizad, Mehdi Amouri, Hasan Bagheri PII:
S2405-6561(19)30059-8
DOI:
https://doi.org/10.1016/j.petlm.2019.12.002
Reference:
PETLM 294
To appear in:
Petroleum
Received Date: 31 March 2019 Revised Date:
26 October 2019
Accepted Date: 17 December 2019
Please cite this article as: G. Zargar, A.A. Tanha, A. Parizad, M. Amouri, H. Bagheri, Reservoir rock properties estimation based on conventional and NMR log data using ANN-Cuckoo: A case study in one of super fields in Iran southwest, Petroleum (2020), doi: https://doi.org/10.1016/j.petlm.2019.12.002. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [COPYRIGHT YEAR] Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. All rights reserved.
Author statement I have made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND I have drafted the work or revised it critically for important intellectual content; AND I have approved the final version to be published; AND I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Reservoir Rock Properties Estimation Based on Conventional and NMR log Data Using ANN-Cuckoo: A Case Study in One of Super Fields in Iran Southwest Ghasem Zargar1, Abbas Ayatizadeh Tanha1,2, Amirhossein Parizad1,3*, Mehdi Amouri2 ,Hasan Bagheri2 1) Petroleum University of Technology, Iran 2) National Iranian Drilling Company, Well Logging Department, Ahwaz, Iran 3) Petro Gostaran Ofogh (PGO), Mud logging Department, Ahwaz, Iran *Corresponding Author, Email: [email protected] Abstract This work highlights the application of Artificial Neural Networks optimized by Cuckoo optimization algorithm for predictions of NMR log parameters including porosity and permeability by using field log data. The NMR logging data have some highly vital privileges over conventional ones. The measured porosity is independent from bearer pore fluid and is effective porosity not total. Moreover the permeability achieved by exact measurement and calculation considering clay content and pore fluid type. Therefore availability of the NMR data brings a great leverage in understanding the reservoir properties and also perfectly modelling the reservoir. Therefore, achieving NMR logging data by a model fed by a far inferior and less costly conventional logging data is a great privilege. The input parameters of model were neutron porosity (NPHI), sonic transit time (DT), bulk density (RHOB) and electrical resistivity (RT). The outputs of model were also permeability and porosity values. The structure developed model was build and trained by using train data. Graphical and statistical validation of results showed that the developed model is effective in prediction of field NMR log data. Outcomes show great possibility of using conventional logging data be used in order to reach the precious NMR logging data without any unnecessary costly tests for a reservoir. Moreover, the considerable accuracy of newly ANN-Cuckoo method also demonstrated. This study can be an illuminator in areas of reservoir engineering and modelling studies were presence of accurate data must be essential. Keywords: Neural Network, ANN-Cuckoo, NMR Logging, Permeability Modeling, Porosity Modeling.
1
Introduction
Permeability and porosity are pivotal factors in reservoir modeling and planning and are basic needs in doing so. Therefore, avaibility and quality of them are in great concern. Nuclear magnetic resonance (NMR) logging is one of the methods in the field of well logging which utilizes magnetic fields to gain information from layers of a formation. In the center of NMR tool a magnet creates a permanent magnetic field magnetizing the formation materials. Then, time repeated radio-frequency energy is transmitted into the formation through utilizing an antenna which surrounds the magnet. The protons in the hydrogen atoms of hydrocarbon and water molecules which are aligned in the direction of created magnetic field produce a decaying “echo” signal which is detected by this antenna [1-3]. There is a linear relation between the proton resonance frequency and the strength of magnetic field. Hence, it is possible to modify and tune the frequency of incoming and outgoing energy to evaluate and characterize cylindrical regions which are located at various distances from the NMR tool. Basically it is possible to obtain different characteristics of formation from NMR logs including fluid quantity of formation, properties of formation fluids for example their viscosity and information about the pore size and porosity of formation. Porosity and permeability of formation are two important and complex features which have notable impact on the reservoir characterization and flow regime determination [3-5]. Measurement and evaluation of the parameters by using NMR logs is a difficult, expensive and time-consuming process. Another difficulty which is encountered in using NMR logs is that it is not possible to use them in cased wells [6, 7]. Direct method also is available. Coring could be performed and exact measures of porosity and permeability would be available by direct measurement in laboratories. The direct measurement is the ideal method whereas its utilization is greatly confined by financial limits and other concerns. Usually, it is limited to exploration wells and almost would not include most intervals. Therefore, seldom this option is available [8, 9]. Developing accurate methods and techniques for estimation of permeability and porosity in an efficient, quick and inexpensive manner is crucial. Developing quantitative correlating and modeling approaches for the classical well logs is an efficient manner to access the aforementioned goal. There are several reports in the literature for predictions of petro physical data from well logs [6, 7, 10].
Artificial Neural Networks are strongly capable of identifying non-linear and complex systems. The algorithms utilized for ANN training, are usually subjected to local minima. The optimum weights of neurons could result in better collinearity between outputs and real data. The new Cuckoo Optimization Algorithm is used to train the weights of the neural network. Such an algorithm is a new evolutionary technique grasped from the behavior of a certain type of bird: the cuckoo [11]. Among the benefits of this technique, faster convergence, high accuracy, lower possibility of trapping in the local minima, and fast solution of optimization problems with high range dimensions can be mentioned. Such advantages are the main reason why the use of such a technique has become so widespread [12, 13]. This optimization algorithm is run so as to achieve enhanced identification through exploring the optimized values of the weights of the neural network. As far as the authors are cognizant, this may be the first time that such an identification method is used for a gas distribution network. 2
Literature Review
Many researchers investigated the application of soft computing approaches and intelligent models in the field of geoscience. Valentin et al, used borehole Image Data Logs (Ultrasonic and Microresistivity) as source and estimated porosity and permeability of Brazilian pre-salted carbonate using deep auto encoders with 96% accuracy [14]. Zhu et al proposed an efficient and new integrated hybrid neural network method in order to estimate total carbon content (TOC) from conventional logging data. The model has a very high accuracy in order to estimate TOC [15]. Mohaghegh utilized neural networks (NNs) for prediction of parameters related to NMR log of one of the East Texas fields [16]. Zhu et al conducted a cohesive case study and introduced a new method based on Multiboost-Kernel extreme learning machine and machine learning technique and accurately estimated of TOC respectively [17]. Malki and Baldwin investigated the applicability of neuro-fuzzy techniques for estimation of NMR log parameters by using coupled ability of Fuzzy Logic (FL) and an optimization algorithm named Genetic Algorithm (GA) [18]. Ahmadi and Chen compared learning approached and tested on porosity and permeability data samples gathered from northern Persian Gulf reservoirs. The permeability of one of northern Persian Gulf reservoirs has been modeled based on conventional logging data. The results cleared the supremacy of hybridized machine learning methods [19]. In this paper a more accurate model is conducted by new ANN-Cuckoo method. This model is fed by conventional
logging data and real field NMR permeability and effective porosity data and gives permeability and also effective porosity based on conventional logging data. NMR logging tool can yield the permeability and more notably, the effective porosity directly without using any intermediary calculations or costly laboratory measurements in large intervals. Ahmadi and Ebadi introduced a new method in order to have porosity and permeability accurately with availability of conventional logging data. The conventional logging data and porosity and permeability data were given to construct models by GA-LSSVM and GA-FL. This should be noted, the outcome models were highly accurate [20]. In this paper, direct measured effective porosity and permeability are set as reference data and the inaccuracy of calculating porosity and permeability by conventional correlations is tackled accordingly. Moreover, novel ANN-Cuckoo algorithm is applied as modeling algorithm and considerably accurate model is generated accordingly. Ahmadi et al, proposed an accurate model to conjoin permeability and porosity and bypass inaccuracy raised by conventional correlations between permeability and porosity. The model was conducted by utilizing ANN and optimized ANN methods [21]. In this research it is aimed to introduce an accurate model that can present accurate and trustworthy estimation of permeability and effective porosity. Therefore, new ANN-Cuckoo method and NMR data are used in this regard and an accurate model is introduced respectively. It should be noted, the NMR logging yields effective porosity without any mediatory and this is a huge advantage in this regard. Thank to great ability of Artificial Neural Networks (ANNs) for gaining information and results from complex data, they can be utilized for pattern recognition in highly nonlinear and complex problems [22, 23]. Most of modeling and training problems requires optimization techniques and optimization algorithms such as Genetic Algorithm (GA), Coupled Simulated Annealing (CSA), Particle Swarm Optimization (PSO) and Cuckoo can be used in this regard. Using these algorithms in conjunction with ANNs have benefits like as preventing from getting stuck on local minima, determining the most possible optimum solution for problem under consideration and etc [11, 24-26]. There is no report in the literature on the application of ANNs coupled with Cuckoo optimization algorithm for prediction of related parameters of NMR logs. Therefore, this study highlights the prediction of NMR logging parameters by using ANN in conjunction with Cuckoo optimization algorithm.
3
Artificial neural networks
Multilayer Perceptron (MLP) with one or more hidden layer(s), which belong to the feedforward ANN family, are universal approximators and have shown great performance in system identification [27 ,11] . Structure of the utilized MLP with one hidden layer is depicted in Figure 1. The MLP configuration entails selection of appropriate number of hidden layer(s) and number of neurons in each layer, to provide the approximation of proposed distillation column to any arbitrary degree of accuracy. In the present article, the sigmoid activation function is selected for hidden layer, while linear activation function is utilized for output layer. Number of neurons in each layer is set by trial and error and are three, fifteen and two for input, hidden and output layers, respectively. Inputs are DT, CN, RHOB and Rt and outputs Φeff and k.
Figure 1: Schematic of the Multi-layer ANN model The crucial factor affecting MLPs performance, the learning phenomena, deals with adjustment of the weights and biases of MLP interconnections to minimize an objective function by means of MSE criterion [27]. As stated previously, the widely used backpropagation algorithm suffers from two major drawbacks, such as the possibility of entrapment in non-optimal local minimum and slow speed of convergence. To overcome these weaknesses the Cuckoo optimization algorithm (COA) is utilized and is stated in section 2.2.
4
Cuckoo optimization algorithm
The Cuckoo Algorithm, inspired from the behavior of the bird of the same name, is one of the strongest evolutionary optimization algorithms available. Like other evolutionary algorithms, this algorithm also starts with a population. The primary populations of cuckoos are composed of assorted groups each of which resides in a specific location and lay eggs in hosting nests [11]. Eggs with a higher degree of similarity to the hosting bird's would enjoy a greater chance of survival, while those with less similarity would be identified and finally destroyed by the hosting birds. The larger the number of eggs that survive in a zone, the greater the chances of the attitudes from the cuckoos remaining there [11]. In order to increase the chances of the eggs’ salvation, the cuckoos migrate, seeking the best zones. Accordingly, they inhabit the location nearest to the present zone. Considering the number of eggs laid by each cuckoo and the distance to the best-optimized present zone, an Egg Laying Radius (ELR) is achieved. Then, the cuckoos start laying eggs randomly in their ELR. The process continues until the best location for laying eggs is achieved. The optimized zone is where the most eggs are laid, i.e., the most eggs are saved and the fewest are destroyed [11]. 5
Results and discussions
In this study 9000 data points were gathered. The data belongs to one of super oil fields in Iran southwest. The region that data belongs to is shown in Figure 2.
Figure 2. Major oil and gas fields in Southwest of Iran 7000 points were set for train and rest of them used for testing of networks. Specification of the networks and optimization algorithms are as follow Table 1: initial and steady states values of output ANN
Number of
Hidden layer
Output layer
Number of neurons
Number of neurons
transfer function
transfer function
in input layer
in hidden layer
sigmoid
linear
4
15
2
minimum number
ELR
neurons in output layer
COA maximum
minimum
maximum number
number of
number of
Cuckoo
Cuckoo
15
5
of eggs
of eggs
10
2
0.8
The Effective porosity (Φeff) has been modeled by ANN and ANN- Cuckoo networks. The Performance of predicted values and the result of prediction by ANN network are shown in Figure 3 and 4. The performance of training is acceptable however in the regard of testing, there is significant
difference between predicted values and real data. Moreover, at the maximum and minimum of data range, there are considerable difference in predicted and observed values.
Figure 3. Performance of predicted values of Φeff vs. the measured for the Training and Testing data
Figure 4. Results of ANN network for Φeff simulation in Training and Testing data The Φeff also simulated by ANN-Cuckoo algorithm. The performance and result are presented in Figures 5 and 6. The model accurately follow the data and the outputs match the real data. In both training and testing the model outperformed the ANN algorithm. Therefore, a reliable relation conducted between inputs and Φeff thorough modeling by ANN optimized by Cuckoo.
Figure 5. Performance of predicted values of Φeff vs. the measured for the Training and Testing data
Figure 6. Results of ANN-cuckoo network for Φeff simulation in Training and Testing data The modeling also has been performed for permeability (K). The result and performance of ANN and ANN-Cuckoo models for permeability are in some ways analogous to that of porosity modeling. The performance and result of ANN modeling for K are shown in Figures 7 and 8. Based on results, the model is properly modeled the permeability based on the inputs and this is evident in both training and testing performances. Furthermore, the outputs are not following the real data properly.
Figure 7. Performance of predicted values of K vs. the measured for the Training and Testing data
Figure 8. Results of ANN network for K simulation in Training and Testing data The performance and result of K modelling by ANN-Cuckoo are presented in figures 9 and 10. The result and performance of the model are good and the model predicted the real data correctly. The model has been well trained and showed very good test result.
Figure 9. Performance of predicted values of K vs. the measured for the Training and Testing data
Figure 10. Results of ANN-cuckoo network for K simulation in Training and Testing data The performance of the models are tabulated numerically in Tables 2 and 3. The mean square error (MSE) and regression coefficient (R2) are given accordingly. The modeling by ANN-
Cuckoo algorithm has given much more accurate model. The much lower MSE and R2 close to 1 indicates better performance of the respected model. Table 2: Performance of the ANN for the testing and training data sets without optimization R2
MSE Data set
K
K
Training
1.5711
62.2380
0.9573
0.9279
Testing
1.3322
16.2440
0.9230
0.8877
Table 3: Performance of the ANN-Cuckoo for the testing and training data sets without optimization R2
MSE Data set
K
K
Training
0.1556
7.1379
0.9996
0.9991
Testing
0.6749
8.3798
0.9802
0.9701
Figures 11 and 12 show root mean square error (RMSE) and regression coefficient (R2) of the models. The ANN-Cuckoo algorithm is capable in prediction and simulation of Φeff and K accurately and efficiently.
Figure 11. Comparing the RMSE of ANN-Cuckoo and ANN for Train and Tests data
Figure 12. Comparing the R2 of ANN-Cuckoo and ANN for Train and Tests data
Conclusion In this paper the NMR logging data for one of Iranian super oil fields have been simulated based on conventional logging data. The ANN-Cuckoo algorithm can precisely simulate the porosity and permeability of the respected field. The MSE, RMSE and R2 criteria briefly and effectively have indicated in what extent the ANN-Cuckoo algorithm is accurate and effective. The ANNCuckoo is much more precise and effective than ANN algorithm and the optimization of ANN by Cuckoo is very effective and beneficial. The ANN-Cuckoo can contribute great role in modeling such data. Such modeling would predict the required data precisely and would decrease the cost significantly by diminishing the need of direct measurements. The new simulation methods like ANN-Cuckoo would evolve the simulation method and would hike reliance on modeling rather than direct costly measurements.
Nomenclature ANN
Artificial Neural Network
COA
Cuckoo Optimization Algorithm
DT
Sonic Transit Time
K
Permeability
NMR
Nuclear Magnetic Resonance
NPHI
Neutron Porosity
MSE
Mean Square Error
R2
R-Squared
RHOB
Bulk Density
RMSE
Root Mean Square Error
RT
Electrical Resistivity
TOC
Total Carbon Content
Φeff
Effective Porosity
Acknowledgements The authors acknowledge the National Iranian Drilling Company (NIDC) for the support rendered in carrying out this research.
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The Authors hereby confirm there is no conflict of interest.
S2405-6561(19)30059-8
DOI:
https://doi.org/10.1016/j.petlm.2019.12.002
Reference:
PETLM 294
To appear in:
Petroleum
Received Date: 31 March 2019 Revised Date:
26 October 2019
Accepted Date: 17 December 2019
Please cite this article as: G. Zargar, A.A. Tanha, A. Parizad, M. Amouri, H. Bagheri, Reservoir rock properties estimation based on conventional and NMR log data using ANN-Cuckoo: A case study in one of super fields in Iran southwest, Petroleum (2020), doi: https://doi.org/10.1016/j.petlm.2019.12.002. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [COPYRIGHT YEAR] Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. All rights reserved.
Author statement I have made substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND I have drafted the work or revised it critically for important intellectual content; AND I have approved the final version to be published; AND I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Reservoir Rock Properties Estimation Based on Conventional and NMR log Data Using ANN-Cuckoo: A Case Study in One of Super Fields in Iran Southwest Ghasem Zargar1, Abbas Ayatizadeh Tanha1,2, Amirhossein Parizad1,3*, Mehdi Amouri2 ,Hasan Bagheri2 1) Petroleum University of Technology, Iran 2) National Iranian Drilling Company, Well Logging Department, Ahwaz, Iran 3) Petro Gostaran Ofogh (PGO), Mud logging Department, Ahwaz, Iran *Corresponding Author, Email: [email protected] Abstract This work highlights the application of Artificial Neural Networks optimized by Cuckoo optimization algorithm for predictions of NMR log parameters including porosity and permeability by using field log data. The NMR logging data have some highly vital privileges over conventional ones. The measured porosity is independent from bearer pore fluid and is effective porosity not total. Moreover the permeability achieved by exact measurement and calculation considering clay content and pore fluid type. Therefore availability of the NMR data brings a great leverage in understanding the reservoir properties and also perfectly modelling the reservoir. Therefore, achieving NMR logging data by a model fed by a far inferior and less costly conventional logging data is a great privilege. The input parameters of model were neutron porosity (NPHI), sonic transit time (DT), bulk density (RHOB) and electrical resistivity (RT). The outputs of model were also permeability and porosity values. The structure developed model was build and trained by using train data. Graphical and statistical validation of results showed that the developed model is effective in prediction of field NMR log data. Outcomes show great possibility of using conventional logging data be used in order to reach the precious NMR logging data without any unnecessary costly tests for a reservoir. Moreover, the considerable accuracy of newly ANN-Cuckoo method also demonstrated. This study can be an illuminator in areas of reservoir engineering and modelling studies were presence of accurate data must be essential. Keywords: Neural Network, ANN-Cuckoo, NMR Logging, Permeability Modeling, Porosity Modeling.
1
Introduction
Permeability and porosity are pivotal factors in reservoir modeling and planning and are basic needs in doing so. Therefore, avaibility and quality of them are in great concern. Nuclear magnetic resonance (NMR) logging is one of the methods in the field of well logging which utilizes magnetic fields to gain information from layers of a formation. In the center of NMR tool a magnet creates a permanent magnetic field magnetizing the formation materials. Then, time repeated radio-frequency energy is transmitted into the formation through utilizing an antenna which surrounds the magnet. The protons in the hydrogen atoms of hydrocarbon and water molecules which are aligned in the direction of created magnetic field produce a decaying “echo” signal which is detected by this antenna [1-3]. There is a linear relation between the proton resonance frequency and the strength of magnetic field. Hence, it is possible to modify and tune the frequency of incoming and outgoing energy to evaluate and characterize cylindrical regions which are located at various distances from the NMR tool. Basically it is possible to obtain different characteristics of formation from NMR logs including fluid quantity of formation, properties of formation fluids for example their viscosity and information about the pore size and porosity of formation. Porosity and permeability of formation are two important and complex features which have notable impact on the reservoir characterization and flow regime determination [3-5]. Measurement and evaluation of the parameters by using NMR logs is a difficult, expensive and time-consuming process. Another difficulty which is encountered in using NMR logs is that it is not possible to use them in cased wells [6, 7]. Direct method also is available. Coring could be performed and exact measures of porosity and permeability would be available by direct measurement in laboratories. The direct measurement is the ideal method whereas its utilization is greatly confined by financial limits and other concerns. Usually, it is limited to exploration wells and almost would not include most intervals. Therefore, seldom this option is available [8, 9]. Developing accurate methods and techniques for estimation of permeability and porosity in an efficient, quick and inexpensive manner is crucial. Developing quantitative correlating and modeling approaches for the classical well logs is an efficient manner to access the aforementioned goal. There are several reports in the literature for predictions of petro physical data from well logs [6, 7, 10].
Artificial Neural Networks are strongly capable of identifying non-linear and complex systems. The algorithms utilized for ANN training, are usually subjected to local minima. The optimum weights of neurons could result in better collinearity between outputs and real data. The new Cuckoo Optimization Algorithm is used to train the weights of the neural network. Such an algorithm is a new evolutionary technique grasped from the behavior of a certain type of bird: the cuckoo [11]. Among the benefits of this technique, faster convergence, high accuracy, lower possibility of trapping in the local minima, and fast solution of optimization problems with high range dimensions can be mentioned. Such advantages are the main reason why the use of such a technique has become so widespread [12, 13]. This optimization algorithm is run so as to achieve enhanced identification through exploring the optimized values of the weights of the neural network. As far as the authors are cognizant, this may be the first time that such an identification method is used for a gas distribution network. 2
Literature Review
Many researchers investigated the application of soft computing approaches and intelligent models in the field of geoscience. Valentin et al, used borehole Image Data Logs (Ultrasonic and Microresistivity) as source and estimated porosity and permeability of Brazilian pre-salted carbonate using deep auto encoders with 96% accuracy [14]. Zhu et al proposed an efficient and new integrated hybrid neural network method in order to estimate total carbon content (TOC) from conventional logging data. The model has a very high accuracy in order to estimate TOC [15]. Mohaghegh utilized neural networks (NNs) for prediction of parameters related to NMR log of one of the East Texas fields [16]. Zhu et al conducted a cohesive case study and introduced a new method based on Multiboost-Kernel extreme learning machine and machine learning technique and accurately estimated of TOC respectively [17]. Malki and Baldwin investigated the applicability of neuro-fuzzy techniques for estimation of NMR log parameters by using coupled ability of Fuzzy Logic (FL) and an optimization algorithm named Genetic Algorithm (GA) [18]. Ahmadi and Chen compared learning approached and tested on porosity and permeability data samples gathered from northern Persian Gulf reservoirs. The permeability of one of northern Persian Gulf reservoirs has been modeled based on conventional logging data. The results cleared the supremacy of hybridized machine learning methods [19]. In this paper a more accurate model is conducted by new ANN-Cuckoo method. This model is fed by conventional
logging data and real field NMR permeability and effective porosity data and gives permeability and also effective porosity based on conventional logging data. NMR logging tool can yield the permeability and more notably, the effective porosity directly without using any intermediary calculations or costly laboratory measurements in large intervals. Ahmadi and Ebadi introduced a new method in order to have porosity and permeability accurately with availability of conventional logging data. The conventional logging data and porosity and permeability data were given to construct models by GA-LSSVM and GA-FL. This should be noted, the outcome models were highly accurate [20]. In this paper, direct measured effective porosity and permeability are set as reference data and the inaccuracy of calculating porosity and permeability by conventional correlations is tackled accordingly. Moreover, novel ANN-Cuckoo algorithm is applied as modeling algorithm and considerably accurate model is generated accordingly. Ahmadi et al, proposed an accurate model to conjoin permeability and porosity and bypass inaccuracy raised by conventional correlations between permeability and porosity. The model was conducted by utilizing ANN and optimized ANN methods [21]. In this research it is aimed to introduce an accurate model that can present accurate and trustworthy estimation of permeability and effective porosity. Therefore, new ANN-Cuckoo method and NMR data are used in this regard and an accurate model is introduced respectively. It should be noted, the NMR logging yields effective porosity without any mediatory and this is a huge advantage in this regard. Thank to great ability of Artificial Neural Networks (ANNs) for gaining information and results from complex data, they can be utilized for pattern recognition in highly nonlinear and complex problems [22, 23]. Most of modeling and training problems requires optimization techniques and optimization algorithms such as Genetic Algorithm (GA), Coupled Simulated Annealing (CSA), Particle Swarm Optimization (PSO) and Cuckoo can be used in this regard. Using these algorithms in conjunction with ANNs have benefits like as preventing from getting stuck on local minima, determining the most possible optimum solution for problem under consideration and etc [11, 24-26]. There is no report in the literature on the application of ANNs coupled with Cuckoo optimization algorithm for prediction of related parameters of NMR logs. Therefore, this study highlights the prediction of NMR logging parameters by using ANN in conjunction with Cuckoo optimization algorithm.
3
Artificial neural networks
Multilayer Perceptron (MLP) with one or more hidden layer(s), which belong to the feedforward ANN family, are universal approximators and have shown great performance in system identification [27 ,11] . Structure of the utilized MLP with one hidden layer is depicted in Figure 1. The MLP configuration entails selection of appropriate number of hidden layer(s) and number of neurons in each layer, to provide the approximation of proposed distillation column to any arbitrary degree of accuracy. In the present article, the sigmoid activation function is selected for hidden layer, while linear activation function is utilized for output layer. Number of neurons in each layer is set by trial and error and are three, fifteen and two for input, hidden and output layers, respectively. Inputs are DT, CN, RHOB and Rt and outputs Φeff and k.
Figure 1: Schematic of the Multi-layer ANN model The crucial factor affecting MLPs performance, the learning phenomena, deals with adjustment of the weights and biases of MLP interconnections to minimize an objective function by means of MSE criterion [27]. As stated previously, the widely used backpropagation algorithm suffers from two major drawbacks, such as the possibility of entrapment in non-optimal local minimum and slow speed of convergence. To overcome these weaknesses the Cuckoo optimization algorithm (COA) is utilized and is stated in section 2.2.
4
Cuckoo optimization algorithm
The Cuckoo Algorithm, inspired from the behavior of the bird of the same name, is one of the strongest evolutionary optimization algorithms available. Like other evolutionary algorithms, this algorithm also starts with a population. The primary populations of cuckoos are composed of assorted groups each of which resides in a specific location and lay eggs in hosting nests [11]. Eggs with a higher degree of similarity to the hosting bird's would enjoy a greater chance of survival, while those with less similarity would be identified and finally destroyed by the hosting birds. The larger the number of eggs that survive in a zone, the greater the chances of the attitudes from the cuckoos remaining there [11]. In order to increase the chances of the eggs’ salvation, the cuckoos migrate, seeking the best zones. Accordingly, they inhabit the location nearest to the present zone. Considering the number of eggs laid by each cuckoo and the distance to the best-optimized present zone, an Egg Laying Radius (ELR) is achieved. Then, the cuckoos start laying eggs randomly in their ELR. The process continues until the best location for laying eggs is achieved. The optimized zone is where the most eggs are laid, i.e., the most eggs are saved and the fewest are destroyed [11]. 5
Results and discussions
In this study 9000 data points were gathered. The data belongs to one of super oil fields in Iran southwest. The region that data belongs to is shown in Figure 2.
Figure 2. Major oil and gas fields in Southwest of Iran 7000 points were set for train and rest of them used for testing of networks. Specification of the networks and optimization algorithms are as follow Table 1: initial and steady states values of output ANN
Number of
Hidden layer
Output layer
Number of neurons
Number of neurons
transfer function
transfer function
in input layer
in hidden layer
sigmoid
linear
4
15
2
minimum number
ELR
neurons in output layer
COA maximum
minimum
maximum number
number of
number of
Cuckoo
Cuckoo
15
5
of eggs
of eggs
10
2
0.8
The Effective porosity (Φeff) has been modeled by ANN and ANN- Cuckoo networks. The Performance of predicted values and the result of prediction by ANN network are shown in Figure 3 and 4. The performance of training is acceptable however in the regard of testing, there is significant
difference between predicted values and real data. Moreover, at the maximum and minimum of data range, there are considerable difference in predicted and observed values.
Figure 3. Performance of predicted values of Φeff vs. the measured for the Training and Testing data
Figure 4. Results of ANN network for Φeff simulation in Training and Testing data The Φeff also simulated by ANN-Cuckoo algorithm. The performance and result are presented in Figures 5 and 6. The model accurately follow the data and the outputs match the real data. In both training and testing the model outperformed the ANN algorithm. Therefore, a reliable relation conducted between inputs and Φeff thorough modeling by ANN optimized by Cuckoo.
Figure 5. Performance of predicted values of Φeff vs. the measured for the Training and Testing data
Figure 6. Results of ANN-cuckoo network for Φeff simulation in Training and Testing data The modeling also has been performed for permeability (K). The result and performance of ANN and ANN-Cuckoo models for permeability are in some ways analogous to that of porosity modeling. The performance and result of ANN modeling for K are shown in Figures 7 and 8. Based on results, the model is properly modeled the permeability based on the inputs and this is evident in both training and testing performances. Furthermore, the outputs are not following the real data properly.
Figure 7. Performance of predicted values of K vs. the measured for the Training and Testing data
Figure 8. Results of ANN network for K simulation in Training and Testing data The performance and result of K modelling by ANN-Cuckoo are presented in figures 9 and 10. The result and performance of the model are good and the model predicted the real data correctly. The model has been well trained and showed very good test result.
Figure 9. Performance of predicted values of K vs. the measured for the Training and Testing data
Figure 10. Results of ANN-cuckoo network for K simulation in Training and Testing data The performance of the models are tabulated numerically in Tables 2 and 3. The mean square error (MSE) and regression coefficient (R2) are given accordingly. The modeling by ANN-
Cuckoo algorithm has given much more accurate model. The much lower MSE and R2 close to 1 indicates better performance of the respected model. Table 2: Performance of the ANN for the testing and training data sets without optimization R2
MSE Data set
K
K
Training
1.5711
62.2380
0.9573
0.9279
Testing
1.3322
16.2440
0.9230
0.8877
Table 3: Performance of the ANN-Cuckoo for the testing and training data sets without optimization R2
MSE Data set
K
K
Training
0.1556
7.1379
0.9996
0.9991
Testing
0.6749
8.3798
0.9802
0.9701
Figures 11 and 12 show root mean square error (RMSE) and regression coefficient (R2) of the models. The ANN-Cuckoo algorithm is capable in prediction and simulation of Φeff and K accurately and efficiently.
Figure 11. Comparing the RMSE of ANN-Cuckoo and ANN for Train and Tests data
Figure 12. Comparing the R2 of ANN-Cuckoo and ANN for Train and Tests data
Conclusion In this paper the NMR logging data for one of Iranian super oil fields have been simulated based on conventional logging data. The ANN-Cuckoo algorithm can precisely simulate the porosity and permeability of the respected field. The MSE, RMSE and R2 criteria briefly and effectively have indicated in what extent the ANN-Cuckoo algorithm is accurate and effective. The ANNCuckoo is much more precise and effective than ANN algorithm and the optimization of ANN by Cuckoo is very effective and beneficial. The ANN-Cuckoo can contribute great role in modeling such data. Such modeling would predict the required data precisely and would decrease the cost significantly by diminishing the need of direct measurements. The new simulation methods like ANN-Cuckoo would evolve the simulation method and would hike reliance on modeling rather than direct costly measurements.
Nomenclature ANN
Artificial Neural Network
COA
Cuckoo Optimization Algorithm
DT
Sonic Transit Time
K
Permeability
NMR
Nuclear Magnetic Resonance
NPHI
Neutron Porosity
MSE
Mean Square Error
R2
R-Squared
RHOB
Bulk Density
RMSE
Root Mean Square Error
RT
Electrical Resistivity
TOC
Total Carbon Content
Φeff
Effective Porosity
Acknowledgements The authors acknowledge the National Iranian Drilling Company (NIDC) for the support rendered in carrying out this research.
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The Authors hereby confirm there is no conflict of interest.