Development of Artificial Neural Networks (ANNs) to Synthesize Petrophysical Well Logs

Transcription

1 International Journal of Petroleum and Geoscience Engineering (IJPGE) 1 (3): ISSN Academic Research Online Publisher Research Article Development of Artificial Neural Networks (ANNs) to Synthesize Petrophysical Well Logs Sh. Esmaeilzadeh a, *, A. Afshari b,n. Sa`adatnia c a Department of Petroleum Engineering, Imam Khomeini International University (IKIU), Qazvin, Iran b Pars Oil and Gas Company (POGC), a subsidiary of National Iranian Oil Company (NIOC), Asaluyeh, Iran, c Department of Petroleum Engineering, Abadan Faculty of Petroleum Engineering, Petroleum University of Technology, Abadan, Iran. * Corresponding author. Address: afshari_ahmad@yahoo.com. A b s t r a c t Keywords: Synthesizing petrophysical, well logs, Artificial Neural Networks (ANNs), Porosity, Well logs, Carbonate oil reservoir. Accepted:25 September2013 Porosity is one of the fundamental petrophysical properties which should be evaluated for hydrocarbon bearing reservoirs. Petrophysical well logs are the most essential instruments for the evaluation of hydrocarbon reservoirs. There are three main petrophysical logging tools for porosity determination namely: neutron, density and sonic well logs. Porosity can be determined using each of these tools; however, a precise analysis requires a complete set of these tools. Log sets are commonly either incomplete or unreliable for many reasons (i.e. incomplete logging, measurement errors and loss of data owing to unsuitable data storage). To overcome this issue, the current study presents an intelligent technique using Artificial Neural Networks (ANN) to synthesize petrophysical well logs including: neutron, density and sonic logs. To accomplish this, the petrophysical well logs data collected from six wells was utilized for constructing optimum ANN model and a seventh well data from the field was employed to evaluate the reliability of the model. The proposed methodology is presented with an application to field information of a carbonate oil reservoir, located in Persian Gulf, Iran. The corresponding correlation was obtained through the comparison of synthesized log values to real log amounts. The results demonstrate that ANNs are successful in synthesizing petrophysical well logs with a high degree of accuracy. Academic Research Online Publisher. All rights reserved. 1. Introduction Well logging has been commonly used for about a century as a critical tool for determination of potential production in hydrocarbon reservoirs. Well log analysis interprets the data from the log in order to determine the petrophysical parameters of the well. However, for economic reasons, companies do not always run a full set of logs vital to determining reservoir characteristics. This paper

2 presents a methodology that can solve this issue by generating synthetic petrophysical well logs for locations where the necessary set of logs to analyze the reservoir properties, are absent or incomplete. The goal of the methodology used here is not to remove well logging in a field but is meant to become a tool for reducing costs for companies whenever logging proves to be insufficient and/or difficult to obtain. This technique in addition, can provide a guide for quality control during the logging process by prediction of the response of the log before the log is acquired. The presented approach involves the use of artificial neural networks as the main tool. To date, ANNs have been successfully used in a variety of related petroleum engineering applications such as reservoir characterization, optimal design of stimulation treatments and optimization of field operations (Lim, 2005; Mohaghegh, 2000; Tamhane et al., 2000). A back-propagation neural network is a supervised training technique that sends the input values forward through the network then computes the difference between calculated output and the corresponding desired output from the training dataset. The error is then propagated backward through the net, and the weights are adjusted during a number of iterations named epochs. The training stops when the calculated output values best approximate the desired values (Hamada, 2009; Bhatt and Helle, 2002). The field under study is located in Persian Gulf. It is a dome structure plunging toward North-East. The concerned formation called Arab is composed of alternation of seven mostly dolomite and minor limestone reservoir layers with interbeded distinct anhydrite layers. The carbonates have been interpreted (Kawaguchi, 1991) as an accumulation of a shallowing upwards sequence from the deeper marine sediments to the supratidalsabkha anhydrite which overlies the reservoir immediately. The Jurassic aged Arab formation is limited to Hith (mainly anhydrite) and Darb formations that are located in the top and bottom of Arab formation respectively. The followings are devoted to a brief explanation about the logs synthesized in the present study, including: neutron, sonic and density logs. Neutron Logs: Neutron logs measure the concentrations of hydrogen atoms (held in water and hydrocarbons) that are present in formation pores, and record them in units of percent porosity. Each neutron has a mass almost identical to the mass of a hydrogen atom. High-energy neutrons are constantly emitted from a radioactive resource in the well log sonde. The amount of energy lost per collision depends on the relative mass of the nucleus with which the neutron collides. After collision, the slowing down of the neutrons and subsequent loss of energy is proportional to the volume of water or hydrocarbon content in the formation which itself is directly related to the porosity of rock, if 100% fluid saturation is supposed (Asquith, 1982). 204 Page

3 Sonic Logs: Sonic logs measure the shortest time required for a compressional wave to travel vertically through one foot of formation adjacent to the well bore. This interval transit time for a given formation depends upon its lithology and porosity. Thus, sonic travel time is used both in porosity and lithology determination specially when combined with the neutron logs or density logs (Serra, 1984). Density Logs: Density logs are tools for determining rock bulk density along a wellbore. The density tool has a nuclear source which continuously emits medium energy gamma rays. These gamma rays collide with the electrons of the formation, lose some of their energy during each collision and are scattered in the formation (Compton scattering). The tool counts the gamma rays that reach the detector with a sufficient energy level. The number of Compton scattering collisions is directly related to the number of electrons in the formation which in turn depends on the density of the rock matrix, the formation porosity and the density of the fluids filling the pores. In low porosity formations (more dense), the gamma rays are scattered more which means there is more absorption by the matrix due to low energy. A combination of this log with neutron or sonic logs helps to determine lithology and provides a more reliable porosity value (Bateman, 1985; Patchett and Coalson, 1982). 2. Methodology The data sets utilized in this study for model construction and evaluation of the reliability of the models came from seven wells of a carbonate oil reservoir located in Persian Gulf, Iran. All of the wells had sonic transit time (DT), bulk density (RHOB), neutron (NPHI), photo electric factor (PEF) and gamma ray (GR) logs. Table 1 describes statistics of each well log data set. Three networks were designed for synthesizing sonic, density and neutron logs. Firstly, well log data were processed and bad-hole intervals were removed. Normalization of the data was also done for a better prediction. Actually, a high range of output in each ANN model causes low performance in synthesizing well logs; therefore in the following models development, the normalized well logs data has been applied and the performance of the models were mentioned in a unit-less scale. Two methods have been used for appropriate input selection: stepwise regression and ANN. Stepwise regression adds and removes variables to the regression model with the aim of recognizing a suitable subset of the predictors. The basic procedure for stepwise regression involves identifying an initial model, iteratively stepping that is repeatedly modifying the model at the previous step by adding or removing a predictor variable in accordance with the stepping criteria and finally terminating the search when stepping is no longer possible based on the assumed stepping criteria. More description about stepping criteria could be found in Minitab Inc. (2006). In this study, stepwise regression has been employed using Minitab statistical software. Because of space considerations, from now on we will just present the obtained results for the sonic ANN model. Results for the other two models are available upon 205 Page

4 request. Table 2 summarizes the stepwise regression analysis results for constructing sonic ANN model. In each step, constants, coefficients related to each variable, correlation coefficient and root mean squared error (RMSE) are presented as could be seen. A more accurate method for determining the appropriate input is constructing ANN. In this order, different combinations of the well logs data are considered as inputs to the network and the performance of the constructed model is averaged in the test data set for a fixed number of runs. Mean squared error (MSE) is a common network performance function which measures the network's performance according to the mean of squared errors. Here, MSE employed and the performance of the constructed model was averaged for ten runs. The corresponding results are summarized in Table3. Each entry in this table represents 20 different trials, where different random initial weights are used in each trial. Considering the results of these two methods, it could be concluded that selecting bulk density, neutron and gamma ray logs data in input layer will be associated with the minimum MSE for synthesizing sonic log. The same methodology was applied for selection of appropriate inputs for both RHOB and NPHI developed model. Selected inputs for each of constructed models are summarized in Table 4. As said before, back propagation error model is a supervised learning method which means a set of training data that has the desired output (real log values here) for any given input is needed. The network computes the difference between the calculated output and corresponding real log values from the training data set. Then the error is propagated backward through the net and the weights are adjusted. The input layer consisted of three neurons of sonic ANN model and inputs were introduced to the network as a two-dimensional matrix, namely a 3 N matrix in which N is the number of given data points. To find the optimum number of neurons in hidden layer, networks with 1 to 20 neurons in their hidden layer were tested for each target and the best result was associated with eight neurons. Similar procedure was followed and six hidden neurons were obtained for neutron ANN model. For bulk density the obtained result was not satisfactory and a network with two hidden layers of four neurons gave the best results. TANSIG was employed as transfer function between input layer and hidden layer and LOGSIG was applied as transfer function from hidden layer to output layer of sonic ANN model but TANSIG and PURELIN was utilized in first and second layers of other two models respectively (Figure 1). The error goal and maximum number of epochs were set to zero and 100 respectively for all of the developed models. Levenberg Marquardt (LM) optimization was used in order to update weight and bias values. LM is a network training function based on an approximation to Newton s method whose details of process and calculation can be found in Hagan and Menhaj (1994), Bishop (1995) and Burney et al. (2004). Finally, the optimum model has been selected among the obtained results of hundreds of runs. After constructing the ANN model using data from six wells of available seven wells, the reliability of each constructed model was evaluated by the seventh well data. Same inputs data was available in the 206 Page

5 seventh well under study; otherwise synthesizing of well log parameters will not be possible as they serve as model inputs. The obtained results are given and discussed in the next section. 3. Results and discussion As mentioned in methodology, a three-layered back propagation error model was employed for design of ANN models in the present study. A schematic diagram of constructed sonic ANN model architecture is demonstrated in Figure 2. In Figure 3, MSE for training, test and validation data against training epochs is shown. According to the figure, after 20 epochs, MSE decreases for training data and increases for validation data. This epoch is the border between over-training and under-training. In other words, if the network stops earlier (i.e. at 19 epochs or less), it means that the network does not learn all the information content of the input data as fully as possible and if it stops later (i.e. at 21 epochs or more), it means that the network loses its ability to generalize. Thus epoch twenty was considered as the border between under-training and over-training of the optimum ANN model for synthesizing sonic log. As mentioned in methodology, to evaluate the reliability of the model data from a well which has not been utilized in construction of the ANN model (data from the seventh well) was introduced to each of the developed ANN models and their generalization capability was checked. Crossplot between the real and ANN synthesized log values of each of these models for the seventh well and also the corresponding correlation coefficients are illustrated in Figure 4. As it is clear, logs have been synthesized with very good accuracy. A comparison between real and synthesized logs along this well is also demonstrated in Figure 5. The synthesized log has obviously followed the trend of real log very closely. Table 1: Statistics of dataset used as inputs to ANN models Variable Min. Max. Mean St. Dev. RHOB DT NPHI GR PEF Table 2: Appropriate input selection; applying stepwise regression for DT Step Constant Page

6 RHOB NPHI GR RMSE R Table 3: Performance of the neural network for synthesizing sonic log, in the test data using several sets of input well log data Inputs MSE ( 10-2 ) RHOB RHOB, NPHI RHOB, GR RHOB, PEF RHOB, NPHI, GR RHOB, NPHI, PEF RHOB, NPHI, GR, PEF Table 4: Obtained appropriate inputs for synthesizing petrophysical well logs Predicted well log DT RHOB NPHI Inputs RHOB, NPHI, GR DT, NPHI DT, RHOB Fig. 1.(A) TANSIG, (B) PURLIN and (C) LOGSIG functions used in first and second layers of networks. 208 Page

7 Fig. 2.A schematic diagram of the constructed ANN architecture for synthesizing sonic log. Fig. 3.MSE for training, test and validation data against training epochs. 209 Page

8 A B C Fig. 4.Cross-plot showing the correlation coefficients between real and synthesized values of the seventh well at Arab reservoir formation interval for (A) RHOB, (B) DT and (C) NPHI logs. 210 Page

9 Fig. 5.A comparison between real and synthesized values of the seventh well at Arab reservoir formation interval for (A) RHOB, (B) DT and (C) NPHI logs. 211 Page

10 4. Conclusions The following conclusions can be drawn from this research: i.this study indicated that intelligent synthesizing of petrophysical well logs by use of other well logs data is a highly feasible method. ii. The developed ANN models were successful in synthesizing petrophysical well logs. A high correlation was obtained between synthesized and real petrophysical well logs for a test well of the studied field. Both synthesized and real petrophysical well logs were presented to demonstrate that well logs were synthesized with a high degree of accuracy. iii. The developed ANN model does not incorporate depth or lithological data as part of the inputs to the network. This means the utilized methodology is applicable to any field. Nomenclature: ANN Artificial Neural Network BP-ANN Back Propagation Artificial Neural Network DT Sonic Transit Time Log ( s/ft) GR Gamma Ray Log (API) LM Levenberg-Marquart NPHI Neutron Log (v/v) RHOB Density Log (gr/cm3) Reference: [1] Asquith, G. B., Basic Well Log Analysis for Geologists, Amer. Assoc. Pet. Geol. Methods in Exploration Series, 1982, 3;216. [2] Bateman, R. M.,Open-Hole Log Analysis and Formation Evaluation, IHRDC,Boston, [31] Bhatt, A., Helle, H. B., Committee Neural Networks for Porosity and Permeability Prediction from Well Logs, Geophys. Prospect,2002, 50:645. [4] Bishop, C.M., Neural Networks for Pattern Recognition, Clarendon Press, Oxford,1995;670. [5] Burney, S.M.A., Jilani, T.A., Ardil, C., Levenberg Marquardt Algorithm for Karachi Stock Exchange Share Rates Forecasting, Trans. Eng. Comput. Technol.2004, 3;1305. [6] Hamada, G. M. and Elshafaei, M. A., Neural Network Prediction of Porosity and Permeability of Heterogeneous Gas Sand Reservoirs, SPE paper , SPE Saudi Arabia Section Technical Symposium and Exhibition, Alkhobar, May, Page

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