Arab J Sci Eng (2015) 40:3345–3349 DOI 10.1007/s13369-015-1685-y
RESEARCH ARTICLE - PETROLEUM ENGINEERING
Total Organic Carbon Prediction in Shale Gas Reservoirs from Well Logs Data Using the Multilayer Perceptron Neural Network with Levenberg Marquardt Training Algorithm: Application to Barnett Shale Sid-Ali Ouadfeul1 · Leila Aliouane2
Received: 7 October 2014 / Accepted: 23 April 2015 / Published online: 10 May 2015 © King Fahd University of Petroleum & Minerals 2015
Abstract The main goal of this paper was to predict the total organic carbon (TOC) from well logs data using the multilayer perceptron (MLP) neural network machine. This can replace the Schmoker’s method in case of discontinuous measurement of the bulk density log. The MLP machine is composed of three layers, an input layer with four neurons corresponding to the Gamma ray, the neutrons porosity, and the slowness of the P and S waves well logs. The output layer is formed with one neuron, which corresponds to the predicted TOC log, and a hidden layer with ten neurons. The MLP machine is trained using the Levenberg– Marquardt algorithm. Data of two horizontal wells drilled in the lower Barnett formation located in USA are used. Comparison between the predicted and calculated TOC log using the Schmoker’s method clearly shows the use of the neural network method to predict the TOC in shale gas reservoirs. Keywords TOC · Prediction · Neural network · MLP · Levenberg Marquardt
1 Introduction The total organic carbon (TOC) prediction from seismic and well logs data has becoming an important topic of research, and Yeon et al. [1] have suggested an enhancement of total
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Sid-Ali Ouadfeul
[email protected]
1
Algerian Petroleum Institute, IAP, Boumerdés, Algeria
2
LABOPHYT, Faculté des Hydrocarbures et de la chimie, Université Mhamed Bougara de Boumerdès, Avenue de l’indépendance, Boumerdés, Algeria
organic carbon forecasting using neural networks discharge model. Bhatt and Helle [2] have used a neural network approach for porosity, permeability and TOC prediction from well logs data using a neural network approach. Ouadfeul and Aliouane [3] have suggested the use of the multilayer perceptron (MLP) neural network model for the prediction of the TOC from well logs data, and the training algorithm is the back propagation. Obtained results clearly show the efficiency of the neural machine to predict the TOC, and the suggested machine is able to replace the Schmoker’s model in case of discontinuous measurement of the bulk density log. Here, we suggest the use of the Levenberg Marquardt training algorithm to predict the TOC from well logs data using the MLP neural network machine. We start the paper by explaining some geophysical definitions of the TOC and the Schmoker’s method; after explaining the principle of the multilayer perceptron and the Levenberg–Marquardt algorithm, the proposed neural machine is applied to well logs data of horizontal wells drilled in the Barnett Shale formation. We end the paper by results interpretation and a conclusion.
2 Total Organic Carbon The TOC is the amount of organic carbon in the source rock, and there is no unit to quantify it. It is very important to have a high TOC (>5 %) to talk about a good shale plays and sweet spots [4]. Three methods are used for TOC measurement and estimation, and the first is based on the direct measurement in the laboratory. The second one is based on the direct measurement using a well logging tool. The last one is based on the empirical measurement. In this case, two methods are
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used: The first one is the so-called the Passey’s method, and the second one is called the Schmoker’s method. 2.1 Schmoker’s Method Two widely used empirical approaches have been developed to quantitatively estimate TOC from log data. The first was developed in Devonian shales using bulk density logs [5,6] and was later refined in Bakken shales [7]. Based on the response of the bulk density measurement to low-density organic matter (∼ 1.0 g/cm3 ), the Schmoker’s method, as it is commonly called, computes TOC [6]: TOC =
154.497 − 57.261 ρb
where ρb is the bulk density in g/cm3 and TOC is reported in wt%. This equation assumes a constant mineral composition and porosity throughout the formation. Although the method was developed and refined based on specific environments, it is frequently used for TOC estimation in a wide variety of shale formations.
When the performance function has the form of a sum of squares (as is typical in training feedforward networks), then the Hessian matrix can be approximated as: H = J ∗ JT and the gradient can be computed as: g = J T e The Levenberg–Marquardt algorithm uses this approximation to the Hessian matrix in the following Newton-like update: −1 ∗ J Te X k+1 = X k − J T ∗ J + μI In practice, this algorithm, in particular in the case of neural networks, can converge with much fewer iterations. But each iteration requires more calculations, in particular for the inversion of the matrix, and therefore, its use is limited to cases where the number of parameters to optimize is not very high. Indeed, the number of operations required for a matrix inversion is proportional to, as the size of the matrix, and also by the size of the vector. For more details about the Levenberg–Marquardt training algorithm, we invite you to read the paper of Hagan and Menhaj [10].
3 The Multilayer Perceptron A neural network is inspired from human biology; each neural network is composed of a set of neurons. Each neuron is connected with some neurons in the network. Each neuron receives a signal from other neurons and transforms to outside using a transfer function. The MLP is a feedforward artificial neural network. The MLP is composed of a set of layers; the first one is called the input layer, while the last one is called the output layer. The set of layers between these two layers are called hidden layers. It is shown that one hidden layer is enough for better approximations and the neural network will react better [8]. The MLP uses the supervised learning mode where the couple input–desired output is known [8]. Many training algorithms have been suggested in the literature, and the backpropagation is one of the classical algorithms [8,9]. Traditional back propagation algorithms have some drawbacks such as getting stuck in local minimum and slow speed of convergence. The Levenberg–Marquardt training algorithm is used to resolve these ambiguities. In the next section, we will explain the principle of the Levenberg– Marquardt training algorithm. 3.1 The Levenberg–Marquardt Training Algorithm The Levenberg–Marquardt (LM) training algorithm is an approximation of Newton’s method for artificial neural network. The LM technique is known to be the best algorithm for optimization problems applied to artificial neural network.
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4 Application to Real Data 4.1 Geological Setting The Barnett shale was deposited over present day North Central Texas during the late Mississippian age in a time marine transgression caused by the closing of the Iapetus Ocean Basin. By the end of the Pennsylvanian, the Ouachita thrust belt began encroaching into the present day North Texas area. The thrust belt owes its existence to the subduction of the South American plate under the North American plate. The Ouachita thrust’s emergence created the foreland basin along the front of the thrust. Early studies of the basin attributed thermal maturation of the Barnett to burial history and the thermal regimes associated with depth of burial. Figure 1a shows the stratigraphic column of Mississippian and the Pennsylvanian ages, our shale gas reservoir target is the lower Barnett, and the top of the reservoir is located at 6650 m [11]. Figure 1b shows the mineralogy and the TOC after Perez [12], we can observe that the lower Barnett is characterized by high to good TOC. The mineralogy tracks show that the lower Barnett is characterized by high quartz content which is good for the hydraulic fracture. The calcite percentage is very low; however, it has average clay content. The briskness index of the lower Barnett is very high, and all these properties make the Barnett a good shale play [13].
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Fig. 1 a Stratigraphic column of the Mississippian, b Mineralogy and TOC content of the lower Barnett after Perez [12]
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Fig. 2 Well logs data recorded in a horizontal well drilled in the lower Barnett used as a pilot
4.2 Data Processing
1.6 1.4
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1.2 1 0.8 0.6 0.4 0.2 0 1 130 259 388 517 646 775 904 1033 1162 1291 1420 1549 1678 1807 1936 2065 2194 2323 2452 2581 2710 2839 2968
Data of two horizontal wells drilled in the lower Barnett are used. The first well W01 is used for the training, and however, the data of the second well W02 are used for the propagation. Figure 2 shows the recorded well logs data of W01, the first track is the depth, the second track presents the bulk density log, the third is the neutron porosity, the fourth and the fifth tracks show the primary and the shear-wave slowness, and the last is the calculated TOC using the Schmoker’s model. In this case, we suppose that we do not have the bulk density measurement and we use the first four logs as an input and the calculated TOC as an output to train a MLP neural network using Levenberg–Marquardt training algorithm. The number of neurons in the hidden layers is equal to 10, and this number is calculated after many numerical experiences. During the training, the root-mean-square error between the calculated and the desired outputs is calculated. Figure 3 shows the root-mean-square error versus the iteration number. After training, the weights of connections between neurons are calculated. To check the efficiency of the neural network machine, the data of the second horizontal well are propagated through the neural machine using the weights of connections calculated previously. Figure 4 shows the measured well logs data for the second well; data that are propagated through the neural machine have the same kind of those used as an input.
Fig. 3 Root-mean-square error versus the iteration number
Figure 5 shows the predicted TOC compared with the estimated TOC using the Schmoker’s model.
5 Results Interpretation Figure 5 shows a comparison between the predicted TOC using Levenberg–Marquardt training algorithm and the TOC using the Schmoker’s model. It is clear that the proposed MLP neural network machine is able to predict with a good precision the TOC in the second horizontal well without measurement of the bulk density. The proposed neural network machine can be greatly used to replace the Schmoker’s model and to provide a value of the TOC in case of discontinuous measurement of the bulk density.
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Fig. 4 Well logs data recorded in a horizontal well used for the data propagation
Total Organic Carbon
References
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Fig. 5 Calculated TOC using Schmoker’s model compared with the predicted TOC using the MLP with Levenberg–Marquardt training algorithm
6 Conclusions In this paper, we have implanted a MLP neural network machine able to predict the TOC and replace the Schmoker’s model in case of absence of the bulk density measurement. The training algorithm is the so-called the Levenberg– Marquardt, application to two horizontal wells drilled in the lower Barnett shale formation, clearly shows the efficiency of the neural machine. We suggest testing the implanted machine in other horizontal wells that are close to the pilot well. The implanted machine can be greatly used in sweet spots discrimination, basin modeling and Kerogen volume estimation.
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