Computational intelligence models for PIV based particle (cuttings) direction and velocity estimation in multi-phase flows

Accepted Manuscript Computational intelligence models for PIV based particle (cuttings) direction and velocity estimation in multi-phase flows Hatice Tombul, A. Murat Özbayoğlu, M. Evren Özbayoğlu PII:

S0920-4105(18)30826-X

DOI:

10.1016/j.petrol.2018.09.071

Reference:

PETROL 5334

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 1 February 2018 Revised Date:

6 September 2018

Accepted Date: 24 September 2018

Please cite this article as: Tombul, H., Özbayoğlu, A.M., Özbayoğlu, M.E., Computational intelligence models for PIV based particle (cuttings) direction and velocity estimation in multi-phase flows, Journal of Petroleum Science and Engineering (2018), doi: https://doi.org/10.1016/j.petrol.2018.09.071. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. 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.

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Computational Intelligence Models for PIV based Particle (Cuttings) Direction and Velocity Estimation in Multi-Phase Flows Hatice Tombul1, A. Murat Özbayoğlu2, M. Evren Özbayoğlu3 1

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TOBB University of Economics and Technology, Department of Computer Engineering, 06560 Ankara- Turkey University of Tulsa, McDougall School of Petroleum Engineering, 74104 Tulsa, OK

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Başkent University, Department of Computer Engineering, 06810 Ankara- Turkey

Abstract

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In multi-phase flow, the gas phase, the liquid phase and the particles (cuttings) within the liquid have different flow behaviors. Particle velocity and particle direction are two of the important aspects for determining the drilling particle behavior in multi-phase flows. There exists a lack of information about particle behavior inside a drilling annular wellbore. This paper presents an approach for particle velocity and direction estimation based on data obtained through Particle Image Velocimetry (PIV) techniques fed into computational intelligence models, in particular Artificial Neural Networks (ANNs) and Support Vector Machines (SVM). In this work, feed forward neural networks, support vector machines, support vector regression, linear regression and nonlinear regression models are used for estimating both particle velocity and particle direction. The proposed system was trained and tested using the experimental data obtained from an eccentric pipe configuration. Experiments have been conducted at the Cuttings Transport and Multi-phase Flow Laboratory of the Department of Petroleum and Natural Gas Engineering at Middle East Technical University. A high speed digital camera was used for recording the flow at the laboratory. Collected experimental data set consisted of 1080 and 1235 data points for 15 degrees inclined wellbores, 1087 and 1552 data points for 30 degrees inclined wellbores and 885 and 1119 data points for horizontal (0°), wellbores respectively to use in estimation and classification problems. Results obtained from computational intelligence models are compared with each other through some performance metrics. The results showed that the SVM model was the best estimator for direction estimation, meanwhile the SVR model was the best estimator for velocity estimation. The direction and speed of the particles were estimated with a reasonable accuracy; hence the proposed model can be used in eccentric pipes in the field.

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Keywords: cuttings transport; horizontal and inclined wellbore; eccentric annular pipe; multi-phase flow; particle image velocimetry, computational intelligence models, SVM, neural networks

1. Introduction

Multi-phase flow is a major field of study in the petroleum industry. During the drilling process, hole cleaning and cuttings transport are among the key operations that involve multi-phase flow, especially in underbalanced operations. Successful estimation and modelling of the flow properties, such as stationary bed height (if any), flow regime, velocity and direction of cuttings (and individual particles) can result in higher operational efficiency, effective usage of resources and higher throughput. In drilling operations, multi-phase flow in eccentric pipes with different inclinations is very common. However, there is a lack of work implemented for particle direction and velocity estimation for multi-phase flow in

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horizontal and inclined annulus. The PIV based velocity models in the literature generally focused on estimating average velocity and other flow properties. This study is one of the first studies conducted on trying to predict direction and velocity characteristics of cuttings transport for horizontal (0°), 15 and 30 degrees of angles pipe flow through machine learning. The data set is generated with PIV techniques through recorded multi-phase pipe flows under different operating environments. Our aim in this study is to be able to predict particle velocities and directions just from operating parameters. To achieve this, computational Intelligence models have been used in estimating the flow behavior in annular pipe flow. This work can be useful for many practical applications. For example, major application of estimating the dynamic characteristics of cuttings during drilling an oil well can be determination of the total transport time of the particles to the surface during a drilling operation, which these cuttings can be used as a very precious and first-hand source of information about drilled formations, once these particles are proven to be generated by the bit. In general, it is very hard to predict the total time for the particles inside the wellbore to reach to the surface since the particles have very different transport velocities than the fluid transporting them. Another good application in the similar field can be estimating the smearing and plastering performance – probability of the cuttings into the wellbore walls.

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The structure of this paper is as follows: In Section 2, a brief literature review will be provided for similar studies about multiphase flows. In Section 3, the experimental setup, data preparation, techniques used for estimation model and the application of these models in our particular study will be explained in separate subsections. In Section 4, obtained results are presented, compared and discussed. In section 5, the conclusion with comments and future study opportunities are provided.

2. Literature Review

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There are some theoretical studies and experimental works performed on flows in annular geometries (i.e., space between two cylindrical pipes having different diameters set into each other) in the literature. During drilling process, bit generates rock chips called cuttings due to penetration into the rock as a vertical force and rotation is applied on the bit. Making effective cleaning of wellbores during drilling operations is one of the fundamental parts of the drilling process. Inefficient cleaning of wells can cause problems such as poor hole condition, high torque and drag, stuck pipe, slow drilling rate, formation fracture [1,2]. Azar et al. [3], discussed some factors such as annular drilling fluid velocity, hole inclination angle, annulus eccentricity, rate of penetration having impact on hole cleaning. Tomren et al. [4] worked on factors such as pipe rotation and eccentricity at the laboratory to assess the cuttings transport performance. Test results showed that fluid annular velocity, hole inclination and drilling fluid properties were among some of the most influential factors for cuttings transport. Ozbayoglu et al. [17] identified the critical fluid velocities that were required to remove cuttings bed in eccentric pipe flow. Although there are so many studies conducted on this topic, some of the most relevant literature is listed as references [13,15,16, and 18].

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Multi-phase flow can be defined as presence of more than one type of material in the flow field, such as different liquids, liquids and solids, gas and solids, liquids and gas, or liquid, gas and solids all together. Drilling fluids are complex structures, having various water, oil, and high and low gravity solid contents, depending on the type and purpose of the fluid (Bourgoyne et al [23]. This complex structure will have impact on the behavior of cuttings transport performance as well as the dynamic behavior of the cuttings. There are a number of studies that have been focused on estimating the multi-phase flow behavior in annular geometry using Particle Image Velocimetry (PIV). Lindken et al. [5] performed velocity measurements with PIV technique on multi-phase flow. Shi Huixian [6] applied Particle Image Velocimetry (PIV) techniques to analyze cluster properties and particle motion in gas-solid two-phase flow. According to the results, clusters can be seen in different positions and velocities may change with time. Kamara et al. [7] used PIV technique to measure mean velocities in oil water flow. Most of the developed models in the literature used PIV to generate a flow velocity model based on operating conditions. There are also some studies that were based on computational intelligence models in flows. Rooki and Rakhshkhorshid [14] used Radial Basis Function (RBF) networks for cuttings concentration estimation in eccentric pipes. Ozbayoglu et al. [8,22] used some different computational intelligence models such as decision tree, nearest neighbor for specifying the flow properties. Yunlong et al. [9] presented a new model based on

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ACCEPTED MANUSCRIPT SVM to identify flow regime in two-phase flow. Rooki et al. [10] predicted terminal velocity of solid spheres in fluid using an Artificial Neural Network. Another approach for characterizing the cuttings dynamic behavior is using Computational Fluid Dynamics. There are numerous studies available in the literature [24]. A good example for such attempts is “Adwell Project”, aiming to address the cuttings transport process [25].

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In this study, the flow properties of drilling cuttings in horizontal (0°), and inclined wells are observed experimentally through PIV techniques. Also, by using this experimental data, some computational intelligence models are developed. The main aim of this study is to be able to predict the flow properties such as direction and velocity without looking at the experimental results. During the experiments, the flow regime was recorded by a digital camera at the laboratory which is then used for collecting the training and testing data. With the developed models, it will be possible to estimate the flow characteristics within the pipe just by using controllable (or measurable) parameters without actually looking at it.

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3. Model Development 3.1. Experimental Setup

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Experiments have been conducted at the Middle and Technical University (METU) Department of Petroleum and Natural Gas Engineering Cuttings Transport and Multi-phase Flow Laboratory and experimental data has been collected. Three phase flow (air-water-cutting) experiments were performed on eccentric pipe flows and using a high speed digital camera, flows have been recorded. The experimental setup consisted of pumps, compressor, control valves, pressure transducer, flow meters, annular test section, high speed digital camera, pipe rotation system and cuttings collection and injection tanks etc. It also included a data acquisition system. A schematic view of the experimental setup is shown in Figure 1.

Cuttings Injection System

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Digital Camera

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Annular Test Section

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Flow Meter

Flow Meter

Control Valve

Differential Pressure Transducers

Gas Vent

Liquid Pump

Liquid Tank

Control Valve

Solid Liquid Seperation

Cuttings Collection System

Gas Compressor + Tank

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The annular test section is a part of experimental setup in which the measurements were made and photographs of the flow were taken. It consists of a transparent pipe which is 5 m long and has 74 mm of inner diameter. The transparent pipe includes a drill pipe which has 47 mm of outer diameter. The drill pipe and the transparent pipe are eccentric and the drill pipe can be rotated at different speeds. Three phase flow experiments were carried out in the eccentric pipe system by using water, air and cuttings at room temperature (25°C) and atmospheric pressure.

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Experimental procedure for three phase flow was as follows: using the centrifugal pump, the liquid was pumped at constant flow rate within the range from 0 to 945 L/min. The pumped liquid passed through the mass flow meter and control valves. While liquid was flowing at a constant flow rate, air was provided at a desired rate through the annular test section by the compressor, which has a maximum rate of 8500 st.L/min. By using the mass flow meter and control valves, flow rate of the supplied air was set to a constant value. After stabilizing air and liquid flow rates, cuttings were supplied to the system from the tank. Immediately after flow rates of cuttings, air and liquid were stabilized, the data acquisition system was activated for collecting the required data of the corresponding flow. Additionally, high speed digital camera was used for recording the flow activities in the test section. Since, the digital camera was a high speed one, video frames only provided digital images for a short time span. These digital images were then used for training the computational intelligence models. The mentioned procedure was carried out in different cuttings, liquid and air flow rates and different pipe rotation speeds. The test matrix values for the flow experiments are tabulated in Table 1. Table 1 Test Matrix for Gas-Cutting-Liquid Three Phase Flow Tests

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Average Water Annular Velocity (m/s) Average In-Situ Gas Annular Velocity (m/s) Rate of Penetration (Cuttings Injection) (m/hrs) Inclination (degrees) Pipe Rotation (1/min) Average Annular Pressure (atm) Temperature (°C) Eccentricity ratio

Minimum 0.2 0.2 24 0 (horizontal) 0 1.07 25 0.623

Maximum 6 38 36 30 120 1.9 30 0.623

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For this study, water is preferred as the liquid phase for two major reasons; 1) it is transparent, and cheap, and 2) under higher temperature conditions, most of the drilling fluids inside the well can be assumed as low apparent viscosity fluids under high shear conditions. However, this study can be expanded with polymeric fluids in the future to simulate non-Newtonian liquid cases.

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3.2. Data Preparation from Digital Images for Computational Intelligence Models As mentioned in the previous section, high speed digital camera recorded the flow in the test section and digital images were acquired. All steps of the flow in the test section were recorded at 60 frames/s with 1032x350 resolution. Experiments have been recorded separately for horizontal (0 degrees), and angled (15 degrees and 30 degrees) status of the test section. Recordings have been performed for different RPM (Rotations Per Minute), ROP (Rate of Penetration), (Liquid Superficial Velocity) and (In-Situ Gas Superficial Velocity) values. Yuksel [11] has divided the recordings into individual frames. In this work, data points were obtained from these prepared individual frames. Then, the machine learning dataset was created by calculating the particle velocity and direction by manual observation of individual particles by tracking it through consecutive frames as shown in Figure 2.

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Figure 2 Recorded video frames

3.3. Computational Intelligence Models

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In this work, for predicting drilling cuttings behavior in multi-phase flow without conducting experiments, various computational intelligence models along with some traditional methods were used. The techniques used in this study were Linear Regression [19], Nonlinear Regression [19], Feedforward Neural Networks [20] and Support Vector Regression [21] for Particle Velocity and Direction Angle Estimation; whereas Particle Direction such as left, right was estimated using Feedforward Neural Networks and Support Vector Machines [20].

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The details of how each model works is presented in the Appendix.

3.4. Velocity and Direction Estimation models used in our study

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Particle Velocity and Direction Angle Estimation is a regression (estimation) problem; Particle Direction such as left, right, forward, backward estimation is a classification problem. For the estimation problem, a total of 1080 data points for the 15-degrees pipe, 1087 data points for the 30-degrees pipe and 885 data points for the horizontal pipe were collected. For the classification problem, a total of 1235 data points for the 15-degrees pipe, 1552 data points for the 30-degrees pipe and 1119 data points for the horizontal pipe were collected. All computational intelligence models were created by using MATLAB®. For all models, RPM (Rotations Per Minute), ROP (Rate of Penetration), (Liquid Superficial Velocity) and (In-Situ Gas Superficial Velocity) values were used as inputs. In addition, x and y coordinates of a particle along with the frame rate difference was also provided in the input vector. As far as the output was concerned, for the estimation problem, angle and velocity values were used, whereas for the classification problems, direction value was used as output. Feedforward neural network algorithm was implemented for both classification and estimation problems as the Artificial Neural Network model. ANN can be used successfully in a multi-class classification problem. In this work, 8 directions were determined and the directions were labeled with numbers. The directions used in ANN model are given in Table 2. The corresponding artificial neural network had one hidden layer with 100 hidden

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Corresponding Label 1 -1 3 -3 0 4 2 -2

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Directions Left forward Right forward Left backward Right backward Forward Backward Left Right

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ANNs can produce more than one output, so angle and velocity estimations were implemented together. For the classification, artificial neural network output was rounded off to the nearest integer between -3 and 4 (after normalization) and the estimated particle direction was calculated accordingly. One reason we preferred a one output model (representing the numeric equivalent of the direction) in our study for the direction classification instead of multiple outputs (in this particular case, 8) is that there exists a relation between the directions. Hence, it is a better choice to use an ordinal model rather than a nominal one, such as the case in a one-hot-vector where all output neurons are zero except one indicating the direction.

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Also, another important detail in our models was the usage of the x and y coordinates and the frame difference values as inputs. For training, these values were necessary in order to be able to model individual particle flow characteristics. For the testing phase, we can assume hypothetical particles and estimate their behaviors according to the trained model. Later, if we want to come up with a general model, we can test various hypothetical particles in different locations and average out their flow characteristics accordingly. Since different operating environment parameters are adapted throughout the study, achieving generalization might be feasible as long as adequate number of particles are considered in the modeling process.

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Support vector machine (SVM) classifies differently than the feed forward neural networks. While feed forward neural network can handle multi-class classification, SVM can only perform binary classification. The directions given in Table 1 were also used for the SVM model. Since SVM has the ability to distinguish only two classes at once, in order to distinguish more than one direction given in Table 1, one versus all approach was used. Neural networks might produce different results on every different training, however SVM produces same results every time, since it finds the optimum classifier based on the given training data set. SVM finds the global minimum and it is more successful than neural networks in general. In this work, “libsvm” [12] was used as the library to train SVM and during the training process, radial basis kernel function was used for SVM classifier.

4. Results and Discussions Individual frames were extracted from all recorded videos in order to get the pixel values from these images. These pixel values constituted the required data for the model estimation and testing. Total collected data was divided into two groups where half of the total data was used for training and the other half was used for testing purposes. Total number of collected experimental data for horizontal (0°), 15°, 30° inclined wells were 885, 1080, 1087 respectively to use in the estimation problem, and 1119, 1235, 1552 respectively to use in the classification problem. These data were collected at different ROP, RPM, and values. In this study, the direction, angular direction and velocity of cuttings in eccentric pipes were predicted. In order to evaluate the accuracy of the estimation models, some performance metrics were used. The performance metrics used in this work were Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Percentage Error

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ACCEPTED MANUSCRIPT (MPE), Correlation Coefficient (r), Determination Coefficient (R2), Variance Accounted For (VAF). Results, obtained from these estimation models, were compared with each other through these performance metrics.

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In the scope of this work some difficulties were encountered for velocity, displacement and angular displacement estimation problems that needed to be overcome. Particle velocity can vary significantly within small distances and can take too remarkably different values so prediction of cuttings velocity is a challenging problem. For example, in the same frame, a particle might move slowly almost like stopping when another particle can move too fast almost not seen in the next frame. Angular direction gives the particle direction with respect to the horizon (in this case the pipe direction) so this angle indicates the particle direction. Besides the angular direction, directions matched with the labels as seen in Table 1 were also used for particle direction estimation. For example, when model output is 1, it means the direction of the particle is left forward. Particle direction estimation is also a hard problem because of the lack of regular behavior of particles. For instance, with the influence of gravity, some particles move in the reverse direction of the flow when pipe angle is increased.

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In our model, we tracked individual particles and tried to come up with a computational intelligence model that can learn the movements of individual particles separately in contrast with the general flow of a cluster of particles (assuming particles in different sections of the pipe might act differently based on the operating characteristics). However it is possible to come up with a cluster flow of particles, if the results of particles within close vicinity are used together. Also, particle sizes were not taken into consideration in our study. Size and shape characteristics might be affecting velocity of particles [13]; however, such properties are not easy to quantify and their influences on the overall flow or individual particle velocities are vague. Hence, we left out the size and shape characteristics of the particles.

4.1. Cuttings Velocity Estimation Results

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In this section, cuttings velocity estimation results for data obtained from horizontal and angled pipes are shown. Performance metrics were calculated separately for training and test data to make a comparison, but only test results are presented here. The general success rates of the models for cuttings velocities are tabulated in Tables 3, 4, and 5. The performance metrics results show that SVR model outperformed the other models to be the best estimator for velocity estimation both horizontal and 15 and 30 degrees angled pipes.

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Table 3 presents the estimation results for the test data in horizontal drilling pipes. The error values of the results obtained from the training data were smaller than the error values of the results obtained from the test data in velocity estimation, so the training data results are not included here. Almost all performance metrics show that the most successful model was SVR while ANN model underperformed the others in estimating the velocity for horizontal drilling pipes. Table 3 Velocity Results for Test Data in Horizontal Drilling Pipes

MODELS Linear Regression Nonlinear Regression Artificial Neural Network Support Vector Regression

RMSE (m/s)

0.4998 0.4854 0.7810 0.2958

MPE (%) 34.5680 35.9091 -3.7084 16.3137

MAPE (%) 54.1072 56.2846 60.6165 30.4830

r 0.6925 0.7139 0.6899 0.9061

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VAF

0.4796 0.5097 0.4759 0.8211

47.9590 50.9611 -27.1544 81.7809

Table 4 shows the estimation results for the test data in 15 degrees angled drilling pipes. SVR is given as the most successful model and nonlinear regression is given as the least successful model by almost all performance metrics.

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MODELS Linear Regression Nonlinear Regression Artificial Neural Network Support Vector Regression

RMSE (m/s) 0.3159 0.3397 0.3296 0.2728

MPE (%) 21.4186 28.2773 12.4617 17.3288

MAPE (%)

r

39.6165 45.3778 37.9413 33.9399

0.6990 0.6456 0.7069 0.7909

R2 0.4886 0.4168 0.4997 0.6255

VAF 48.8641 41.5698 44.4324 61.9265

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Table 5 shows the estimation results for the test data in 30 degrees angled drilling pipes. The performance metrics results obtained from Table 5 was analyzed, the results indicate that the most successful model was SVR and the least successful model was nonlinear regression according to all of the performance metrics. Table 5 Velocity Results for Test Data in 30 Degrees Angled Drilling Pipes

0.3075 0.3365 0.3248 0.2623

MPE (%) 18.0483 23.4739 2.1124 13.8921

MAPE (%) 38.1866 44.6063 34.3784 31.7290

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0.7273 0.6597 0.7461 0.8113

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RMSE (m/s)

R2

0.5290 0.4352 0.5567 0.6581

VAF

52.8620 43.4137 50.8392 65.7810

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MODELS Linear Regression Nonlinear Regression Artificial Neural Network Support Vector Regression

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In Figure-3, the comparison of measured cuttings velocities and estimated cuttings velocities using SVR for horizontal (0°), 15° and 30° inclinations are presented. The dashed lines represent ±20% difference range, and the solid line represents the perfect match.

Figure 3 Direction Classification Results with SVR in Horizontal Pipes

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4.2. Cuttings Angular Direction Estimation Results

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In this section, cuttings angular direction estimation results for the data obtained from horizontal and angled pipes are shown. Performance metrics were calculated separately. The general success rates of the models for cuttings angular directions are tabulated in Tables 6,7 and 8. Almost all performance metrics results show that SVR model was the best estimator for angular direction estimation for horizontal, 15 and 30 degrees angled pipes. Meanwhile, even though estimation performance of SVR was better, ANN turned out to be a better generalizer for 30 degrees.

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The results presented in Table 6 shows the estimation performance for the test data in horizontal drilling pipes. It can be seen that the linear regression came out as the worst estimator for angular direction estimation. For this particular case, we can claim that the data does not provide a linear distribution. SVR models, as expected, were the best estimators for angular direction estimation.

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RMSE (degrees)

Linear Regression Nonlinear Regression Artificial Neural Network Support Vector Regression

MPE (%)

MAPE (%)

-0.3198 -0.3282 0.0065 -0.5949

2.7052 2.6200 3.0683 2.2149

r

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VAF

0.3797 0.4682 0.4811 0.6110

0.1442 0.2192 0.2314 0.3734

14.4130 21.9227 -24.8660 33.6398

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6.3407 6.0600 7.6271 5.6624

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Table 6 Angular Direction Results for Test Data in Horizontal Drilling Pipes

Table 7 provides the estimation results for the test data in 15 degrees angled drilling pipes. The results obtained from Table 7 shows that the SVR model was the best estimator and linear regression model was the worst estimator for angular direction estimation. In this particular case, most of the models performed similarly, however SVR still outperformed all other models even though the margin was slightly less this time.

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Table 7 Angular Direction Results for Test Data in 15 Degrees Angled Drilling Pipes

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Linear Regression Nonlinear Regression Artificial Neural Network Support Vector Regression

RMSE (degrees)

8.7877 8.7346 10.4269 8.2967

MPE (%)

MAPE (%)

0.0650 -0.0454 0.4132 -0.5667

3.6374 3.5215 4.3763 3.2025

r

R2

VAF

0.1510 0.1855 0.2588 0.4199

0.0228 0.0344 0.0670 0.1763

2.1005 3.2706 -37.1504 14.0380

In Table 8 the estimation results for the test data in 30 degrees angled drilling pipes showed a similar outcome. SVR’s estimation performance was the best when compared to other models. However, the overall correlation coefficient results were considerably lower for both 15 and 30 degrees cases for all models. Despite this decline, the results show that the SVR was the best estimator for angular direction estimation in 30 degrees angled pipes. Table 8 Angular Direction Results for Test Data in 30 Degree Angled Drilling Pipes

MODELS Linear Regression

RMSE (degrees)

9.1423

MPE (%)

MAPE (%)

0.3378

3.7342

r

R2

0.1339

0.0179

VAF

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9.2507 12.8159 8.2288

0.3118 -2.9782 -0.2563

3.8079 5.3571 3.2954

0.0582 0.2371 0.4487

0.0034 0.0562 0.2013

-1.1857 -60.8201 19.8928

4.3. Cuttings Direction Estimation Results

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In this section, cuttings direction classification results for the data obtained from horizontal and angled pipes are presented. As indicated in previous sections, directions were labeled between -3 and 4 and error differences were calculated based on these values. For example, even as direction is -2, if SVM finds this direction as -1, estimation error difference would be 45 degrees.

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A total of 1119 data points were used for direction classification in horizontal pipes. 560 of them were used as training data. The general success rates of the SVM model for cuttings direction classification in horizontal pipes are shown in Figure 4. The results obtained from Figure 4 show that when SVM model was tested with the test data, 341 numbers of data was detected with 0 errors, which means the estimation results of 61% of the data points were correct. Besides, incorrect direction values that were estimated by the model were also not too distant from the actual results.

Figure 4 Direction Classification Results with SVM in Horizontal Pipes

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The general success rates of the ANN model for cuttings direction classification in horizontal pipes are shown in Figure 5. The results obtained from Figure 5 show that ANN estimated 300 test data points without error, indicating 53.5% of the directions were correctly estimated.

Figure 5 Direction Classification Results with ANN in Horizontal Pipes

A total of 1235 data points were used for direction classification in 15 degrees angled pipes and 618 of them were used as training data. The general success rates of the SVM model for cuttings direction classification in 15

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degrees angled pipes are shown in Figure 6. The results obtained from Figure 6 shows that SVM model estimated 381 data points with 0 errors for test data with 61.8% accuracy.

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Figure 6 Direction Classification Results with SVM in 15 Degrees Angled Pipes

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The general success rates of the ANN model for cuttings direction classification in 15 degrees angled pipes are shown in Figure 7. The results obtained from Figure 6 show that when ANN was tested with the test data, 256 data point directions were estimated with 0 errors, indicating the ANN model estimated directions with 41.5% accuracy.

Figure 7 Direction Classification Results with ANN in 15 Degrees Angled Pipes

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A total of 1552 data points were used for direction classification in 30 degrees angled pipes. 776 of them were used as training data. The general success rates of the SVM model for cuttings direction classification in 30 degrees angled pipes are shown in Figure 8. The results obtained from Figure 8 show that SVM estimated 112 data points of test data with 0 errors. According to the results, SVM model estimated directions with only 14.4% accuracy. The results obtained for horizontal and 15 degrees were much better than the 30 degrees results for the SVM model. In most of the cases, the direction estimation was off for 45 degrees in average (these values range between 22.5 and 67.5 due to the resolution of the overall model). One of the main reasons behind this significant difference might be explained due to the influence of increasing directional gravitational effect on the flow, which was mostly downward in previous cases (horizontal and 15 degrees). Because of this phenomenon, some particles started moving in reverse flow direction with increasing pipe angles and with that overall success rate was dropped accordingly.

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Figure 8 Direction Classification Results with SVM in 30 Degree Angled Pipes

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The general success rates of the ANN model for cuttings direction classification in 30 degrees angled pipes are shown in Figure 9. The results obtained from Figure 12 show that ANN estimated 373 of the test data with 0 errors. According to the results presented in Figure 9, ANN model estimated directions with 48.1% accuracy which was much higher compared to the SVM model. ANN model used in this model was the widely adapted Multilayer perceptron which, through various examples from literature, happened to be a very good generalizer. Hence, when compared with SVM for this particular case, it provided a more generalized solution. SVM is an optimized generalizer based on maximizing the difference between the two classes using support vectors, but its performance is highly dependent on the data distribution. There is a good chance the sampled training data was not indicative enough for the underlying data distribution, so instead of providing a generalized model, SVM created the best possible classifier model from the available data. The performance might be improved if more data points are trained, and/or different data distributions are tried. Nevertheless, ANN model still provided a reasonably accurate result in the estimation process with an acceptable error rate.

Figure 9 Direction Classification Results with ANN in 30 Degrees Angled Pipes

4.4. Discussion

There are a number of studies in the literature aimed at modeling velocity and flow characteristics mostly based on PIV techniques. However, analyzing individual particles and consolidating that information into a general velocity model using computational intelligence techniques have not been adapted. Conventional models provide velocity estimations and slip profiles based on the general flow patterns, however individual particle behaviors can vary significantly within a flow even though the mean stream seems smooth. With that, the estimation model we have chosen is quite different than the commonly preferred approaches. This phenomenon also makes it harder for the model to be compared against the velocity models proposed in the literature. Even though general velocity models exist in the literature, to the best of our knowledge, none of them used the particle velocities directly. Meanwhile, with our computational intelligence point of view, the developed models try to learn overall flow behavior through individual particles. Furthermore, varying stationary bed sizes

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ACCEPTED MANUSCRIPT and heterogeneous cuttings, liquid and gas layers are implicitly taken into consideration through different operating attributes and environmental parameter selections. As a result, the models might be able to learn the complex multi-phase behavior inside the wellbore. The experimental results and estimation performances indicate developing such models can be viable solutions for industrial usage in the field for cuttings performance in hole cleaning process, especially in underbalanced cases. Applying the correct environmental parameters for optimum cleaning performance during hole cleaning can reduce operational costs and enhance tool lifetime.

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In this study, the computational intelligence models show mostly acceptable estimation results in velocity and directional predictions. The results may be improved with more data collection. Meanwhile, different cuttings concentrations and liquid types can be introduced into a general model. More studies need to be implemented in order to create a fully generalized model to work under any operating condition. Since this is a preliminary work, only a particular snapshot of the overall problem was addressed. However, the initial results are promising and it seems like there is much more room for improvement.

5. Conclusion

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Acknowledgement

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In this study, the direction and velocity of cuttings in eccentric annulus are predicted. The data was collected using an experimental setup with different flow parameters. In order to predict velocity and angular direction a total of 1080, 1087, 885 data points were collected for 15, 30 degrees angled and horizontal drilling pipes respectively. For the direction classification, total of 1235, 1552, 1119 data points were collected for 15, 30 degrees angled and horizontal drilling pipes respectively. In each set, half of the data were used for training purposes and the other half of them were used for testing the developed model. Feed forward neural networks, support vector machines, support vector regression, linear regression, nonlinear regression techniques were used in making estimation or classification for the cuttings velocity and direction. The results indicate that the most successful models have been support vector machines for direction estimation and support vector regression has been for velocity estimation. The developed models can be effectively used for horizontal / angular eccentric annulus particle flow velocity characterization with an acceptable accuracy. For future work, different liquid/gas/cuttings types or concentrations can be included in such models in order to develop a more comprehensive tool.

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This study was funded through TUBITAK (The Scientific and Technological Research Council of Turkey) Project 108M106.

References 1. A. A. Pilehvari, J. J. Azar. State-of-the-Art Cuttings Transport in Horizontal Wellbores, 1999, SPE Drilling & Completion, pp. 169-200. 2. Brown, N. P., Brn, P. A., Weaver, A., BP Research Centre. Cleaning Deviated Holes: New Experimental and Theoretical Studies. 1989. SPE/IADC Drilling Conference. p. 181. 3. Azar J.J, Sanchez R. Alfredo. Important Issues in Cuttings Transport for Drilling Directional Wells, Rio de Janeiro : Society of Petroleum Engineers, 1997.

4. P. H. Tomren, A. W. Iyoho, J. J. Azar. s.l., Experimental Study of Cuttings Transport in Directional Wells, Society of Petroleum Engineers, 1986, Vol. 1.

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ACCEPTED MANUSCRIPT 5. Ralph Lindken, Lichuan Gui and Wolfgang Merzkirch., Velocity Measurements in Multiphase Flow by Means of Particle Image Velocimetry. s.l. : Chemical Engineering Technology, 1999. 6. Hui-xian, Shi., Experimental Research of Flow Structure in A Gas-Solid Circulating Fluidized Bed Riser by PIV. s.l., Journal of Hydrodynamics, 2007.

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7. W.A.S. Kumara, B.M. Halvorsen, M.C. Melaaen, Particle image velocimetry for characterizing the flow structure of of oil water flow in horizontal and slightly inclined pipes. 15, s.l. : Chemical Engineering Science, 2010, Vol. 65. 8. A. Murat Ozbayoglu, H.Ertan Yuksel., Estimation of Multiphase Flow Properties using Computational Intelligence Models., s.l. : Procedia Computer Science, 2011.

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9. Yunlong ZHOUa, Fei CHEN, Bin SUN., Identification Method of Gas-Liquid Two-phase Flow Regime Based on Image Multi-feature Fusion and Support Vector Machine., s.l. : Chinese Journal of Chemical Engineering, 2008, Vol. 16.

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10. R. Rooki, F. Doulati Ardejani, A. Moradzadeh, V.C. Kelessidis, M. Nourozi., Prediction of terminal velocity of solid spheres falling through Newtonian and non-Newtonian pseudoplastic power law fluid using artificial neural network., s.l. : International Journal of Mineral Processing, 2012, Vols. 110-111. 11. Yüksel, Hüsnü Ertan. Analysis of gas–liquid behavior in eccentric horizontal annuli with image processing and artificial intelligence techniques, MS Thesis, 2010. 12. http://www.isis.ecs.soton.ac.uk/resources/svminfo/, Support Vector Machines. [Accessed: 28 Jan 18] 13. E. Ghasemi Kafrudi, S.H. Hashemabadi, Numerical study on cuttings transport in vertical wells with eccentric drillpipe, Journal of Petroleum Science and Engineering 140 (2016) 85–96.

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14. Reza Rooki, Masoud Rakhshkhorshid, Cuttings transport modeling in underbalanced oil drilling operation using radial basis neural network, Egyptian Journal of Petroleum (2017) 26, 541–546. 15. Asep Mohamad Ishaq Shiddiq, Brian Christiantoro, Ildrem Syafri, Abdurrokhim, Bonar Tua Halomoan Marbun, Petra Wattimury & Hastowo Resesiyanto, A Comprehensive Comparison Study of Empirical Cutting Transport Models in Inclined and Horizontal Wells, J. Eng. Technol. Sci., Vol. 49, No. 2, 2017, 275-289.

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16. S. R. Shadizadeh & M. Zoveidavianpoor (2012) An Experimental Modeling of Cuttings Transport for an Iranian Directional and Horizontal Well Drilling, Petroleum Science and Technology, 30:8, 786-799, DOI: 10.1080/10916466.2010.490816.

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17. M. E. Ozbayoglu , A. Saasen , M. Sorgun & K. Svanes (2010) Critical Fluid Velocities for Removing Cuttings Bed Inside Horizontal and Deviated Wells, Petroleum Science and Technology, 28:6, 594-602, DOI: 10.1080/10916460903070181 18. T.I. Larsen, | A.A. Pilehvari, | J.J. Azar, Development of a New Cuttings-Transport Model for High-Angle Wellbores Including Horizontal Wells, SPE-25872-PA, Vol 12, Issue 2, DOI: 10.2118/25872-PA 19. Bethea, R. M.; Duran, B. S.; Boullion, T. L. (1985). Statistical Methods for Engineers and Scientists. New York: Marcel Dekker. ISBN 0-8247-7227-X. 20. Haykin, Simon, Neural Networks, A Comprehensive Foundation, 2nd ed., Prentice Hall, NJ, ISBN-13: 9780132733502 21. R.E. Osgouei, M. Özbayoğlu, E. Özbayoğlu, E. Yüksel, A. Eresen, “Pressure drop estimation in horizontal annuli for liquid–gas 2 phase flow: Comparison of mechanistic models and computational intelligence techniques”, Computers & Fluids, vol 112, pp 108–115, DOI: 10.1016/j.compfluid.2014.11.003, 2015.

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ACCEPTED MANUSCRIPT 22. M. Özbayoğlu, H.E. Yüksel, "Analysis of Gas-Liquid Behavior in Eccentric Horizontal Annuli with Image Processing and Artificial Intelligence Techniques", Journal of Petroleum Science and Engineering, vol 81, pp. 31-40, 2012, DOI: 10.1016/j.petrol.2011.12.008, 2012. 23. T. Bourgoyne, Millheim K., Chenevert M., Young Jr. F., “Applied Drilling Engineering”, ISBN 1-55563001-6, SPE Textbook Series, Vol 2, 1991

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24. Fu T.K., Ettehadi Osgouei R., Ozbayoglu M.E., 'CFD Simulation of Solids Carrying Capacity of a Newtonian Fluid Through Horizontal Eccentric Annulus', ASME FEDSM 16204, ASME 2013 Fluids Engineering Division Summer Meeting, Incline Village, Nevada, July 7 - 11, 2013 25. Adwell Project, http://www.ad-well.no/home

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APPENDIX

A. Linear Regression

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Linear regression is probably the most widely used fundamental estimation technique. In computational intelligence terminology, linear regression is also referred as a linear kernel, or a linear unit. It is based on the assumption that there is a linear relation between the input parameters (independent variables) that represent our data vector and the output (dependent variable). The representative linear regression line (or hyper-plane for multidimensional inputs) is optimally constructed in such a way that the sum of error squares between each data sample and the corresponding line is minimum (see equations A.1 and A.1). +

or more explicitly

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where x is a vector of size m representing m independent variables and y is the dependent variable. The linear regression coefficients a0 to am are optimally chosen such that =

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is minimum. The main reason for linear regression to have such broad popularity is its simplicity. However, in most of the real-life problems, the relation between the inputs and outputs is not linear in nature; as a result, linear regression provides an over-simplified model for such cases (Figure A.1). This phenomenon is also observed in our study.

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Figure A.1 An oversimplfying linear regression model

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B. Nonlinear Regression

Since linear regression might not be sufficient for most complex data estimation problems, a more advanced version of regression is introduced, namely nonlinear regression. It serves the same purpose as its linear counterpart, minimizing the sum of square error values between the data points and the associated regression equation (or hyper-surface for multidimensional inputs). However, this time the corresponding regression equation is not linear, actually it is a polynomial with a degree of m (Equation B.1). =

+

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Even though using nonlinear regression may be a better choice for error minimization in most problems that are nonlinear in nature, it has its own problems. First of all, unlike linear regression where we implement the regression process immediately, we have to decide what degree of polynomial we should be using for our model. The optimization outcome for different polynomial degrees will vary, and there is no straightforward methodology for the selection process. While using a small m will result in a simpler model, it might not be representative enough for the underlying problem, whereas choosing a larger m might create an unnecessarily complex representation of our data.

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Other nonlinear models might also be used instead of polynomial representation like exponential, trigonometric, radial basis, sigmoid etc. Finding the most general model that fits well with the data is a difficult problem. Even though adapting nonlinearity might help the model to reduce the estimation error, it introduces uncertainties based on the choice of the correct nonlinear match. These constitute the problems associated with nonlinear regression. As a result, even though it might provide better results than linear regression, it still is not as popular due to its complexity and lack of generalization properties.

C. Artificial Neural Networks In the last few decades, Artificial Neural Networks (ANN) have become quite popular for data estimation problems. Unlike linear or nonlinear regression models, ANN models have better generalization and error minimization capabilities if correctly trained. Error minimization is also based on sum of error squares; however, ANN models mostly have multilayers which provides an elegant way of data association between inputs and outputs. The outputs of the preceding layers are used as inputs to the following layers and there is a nonlinear mapping process between each layer. The optimization process and mathematical modelling of such

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ANN models are composed of units called neurons. Each neuron actually works exactly as a linear regression model except the linear regression output goes through a nonlinear transformation called transfer or activation function. One of the most commonly used transfer function is the sigmoid or hyperbolic tangent which maps the corresponding values into the range of -1 to 1 (Figure C.1). This result is then fed into the next layer as an input.

Figure C.1 Activation function in a neuron

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There are several different ANN models, however the most commonly used ANN is Multilayer Perceptron (MLP) which is a feedforward neural network type. The learning process in MLP, like most of the ANN models, is an iterative one. Furthermore, there are a lot of parameters involved with the network topology and the learning algorithm. Even though MLP and other ANN models are very powerful, selecting the right operating parameters is not an easy task. A lot of studies are focused on assisting developers and users to tune model parameters in such a way to achieve maximum efficiency and throughput. The basic structure of an MLP network is presented in Figure C.2. The neurons are illustrated with circles in that figure. This particular ANN model has n inputs (n neurons in the input layer), 1 hidden layer with l neurons and m outputs (m neurons in the output).

Figure C.2 A feedforward ANN model

D. Support Vector Machines Support Vector Machines (SVM) is mostly considered as the ultimate traditional machine learning model, at least before the introduction of the deep learning models that recently started dominating the big data analytics environment. SVM, originally, is developed as a binary classifier, which maximizes the distance between the two separating classes through linear parallel support vectors. These support vectors consist of the closest data points in one particular class to the closest data points in the other class, assuming the classes are linearly separable. The decision surface (linear classifier function) will be the sole classifier equation that happens to be

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the parallel line (surface) that will have equal distances from both support vectors. Maximizing the distance between the support vectors accomplishes the optimum classifier criteria, since there will not be any other linear classifier that separates the two classes more than this optimum chosen one. As a result, SVM is also called as the maximum margin classifier. Figure D.1 illustrates the working structure of SVM.

Figure D.1 SVM model illustrating the support vectors and the decision boundary

The classifier decision surface in Figure D.1 is defined by Equation (D.1) "∙

+

=0

(D.1)

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which is the line in between and equidistant from both support vectors. The support vectors are defined by Equation (D.2) +

= 1 &' " ∙

+

= −1

(D.2)

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Hence, the distance between the support vectors with respect to w becomes (=

2 *. 3 ‖"‖

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As a direct result of this representation, the data points are classified into two separate classes according to 3- 00 1 4 " ∙ ,-.&/0 1. 2 3- 00 2 4 " ∙

+ 5 1 *. 4 + 6 −1

1 = ": ∙ " − 2

+ − 1 *. 5

where i=1..n and xi represents ith data point among the dataset of n samples. The problem becomes a constrained optimization problem, that is we are looking for the optimum values of w and b that maximizes the distance between the support vectors as represented in Figure xx. Since we are trying to maximize ( in Equation (D.3), we are actually trying to minimize w in the same equation. We can formulate this problem through the following loss function that we will try to minimize 8 ",

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; "∙

Minimizing the loss function defined in equation (D.5) can be accomplished through solving the Lagrange multipliers (; ) through dual formation of the problem [20].

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ACCEPTED MANUSCRIPT If the constraint for using linear support vectors are loosened, we might achieve higher data estimation performance through nonlinear SVM models. But just as in the case of linear against nonlinear regression, it is not straightforward to decide what type of support vectors we should choose. Different kernels are used for such purpose; however, SVM training is not cheap, especially if the data set gets bigger; so linear SVM models are more commonly preferred.

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When our data estimation problem is a regression problem, the traditional SVM model needs to be modified to be useful in such a case. Support Vector Regression (SVR) is used in regression problems. The underlying model is still intact, the only difference being the margin maximization is based on a regression equation rather than a decision boundary.

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Computational Intelligence Models for PIV based Particle (Cuttings) Direction and Velocity Estimation in Multi-Phase Flows

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Hatice Tombul, A. Murat Özbayoğlu, M. Evren Özbayoğlu Highlights

1) In literature, not many studies combine Particle Image Velocimetry (PIV) along with computational intelligence for flow velocity modeling.

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2) SVM (and SVR for regression problems) is considered the best overall machine learning model in general, our results in particle velocity and direction estimation also confirmed this result. 3) SVM provided a robust estimation model for direction and velocity estimation with high accuracy.

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4) There is not much information available (both theoretical as well as measurement) regarding with the cuttings vectorial velocity information. Such information is important to estimating the true transport velocity, smearing - plastering performance, and hydraulic considerations. This study attempts to provide this information.