Summary This paper presents two artificial neural network (ANN) models to identify the flow regime and calculate the liquid holdup in horizontal multiphase flow. These models are developed with 199 experimental data sets and with three-layer back-propagation neural networks (BPNs). Superficial gas and liquid velocities, pressure, temperature, and fluid properties are used as inputs to the model. Data were divided into three portions: training, cross validation, and testing. The results show that the developed models provide better predictions and higher accuracy than the empirical correlations developed specifically for these data groups. The developed flow-regime model predicts correctly for more than 97% of the data points. The liquid-holdup model outperforms the published models; it provides holdup predictions with an average absolute percent error of 9.407, a standard deviation of 8.544, and a correlation coefficient of 0.9896. Introduction Multiphase flow is defined as the concurrent flow of two or more phases (liquid, solid, or gas) in which the motion influences the interface between the phases. The flow regime or flow pattern is a qualitative description of the phase distribution in the pipe. There are three types of flow regimes in horizontal gas-liquid flow, namely, segregated, intermittent, and distributive flows. Segregated flow is further classified into stratified smooth, stratified wavy, and annular flow regimes. The intermittent flow regimes are slug and plug (elongated bubble) flows. Distributive flow regimes include bubble and mist flows.1 Other investigators2 classified flow regimes in horizontal gas-liquid flow as bubble flow (in which gas bubbles tend to float at the top in the liquid), stratified flow (in which the liquid flows along the bottom of the pipe and the gas flows on top), intermittent or slug flow (in which large frothy slugs of liquid alternate with large gas pockets), and annular flow (in which a liquid ring is attached to the pipe wall with gas blowing through). The layer at the bottom is usually much thicker than the one at the top. The flow regimes in horizontal gas-liquid flow are illustrated in Fig. 1. Predicting flow regimes is essential for properly calculating the pressure drop across the pipe under different multiphase flow conditions. Flow-regime maps have been developed and are used to predict flow regimes in horizontal gas-liquid flow. Most are plots of superficial liquid velocity vs. superficial gas velocity. One of the first maps used in the oil industry is that of Baker.3 Ten years later, it was modified by Scott.4 Beggs and Brill5 and Mandhane6 presented other flow-pattern maps that were constructed based on experimental data. Taitle and Dukler7 developed a theoretical model for the flow regime transitions in horizontal gas-liquid flow. Recently, other studies have been carried out for the prediction of specific transitions. Separate models have been developed for stratified,8–10 slug,11–14 annular,15–16 and dispersed bubble flows.17 An example of these flow-pattern maps is given in Fig. 2. Predicting liquid holdup in the pipeline is very important to the petroleum industry. Liquid holdup, defined as the fraction of pipe occupied by liquid, must be predicted to properly design separation equipment and slug catchers in pipeline operations. Many correlations have been published for predicting this important parameter, of which the most commonly used are Eaton and Brown,18 Guzhov et al.,19 Beggs and Brill,5 Minami and Brill,20 Brill et al.,21 Gregory et al.,22 Mukherjee and Brill,23 Hughmark and Pressburg,24 Hughmark,25 Abdul-Majeed,26,27 Xiao et al., 28 Baker et al.,29 and Gomez et al.30 This paper presents ANN models for identifying the flow regime and predicting the liquid holdup in horizontal gas-liquid flow. Published experimental data were used to train and test the neural-network models developed. Superficial gas and liquid velocities, pressure, temperature, and fluid properties are used as input to the models. The output of the first model is the flow regime, while the other model predicts the liquid holdup. ANNs are parallel-distributed information-processing models that can recognize highly complex patterns within available data. In recent years, neural network use has gained popularity in petroleum applications,31 but few studies were carried out to model multiphase flow using neural networks. Van der Spek and Thomas32 used neural networks to identify the flow regime with band spectra of flow-generated sound. They concluded that the flow regime can be classified correctly by a neural network in up to 87% of all cases studied with one-third octave band spectra of flow-generated sound plus the pipe inclination angle. Ternyik et al.33 used neural networks to predict the holdup and flow pattern in pipes under various angles of inclinations. They developed neural- network models based on experimental data limited to a 1.5-in. pipe and low operating pressures and a Kohonen-type network to classify the flow patterns with all input data. The resulting classifications were used as data input to another model for predicting holdup. Their model predicted holdup values with a correlation coefficient of 0.945. The other neural-network model developed for flow-pattern prediction was based on slug, bubble, annular mist, and stratified flows. It predicted a minimum of 82.8% (in bubble flow) and a maximum of 93.3% (in slug flow).

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractReservoir fluid properties are very important in reservoir engineering computations such as material balance calculations, well test analysis, reserve estimates, and numerical reservoir simulations. Ideally, these properties should be obtained from actual measurements. Quite often, however, these measurements are either not available, or very costly to obtain. In such cases, empirically derived correlations are used to predict the needed properties. All computations, therefore, will depend on the accuracy of the correlations used for predicting the fluid properties.This study presents Artificial Neural Networks (ANN) model for predicting the formation volume factor at the bubble point pressure. The model is developed using 803 published data from the Middle East, Malaysia, Colombia, and Gulf of Mexico fields. One-half of the data was used to train the ANN models, one quarter to cross-validate the relationships established during the training process and the remaining one quarter to test the models to evaluate their accuracy and trend stability. The results show that the developed model provides better predictions and higher accuracy than the published empirical correlations. The present model provides predictions of the formation volume factor at the bubble point pressure with an absolute average percent error of 1.789%, a standard deviation of 2.2053% and correlation coefficient of 0.988. Trend tests were performed to check the behavior of the predicted values of B ob for any change in reservoir temperature, Gas Oil Ratio (GOR), gas gravity and oil gravity. The trends were found to obey the physical laws.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractReservoir fluid properties data are very important in reservoir engineering computations such as material balance calculations, well testing, reserve estimates, and numerical reservoir simulations. Ideally, those data should be obtained experimentally. On some occasions, these data are not either available or reliable; then, empirically derived correlations are used to predict PVT properties. However, the success of such correlations in prediction depends mainly on the range of data at which they were originally developed. These correlations were developed using linear, non-linear, multiple regression or graphical techniques.Recently, researchers utilized artificial neural networks (ANN) to develop more accurate PVT correlations. ANNs are biologically inspired non-algorithmic, non-digital, massively parallel distributive and adaptive information processing systems. They resemble the brain in acquiring knowledge through learning process, and storing knowledge in interneuron connection strengths.The present study presents new models developed to predict the bubble point pressure and, the formation volume factor at the bubble point pressure.The models were developed using 283 data sets collected from Saudi reservoirs. These data were divided into three groups: the first was used to train the ANN models, the second was used to crossvalidate the relationships established during the training process and, the last was used to test the models to evaluate their accuracy and trend stability. Trend tests were performed to ensure that the developed model would follow the physical laws. Results show that the developed models outperform the published correlations in terms of absolute average percent relative error, and standard deviation.

Accurate prediction of pressure drop for multiphase flow in horizontal and near horizontal pipes is needed for effective design of flow lines and piping networks. The increased application of horizontal wells further signified the need for accurate prediction of pressure drop. Several correlations and mechanistic models have been developed since 1950. In addition to the limitations on the applicability of all existing correlations, they all fails to provide the desired accuracy of pressure drop predictions. The recently developed mechanistic models provided some improvements in pressure drop prediction over the empirical correlations. However, there is still a need to further improve the accuracy of prediction for a more effective and economical design of wells and surface piping networks. This paper presents an Artificial Neural Network (ANN) model for prediction of pressure drop in horizontal and near-horizontal multiphase flow. The model 1 ORDER REPRINTS was developed and tested using field data covering a wide range of variables. A total of 225 field data sets were used for training-and 113 sets data for cross-validation of the model. Another 112 sets of data were used to test the prediction accuracy of the model and compare its performance against existing correlations and mechanistic models. The results showed that the present model significantly outperforms all other methods and provides predictions with accuracy that has never been possible. A trend analysis was also conducted and showed that the present model provides the expected effects of the various physical parameters on pressure drop.

Accurate prediction of pressure drop in vertical multiphase flow is needed for effective design of tubing and optimum production strategies.Several correlations and mechanistic models have been developed since 1950.In addition to the limitations on the applicability of all existing correlations, they all fails to provide the desired accuracy of pressure drop predictions.The recently developed mechanistic models provided little improvements in pressure drop prediction over the empirical correlations.However, there is still a need to further improve the accuracy of prediction for a more effective and economical design of wells and better optimization of production operations. This paper presents an Artificial Neural Network (ANN) model for prediction of the bottom-hole flowing pressure and consequently the pressure drop in vertical multiphase flow.The model was developed and tested using field data covering a wide range of variables.A total of 206 field data sets collected from Middle East fields; were used to develop the ANN model. These data sets were divided into training, cross validation and testing sets in the ratio of 3:1:1. The testing subset of data, which were not seen by the ANN model during the training phase, was used to test the prediction accuracy of the model and compare its performance against existing correlations and mechanistic models.The results showed that the present model significantly outperforms all existing methods and provides predictions with higher accuracy.This was verified in terms of highest correlation coefficient, lowest average absolute percent error, lowest standard deviation, lowest maximum error, and lowest root mean square error.A trend analysis was also conducted and showed that the present model provides the expected effects of the various physical parameters on pressure drop. Introduction A reliable and accurate way of predicting pressure drop in vertical multiphase flow is essential for the proper design of well completions and artificial-lift systems and for optimization and accurate forecast of production performance. Because of the complexity of multiphase flow, mostly empirical or semi-empirical correlations have been developed for prediction of pressure drop. Numerous correlations have been developed since the early 1940s. Most of these correlations were developed under laboratory conditions and are, consequently, inaccurate when scaled-up to oil field conditions[1].The most commonly used correlations are those of (Hagedorn and Brown[2]; Duns and Ros[3]; Orkiszewski[4]; Beggs and Brill[5]; Aziz and Govier[6]; Mukherjee and Brill correlation[7]). Numerous studies were done to evaluate and study the applicability of those correlations under different ranges of data[8–15].Most researchers agreed upon the fact that no single correlation was found to be applicable over all ranges of variables with suitable accuracy[1].It was found that correlations are basically statistically derived, global expressions with limited physical considerations, and thus do not render them to a true physical optimization. Mechanistic models are semi-empirical models used to predict multiphase flow characteristics such as liquid hold up, mixture density, and flow patterns. Based on sound theoretical approach, most of these mechanistic models were generated to outperform the existing empirical correlations.The most widely used mechanistic models are those of Hasan and Kabir[16]; Ansari et al.[17].; Chokshi et al.[18]; Gomez et al.[19]. Other studies were conducted to evaluate the validity of such mechanistic models[20–22].Generally, each of these mechanistic models has an outstanding performance in specific flow pattern prediction and that is made the adoption for certain model of specific flow pattern by investigators to compare and yield different, advanced and capable mechanistic models.