Available online at http://ijcpe.uobaghdad.edu.iq and www.iasj.net 

Iraqi Journal of Chemical and Petroleum 
 Engineering  

Vol.23 No.4 (December 2022) 49 – 58 
EISSN: 2618-0707, PISSN: 1997-4884 

 

Corresponding Authors:  Name: Jassim M. Al Said Naji, Email: 150100@uotechnology.edu.iq, Name: Ghassan H. Abdul-Majeed, Email: 

ghassan@uob.edu.iq, Name: Ali K. Alhuraishawy, Email: ali19_82@yahoo.com  

IJCPE is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. 

 

Comparison of Estimation Sonic Shear Wave Time Using 

Empirical Correlations and Artificial Neural Network 

 
Jassim M. Al Said Najia, Ghassan H. Abdul-Majeedb, and Ali K. Alhuraishawyc 

 
a Petroleum Engineering Department, College of Engineering, University of Baghdad, Baghdad, Iraq. 

b Department of Scientific Affairs, University of Baghdad, Baghdad, Iraq.  
c Reservoir and Field Development Directorate, Ministry of Oil, Baghdad, Iraq. 

 

Abstract 

 
   Wellbore instability and sand production onset modeling are very affected by Sonic Shear Wave Time (SSW). In any field, SSW is 

not available for all wells due to the high cost of measuring. Many authors developed empirical correlations using information from 

selected worldwide fields for SSW prediction. Recently, researchers have used different Artificial Intelligence methods for estimating 

SSW. Three existing empirical correlations of Carroll, Freund, and Brocher are used to estimate SSW in this paper, while a fourth new 

empirical correlation is established. For comparing with the empirical correlation results, another study's Artificial Neural Network 

(ANN) was used. The same data that was adopted by the ANN study was used here where it is comprised of 1922 measured points of 

SSW and the other nine parameters of Gamma Ray, Compressional Sonic, Caliper, Neutron Log, Density Log, Deep Resistivity, 

Azimuth Angle, Inclination Angle, and True Vertical Depth from one Iraqi directional well. Three existing empirical correlations are 

based only on Compressional Sonic Wave Time (CSW) for predicting SSW. In the same way of developing previous correlations, a 

fourth empirical correlation was developed by using all measured data points of SSW and CSW. A comparison demonstrated that 

utilizing ANN was better for SSW predicting with a higher R2 equal to 0.966 and lower other statistical coefficients than utilizing four 

empirical correlations, where correlations of Carroll, Freund, Brocher, and developed fourth had R2 equal to 0.7826, 0.7636, 0.6764, 

and 0.8016, respectively, with other statistical parameters that show the new developed correlation best than the other three existing. 

The use of ANN or new developed correlation in future SSW calculations is relevant to decision makers due to a number of 

limitations and target SSW accuracy.    

      
Keywords: Empirical correlations, artificial neural network, sonic shear wave, wellbore deviation, azimuth and inclination. 
 
Received on 25/06/2022, Accepted on 19/07/2022, Published on 30/12/2022 

 

https://doi.org/10.31699/IJCPE.2022.4.7  

 
1- Introduction 
 

   Generally, sonic logs are classified alongside Density 

Logs (DL) and Neutron Logs (NL) as porosity logs where 

two types of sonic waves exist: Compressional Sonic 

Wave Time (CSW) and Sonic Shear Wave Time (SSW) 

[1]. CSW and SSW are measured either by Dipole Sonic 

Log (DSI) on site or by experiments in the laboratory by 

utilizing core plug samples [2] but computing SSW from 

core plug tests is an expensive and time-consuming 

method, and DSI is not running for all wells [3]. Sonic 

waves with density are key parameters for calculating 

some elastic rock mechanic properties such as Biot's 

coefficient, Poisson ratio, shear modulus, rock 

compressibility factor, and young modulus [4]. Elastic 

rock mechanic properties are important in geomechanical 

studies for prediction of wellbore instability and sand 

production onset [5]. Formation lithology and its 

properties, type of fluids that filled rocks and their 

properties, reservoir temperature, and hydrostatic pressure 

of the rock column are all parameters that affect sonic 

wave velocities or transmitted time. Laminated clay and 

structural shale content are making sonic wave 

transmitting time increase [6] while decreasing in water 

saturated rocks rather than dry rocks, where at 10% water 

saturated, sonic waves have a strong decrease in intensity 

that means an increase in wave transmitting time [7]. 

From the sixties of last century till now, many empirical 

correlations have been developed based on logs and core 

test data of selected worldwide reservoirs as summarized 

in Table 1 [8-15]. All these empirical correlations in 

Table 1. are developed to calculate SSW in terms of Shear 

Sonic Velocity (SSV) and Compressional Sonic Velocity 

(CSV) with velocity units of kilometer per second 

(km/sec), where SSV and CSV are reciprocals of SSW and 

CSW respectively. 

   Recently, at the beginning of the present century, 

authors have gone to work on Artificial Intelligent (AI) 

methods for estimating SSW because of past simple 

regression correlations shown in Table 1. were for special 

reservoir cases and did not take into account all effective 

SSW parameters. Rezaee et al. (2007) [16] applied three 

AI methods: fuzzy logic, neurofuzzy, and Artificial 

Neural Network (ANN) to data from two wells in the 

Carnarvon basin, NW shelf of Australia's sandstone 

reservoir, with a third well used for validation. The 

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J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

50 
 

datasets used were Gamma Ray (GR), CSV, NL, Deep 

Resistivity Log (DRL), and DL. Tabari et al. (2012) [17] 

utilized the ANN method for predicting SSV by using a 

dataset of GR, NL, DL, and CSV of one well, while data 

from two wells was used for ANN validation. Hadi and 

Nygaard (2018) [18] used ANN for prediction of SSV by 

utilizing data from the production section in the south of 

Iraq where CSV and DL are used as input parameters of 

the input layer. Al Ghaithi and Prasad (2020) [19] adopted 

Feedforward Neural Network (FNN) for predicting SSV 

by using field data from the Norwegian North Sea where 

the dataset comprised GR, DL, CSW, DRL, NL, and 

Measured Depth (MD). Al Said Naji et al (2022) [20] on 

their submitted paper to the Iraqi geological journal are 

working on ANN for predicting SSW based on one Iraqi 

directional well and 1922 measured points of SSW that 

were used as the output of the proposed ANN, beside nine 

parameters of CSW, GR, NL, DL, DRL, Caliper (CAL), 

True Vertical Depth (TVD), Azimuth Angle (AZI), and 

Inclination Angle (INC) that utilized as inputs. They 

obtained the following mathematical model for SSW 

prediction for any directional well: 

   
𝑆𝑆𝑊 =

∑ 𝑊2𝑗
12
𝑗=1 (

2

1+𝑒
−2(𝑊1𝑗,1 𝑇𝑉𝐷 + 𝑊1𝑗,2 𝐶𝑆𝑊 + 𝑊1𝑗.3 𝐺𝑅 + 𝑊1𝑗,4 𝐶𝐴𝐿 + 𝑊1𝑗.5 𝑁𝐿 + 𝑊1𝑗,6 𝐷𝑅𝐿 + 𝑊1𝑗,7 𝐷𝐿 + 𝑊1𝑗,8 𝐼𝑁𝐶 + 𝑊1𝑗,9 𝐴𝑍𝐼 + 𝑏1𝑗) 

−

1) + 𝑏2                                                                                 (1) 

 

   Where W2j is an output-hidden layers weight, W1ji is an 

input-hidden layers weights, j is the hidden layer neurons, 

b1j is a hidden layer biases and b2 represents bias of 

output layer. 

   The present study is aimed at making a comparison 

between utilizing three existing empirical correlations of 

Carroll (1969), Freund (1992) and Brocher (2005) and 

developing a fourth with the results of constructed ANN 

by Al Said Naji et al. (2022) for SSW estimation. 

 

Table 1. Summary of Developed Empirical Correlation for SSV Estimation 
References Year Correlation of SSV relation with CSV (km/sec) Eq. number Lithology Type 

Pickett 1963 𝑆𝑆𝑉 = 0.526. 𝐶𝑆𝑉 (2) Limestone 
Pickett 1963 𝑆𝑆𝑉 = 0.556. 𝐶𝑆𝑉 (3) Dolomite 
Carroll 1969 𝑆𝑆𝑉 = 0.75609. 𝐶𝑆𝑉 0.81846 (4) Various rock types 
Castsgna, et. al 1985 𝑆𝑆𝑉 = −0.05509. 𝐶𝑆𝑉 2 + 1.0168. 𝐶𝑆𝑉 − 1.305 (5) Limestone 
Freund 1992 𝑆𝑆𝑉 = 0.763. 𝐶𝑆𝑉 − 0.603 (6) Various rock types 
Eskandari, et.al 2004 𝑆𝑆𝑉 = −0.1236. 𝐶𝑆𝑉 2 + 1.6126. 𝐶𝑆𝑉 − 2.3057  (7) Carbonate rocks 
Brocher 2005 𝑆𝑆𝑉 = 0.7858 − 0.1244. 𝐶𝑆𝑉 + 0.7949. 𝐶𝑆𝑉 2 −

0.21238. 𝐶𝑆𝑉 3 + 0.006. 𝐶𝑆𝑉 4  
(8) Various rock types 

Ameen et al 2009 𝑆𝑆𝑉 = 0.52. 𝐶𝑆𝑉 + 0.25251 (9) Carbonate rocks 
Al-Kattan 2015 𝑆𝑆𝑉 = 0.699. 𝐶𝑆𝑉 0.969 (10) Carbonate rocks 

 

 Field of Study and Reservoir Description 
 

   The Fauqi oil field is located in the Missan governorate 

in the south of Iraq. It is 50 km to the north–east of 

Ammara city and 175 km north of Basrah city, as shown 

in Fig. 1. It has two domes with north-west, south-east 

anticlines in the north and south, respectively, and some 

of its northern dome stretch is in Iran.  The field length is 

approximately 23 km and the width is approximately 7 

km. The Fauqi oil field has two reservoirs: Asmari and 

Mishrif. Asmari is an Iranian name, and it corresponds to 

three Iraqi names for the reservoir, which are: Jeribe-

Euphrates formation, Upper Kirkuk formation, and 

Middle-Lower Kirkuk formation. The Jeribe-Euphrates 

formation is the upper part of the Asmari reservoir that 

was deposited during the Neogene geological period. It is 

represented as an A unit with sub divisions of (A1, A2, 

and A3) and an average thickness of 40 m. It has a 

lithology that consists mainly of 85% dolomite alternated 

with moderately thin shale. The Upper Kirkuk formation 

is a middle sub-reservoir of the Asmari formation, 

deposited during the Paleogene geological period. It is 

denoted as the B unit with its classifications (B1, B2, B3 

and B4) and consists basically of thick shale, alternated 

with thin sandstone, argillaceous limestone, calcareous 

shale and limestone. The sandstone portion is gray, poorly 

consolidated, fine to medium grained, subangular to sub-

rounded, moderately sorted, predominantly quartz, and 

argillaceous. It has an average interval of 120 m. The 

Middle-Lower Kirkuk formation is a lower sub-reservoir 

of the Asmari formation. During the Paleogene geological 

epoch, the Oligocene series and stage of Aquitanian to 

lower Oligocene, this reservoir was deposited. It is 

represented as C and D units in past studies and C unit in 

modern studies where they are water submerged zones. Its 

lithology is composed mainly of thick Shale and 

Argillaceous Siltstone alternated with moderately thick 

Argillaceous Limestone and Sandstone with an average 

thickness of 200 m [21, 22]. 

 

 
Fig. 1. Iraqi Fauqi Oil Field Location on Iraq Map [23] 

 

2- Materials and Methods 
  

   The same dataset utilized by Al Said Naji et al (2022) 

[20] is used for the present paper. The selected dataset is 

from one directional well that penetrated the Asmari 

reservoir in the Iraqi Fauqi oil field. The data of the 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

51 
 

mentioned directional well is comprised of 1922 

measured points of SSW, beside nine parameters, CSW, 

GR, NL, DL, DRL, CAL, TVD, AZI, and INC, as 

illustrated in Fig. 2. As mentioned above, Al Said Naji et 

al. (2022) [20] used these data to construct an ANN for 

SSW prediction while considering the effects of well 

deviation parameters (INC and AZI). Eq. 1 resulted as a 

mathematical model of two loops to predict SSW for 

directional wells. Table 2 summarizes the used dataset of 

selected directional well.  

 

 
Fig. 2. Used Data of Directional Well Logs Track [20] 

 

Table 2. Ranges Summary of Used Dataset 
Parameter Minimum Maximum Mean 

SSW, (us/ft) 89.05 156.94 112.032 

TVD, (m) 2993 3185.1 3089.05 

CSW, (us/ft) 48.58 114.3 64.09 

GR, (GAPI) 6.56 132.011 44.94 

CAL, (in) 8.43 14.698 8.77 

NL, (dimensionless) 0.301 44.6 16.097 

DRL, (ohm.m) 0.311 461.54 7.064 

DL, (gm/cc) 2.15 2.94 2.569 

INC, (deg) 44.55 48.29 47.19 

AZI, (deg) 321.14 323.44 322.318 

 

2.1. Existing Empirical Correlations  
 

   Selection of an appropriate SSW prediction correlation 

for a given field is a very big challenge where any 

mistake in SSW estimation leads to poor prediction of 

rock elastic properties, making decisions on investments 

and losses very difficult [24]. Asmari reservoir, as 

described above, consists of different rock types, so any 

developed empirical correlation from literature based on 

one rock type cannot be used to calculate SSW. Three 

empirical correlations suitable for various lithology types 

were used to calculate SSW based on CSW data. These 

existing empirical correlations are Carroll (1969), Freund 

(1992), and Brocher (2005), illustrated in Table 1. as Eq. 

4, Eq. 6, and Eq. 8 respectively. Carroll in 1969 

developed an empirical correlation for SSV determination 

by using data obtained from the volcanic region of 

Nevada where 62 dry core samples were collected with 

the same measured log data from different intervals. This 

correlation was established for all rock types by studying 

and testing the effects of lithology kinds and hydrostatical 

loads on SSV estimation [9]. Freund in 1992 established 

an empirical correlation based on 57, 25 and 5 samples of 

sandstone, siltstone, and claystone, respectively, for the 

well penetrated Rotliegendes reservoir in Germany. 

Samples had porosity ranges of 0.01–0.5 and clay content 

of 0.01–0.88 while measurements were made at pressure 

ranges between 10–300 Mpa. [11]. Brocher (2005) 

introduced a global empirical correlation for SSV 

determination. He used SSV and CSV datasets from 

various fields in California: (1) fine-grained Holocene 

deposits in San Francisco Bay; (2) wells with a depth of 

more than 410 m at Santa Clara; (3) Miocene sedimentary 

rocks from the central of California; (4) granodiorite and 

salinan terrane granites from a pilot hole at Park-field; 

and (5) other logs and core plugs from various fields and 

previous studies [13]. 

   In this paper, the use of these three global correlations 

in SSW calculating is based on the mentioned measured 

data, 1922 points of CSW, by using Excel 2022 in the 

following sequence: (1) invert CSW to CSV; (2) multiply 

the 304.8 conversion factor to convert units from ft/us to 

km/sec; (3) use correlations to calculate SSV in units of 

km/sec; and (4) invert SSV to SSW and use the conversion 

factor to make it in units of us/ft. 

 

2.2. Development of New Empirical Correlation  

 

   A new polynomial second order empirical correlation 

was developed by using the same data of CSW and SSW 

that consisted of 1922 measured points which used by Al 

Said Naji et al. (2022) [20]. This correlation is established 

in the same way of developing past empirical correlations 

mentioned in Table 1. where its development was based 

on the plot in Fig. 3 below, which has the following 

formula with a correlation coefficient (R2) equal to 

0.8293: 
 

𝑆𝑆𝑊 = −0.0143. 𝐶𝑆𝑊 2 +  3.1521. 𝐶𝑆𝑊 − 29.73                     (11)  

 

 
Fig. 3. Plot of Development Polynomial Second Order 

Empirical Correlation 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

52 
 

2.3. Artificial Neural Network (ANN)  

 

   The ANN, constructed by Al Said Naji et al. (2022) [20] 

in their submitted paper to the Iraqi geological journal, is 

used in this study to compare with the results of utilizing 

three existing empirical correlations and a developed 

fourth. They built ANN by a dataset of one directional 

well from Iraqi Fauqi oil field with measured 1922 points 

of SSW and nine parameters of TVD, CSW, GR, CAL, NL, 

DRL, DL, INC, and AZI using MATLAB R2012b. Using 

multi parameters for ANN construction to was based on 

their effects on SSW values where some of the past 

literatures [2, 3, 25, 26] explained SSW response against 

different log measurements of CSW, GR, CAL, NL, DRL, 

and DL while Al Said Naji et al 2022 [20] on their paper 

demonstrated the positive impact of hole deviation 

parameters INC and AZI and the negative effect of TVD 

on SSW as summarized in Table 3. 

 

Table 3. Multi Logs Parameters Impact on SSW 

Prediction 
Parameter Impact on SSW Estimation 

TVD Negative 

CSW Positive 

GR Dual 
CAL Dual 

NL Positive 

DRL Negative 
DL Negative 

INC Positive 

AZI Positive 

 

   Measured SSW was used as a neuron of output layer 

while others nine parameters were entered as input layer 

neurons. Tangent function was adopted as hidden layer 

activation function as appearing in Eq. 13 while linear 

function showed below in Eq. 14 used for activating of 

output layer [27]. 1922 measured points are classified to 

three parts 70%, 15%, and 15% for ANN three processing 

sequences of training, validation and testing. Constructed 

ANN had optimum structure of (ANN 9-12-1) based on 

obtained maximum R2 and minimum mean square error 

(MSE) as appear in Fig. 4 in shape of multiple layer 

perceptron (MPL) with single hidden layer. MPL is the 

popular structured of networks for functions regression 

that consisting from three layers input, hidden and output. 

Any layer contains number of neurons that connected 

with others of next layers with factor called weight (W) 

while another factor works on adding freedom degree in 

neurons connection called bias (bi) [28]. Each neuron of 

layers before hidden layer are combining and modifying 

by acting of hidden and output layers neurons in term of 

collection junction by following function [29]: 

 

𝑆𝑗 = ∑ 𝑋𝑖  𝑊1𝑗𝑖 +  𝑏1𝑗
𝑛
𝑖=1                                                       (12) 

 

𝑓(𝑆𝑗 ) =
2

1+𝑒
−2 𝑆𝑗

− 1                                                            (13) 

 

𝑍𝑃 = ∑ 𝑊2𝑗
𝑘
𝑗=1  𝑓(𝑆𝑗 ) + 𝑏2𝑗                                                   (14) 

   

   Where n is the neurons number of input layer, Xi is the 

input vector, W1ji is the weight of connection between Xi 

and j, Sj is the summation of input weights and biases, 

b1j. outputs are resulting from passing of Sj though an 

appropriate activation function, Zp represents estimated 

(SSW) value, W2j is an output hidden layer weight, b2j 

represents bias of output layer, while k is the neurons of 

hidden layer. 

   ANN mathematical model was obtained in Eq. 1 was by 

combining Eq. 12, Eq. 13 and Eq. 14 with substituting of 

inputs and output variables to simplify SSW calculations.  

 

 
Fig. 4. ANN Structure for SSW Prediction 

 

3- Results and Discussion 
 

   Comparison between empirical correlations and ANN 

results was based on statistical parameters of average 
percent error (APE), absolute average percent error 

(AAPP), standard deviation (SD), mean square error 

(MSE), and correlation coefficient R-Square (R2) as 

shown in the following equations respectively: 

 

𝐴𝑃𝐸 =
1

𝑛
∑ (

𝑍𝑚𝑖−𝑍𝑝𝑖

𝑍𝑚𝑖
 )

𝑛

𝑖=1
                                                          (15) 

 

𝐴𝐴𝑃𝐸 =  
1

𝑛
 ∑ |𝑍𝑚𝑖 − 𝑍𝑝𝑖|𝑛𝑖=1                                                 (16) 

 

𝑆𝐷 = ( 
∑ (𝑍𝑝,𝑖−𝑍𝑝𝑎𝑣𝑔)

2𝑛
𝑖=1

𝑛
)

0.5

                                                    (17) 

  

𝑀𝑆𝐸 =  
1

𝑛
 ∑ (𝑍𝑚,𝑖 − 𝑍𝑃,𝑖 )

2𝑛
𝑖=1                                                (18) 

 

𝑅2 = 1 −
∑ (𝑍𝑚,𝑖−𝑍𝑃𝑖)

2𝑛
𝑖=1

∑ (𝑍𝑚,𝑖−𝑍𝑝𝑎𝑣𝑔)
2𝑛

𝑖=1

                                                    (19)    

 

   Where Zmi, Zpi and Zpavg are measured, predicted and 

averaged predicted SSW. Fig. 5 and Fig. 6 is explaining 

the performance of both ANN and empirical correlations. 

As note from first looking on these two figures, ANN 

performance is better than four empirical correlations that 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

53 
 

mean applying Eq. 1 for any directional well for SSW 

calculation is better than using Eq. 4, Eq. 6, Eq. 8 and Eq. 

11.  

 

 
Fig. 5. ANN Performance Evaluation [20] 

 

 
Fig. 6. Empirical Correlations Performance Evaluation 

 

  Statistical coefficients for four empirical correlations and 

ANN methods are summarized in Table 4. as can be seen, 

the ANN approach is superior than the rest of the 

empirical models where it had higher R2 and lower APE, 

AAPE, MSE, and SD. A new developed empirical 

correlation Eq. 11 is better than other existing correlations 

of Carroll (1969), Freund (1992), and Brcocher (2005) 

Eq. 4, Eq. 6, and Eq. 8 respectively. 

Table 4. Statistical Parameters of SSW Prediction 

Methods 
Model APE AAPE MSE SD 2R 

Carroll, 1969 0.29345 5.353119 50.93531 15.27 0.7826 

Freund, 1992 10.03937 13.77396 239.4537 21.22 0.7636 

Brocher, 2005 6.0883475 9.436357 228.8576 22.19 0.6764 

Polynomial 

Second 

Order, 2022 

0.16461 4.794007 38.65837 12.52 0.8016 

ANN, 2022 0.006 2.168 9.62 2.69 0.966 

 

   To support the above results in Table 4., and reinforce 

what has been reached in the above sentences, we created 

the following illustrated plots. These plots: Fig. 7 presents 

a plot of measured and predicted SSW by Carroll (1969) 

on the X-axis with TVD on the Y-axis. The statistical 

parameters in Table 4 with this figure demonstrated that 

the Carroll correlation outperformed the Freund (1992) 

and Brocher (2005) correlations. Fig. 8 and Fig. 9 state 

measured SSW against that predicted by Freund and 

Brocher with TVD, respectively. Brocher was a bad 

correlation for SSW prediction of Asmari reservoir. Fig. 

10 is applying measured and predicated SSW by a new 

developed polynomial second order correlation with TVD. 

The results show that the new developed correlation is 

better than the other three utilized empirical correlations, 

and that is expected where the new correlation was 

established based on measured data related to the target 

SSW of the Asmari reservoir, while others were developed 

by adopting data from different worldwide reservoirs that 

had properties different than Asmari. Fig. 11 shows the 

SSW of ANN with measured. Results obtained from ANN 

are much more accurate than results of other empirical 

methods according to account as much as possible the 

high number of influencing parameters on SSW in 

addition to consider wellbore deviation parameters INC 

and AZI. Using the ANN mathematical model Eq. 1 or the 

developed empirical correlation Eq. 11 is related to 

decision makers, so using the ANN resulted model will 

obtain high accuracy results of SSW but requires data 

availability and people with programming software 

knowledge due to the need to make two loops code for 

SSW estimation, whereas utilizing a new developed 

equation is easier than the ANN model and only requires 

CSW data but will give low accurate SSW prediction. 
 

 
Fig. 7. Plot of Measured and Estimated SSW by Carroll Correlation with TVD 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

54 
 

 
Fig. 8. Plot of Measured and Estimated SSW by Freund Correlation with TVD 

 

 
Fig. 9. Plot of Measured and Estimated SSW by Brocher Correlation with TVD 

 

 
Fig. 10. Plot of Measured and Estimated SSW by Polynomial Second Order Correlation with TVD 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

55 
 

 
Fig. 11. Plot of Measured and Estimated SSW by ANN with TVD 

 

   To apply Eq. 1 to any directional well, use the ANN 

matrix parameters obtained by Al Said Naji et al. (2022) 

study in Table 5. Constructed ANN was (9-12-1) in that 

each neuron in the hidden layer had twelve weights 

connected to it for each parameter in the input layer. Also, 

twelve weights were connected between the hidden layer 

neurons and the output layer neuron. Twelve biases add 

some degree of freedom to each neuron at the hidden 

layer, while a single bias supports the output layer neuron. 

Applying Eq. 1 using Table 5. parameters, you need to 

write code for two loops to calculate SSW. 

   The lack of sufficient data prevented the validation of 

established models. We recommend validating the 

developed models by using data from other fields. 

 

Table 5. Constructed ANN Matrix [20] 
W1j, TVD W1j, CSW W1j, GR W1j, CAL W1j, NL W1j, DRL W1j, DL W1j, INC W1j, AZI jb1 jW2 b2 

1.547 -6.385 3.107 4.66 -0.938 5.056 -4.332 1.003 1.133 3.488 -0.157  

 

 
 

 

 
0.223 

0.603 -0.567 0.591 0.455 0.497 2.959 -0.013 0.598 -0.978 -3.935 0.583 

1.117 -1.055 2.383 19.42 -3.598 -8.034 -4.075 1.5398 -7.747 15.158 0.382 

3.7 3.088 -2.798 -1.775 3.655 -16.18 -3.027 4.316 -2.073 -19.72 0.109 

-0.709 0.2396 -0.84 -1.375 -0.565 9.056 -0.346 -0.348 0.787 7.869 -0.741 

-5.465 -9.212 -5.083 7.27 3.058 6.371 -15.55 -11.23 0.752 12.453 0.0763 

-2.326 -0.749 0.991 1.715 -1.051 -3.229 -1.42 16.492 -10.83 -4.423 0.584 

-19.58 7.553 -7.6296 4.557 1.941 19.58 3.476 0.821 17.756 21.856 -0.133 

1.805 -3.608 1.336 1.612 1.311 -6.774 -1.252 -6.347 2.704 -1.796 -0.226 

1.808 3.937 -0.914 1.473 -1.629 3.678 -2.646 1.773 -8.731 0.778 0.1651 

7.043 0.634 0.949 -1.104 -1.802 -3.921 -1.334 5.821 -8.471 -4.005 0.645 

2.589 -0.912 0.643 1.908 -0.162 -1.138 -0.412 3.676 -5.105 -0.39 -1.477 

 

4- Conclusions 
 

   This work is presenting comparison between empirical 

correlations and ANN results for SSW estimation. Same 

dataset adopted by Al Said Naji et al 2022 is used in 
present study and it comprised of 1922 measured points 

of SSW with other nine parameters TVD, CSW, GR, CAL, 

NL, DRL, DL, INC and AZI. Three global existing 

empirical correlations of Carroll 1969, Freund 1992, and 

Brocher 2005 used for SSW predicting by utilizing all 

measured points of CSW from dataset. A Polynomial 

second order empirical correlation developed by using all 

measured points of SSW and CSW. ANN constructed by 

Al Said Naji et al 2022 results is used to compare with 

empirical correlations results. Statistical parameters 

demonstrated that ANN was very superior than others 

empirical correlations where it had higher R2 and lower 

APE, AAPE, MSE and SD. Developed second order 

empirical correlation was best than other correlations of 
Carroll (1969), Freund (1992), and Brocher (2005) 

because the last were established based on worldwide 

fields data different than used dataset of Asmari reservoir. 

Using either ANN mathematical model equation or new 

developed second order empirical equation by any 

consequent authors will depend on data availability, 

persons knowledge in programming softwares and target 

SSW accuracy.  

 

Acknowledgments 

 

     The authors are grateful for supporting universities of 

Baghdad, and Technology, Ministry of oil: petroleum 



J. M. Al Said Naji et al. / Iraqi Journal of Chemical and Petroleum Engineering 23,4 (2022) 49 - 58 

 

 

56 
 

Research Develop Center and Reservoir and Development 

Directorate.  

 

Nomenclature 

 

AAPE Absolute average percent error 

ANN Artificial neural network 

APE Average percent error 

AZI Azimuth angle (dego) 

b1j Input - hidden layers biases 

CAL Caliper log (in) 

CSV Compressional sonic velocity (ft/us) or 

(km/sec) 

CSW Compressional sonic wave time (us/ft) 

DL Density log (gm/cc) 

DRL Deep resistivity log (ohm.m) 

DSI Dipole sonic imager tool 

FNN Feedforward neural network 

GR Gamma ray log (GAPI) 

INC Inclination angle (dego) 

j Hidden layer neurons 

MD Measured depth (length unit) 

MSE Mean square error 

n Neurons number of input layer 

NL Neutron log (%) 

R2 Correlation coefficient 

SD Standard deviation 

Sj Summation of input weights and biases 

SSV Shear sonic velocity (ft/us) or (km/sec) 

SSW Sonic shear wave time (us/ft) 

SW Water saturation (%) 

TVD True vertical depth (m) 

W1ji Input – hidden layer neurons 

connection weights 

W2j Output - hidden layer connection 

weights 

Xi Input vector 

Zmi Measured shear sonic wave time (us/ft) 

Zp Predicted sonic shear wave time (us/ft) 

Zpavg Average predicted sonic shear wave 

time (us/ft) 

 

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كة مقارنة في تخمين زمن موجة القص الصوتية بأستخدام المعادالت التجريبية والشب
 العصبية االصطناعية 

 

 3 الحريشاوي علي خيون و , 2, غسان حميد عبد المجيد1 جاسم محمد السيد ناجي
 

 جامعة بغداد, كلية الهندسة, قسم هندسة النفط, بغداد, العراق. 1
 جامعة بغداد, بغداد, العراق. 2

 وزارة النفط, دائرة المكامن وتطوير الحقول, بغداد, العراق. 3
 

 الخالصة
 

ر زمن حقل ال يتوفنمذجة ثبوتية البئر والتنبأ بأنتاج الرمل تتأثر جدا بزمن موجة القص الصوتية. في اي    
ة موجة القص الصوتية لكل اآلبار نسبة لكلف قياسه العالية. العديد من الباحثين طوروا معادالت تجريبي

ذكاء بأستخدام بيانات بعض الحقول العالمية لحساب زمن موجة القص الصوتية. مؤخرا استخدم الباحثون طرق ال
ق تجريبية موجودة لكل من كارول وفريوند وبرونشر االصطناعي لحساب زمن موجة القص الصوتية. ثالث طر 

تائج نتم استخدامها لحساب زمن موجة القص الصوتية في هذا البحث, بينما الرابعة تم تطويرها. للمقارنة مع 
ن ساب زمالمعادالت التجريبية المستخدمة تم استخدام نتائج دراسة استخدمت فيها الشبكة العصبية االصناعية لح

ل الصوتية. نفس البيانات المستخدمة في دراسة الشبكة االصطناعية تم اعتمادها هنا حيث تشتمموجة القص 
نقطة مقاسة من عمليات الجس لزمن موجة القص الصوتية مع قياسات تسعة  1922هذه البيانات على 

ترون مجسات تشمل مجس اشعة كاما ومجس زمن الموجة الصوتية االنضغاطية ومجس قطر البئر ومجس النيو 
العمق ومجس الكثافة ومجس المقاومية العميقة باالضافة لقراءات زاوية ميل البئر وزاوية الميل عن الشمال و 

الشاقولي لبئر اتجاهي عراقي. المعادالت التجريبية الثالث الموجودة تستند في حساب زمن موجة القص 
ها معادلة التجريبية الرابعة تم تطوير الصوتية على نقاط قياسات ازمان الموجات الصوتية االنضغاطية. ال

باستخدام كل النقاط المقاسة الزمان موجات القص واالنضغاط الصوتيتان. المقارنة بين الطرق وضحت ان 
واقل عوامل  0,966طريقة الشبكة العصبية االصطناعية كانت االفضل بأعلى معامل ترابط مساوي ل 

ل ن كارو مة االربع حيث ان معامل ترابط المعادالت التجريبية  لكل احصائية اخرى بالمقارنة مع الطرق التجريبي
على التوالي  0,8016و 0,6764و  0,7636و  0,7826وفريوند وبرونشر والمعادلة المطورة الرابعة كان 

 باالضافة الى بقية المعامالت االحصائية التي اثبتت ان المعادلة التجريبية المطورة افضل من الثالث
جة . استخدام طريقة الشبكة االصطناعية او المعادلة التجريبية المطورة مستقبال لحساب زمن مو الموجودات

  .القص الصوتية متعلق بصانعي القرار نسبة لعدد من المحددات ودقة نتائج موجة القص الصوتية المستهدفة
 

بئر ة ميل الالقص الصوتية, انحراف حفرة البئر, زاويالكلمات الدالة: المعادالت التجريبية, الشبكة العصبية االصطناعية, موجة 
 وزاية االنحراف عن الشمال.