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Experimental Studies and Probabilistic Neural Network Prediction on Flow Pattern of Viscous Oil−Water Flow through a Circular Horizontal Pipe Anjali Dasari, Anand B. Desamala, Ashok Kumar Dasmahapatra,* and Tapas K. Mandal* Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati−781039, Assam, India S Supporting Information *

ABSTRACT: We report detailed analysis on the flow patterns of moderately viscous oil−water two-phase flow through a circular horizontal pipe with an internal diameter of 0.025 m. Lubricating oil and water with viscosity and density ratio of 107 and 0.889, respectively, have been selected as system fluids with interfacial tension 0.024 N/m. We have applied visual and imaging techniques to identify different flow patterns (viz., plug flow, slug flow, wavy stratified flow, stratified mixed flow, dispersion of oil in water, and dispersion of water in oil flow) for a wide range of superficial velocities of oil (USO = 0.015 to 1.25m/s) and water (USW = 0.1 to 1.1 m/s). The present map has also been correlated with the prediction by probabilistic neural network (PNN) along with six other flow pattern maps from the literature, having the wide variation of system properties to establish the PNN as a predictive tool for flow pattern map. For the construction of PNN, phase superficial velocities, conduit diameter, pipe inclination, viscosity, interfacial tension, and density are used as governing parameters of the flow patterns. phase flow with the help of visualization, imaging,1−6,14−17 and probe10,18−21 (intrusive and nonintrusive) techniques. Flow pattern is greatly affected by several parameters such as, pipe diameter, density ratio, interfacial tension of the fluids, and pipe material, including the viscosity ratio of two fluids. Tables 1a and 1b summarize the literature1−6,14−17,22,23 based on low (1.2−71.17 mPa·s) and high viscous (viscosity ≥500 mPa·s) fluids, respectively, corresponding to the system properties. Higher viscosity increases a possibility of slug and annular flow compared to the lower viscosity, as understood from the work reported by Russell et al.4 and Grassi et al.16 (Tables 1a and 1b, respectively). Similarly, Beretta et al.2 identified bubbly flow (BO) which is not reported by Andreini et al.,15 although all other system properties are identical except viscosity. The tables demonstrate that the effect of viscosity (in the medium range) on the flow pattern is not well explored. To complement the experimental works, some of the researchers have theoretically predicted flow patterns by various correlations,24−26 analytical model19,27,28 and artificial intelligence like artificial neural network (ANN).29−31 An artificial neural network (ANN) is a computational tool, extensively used in various fields of science and technology, especially for pattern recognition. It is an information processing tool, which processes input data to develop a best possible correlation. On the basis of this correlation it can predict the patterns of the input data. The information processing is carried out in its various inbuilt nodes which are very closer to the human brain.32 We will give details on this tool in the respective section (section 3). It has been successfully applied by several researchers to predict the flow pattern map of air−water29,30

1. INTRODUCTION The flow of two immiscible liquids in conduits is widely encountered in the chemical and petroleum industries.1−3 Knowledge of hydrodynamics of two immiscible liquids is important for the efficient design of extractors, reactors, and transportation pipeline networks, etc. During the flow of two immiscible fluids through pipe lines, phases can distribute themselves in different interfacial configurations known as flow patterns to minimize their total energy. Pressure drop of such flow cannot be predicted accurately without prior knowledge of flow patterns. The most common way to identify the interfacial configuration is visual observation. Still and motion imaging techniques have also been widely used by many researchers4−7 in supplement to visual observation at low and moderate superficial velocity of the phases. Commonly reported literature flow patterns for liquid−liquid two-phase horizontal flow1,8−11are smooth stratified (SS), wavy stratified (SW), stratified mixed (SM), plug (P), slug (S), core annular flow (CAF), dispersion of oil in water (DO/W), dispersion of oil in water and water (DO/W&W), dispersion of water in oil (DW/O), and dispersion of water in oil and oil (DW/O&O). A brief overview of the past research work has been described below to highlight the lacuna of liquid−liquid horizontal two-phase flow. Interest in oil−water flows has been sustained for more than 60 years due to its fundamental and technological importance. Clark and Shapiro12 have observed that the addition of a small amount of water into viscous oil reduces the pressure drop. Pressure drop also depends on the interfacial distribution of two fluids during flow. Russell and Charles13 theoretically proved that pressure drop is minimum if two phases arrange themselves in a concentric configuration in which high viscous fluid occupies the core and a less viscous fluid wraps the core. This work established the influence of flow patterns on pressure drop in multiphase flow and motivated several researchers toward the identification of flow patterns in liquid−liquid two© XXXX American Chemical Society

Received: May 31, 2012 Revised: April 22, 2013 Accepted: May 10, 2013

A

dx.doi.org/10.1021/ie301430m | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Table 1a. Flow Patterns of Horizontal Low Viscous Oil−Water Flow pipe material

viscosity ratio

density ratio

Russell et al.4 Charles et al.1

authors

0.0203 0.0264

pipe id (m)

cellulose acetate butyrate cellulose acetate butyrate

Fujji et al.14 Trallero et al.5 Beretta et al.2

0.025 0.0508 0.003

acrylic acrylic borosilicate glass

Nadler and Mewes18 Raj et al.23 Rodriguez and Oliemans22 Mandal et al.6

0.059 0.0254 0.0828 0.025 and 0.012

perspex acrylic steel PMMA

20.13 6.29 16.8 65 61.5 29.7 9.87 51.325 71.17 20 1.2 9.434 1.2

0.84 1 1 1 0.98 0.852 0.87 0.877 0.874 0.841 0.787 0.776 0.787

pipe ID (cm)

pipe material

viscosity ratio

density ratio

Andreini et al.15

0.003 and 0.006

borosilicate glass, steel, copper, PVC

562 920 1307 500

0.886 0.889 0.893 925

Bannwart et al.3 Grassi et al.16

0.0284

glass

0.021

polycarbonate

800

0.866

Sotgia et al.17

0.026, 0.04

plexiglas pyrex

900

0.9

BO, BW, SO, SW, A ST, SM, DO/W&W, DO/W, DW/O, DO/W, DW/O DO/W, A, SO, BO, P

SS, SM, DO/W&W, DW/O&W, DO/W, DW/O P, SS, SW,TL, DO/W, DW/O, DO/W&W ST, SM, DW/O, DO/W, DO/W&W, DO/W, DW/O P, S, SS, SW, TL, R, C, DO/W, white emulsion

input parameters of the network were superficial velocities of both the fluids, diameter of the conduit, angle of pipe inclination, viscosity ratio, density ratio, and interfacial tension of the two liquids.

Table 1b. Flow Patterns of Horizontal High Viscous Oil− Water Flow authors

flow patterns SM, DO/W, BO DO/W, A, SO, BO

flow patterns DO/W, A, SO, P

2. EXPERIMENTAL SECTION 2.1. Method of Experiment. The schematic representation of the experimental setup used for the identification of flow patterns in liquid−liquid horizontal pipe is shown in Figure 1. It consists of an entry section (EN), a test section (TS), and an exit section (EX) in the direction of flow of liquids. The exit section is connected with the decanter (D). The test section is made up with 0.025 m internal diameter perspex pipe of 1 m length. Transparent perspex pipe is selected for better visualization and imaging studies. In the test section a view box (VB) is provided to minimize the lens effect of pipe material during the photography. In between EN and TS, an L/D ratio of 120 is provided for obtaining fully developed flow, and the same ratio is maintained from test to exit section to minimize the end effect of the fluids. Test fluids are lube oil and filtered water. The viscosity and density of lube oil are μo = 107 mPa s and ρo = 889 kg/m3 (at 25 °C), respectively. The viscosity of filtered water is μw = 1 mPa s, and density is 1000 kg/m3. Oil− water interfacial tension is σ = 24 × 10−3 N/m measured by a

DO/W, A, ST, BO, ST, DO/W, A, SO, ST, DO/W DO/W, A, SO, SW

and water−kerosene31 two-phase flow. All the data are based on the single fluid pair during the training of the network. The objectives of the present research work are twofold: (a) identification of flow regimes of moderately viscous oil−water two-phase (viscosity ratio: 107) flow through horizontal pipe line; (b) prediction of the flow patterns using probabilistic neural network (PNN) which is a special type of artificial neural network (ANN). The network has been prepared using a data bank of 2441 data points (with wide range of fluid properties) from literature including the data from our experiments. The

Figure 1. Schematic of the experimental setup. B



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vector machine (SVM) are some types of artificial neural networks. The selection of a neural network has also been a tricky task. Appropriate selection of ANN involves the ANN topology, which depends on classification of the problem. PNN, a special type of artificial neural network (ANN) is selected for the current study for its accuracy in prediction, swiftness, and ease in operation. PNN is a feed forward neural network based on Bayes− Parzen classification theory which was first introduced by Spect.36 The PNN approach combines both the Bayes theorem of conditional probability and Parzen’s method for estimating the probability density functions of the random variables.37 The detailed description of Bayes−Parzen theory has been given in Hajmeer and Basheer.37 Classification can be estimated from Bayes’ strategy if the probability density f k(x) of a sample is known. In most of the cases it is unknown and a Gaussian distribution is assumed to get the classification. High scale of misclassification is observed if there is a large difference between assumed distribution and true distribution of the sample. This misclassification can be minimized by introducing the concept of multivariate probability density function (PDF) estimator, g(x), which is given by the following equation for the case of all equal smoothing parameters and a bell-shaped Gaussian function.

tensiometer (make KRUSS, Germany; model K9). Water is circulated by centrifugal pump (P1) to the entry section. Flow rate of water is adjusted with the help of bypass valve (G2) and by the control valves (C1 and C2). The flow rate of water is measured by pre calibrated rotameters (RM1 and RM2). Rotameter RM1 is used for lower flow rates (1.667 × 10−5− 1.667 × 10−4 m3/s) whereas rotameter RM2 is used for higher flow rates (1.667 × 10−5−9.17 × 10−4 m3/s). Oil is pumped to the entry section by a gear pump (GP). The flow rate of oil is controlled by the simultaneous adjustment of bypass valve (G1) and control valve (C3). Oil flow rate (7.4 × 10−6−6.1 × 10−4 m3/s) is measured by volumetric method where volumetric flow rate of oil which is obtained by subtracting volumetric flow rate of water (obtained from pre calibrated rotameter) from total volumetric flow rate of oil−water mixture. Mixture volumetric flow rate (total volumetric flow rate) is measured from total liquid height of the mixture present in the calibrated decanter at the exit and time required to reach a particular liquid level. We have carried out our experiments at the ambient temperature. To avoid any temperature effect on the physical properties of fluids, we run for around 15 min and stopped for around 1.5 h (for separating oil from oil−water mixture). The experiments have been repeated thrice to check the reproducibility of volumetric flow rate and a good reproducibility has been observed with an average deviation of 0.5%. A detailed uncertainty analysis in measurement of volumetric flow rate shows less error, on the order of 10−4. 2.2. Identification of Flow Patterns. The experiments have been carried out in a wide range of superficial velocities for both fluids to get all probable flow patterns. Superficial velocity of oil (USO) varies from 0.015 to 1.25 m/s, and for water (USW) it varies from 0.1 to 1.1 m/s. During the experiment water has been pumped first into the test section and then oil. After reaching steady state, observations have been noted and a snapshot of the phenomena has been taken with a camera (model no. DSC-HX100 V, make Sony) at the test section. A flow pattern has been identified from this photograph. The same experiment has been repeated thrice at the same flow conditions to check the reproducibility of flow pattern and more than 99% reproducibility has been observed. Then, a new set of experiment has been started to get the results at next flow rate. For this, water superficial velocity has been kept constant, whereas the oil superficial velocity has been increased to the next higher value. After completion of one set of experiments, oil and water have been separated from the mixture present in the decanter (where the gravity separation taking place due to density difference of the fluids). Separated oil and water have been recycled into the respective storage tanks.

gk (x) =

1 (2π ) p /2 nσ p

n

⎛ ∥x − x ∥2 ⎞ i ⎟ 2 ⎝ 2σ ⎠

∑ exp⎜ i=1

(1)

Where, “x” is the vector of scattered variables and “xi” is the ith training vector. σ is the smoothing parameters (also called bandwidth or kernel width) representing standard deviation around the mean of “p” random variables x1, x2, ..., xp, and “n” is the total number of training data in the sample. Schematic representation of a simple PNN architecture has been given in Figure 2, which consists of four layers namely input layer,

3. METHOD OF PREDICTION 3.1. About Probabilistic Neural Network (PNN). The present flow pattern map has also been predicted using artificial neural network, an artificial intelligence technique which is implemented to predict flow patterns of viscous oil−water flow through different pipe inclinations. Neural networks have vast applications such as pattern recognition, identification, classification, control systems, image processing, clustering of data, forecasting33 prediction, and identification of flow patterns.29−31,34 For many complex and nonlinear problems, ANN has been found to be an alternative tool to solve the problem.35 Feed forward back-propagation (FFBP), generalized regression neural networks (GRNN), radial basis network (RBN), probabilistic neural network (PNN), and support

Figure 2. Simple probabilistic neural network (PNN). Adapted from ref 37.

pattern layer, summation layer, and output layer. When an input is presented, the input layer does not carry out any computational or arithmetic operations rather it simply passes the inputs to a pattern layer. The number of nodes in the pattern layer is the same as the number of input data points. The pattern layer computes Euclidean distances from the input vector to the training input vectors and produces a vector which is close to a training input vector. The summation layer sums these contributions for each class of inputs “Ck” to C



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Table 2. Source of Data Used in PNN sl no.

angle of inclination from horizontal (deg)

interfacial tension (N/m)

pipe i.d. (m) and material

viscosity ratio

density ratio

65

1

0.03

0.877, 0.874 0.776.

0.036 0.0204

1

0

2

0

0.0264 cellulose acetate butyrate 0.003 glass

3

+1, +2, +5*

0.0828 steel

51.33, 71.17 9.434

4

90

0.012 acrylic

1.2

0.787

0.0315

5

0

0.0284 glass

500

0.925

0.029

6

0, +10, +15

0.889

0.05

7

0

0.9

0.02

8 total

0

0.021 800 polycarbonate 0.026 plexiglas and 900 0.004 pyrex 0.0254 perspex 107

0.889

0.021

ref Charles et al.1 (1961) Beretta et al.2 (1997) Rodriguez and Oliemans22 (2006) Mandal et al.38 (2010) Bannawart et al.3 (2004) Grassi et al.16 (2008) Sotgia et al.17 (2008) present work

total no. of data points

no. of points used in training

no. of points used in testing

416

292

124

117

82

35

116

83

33

153

108

45

346

243

103

405

284

121

439

308

131

449 2441

315 1715

134 726

*

The + sign indicates upward flow with the horizontal as the reference axis.

produce an arithmetic mean of its output vector of probabilities and from the maximum of these probabilities the summation layer picks a complete transfer function. The output layer classifies any random variable by comparing the output of summation layer for each class and then following the Bayes’ classification theorem as Ck(x) = arg max{gk (x)}

(2)

The PNN working procedure includes three basic steps, development of the network, training and testing of the network, and prediction of the patterns. Accuracy of PNN totally depends on training of the network, and it requires a huge amount of training data. Therefore, collection of data is an important step prior to the construction of a PNN. 3.2. Collection of Data and Flow Pattern Classification. About 2441 data points have been collected from seven literature works1−3,16,17,22,38 and the present work to construct the network which is shown in Table 2. It covers the diameter range from 0.3 to 8.29 cm, viscosity ratio ranging from 1.2 to 900, and inclination ranging 0−90°. Table 2 is also shows the number of data of individual past work used for training and testing. In aggregate, 1751 points of data (70%) out of 2441 have been used for training, and the rest (30%) have been used for testing. This satisfies the basic requirement of an artificial neural network, which states that maximum 80% can be used in training and minimum 20% data should be used in testing.37 It has been noticed that terminology used by various authors for the same interfacial configurations are different from each other which created lots of perplexity. So for simplicity, few flow patterns with similar nature have been grouped together and a single nomenclature is chosen for this group which is explained in Figure 3. For example, plug flow and slug flow have been considered here as slug flow (Figure 3a). Similarly, smooth stratified and stratified wavy flow patterns are taken as stratified flow (Figure 3b). Three layer flow and stratified mixed flow patterns have been considered as stratified mixed flow pattern (Figure 3c). “Dispersion of oil in water and water” flow pattern, “dispersion of oil in water”, and other oil dispersed flow (like oil in water homogeneous dispersion,22 oil bubbles in water,1 etc.) have been combined together and are considered as the dispersion of oil in water flow pattern (DO/W) (Figure 3d).

Figure 3. Grouping of the flow patterns.

Similarly the “dispersion of water in oil and water” flow pattern, dispersion of water in oil, and other water dispersed flow (like water in oil homogeneous dispersion,22 water bubbles in oil,1 etc.) have been taken as dispersion of water in oil flow pattern (DW/O, Figure 3e) to avoid the ambiguity coming from various terminologies. All kinds of annular flow like core annular,16,17 wavy annular,3,17 and dispersed annular,3,16 etc., have been D



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consider as annular flow (A) (Figure 3f). Schematics of a few flow patterns based on oil dispersion, water dispersion, and annular flow have been shown in Figure 3d−f, respectively. During the training of PNN, flow patterns have been represented by numerical values and symbols which are given in Table3.

accuracy in testing also, then this spread constant has been used to predict the unknown data. The spread constant in the present network has been selected from two graphs shown in Figure 4. Figure 4a shows

Table 3. Numerical Values and Symbols of Different Flow Patterns Used in PNN flow pattern

numerical value

symbol

slug flow (S) stratified flow (SW) stratified mixed flow (SM) dispersion of oil in water (DO/W) dispersion of water in oil (DW/O) annular flow (A)

1 2 3 4 5 6

■ ● ▲ ◀ ▼ ◆

3.3. Design, Training, and Testing. A PNN has been designed, trained, tested, and applied for prediction using the inbuilt function in Matlab R2008 and the data listed in Table 2. If “P” is input vectors (here these are superficial velocities of both the liquids, conduit diameter, angle of inclination, and physical properties of fluids such as density, viscosity, and interfacial tension) and “T C” is the target indices of corresponding input vector (here it is flow patterns), then target indices is converted into vector “T” by using the “ind2vec(Tc)” function before forming a PNN. A new probabilistic neural network (PNN) has been created by using function “newpnn”. It is used for initializing the weights of matrices to small random numbers and to set neurons. The function, “newpnn” consists of input vectors (superficial velocities of both the phases, physical properties of the fluids, pipe diameters, and inclination), target vectors (corresponding flow patterns), and spread constant value as input parameters. In this step, the selection of an optimum value of spread constant or smoothing parameter (σ) is very important as the shape of Gaussian function is totally influenced by this constant which is very important to create a good PNN. Various algorithm and techniques have been reported, to estimate the optimum spread constant such as genetic algorithm39 and the trial and error method.30,37 This value is selected by the trial and error method in the present work as it involves simple operation processes. The function “sim” simulates the probabilistic neural network which is required for testing the developed network on the design input vector. Finally output vectors are converted to indices to get the predicted class or pattern. In the testing process, the output obtained has been compared with the target values; it undergoes regression analysis which gives regression coefficient “R” (R = 1 for perfect training). With higher regression coefficient and proper spread value, the network has been prepared and tested with known data to get the accuracy in prediction. For a set of two input parameters’ value (input and target vectors), one value of spread constant has been assumed in the function of “newpnn” during training. Flow patterns along with an optimum regression coefficient have been obtained as an output of the network by running the “sim” function. An optimum spread value has been selected based on highest average percent accuracy obtained in the prediction during tanning. The optimum value of spread constant has been used in testing steps to check accuracy of the trained PNN. If it gives good

Figure 4. (a) Variation of regression coefficient with spread constant. (b) Variation of percent accuracy in prediction with spread constant.

the variation of regression constant with spread values for a set of 1751 training data points. Similarly, Figure 4b shows variation of average percentage accuracy in the prediction with different spread values for the same set of data. Comparing these two figures (Figure 4a and b), it can be concluded that a good training of the PNN has been achieved at a spread value of 0.02 with regression coefficient of 0.991 (Figure 4a), which gives maximum average percent correct prediction (Figure 4b).

4. RESULTS AND DISCUSSION 4.1. Observed Flow Patterns. The different flow patterns observed during the experiments are plug flow, slug flow, wavy stratified flow, stratified mixed flow, dispersion of oil in water, and dispersion of water in oil. Images of the observed flow patterns are shown in Figures 5a−f as they appeared during the experiments with increasing the mixture velocity. At lower phase superficial velocities of both the fluids, it is observed that oil slugs are periodically appearing in the continuous water medium. This flow pattern is known as slug flow and image of the pattern is shown in Figure 5a. The figure shows a distinct liquid bridge between two consecutive oil slugs. With increasing the water superficial velocity at the same oil superficial velocity, the length of the slug is broken into small oil plugs, sized less than the slugs appeared at lower superficial velocity. This type of flow pattern is termed as plug E



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a wide range of superficial velocities of both phases. The onset of dispersion has been observed on further increasing the water superficial velocity. At higher water superficial velocities oil drops distributed uniformly in the continuous water phase. This phenomenon is designated as oil dispersed in water (DO/W), and a picture of the same is given in Figure 5e. At higher superficial velocity of oil, it is observed that some amount of water is dispersed into the continuous oil phase, which was termed as inverted dispersion or dispersion of water in oil (DW/O) as shown in Figure 5f. 4.2. Flow Pattern Map. The flow patterns observed during aforementioned experiments have been shown in graphical form in Figure 6 which is known as the flow pattern map.

Figure 6. Experimental flow pattern map: (left-pointing triangle) plug flow, (square) slug flow, (circle) wavy stratified flow, (up-pointing triangle) stratified mixed flow, (diamond) dispersion of oil in water flow (DO/W), (down-pointing triangle) dispersion of water in oil flow (DW/O).

Water superficial velocity has been plotted along Y-axis, and oil superficial velocity, along X-axis in the figure. Different symbols and abbreviations have been used for various flow patterns in the flow pattern map. The significance of symbols has been mentioned in figure caption and abbreviations of the corresponding flow patterns in the section of description of observed flow patterns. Figure 6 shows that slug flow has been observed at lower oil and water velocities. The present data shows that the slug flow regime begins at oil velocity of USO = 0.015 m/s and at water velocity of USW = 0.1 m/s. It continues up to USO = 0.035 m/s at the same water velocity. The flow pattern exists up to the velocity range of USO = 0.015−0.327 m/s and USW = 0.6 m/s. The plug flow pattern starts at USO = 0.038 m/s and USW = 0.2 m/s and extends up to USO = 0.031 m/s and USW = 0.4 m/s in the map. Further incrementing the phase velocity, the flow pattern that appears is totally gravity dominant and the flow configuration is separated flow with a wavy interface (viz., wavy stratified flow). The existing range of wavy stratified flow regime is USO = 0.09−0.286 m/s and USW = 0.1−0.43 m/s. The map shows that the stratified mixed flow region occupied a wide range of superficial velocities of both the phases (USO = 0.273−0.73 m/s and USW = 0.1−0.933 m/s). It is sandwiched between stratified wavy and inverted dispersion in the flow pattern map. Various dispersions have appeared at two extreme sides of the map. Dispersion of oil in water appears in an oil velocity range of USO = 0.155−0.53 m/s and water velocity range of USW = 0.433−1.1 m/s at the upper portion of the map. Whereas dispersion of water in oil is noticed at extreme right of the map in a velocity range of oil and water USO = 0.532−1.22

Figure 5. Photographs of different flow patterns. (a) Slug flow (USO = 0.04 m/s; USW = 0.132 m/s). (b) Plug flow (USO = 0.082m/s; USW = 0.433 m/s). (c) Wavy stratified flow (USO = 0.103 m/s; USW = 0.267 m/s). (d) Stratified mixed flow (USO = 0.4 m/s; USW = 0.55 m/s). (e) Dispersion of oil in water (USO = 0.188 m/s; USW = 0.8 m/s). (f) Dispersion of water in oil (USO = 1.1 m/s; USW = 0.4 m/s).

flow (P, Figure 5b). Now keeping water superficial velocity constant and continuously increasing the oil superficial velocity, the length of liquid bridge is decreased and it is finally disappeared. As a result, two continuous streams appear in the form of stratification. It has been observed that the interface between two phases is wavy. The amplitude of the wave increases with increasing phase superficial velocities. This type of flow is known as a wavy stratified flow pattern (SW), and photograph is given in Figure 5c. The flow pattern shown in Figure 5d where stratification of the phases persists but oil droplets appeared at the oil−water interface, gradually increasing the phase velocity of oil. This is termed as the three layer (TL) flow pattern or stratified mixed flow (SM) pattern in the literature. With an increase in oil velocity, the number of droplets at the interface is increased. This pattern occurred at moderate phase velocities of two fluids and covered F



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m/s and USW = 0.133−1.1 m/s, respectively. In the next section, we predict this flow pattern map with PNN. 4.3. Predicted Flow Pattern Map by PNN. The completely trained PNN is tested for all flow regimes with different sets of data which was not used during the training as discussed in section 3.3. This well trained and tested PNN has been used to predict the experimental flow pattern map of oil− water flow through a horizontal pipe with viscosity and density ratios of 107 and 0.889, respectively. The predicted flow pattern map has been shown in Figure 7, and the experimental Figure 8. Percentage of correct predictions of different flow patterns: (1) slug flow, (2) stratified flow, (3) stratified mixed flow, (4) dispersion of oil in water, (5) dispersion of water in oil.

pattern recognition capability of PNN as a predictive tool and its robustness. For this purpose, six flow pattern maps, namely, those of (1) Charles et al.,1 (2) Rodriguez and Oliemans22 at 5° upward inclined, (3) Sotgia et al.,17 (4) Rodriguez and Oliemans22 at 0° (horizontal), (5) Fujji et al.,14 and (6) Raj et al.23 have been selected for the prediction, dividing into two categories: (a) data which are used in training and (b) data which are not used in training. Data of the first three have been used during the training process and a predicted map of these are shown in Figure 9. Predicted maps of remaining three (data not used during PNN training) are presented in Figure 10. The last three data sets are completely independent of the trained PNN. These maps (all of the six references) have been selected to test the suitability of the developed PNN for a wide range of system properties. In all the figures, scattered data points are obtained from PNN prediction and the solid lines are their respective experimental transition boundaries. The mismatched points are marked by circles. The nomenclature of the flow patterns is kept same as they appear in the original maps to avoid confusion. Predictions of flow pattern map for the above two cases are discussed below. a. Prediction of Flow Pattern Data Used in Training. Figure 9 represents the PNN predicted flow pattern map of Charles et al.1 with the viscosity ratio of 65, which is almost half of the viscosity ratio used in the present study. The X-axis and Y-axis represent water and oil superficial velocity (ft/s), respectively. The trained PNN successfully predicts oil slug flow which is considered as slug flow during flow pattern classification in the present work and is represented by a blue square symbol in Figure 9. PNN also predicts oil bubble in water and oil drops in water (black triangles) as oil dispersed in water with good agreement. We have segregated the predicted data (oil dispersed in water as per our classification) according to their classification (oil drops in water and oil bubbles in water) and have plotted in the figure to maintain similarity with Charles et al.’s1 proposed flow pattern map. Few predicted data points are mismatched with the original map as marked by circles. Water dispersed in oil flow patterns have been predicted in a similar way and represented by inverted green triangles in the figure with a little deviation as marked in the figure. PNN is not trained for water slugs (due to a lack of a good amount of literature data), and it predicts this region as a combination of oil slugs and annular flow pattern in the flow pattern map of Charles et al.1 The pink diamonds shown in Figure 9 represent the annular flow pattern predicted by PNN and resulted in good accuracy in prediction. Two major differences have been observed between the present work and the work by Charles et

Figure 7. Predicted flow pattern map using PNN: (square) slug flow, (circle) stratified flow, (up-pointing triangle) stratified mixed, (leftpointing triangle) dispersion of oil in water (DO/W), (down-pointing triangle) dispersion of water in oil (DW/O), () transition boundary between slug flow and wavy stratified flow, (- - -) transition boundary between wavy stratified flow and stratified mixed flow, (− - - −) transition boundary between stratified mixed flow and dispersion of water in oil flow, (− −) transition boundary between slug flow and dispersion of oil in water flow. Circled points show the mismatch between experimental and PNN prediction.

transition boundaries of different flow patterns have been drawn on the predicted map as shown for comparison. The experimental transition boundaries have been drawn based on the outermost data series for a particular flow pattern. In Figure 7, scattered data points are the flow patterns predicted by PNN and lines are experimental transition boundaries of various flow patterns observed in the present study. The points in the circle show the mismatching points of the flow patterns predicted by PNN. From this figure, it is clear that the mismatching points are very less in the predicted flow regime map. The PNN predicts few points as annular (A) flow in the stratified mixed region of the experimental map, which are not observed in experiment (marked by circles in Figure 7). The accuracy in predicting different flow patterns using PNN has been shown in Figure 8. The accuracy of prediction strongly depends on the number of data points used in the PNN training. The available data point for DW/O is much more compared to the stratified flow. As a result, DW/O achieves 98.4% accurate prediction compared to 89.5% accuracy of the stratified flow. Figure 8 demonstrates that PNN has successfully predicted all the five flow patterns with an average error of 6.5%. 4.3.1. PNN as a Predictive Tool. The trained PNN successfully predicted the present flow pattern map. A well trained PNN can also predict a wide range of flow pattern data irrespective of system properties. So it can be used as a predictive tool for flow pattern maps. Different flow patterns from the literature have been predicted demonstrating the G



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showing the wide applicability of a well-trained PNN. The Xaxis and Y-axis of the plot represent oil and water superficial velocities in meters per second, respectively, as commonly done in the literature. The PNN successfully predicts all the flow patterns, except a few data points in the dispersion of oil in water and water, and oil in water homogeneous dispersion region22 as shown in Figure 9b. Their flow pattern map consists of only stratified mixed flow and both the dispersion (oil dispersion in water and water dispersion in oil), which is according to our flow pattern classification. The difference in flow pattern map (as compared to the present flow pattern map) is due to lower viscosity ratio (one tenth of the present work), higher pipe diameter (more than three times the present work), and upward inclination (+5°), which destabilize the interface. Good prediction of flow pattern proves that all these effects have been successfully accounted for by our trained PNN. Until now, we have tested the trained PNN against the fluids having lower viscosity as compared to our fluid’s viscosity. To demonstrate the applicability of trained PNN with a higher viscosity ratio, we have selected another flow pattern map proposed by Sotgia et al.17 for a fluid pair having viscosity ratio of 900, which is almost 9 times higher than our value. The predicted map (Figure 9c) shows that PNN predicts well for all the flow patterns. The mismatching is found in their transition flow region, which is considered as oil dispersion in water in the present work. A relatively small deviation is observed in the slug flow region with a few mismatching points in the annular flow region. Here, wavy annular and core annular flow have been considered as annular flow (See Figure 3). Sotgia et al.17 observed core annular flow in a wide range of superficial velocity of both the fluids because higher viscosity favors such a kind of flow. b. Prediction of Flow Pattern Data Not Used in Training. We observed successful predictions of flow pattern maps by the trained PNN for the cases, where data have been incorporated during PNN development. Now, we report the prediction of flow pattern maps for the cases, where data have not been incorporated during PNN development. It will also help to check its robustness in prediction. For this, we have predicted three flow pattern maps (horizontal) from the literature with various fluid properties; they are the flow pattern maps of Rodriguez and Oliemans,22 Fujji et al.,14 and Raj et al.23 presented in Figure 10a, b, and c, respectively. Figure 10a shows good agreement with Rodriguez and Oliemans’s22 map, except for a few mismatching points. Their “oil in water homogeneous dispersion” and “dispersion of oil in water and water” are considered as oil dispersed in water in the PNN. Similarly, “water in oil homogeneous dispersion” and “dispersion of water in oil and oil in water” are considered as water dispersed in oil flow. They observed smooth stratified flow in a horizontal pipe which was absent in their 5° upward flow pattern map (see section 4.3.1.a). This difference is due to the absence of instability at the interface caused by the slope of the pipe line as discussed earlier. This difference is successfully accounted for by the developed PNN. In the present work, a wavy flow pattern (long wave and short wave) is identified instead of smooth stratified flow in Rodriguez and Oliemans’s22 work. This is due to a long wave leading to a smooth interface in larger diameter pipe. On the other hand, higher viscosity and smaller diameter enhance the onset of waviness at the interface as observed in the present work. Similarly, the trained PNN gives good prediction for the flow pattern map reported by

Figure 9. (a) Predicted flow pattern map of Charles et al.1 using PNN: (square) slug flow, (left-pointing triangle) dispersion of oil in water (DO/W), (down-pointing triangle) dispersion of water in oil (DW/O), (diamond) annular flow, () experimental transition boundaries. (b) Predicted flow pattern map (+5°) of Rodriguez and Oliemans22 using PNN: (up-pointing triangle) stratified mixed flow, (left-pointing triangle) dispersion of oil in water (DO/W), (downpointing triangle) dispersion of water in oil (DW/O), () experimental transition boundaries. (c) Predicted flow pattern map of Sotgia et al.17 using PNN: (square) slug flow, (left-pointing triangle) dispersion of oil in water (DO/W), (diamond) annular flow, (circle) stratified flow, () experimental transition boundaries. The experimental transition boundaries have been drawn based on the outermost data series for a particular flow pattern.

al.:1 (a) we have not observed annular flow and water slugs and (b) we have observed stratified flow (wavy stratified and stratified mixed flow), which is not reported by Charles et al.1 It is important point to note that the developed PNN successfully predicts the effect of system properties on flow pattern maps. Prediction of a flow pattern map for 5° upward inclined (+5°) pipe line22 of a fluid pair having viscosity ratio of 9.4 and pipe diameter of 0.083 m has been presented in Figure 9b for H



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been predicted as dispersion of oil in water flow pattern. Slug flow has been predicted with good accuracy with a few mismatched points marked by circles in Figure 10b. The present PNN has predicted inverted annular14 as the annular flow pattern with good accuracy. The annular flow pattern reported by Fujji et al.14 has been predicted with poor accuracy by the present PNN. This is because they reported a different kind of annular flow (water in core and oil in annulus) in their work, and these types of data are not used in development of PNN. However, PNN gives good prediction for their inverted annular flow (as annular flow) which is commonly reported as annular flow in the literature. They did not observe stratified flow patterns in their experimental study. The developed PNN successfully predicted a flow pattern map of Fujji et al.14 with a wide range of fluid properties. The trained PNN has also predicted the flow pattern map of a low viscous oil−water system reported by Raj et al.23 with a viscosity ratio of 1.2 and a density ratio of 0.787 in 0.025 m diameter pipe line. The developed PNN shows good prediction for the flow pattern map of Raj et al.23 (Figure 10c) with very less mismatched points. During the PNN prediction we have observed that the prediction accuracy is highly influenced by the viscosity of the fluids. Therefore, to enhance the prediction accuracy for all the cases, the closer value of viscosity data should be used in development of PNN. It is also true for the pipe inclination.

5. CONCLUSIONS In the present study, we have identified flow patterns of moderately viscous oil−water two-phase flow through horizontal pipe line by visual and imagining technique and correlated with the prediction by probabilistic neural network (PNN). We have identified six different flow patterns: plug flow, slug flow, wavy stratified flow, stratified mixed flow, dispersion of oil in water, and dispersion of water in oil flow. Our observed flow pattern map is in accord with the literature. However, we did not observe the core−annular flow in our study as compared to the work of Charles et al.1 This may be attributed to the type of nozzle and the arrangement of two fluids at the entry section. A specific type of nozzle or coaxial arrangement of entering fluids may be required to achieve annular flow which can produce annular configuration. Finally, we have successfully applied PNN to predict flow patterns of liquid−liquid two-phase flow through horizontal, inclined, and vertical pipe line covering wide range of input data. A total of seven flow pattern maps have been predicted including the present work. Out of seven flow pattern maps, the data of Rodriguez and Oliemans22 at 0° (horizontal), Fujji et al.,14 and Raj et al.23 were not incorporated in the development of PNN. Percentage accuracy in the prediction of all the flow patterns is ≥90. Further, the accuracy may be increased by incorporating the closer viscosity and pipe inclination data into the trained PNN. The present investigation on the moderately viscous oil−water flow will be helpful to oil and petrochemical industries for design of transportation pipeline network and different unit operations like the gas−oil separator, settler, etc.

Figure 10. (a) Predicted flow pattern map (0°) of Rodriguez and Oliemans22 using PNN: (circle) stratified flow, (up-pointing triangle) stratified mixed flow, (left-pointing triangle) dispersion of oil in water (DO/W), (down-pointing triangle) dispersion of water in oil (DW/O), () experimental transition boundaries. (b) Predicted flow pattern map of Fujji et al.14 using PNN: (left-pointing triangle) dispersion of oil in water (DO/W), (down-pointing triangle) dispersion of water in oil (DW/O), (diamond) annular flow, (square) slug flow, () experimental transition boundaries. (c) Predicted flow pattern map of Raj et al.23 using PNN: (square) slug flow, (circle) stratified flow, (up-pointing triangle) stratified mixed flow, (left-pointing triangle) dispersion of oil in water (DO/W), (down-pointing triangle) dispersion of water in oil (DW/O), () experimental transition boundaries. The experimental transition boundaries have been drawn based on the outermost data series for a particular flow pattern.

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Fujji et al.14 They used a moderately viscous oil with a viscosity ratio of 61.5 and a density ratio of 0.98 in 0.025 m diameter horizontal pipe line. The trained PNN has predicted bubbly flow reported by Fujji et al.14 as a dispersion of water in oil flow pattern. Similarly, inverted slug and inverted bubbly flow have

ASSOCIATED CONTENT

S Supporting Information *

Basic code for PNN training and testing. This material is available free of charge via the Internet at http://pubs.acs.org. I



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Article

(15) Andreini, P. A.; Greeff, P.; Galbiati, L.; Kuklwetter, A.; Sutgia, G. Oil-water flow in small diameter tubes. International Symposium on Liquid−Liquid Two-Phase Flow And Transport Phenomena, Antalya,Turkey, Nov 3−7, 1997; p 41. (16) Grassi, B.; Strazza, D.; Poesio, P. Experimental validation of theoretical models in two-phase high-viscosity ratio liquid−liquid flows in horizontal and slightly inclined pipes. Int. J. Multiphase Flow 2008, 34, 950−965. (17) Sotgia, G.; Tartarini, P.; Stalio, E. Experimental analysis of flow regimes and pressure drop reduction in oil−water mixtures. Int. J. Multiphase Flow 2008, 34, 1161−1174. (18) Nadler, M.; Mewes, D. Flow induced emulsification in the flow of two immiscible liquids in horizontal pipes. Int. J. Multiphase Flow 1997, 23, 55−68. (19) Vedapuri, D.; Bessette, D.; Jepson, W. P. A segregated flow model to predict water layer thickness in oil-water flows in horizontal and slightly inclined pipelines. In Proceedings of Multiphase’97, Cannes, France, June 18−20, 1997; pp 75−105. (20) Angeli, P.; Lovick, S.; Lum, Y. L. investigations on the threelayer pattern during L-L flows. 40th European two-phase flow group meeting, , Stockholm, June 10−13, 2002. (21) Chakrabarti, D. P.; Das, G.; Das, P. K. Identification of stratified liquid−liquid flow through horizontal pipes by a non-intrusive optical probe. Chem. Eng. Sci. 2007, 62, 1861−1876. (22) Rodriguez, O. M. H.; Oliemans, R. V. A. Experimental study on oil−water flow in horizontal and slightly inclined pipes. Int. J. Multiphase Flow 2006, 32, 323−343. (23) Raj, T. S.; Chakrabarti, D. P.; Das, G. Liquid-liquid stratified flow through horizontal conduits. Chem. Eng. Technol. 2005, 28, 899− 907. (24) Wallis, G. B. One dimensional two-phase flow; McGraw-Hill: New York, 1969. (25) Arirachakaran, S.; Oglesby, K. D.; Malinowsky, M. S.; Shoham, O.; Brill, J. P. An analysis of oil/water flow phenomena in horizontal pipes. Presented at SPE Production and Operation Symposium; Oklahoma, March 1989; SPE paper 18836, pp 155−187. (26) Brauner, N. On the relation between two-phase flow under reduced gravity and earth experiment. Int. Commun. Heat Mass Transfer 1990, 17, 271−282. (27) Brauner, N. The prediction of flow dispersed boundaries in liquid-liquid and gas-liquid systems. Int. J. Multiphase flow 2001, 27, 885−910. (28) Brauner, N.; Ullmann, A. Modeling of phase inversion phenomenon in the two-phase flows. Int. J. Multiphase Flow 2002, 28, 1177−1204. (29) Julia, E. J.; Basar, O.; Jae-Jun, J.; Takashi, H.; Mamoru, I. Flow regime development analysis in adiabatic upward two-phase flow in a vertical annulus. Int. J. Heat Fluid Flow 2011, 32, 164−75. (30) Sharma, H.; Das, G.; Samanta, A. N. ANN-Based prediction of two-phase gas-liquid flow patterns in a circular conduit. AIChE J. 2006, 52, 3018−3028. (31) Chakrabarti, D. P.; Piligrim, A.; Sastry, M. K. S.; Das, G. Identification of Liquid-Liquid Flow Pattern in a Horizontal Pipe Using Artificial Neural Networks. Chem. Eng. Commun. 2011, 198, 273−285. (32) Sivanandam, S. N.; Sumathi, S.; Deepa, S. N. Introduction to neural networks using matlab 6.0; Tata McGraw Hill: New Delhi, 2010. (33) Basheer, I. A.; Hajmeer, M. Artificial neural networks: fundamentals, computing, design and application. J. Microbiol. Methods 2000, 43, 3−31. (34) Xie, T.; Ghiaasiaan, S. M.; Karrila, S. Artificial neural network approach for flow regime classification in gas-liquid-fiber flows based on frequency domain analysis of pressure signals. Chem. Eng. Sci. 2004, 59, 2241−2251. (35) Panagou, E. Z.; Kodogiannis, V.; Nychas, G. J. E. Modelling fungal growth using radial basis neural networks: The case of the ascomycetous fungus Monascusruber van Tieghem. Int. J. Food Microbiol. 2007, 117, 276−286.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +91-361-2582273. Fax: +91-361-2582291. E-mail: [email protected] (A.K.D.). Tel.: +91-361-2582271. Fax: +91-361-2582291. E-mail: [email protected] (T.K.M.). Notes

The authors declare no competing financial interest.

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NOMENCLATURE BO = bubbly flow (oil) BW = bubbly flow (water) P = plug flow SO = slug flow (oil) SW = slug flow (water) A = annular SS = smooth stratified SW = wavy stratified ST = stratified flow SM = stratified mixed TL = three-layer flow R = rivulet flow C = churn flow DO/W&W = dispersion of oil in water and water DO/W = dispersion of oil in water DW/O = dispersion of water in oil

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