2. and continuous evaluation of TOC is required. Direct measurement of
TOC from core samples in the laboratory is accurate but it is costly and
time consuming. On the other hand, the current practice of TOC esti-
mation based on bulk density log alone or based on the conventional
sonic (or density) logs and resistivity log using empirical correlations is
fast but not accurate enough due to the assumptions implied in these
correlations (Renchun et al., 2015).
Currently two proven techniques of estimating TOC from well-log
data are used; these methods are: the Schmoker density log based
technique (Schmoker, 1980, 1979) and ΔlogR method (Passey et al.,
1990).
Schmoker correlation was developed for Devonian shale formation,
Eq. 1, based on treating the Devonian shale as a four-component system
(matrix, interstitial pores, pyrite, and organic matter). He considered
the total density of the formation as a function of the densities and
fractional volumes of these four components, and setting the pyrite,
organic matter and matrix densities of 5.0, 1.0, and 2.69 g/cm3
, re-
spectively. The pyrite volume was assumed to increase linearly with the
increase of the organic matter.
Based on these assumptions, Sckmoker derived Eq. 1 to calculate the
organic content in volume percent. TOC in wt% can be obtained by
converting the volume to weight percent. There is a well-established
correlation between wt% and volume percent for Devonian shale
(Schmoker, 1979). The author concluded that this method was applic-
able to a large area (135,000 square km) of Appalachian basin.
= −TOC(vol%) (ρ ρ)
1.378B
(1)
where TOC is the total organic carbon, ρB is the formation density in
absence of organic matter (g/cm3
), ρ is the formation bulk density (g/
cm3
).
Schmoker model was then refined in Bakken shale formation, Eq. 2.
The relation of pyrite-organic matter volumes, which was originally
developed for Devonian shale, was also considered to be applicable for
Bakken formation. A general TOC correlation (Eq. 2) for Bakken for-
mation (upper and lower members) was derived by assuming constant
porosity and pore fluid density profiles. Then by considering the or-
ganic matter density of 1.01 g/cm3
, a matrix density of 2.68 g/cm3
and
organic matter content to organic carbon content ratio of 1.3, the re-
lation was simplified, Eq. 3 (Schmoker and Hester, 1983). The authors
compared the results of fifty nine laboratory measurements from thirty
nine wells in Bakken shale with organic content ranging from 6 to 20 wt
% with those of Eq. 3 and found that Eq. 3 yielded good estimation of
TOC with AAD of 1.1% compared to laboratory analysis.
=
− −
− −
TOC(wt%)
[(100ρ )(ρ 0 .9922ρ 0.039)]
[(Rρ)(ρ 1 .135ρ 0.675)]
o mi
o mi (2)
= −( )TOC(wt%) 154.497
ρ 57.261
(3)
where ρo is the organic matter density (g/cm3
), ρmi is the volume-
weighted average density of grain and pore fluid (g/cm3
), R is the ratio
of weight-percent organic matter to weight-percent organic carbon.
The major disadvantage of Schmoker method is that it assumes the
formation bulk density and porosity are constant, and any change in the
bulk density is due to presence or absence of low density organic
kerogen.
Passey et al. (1990) proposed ΔlogR method for estimating the TOC
content which is now the widely used method. In this technique, the
separation between the properly scaled porosity indicator log (e.g sonic
transit time curve) and deep resistivity reading considered to give an
indication about the availability of organic-rich rocks. The separation
caused by the organic-rich rocks is related to: the effect of the low
density and low velocity of kerogen on the porosity logs and the re-
sponds of the resistivity logs to the formation fluids, Eqs. 3 and 4.
= + × −ΔlogR log (R R ) 0.02 (Δt Δt )10 baseline baseline (4)
= × − ×ΔTOC logR 10(2.297 0.1688 LOM)
(5)
where ΔlogR is the resistivity porosity logs separation, R and Δt are the
target formation resistivity (Ω·m), and sonic transient time (μs/ft), re-
spectively, Rbaseline and Δtbaseline are the base formation resistivity (Ω·m)
and base sonic transit time (μs/ft), respectively, corresponding to a
reference line of organic lean shale in the same formation, LOM is the
level of maturity.
ΔlogR technique has two major drawbacks: the first one is the as-
sumption that the rock composition, texture, and compaction do not
change, this method may lead to incorrect estimation of the target
shale. Since in reality the composition and texture of the organic rich
shale extremely vary for different resource play (Rokosh et al., 2010).
The second drawback is the limited ranges of applicability for sonic
transit time and resistivity for this method because of the assumption of
1:50 linear relationship (constant slope of 0.02, Eq. 4) between the
porosity and logarithmic resistivity logs. The use of LOM is another
weakness of ΔlogR technique since LOM is an uncommonly used
measure of organic matter thermal alteration (Wang et al., 2016).
Charsky and Herron (2013) examine Schmoker and ΔlogR models
into four different wells drilled with both water and oil-based muds,
and covering a variety of formations. They reported that these models
have low accuracy with an average AAD from core derived TOC of
1.6 wt% and 1.7 wt% for Schmoker and ΔlogR methods, respectively.
Also, when Schmoker model was used in Bakken shale formation, which
was used originally by Schmoker to develop and test this model, the
AAD from the core derived TOC was 1.2 wt% which is relatively high.
Wang et al. (2016) modified the sonic-/density-based ΔlogR models
for TOC determination based on Gamma Ray (GR), resistivity, sonic,
and density well logs. In their models they redefined ΔlogR with esti-
mated slopes related to target shale to remove the assumed linear ap-
proximation. They also suggested the use of more common thermal
indicators (Tmax or vitrinite reflectance (Ro)) instead of LOM, since the
use of LOM requires a conversion between (Tmax or Ro%) and LOM
which can lead to a problem in practice (Crain, 2000).
Wang et al. (2016) also introduced the use of GR log to improve the
prediction of TOC. The revised ΔlogR values based on sonic and density
logs are expressed as shown in Eqs. 6 and 7, respectively. The TOC from
the modified ΔlogR including GR can be calculated using Eq. 8. The
modified models showed better results in estimating the TOC when
applied in Devonian shale (R2
was > 0.92) compared to the original
ΔlogR technique (R2
of 0.82). The residue analysis indicates the mod-
ified models are unbiased statistically compared to the original models.
= +
−
× −ΔlogR log (R R )
1
ln 10
m
Δt Δt
(Δt Δt )10 baseline
m
baseline
(6)
= +
−
× −ΔlogR log (R R )
1
ln 10
m
ρ ρ
(ρ ρ )10 baseline
m
baseline
(7)
= + − × +TOC [α ΔlogR β(GR GR )] 10baseline
(δ η T )max (8)
where Δtm is the matrix sonic transit time (μs/ft), m is the cementation
exponent, ρm is the matrix density (g/cm3
), ρbaseline is the baseline
density corresponding to the Rbaseline value (g/cm3
), α, β, δ and η are
matrix constants to be determined, Tmax is the maturity indicator (°C),
GRbaseline is the baseline value of shale (API).
The estimation of TOC using Wang Models requires the determi-
nation of matrix constants which depend on the matrix composition.
These parameters will be different for different formations. This means
these parameters have to be estimated for any formation before using
the model and this requires the knowledge of TOC from the laboratory.
Based on literature survey, current TOC prediction models either
cannot predict the TOC accurately or needs tedious laboratory work to
determine the fitting parameters. The objective of this paper is to de-
velop a new robust empirical correlation that can be used to predict the
TOC with high accuracy based on conventional well logs using artificial
neural network technique (ANN). The developed TOC correlation was
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
73
3. trained and built for Barnett shale formation and tested in both Barnett
and Devonian formations. Moreover, the performance of this correla-
tion in predicting TOC for Devonian shale was compared with the
available correlations developed mainly for Devonian shale.
2. Methodology
2.1. Core samples collection
The core samples analyzed for TOC determination were collected
from the Mississippian Barnett shale formation (Fort Worth Basin
(FWB), North of Texas, United States). TOC was estimated using Rock-
Eval 6, the samples were crushed (< 63 μm), 5.2 mg of every sample
was subjected to Rock-Eval pyrolysis analysis. The details about pro-
cedures and considerations for preparing the shale samples for TOC
estimation using Rock-Eval 6 can be found in (Carvajal-Ortiz and
Gentzis, 2015; Chen et al., 2016; Hazra et al., 2016).
2.2. Proposed ANN-based methodology
Artificial neural network (ANN) is developed under the category of
artificial intelligent (AI) to provide a brain-like tool which has the
ability to estimate, identify, classify or make a decision by a machine
program in various conditions or situations. ANNs are available in
several structures. Multi-layered perceptron (MLP) is the simplest ANN
structure, which consists of input layer, one or several hidden layers
(mid-layers) and output layer. The proposed MLP model in this work
was trained based on one hidden layer, so the whole structure has three
layers.
ANN model was trained using 442 data sets from Barnett shale (90%
of the data sets was used for training and 10% was used for validation),
the model was trained using four inputs; (Aguilera and Radetzki, 2013)
Deep induction resistivity log data (RILD), which is believed to be al-
tered because of the presence of kerogen in the rock (Passey et al.,
1990; Heslop, 2010), (Carvajal-Ortiz and Gentzis, 2015) Sonic transit
time (Δt), which decreases as the TOC in the rock increases (Liu et al.,
2013), (Charsky and Herron, 2013) Formation bulk density (ρb), gen-
erally decreases as the kerogen content increases, and hence, organic
matter in the formation increases (Schmoker, 1979), (Chen et al., 2016)
Gamma ray (GR), although the relationship between gamma ray and
TOC is controversial (Luning and Kolonic, 2003; Jacobi et al., 2008;
Gonzalez et al., 2013), several authors confirmed that including GR
data into TOC models can enhance the performance of these models
(Heslop, 2010; Wang et al., 2016; Zhao et al., 2015). GR is included in
this study to train the ANN model. The TOC values derived from core
analysis (explained earlier in Section 2.1) were targeted as outputs for
training the model.
Table 1 lists the data range and the statistical analysis of the training
parameters. GR ranged from 23.01 to 179.85 API, RILD ranged from
3.65 to 171.90 Ω·m, Δt ranged from 52.29 to 97.09 μsec/ft., ρb ranged
from 2.40 to 2.77 g/cm3
, and TOC ranged from 0.75 to 5.55 wt%. The
structure of the proposed ANN model is shown in Fig. 1.
The developed model was optimized by studying the effect of dif-
ferent parameters (the learning function, the transfer function, number
of hidden layers, number of neurons, and number of iterations) on TOC
prediction capability of the model. The optimum combination of the
model parameters (except the number of iterations) which will optimize
the performance of the model was selected by constructing an inserted
for loops in Matlab. Each for loop was changed over all the possible
values of one of the model parameters (e.g: number of layers, number of
neurons in each layer, training function, etc.…). The AAD and R2
for all
of the combinations were compared and the combination of the lowest
AAD and highest R2
was selected.
The optimum number of iterations was selected based on the
training and validation errors. The optimum number of iterations is the
one which will give the lowest training error and prevent model
memorization (model memorization starts when validation error begins
to increase after a decreasing period while training error is decreasing,
Fig. 2). Levenberg-Marquardt training method (trainlm), which is one
of the well-known methods of optimization, was used because it
showed the highest prediction performance for the model compared to
other methods (e.g: traingdm, trainbr, traingda, traincgf). The use of
tangent sigmoid transfer functions between inputs and mid layer and
pure-line function for output layer enhanced the performance of the
developed model. To select the optimum number of hidden layers and
neurons, the model was tested in the ranges of (Aguilera and Radetzki,
2013; Carvajal-Ortiz and Gentzis, 2015; Charsky and Herron, 2013)
layers and (Charsky and Herron, 2013; Chen et al., 2016; Cook and
Bally, 1975; Crain, 2000; Creaney et al., 1994; Elkatatny et al., 2016;
Ewing, 2006; Gonzalez et al., 2013; Hazra et al., 2016; Heslop, 2010;
Jacobi et al., 2008; Jia et al., 2012; Jinliang et al., 2012; Lee et al.,
2011; Liu et al., 2013; Luning and Kolonic, 2003; Montgomery et al.,
2005; Munn and Riddle, 1957; Passey et al., 1990; Pollastro et al., 2007;
Renchun et al., 2015; Rokosh et al., 2012; Rokosh et al., 2010; Romero-
Sarmiento et al., 2013; Schmoker, 1979; Schmoker, 1980; Schmoker
and Hester, 1983; Thomas, 2003) neurons for each layer. One hidden
layer with five neurons showed the optimized performance for the
suggested ANN model, and the optimum number of iterations is 42.
Table 1
Ranges of the parameters used for training the ANN model.
Parameters
GR RILD Δt ρb TOC
(API) (Ω·m) (μsec/ft) (g/cm3
) (wt%)
Minimum 23.01 3.65 52.29 2.40 0.75
Maximum 179.85 171.90 97.09 2.77 5.55
Mean 91.67 47.39 75.88 2.57 2.59
Mode 60.30 5.67 78.35 2.49 0.76
Range 156.84 168.25 44.80 0.37 4.80
Coefficient of variation 0.346 0.893 0.143 0.032 0.472
GR is gamma ray, RILD is the deep induction resistivity log, Δt is the compressional
transient time and ρb is the bulk formation density.
Fig. 1. Designed structure for ANN model, with single hidden layer and 5 neurons.
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
74
4. Table 2 summarizes the optimized parameters for the proposed ANN-
based model for TOC estimation.
2.3. Log data collection and preparation
In this work, the training data set (465 sets) was collected from
Barnett shale formation. The training set was evaluated statistically to
remove all outliers and unrealistic values. The outliers are removed
based on the standard deviation (SD) all the values outside the range
of ± 3.0 SD are considered as outliers and removed from the training
data set. After pre-processing, the training set (identifying the outliers
and unrealistic values) 442 out of the 465 data sets were selected to
train the ANN model based on four variables (deep induction resistivity
log, gamma ray log, bulk density log, and compressional transit time).
The input parameters were selected based on their relative effect on the
measured TOC. Fig. 3 shows that TOC is a strong function GR, com-
pressional time, and bulk density. The correlation coefficients were
0.81, 0.77, and −0.89 for GR, compressional time, and bulk density,
respectively. TOC was found to be a moderate function of the re-
sistivity, where the correlation coefficient was 0.51, Fig. 3. The selected
training data after preprocessing has the statistical properties listed in
Table 1.
To evaluate the developed ANN model, data from two different
wells was used. The first well in Barnett shale formation, and the second
well in Devonian shale formation. For the testing sets, the outliers and
the data points which are outside the applicable range for the suggested
ANN model (based on the ranges showed earlier in Table 1) were re-
moved.
2.4. Evaluation criteria
As mentioned earlier the proposed model was tested in two wells,
the first well from Barnett Shale formation which is the formation used
Fig. 2. The training error and validation error with iterations, the optimum number of iterations is 42 (less iterations will lead to higher error and more iterations will result in model
memorization as validation error starts increasing with the decrease in training error).
Table 2
Optimized parameters for the proposed ANN model.
Parameter Value
Learning function trainlm
Transfer function tansig
Number of hidden layers 1.0
Number of neurons 5.0
Gamma Ray
Resistivity
Compression time
Bulk Density
CorrelationCoefficient,R
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.81
0.51
0.77
-0.89
Fig. 3. The relative importance of the different parameters considered to learn the ANN
model.
Actual TOC (wt%)
0.0 1.0 2.0 3.0 4.0 5.0 6.0
PredictedTOC(wt%)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
R2
= 0.94
Fig. 4. A crossplot of predicted TOC from the proposed ANN model vs the actual TOC for
training set in Barnett formation, R2
= 0.94.
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
75
5. to train this model, and the second well is from Devonian Shale. The
second well is used to check the possibility of generalizing the devel-
oped model. The prediction capability of the proposed approach was
evaluated in terms of the average absolute deviation (AAD) and
coefficient of determination (R2
) between the actual laboratory mea-
sured TOC and the predicted TOC (from this model and the available
correlations).
Table 3
The proposed ANN-based weights and biases for TOC calculations with Eq. 11.
Input layer Output layer
Weights (w1) Biases (b1) Weights (w2) Bias (b2)
j = 1 j = 2 j = 3 j = 4
No. of neurons i = 1 0.9517 0.5817 0.9676 −2.5309 −0.2742 −1.7182 −1.2152
i = 2 0.5742 0.6430 0.7720 −2.1296 −0.0267 2.2211
i = 3 5.4001 0.7938 1.0230 2.9429 0.7237 0.1883
i = 4 0.7955 −0.0550 −0.4142 0.2749 1.2092 −0.9094
i = 5 −0.1984 7.8703 −0.4421 −0.1181 8.9550 1.7738
GR (API)
0 180
Depth
(ft)
7800
7900
8000
8100
8200
8300
RILD (ohmm)
0 180
dt (μft/sec)
50 100
ρ
b
(g/cm3
)
2.3 2.8
TOC (wt%)
0 6
Predicted TOC
Actual TOC
Fig. 5. Well-logging curves and comparison of predicted and measured TOC from well (Aguilera and Radetzki, 2013) in Barnett shale formation (testing set-1), the AAD of TOC predicted
by Eq. 11 from laboratory measured Ones is 0.91 wt% of TOC.
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
76
6. 3. Application examples to Barnett and Devonian shale
Two different depositional environments were considered to eval-
uate the performance of the proposed correlation. The first formation is
the Mississippian Barnett Shale. According to the United States Energy
Information Administration this formation was formerly considered as
the main source rock of the conventional hydrocarbon plays in the FWB
(Montgomery et al., 2005; Pollastro et al., 2007; Romero-Sarmiento
et al., 2013). In 2011, the cumulative gas production rate from this
formation was 8.0 trillion cubic feet (TCF), with a proven reserve
of > 31 TCF. Several publications contain general geologic background
for Barnett Shale play (e.g: Munn and Riddle, 1957; Cook and Bally,
1975; Thomas, 2003; Ewing, 2006; Pollastro et al., 2007).
The second formation considered in this work is the Devonian
Duvernay shale in the Western Canada Sedimentary Basin (WCSB)
which is a well-known organic rich source rock in the Devonian con-
ventional hydrocarbon system (Creaney et al., 1994). Rokosh et al.
(2012) suggest that this shale formation contains oil in place and gas in
place of 61.7 Billion barrels and 443 Tcf, respectively. Recent industry
production data confirmed that this shale play is liquid rich (Rokosh
et al., 2012).
The measured TOC range for the area of Barnett formation con-
sidered in this work is between 0.75 and 5.50 wt% for a depth interval
between 7750 and 8320 ft. The measured TOC of Devonian formation is
between 0.75 and 5.12 wt% for the depth interval between 1106 and
1178 ft.
4. Results and discussion
4.1. Building ANN-model
The training set gave the best prediction of the measured TOC by
using the parameters summarized earlier in Tables 2, and 442 data
points of (resistivity log, gamma ray log, bulk density log, and sonic
porosity transient time) as inputs and the corresponding core TOC va-
lues as an output. The coefficient of determination between actual and
predicted TOC for the training set is 0.94 as shown in Fig. 4, and the
AAD is 0.99 wt% of TOC. The weights and biases of the developed
model were extracted and summarized in Table 3.
It should be noted that the data provided into ANN model are au-
tomatically normalized between −1 and 1 by two points slope, Eqs. 5
and 6.
−
−
=
−
−
Y Y
Y Y
X X
X X
min
max min
min
max min (9)
⎜ ⎟= ⎛
⎝
−
−
⎞
⎠
− +Y
X X
X X
(Y Y ) Ymin
max min
max min min
(10)
Y is the normalized input parameter, Ymin = −1, Ymax = 1, X is the
input parameter (deep induction resistivity log, gamma ray log, bulk
density log, or compressional transient time) which will be normalized
by ANN, Xmin is the minimum value of input, Xmax is the maximum
input value, the minimum and maximum values of different inputs used
in this work to develop the ANN model are summarized in Table 1. For
example, the minimum value of GR (Xmin) is 23.01 API and the max-
imum value (Xmax) is 179.85 API, so GR of 50 API equals to −0.6558
API in normalized form.
Eq. 11 below can be used with the weights and biases listed in
Table 3 for calculating TOC in normalized form.
∑ ∑=
⎡
⎣
⎢
⎢
⎛
⎝
⎜
+
⎞
⎠
⎟
⎤
⎦
⎥
⎥
+
=
−
=
−TOC w tansig w Y b b
i 1
N
2 i
j 1
J
1 i,j j 1i 2
(11)
where N is the total number of neurons, J is the number of inputs
(gamma ray log, deep induction resistivity log, compressional transient
time, and bulk density log) w1 and b1 are the weight and bias of hidden
Actual TOC (wt%)
0.0 1.0 2.0 3.0 4.0 5.0 6.0
PredictedTOC(wt%)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
R2
= 0.93
Fig. 6. A crossplot of predicted TOC Eq. 11 vs the actual TOC for well (Aguilera and
Radetzki, 2013) in Barnett formation (testing set-1), R2
= 0.93.
TOC(wt%)
0 8
Depth
(ft)
1100
1120
1140
1160
1180
1500
1520
1540
1560
TOC(wt%)
0 8
TOC(wt%)
0 8
Actual TOC ANN Model Wang Sonic Based Model Wang Density Based Model
Fig. 7. A comparison of the TOC predicted from (Aguilera and Radetzki, 2013) Eq. 11,
(Carvajal-Ortiz and Gentzis, 2015) Wang sonic based model, and (Charsky and Herron,
2013) Wang density based model, with the actual TOC, for well (Carvajal-Ortiz and
Gentzis, 2015) in WCSB (Devonian shale), testing set-2.
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
77
7. layer, w2 and b2 are the weight and bias of output layer. Weights and
biases of hidden and output layers are summarized in Table 3, Y is the
input value in the normalized form. The use of equation form (like Eq.
11) based on weights and biases for calculating the desired outputs in
suggested before by many authors “e.g: (Elkatatny et al., 2016)”.
For example prediction of TOC from (gamma ray log, deep induc-
tion resistivity log, compressional transient time, and bulk density log),
the values of w1 will be taken at j = 1 for GR, at j = 2 for RILD, at j = 3
for Δt and j = 4 for ρb. Yj in Eq. 11 are as follow; Y1 is the normalized
GR, Y2 is the normalized RILD, Y3 is normalized Δt, and Y3 is normalized
ρb. so the term ∑ = −w Yj 1
J
1 i,j j in Eq. 11 for the first neuron can be
calculated as ∑ = + + += − − − − −w Y w Y w Y w Y w Yj 1
J
1 i,j j 1 1,1 1 1 1,2 2 1 1,3 3 1 1,4 4
where w1–1,1, w1–1,2, w1–1,3 and w1–1,4 are 0.9517, 0.5817, 0.9676, and
−2.5309, respectively, (from first row of Table 3“for first neuron”),
this could be repeated for all other 4 neurons.
4.2. Testing ANN-model
Eq. 11 was tested firstly in Barnett shale formation, using an unseen
data set and then it was tested in Devonian Duvernay shale. The per-
formance of the ANN model in Duvernay formation was compared to
available correlations (those were developed initially for this shale) to
Actual TOC (wt%)
0.0 1.0 2.0 3.0 4.0 5.0 6.0
PredictedTOC(wt%)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
ANN Model, R2
= 0.89
Wang Sonic Based Model, R2
= 0.65
Actual TOC (wt%)
0.0 1.0 2.0 3.0 4.0 5.0 6.0
PredictedTOC(wt%)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
ANN Model, R2
= 0.89
Wang Density Based Model, R2
= 0.22
(A)
(B)
Fig. 8. A comparison of the TOC predicted from (A) Eq. 11 and Wang sonic based model (B) Eq. 11 and Wang density based model, with the actual TOC for well (Carvajal-Ortiz and
Gentzis, 2015) in WCSB (Duvernay Shale), testing set-2, in term of coefficient of determination.
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
78
8. check the possibility of generalizing the developed model.
Fig. 5 shows the well logs for well (Aguilera and Radetzki, 2013)
(testing set-1) which is from Barnett formation. Track five shows the
actual TOC (from conventional core analysis) and the estimated TOC
(using this model). It is clear that there is an excellent match between
the TOC from the ANN-based empirical equation and core derived TOC,
the estimated TOC has an AAD of 0.91 wt% of TOC and the coefficient
of determination between laboratory-measured and estimated TOC is
0.93 as shown in Fig. 6.
Eq. 11 was examined in Duvernay formation (which is not the for-
mation used to develop this model). The performance of Eq. 11 was
compared with two of the recently revised ΔlogR methods suggested for
Duvernay formation by Wang et al. (2016). The performance of Eq. 11
was found to surpass the revised ΔlogR models.
Fig. 7 compares the predicted TOC from the developed correlation
based on ANN model, Wang sonic based and density based models
(Wang et al., 2016), with the actual measured TOC. Fig. 7 shows that
the developed correlation of TOC based on the optimized ANN model
(Eq. 11) is better than Wang models. For TOC values < 1.5 wt%, Wang
sonic based model prediction was twice the actual TOC, while Wang
density based model values was more than three times the actual ones.
The AAD of the developed ANN equation was 0.99 wt% TOC, while
Wang models (those developed for Devonian formation) have TOC of
1.16 wt% and 1.55 wt% for sonic based and density based models, re-
spectively.
The coefficient of determination for the TOC predicted from the
developed equation based on the optimized ANN model and actual TOC
is 0.89, which is higher than the ones calculated form Wang revised
models. The coefficients of determination between Wang sonic based
and density based methods with laboratory measured TOC is 0.65 and
0.22, respectively, as shown in Fig. 8.
Fig. 9 compares the performance of Eq. 11, Wang sonic based, and
Wang density based models in term of ADD and R2
, it shows clearly that
Eq. 11 outperformed both Wang models (revised Δlog R models) with
the minimum ADD (0.99 wt%) and maximum R2
(0.89).
5. Conclusions
ANN model was proposed to estimate TOC for unconventional shale
resources in Barnett and Duvernay shale formations using conventional
log data (gamma ray log, deep induction resistivity log, compressional
transient time, and bulk density log). Based on the obtained results, the
following conclusions can be drawn:
• ANN model provides better TOC estimations compared to available
methods by two criteria, lower average absolute deviation and
higher coefficient of determination than available techniques for
Duvernay shale example.
• The AAD is 0.99 wt% of TOC and the R2
of 0.89 as compared to
AAD's of 1.15 wt% and 1.55 wt% of TOC and R2
's of 0.65 and 0.22
from Wang sonic based and density based methods, respectively.
• For the first time, a new TOC empirical correlation was extracted
based on the weights and the biases of the optimized ANN model.
The developed equation can be used to estimate the TOC based on
conventional log data with a high accuracy without the need for
ANN model.
Acknowledgements
The authors thank College of Petroleum and Geosciences, King Fahd
University of Petroleum and Minerals for Support of this work.
Appendix A. Mathematical formulas for error calculations
This appendix summarizes the formulas used in this work for error calculations.
Average Absolute Difference (AAD).
∑= −
=
AAD
1
N
|(TOC ) (TOC )|
i 1
N
m i a
(A-1)
Coefficient of Determination (R2
).
=
∑ − − −
∑ − ∑ −
=
= =
R
[((TOC ) TOC ) ((TOC ) TOC )]
[(TOC ) TOC ] [(TOC ) TOC ]
2 i 1
N
a i a m i m
i 1
N
a i a
2
i 1
N
m i m
2
(A-2)
where N is the total number of samples, TOCm is the estimated TOC, TOCa is the average actual TOC, and TOCm is the average estimated TOC.
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![and continuous evaluation of TOC is required. Direct measurement of
TOC from core samples in the laboratory is accurate but it is costly and
time consuming. On the other hand, the current practice of TOC esti-
mation based on bulk density log alone or based on the conventional
sonic (or density) logs and resistivity log using empirical correlations is
fast but not accurate enough due to the assumptions implied in these
correlations (Renchun et al., 2015).
Currently two proven techniques of estimating TOC from well-log
data are used; these methods are: the Schmoker density log based
technique (Schmoker, 1980, 1979) and ΔlogR method (Passey et al.,
1990).
Schmoker correlation was developed for Devonian shale formation,
Eq. 1, based on treating the Devonian shale as a four-component system
(matrix, interstitial pores, pyrite, and organic matter). He considered
the total density of the formation as a function of the densities and
fractional volumes of these four components, and setting the pyrite,
organic matter and matrix densities of 5.0, 1.0, and 2.69 g/cm3
, re-
spectively. The pyrite volume was assumed to increase linearly with the
increase of the organic matter.
Based on these assumptions, Sckmoker derived Eq. 1 to calculate the
organic content in volume percent. TOC in wt% can be obtained by
converting the volume to weight percent. There is a well-established
correlation between wt% and volume percent for Devonian shale
(Schmoker, 1979). The author concluded that this method was applic-
able to a large area (135,000 square km) of Appalachian basin.
= −TOC(vol%) (ρ ρ)
1.378B
(1)
where TOC is the total organic carbon, ρB is the formation density in
absence of organic matter (g/cm3
), ρ is the formation bulk density (g/
cm3
).
Schmoker model was then refined in Bakken shale formation, Eq. 2.
The relation of pyrite-organic matter volumes, which was originally
developed for Devonian shale, was also considered to be applicable for
Bakken formation. A general TOC correlation (Eq. 2) for Bakken for-
mation (upper and lower members) was derived by assuming constant
porosity and pore fluid density profiles. Then by considering the or-
ganic matter density of 1.01 g/cm3
, a matrix density of 2.68 g/cm3
and
organic matter content to organic carbon content ratio of 1.3, the re-
lation was simplified, Eq. 3 (Schmoker and Hester, 1983). The authors
compared the results of fifty nine laboratory measurements from thirty
nine wells in Bakken shale with organic content ranging from 6 to 20 wt
% with those of Eq. 3 and found that Eq. 3 yielded good estimation of
TOC with AAD of 1.1% compared to laboratory analysis.
=
− −
− −
TOC(wt%)
[(100ρ )(ρ 0 .9922ρ 0.039)]
[(Rρ)(ρ 1 .135ρ 0.675)]
o mi
o mi (2)
= −( )TOC(wt%) 154.497
ρ 57.261
(3)
where ρo is the organic matter density (g/cm3
), ρmi is the volume-
weighted average density of grain and pore fluid (g/cm3
), R is the ratio
of weight-percent organic matter to weight-percent organic carbon.
The major disadvantage of Schmoker method is that it assumes the
formation bulk density and porosity are constant, and any change in the
bulk density is due to presence or absence of low density organic
kerogen.
Passey et al. (1990) proposed ΔlogR method for estimating the TOC
content which is now the widely used method. In this technique, the
separation between the properly scaled porosity indicator log (e.g sonic
transit time curve) and deep resistivity reading considered to give an
indication about the availability of organic-rich rocks. The separation
caused by the organic-rich rocks is related to: the effect of the low
density and low velocity of kerogen on the porosity logs and the re-
sponds of the resistivity logs to the formation fluids, Eqs. 3 and 4.
= + × −ΔlogR log (R R ) 0.02 (Δt Δt )10 baseline baseline (4)
= × − ×ΔTOC logR 10(2.297 0.1688 LOM)
(5)
where ΔlogR is the resistivity porosity logs separation, R and Δt are the
target formation resistivity (Ω·m), and sonic transient time (μs/ft), re-
spectively, Rbaseline and Δtbaseline are the base formation resistivity (Ω·m)
and base sonic transit time (μs/ft), respectively, corresponding to a
reference line of organic lean shale in the same formation, LOM is the
level of maturity.
ΔlogR technique has two major drawbacks: the first one is the as-
sumption that the rock composition, texture, and compaction do not
change, this method may lead to incorrect estimation of the target
shale. Since in reality the composition and texture of the organic rich
shale extremely vary for different resource play (Rokosh et al., 2010).
The second drawback is the limited ranges of applicability for sonic
transit time and resistivity for this method because of the assumption of
1:50 linear relationship (constant slope of 0.02, Eq. 4) between the
porosity and logarithmic resistivity logs. The use of LOM is another
weakness of ΔlogR technique since LOM is an uncommonly used
measure of organic matter thermal alteration (Wang et al., 2016).
Charsky and Herron (2013) examine Schmoker and ΔlogR models
into four different wells drilled with both water and oil-based muds,
and covering a variety of formations. They reported that these models
have low accuracy with an average AAD from core derived TOC of
1.6 wt% and 1.7 wt% for Schmoker and ΔlogR methods, respectively.
Also, when Schmoker model was used in Bakken shale formation, which
was used originally by Schmoker to develop and test this model, the
AAD from the core derived TOC was 1.2 wt% which is relatively high.
Wang et al. (2016) modified the sonic-/density-based ΔlogR models
for TOC determination based on Gamma Ray (GR), resistivity, sonic,
and density well logs. In their models they redefined ΔlogR with esti-
mated slopes related to target shale to remove the assumed linear ap-
proximation. They also suggested the use of more common thermal
indicators (Tmax or vitrinite reflectance (Ro)) instead of LOM, since the
use of LOM requires a conversion between (Tmax or Ro%) and LOM
which can lead to a problem in practice (Crain, 2000).
Wang et al. (2016) also introduced the use of GR log to improve the
prediction of TOC. The revised ΔlogR values based on sonic and density
logs are expressed as shown in Eqs. 6 and 7, respectively. The TOC from
the modified ΔlogR including GR can be calculated using Eq. 8. The
modified models showed better results in estimating the TOC when
applied in Devonian shale (R2
was > 0.92) compared to the original
ΔlogR technique (R2
of 0.82). The residue analysis indicates the mod-
ified models are unbiased statistically compared to the original models.
= +
−
× −ΔlogR log (R R )
1
ln 10
m
Δt Δt
(Δt Δt )10 baseline
m
baseline
(6)
= +
−
× −ΔlogR log (R R )
1
ln 10
m
ρ ρ
(ρ ρ )10 baseline
m
baseline
(7)
= + − × +TOC [α ΔlogR β(GR GR )] 10baseline
(δ η T )max (8)
where Δtm is the matrix sonic transit time (μs/ft), m is the cementation
exponent, ρm is the matrix density (g/cm3
), ρbaseline is the baseline
density corresponding to the Rbaseline value (g/cm3
), α, β, δ and η are
matrix constants to be determined, Tmax is the maturity indicator (°C),
GRbaseline is the baseline value of shale (API).
The estimation of TOC using Wang Models requires the determi-
nation of matrix constants which depend on the matrix composition.
These parameters will be different for different formations. This means
these parameters have to be estimated for any formation before using
the model and this requires the knowledge of TOC from the laboratory.
Based on literature survey, current TOC prediction models either
cannot predict the TOC accurately or needs tedious laboratory work to
determine the fitting parameters. The objective of this paper is to de-
velop a new robust empirical correlation that can be used to predict the
TOC with high accuracy based on conventional well logs using artificial
neural network technique (ANN). The developed TOC correlation was
A.A.A. Mahmoud et al. International Journal of Coal Geology 179 (2017) 72–80
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