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New approach to obtain the rheological properties of drill-in fluid on a real-time using artificial intelligence
Journal Pre-proof New approach to obtain the rheological properties of drill-in fluid on a real-time using artificial intelligence Salaheldin Elkatatny, Ibrahim Gomaa, Tamer Moussa PII:
S2405-6561(18)30215-3
DOI:
https://doi.org/10.1016/j.petlm.2019.11.004
Reference:
PETLM 287
To appear in:
Petroleum
Received Date: 8 December 2018 Revised Date:
3 August 2019
Accepted Date: 15 November 2019
Please cite this article as: S. Elkatatny, I. Gomaa, T. Moussa, New approach to obtain the rheological properties of drill-in fluid on a real-time using artificial intelligence, Petroleum (2019), doi: https:// doi.org/10.1016/j.petlm.2019.11.004. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [COPYRIGHT YEAR] Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. All rights reserved.
New Approach to Obtain the Rheological Properties of Drill-in Fluid on A Real-Time Using Artificial Intelligence
Salaheldin Elkatatny* Associate Professor Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected] *Corresponding Author E-mail: [email protected]
Ibrahim Gomaa Master Student Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected] Tamer Moussa PhD Student Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected]
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New Approach to Obtain the Rheological Properties of Drill-in Fluid on A Real-Time Using Artificial Intelligence Salaheldin Elkatatny, Ibrahim Gomaa, and Tamer Moussa. King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.
Abstract Optimizing the drilling operation is highly controlled by the rheological properties of the drilling fluid. Rheological properties such as yield point (YP), plastic viscosity (PV), flow behavior index (n) and consistency index (k) are very vital inputs in managing rig hydraulics, margins of surge and swab pressure, equivalent circulation density (ECD) and hole cleaning. Measuring drilling fluid rheological properties in the laboratory is a time consuming job and depending on specific equipment such as mud balance and Fan rheometer. The main goal of this study is to build novel empirical models that are capable of predicting the above mentioned rheological properties of NaCl water-based drill-in fluid in a real-time. These models were built based on mud weight, Marsh funnel viscosity, and solid volume percent. About 1000 data points where were recorded in the field were used to feed an artificial neural network (ANN) in order to develop these novel empirical models. The developed models using the ANN technique showed a high accuracy for predicting the different drilling fluid rheological properties. Five empirical correlations were developed each one is for predicting single rheological property. The obtained results showed that the average absolute percentage error (AAPE) was less than 6.5% with a coefficient of determination (R2) higher than 90%. Keywords: Drill-in fluid properties, mud rheological properties, NaCl–polymer mud, artificial intelligence, artificial neural network. 1 Introduction The drilling fluids play a very vital role in the drilling process. The density of the drilling fluids is exploited for controlling the formation pressure [1-2]. Keeping the drilling cuttings suspended and carrying them out of the hole to the surface are two main other functions of the drilling fluid which are accomplished through proper viscosity and yield point [3-4]. In addition, the drilling fluids are used to lubricate and cool the drilling bit and the drill string and form a proper thin impermeable filter cake to assure hole stability [5-7]. The drilling fluids is categorized according to their base fluid into water, oil and gas based drilling fluids [8]. NaCl water-based drill-in fluid is mainly used while drilling the reservoir section. The NaCl salt is used as a weighting material for increasing mud density while the Na+ ions work as shale stabilizers [9]. NaCl polymer mud is characterized as an inhibited, nondispersed drilling fluid in which the viscosity control and the filtration properties are enhanced by using some types of polymers such as xanthan gum and starch. This helps in reducing the possibility of formation damage [10].
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Measuring the rheological parameters in the lab is a very time-consuming job. Mud density and Marsh funnel viscosity are frequently measured every 15 to 20 minutes on the rig site while the complete mud test is only carried out two times per day (morning and night). The idea of the Marsh funnel was firstly introduced by Marsh [11]. The Marsh funnel viscosity can be used as an indication for many mud rheological properties with high accuracy such as fluid yield stress [12]. The rheology control additives, as well as the fine tiny particles of the drilled formations together, form the different drilling fluid properties. Measuring these parameters is very critical as they play a vital role in controlling the drilling process [13]. The ratio between the mud yield stress over the yield point () is a central parameter in characterizing the mud rheology. Parameters such as PV, YP and τy are crucial parameters that define and characterize the drilling fluid [14]. Power and Zamora [13] stated the accepted ratio of τy/YP for water-based drilling fluid is to be within the range of 0.2–0.4. Hussaini and Azar [15] concluded that if the drilling fluid annular velocity is less than 120 ft/min, the cutting transportation process will be highly influenced by the mud rheological properties. The k is the main controlling parameter of the carrying capacity index (CCI) [16]. Zhang et al. [17] stated that not only the mud rheological properties that highly affect the rig hydraulic calculations but there are also other critical factors such as solid content and hole diameter. They also illustrated that the effect of solid percent on the pressure profile at low flow rates is remarkable, unlike the high flow rate conditions. The hole geometry, in its turn, affects the hydraulic performance and the efficiency of hole cleaning. Unlike circular holes, noncircular holes may lower pressure gradient and hence they may have better hole cleaning conditions [18]. Adams [19] stated that the increase in the value of plastic viscosity is just a reflection to the increase in the mud solid content. The increase in the value of the plastic viscosity can highly affect the drilling operations as it will lead to increase the equivalent circulating density (ECD), surge and swab pressure and the potential of stuck pipe (differential sticking). Moreover, the rate of penetration will be decreased by the increase in the plastic viscosity [20-21]. Yield point of the drilling fluid is formed by the antiparticle attraction of the contained solids. Chemicals such as thinners, dispersants, and viscosifiers can be used to control the drilling fluid yield point [19]. Lower yield point is preferred for the case of turbulent flow regime for more efficient lifting force while for laminar flow regime, higher yield point is more convenient to remove the cutting [22]. To increase the hole cleaning efficiency during laminar flow regimes, the ratio of YP/PV should be increased [23]. Throughout the literature, there are two correlations that rely the drilling fluid apparent viscosity to specific mud properties such as mud weight and Marsh funnel time. The first one is for Pitt [24] using Eq. (1), in which a constant of 25 is used. The second one is for Almahdawi et al. [25] which is represented by Eq. (2) where a constant of 28 was found to be more convenient than the one that Pitt [24] used. = ( − 25)
(1)
= ( − 28) (2) 3
Where; AV represents the value of mud apparent viscosity in cP, is mud weight is g/cc and t is Marsh funnel viscosity in sec/quart. The goal of this research is to develop novel empirical models that capable of acquiring the rheological properties of NaCl polymer mud using artificial neural networks (ANN) using 1000 field measurements of mud density, Marsh funnel viscosity and solid volume percent. Additional to taking the solid percent into consideration for the first time in literature while developing these models, the novelty of this research is getting a real-time prediction (every 10 to 15 minutes) of the mud rheological properties.
1.1 Applications of Artificial Intelligence in Petroleum Engineering McCarthy [26] defined artificial intelligence (AI) as the technique of designing computer programs that enable the machines to act intelligently the same way as a human being. Since the oil filed is one of the largest fields that contain huge amount of data, AI found it as a fertile environment for various applications. Adaptive neuro fuzzy inference system (ANFIS), artificial neural networks (ANN) and support vector machines (SVM) were used as AI tools to determine some reservoir properties like porosity and permeability from well logs with high accuracy compared with the conventional used methods [27-30]. ANFIS and ANN are also used to predict some reservoir fluid properties such as the bubble point pressure (BPP) [31]. The authors concluded that (ANFIS) models could accurately predict the bubble point pressure in a way better than all the ANN models as well as the most common published empirical correlations. In the area of drilling fluid density, the least square support vector machine (LSSVM) was used to predict the actual mud weight at wellbore conditions [32]. The same technique (LSSVM) was used to determine the solubility of carbon dioxide (CO2) in brine solutions with an AAPE less than 0.1% [33]. Feed-forward artificial neural network (ANN) was optimized using an imperialist competitive algorithm (ICA) to predict asphaltene precipitation with high accuracy compared to the previously used models [34]. The same author used another optimization technique called unified particle swarm optimization (UPSO) with backpropagation artificial neural networks for asphaltene precipitation prediction [35]. Elkatatny and Mahmoud [36] used the ANN (white box) for the first time to predict the oil formation volume factor. They could extract the weights and the biases of the empirical correlation. Their model showed a tremendous accuracy with R2 of 0.997 and AAPE of less than 1% between the actual measurements and the model predicted ones. The self-adaptive differential evolution technique (SaDE) was used to optimize the structure of the artificial neural networks in order to predict the rate of penetration (ROP) as a function of some rig surface parameters [37]. This technique could produce a robust ANN model with high prediction accuracy and low deviation from the actual measured values. Since the issue of determining the mud rheological properties has great importance in the drilling field. The ANN technique is used to intensively predict the mud rheological properties for different types of drilling fluids such as KCl water-based drilling fluid and invert emulsion drilling fluid [38-39].
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1.2
Artificial Neural Network
Fausett [40] illustrated that ANN is capable of approximating any non-linear complex function between inputs and output parameters. The ANN structure consists of three main sections, the learning/training functions, the transfer functions and then network simulation. The network layers are connected together with the aid of weights. Optimizing these weights affects the performance of the network so greatly. The process of building the ANN starts by training the network. The goal of the training can be defined as the minimum accepted or desired error for the results of the model. Therefore the ANN continue to be trained until this goal is reached [41]. Each training iteration is called epoch. At the end of each epoch, the error is checked and compared with the stated goal. If the error is accepted, the ANN will terminate. If not, the predicted data will be sent back to the network again trying to reoptimize the weights and biases for each layer. In order to reach acceptable results, the number of hidden layers and the number neurons as well have to be optimized. Under-fitting between the actual and predicted data can be due to having fewer number of neurons than required. On the other hand, an excessive number of neurons can cause over-fitting [42-43]. Among the other available AI techniques, ANN was chosen for going through this research work as it is very convenient to extract the final empirical model that represents the solution to the suggested problem from the ANN with high accuracy. Another advantage of the developed empirical correlations is the ability to use it without any special software requirements. This greatly eases its implementation with the drilling rig system. 2 Field Data Description A sample of all the available data (1000 points) of the investigated mud is listed in Table 1. Mud weight (PCF), Marsh funnel viscosity (sec/quart), solid content (vol.%), plastic viscosity (cP) and yield point (lb.f/100 ft2) values are measured at the rig site using standard drilling fluid tests and equipment such as mud balance, Marsh funnel, retort and Fan VG rheometer. Both mud weight and Marsh funnel viscosity are measured under atmospheric pressure and temperature using mud balance and Marsh funnel respectively. The used rheometer for measuring plastic viscosity and yield point was operated under a temperature of 120oF and ambient pressure [4445]. Finally, the mud liquid phase was evaporated in a retort and the remaining solids were collected in order to measure the solid content of the drilling fluid. By investigating the available data, it was found that a wide range of mud properties is covered within these data values; e.g. the mud density data covers the range of 63 to 150 pcf, the Marsh funnel time data ranges between 38 to 102 sec/ quart, the mud solid content ranges between 0 to 50 vol.%, plastic viscosity data varies between 8 to 70 cP and finally, the yield point data covers the range between 19 to 80 lb/100 ft2.
3 Development of Empirical Models Using ANN In order to develop a robust model, data variation is eliminated by normalizing all the data values between -1 and 1 using Eqs. 3 and 4:
5
=
=
(3)
(2) − 1
(4)
Where; Y is the final normalized value of the input parameter, Ymax= 1 (the upper normalized limit), Ymin= -1 (the lower normalized limit), Xmax and Xmin are the maximum and minimum values in the input vector respectively, and X is any value of the input vector that needs to be normalized An example from marsh funnel data; where the minimum value (Xmin) equals 38 sec/quart, the maximum value (Xmax) equals 102 sec/quart, a value of 50 sec/quart would be normalized according to Eq (4) to be -0.625. According to the fluid behavior models for Bingham [46] and Metzner [47], NaCl polymer drilling fluid behavior can be characterized as plastic or pseudo-plastic fluid. Using the data available in Table 1, viscometer reading at 300 rpm (R300) and at 600 rpm (R600) can be calculated using Eqs. 5 and 6 [48]. Hence, flow index (n) can be calculated using the values of R300 and R600 throughout Eq. (7). = + (5)
= + (6)
! = 3.32 ∗ log ( ) (7) To ensure that the model is trained and tested properly, the data was divided as 70% for model training and the rest 30% for testing the model.
4 Results and Discussion The results of the ANN model built for predicting R300 were compared to the actual calculated R300 values and the final relationship is shown in Figure 1. The ANN for predicting R300 shows high accurate results with an AAPE of 3.46% and a correlation coefficient (R) between the actual predicted values of R300 is as high as 0.99, Figure 1. The final form of the empirical model is described by Eq. 8 after extracting the weights and biases from the ANN model and converting it to a white box. The Z value in Eq. 8 represents the normalized value of R300. Eq. 9 can be used to get the de-normalized value of R300.
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/
+ = ,∑E FG1 w/ 0
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
D H + I2
= 57.5458 + + 87.45305
(8)
(9)
Where; N is the optimized number of neurons used to acquire the highest correlation coefficient between the predicted and actual values of R300; ρM ,NM and OM are the input parameters which in this case represents the normalized form of mud weight, Marsh funnel viscosity and solid volume percent respectively. P1 and I1 are is the optimized weight and bias of the network hidden layer respectively; P/ and I/ are the optimized weight and bias of the network output layer respectively. Table 2 lists the values of all the input parameters for Eq. 8. After so many iterations, the number of the network neurons was determined to be 20 neurons for the optimum results. This number of neurons gives us the highest network efficiency represented by the lowest AAPE and the highest R2 between the predicted and actual values of R300. For R600 prediction, the ANN was used with the same procedures as R300. Figure 2 represents the results of R600 prediction model with AAPE of 3.43% and R of 0.99 between the actual and predicted R600 values. The final empirical correlation is represented by Eq. 10 where Z represents the normalized value of R600. Table 3 lists the required inputs (weights and biases) for Eq. (10). To get the de-normalized value of R600, Eq. 11 could be used.
+ = ,∑E FG1 w/ 0
/
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
D H + I2 (10)
= 85.8445 Q + + 124.6091 (11) The optimum number of neurons, in this case, was also found to be 20 neurons after changing it from 8 to 40 neurons within more than 5000 iterations to get the most suitable number of neurons. The mud flow behavior index (n) was predicted using the same technique and procedures. The model results are shown in Figure 3 with AAPE of 3.25% and R of 0.96 between the predicted (n) values and the other calculated from Eq. 7. The final developed empirical correlation for predicting the normalized (n) values can be represented by Eq. 12 where Eq. 13 can be used to retain the de-normalized values of the predicted (n). Table 4 list the values of all the input parameters for Eq. 12. + = ,∑E FG1 w/ 0
/
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
7
D H + I2 (12)
! = 0.215801 Q + + 0.555492 (13) 4.1 Model Validation In order to validate the developed models, the predicted values of R300 and R600 were used to calculate the plastic viscosity. By comparing the actual plastic viscosity values that were measured in the field with the calculated ones, the AAPE was only 6% and the R between the two values (predicted and actual) of plastic viscosity was 0.98 as shown in Figure 4. For additional verification of the developed models, the values of predicted R600 and (n) were used to calculate the flow consistency index (k) according to Eq. 14. S =
(14) 1022M
The values of the actual k that come from the actual measured values of R600 and n, were compared to the calculated values of k. The results are represented in Figure 5 which shows an AAPE of 6.5% and a coefficient of determination (R2) 0f 0.92 between the two types of k values. 4.2 Apparent Viscosity (AV) from Marsh Funnel In order to predict the apparent viscosity (AV), the ANN model was developed following the same sequence mentioned above. The model input parameters are normalized mud weight, Marsh funnel viscosity and solid percent. The final empirical correlation for predicting AV can be represented by Eq. 15 where Z represents the normalized value of AV and the de-normalized value could be obtained from Eq. 16. The input parameters for Eq. 15 are listed in Table 5. The comparison between the actual AV values and predicated AV values can be shown in Figure 6. The AAPE, in this case, was 3.96% and R is 0.99. Z = ,∑E FG1 w/9 0
/
45 678 ;< = 78 U< = 78 @A< = B8 C 9,8 9,5 9,? 9 123
AV = 41.82171 Z + 61.3295
D H + b2
(16)
(17)
Apparent viscosity values are also calculated from Eqs. 1 and 2 mentioned in the literature. A comparison between the actual AV values and the resulted values from Pitt’s correlation is shown in Figure 7a. The results of Pitt’s correlation seem to overestimate the values of apparent viscosity. It gives an AAPE of 22.14% between the actual and the resulted AV from Pitt’s correlation with R2 of 0.81. The results for AV from Almahdawi et al. [25] were not better than the case of Pitt [24]. An AAPE of 32.89% and R2 of 0.79 were found when comparing the values of AV resulted from Almahdawi et al. [25] and the actual values, Figure 7b.
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5 Conclusions ANN technique was used to generate empirical correlations that are capable of predicting the rheological parameters of NaCl water-based drill-in fluid at real-time. The model inputs are about 1000 real field measured points of mud weight, Marsh funnel viscosity and solid volume percent. According to the above-reached results of this research, it can be concluded that: 1. It is the first time in literature to get a correlation that takes into consideration the effect of mud solid content on the rheological properties. 2. The developed model showed a high proficiency (maximum AAPE of 6%) in predicting the rheological properties such as PV, YP, AV, n, and k using the frequently measured mud weight, Marsh funnel time and solid volume percent. 3. The target of the developed model is not only predicting the mud rheological parameters but it is extended also to obtain a good estimation at real time for the equivalent circulating density (ECD), surge and swab pressures and the rig hydraulics. 4. Since this developed models are not expensive and do not require any additional requirement, they will be so practical and helpful for the drilling engineers to use it in the rig site.
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Table 1 : Sample of field data for NaCl polymer drill-in fluid (total of 1000 data points). Mud Density, lb/ft3
Funnel Viscosity, sec/quart
Solid, Vol. %
Plastic Viscosity, cP
Yield Point, lb/100 ft3
65 76 84 90 100 110 120 145 150
64 57 63 58 55 90 63 62 60
7 8 17 17 21.2 27 32 45 47
18 21 22 28 30 65 36 45 47
28 26 31 30 26 34 34 35 33
Table 2: Coefficients for R300, Eq. 8. Input Layer Weight Matrix W1 1 2 3 2.329401 -0.20559 -2.02339 1.939035 -0.89537 1.365356 6.405794 -3.77452 3.01353 -1.89163 2.998197 5.172153 -0.08256 6.915863 6.314727 -0.59716 -1.41493 4.613179 -0.14479 2.883756 1.979611 3.091832 -3.317 2.956403 4.938758 -8.9659 -5.04023 2.944139 -3.88358 -4.86364 -6.78909 4.554291 -7.93613 0.187648 0.945442 8.234722 1.697892 -0.29176 0.201629 -1.21157 0.182793 -2.40954 3.310136 -0.70595 2.589708 1.332157 1.511376 -3.70532 2.525913 -4.46807 -7.51114 -2.24865 1.625613 1.236202 -3.66301 -8.12741 1.821321 -6.64751 0.766355 3.764778
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -1.0023 0.665636 0.584761 -0.071 -0.27087 -0.49484 1.0367 -0.12786 0.028309 0.394874 0.515869 0.156485 -1.26147 -1.18327 0.38392 -0.25591 -0.57072 -1.26235 -0.04626 -0.22905
W2 -5.85313 -4.61699 -1.0516 4.060767 -2.67528 2.777596 -1.29776 0.926438 -0.61439 2.07307 1.069578 0.56074 1.366898 -3.16818 2.239643 -1.51951 7.606894 -2.97239 -4.92217 -2.22912
b2 -1.37924
13
Table 3: Coefficients for R600, Eq. 10. Input Layer Weight Matrix W1 1 2 3 -2.1438 -0.29581 -2.4211 -0.59851 -3.34112 -0.17731 6.8501 -7.32713 -0.0448 9.350106 5.89277 -5.16944 -1.25375 7.54361 0.293227 -18.5239 0.308849 14.68826 2.251219 -2.56763 2.745431 -0.10828 0.103068 0.068019 4.755943 10.18177 -3.86769 0.786798 -4.36412 3.801038 -3.14623 -0.54116 -7.67946 2.262903 -2.08138 2.731204 1.405411 -6.13887 0.605887 -2.61311 3.291111 10.13724 -7.95483 -5.0229 4.246021 1.431282 -1.18933 -5.47035 6.727577 -3.4548 -11.8862 6.285891 -6.61224 0.006235 -5.92251 -1.33424 -1.97902 -2.54554 -1.8153 -1.02812
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -0.61389 -0.86573 -1.3343 1.042025 0.158678 -0.09062 2.794765 -4.09203 0.150763 -0.19361 -0.18058 -3.2484 -0.24588 0.248251 1.278928 -0.36435 -0.06912 1.493386 -0.46022 1.431026
W2 -0.88428 -3.23087 2.181468 2.918715 2.410482 -4.35866 -0.31512 -0.10195 -1.59377 5.347313 0.861766 -0.1457 0.676063 -6.25524 -2.50971 -4.26172 -3.18344 2.077372 -7.70114 -4.33713
b2 -0.55768
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -1.1943 0.87218 -2.07318 -0.7947 0.33606 -0.0782 0.583915 -0.34356 0.995133 -3.20732 2.556532 0.402774 1.752369 0.275773 -0.52309 0.909558 -0.36975 -0.79858 2.357199 -2.18726
W2 -2.71536 -2.97817 3.946909 2.227292 2.727167 2.107876 -2.65083 -0.40327 -2.75718 -0.83957 1.115953 -0.78657 -1.5776 2.055301 -4.04643 3.768141 2.911888 -1.83443 4.767891 4.14005
b2 -0.37036
Table 4: Coefficients for n, Eq. 12. Input Layer Weight Matrix W1 1 2 3 2.936113 1.924889 1.011028 3.686852 -1.27555 2.562502 -0.1046 0.500972 -4.13625 0.81217 -2.43693 -4.30573 -3.32135 -0.35365 -0.99193 -0.55599 3.981899 0.144122 -1.62507 -4.53162 -1.23763 5.642359 -2.01562 0.677415 2.02772 -0.08493 -5.42186 0.153548 -0.86912 -2.58223 0.611784 0.576017 -2.5903 0.862635 -2.96844 4.325228 -0.11376 -1.33785 -3.76812 7.392567 1.133884 -6.3525 -1.81848 -5.13044 -3.00254 3.139578 -2.01959 1.37071 2.248196 2.139663 -1.22494 0.018853 3.283599 -0.34606 0.257376 -0.2036 5.317304 2.225812 -1.06831 2.90198
14
Table 5: Coefficients for apparent viscosity, Eq. 16. Input Layer Weight Matrix W1 1 2 3 -1.58853 -8.18093 3.448302 1.049703 -1.91443 0.451884 0.906379 -0.67676 11.5662 4.236579 -2.17674 2.98752 13.94177 -3.53596 0.725284 -3.36605 0.208504 2.659836 2.331358 2.863177 -0.56077 -2.98745 0.32097 1.441864 -5.10113 0.230718 -2.25216 9.283254 14.68367 -0.66788 1.539603 -4.59674 1.525181 -0.75444 -9.76895 -1.67204 -0.79983 5.921717 -2.1431 7.225208 1.825331 -0.8595 3.524655 -2.04897 0.463265 16.438 -0.24212 -12.5915 -1.11719 1.9865 2.928407 5.872482 -3.44871 1.69972 -4.19689 3.047375 1.720885 -3.9058 2.134791 -2.4342
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -0.09329 -1.29317 0.0512 -2.56621 -0.18602 0.428688 0.221267 0.141673 0.186127 0.08475 -0.35108 -0.08458 -0.2328 0.169146 0.35017 0.117314 0.650627 0.125011 -0.2191 -2.78524
W2 -6.59117 -6.30391 9.835752 -0.53904 -5.17323 -0.25328 2.372333 7.16042 -4.82815 -0.36577 0.115195 0.840183 0.450564 0.966257 1.75035 4.248086 -2.37178 -5.14241 -3.25757 0.625767
b2 -1.47169
15
Fig. 1: Estimated values of R300 using ANN model vs. the actual one.
16
Fig. 2: Estimated values of R600 using ANN model vs. the actual one.
17
Fig. 3: Estimated values of flow behavior index using ANN model vs. the actual one.
18
Fig. 4: Calculated values of plastic viscosity vs. actual values.
Fig. 5: Calculated values of flow consistency index vs. actual values.
19
Fig. 6: Predict values of apparent viscosity using ANN technique vs. actual values.
Fig. 7: Prediction of apparent viscosity using Pitt [24] and Almahdawi et al. [25] correlations.
20
Conflict of Interest The authors have no conflicts of interest to declare
S2405-6561(18)30215-3
DOI:
https://doi.org/10.1016/j.petlm.2019.11.004
Reference:
PETLM 287
To appear in:
Petroleum
Received Date: 8 December 2018 Revised Date:
3 August 2019
Accepted Date: 15 November 2019
Please cite this article as: S. Elkatatny, I. Gomaa, T. Moussa, New approach to obtain the rheological properties of drill-in fluid on a real-time using artificial intelligence, Petroleum (2019), doi: https:// doi.org/10.1016/j.petlm.2019.11.004. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © [COPYRIGHT YEAR] Southwest Petroleum University. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd. All rights reserved.
New Approach to Obtain the Rheological Properties of Drill-in Fluid on A Real-Time Using Artificial Intelligence
Salaheldin Elkatatny* Associate Professor Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected] *Corresponding Author E-mail: [email protected]
Ibrahim Gomaa Master Student Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected] Tamer Moussa PhD Student Department of Petroleum Engineering, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; E-mail: [email protected]
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New Approach to Obtain the Rheological Properties of Drill-in Fluid on A Real-Time Using Artificial Intelligence Salaheldin Elkatatny, Ibrahim Gomaa, and Tamer Moussa. King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.
Abstract Optimizing the drilling operation is highly controlled by the rheological properties of the drilling fluid. Rheological properties such as yield point (YP), plastic viscosity (PV), flow behavior index (n) and consistency index (k) are very vital inputs in managing rig hydraulics, margins of surge and swab pressure, equivalent circulation density (ECD) and hole cleaning. Measuring drilling fluid rheological properties in the laboratory is a time consuming job and depending on specific equipment such as mud balance and Fan rheometer. The main goal of this study is to build novel empirical models that are capable of predicting the above mentioned rheological properties of NaCl water-based drill-in fluid in a real-time. These models were built based on mud weight, Marsh funnel viscosity, and solid volume percent. About 1000 data points where were recorded in the field were used to feed an artificial neural network (ANN) in order to develop these novel empirical models. The developed models using the ANN technique showed a high accuracy for predicting the different drilling fluid rheological properties. Five empirical correlations were developed each one is for predicting single rheological property. The obtained results showed that the average absolute percentage error (AAPE) was less than 6.5% with a coefficient of determination (R2) higher than 90%. Keywords: Drill-in fluid properties, mud rheological properties, NaCl–polymer mud, artificial intelligence, artificial neural network. 1 Introduction The drilling fluids play a very vital role in the drilling process. The density of the drilling fluids is exploited for controlling the formation pressure [1-2]. Keeping the drilling cuttings suspended and carrying them out of the hole to the surface are two main other functions of the drilling fluid which are accomplished through proper viscosity and yield point [3-4]. In addition, the drilling fluids are used to lubricate and cool the drilling bit and the drill string and form a proper thin impermeable filter cake to assure hole stability [5-7]. The drilling fluids is categorized according to their base fluid into water, oil and gas based drilling fluids [8]. NaCl water-based drill-in fluid is mainly used while drilling the reservoir section. The NaCl salt is used as a weighting material for increasing mud density while the Na+ ions work as shale stabilizers [9]. NaCl polymer mud is characterized as an inhibited, nondispersed drilling fluid in which the viscosity control and the filtration properties are enhanced by using some types of polymers such as xanthan gum and starch. This helps in reducing the possibility of formation damage [10].
2
Measuring the rheological parameters in the lab is a very time-consuming job. Mud density and Marsh funnel viscosity are frequently measured every 15 to 20 minutes on the rig site while the complete mud test is only carried out two times per day (morning and night). The idea of the Marsh funnel was firstly introduced by Marsh [11]. The Marsh funnel viscosity can be used as an indication for many mud rheological properties with high accuracy such as fluid yield stress [12]. The rheology control additives, as well as the fine tiny particles of the drilled formations together, form the different drilling fluid properties. Measuring these parameters is very critical as they play a vital role in controlling the drilling process [13]. The ratio between the mud yield stress over the yield point () is a central parameter in characterizing the mud rheology. Parameters such as PV, YP and τy are crucial parameters that define and characterize the drilling fluid [14]. Power and Zamora [13] stated the accepted ratio of τy/YP for water-based drilling fluid is to be within the range of 0.2–0.4. Hussaini and Azar [15] concluded that if the drilling fluid annular velocity is less than 120 ft/min, the cutting transportation process will be highly influenced by the mud rheological properties. The k is the main controlling parameter of the carrying capacity index (CCI) [16]. Zhang et al. [17] stated that not only the mud rheological properties that highly affect the rig hydraulic calculations but there are also other critical factors such as solid content and hole diameter. They also illustrated that the effect of solid percent on the pressure profile at low flow rates is remarkable, unlike the high flow rate conditions. The hole geometry, in its turn, affects the hydraulic performance and the efficiency of hole cleaning. Unlike circular holes, noncircular holes may lower pressure gradient and hence they may have better hole cleaning conditions [18]. Adams [19] stated that the increase in the value of plastic viscosity is just a reflection to the increase in the mud solid content. The increase in the value of the plastic viscosity can highly affect the drilling operations as it will lead to increase the equivalent circulating density (ECD), surge and swab pressure and the potential of stuck pipe (differential sticking). Moreover, the rate of penetration will be decreased by the increase in the plastic viscosity [20-21]. Yield point of the drilling fluid is formed by the antiparticle attraction of the contained solids. Chemicals such as thinners, dispersants, and viscosifiers can be used to control the drilling fluid yield point [19]. Lower yield point is preferred for the case of turbulent flow regime for more efficient lifting force while for laminar flow regime, higher yield point is more convenient to remove the cutting [22]. To increase the hole cleaning efficiency during laminar flow regimes, the ratio of YP/PV should be increased [23]. Throughout the literature, there are two correlations that rely the drilling fluid apparent viscosity to specific mud properties such as mud weight and Marsh funnel time. The first one is for Pitt [24] using Eq. (1), in which a constant of 25 is used. The second one is for Almahdawi et al. [25] which is represented by Eq. (2) where a constant of 28 was found to be more convenient than the one that Pitt [24] used. = ( − 25)
(1)
= ( − 28) (2) 3
Where; AV represents the value of mud apparent viscosity in cP, is mud weight is g/cc and t is Marsh funnel viscosity in sec/quart. The goal of this research is to develop novel empirical models that capable of acquiring the rheological properties of NaCl polymer mud using artificial neural networks (ANN) using 1000 field measurements of mud density, Marsh funnel viscosity and solid volume percent. Additional to taking the solid percent into consideration for the first time in literature while developing these models, the novelty of this research is getting a real-time prediction (every 10 to 15 minutes) of the mud rheological properties.
1.1 Applications of Artificial Intelligence in Petroleum Engineering McCarthy [26] defined artificial intelligence (AI) as the technique of designing computer programs that enable the machines to act intelligently the same way as a human being. Since the oil filed is one of the largest fields that contain huge amount of data, AI found it as a fertile environment for various applications. Adaptive neuro fuzzy inference system (ANFIS), artificial neural networks (ANN) and support vector machines (SVM) were used as AI tools to determine some reservoir properties like porosity and permeability from well logs with high accuracy compared with the conventional used methods [27-30]. ANFIS and ANN are also used to predict some reservoir fluid properties such as the bubble point pressure (BPP) [31]. The authors concluded that (ANFIS) models could accurately predict the bubble point pressure in a way better than all the ANN models as well as the most common published empirical correlations. In the area of drilling fluid density, the least square support vector machine (LSSVM) was used to predict the actual mud weight at wellbore conditions [32]. The same technique (LSSVM) was used to determine the solubility of carbon dioxide (CO2) in brine solutions with an AAPE less than 0.1% [33]. Feed-forward artificial neural network (ANN) was optimized using an imperialist competitive algorithm (ICA) to predict asphaltene precipitation with high accuracy compared to the previously used models [34]. The same author used another optimization technique called unified particle swarm optimization (UPSO) with backpropagation artificial neural networks for asphaltene precipitation prediction [35]. Elkatatny and Mahmoud [36] used the ANN (white box) for the first time to predict the oil formation volume factor. They could extract the weights and the biases of the empirical correlation. Their model showed a tremendous accuracy with R2 of 0.997 and AAPE of less than 1% between the actual measurements and the model predicted ones. The self-adaptive differential evolution technique (SaDE) was used to optimize the structure of the artificial neural networks in order to predict the rate of penetration (ROP) as a function of some rig surface parameters [37]. This technique could produce a robust ANN model with high prediction accuracy and low deviation from the actual measured values. Since the issue of determining the mud rheological properties has great importance in the drilling field. The ANN technique is used to intensively predict the mud rheological properties for different types of drilling fluids such as KCl water-based drilling fluid and invert emulsion drilling fluid [38-39].
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1.2
Artificial Neural Network
Fausett [40] illustrated that ANN is capable of approximating any non-linear complex function between inputs and output parameters. The ANN structure consists of three main sections, the learning/training functions, the transfer functions and then network simulation. The network layers are connected together with the aid of weights. Optimizing these weights affects the performance of the network so greatly. The process of building the ANN starts by training the network. The goal of the training can be defined as the minimum accepted or desired error for the results of the model. Therefore the ANN continue to be trained until this goal is reached [41]. Each training iteration is called epoch. At the end of each epoch, the error is checked and compared with the stated goal. If the error is accepted, the ANN will terminate. If not, the predicted data will be sent back to the network again trying to reoptimize the weights and biases for each layer. In order to reach acceptable results, the number of hidden layers and the number neurons as well have to be optimized. Under-fitting between the actual and predicted data can be due to having fewer number of neurons than required. On the other hand, an excessive number of neurons can cause over-fitting [42-43]. Among the other available AI techniques, ANN was chosen for going through this research work as it is very convenient to extract the final empirical model that represents the solution to the suggested problem from the ANN with high accuracy. Another advantage of the developed empirical correlations is the ability to use it without any special software requirements. This greatly eases its implementation with the drilling rig system. 2 Field Data Description A sample of all the available data (1000 points) of the investigated mud is listed in Table 1. Mud weight (PCF), Marsh funnel viscosity (sec/quart), solid content (vol.%), plastic viscosity (cP) and yield point (lb.f/100 ft2) values are measured at the rig site using standard drilling fluid tests and equipment such as mud balance, Marsh funnel, retort and Fan VG rheometer. Both mud weight and Marsh funnel viscosity are measured under atmospheric pressure and temperature using mud balance and Marsh funnel respectively. The used rheometer for measuring plastic viscosity and yield point was operated under a temperature of 120oF and ambient pressure [4445]. Finally, the mud liquid phase was evaporated in a retort and the remaining solids were collected in order to measure the solid content of the drilling fluid. By investigating the available data, it was found that a wide range of mud properties is covered within these data values; e.g. the mud density data covers the range of 63 to 150 pcf, the Marsh funnel time data ranges between 38 to 102 sec/ quart, the mud solid content ranges between 0 to 50 vol.%, plastic viscosity data varies between 8 to 70 cP and finally, the yield point data covers the range between 19 to 80 lb/100 ft2.
3 Development of Empirical Models Using ANN In order to develop a robust model, data variation is eliminated by normalizing all the data values between -1 and 1 using Eqs. 3 and 4:
5
=
=
(3)
(2) − 1
(4)
Where; Y is the final normalized value of the input parameter, Ymax= 1 (the upper normalized limit), Ymin= -1 (the lower normalized limit), Xmax and Xmin are the maximum and minimum values in the input vector respectively, and X is any value of the input vector that needs to be normalized An example from marsh funnel data; where the minimum value (Xmin) equals 38 sec/quart, the maximum value (Xmax) equals 102 sec/quart, a value of 50 sec/quart would be normalized according to Eq (4) to be -0.625. According to the fluid behavior models for Bingham [46] and Metzner [47], NaCl polymer drilling fluid behavior can be characterized as plastic or pseudo-plastic fluid. Using the data available in Table 1, viscometer reading at 300 rpm (R300) and at 600 rpm (R600) can be calculated using Eqs. 5 and 6 [48]. Hence, flow index (n) can be calculated using the values of R300 and R600 throughout Eq. (7). = + (5)
= + (6)
! = 3.32 ∗ log ( ) (7) To ensure that the model is trained and tested properly, the data was divided as 70% for model training and the rest 30% for testing the model.
4 Results and Discussion The results of the ANN model built for predicting R300 were compared to the actual calculated R300 values and the final relationship is shown in Figure 1. The ANN for predicting R300 shows high accurate results with an AAPE of 3.46% and a correlation coefficient (R) between the actual predicted values of R300 is as high as 0.99, Figure 1. The final form of the empirical model is described by Eq. 8 after extracting the weights and biases from the ANN model and converting it to a white box. The Z value in Eq. 8 represents the normalized value of R300. Eq. 9 can be used to get the de-normalized value of R300.
6
/
+ = ,∑E FG1 w/ 0
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
D H + I2
= 57.5458 + + 87.45305
(8)
(9)
Where; N is the optimized number of neurons used to acquire the highest correlation coefficient between the predicted and actual values of R300; ρM ,NM and OM are the input parameters which in this case represents the normalized form of mud weight, Marsh funnel viscosity and solid volume percent respectively. P1 and I1 are is the optimized weight and bias of the network hidden layer respectively; P/ and I/ are the optimized weight and bias of the network output layer respectively. Table 2 lists the values of all the input parameters for Eq. 8. After so many iterations, the number of the network neurons was determined to be 20 neurons for the optimum results. This number of neurons gives us the highest network efficiency represented by the lowest AAPE and the highest R2 between the predicted and actual values of R300. For R600 prediction, the ANN was used with the same procedures as R300. Figure 2 represents the results of R600 prediction model with AAPE of 3.43% and R of 0.99 between the actual and predicted R600 values. The final empirical correlation is represented by Eq. 10 where Z represents the normalized value of R600. Table 3 lists the required inputs (weights and biases) for Eq. (10). To get the de-normalized value of R600, Eq. 11 could be used.
+ = ,∑E FG1 w/ 0
/
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
D H + I2 (10)
= 85.8445 Q + + 124.6091 (11) The optimum number of neurons, in this case, was also found to be 20 neurons after changing it from 8 to 40 neurons within more than 5000 iterations to get the most suitable number of neurons. The mud flow behavior index (n) was predicted using the same technique and procedures. The model results are shown in Figure 3 with AAPE of 3.25% and R of 0.96 between the predicted (n) values and the other calculated from Eq. 7. The final developed empirical correlation for predicting the normalized (n) values can be represented by Eq. 12 where Eq. 13 can be used to retain the de-normalized values of the predicted (n). Table 4 list the values of all the input parameters for Eq. 12. + = ,∑E FG1 w/ 0
/
45 678 ;< = 78 >< = 78 @A< = B8 C 9,8 9,5 9,? 123
7
D H + I2 (12)
! = 0.215801 Q + + 0.555492 (13) 4.1 Model Validation In order to validate the developed models, the predicted values of R300 and R600 were used to calculate the plastic viscosity. By comparing the actual plastic viscosity values that were measured in the field with the calculated ones, the AAPE was only 6% and the R between the two values (predicted and actual) of plastic viscosity was 0.98 as shown in Figure 4. For additional verification of the developed models, the values of predicted R600 and (n) were used to calculate the flow consistency index (k) according to Eq. 14. S =
(14) 1022M
The values of the actual k that come from the actual measured values of R600 and n, were compared to the calculated values of k. The results are represented in Figure 5 which shows an AAPE of 6.5% and a coefficient of determination (R2) 0f 0.92 between the two types of k values. 4.2 Apparent Viscosity (AV) from Marsh Funnel In order to predict the apparent viscosity (AV), the ANN model was developed following the same sequence mentioned above. The model input parameters are normalized mud weight, Marsh funnel viscosity and solid percent. The final empirical correlation for predicting AV can be represented by Eq. 15 where Z represents the normalized value of AV and the de-normalized value could be obtained from Eq. 16. The input parameters for Eq. 15 are listed in Table 5. The comparison between the actual AV values and predicated AV values can be shown in Figure 6. The AAPE, in this case, was 3.96% and R is 0.99. Z = ,∑E FG1 w/9 0
/
45 678 ;< = 78 U< = 78 @A< = B8 C 9,8 9,5 9,? 9 123
AV = 41.82171 Z + 61.3295
D H + b2
(16)
(17)
Apparent viscosity values are also calculated from Eqs. 1 and 2 mentioned in the literature. A comparison between the actual AV values and the resulted values from Pitt’s correlation is shown in Figure 7a. The results of Pitt’s correlation seem to overestimate the values of apparent viscosity. It gives an AAPE of 22.14% between the actual and the resulted AV from Pitt’s correlation with R2 of 0.81. The results for AV from Almahdawi et al. [25] were not better than the case of Pitt [24]. An AAPE of 32.89% and R2 of 0.79 were found when comparing the values of AV resulted from Almahdawi et al. [25] and the actual values, Figure 7b.
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5 Conclusions ANN technique was used to generate empirical correlations that are capable of predicting the rheological parameters of NaCl water-based drill-in fluid at real-time. The model inputs are about 1000 real field measured points of mud weight, Marsh funnel viscosity and solid volume percent. According to the above-reached results of this research, it can be concluded that: 1. It is the first time in literature to get a correlation that takes into consideration the effect of mud solid content on the rheological properties. 2. The developed model showed a high proficiency (maximum AAPE of 6%) in predicting the rheological properties such as PV, YP, AV, n, and k using the frequently measured mud weight, Marsh funnel time and solid volume percent. 3. The target of the developed model is not only predicting the mud rheological parameters but it is extended also to obtain a good estimation at real time for the equivalent circulating density (ECD), surge and swab pressures and the rig hydraulics. 4. Since this developed models are not expensive and do not require any additional requirement, they will be so practical and helpful for the drilling engineers to use it in the rig site.
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17. 18.
19. 20. 21. 22. 23. 24. 25. 26.
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Table 1 : Sample of field data for NaCl polymer drill-in fluid (total of 1000 data points). Mud Density, lb/ft3
Funnel Viscosity, sec/quart
Solid, Vol. %
Plastic Viscosity, cP
Yield Point, lb/100 ft3
65 76 84 90 100 110 120 145 150
64 57 63 58 55 90 63 62 60
7 8 17 17 21.2 27 32 45 47
18 21 22 28 30 65 36 45 47
28 26 31 30 26 34 34 35 33
Table 2: Coefficients for R300, Eq. 8. Input Layer Weight Matrix W1 1 2 3 2.329401 -0.20559 -2.02339 1.939035 -0.89537 1.365356 6.405794 -3.77452 3.01353 -1.89163 2.998197 5.172153 -0.08256 6.915863 6.314727 -0.59716 -1.41493 4.613179 -0.14479 2.883756 1.979611 3.091832 -3.317 2.956403 4.938758 -8.9659 -5.04023 2.944139 -3.88358 -4.86364 -6.78909 4.554291 -7.93613 0.187648 0.945442 8.234722 1.697892 -0.29176 0.201629 -1.21157 0.182793 -2.40954 3.310136 -0.70595 2.589708 1.332157 1.511376 -3.70532 2.525913 -4.46807 -7.51114 -2.24865 1.625613 1.236202 -3.66301 -8.12741 1.821321 -6.64751 0.766355 3.764778
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -1.0023 0.665636 0.584761 -0.071 -0.27087 -0.49484 1.0367 -0.12786 0.028309 0.394874 0.515869 0.156485 -1.26147 -1.18327 0.38392 -0.25591 -0.57072 -1.26235 -0.04626 -0.22905
W2 -5.85313 -4.61699 -1.0516 4.060767 -2.67528 2.777596 -1.29776 0.926438 -0.61439 2.07307 1.069578 0.56074 1.366898 -3.16818 2.239643 -1.51951 7.606894 -2.97239 -4.92217 -2.22912
b2 -1.37924
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Table 3: Coefficients for R600, Eq. 10. Input Layer Weight Matrix W1 1 2 3 -2.1438 -0.29581 -2.4211 -0.59851 -3.34112 -0.17731 6.8501 -7.32713 -0.0448 9.350106 5.89277 -5.16944 -1.25375 7.54361 0.293227 -18.5239 0.308849 14.68826 2.251219 -2.56763 2.745431 -0.10828 0.103068 0.068019 4.755943 10.18177 -3.86769 0.786798 -4.36412 3.801038 -3.14623 -0.54116 -7.67946 2.262903 -2.08138 2.731204 1.405411 -6.13887 0.605887 -2.61311 3.291111 10.13724 -7.95483 -5.0229 4.246021 1.431282 -1.18933 -5.47035 6.727577 -3.4548 -11.8862 6.285891 -6.61224 0.006235 -5.92251 -1.33424 -1.97902 -2.54554 -1.8153 -1.02812
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -0.61389 -0.86573 -1.3343 1.042025 0.158678 -0.09062 2.794765 -4.09203 0.150763 -0.19361 -0.18058 -3.2484 -0.24588 0.248251 1.278928 -0.36435 -0.06912 1.493386 -0.46022 1.431026
W2 -0.88428 -3.23087 2.181468 2.918715 2.410482 -4.35866 -0.31512 -0.10195 -1.59377 5.347313 0.861766 -0.1457 0.676063 -6.25524 -2.50971 -4.26172 -3.18344 2.077372 -7.70114 -4.33713
b2 -0.55768
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -1.1943 0.87218 -2.07318 -0.7947 0.33606 -0.0782 0.583915 -0.34356 0.995133 -3.20732 2.556532 0.402774 1.752369 0.275773 -0.52309 0.909558 -0.36975 -0.79858 2.357199 -2.18726
W2 -2.71536 -2.97817 3.946909 2.227292 2.727167 2.107876 -2.65083 -0.40327 -2.75718 -0.83957 1.115953 -0.78657 -1.5776 2.055301 -4.04643 3.768141 2.911888 -1.83443 4.767891 4.14005
b2 -0.37036
Table 4: Coefficients for n, Eq. 12. Input Layer Weight Matrix W1 1 2 3 2.936113 1.924889 1.011028 3.686852 -1.27555 2.562502 -0.1046 0.500972 -4.13625 0.81217 -2.43693 -4.30573 -3.32135 -0.35365 -0.99193 -0.55599 3.981899 0.144122 -1.62507 -4.53162 -1.23763 5.642359 -2.01562 0.677415 2.02772 -0.08493 -5.42186 0.153548 -0.86912 -2.58223 0.611784 0.576017 -2.5903 0.862635 -2.96844 4.325228 -0.11376 -1.33785 -3.76812 7.392567 1.133884 -6.3525 -1.81848 -5.13044 -3.00254 3.139578 -2.01959 1.37071 2.248196 2.139663 -1.22494 0.018853 3.283599 -0.34606 0.257376 -0.2036 5.317304 2.225812 -1.06831 2.90198
14
Table 5: Coefficients for apparent viscosity, Eq. 16. Input Layer Weight Matrix W1 1 2 3 -1.58853 -8.18093 3.448302 1.049703 -1.91443 0.451884 0.906379 -0.67676 11.5662 4.236579 -2.17674 2.98752 13.94177 -3.53596 0.725284 -3.36605 0.208504 2.659836 2.331358 2.863177 -0.56077 -2.98745 0.32097 1.441864 -5.10113 0.230718 -2.25216 9.283254 14.68367 -0.66788 1.539603 -4.59674 1.525181 -0.75444 -9.76895 -1.67204 -0.79983 5.921717 -2.1431 7.225208 1.825331 -0.8595 3.524655 -2.04897 0.463265 16.438 -0.24212 -12.5915 -1.11719 1.9865 2.928407 5.872482 -3.44871 1.69972 -4.19689 3.047375 1.720885 -3.9058 2.134791 -2.4342
Input Layer Bias Vector
Hidden Layer Weight Vector
Output Layer Bias Vector
b1 -0.09329 -1.29317 0.0512 -2.56621 -0.18602 0.428688 0.221267 0.141673 0.186127 0.08475 -0.35108 -0.08458 -0.2328 0.169146 0.35017 0.117314 0.650627 0.125011 -0.2191 -2.78524
W2 -6.59117 -6.30391 9.835752 -0.53904 -5.17323 -0.25328 2.372333 7.16042 -4.82815 -0.36577 0.115195 0.840183 0.450564 0.966257 1.75035 4.248086 -2.37178 -5.14241 -3.25757 0.625767
b2 -1.47169
15
Fig. 1: Estimated values of R300 using ANN model vs. the actual one.
16
Fig. 2: Estimated values of R600 using ANN model vs. the actual one.
17
Fig. 3: Estimated values of flow behavior index using ANN model vs. the actual one.
18
Fig. 4: Calculated values of plastic viscosity vs. actual values.
Fig. 5: Calculated values of flow consistency index vs. actual values.
19
Fig. 6: Predict values of apparent viscosity using ANN technique vs. actual values.
Fig. 7: Prediction of apparent viscosity using Pitt [24] and Almahdawi et al. [25] correlations.
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Conflict of Interest The authors have no conflicts of interest to declare