Ghasem Zargar,Aas Ayatizadeh Tanha,Amirhossein Parizad,Mehdi Amouri,Hasan Bagheri

a Petroleum University of Technology,Iran

b National Iranian Drilling Company,Well Logging Department,Ahwaz,Iran

c Petro Gostaran Ofogh (PGO),Mud Logging Department,Ahwaz,Iran

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 effi-cient,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 nonlinear 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 presalted 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 neurofuzzy 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 ANNCuckoo 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 ANNCuckoo 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[11,27].Structure of the utilized MLP with one hidden layer is depicted in Fig.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 Rtand outputs Φeffand k.

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.

Fig.1.Schematic of the Multi-layer ANN model.

Fig.2.Major oil and gas fields in Southwest of Iran.

Fig.4.Results of ANN network for Φeff simulation in Training and Testing data.

Fig.5.Performance of predicted values of Φeff vs.the measured for the Training and Testing data.

Fig.6.Results of ANN-cuckoo network for Φeff simulation in Training and Testing data.

Fig.7.Performance of predicted values of K vs.the measured for the Training and Testing data.

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 Fig.2.

Fig.8.Results of ANN network for K simulation in Training and Testing data.

Fig.9.Performance of predicted values of K vs.the measured for the Training and Testing data.

Fig.10.Results of ANN-cuckoo network for K simulation in Training and Testing data.

Table 1 Initial and steady state values of output.

Table 2 Performance of the ANN for the testing and training data sets without optimization.

Table 3 Performance of the ANN-Cuckoo for the testing and training data sets without optimization.

Fig.11.Comparing the RMSE of ANN-Cuckoo and ANN for Train and Tests data.

Fig.12.Comparing the R2 of ANN-Cuckoo and ANN for Train and Tests data.

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.

The Effective porosity (Φeff)has been modeled by ANN and ANNCuckoo networks.The Performance of predicted values and the result of prediction by ANN network are shown in Figs.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.

The Φeffalso simulated by ANN-Cuckoo algorithm.The performance and result are presented in Figs.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 Φeffthorough modeling by ANN optimized by Cuckoo.

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 Figs.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.

The performance and result of K modelling by ANN-Cuckoo are presented in Figs.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.

Initial and staeady state values are presented in Table 1.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 R2close to 1 indicates better performance of the respected model.

Figs.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 Φeffand K accurately and efficiently.

6.Conclusions

In this paper the NMR logging data for one of Iranian super oil fields have been simulated based on conventional logging data.The ANNCuckoo algorithm can precisely simulate the porosity and permeability of the respected field.The MSE,RMSE and R2criteria briefly and effectively have indicated in what extent the ANN-Cuckoo algorithm is accurate and effective.The ANN-Cuckoo 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 ANNCuckoo would evolve the simulation method and would hike reliance on modeling rather than direct costly measurements.

Acknowledgements

The authors acknowledge the National Iranian Drilling Company(NIDC)for the support rendered in carrying out this research.

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

R2R-Squared

RHOB Bulk Density

RMSE Root Mean Square Error

RT Electrical Resistivity

TOC Total Carbon Content

ΦeffEffective Porosity

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.petlm.2019.12.002.