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Mathematical Geosciences ISSN 1874-8961 Math GeosciDOI 10.1007/s11004-012-9421-6

Marcellus Shale Lithofacies Prediction byMulticlass Neural Network Classification inthe Appalachian Basin

Guochang Wang & Timothy R. Carr

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Math GeosciDOI 10.1007/s11004-012-9421-6

Marcellus Shale Lithofacies Prediction by MulticlassNeural Network Classification in the Appalachian Basin

Guochang Wang · Timothy R. Carr

Received: 24 May 2012 / Accepted: 3 September 2012© International Association for Mathematical Geosciences 2012

Abstract Marcellus Shale is a rapidly emerging shale-gas play in the Appalachianbasin. An important component for successful shale-gas reservoir characterization isto determine lithofacies that are amenable to hydraulic fracture stimulation and con-tain significant organic-matter and gas concentration. Instead of using petrographicinformation and sedimentary structures, Marcellus Shale lithofacies are defined basedon mineral composition and organic-matter richness using core and advanced pulsedneutron spectroscopy (PNS) logs, and developed artificial neural network (ANN)models to predict shale lithofacies with conventional logs across the Appalachianbasin. As a multiclass classification problem, we employed decomposition technol-ogy of one-versus-the-rest in a single ANN and pairwise comparison method in amodular approach. The single ANN classifier is more suitable when the availablesample number in the training dataset is small, while the modular ANN classifierperforms better for larger datasets. The effectiveness of six widely used learning al-gorithms in training ANN (four gradient-based methods and two intelligent algo-rithms) is compared with results indicating that scaled conjugate gradient algorithmsperforms best for both single ANN and modular ANN classifiers. In place of usingprincipal component analysis and stepwise discriminant analysis to determine inputs,eight variables based on typical approaches to petrophysical analysis of the conven-tional logs in unconventional reservoirs are derived. In order to reduce misclassifi-cation between widely different lithofacies (for example organic siliceous shale andgray mudstone), the error efficiency matrix (ERRE) is introduced to ANN during

G. Wang (�) · T.R. CarrDepartment of Geology & Geography, West Virginia University, 98 Beechurst Ave, 330 Brooks Hall,P.O. Box 6300, Morgantown, WV 26506-6300, USAe-mail: [email protected]

G. WangPetroleum Engineering Department, China University of Geosciences (Wuhan), Wuhan, Hubei430074, China

Author's personal copy

mailto:[email protected]

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training and classification stage. The predicted shale lithofacies provides an opportu-nity to build a three-dimensional shale lithofacies model in sedimentary basins usingan abundance of conventional wireline logs. Combined with reservoir pressure, ma-turity and natural fracture system, the three-dimensional shale lithofacies model ishelpful for designing strategies for horizontal drilling and hydraulic fracture stimula-tion.

Keywords Marcellus organic-rich shale · Lithofacies · Artificial neural network ·Error efficient matrix · Petrophysical analysis

1 Introduction

Lithofacies, the lithologic aspect of facies, is a basic property of rocks and has strongeffects on many subsurface reservoir properties (Rider 1996; Chang et al. 2000, 2002;Saggaf and Nebrija 2003; Jungmann et al. 2011). Historically, interest in lithofaciesresearch has focused on carbonate and siliciclastic reservoirs, especially the methodsto predict lithofacies with wireline logs (Chang et al. 2000, 2002; Saggaf and Nebrija2003; Yang et al. 2004; Qi and Carr 2006). The widespread recent success of oil andgas exploration and production from unconventional shale reservoirs in such units asthe Bakken Formation, Barnett Shale, Marcellus Shale, New Albany Shale, AntrimShale and Woodford Shale has refocused lithofacies research on organic-rich shale.Papazis (2005) explored the petrographic features of the Barnett Shale from core andthin-section photographs. Most of the shale lithofacies research focused in BarnettShale used core petrographic data (Hickey and Henk 2007; Loucks and Ruppel 2007;Singh 2008) and well logs (Perez 2009; Vallejo 2010). This has been supplementedwith the mechanical properties of lithofacies in the Woodford Shale (Sierra et al.2010), seismic attributes of lithofacies in the Marcellus Shale (Koesoemadinata et al.2011), and numerous outcrop studies (Walker-Milani 2011).

Shale-gas reservoirs, as unconventional reservoirs, are quite different from sand-stone and carbonate reservoirs in reservoir properties and strategies of hydrocar-bon exploration and development. A strong relationship between total organic car-bon (TOC) and gas content is generally observed in shale-gas reservoirs. Artificialfracturing is routinely operated in most of the shale-gas wells due to the extremelylow matrix permeability (nano-Darcies). The experience from Barnett Shale indicatesthat key for shale-gas reservoir characterization is determining facies amenable to hy-draulic fracture stimulation that contain significant organic-matter and gas concentra-tion (Bowker 2007). Shale-gas reservoirs can be characterized in a multi-dimensionalmodel of lithofacies, which is defined mainly by mineral composition and richness oforganic matters using geochemical logs (Jacobi et al. 2008). However, geochemicallog data, which is more expensive than conventional logs, is available in only a smallnumber of wells limiting the ability to build large-scale three-dimensional modelsof shale lithofacies. Conventional logs are available in the majority of recent wellsand record geological properties of subsurface formations that have been utilized topredict lithofacies of carbonate and sandstone, but rarely for shale lithofacies. Wepropose to integrate core and geochemical logs with the more abundant conventionallogs to create an opportunity to improve the prediction of shale lithofacies.


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Fig. 1 Map showing study area, the location of more than 3,880 wells with conventional wire-line logs(gray circles), seventeen wells with pulsed neutron spectroscopy (PNS) logs (red-filled triangles), andeighteen wells with core XRD and TOC data (green-filled circles). The blue-filled circles with trianglesindicate wells with both core data and PNS logs. The red lines are interpreted faults; the green lines arethe structure contour of the top of Marcellus Shale (contour interval 1500 feet [457 m]); the filled colorsindicate the isopach of Marcellus Shale (contour interval 50 feet [15 m])

The fuzzy feature of conventional logs is intrinsic to the prediction of lithofa-cies due to the wide range of responses for each lithofacies, the different scales be-tween logging data and core data, and the varying borehole environment (Dubois et al.2007). The fuzzy nature of petrophysical response creates a complex and non-linearrelationship between log response and shale lithofacies. Artificial neural networks(ANN) are widely used in complex classification problems because of the abilityto unravel non-linear relationships, quantify learning from training data, and workin conjunction with other kinds of artificial intelligence (Bohling and Dubois 2003;Kordon 2010). Support vector machine, as a relatively new approach, has been intro-duced into lithofacies prediction (Al-Anazi and Gates 2010; El-Sebakhy et al. 2010).In this paper, we test aspects of ANN including design for multiclass classification,network architecture, learning algorithms, and performance.

The Marcellus Shale is an organic-rich shale covering most of the Appalachianbasin (Fig. 1) and contains up to 1.38 × 1013 m3 recoverable gas (Engelder 2009).


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The major objectives for application of ANN to Marcellus Shale are to improve theidentification of shale lithofacies in wells with conventional logs and construct three-dimensional lithofacies models to better understand depositional process and improvethe design of horizontal well trajectories and placement of hydraulic fracture stimu-lation.

2 Methodology

An integrated method of identifying shale lithofacies includes the following steps:(1) classifying lithofacies at core-scale; (2) predicting lithofacies with wireline logsat the well-scale; and (3) building a three-dimensional lithofacies model or a two-dimensional map or cross section of lithofacies distribution. This paper focuses onthe prediction of shale lithofacies in wells by integrating log data with core data. Thedirect observation and information richness of lithofacies are the major advantage ofcore data. However, in most cases core data are available from only a very limitednumber of wells, while wireline logs are available from a significantly larger numberof wells to better define the areal variations in lithofacies. Compared to the unsuper-vised learning algorithms (for example clustering), the supervised algorithms werepreferred for building the relationship between core-defined lithofacies and log re-sponses. Pre-processing of training dataset, design of classifier and post-processingof outputs from classifier are necessary to build a reliable result to recognize shalelithofacies. The pre- and post-processing of data is discussed in the following sec-tions with an emphasis on designing the classification system. In this section, we willdiscuss the details of classifier design.

Artificial neural network is not a unique classifier for pattern recognition; how-ever, the merits of ANN result in its broad application within various scientific andacademic fields (Micheli-Tzanakou 2000). ANN has also been used to predict litho-facies (Chang et al. 2000, 2002; Bohling and Dubois 2003; Saggaf and Nebrija 2003;Yang et al. 2004; Qi and Carr 2006; Ma 2011). However, ANN has not received ex-tensive application for integrating core data with conventional and pulsed neutronspectroscopy logs to characterize organic-rich shale lithofacies typical of unconven-tional hydrocarbon reservoirs.

2.1 Multiclass ANN Classification

Lithofacies recognition is a typical multiclass classification problem. The conven-tional logs are the observations (input variables), while the shale lithofacies as thepredefined classes from the core data are the target outputs. It is easier to designmachine learning algorithms for two-class (binary) classification, so most algorithmswere developed first for binary classification problems (Dietterich and Bakiri 1995;Li et al. 2003; Ou and Murphey 2007). The algorithms, including decision tree, dis-criminant analysis and nearest neighborhoods, can be extended to multiclass cases (Liet al. 2003); however, other algorithms must be decomposed into a set of binary clas-sification problems (Dietterich and Bakiri 1995; Allwein et al. 2000; Li et al. 2003;Ou and Murphey 2007). ANN is one of the algorithms that needs to decompose mul-ticlass classification into a set of binary classification problems. Using a set of binary


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classifiers to handle multiclass classification consists of two stages: in the trainingstage, the binary classifiers are built based on suitable partition of the set of trainingexamples; in the classification stage, the computed outputs from binary classifiers arecombined to determine the overall classes.

It is not a trivial task to reduce multiclass to binary classification problems, sinceeach method has unique limitations (Allwein et al. 2000; Li et al. 2003). The popular-ized decomposition techniques include one-versus-the-rest method (Li et al. 2003),pairwise comparison (Hastie and Tibshirani 1998), and error-correcting output cod-ing (ECOC) (Dietterich and Bakiri 1995). The idea behind the one-versus-the-restmethod is to set the desired output of one class as one and all the rest as zero. Fora given number of classes (k), the one-versus-the-rest method can be implementedby one single ANN with k output nodes or a set of k binary ANNs with one outputnode for each ANN. The strengths of one single ANN are: (1) classes can share in-formation (Ou and Murphey 2007); (2) the probability minimizes the uncovered andoverlapped regions; and (3) it is relatively simple to design and train a single ANN.The single ANN with seven output nodes is employed to test the effectiveness of theone-versus-the-rest method for predicting Marcellus Shale lithofacies (Fig. 2(a)). Anobvious drawback of one-versus-the-rest is to exacerbate the imbalanced situation ofthe training examples. The pairwise comparison method can only be implemented byconstructing a total of (k−1)k/2 independent binary classifiers for each possible pairof classes (Fig. 2(b)), which forms a modular neural network (Haykin 1999). If k islarge, a large number of independent binary classifiers should be built. With regard toMarcellus Shale lithofacies, the k of seven which is relatively small, permits testingthe effectiveness of the pairwise comparison method.

During classification stage, the decision function is used to determine the shalelithofacies according to the outputs from the single ANN or the modular ANN.The common methods consist of max-win method, voting method, and the closestHamming distance method for ECOC (Dietterich and Bakiri 1995). In the max-winmethod, the overall class is the class with maximal output value, and is combined withthe one-versus-the-rest method. The voting method is used for the modular ANN,which has 21 votes from all the binary ANNs, and the class with the most votes is theoverall class.

2.2 Supervised Learning Algorithms

Several algorithms for optimization problems have been introduced to minimize theerrors between target and computed outputs in the training of ANNs. These algo-rithms can be categorized into two groups. The first group consists of gradient-based methods, which include four popular algorithms: steepest descent gradient(SDG), steepest descent gradient with momentum (SDGM), scaled conjugate gra-dient (SCG), and Levenberg–Marquardt (LM). These algorithms optimize ANNthrough back-propagating errors between target and predicted outputs. The secondgroup includes stochastic optimization and intelligent algorithms. The major merit isavoidance of local non-optimal minimums by adding random noise. Representativealgorithms of this group include simulated annealing, Boltzmann machine learning,and pattern extraction (Micheli-Tzanakou 2000). Artificial or swarm intelligence has


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Fig. 2 The architecture of an artificial neural network (ANN) for Marcellus Shale lithofacies prediction.(a) One single ANN with seven output nodes for the one-versus-the-rest method; (b) the modular ANNconsisting of twenty-one binary ANN classifiers with one output node for the pairwise comparison method

inspired additional optimization methods, such as genetic algorithm (GA) and parti-cle swarm optimization (PSO). Randomness is employed to generate new offspringfor GA and new moving direction and velocity for PSO for optimizing weights andbias.

2.3 Performance Evaluation

The right ratio from cross validation is an important criterion for evaluating the per-formance of classifiers, but it is not sufficient for multiclass recognition. In multi-class classification problems, the hierarchical structure and its corresponding classproximity are very important, but generally ignore issues for evaluating performanceof classifiers. Misclassification into a very different class incurs a larger error thanmisclassification into a different but similar class. The proximity-based estimation ofclassifier performance is distinctive from the cost-based estimation in two aspects:(1) the proximity-based estimation is inspired by the intrinsic features of the mul-


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Table 1 The contrast matrix of shale lithofacies indicating the proximity among Marcellus Shale litho-facies. A higher relative value implies a larger difference between the two classes. Marcellus lithofaciesare classified as organic siliceous shale (OSS); organic mixed shale (OMS); organic mudstone (OMD);gray siliceous shale (GSS); gray mixed shale (GMS); gray mudstone (GMD); and carbonate (CARB). Forcertain unique classes (e.g., carbonate), its contrast is calculated by setting a relatively bigger value for the

position |P i2 − P

j2 |

Contrast OSS OMS OMD GSS GMS GMD CARB

OSS 0 1 2 1 2 3 4

OMS 1 0 1 2 1 2 4

OMD 2 1 0 3 2 1 4

GSS 1 2 3 0 1 2 3

GMS 2 1 2 1 0 1 3

GMD 3 2 1 2 1 0 3

CARB 4 4 4 3 3 3 0

Fig. 3 The tree diagram for deciding contrast matrix for Marcellus Shale lithofacies. The shale lithofaciesis classified according to two criteria: organic matter richness (C1) and mineral composition (C2). Thenumber (P1,P2) under each lithofacies indicates the position of classes. The contrast between two classes

is defined as: Ci,j = C1 × |P i1 − P

j1 | + C2 × |P i

2 − Pj2 |

tiple classes, while the cost-based estimation depends on the application (Blockeelet al. 2002); (2) misclassifying class A to B and B to A has the same performancepenalty for proximity-based estimation, but the performance penalty usually variesfor cost-based estimation.

In order to introduce class proximity to the neural network, we generate a contrastmatrix and error efficiency matrix (ERRE). The contrast matrix describes the relativedifference between each pair of classes, which can be decided by input variables orthe position of each class in a tree diagram (Table 1; Fig. 3). A higher value implies


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Table 2 Error efficiency matrix of Marcellus Shale lithofacies derived from contrast matrix where factorhas been set to twenty. Misclassification into a very different class (e.g., Facies OSS → Facies CARB)incurs a larger error than into an incorrect, but similar class (e.g., OSS → OMS). The Marcellus Shalelithofacies codes are the same as defined in Table 1

ERRE OSS OMS OMD GSS GMS GMD CARB

OSS 1 1.05 1.1 1.05 1.1 1.15 1.2

OMS 1.05 1 1.05 1.1 1.05 1.1 1.2

OMD 1.1 1.05 1 1.15 1.1 1.05 1.2

GSS 1.05 1.1 1.15 1 1.05 1.1 1.15

GMS 1.1 1.05 1.1 1.05 1 1.05 1.15

GMD 1.15 1.1 1.05 1.1 1.05 1 1.15

CARB 1.2 1.2 1.2 1.15 1.15 1.15 1

Table 3 An example to explain how error efficiency matrix (ERRE) affects the prediction of MarcellusShale lithofacies

Targetoutputof OMS

Computed output Error −−−−−−⇀ERRE·,2for OMS

Error weighted by ERRE

(a) (b) (a) (b) (a) (b)

Vector 0 0.40 0.01 0.40 0.01 1.05 0.420 0.0105

1 0.30 0.30 −0.70 −0.70 1.00 −0.700 −0.700

0 0.10 0.10 0.10 0.10 1.05 0.105 0.105

0 0.05 0.05 0.05 0.05 1.10 0.055 0.055

0 0.04 0.04 0.04 0.04 1.05 0.042 0.042

0 0.10 0.10 0.10 0.10 1.10 0.110 0.110

0 0.01 0.40 0.01 0.40 1.20 0.012 0.480

MSE — — — 0.1173 0.1173 — 0.1190 0.1236

a larger difference between the two classes (Table 1). ERRE is derived from contrastmatrix as following

ERRE = C/factor + 1, (1)

where ERRE is the error efficiency matrix; C is the contrast matrix; and factor is avalue to control the upper limitation of ERRE, and is problem-dependent (Table 2).

The learning algorithms are affected by modifying the errors between target andcomputed outputs as in the following

−−⇀err = −−−−−−−⇀ERRE·,j × (

−⇀O − −⇀

T ), (2)

where −−⇀err stands for error vector between computed output vector−⇀O and target output

vector−⇀T ;

−−−−−−−⇀ERRE·,j is the j th column of the ERRE matrix, standing for the difference

of class j from all the other classes. Without using ERRE, the performance, as mea-sured by mean squared error (MSE), is the same for the two computed outputs inTable 3. The MSE is increased more when the error is between radically differentfacies such as the organic mixed shale lithofacies and the carbonate lithofacies. For


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the gradient-based methods, both the value and direction of gradient are modifieddue to the weighted −−⇀err by ERRE. Through setting higher value for more differentclasses, the gradient-based algorithms decrease the errors between much differentclasses first, reducing the misclassification among more distinct classes. However,the arbitrary modification of gradient has a high probability of increasing the timecost in finding the best solution, especially when ERRE has large values. As for GAand PSO algorithms, the modified error function influences the fitness (score) func-tion which is employed to generate new offspring for GA and moving direction andvelocity for PSO.

The ERRE method is not only utilized in training weight and bias of ANN,but also in the evaluation of network topology. Right ratio is the primary criterionin determining ANN topology for classification problems. ERRE produces a newparameter, ERREScore, as the secondary criterion. If the right ratio is the same,higher ERREScore implies greater misclassification between more distinct classes.The ERREScore is used to decide the best topology for predicting Marcellus Shalelithofacies when the right ratio is similar (such as ±5 %). ERREScore is defined as

ERREScore =∑∑(|CM − DM|· × ERRE

), (3)

where CM is the confuse matrix of predicted lithofacies (an example is shown inTables 7 and 8 below); and DM is the diagonal matrix of real lithofacies.

2.4 Cross Validation

Cross validation is a significant technique to evaluate the ability of classifiers. Inthis research, the training dataset is partitioned into two groups: training group andvalidation group. The training dataset accounts for 90 % of the entire dataset and isused to calculate errors and adjust connection weights and bias. The validation groupis used to avoid over-training or over-fitting through detecting the predicted results invalidation group. In practice, the training dataset is randomly divided into ten equalparts and each part is applied as a validation group. The jackknife statistical approachis run ten times using subsets of available data with nine parts composing the traininggroup and the remaining data subset used as the validation group.

3 Marcellus Shale Lithofacies

In terms of the original definition (Teichert 1958), lithofacies is the sum of all thelithologic features in sedimentary rocks, including texture, color, stratification, struc-ture, components and grain-size distribution. While widely used in sandstone andcarbonate studies many lithologic features are limited in subsurface shale-gas reser-voirs. The qualitative features, such as texture, color, stratification and grain-size dis-tribution, are primarily employed to interpret depositional environments and hydro-dynamic conditions for sandstone and carbonate. However, shale is deposited undermuch more uniform depositional environments and hydrodynamic conditions, andthese qualitative features are relatively homogeneous. In addition, shale lithofaciesstudies on unconventional reservoir characterization are focused on improving ourunderstanding of mineralogy, geomechanical properties and organic-matter richness,


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Fig. 4 Vertical distribution of XRD and TOC data from cores in eighteen wells in Middle Devonian ofthe Appalachian basin. The value at the bottom is the number of XRD and TOC data points for each well.The black-filled diamonds indicate the relative location of data points and the sampling interval. The blackline with tick marks implies the vertical scale for each well, and the distance between every two tick marksrepresents approximately twenty feet. Due to the large thickness of Mahantango Formation, the fourthcolumn shows the ratio of formation thickness. The well locations with core are shown in Fig. 1

which are important for the design of horizontal well trajectories and optimization ofhydraulic fracture stimulation. Finally, in the subsurface we are largely limited to con-ventional log responses, which do not reflect rock lithologic features, such as texture,color, stratification and structure. Conventional well logs can only reliably identifylithofacies defined by properties that give rise to change of response in the loggingtools. Given the task of predicting shale lithofacies in terms of commonly available


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Fig. 5 The mineralogical characteristics of Marcellus black shale from XRD and geochemical data ob-tained from core samples. The central red line in the blue box is the median value of each mineral andtotal organic content; the two edges of box indicate the 25th and 75th percentiles; the whiskers implies theboundary of normal values (2σ ); the red crosses stand for the atypical values. The percentage of mineralsis by volume, while the TOC is by weight

conventional logs, it is more feasible and suitable to manually define shale lithofa-cies according to mineralogy and richness of organic matter. In this research, coredata and PNS logs were used separately and integrated to provide sufficient informa-tion to define classes (lithofacies) based primarily on mineralogy and organic-mattercontent.

X-ray diffraction (XRD) is the major technology employed by the petroleum in-dustry to measure the mineral composition of rocks according to the elastic scatteringof X-rays. The TOC is measured by a pyrolysis tool. We collected 190 core XRD andTOC data points in 18 wells located in West Virginia and southwest Pennsylvania(Fig. 1). Most of the core data were sampled in Marcellus Shale, supplemented withlimited data from the overlying Mahantango Formation (Fig. 4). Based on the avail-able XRD data, while highly variable among samples the most abundant minerals arequartz and illite with average content of over 35 % and 25 %, respectively (Fig. 5).Chlorite, pyrite, calcite, dolomite and plagioclase are next in abundance, followedby K-feldspar, kaolinite, mixed-layer illite-smectite and apatite. The median valueof TOC is about 5 %, while the highest value is up to 20 %. Using the core XRDand TOC data, we recognized seven lithofacies in the Marcellus Shale based on vi-sual classification using a ternary plot (Fig. 6(a) and 7; Table 4). Three shale lithofa-cies, organic siliceous shale, organic mixed shale, and organic mudstone, have higherorganic richness (TOC > 6.5 %). The other three shale lithofacies, gray siliceousshale, gray mixed shale, and gray mudstone, have a relatively lower organic richness(TOC < 6.5 %). The organic siliceous shale and gray siliceous shale contains morequartz than all other lithofacies. As a result these two organic-rich shale facies should


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Fig. 6 Ternary plot showing thecharacteristics of mineralcomposition and organic matterrichness and the classificationmethod of Marcellus Shalelithofacies based on coredata (a) and pulsed neutronspectroscopy logs (b). Theorganic-rich facies have TOCvalues (>6.5 %) are indicatedby the warmer colors

be relatively more brittle and easier to fracture stimulate. The organic mixed shaleand gray mixed shale are next in brittleness, while the organic mudstone and graymudstone facies would be relatively ductile making it difficult to create and main-tain extensive and open fractures. The final lithofacies are carbonate-rich and occuras interlayers in Marcellus Shale. The carbonate lithofacies possesses very differentpetrophysical properties compared to all the other shale lithofacies and may formbarriers to fracture propagation.

In addition, the pulsed neutron spectroscopy (PNS) logs were acquired in a few ofthe most recent wells. These logs measure different elements in the formation usinginduced gamma-ray spectroscopy with a pulsed neutron generator. The elemental ra-tios can be modeled to provide estimates of mineral composition, TOC content, and


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Fig. 7 The workflow showing the method used to define Marcellus Shale lithofacies from core analysisXRD and TOC data and PNS logs

hydrocarbon volume (Fig. 8, the fourth track). The estimated mineral compositionand TOC content derived from the PNS logs are calibrated by the logging companywith available core XRD and TOC data and as a result should have a strong rela-tionship (Fig. 9). The modeled mineralogy from the PNS logs compared to our coreXRD data tend to underestimate the percentage of quartz and carbonate, and over-value the clay content. The TOC content by pyrolysis tool is approximately 1.8 timeshigher than that estimated by PNS logs. We have normalized the PNS-modeled min-eral composition and TOC content to better scale with our core XRD and TOC data.The resulting ternary plot shows that the PNS logs can define the same seven Mar-cellus Shale lithofacies with a similar distribution as defined by core data (Fig. 6(b)).Both the core- and PNS-defined shale lithofacies are applied as the training datasetfor ANN classifier.

4 Pre-processing of the Training Dataset

To develop a model for Marcellus Shale lithofacies prediction, the pre-processing oftraining dataset includes: (1) manually defining shale lithofacies with core and PNSlog data; (2) selecting and normalizing sensitive conventional logs for shale lithofa-cies; and (3) log analysis to generate input variables based on typical approaches topetrophysical analysis of the conventional logs in unconventional reservoirs. We willdiscuss the last two aspects in detail in this section.

4.1 Selection of Sensitive Conventional Logs

The conventional log curves sensitive to minerals and organic-matter include gammaray, density, neutron, photoelectric, and deep resistivity/induction. The gamma-ray


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Table 4 A summary of characteristics of the seven Marcellus Shale lithofacies defined by core XRD andTOC data and PNS logs

Lithofacies Features of core dataand pulsed neutronspectroscopy logs

Features of conventional logs

GR(API)

RHOB(g/m3)

NEU(%)

ILD(ohmm)

PE URAN(ppm)

Organic SiliceousShale (OSS)

TOC ≥ 6.5 % (9.7);Vclay < 40 % (25.6);Vqtz/Vcarb > 3

278–785

449

2.1–2.48

2.39

18.0–30.4

24.1

152–2505

854

2.7–7.9

3.5

20–80

40

Organic MixedShale (OMS)

TOC ≥ 6.5 % (9.6);Vclay < 40 % (19.8);1/3 < Vqtz/Vcarb < 3

242–628

424

2.3–2.59

2.47

13.3–27.5

20.3

95–1475

450

3.3–6.3

4.3

18–73

34

OrganicMudstone (OM)

TOC ≥ 6.5 % (6.1);Vclay ≥ 40 % (47.6)

315–793

491

2.4–2.64

2.53

21.8–29.7

25.7

26–414

164

3.4–7.0

4.4

17–74

36

Gray SiliceousShale (GSS)

TOC < 6.5 % (4.0);Vclay < 40 % (32.0);Vqtz/Vcarb > 3

115–277

193

2.4–2.62

2.59

15.5–24.1

19.8

20–241

94

2.8–4.8

3.5

2–14

8

Gray MixedShale (GMS)

TOC < 6.5 % (2.5);Vclay < 40 % (17.1);1/3 < Vqtz/Vcarb < 3

87–178

131

2.5–2.75

2.66

6.3–23.4

14.4

24–282

103

3.5–5.1

4.2

1.5–12

5.4

Gray Mudstone(GM)

TOC < 6.5 % (1.5);Vclay ≥ 40 % (46.9)

139–229

209

2.4–2.70

2.60

17.2–27.7

22.6

19–121

56

3.3–5.5

3.8

2–15

8.1

Carbonate(CARB)

TOC < 6.5 % (1.3);Vclay < 40 % (5.6);Vqtz/Vcarb < 1/3

24–135

82

2.6–2.75

2.69

1.8–15.2

6.2

61–1432

636

3.9–5.1

4.7

0–7.7

3.1

(GR) log measures the natural radiation of uranium series, thorium series, andpotassium-40 isotope in sedimentary rocks. The clay minerals have a high level ofradiation due to absorption of uranium, high content of potassium in clay mineralsand uranium fixed by organic matter (Doveton 1994). The increase of TOC con-tent generally results in the increase of natural radioactivity of rocks, and so thegamma-ray log has been used to identify organic-rich units and/or predict organicrichness (Beers 1945; Swanson 1960; Schmoker 1981; Fertl and Chilingar 1988;Boyce and Carr 2010). In the Marcellus Shale, the GR can differentiate clay mineralsand organic matter from non-clay minerals like quartz, feldspar, calcite and dolomite.The density of minerals is distinct: calcite (2.71 gm/cc) and dolomite (2.85 gm/cc)have higher density than quartz (2.65 gm/cc) and K-feldspar (2.56 gm/cc); most ofthe clay minerals have relatively low density (2.12 to 2.52 gm/cc) except chlorite(2.76 gm/cc). The organic matter and fluids in pore space have a much lower densitythan the minerals. Therefore, the density log (RHOB) is a useful porosity log andlithology indicator. The neutron log (NEU) is primarily a measure of hydrogen con-centration, and is used as a measure of the fluid/gas in the pore space (porosity), but


Math Geosci

Fig. 8 A type log showing conventional log suites in the first three tracks. The mineralogic and TOCmodel derived from the PNS logs is shown in the fourth track. The comparison between core XRD miner-alogical data and individual mineral composition generated from the PNS logs are shown in the last threetracks. Core data is shown as discrete points. As modeled, the PNS logs provide an excellent estimate ofmineral and organic content

is also affected by bound water on the clay components. The overlay of density andneutron logs combined with the photoelectric curve (PE) are powerful and widely uti-lized determinates of lithology. The resistivity log, especially the deep resistivity log


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Fig. 9 The relationship of mineralogy and TOC content measured by core analysis data and modeled byPNS logs of Marcellus Shale in the Appalachian Basin

Fig. 10 Statistical analyses of the five conventional log series after normalization and log analysis: (a) thedeep resistivity histogram for the seven Marcellus Shale lithofacies; (b) RHOmaa–Umaa crossplot; (c) ura-nium–average porosity crossplot: the circles indicting the values in the range between upper and lowerquartiles (25 %) and the end points of the lines standing for maximum and minimum values; (d) boxplotof GR/RHOB with maximum and minimum value, lower and upper quartiles (25 %), and mean value


Math Geosci

Fig. 11 The gamma ray log showing the thick shale unit above Marcellus Shale (high gamma-ray values)and the underlying Onondaga Limestone with relatively low-gamma-ray. The Onondaga Limestone andthe thick shale are the reference layers for GR log normalization. The green line shows the shale base lineand the blue line is the clean limestone base line. The locations of the wells in this cross section are shownin Fig. 20

(ILD), reflects the resistivity of rock. Increased organic matter and reduced porositycontributes to a higher resistivity. The statistical analyses of these five log curves arecarried out to evaluate the predictor variables for ANN classifiers (Table 4; Fig. 10).

4.2 Normalization and Petrophysical Analysis

Well log normalization is critical to obtain meaningful log data by eliminating sys-tematic errors for regional studies with multiple wells (Shier 2004). GR was normal-ized according to two reference formations and crossplot was employed to normalizeNEU (Figs. 11–12; Wang and Carr 2012). The feature space of input variables is themost important factor that controls the quality of classifiers, even though the designof classifiers also influences the quality. Principal component analysis and stepwisediscriminant analysis are two major methods used for feature extraction, which canimprove the accuracy and stability of classifiers by removing useless, non-distinctiveand interrelated features (Jungmann et al. 2011). However, we believe each con-ventional log provides some unique information, even though similar features existamong the different logs. We use petrophysical analysis to generate eight variablesbased on typical approaches to petrophysical analysis of the conventional logs inunconventional reservoirs to be used as input variables instead of feature extractionmethods to reduce the correlation of input variables and improve the feature spaces.Another advantage of petrophysical analysis is the ability to base the mathematicclassifiers on the knowledge and experience in geologic interpretation of wireline


Math Geosci

Fig. 12 Cross-plots of gamma ray versus neutron (a), density (b), photo-electric (c) and deep resistiv-ity (d) for normalization. There is obvious difference between Group I and Group II for neutron logs,which appear to be related to wells drilled on either air or water. A scaling factor of 2.27 is utilized toconvert the neutron curves of Group II to Group I. The other logs are consistent enough and normalizationwas unnecessary

logs in unconventional reservoirs. Eight derived parameters were used to enhance theability of conventional logs to predict shale lithofacies:

1. Uranium concentration: The accumulation and preservation of organic matterusually depletes oxygen in water and builds oxygen-deficient systems, trigger-ing the precipitation of uranium through the reduction of soluble U6+ ion toinsoluble U4+ ion. As one of the three radioactive sources for natural gammaray, uranium content has a stronger relationship with TOC content than standardgamma ray. Well-defined relationships have been created to predict TOC by ura-nium from the standard gamma ray (Schmoker 1981; Lüning and Kolonic 2003;Boyce and Carr 2010). The spectral gamma-ray log and pulsed neutron spec-troscopy log provides standard GR and uranium content, and so an improved rela-tionship between GR and uranium content was constructed for Middle Devonianintervals with the abundant data (Fig. 13).

2. Shale volume (Vsh) or brittleness (1-Vsh): The computed gamma ray (CGR), sub-tracting uranium from total gamma ray, is the summation of thorium and potas-sium sources (Doveton 1994). Therefore, the CGR is an improved parameter to


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Fig. 13 Plot of the uranium concentration (ppm) from fourteen wells based on the spectral gamma ray logand PNS log curve against the standard GR log curve (SGR in API units) for the Middle Devonian intervalsof the Appalachian basin. The uranium concentration increase smoothly with the increase of gamma ray,and is adequately fit with a quadratic equation

evaluate Vsh. The ratio of quartz volume to the volume of all minerals was com-puted as 1-Vsh, and interpreted as the brittleness (Jarvie et al. 2007).

3. RHOmaa: is derived from neutron porosity and bulk density (Doveton 1994)which removes the effects of fluids in pores.

4. Umaa: is derived from photoelectric index, neutron porosity and bulk density(Doveton 1994). RHOmaa and Umaa are widely utilized to evaluate the matrixminerals in sandstone, carbonate and other common rocks. Even though RHOmaaand Umaa are rarely used in shale, the relatively high quartz and carbonate contactmakes these two parameters valuable mineralogic inputs for lithofacies prediction.

5. Average porosity (PHIA): the average porosity of neutron porosity and densityporosity is also related to the content of the matrix minerals, the concentration oforganic matter and bound water on the clay components.

6. Porosity difference (PHIdiff): the difference between neutron porosity and densityporosity reflects the mineralogy and organic-matter concentration.

7. LnILD: the natural logarithm of deep resistivity is related to the matrix porosity,bound water on the clays and the concentration of organic matter.

8. GR/RHOB: Both GR and density log has been used to predict TOC content inshale (Schmoker 1981; Fertl and Chilingar 1988) separately, and the ratio of GR


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Fig. 14 The average distance between different Marcellus Shale lithofacies calculated from input variablespace: the conventional logs directly (a) and the eight derived parameters (b). The lithofacies are definedin Table 4

Fig. 15 The chart used to weaken or remove the effect of pyrite and barite. The pyrite effect lines arebased on rock density and volumetric measurement and are the arithmetic average of all minerals andkerogen weighted by their percentage (Doveton 1994). The purple and blue arrows indicate the decreasinggradient of density and PE due to the occurrence of pyrite and barite, respectively

to density will enhance the ability to detect organic zone and remove parts of thenoise.

These eight derived input variables show large variations among the seven shalelithofacies and provide improved inputs for the ANN model to predict shale lithofa-cies. The average distance between different classes is obviously increased throughderiving the eight parameters, which generally indicate an improvement of input vari-


Math Geosci

Tabl

e5

The

Mar

cellu

sSh

ale

litho

faci

espr

edic

tion

resu

ltsby

the

sing

leA

NN

with

the

eigh

tde

rive

dpe

trop

hysi

cal

para

met

ers

asin

put

vari

able

san

dth

eco

reda

taas

the

trai

ning

data

set.L

M:L

even

berg

–Mar

quar

dt;S

CG

:sca

led

conj

ugat

egr

adie

nt;S

DG

:ste

epes

tdes

cent

grad

ient

;SD

GM

:ste

epes

tdes

cent

grad

ient

with

mom

entu

m;G

A:g

enet

ical

gori

thm

;PS

O:

part

icle

swar

mop

timiz

atio

n.E

RR

Eis

used

tode

crea

sem

iscl

assi

ficat

ion

betw

een

very

diff

eren

tlit

hofa

cies

.T

hebo

lded

colo

rin

dica

tes

the

high

est

cros

s-va

lidat

ion

righ

trat

io

Lea

rnin

gal

gori

thm

Art

ifici

alne

ural

netw

ork

topo

logy

2025

3035

4045

5015

–10

20–1

020

–15

25–1

025

–15

25–2

030

–10

30–1

530

–20

30–2

5

LM

79.7

70.9

81.9

81.3

77.5

75.8

83.0

84.1

76.4

78.6

76.9

84.1

79.1

76.9

79.7

80.8

80.8

SCG

82.4

81.3

84.1

80.8

75.3

79.1

85.2

82.4

84.6

59.9

79.7

83.5

81.3

81.3

84.6

85.7

83.5

SDG

45.6

56.0

49.5

54.4

54.4

59.3

52.7

51.6

52.2

52.7

47.3

52.7

53.3

31.3

46.2

50.0

49.5

SDG

M49

.555

.550

.054

.953

.859

.953

.852

.252

.252

.247

.352

.254

.933

.046

.251

.150

.5

GA

78.0

81.3

74.7

74.7

73.6

76.4

74.7

78.0

73.1

74.2

75.8

73.6

74.7

76.4

74.7

72.5

72.5

PSO

76.4

76.9

75.3

73.6

76.9

74.7

75.8

73.1

78.0

73.1

76.4

73.6

73.6

76.4

73.6

69.2

67.6

The

litho

faci

esar

ede

fined

inTa

ble

4


Math Geosci

Fig. 16 The statistic features of the six supervised learning algorithms for the core training dataset used forMarcellus Shale lithofacies prediction. The GA and PSO are more steady to optimize the ANN classifiersfor different topologies; the SCG and LM algorithms performs best in optimizing the ANN classifiers,but is less steady; the SDG and SDGM algorithms are not recommended for Marcellus Shale lithofaciesprediction

able space (Fig. 14). The pyrite, a common mineral in organic-rich shale (Fig. 5), isdetrimental for Marcellus Shale lithofacies prediction due to its high density and PEvalue. It is better to remove or at least decrease the effect of pyrite on the density andphotoelectric values (Fig. 15).

5 Building ANN Classifiers and the Training Results

5.1 ANN Topology and Supervised Learning Algorithms

The design of network architecture is a subjective task and problem-dependent. Itis almost impossible to a priori decide the best topology for a special problem (forexample Marcellus Shale lithofacies prediction). If the accuracy is acceptable, a rel-atively simple topology is preferred over a complex topology. Thus, we only test thetopology with one and two hidden layers with the nodes in each hidden layer beingless than 70, and show only part of the training results (Table 5) and the statisticalfeatures (Fig. 16). All six supervised learning algorithms were applied to train allthe ANNs with varying topology starting at the same initial condition (weights andbias).

For the single ANN classifier, the scaled conjugate gradient algorithm performedthe best using the relative small sample represented by the core training dataset (Ta-ble 5; Fig. 16). The maximum and average right ratio are higher than all the other fivealgorithms, even though it cost more time than the Levenberg–Marquardt algorithm(Fig. 17) and is less steady than GA and POS algorithms (Fig. 16). The steepest de-scent gradient with (SDG) and without momentum (SDGM) were not effective forsolving the shale lithofacies prediction by a single ANN classifier. A possible rea-son is that when the number of output nodes is large, the SDG and SDGM methodcannot find a suitable steepest descent gradient for all the output nodes. All the al-gorithms are not effective in optimizing the single ANN classifier for PNS training


Math Geosci

Fig. 17 An example of single ANN classifier showing its MSE decline curves trained by fourgradient-based learning algorithms and two intelligent algorithms. As for the two intelligent algorithms,we shows not only the MSE curves from the best individual but also the worst individual (purple line) andthe average MSE values of all the individuals (light blue line)

dataset with a large number of data samples, but perform well for the modular ANNclassifier.

The design of the modular ANN classifier is more complex than the single ANNclassifier making determination of the best topology and learning algorithms diffi-cult. Except for designing the network topology and learning algorithms, the trainingdata preparation, input variables for each binary ANN classifier, and the design ofcross validation are more difficult. As for one binary classifier, only one output nodeis required due to the decomposition of the multiclass problem, and thus a simpletopology is sufficient to solve the prediction of shale lithofacies. We tested the topol-ogy with one or two hidden layers and less than 20 hidden nodes for each binaryANN classifier. The modular ANN admits different input variable sets for each bi-nary ANN classifier, which is the advantage of modular ANN. The modular ANN ismore effective in predicting lithofacies using the larger PNS training dataset, and thebest architecture is shown (Table 6). Finally, we employed two ANN classifiers topredict the shale lithofacies: the single ANN classifier with two hidden layers (30–20) trained by SCG and core dataset and the modular ANN classifier trained by SCGusing the PNS dataset (Table 6).

5.2 ERRE Effect on the ANN Classifier

The major objective of ERRE is to avoid misclassification between very differentlithofacies (Tables 7 and 8). If the value of ERRE is large, it will damage the su-pervised learning methods due to the obvious variation of the error function duringtraining stage. The training time and iteration may be increased, and the stability


Math Geosci

Table 6 The design of modular ANN for Marcellus Shale lithofacies prediction showing the selection ofinput variables, hidden layers and supervised learning algorithms

ID ofmodular ANNa

Training method: SCG Training method: L-M Training method: SCG

Inputvariablesb

Hiddennodes

Inputvariablesb

Hiddennodes

Inputvariablesb

Hiddennodes

OSS–OMS 1 2 3 4 7 16-5 1 2 3 4 7 16-5 1–8 16-5

OSS–OMD 1 2 3 4 5 8 12-5 1 2 3 4 5 8 12-5 1–8 12-5

OSS–GSS 1 3 5 6 7 8 18 1 3 5 6 7 8 18 1–8 18

OSS–GMS 1 2 3 5 6 7 15-5 1 2 3 5 6 7 15-5 1–8 15-5

OSS–GMD 1 3 5 6 7 8 15-5 1 3 5 6 7 8 15-5 1–8 15-5

OSS–CARB 1 2 3 4 6 7 8 18-5 1 2 3 4 6 7 8 18-5 1–8 18-5

OMS–OMD 1 2 3 4 5 8 14-4 1 2 3 4 5 8 14-4 1–8 14-4

OMS–GSS 2 3 4 5 6 7 18-9 2 3 4 5 6 7 18-9 1–8 18-9

OMS–GMS 1 2 4 5 6 7 20-10 1 2 4 5 6 7 20-10 1–8 20-10

OMS–GMD 3 4 5 6 7 8 15-5 3 4 5 6 7 8 15-5 1–8 15-5

OMS–CARB 1 2 3 4 6 7 8 18-5 1 2 3 4 6 7 8 18-5 1–8 18-5

OMD–GSS 1 2 3 5 6 7 8 15-5 1 2 3 5 6 7 8 15-5 1–8 15-5

OMD–GMS 1 2 3 4 5 6 7 8 15-5 1 2 3 4 5 6 7 8 15-5 1–8 15-5

OMD–GMD 1 3 5 6 7 8 15-5 1 3 5 6 7 8 15-5 1–8 15-5

OMD–CARB 1 2 3 4 6 7 8 15-5 1 2 3 4 6 7 8 15-5 1–8 15-5

GSS–GMS 1 2 3 4 7 18-6 1 2 3 4 7 18-6 1–8 18-6

GSS–GMD 1 2 3 4 5 8 15-5 1 2 3 4 5 8 15-5 1–8 15-5

GSS–CARB 1 2 3 4 6 7 8 15-5 1 2 3 4 6 7 8 15-5 1–8 15-5

GMS–GMD 1 2 3 4 5 7 8 15-5 1 2 3 4 5 7 8 15-5 1–8 15-5

GMS–CARB 1 2 3 4 6 7 8 13-5 1 2 3 4 6 7 8 13-5 1–8 13-5

GMD–CARB 1 2 3 4 6 7 8 15-5 1 2 3 4 6 7 8 15-5 1–8 15-5

Cross validation right ratio 77.76 % 72.24 % 75.42 %

The lithofacies are defined in Table 4aThe modular ANN consists of twenty-one binary ANNs; ‘OSS–OMS’ as the ID of modular ANN meansthat the binary ANN for lithofacies OSS and OMS;b1: PHIA; 2: Umaa; 3: RHOmaa; 4: PHIdiff; 5: LnILD; 6: URAN; 7: GR/RHOB; 8: Vsh

of the ANN classifiers may be decreased. However, ERRE does not necessarily re-duce the right rate of predicted lithofacies (Fig. 18). We tested several ERRE withthe factor from four to 30, and determined that the ERRE worked best for the singleANN and the modular ANN when the factor is equal to 20.

5.3 Comparison of Prediction from Core and ECS Training Datasets

The effectiveness of single ANN and modular ANN is further demonstrated by thecomparison of lithofacies recognized directly by pulsed neutron spectroscopy logsand predicted by the ANN models from core and PNS training datasets (Fig. 19).Even though small differences occur, the three modeled lithofacies sections are very


Math Geosci

Table 7 The confuse plot of the predicted seven shale lithofacies with ERRE, showing correctly predictedlithofacies on the diagonal and miss-classified lithofacies in the off diagonal locations. Adjacent facies aremost similar

Core-definedlithofacies

Predicted lithofacies Coretotal

RightrateOSS OMS OMD GSS GMS GMD CARB

OSS 34 1 2 2 39 87.18 %

OMS 1 8 1 1 11 72.73 %

OMD 6 16 1 23 69.57 %

GSS 1 1 15 1 18 83.33 %

GMS 1 14 2 1 18 77.78 %

GMD 1 2 54 57 94.74 %

CARB 1 15 16 93.75 %

Predicted total 42 10 21 18 18 57 16 182 85.71 %

Predicted/core 1.077 0.909 0.913 1.000 1.000 1.000 1.000 ERRE score 54.05

Lithofacies are defined in Table 4

Table 8 The confuse plot of the predicted seven shale lithofacies without ERRE, showing correctly pre-dicted lithofacies on the diagonal and miss-classified lithofacies in the off diagonal locations. Adjacentfacies are most similar

Core-definedlithofacies

Predicted lithofacies Coretotal

RightrateOSS OMS OMD GSS GMS GMD CARB

OSS 33 2 4 39 84.62 %

OMS 3 7 1 11 63.64 %

OMD 8 15 23 65.22 %

GSS 1 15 1 1 18 83.33 %

GMS 1 15 2 18 83.33 %

GMD 1 1 55 57 96.49 %

CARB 1 15 16 93.75 %

Predicted total 45 9 21 16 18 58 15 182 85.16 %

Predicted/core 1.154 0.818 0.913 0.889 1.000 1.018 0.938 ERRE Score 56.30

Lithofacies are defined in Table 4

similar. Based on visual observation, it is difficult to determine whether the sin-gle ANN trained by core dataset is better than the modular ANN trained by thepulsed neutron spectroscopy dataset. Thus, both can be utilized and evaluated inthe construction of deterministic and stochastic three-dimensional geologic mod-els. Through evaluation of the spatial distribution of predicted and observed litho-facies, it may be possible to evaluate the relative merits of each ANN classifier.As an example based on the lithofacies cross section generated by ANN, the or-


Math Geosci

Fig. 18 The cross plot showing the effect of ERRE on cross-validation right rate of the six learningalgorithms. The ERRE matrix is shown in Table 2. The table in the lower right indicates the ratio ofsamples located above or below the reference line. The lithofacies are defined in Table 4

ganic siliceous shale becomes the dominant lithofacies in the central West Virginia(Fig. 20).

6 Conclusions

Shale lithofacies research is only at the initial stages, but is an important research areain both scientific and industrial domains to better understand depositional processesthat result in variations in mineralogy and organic content, and to design a horizontallateral and optimize the location and extent of hydraulic fracture stimulation stages.Marcellus Shale lithofacies can be defined from core and PNS logs in terms of min-eral composition and organic-matter richness: clay percentage, the ratio of quartz andcarbonate and TOC content. Petrophysical analysis instead of conventional feature se-lection methods have advantages in combining knowledge and experience in geologicinterpretation of wireline logs to ANN and improving the input variable space forclassifiers; the eight derived parameters with removing partly the effect of pyrite im-proved the prediction ability of ANN. The scaled conjugate gradient performed bestfor the single ANN with 30–20 hidden nodes in two hidden layers trained by the coretraining dataset; the modular ANN worked better for the PNS training dataset whichhas a large number of samples. An Error Efficiency matrix (ERRE) was introducedinto the neural network for handling the proximity of different classes (lithofacies) inboth training and classification stages. The ERRE matrix can effectively avoid seri-ous misclassification among very different lithofacies (for example OSS and CARBlithofacies). The two ANN classifiers were employed in combination to predict theMarcellus Shale lithofacies: the single ANN classifier with two hidden layers (30–20)trained by SCG using the core dataset and the modular ANN classifier trained by SCGusing pulsed neutron spectroscopy dataset (Fig. 19). The resulting Marcellus Shale


Math Geosci

Fig. 19 An example of predicted shale lithofacies by single ANN based on core training dataset (3rdtrack) and modular ANN based on pulsed neutron spectroscopy (PNS) log training dataset (4th track)compared to PNS-defined lithofacies in Well #6 (Fig. 1) of Middle Devonian intervals, Appalachian basin.Lithofacies are defined in Table 4

lithofacies classification is very promising but requires further evaluation by mappingthe spatial distribution in a three-dimensional shale lithofacies model and testing thepredicted lithofacies relationship with production data and hydraulic fracturing oper-ations.

Acknowledgements This research was supported by the U.S. Department of Energy National EnergyTechnology Laboratory’s Regional University Alliance (NETL-RUA) under the contract RES1000023/155(Activity 4.605.920.007) and National Natural Science Foundation of China (No. 698796867). Specialthanks to Energy Corporation of America, Consol Energy, EQT Production and Petroleum Develop Cor-poration for providing core and log data.


Math Geosci

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Math Geosci

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