�nowled�e Discovery for Classi�cation of Three-Phase Vertical Flow Patterns of Heavy Oil from Pressure Drop and Flow Rate Data

is paper focuses on the use of arti�cial intelligence �AI� techniques to identify �ow patterns acquired and recorded from experimental data of vertical upward three-phase pipe �ow of heavy oil, air, and water at several diﬀerent combinations, in which water is injected to work as the continuous phase �water-assisted �ow�. We investigate the use of data mining algorithms with rule and tree methods for classifying real data generated by a laboratory scale apparatus. e data presented in this paper represent diﬀerent heavy oil �ow conditions in a real production pipe.


Introduction
e design of oil production pipelines involves evaluation of �ow lines subject to multiphase �ow of oil, water, and gas, where oscillations in pressure, temperature, and phase concentration typically occur. Furthermore, the phases usually �ow on different geometrical distributions inside the pipe, named �ow patterns. e identi�cation of �ow patterns is essential for the economic evaluation of the project, such as pressure drop and �ow rate along the pipeline. ese aspects are critical on offshore production conditions, where extensive distances and high costs are involved. Flow pattern identi�cation is an important step to design separation equipments, slug catchers, gas li operations, wellhead gathering systems, and production management and control. With the discovery of heavy oil reservoirs the lack of tools and methodologies for �ow pattern identi�cation deserves attention because the existing multiphase �ow correlations are made for low API oils, where the oil-water mixture may be treated as a single liquid phase with average properties. However, for water-continuous �ow of heavy oil below bubble-point, three distinct phases are present, that is, oil, water, and gas, thus making the traditional approach of �ow pattern classi�cation and pressure drop prediction in three-phase �ow may have poor accuracy.
Basically, there are two types of models for �ow pattern prediction: empirical and mechanistic. Empirical models are related to experimental data, where �ow pattern maps are experimentally determined and analyzed with respect to mathematical relations representing the boundaries between the �ow pattern regions. ese relations depend on the amount of experimental data used and on the coordinate system in which the data are presented. Mechanistic models are based on balance equations [1]. Notwithstanding, these models are formulated to describe single or two-phase �ows, and they cannot be highly extended for oil-gas-water mixtures, when the phases are considered heterogeneous, as in the �water-assisted �ow� case, because of the complexity of phase interaction in the multi-phase �ow. e same inadequate extension from two-to three-phase representation occurs for correlation models.
Pressure drop control for heavy oil production and transportation can be achieved by injecting water in the pipeline so as to create a water-continuous �ow known as �water-assisted �ow. � In view of the complexity of three-phase �ow, the development of an objective �ow pattern identi�cation scheme is of fundamental importance to obtain useful information about the �ow nature and control purposes as well.
In a previous paper [2], the three-phase water-assisted �ow of heavy crude oil with gas (air) in a vertical pipe was investigated at a low pressure laboratory set up. For each trio of �ow rates, �ow patterns were identi�ed by means of direct visualization (with the help of movie recording, if necessary) and total pressure drop was measured for comparison with existing correlations.
e main difficulty in visual observation is that the picture is oen confusing and difficult to interpret, especially when dealing with high velocity �ows. So, in an automatic �ow pattern identi�cation tool is broadly interesting and useful for online applications in the oil industry, particularly when the �ow visualization is not available.
In the present work, we investigate the automatic clas-si�cation of the three-phase �ow patterns described in [2] from the correspondent �ow rates and pressure drop data. is topic is suitable for �eld applications when direct visualization or tomography (impedance, ultrasonic, optical, or other) of the �ow is not possible or impracticable. So, the automatic classi�cation can be used, for instance, as a �rst step of a decision making system for analyses of real heavy oil production pipelines. It might be regarded as an alternative to the traditional physical modeling of �ow pattern transitions in rather complex �ows such as threephase, for which a uni�ed predicting model is, to the best of our knowledge, unavailable.
As an alternative to overcome the prediction difficulties with empirical and mechanistic modeling, neural networks and other data mining techniques can be used at pattern recognition and trend prediction for processes that are nonlinear, poorly understood, and too complex for accurate mathematical modeling, as three-phase �ow pattern classi�cation/identi�cation. Classi�cation is one of the important data mining tasks. Data mining is a progress to extract implicit, nontrivial, previously unknown and potentially useful information (such as knowledge rules, constraints, regularities) from data in database. Data mining is an interdisciplinary �eld. e obtained results must conform to three major requisites: accuracy, comprehensibility, and interest for the user [3].
e classi�cation corresponding to the vertical upward �ow patterns were elaborated by visual inspection by a petroleum engineer and some data mining methods were trained to learn this classi�cation: PSO/ACO2 algorithm, neural networks, support vector machines (SVM), decision tree learning algorithms (J48, REPTree and LMT), rule induction algorithm (JRIP) [4], and rules built by an expert.
Many classi�cation algorithms have been constructed and applied to discover knowledge from data in different applications, yet many suffer from poor performance in prediction accuracy in many practical domains. While it seems unlikely to have an algorithm to perform best in all the domains, it may well be possible to produce classi�ers that perform better on a wide variety of real-world domains [5].
In this paper we have also two additional purposes. e �rst one is to study the contribution of recent natural computing algorithms to solve real-world applications in the petroleum engineering area. For this goal, the PSO/ACO2 algorithm receives special attention.
Rule and tree based methods are particularly recommended in applications where knowledge comprehensibility is very important, such as in engineering processes-where discovered knowledge should be carefully validated and interpreted by experts before they are actually used to diagnose a problem, suggest an intervention procedure or recognize a pattern, rather than blindly trust the result provided by an algorithm. In this context, the second purpose is to �nd the algorithm that leads to a best comprehensibility of the real problem, because it is very important topic whenever discovered knowledge will be used for supporting a decision made by a human user. When properly designed and trained, a classi�cation tool for applications in multiphase �ow systems can potentially improve on-line monitoring and diagnostics, playing the role of a reliable, objective, and quantitative indicator of �ow regime.

Experiments in Three-Phase Water-Assisted Flow of Heavy Oil with Gas
In the following we summarize the test conditions and the main results obtained in the experiments described by Bannwart et al. [2]. e test section consisted of a 2.84 cm i.d., 2.5 m long vertical glass tubing for the three-phase �ow. e oil �ow rate was measured with a Coriolis mass �ow meter, whereas the water and air �ow rates were read in rotameters. Pressure data in the test section were measured with differential and absolute pressure transducers connected to a data acquisition system. e oil utilized was a blend of crude dead oil with a viscosity of = 5, 040 mPa⋅s and a density of = 971 kg/m 3 at 25 ∘ C. e oil phase was observed to be a w/o emulsion. e water used was tap water contained in the separator tank and the air was provided by an existing group of compressors. e experiments consisted of simultaneously �owing water, crude oil and air at several �ow rate combinations. For each set a video footage of the established �ow pattern was taken with a high-speed camera (1000 frames/s) and pressure data were collected. e experimental super�cial velocities ( varied within the following ranges: (i) oil: 0.02 < < 1.2 m/s, (ii) air: 0.04 < < 9 m/s, (iii) water: 0.04 < < 0.5 m/s. e experiments took place at ambient temperature and near atmospheric pressure. In all runs, water was always injected �rst (in order to make sure that it would be the continuous phase), followed by oil and air. e glass pipe was never observed to be fouled (hydrophilic behavior). Steady state operation was achieved aer the �ow rates and average pressure drop readings were observed to be stable.  e recorded movies were played in slow motion in order to make possible the identi�cation of the �ow patterns. Figure  1 illustrates the si� identi�ed �ow patterns, all of them watercontinuous, which were named according to the gas and oil distributions within the water-continuous phase. Figure 2 provides details of one of the �ow patterns observed in the test section.
Following a brief description of each �ow pattern is presented.
(a) Bg-Ao: Bubbly Gas-Annular Oil. is pattern is similar to heavy oil-water core �ow, e�cept that here gas bubbles are seen in the water phase. e oil-water interface is typically sinuous. is pattern occurs for high oil and low gas super�cial velocities.
(b) Ig-Ao: Intermittent Gas-Annular Oil. e gas phase forms large bubbles which partly surround a still continuous oil core. is pattern occurs for high oil and moderate gas super�cial velocities.
(c) Bg-Io: Bubbly Gas-Intermittent Oil. e gas forms small bubbles and the oil forms large bubbles. is pattern occurs for moderate oil and low gas super�cial velocities.
(d) Bg-Bo: Bubbly Gas-Bubbly Oil. is pattern was observed for low oil and gas super�cial velocities, but only when the water super�cial velocity was higher than about 0.3 m/s, which was enough to disperse the oil into bubbles.
(e) Ig-Io: Intermittent Gas-Intermittent Oil. e gas and the oil both form large bubbles which are very close to each other. Detailed observation shows that the oil bubble is sucked towards the low pressure wake behind the gas bubble. In this pattern, small oil and gas bubbles are spread in the water. �n illustration of this �ow pattern is shown in Figure 2.
is pattern occurs for high gas and oil super�cial velocities, and also for moderate gas and oil super�cial velocities.
(f) Ig-Bo: Intermittent Gas-Bubbly Oil. At high gas super�cial velocities the gas forms large, high speed bubbles and the oil is dispersed into small bubbles. is pattern is typically pulsating, indicating a transition to annular gas-liquid �ow.

Data Mining Methods
In this section, we present a brief description of the classi�cation methods used in this work: PSO/ACO2 algorithm, J48, REPTree, LMT, JRIP, neural networks, and SVM.

PSO/ACO2
Algorithm. e algorithm PSO/ACO1, originally proposed in [6,7], an algorithm proposed for the discovery of classi�cation rules in data mining problems. It was designed to hierarchical classi�cation, where the classes to be predicted are arranged in a tree-like hierarchy. is algorithm uses concepts of the Particle Swarm Optimization (PSO) algorithm, which is mainly inspired by social behavior patterns of organisms that live and interact within large groups [8], combined with Ant colony optimization (ACO), which takes inspiration from the foraging behavior of some real ant species [9].
e modi�ed version of the PSO/ACO algorithm used in this paper, hereaer denoted PSO/ACO2 [10], uses a sequential covering approach to discover one-classi�cationrule-at-a-time. e modi�cations in this algorithm include changes in the pheromone update procedure, in the quality measure evaluation, and in the rule initialization method, as well as the splitting of the rule discovery process into two separated phases.
A rule consists of an antecedent (a set of attribute-values) and a consequent (class). e consequent of the rule is the class that is predicted by that rule. e antecedent consists of a set of terms. A term is de�ned by a triple ⟨attribute, operator, value⟩, where value is a value belonging to the domain of attribute. e operator used is "=" in the case of categorical/nominal attributes, or "≤" and ">" in the case of continuous attributes. In this context, each case is assigned to one prede�ned class according to the values of its attributes for the case. e discovered knowledge is expressed in the form of -rules (1), as follows: 3.2. J48. J48 is an implementation of the well-known Quinlan algorithm (C4.5) [11], which is an improvement of the basic I�3 algorithm. is classi�er builds a decision tree for the given dataset, whose nodes represent discrimination rules acting on selective features by recursive partitioning of data, using depth-�rst strategy. e algorithm uses the fact that each attribute of the data can be used to make a decision by splitting the data into smaller subsets. To make the decision, the algorithm considers all the possible tests that can split the data set and culls a test that gives the highest information gain. For each discrete attribute, one test with outcomes for each distinct value of the attribute is considered. For each continuous attribute, binary tests involving every distinct values of the attribute are considered. In order to gather the entropy gain of all these binary tests efficiently, the training data set belonging to the node in consideration is sorted for the values of the continuous attribute and the entropy gains of the binary cut based on each distinct values are calculated in one scan of the sorted data. en a new feature is chosen and the splitting process is repeated for each attribute in a recursive manner until further splitting is not gainful. In the resulting tree structure, each inner node in the tree corresponds to an attribute, each branch represents a possible value or range of values of that attribute and each leaf represents the predicted value of target attribute.

REPTree. Reduced Error
Pruning Tree (REPTree) is a simple procedure for learning and pruning decision trees. It can build a decision or regression tree using information gain as the splitting criterion and prunes trees using reduced-error pruning. It only sorts values for numeric attributes once.
e procedure covers the internal nodes of the tree from the bottom to the top and veri�es each internal node. e goal is to state whether replacing it with the most frequent class does not reduce the trees accuracy. If accuracy is not reduced then the node is pruned. Pruning is used to �nd the best subtree of the initially grown tree with the minimum error for the test set. is process continues until any further pruning would decrease the accuracy. e procedure stops with the smallest accurate (lowest classi�cation error) sub-tree with respect to a given pruning set.

LMT. Logistic
Model Tree (LMT) combines a standard tree structure with logistic regression functions at the leaves using posterior class probabilities to produce a single decision tree [12]. LMT consists of a tree structure that is made up of a set of inner nodes and a set of leaves or terminal nodes in an instance space. A test on one of the attributes is associated with every inner node. For numeric attributes, the leaf node has two child nodes which is branched right and le depending on the threshold. If the value of the numeric attribute is smaller than the threshold it is sorted to le branch and value of attribute greater than the threshold it is sorted to right branch otherwise. e threshold is usually �xed by Logit Boost method. For nominal attributes with values, the branch has child nodes, so that the instances are sorted down one of the branches, according to their value of the attribute.
An algorithm for building logistic model trees has the following three steps: growing the tree, building the logistic models, and pruning. Brie�y, the tree induction process iden-ti�es subdivisions by recursively splitting the instance space in a divide-and-conquer fashion until further subdivisions are not gainful.
3.5. JRIP. JRIP implements repeated incremental pruning to produce error reduction (RIPPER) in Java, a prepositional rule learner, as proposed by Cohen [13]. e RIPPER rule learning algorithm is an extended version of learning algorithm IREP (incremental reduced error pruning). Rules are Journal of Petroleum Engineering 5 created for every class in the training set and are then pruned. In this algorithm, the discovered knowledge is represented in the form of -prediction rules, which have the advantage of being a high-level and symbolic knowledge representation contributing towards the comprehensibility of the discovered knowledge [14].
e method is based on the construction of a rule set in which all positive examples are covered. Initially, the current set of training examples are partitioned into two subsets, a growing set and a pruning set. e rule is constructed from examples in the growing set. e rule set initiates with an empty rule set and rules are added incrementally to the rule set until no negative examples are covered. Aer that, JRIP replaces or revises individual rules by using reduced error pruning in order to increase the accuracy of rules. It replaces or revises individual rules by using reduced error pruning. To prune a rule the algorithm takes in account only a �nal sequence of conditions from the rule and sorts the deletion that maximizes the function.

Neural Networks.
Arti�cial neural networks (ANNs) are adaptive systems with the power of a universal computer. ey are massive parallel processors comprised of single interconnected arti�cial neurons and are able to realize an arbitrary mapping (association) of one vector space (inputs) to the other vector space (outputs) �nding patterns in data, using a computational model for information processing. ey are being used with increasing frequency for high dimensional problems, either to approximate a posteriori probabilities for classi�cation or regression [4]. Neural networks are analytical techniques, which are capable of acquiring the knowledge of the complex process of an environment from the observed data, storing the knowledge of underlying process, and making it available to apply to new observations of same data types for pattern recognition purposes. Two commons neural networks' models used for these tasks are Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF).
In the most common form, neural networks are composed by hidden layers of multiple arti�cial neurons connected to the inputs and outputs neurons with different weights, which correspond to synapses in the biological neuron. Neurons are processing units that that apply nonlinear activation functions to approximate complex functions in the data. e weights are iteratively adjusted during the training procedure using any given approximation technique, such as gradient descendent method, by comparing desired inputs with observed inputs, until a stop criterion is reached. Training or learning procedure is the process of �nding the best set of weights for the neural network, mapping the relationships between predictor and target variables.
One key criticism of ANNs is that are a "black box. " e nature of the relationship between independent (inputs) and dependent variables (outputs) is usually not revealed and the importance of each variable is not made explicit. Any functional form or map of the relationships is not supplied by ANNs, because of the complexity of the functions used in the neural network approximations.

Support Vector Machine. Support Vector Machine
(SVM) is primarily a classi�er method that performs grouping tasks by constructing hyperplanes in a multidimensional space that separates cases of different class labels. In order to construct an optimal hyperplane, SVM employees an iterative training algorithm, that is used to minimize an error function. e foundations of SVM have been developed by Vapnik [15] and are gaining popularity due to many attractive features, and promising empirical performance.
SVM �nds a linear separating hyperplane with the maximal margin in this higher dimensional space. e kernel function allows the algorithm to �t the maximum-margin hyperplane in the transformed feature space. ere are four basic kernels: linear, polynomial, radial basic function (RBF) and sigmoid. SVMs are based on the structural risk minimization (SRM) principle from statistical learning theory.
is classi�er method is also considered a "black-box" and does not offer typically any interpretation about the relationship between independent and dependent variables.

Results and Discussion
e classi�ers tested in this work were modeled using the four inputs, representing the independent variables, which in this case are the super�cial velocities of oil, water and gas (respectively, , , ) and pressure gradient (Δ . e output is one of the six target class previously classi�ed by the expert (Bg-Ao, Bg-Bo, Bg-Io, Ig-Ao, Ig-Bo, and Ig-Io) representing each �ow pattern according to Figure 1.
Experimental records of three-phase �ow of heavy oil with gas and water in a vertical pipe data set consisting of 119 samples were used for the training and evaluation of the implemented classi�er. For the classi�ers' training, the whole data set was randomly separated into two subsets: 75% as training subsets (89 samples) and 25% as testing subsets (30 samples) aer training. e training set contains 9, 5, 6, 21, 38 and 10 samples, respectively, for Bg-Ao, Bg-Bo, Bg-Io, Ig-Ao, Ig-Bo, and Ig-Io classes. e correspondent distribution for the test dataset is 2, 1, 3, 5, 13, and 6 samples, respectively.
In the classi�cation task, aer the discovered rules from a set of training data, those rules must be applied to a set of test data (unseen during training), and hopefully predict the correct class in the test set. us, the accuracy rate for unseen samples is for us the most important index to evaluate the classi�er's e�ciency, because it proofs its generalization ability.
e performance of the PSO/ACO2 classi�er employed to identify the �ow patterns was assessed through comparisons between original and estimated outputs taken from the data subsets used both in training and in testing procedure samples for four different types of machine learning algorithms, one knowledge rule model developed by a petroleum engineer expert, two neural networks model and three SVM kernels. Experiments for classi�cation with swarm intelligence techniques were conducted using PSO/ACO2 soware developed by Nicholas Holden and provided in the Source-Forge (available at http://sourceforge.net/projects/psoaco2/) project site. Upon experimentation, the suitable numbers of particles and iterations were found to be both 100 and the number of uncovered examples per class (MaxUncovExamp-PerClass) to 2. For PSO algorithm the constriction factor is , and cognitive and social learning coefficients are 1 5. For the Machine Learning experiments with rule and tree based algorithms (JRip, J48, RepTree and LMT), we used well-known tree and rule based classi�cation algorithms available in the Waikato Environment for Knowledge Analysis (WEKA) soware package [14].
e neural networks (NN) models explored for this experiment are: Multi-Layer Perceptron (MLP) and Radial Basis Function (RBF). On MLP neural network, four neurons were used in input layer, representing the independent variables like PSO/ACO2, ten neurons were employed in hidden layer and six neurons were used in output layer, representing each �ow pattern. e amount of neurons in the hidden layer was found by experimentation, aer assessing which con�guration would yield the least global training error. e activation function used at each level was sigmoid tangent for hidden and output layer neurons. e supervised training algorithm used was the Backpropagation with weights and biases updating according to Levenberg-Marquardt optimization algorithm. For the RBF network, 35 hidden layer neurons were employed using Gaussian function with coefficient of spread ( ) equal to 0.1, with a linear activation function had been used on the six output neurons. e soware Matlab MathWorks Inc. v.7.4 was used to implement the neural networks models employed in this work.
We have also used multi-class SVM Type 1 for the classi�cation task, considering the �one-against-one� method for decomposing multi-class problem in binary subproblems. Linear, polynomial, and RBF functions were tested as the mapping function (kernel) for the classi�cation system. Matlab was used to implement the SVM model mentioned in this work. e SVM classi�er was modeled using the four inputs, representing the independent variables and the output is one of the six target class, as de�ned before. e complete description of this procedure can be consulted in [15].
In this work, the data were also interpreted according to the set of preestablished rules by an expert. e human knowledge was represented by a set of -rules. In order to build these rules, human knowledge regarding characteristics of each �ow pattern and the relation of each pattern with the four parameters measured with the experiment was determined by inspection of the dataset. For sake of comparing with the other data mining methods, the data were separated in the same training and test sets for evaluation with the expert rules.
All the experiments were obtained on a Centrino Duo PC (CPU 1.83 GHZ, RAM 2 GB) for the same datasets. Table 1 indicates the classi�cation accuracy of PSO/ ACO2 algorithm for training and test sets, in the classi�cation task of vertical �ow patterns, using the settings parameters mentioned earlier and the discovered rules, compared with others data mining methods. e PSO/ACO2 algorithm was able to achieve a success rate of 68.56% in the training set, the worst performance among the other methods, and 70% in the test set, one of the best performances among the other classi�ers. e hybrid particle swarm optimization/ant colony optimization algorithm produced in the training phase 13 classi�cation rules used to identify the vertical �ow patterns as indicated in Algorithm 1. All patterns were covered with this rule set.
In contrast with JRIP, which is another classi�er based on discovering rules, PSO/ACO2 presented a best performance for unseen data (test set). JRIP produced only six simple rules for classifying the �ow patterns, as detailed in Algorithm 1. e methods based on decision trees, J48, RepTree, and LMT demonstrated better results to learn the patterns during the training, notwithstanding the scores for testing do not outperformed PSO/ACO2, except RepTree, which had the same efficiency (70%). Figure 3 displays the knowledge tree provided by Rep-Tree, containing 17 decision leaves. e variable is referred only to distingue the Ig-Ao and Bg-Ao classes. In the tree we can observe that no rules for Bg-Bo and Ig-Io were created. us, the recognition of these patterns is completely wrong using this solution.
Expert rules have found 80% of success in identifying the test samples, with a lower rate for the training set (73.03%), which was the worst among all the other techniques, apart from PSO/ACO2 algorithm. e expert has used nine rules to represent his knowledge about de �ow patterns. According to those rules, the variable is used only to aid detecting the Bg-Bo class. A comprehensive observation of the rules appoint that a pressure drop (Δ superior to 9300 Pa/m causes almost always a bubble regime in the gas phase, where the oil regime is determined by the super�cial velocities. Otherhand, a pressure drop lower than 8700 Pa/m originates certainly an intermittent regime in the gas phase, so that the oil regime is determined by the others variables. In the intermediate range of drop pressure, between 8700 and 9300 Pa/m, depending on the values of the four measured variables, the possible �ow patterns are only Bg-Bo, Ig-Io and Ig-Ao.
Despite their ineptitude to generate descriptive information about the classi�cation process, which could useful to better understand the physical phenomenon under study, neural networks and SVMs have presented superior prediction accuracy for both training and test sets than the metaheuristic methods and expert rules, as observed in Table 1. Polynomial SVM presented the best recognition score among all methods, classifying correctly all samples of the training set and obtaining 73.33% of recognition score for the test set.
With regard to the moderate accuracy rate for the vertical upward �ow pattern classi�cation of the investigated methods, it is supposed that this survey is due to the intermittent phase, which makes complex a correct prediction as reported in [16]. In all runs with every classi�er, the patterns composed with a part of the intermittent regime had an expressive misrecognition, principally the Ig-Io class.

Conclusion
Flow pattern prediction in industrial systems that rely on complex multi-phase �ows is essential for their safety, control, diagnostics, and operation. In oil extraction and oilgas-water mixture transporting processes, the identi�cation of �ow regime is one of the essential tasks for the purpose of maintaining optimal operating and improving the performance of equipment. Usually, different �ow regimes produce distinct performances of the system. However, identifying/classifying multiphase mixture continuously and precisely is still a signi�cant and unsolved problem, due to the highly nonlinear nature of the forces which rule the �ow regime transitions.
In this paper, we use the PSO/ACO2 algorithm for data mining, a hybrid method for mining classi�cation rule. We have compared the performance of PSO/ACO2 with others data mining methods. Experimental results show that PSO/ACO2 has a predictive accuracy for untrained data (test set) greater than the others evaluated heuristic methods. Nevertheless, the black-box methods (neural networks and SVM) have shown a higher precision for predicting patterns than PSO/ACO2 and the others heuristic algorithms. Because the application of swarm intelligent algorithm in data mining, especially in classi�cation rule mining, is still in infant periods, we believe that improvements in this methodology could increase the accuracy for the pattern detection, so that this kind of approach could be suitable for real world applications in Petroleum Engineering area.
Rule base methods are particularly recommended in applications where rule comprehensibility is very important, such as in engineering processes-where discovered rules should be carefully interpreted by experts before they are actually used to recognize a pattern.
Although the generation of classi�cation rules by an expert is a feasible process, producing good results, it is an exhaustive and tedious task, mainly when a great number of parameters and samples must be analyzed. e automated classi�cation of the data is vital when a huge volume of information is involved. e approach and methods used in this work contribute to an in-depth understanding of �ow patterns dynamics, especially in the cases of multiphase �ows, aiming extraction of simple rules for identifying �ow pattern features. We intend to encourage researchers of the Petroleum Engineering area to use data mining to analyze real data in different domains as well.
A future research direction consists of exploring others techniques based on rule mining. Further work includes also dealing with a deeper study of the important features of threephase �ow of heavy oil in vertical pipe in order to obtain better classi�er systems.