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The prediction of volume fractions in order to measure the multiphase flow rate is a very important issue and is the key parameter of multi-phase flow meters (MPFMs). Currently, the gamma ray attenuation technique is known as one of the most precise methods for obtaining volume fractions. The gamma ray attenuation technique is based on the mass attenuation coefficient, which is sensitive to density changes; density is sensitive in turn to temperature and pressure fluctuations. Therefore, MPFM efficiency depends strongly on environmental conditions. The conventional solution to this problem is the periodical recalibration of MPFMs, which is a demanding task. In this study, a method based on dual-modality densitometry and artificial intelligence (AI) is presented, which offers the advantage of the measurement of the oil–gas–water volume fractions independent of density changes. For this purpose, several experiments were carried out and used to validate simulated dual modality densitometry results. The reference density point was established at a temperature of 20 °C and pressure of 1 bar. To cover the full range of likely density fluctuations, four additional density sets were defined (at changes of ±4% and ±8% from the reference point). An annular regime with different percentages of oil, gas and water at different densities was simulated. Four features were extracted from the transmission and scattered detectors and were applied to the artificial neural network (ANN) as inputs. The input parameters included the 241Am full energy peak, 137Cs Compton edge, 137Cs full energy peak and total scattered count, and the outputs were the oil and air percentages. A multi-layer perceptron (MLP) neural network was used to predict the volume fraction independent of the oil and water density changes. The obtained results show that the proposed ANN model achieved good agreement with the real data, with an estimated root mean square error (RMSE) of less than 3.

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... This is unsuitable for area-averaged measurements across the pipe cross section. For this purpose, broad beam gamma ray techniques are in use (Hanus et al., 2018;Nazemi et al., 2016;Roshani et al., 2015Roshani et al., , 2017. In the broad beam method, instead of a collimated beam, a diverging gamma beam covering the entire pipe diameter is used. ...

Flow-induced vibration (FIV) is a common phenomenon observed in internal flows and is frequently encountered in technical systems like process plants, nuclear plants, oil-piping or heat exchangers. Compared to single-phase flows, FIV is more difficult to predict and analyze for internal two-phase flows. As a result, experimental data and analysis tools related to two-phase flow are limited to specific aspects or conditions. Another problem is that for real-world applications, FIV analysis is applied to multi-structural components, which becomes complicated due to the size of the technical systems. Thus, experimental studies are usually realized first within the laboratory using a prototype of the original structure. Besides experimental investigations, Computational Fluid Dynamics (CFD) is increasingly adopted and already a prevalent tool for FIV assessment. However, further development in CFD models and methods is necessary in order to complement the experimental database. Additionally, CFD is useful for enhanced understanding of fundamental aspects of two-phase flows, and for gaining insights from situations where experiments are difficult or infeasible, such as in deep-sea bore-wells, sub-sea riser pipelines, and in nuclear installations. It is also known that there is a lack of sufficiently accurate empirical correlations for terms related to mass, momentum, and energy transfer across the phases for two-phase flows, and CFD can be useful in this respect. Furthermore, for estimating the accuracy of CFD models, comparisons with benchmark results for two-phase, internal, multi-structural flows are necessary. Unfortunately, the experimental database involving internal two-phase flows is very limited, and this is a bottleneck for the development of computational techniques. The following contribution presents a review of the research on FIV involving two-phase internal flows with relevance to multi-structural components. Methodological literature for two-phase flow measurements along with the latest applications are put forth. Problem areas of two-phase FIV systems have been brought out, and future avenues of research for two-phase, internal FIV are identified. The following specific areas of two-phase FIV are reviewed. Two-phase FIV in subsea risers and in pipeline riser systems is discussed. The slug flow regime is analyzed in particular due its predominant impact on two-phase FIV. Parameters affecting two-phase FIV along with two-phase correlations are discussed. Power Spectrum Density (PSD) and Fourier transform applications for two-phase FIV form another section. Latest research efforts involving the two-way interaction of fluid and structure are presented. Both numerical and experimental works have been reviewed. The bulk of the important works for two-phase FIV is experimental in nature. Numerical models and computational power have not been developed enough for simulating more complex, multistructural flows. They are limited to simple cases involving simplified computational models. Experimental efforts for large multistructural components involve the initial use of prototypes and can prove to be costly for fully developed industrial-scale rigs. However, experimentation currently holds an irreplaceable position in two-phase FIV studies.

... To evaluate the performances of the proposed ANFIS-FFA method, the traditional ANFIS, the back propagation neural network (BPNN) and the extreme learning machine (ELM), four statistical benchmark indices, including the root mean squared error (RMSE), the correlation coefficient (R), the mean absolute error (MAE), and the mean absolute percentage error (MAPE), were adopted in this study and were expressed as follows [25,26]: where y i and ŷ i are the actual and predicted compressive strengths of HSC, respectively. y i and ŷ i are the average results of the actual and predicted compressive strengths of HSC, respectively. ...

To estimate the compressive strength of high-strength concrete (HSC), a hybrid model integrating the firefly algorithm (FFA) and fuzzy c-means (FCM) clustering method into the adaptive neuro fuzzy inference system (ANFIS) was developed in this paper. The FFA and FCM techniques were utilized to improve the forecasting accuracy of the proposed ANFIS. To establish the hybrid ANFIS-FFA model, five main constituents of HSC, cement, water, fine and coarse aggregates, and superplasticizer, are considered the input variables, and the compressive strength of HSC is used as the output variable. A comparison was conducted among four artificial intelligence models, including the proposed ANFIS-FFA model, the traditional ANFIS, the back propagation neural network (BPNN) and the extreme learning machine (ELM), in terms of four statistical indices. In addition, a detailed parametric study was conducted to investigate the influence of each input variable on the compressive strength of HSC. The results showed that the developed ANFIS-FFA model exhibits greater accuracy than the other three models, with a higher correlation coefficient (R) and lower root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) values, and it has great potential to accurately estimate the compressive strength of HSC.

... A few possibilities are the measurement of void fraction in two-phase flows independent of the flow regime, which is an essential parameter in oil production (Nazemi et al., 2016); the identification of changes in fluid flow properties that can interfere in the equipment used to measure multiphase flow in pipelines (Roshani et al., 2017); the identification of the interface region formed in the transport of oil by-products in pipelines (Salgado et al., 2020); or the identification of type and amount of oil by-products transported in pipelines, so that possible mixtures can be redirected to separation tanks (Roshani et al., 2020). Other examples can be found in the references Johansen et al., 2000;Holstad et al., 2005;Khabaz et al., 2015;and Roshani et al., 2015. In this study, a noninvasive method to determine the salt concentration in seawater was developed. ...

In the oil production industry, water is used as a fluid injected into the well to raise the oil when the well is depressurized. Water thus produced presents variations in the concentrations of dissolved salts, as there is a mixture of different types of water, related to its origin (such as connate water, sea water). Because it is reused in oil production, water needs to be monitored to maintain the standard suitable for its use as it can be hypersaline, contributing to the encrustation of pipes and contamination of underground water reservoirs. In this study, a noninvasive method was developed to determine the salt concentration in seawater. The method uses a detection system that contains a NaI(Tl) detector, a²⁴¹Am source, and a sample holder to measure the mass attenuation coefficient of saltwater samples. For validation, the same setup was also simulated using the MCNPX code. Saltwater samples with different concentrations of NaCl and KBr were used as a proxy for seawater. The mass attenuation coefficients for the simulation exhibited the smallest relative errors (up to 6.2%), and the experimental ones exhibited the highest relative errors (up to 25%) when compared with theoretical values.

... In [22], a method was proposed in order to determinate the void fraction in two-phase flow independent of density changes using ANN. In [23], it was shown that a combination of ANN and gamma-ray densitometer can be used to measure the volume fractions independent of density changes in multiphase flows. ...

The main objective of the present research is to combine the effect of scale thickness on the flow pattern and characteristics of two-phase flow that is used in oil industry. In this regard, an intelligent nondestructive technique based on combination of gamma radiation attenuation and artificial intelligence is proposed to determine the type of flow pattern and gas volume percentage in two phase flow independent of petroleum pipeline’s scale layer thickness. The proposed system includes a dual energy gamma source, composed of Barium-133 and Cesium-137 radioisotopes, and two sodium iodide detectors for recording the transmitted and scattered photons. Support Vector Machine was implemented for regime identification and Multi-Layer Perceptron with Levenberg Marquardt algorithm was utilized for void fraction prediction. Total count in the scattering detector and counts under photo peaks of Barium-133 and Cesium-137 were assigned as the inputs of networks. The results show the ability of presented system to identify the annular regime and measure the void fraction independent of petroleum pipeline’s scale layer thickness.
(https://www.sciencedirect.com/science/article/pii/S1110016820306256?via%3Dihub)

... Moreover, the optimization of three-phase flow metering setup using two transmission detectors have been reported using gamma-ray technique and ANN modeling in the literature (Roshani et al., 2017a). In all previous studies, different methods such as dual modality, multi-beam gamma-ray and etc. have been utilized to identify the regime and volume fraction in a static condition while they assumed that the temperature was fixed (Nazemi et al., 2014;Roshani et al., 2015). However, an experimental study was not reported yet to address the investigation of temperature effect on the two-phase flow systems in dynamic conditions. ...

In radiation-based multiphase systems, the temperature can affect radiation counting and consequently cause an error in the
measurement of flow rates as well as volume fractions. In this work, a new methodology was proposed and implemented for identification of flow rates independent of temperature that includes a neural network modeling in addition to the experimental works on a two-phase flow loop in the laboratory. The proposed ANN model was trained and tested in normal working temperature of 295 K. To predict the air and the water flow rates corresponding to the other temperatures defined in the range, detector response was corrected using the calibration curve and then fed to the ANN. The results showed that the average value of relative differences pertaining to the water and the air flow
rates was efficiently reduced below 10%, after correcting the temperature effects. Overall results revealed that using the methods and procedures in this work, two-phase flow rates can be accurately predicted not only independent of the temperature effects but also with a minimum effort needed for training a simple neural network.

... Artifi cial neural networks (ANNs) constitute a conventional technique for the classifi cation and analysis of data. Processing various data in the ANNs may yield helpful information about the system; hence, data adjustment plays a signifi cant role in their application [11][12][13][14]. An ANN is defi ned as an input--output system in which hidden layers do the required processes. ...

Multiphase flow meters are used to measure the water-liquid ratio (WLR) and void fraction in a multiphase fluid stream pipeline. In the present study, a system of multiphase flow measurement has been designed by application of three thallium-doped sodium iodide scintillators and a radioactive source of 133Ba simulated by Monte Carlo N-particle (MCNP) transport code. In order to capture radiations passing across the pipe, two direct detectors have been installed on opposite sides of the radioactive source. Another detector has been placed perpendicular to the transmission beam emitted from the 133Ba source to receive radiations scattered from the fluid flow. Simulation was done by the MCNP code for different volumetric fractions of water, oil, and gas phases for two types of flow regimes, namely, homogeneous and annular; training and validation data have been provided for the artificial neural network (ANN) to develop a computation model for pattern recognition. Depending on applications of the neural system, several structures of ANNs are used in the current paper to model the flow measurement relations, while the detector outputs are considered as the input parameters of the neural networks. The first, second, and third structures benefit from two, three, and five multilayer perceptron neural networks, respectively. Increasing the number of ANNs makes the system more complicated and decreases the available data; however, it increases the accuracy of estimation of WLR and gas void fraction. According to the results, the maximum relative difference was observed in the scattering detector. It was clear that transmission detectors would demonstrate the difference between the flow regimes as well. It is necessary to note that the error calculated by the MCNP simulator is

... In the ANFIS context, if the RMSE measure is not satisfactory, the adjustment of membership functions and the rule refinement procedure is activated towards better optimisation of the model. Therefore, the RMSE is used to evaluate the performance of ANFIS in this study, as shown in the following equation (Roshani, Feghhi, & Setayeshi, 2015;Eftekhari Zadeh, Feghhi, Roshani, & Rezaei, 2016): ...

This paper presents an adaptive neuro-fuzzy inference system (ANFIS) for the assessment of internal stability of soils under seepage. The training of fuzzy system was performed by a hybrid method of back-propagation (BP) and least mean square algorithm, and the subtractive clustering algorithm was utilised for optimising the number of fuzzy rules. Experimental data on internal stability of soils in the literature were used to validate and evaluate the performance of the proposed ANFIS model. Further, predictions from three models (the BP model, the particle swarm optimisation-BP model and the ANFIS model) were compared with the experimental data. The results show that the ANFIS model is a feasible, efficient and accurate tool for predicting the internal stability of soils according to Wan and Fell’s criterion.

... In the ANFIS context, if the RMSE measure is not satisfactory, the adjustment of membership functions and the rule refinement procedure is activated towards better optimisation of the model. Therefore, the RMSE is used to evaluate the performance of ANFIS in this study, as shown in the following equation (Roshani, Feghhi, & Setayeshi, 2015;Eftekhari Zadeh, Feghhi, Roshani, & Rezaei, 2016): ...

This paper presents a hybrid genetic algorithm (GA) and support vector machine (SVM) techniques to predict the potential of soil liquefaction. GA is employed in selecting the optimal values of the kernel function and the penalty parameter in SVM model to improve the forecasting accuracy. The database used in this study includes 109 CPT-based field observations from five major earthquakes between 1964 and 1983. Several important parameters, including the cone resistance, total vertical stress, effective vertical stress, mean grain size, normalized peak horizontal acceleration at ground surface, cyclic stress ratio, and earthquake magnitude, were used as the input parameters, while the potential of soil liquefaction was the output parameter. The predictions from the GA-SVM model were compared with those from three methods: grid search (GS) method, artificial neural network (ANN) model, and C4.5 decision tree approach. The overall classification success rates for the entire dataset predicted by GA-SVM, ANN, C4.5 decision tree, and GS-SVM models are 97.25, 97.2, 96.3, and 92.66 %, respectively. The study concluded that the proposed GA-SVM model improves the classification accuracy and is a feasible method in predicting soil liquefaction.

Multiphase flowmeters have an important role to play in the industry and any attempts that lead to improvements in this field are of great interest. In the current study, group method of data handling (GMDH) technique was applied in order to increase measuring precision of a simple photon attenuation based two-phase flowmeter that has the ability to estimate the gas volumetric percentage in a two-phase flow without any dependency to flow regime pattern. The simple photon attenuation based system is comprised of a cobalt-60 radioisotope and only one 25.4 mm × 25.4 mm sodium iodide crystal detector. Four extracted features from recorded photon spectrum in sodium iodide crystal detector were used as the inputs of GMDH neural network. Equations related to the combination of the features and the error rate of each approximation is also reported in this paper. Applying the mentioned technique, the gas volumetric percentage in an oil-gas two phase flow was determined with the root mean square error of less than 2.71 without any dependency to the flow pattern. The obtained measuring precision in this study is at least 2.1 times better than reported in previous studies.

Real-time flow estimation plays a vital role in multi-product pipeline operations, and the accuracy of real-time flow estimation is affected by noise interference and instrument accuracy and cannot be performed by direct observation of flow meter. Pipeline flow models based on the first principle method are established and employed as soft sensors of pipeline real-time flow rate. However, these models are validated by the controlled experimental pipeline, which may be ineffective regarding actual pipelines with uncertain physical parameters. In this paper, a novel approach integrating data-driven and model-driven method is proposed to estimate the flow rate of petroleum products on-line. The difference between the theoretical model and actual state of a pipeline is accounted for by the friction coefficient, and on-line calibration is achieved by solving multi-objective optimisation problems with asynchronous operation data. The flow state of the pipeline is obtained in real time by the particle filter when new pressure observations with noise become available. The estimation performance of local pressure mutation points is improved by adopting the recurrent nonlinear autoregressive neural network modelling blue of the data-driven method. The effectiveness of the proposed method is evaluated blue by examining actual data of the pipeline over a period of time. The prediction results of some other model-driven and data-driven methods are also compared to blue that of the proposed method. The results blue indicate that the proposed method improves the accuracy and reliability of the product flow rate estimations even under unforeseen operation conditions.

In this study, an adaptive neuro-fuzzy inference system (ANFIS) model is proposed for the prediction of daily diffuse solar radiation. Eight factors including month of the year, sunshine duration, barometric pressure, relative humidity, mean temperature, wind speed, rainfall and daily global solar radiation are used as the inputs, while the daily diffuse solar radiation is the output. To compare the performance of the ANFIS, artificial neural network (ANN) and Iqbal models, two statistical benchmark indices, root-mean-squared error (RMSE) and coefficient of determination (R²), are adopted in this study. The results show that the proposed ANFIS model has potential in accurately predicting the daily diffuse solar radiation.

In this study, subtractive clustering algorithm (SCA) and fuzzy c-mean clustering (FCM) method were employed to construct an adaptive neuro-fuzzy inference system (ANFIS) model for the prediction of blast-induced ground vibration. To develop the ANFIS models, the charge weight per delay, distance, and scaled distance were taken into account as the input parameters, while peak particle velocity (PPV) was the output parameter. The performances of the both two ANFIS models and some conventional methods were compared in terms of three statistical indexes. The results shown that the FCM-ANFIS model can provide a precise evaluation of PPV if proper input data are provided.

Two-Phase Flows is Significant for Many Industries. in This Paper Three Different Regimes Including Annular, Stratified and Homogeneous in The Range of %5-90% Void Fraction, Were Simulated by Mont Carlo N-Particle(MCNP) Codes. in This Simulation, a Cesium 137 Source and Two Nal Detectors Were Used to Record Received Photons. Features of Signals in the Frequency Domain Were Obtained by the Fast Fourier Transform. the Features of Signals Were Extracted Using the Received Signals of Both Detectors and MATLAB Software in Frequency Domain Including Average Value of Fast Fourier Transform and Amplitude of Dominant Frequency. Finally, The Separation Ability of Extracted Features Was Compared by Correlation Coefficient in Order to Identify Flow Regimes and Predict Void Fraction.in This Way, Average Value of Fast Fourier Transform Was Selected as the Best Feature for Identification Regimes and Predicting Void Fraction.

Gas–liquid two phase f low is probably the most important form of multiphase f lows and is found widely in industrial applications, particularly in the oil and petrochemical industry. In this study, in the first instance a gas–liquid two phase f low test loop with both vertical and horizontal test tube was designed and constructed. Different volume fractions and f low regimes were generated using this test loop. The measuring system consists of a ¹³⁷Cs single energy source which emits photons with 662 keV energy and two 1-inch NaI (Tl) scintillation detectors for recording the scattered and transmitted counts. The registered counts in the scattering detector were applied to the Multi-Layer Perceptron neural network as inputs. The output of the network was gas volume fraction which was predicted with the Mean Relative Error percentage of less than 0.9660%. Finally, the predicted volume fraction via neural network and the total count in transmission detector were chosen as inputs for another neural network with f low regime type as output. The f low regimes were identified with mean relative error percentage of less than 7.5%.

Artificial neural network (ANN) is an appropriate method used to handle the modeling, prediction and classification problems. In this study, based on nuclear technique in annular multiphase regime using only one detector and a dual energy gamma-ray source, a proposed ANN architecture is used to predict the oil, water and air percentage, precisely. A multi-layer perceptron (MLP) neural network is used to develop the ANN model in MATLAB 7.0.4 software. In this work, number of detectors and ANN input features were reduced to one and two, respectively. The input parameters of ANN are first and second full energy peaks of the detector output signal, and the outputs are oil and water percentage. The obtained results show that the proposed ANN model has achieved good agreement with the simulation data with a negligible error between the estimated and simulated values. Defined MAE% error was obtained less than 1%.

ANNs are nonlinear regression computational devices that have been used for over 45 years in classification and survival prediction in several biomedical systems, including colon cancer. Described in this article is the theory behind the three-layer free forward artificial neural networks with backpropagation error, which is widely used in biomedical fields, and a methodological approach to its application for cancer research, as exemplified by colon cancer. Review of the literature shows that applications of these networks have improved the accuracy of colon cancer classification and survival prediction when compared to other statistical or clinicopathological methods. Accuracy, however, must be exercised when designing, using and publishing biomedical results employing machine-learning devices such as ANNs in worldwide literature in order to enhance confidence in the quality and reliability of reported data.

This paper presents the application of adaptive neuro-fuzzy inference system (ANFIS) for prediction of fluid density in a previously designed and constructed gamma ray densitometer for pipes of various diameters and different fluids densities. The input parameters of the proposed ANFIS model are the pipe diameter and the number of the counted photons and the output is the density of the considered material. The required data for training and testing the ANFIS model has been obtained based on simulations using MCNP4C Monte Carlo code. A hybrid learning algorithm consists of back-propagation and least-squares estimation is used for training the proposed ANFIS model. Simulations for 4-in. polyethylene pipe had been validated with the experimental data previously. The proposed ANFIS model has achieved good agreement with the experimental results and has a small error between the estimated and experimental values. The obtained results show that the mean relative error percentage (MRE%) for training and testing data are less than 2.14% and 2.64%, respectively.

One of the non-intrusive and accurate methods of measuring void fraction in two-phase gas liquid pipe flows is the use of the gamma-transmission void fraction measurement technique. The goal of this study is to describe low-energy gamma-ray densitometry using an 241Am source for the determination of void fraction and flow regime in water/gas pipes. The MCNP code was utilized to simulate electron and photon transport through materials with various geometries. Then, a neural network was used to convert multi-beam gamma-ray spectra into a classification of the flow regime and void fraction. The simulations cover the full range of void fraction with Bubbly, Annular and Droplet flows. By using simulation data as input to the neural networks, the void fraction was determined with an error less than 3% regardless of the flow regime. It has thus been shown that multi-beam gamma-ray densitometers with a detector response examined by neural networks can analyze a two-phase flow with high accuracy.

Flow regime information can be used to improve measurement accuracy on gas volume fractions and as complementary information for other types of flow instrumentation in order to enhance their accuracy. In this study a method based on dual modality densitometry using artificial neural network (ANN) was presented to first identify the flow regime and then predict the void fraction in two-phase flows. The full energy peak (transmission count), photon counts of Compton edge in transmission detector and total count in the scattering detector, were chosen as the three inputs of the ANN. The stratified, homogenous and annular regimes with various void fractions were simulated by the Monte Carlo N-Particle (MCNP) code, version X, in order to obtain adequate data set used for training and testing the ANN. To validate the simulated results, several experiments were carried out in the annular regime of two-phase flow. Experimental results were in good agreement with the simulated data. The maximum difference between experimental and simulated results for the transmission, Compton edge and scattered counts, is 3.4%, 3.8% and 3.6%, respectively. By applying this method, all the three regimes were correctly distinguished and void fraction was predicted in the range of 5-95% with error of less than 1.1%.

Artificial Neural Networks (ANNs) have been applied to deal with flow and heat transfer problems over the past two decades. In the present paper, recent work on the applications of ANNs for predicting the flow regime, pressure drop, void fraction, critical heat flux, onset of nucleate boiling, heat transfer coefficient and boiling curve has been reviewed, respectively. As can be noted in this review work, various types of ANNs can be employed as predictors with acceptable precisions. At the end of this review, methods to improve performance of ANNs and further applications of ANNs in flow and heat transfer problems were introduced.

This work investigates the response of attenuation gamma-rays in volume fraction prediction system for water–gas–oil multiphase flows considering variations in salinity of water. The approach is based on pulse height distributions pattern recognition by artificial neural network. The detection system uses fan beam geometry, comprised of a dual-energy gamma-ray source and two NaI(Tl) detectors in order calculate transmitted and scattered beams. Theoretical models for annular and stratified flow regimes have been developed using MCNP-X code to provide data for the network.

In this paper, an optimized design of anode shape in order to achieve highest X-ray yield in a plasma focus device filled with nitrogen gas based on artificial neural networks (ANNs) is presented. Multi-layer perceptron neural network structure with the back-propagation algorithm is used for the training of the proposed model. The model has achieved good agreement with the training data and has yielded satisfactory generalization. This shows that the ANN model is an accurate and reliable approach to predict the highest X-ray yield in plasma focus devices.

Dual-energy gamma densitometry offers a powerful technique for the non-intrusive analysis of multiphase flows. By employing multiple beam lines, information on the phase configuration can be obtained. Once the configuration is known, it then becomes possible in principle to determine the phase fractions. In practice, however, the extraction of the phase fractions from the densitometer data is complicated by the wide variety of phase configurations which can arise, and by the considerable difficulties of modelling multiphase flows. In this paper we show that neural network techniques provide a powerful approach to the analysis of data from dual-energy gamma densitometers, allowing both the phase configuration and the phase fractions to be determined with high accuracy, whilst avoiding the uncertainties associated with modelling. The technique is well suited to the determination of oil, water and gas fractions in multiphase oil pipelines. Results from linear and non-linear network models are compared, and a new technique for validating the network output is described.

For oil production fields, there is a need for downhole measurements of the gas/water/oil multiphase flow. In extreme conditions a relatively simple, robust, and non-intrusive system will be appropriate. A measurement setup that combines multiple gamma beam (MGB) and dual modality densitometry (DMD) measurements, would be able to determine the gas volume fraction (GVF) independently of the flow pattern, and monitor changes in water salinity. MGB measurements of gamma-ray transmission along multiple sections across the oil pipe will provide information on the flow pattern. Whereas the DMD principle will give information on changes in salinity from a combination of transmission and scattering gamma-radiation measurements. In this work we present the results from MGB and DMD measurements of a multiphase flow with high-speed gamma-ray tomograph measurements as reference for the flow pattern. The MGB measurements should enable us to distinguish between stratified or wavy/slug and annular or slug flow. Flow patterns with several minor components distributed evenly over the measurement cross section, like bubble flow, will be interpreted as homogeneous flow. The DMD measurements can be used to monitor salinity changes of the water component for intervals where the GVF is low and the water cut of the liquid is high. Combined with other gauges for water cut measurements, the MGB and DMD measurement setup should improve the multiphase flow measurements, and enable increased oil/gas recovery and production water monitoring.

Artificial neural networks are being extensively applied in many fields of science and engineering. Despite their wide range of applications and their flexibility, there is still no general framework or procedure through which the appropriate neural network for a specific task can be designed. The design of neural networks is still very dependent upon the designer's experience. This is an obvious barrier to the wider application of neural networks. To mitigate this barrier methods have been developed to automate the design of neural networks. A new method for the auto-design of neural networks was developed, which is based on genetic algorithms (GA) and Lindenmayer Systems. The method is less computationally intensive than existing iterative design procedures, hence it can be applied to the automatic design of neural networks for complex processes. To evaluate the performance of the new design procedure, it was tested for the design of industry standard neural networks. The method was also applied to design neural networks to model the dynamics of a pH neutralization process and a CSTR reactor in which a set of nonlinear reactions takes place. The networks obtained by the new algorithm for these typical chemical processes was much simpler, yet more accurate than those designed by traditional methods.

This paper describes low-energy gamma-ray densitometry using a 241Am source for the determination of void fraction and flow regime in oil/gas pipes. Due to the reduced shielding requirements of this method compared to traditional gamma-ray densitometers using 137Cs sources, the low-energy source offers a compact design and the advantage of multi-beam configuration. One of the aims of this investigation was to demonstrate the use of a neural network to convert multi-beam gamma-ray spectra into a classification of the flow regime and void fraction, as well as to determine which detector positions best serve this purpose. In addition to spectra obtained from measurements on a set of phantom arrangements, simulated gamma-ray spectra were used. Simulations were performed using the EGS4 software package. Detector responses were simulated for void fractions covering the range from 0 - 100%, and the simulations were performed with homogeneous, annular and stratified flows. Neural networks were trained on the simulated gamma-ray data and then used to analyse the measured spectra. This analysis allowed determination of the void fraction with an error of 3% for all of the flow regimes, and the three types of flow regime were always correctly distinguished. It has thus been shown that multi-beam gamma-ray densitometers with detector responses examined by neural networks can analyse a two-phase flow with high accuracy.

Methods are described for determining the in situ volume fractions of materials flowing in pipelines. By using a number of discrete gamma -ray energies the method can be extended in theory to cover as many different types of material as required. In practice, clearly defined gamma -ray energies are required and the materials must have substantially different absorption coefficients. Results are presented for oil-air, oil-water and air-water mixes and for the oil-air-water combination. Applications are presented for homogeneous, annular, and stratified flow patterns.

This work presents a new methodology for flow regimes identification and volume fraction predictions in water–gas–oil multiphase systems. The approach is based on gamma-ray pulse height distributions (PHDs) pattern recognition by means the artificial neural networks (ANNs). The detection system uses appropriate fan beam geometry, comprised of a dual-energy gamma-ray source and two NaI(Tl) detectors adequately positioned in order measure transmitted and scattered beams, which makes it less dependent on the regime flow. The PHDs are directly used by the ANNs without any parameterization of the measured signal. The system comprises four ANNs. The first identifies the flow regime and the other three ANNs are specialized in volume fraction predictions for each specific regime. The ideal and static theoretical models for annular, stratified and homogeneous regimes have been developed using MCNP-X mathematical code, which was used to provide training, test and validation data for the ANNs. The energy resolution of NaI(Tl) detectors is also considered on the mathematical model. The proposed ANNs could correctly identify all three different regimes with satisfactory prediction of the volume fraction in water–gas–oil multiphase system, demonstrating to be a promising approach for this purpose.

Gamma-ray densitometry is a frequently used non-intrusive method for determining void fraction in two- and multi-phase gas liquid pipe flows. The traditional gamma-ray densitometer using a 137Cs source and a scintillation PMT detector has proved itself reliable and robust. This paper presents a method using a low energy source (241Am), which offers the advantages of reduced size due to reduced shielding requirements, compact detectors, and lesser dependence on flow regime, due to its multibeam measurement configuration. These are important aspects with regard to future subsea and down-hole fluid flow measurement applications. The performance of single-beam and the compact multi-beam low-energy gamma-ray measurement principles was compared. Consideration of the measurement volume, defined by the detector area and the radiation beam, demonstrated the flow regime dependency of single-beam gamma-ray measurement principles. With the multi-beam low-energy gamma-ray measurement principle, the dependence on flow regime is negligible when several detector responses are combined. Use of phantoms and one movable detector verified the multi-beam gamma-ray measurement principle. The detector responses at several positions around the pipe were obtained for different flow regimes and void fractions.

Recently, multiple input, single output, single hidden-layer feedforward neural networks have been shown to be capable of approximating a nonlinear map and its partial derivatives. Specifically, neural nets have been shown to be dense in various Sobolev spaces. Building upon this result, we show that a net can be trained so that the map and its derivatives are learned. Specifically, we use a result of Gallant's to show that least squares and similar estimates are strongly consistent in Sobolev norm provided the number of hidden units and the size of the training set increase together. We illustrate these results by an application to the inverse problem of chaotic dynamics: recovery of a nonlinear map from a time series of iterates. These results extend automatically to nets that embed the single hidden layer, feedforward network as a special case.

The models of dual modality densitometry were developed. It can be used for measuring the gas volume fraction and water volume
fraction in oil water gas pipe flow. The models are complex. In order to solve models, it often uses simplified models. This
reduces measurement precision. The method of measuring gas and water volume fraction using neural networks was presented.
The simulation data was gotten using Geant4. The radial basis function networks were trained and tested on computer simulation
data. The results show that networks predicted gas volume fraction fit true gas fraction well and water volume fraction has
some deviations.

Dual mode densitometry is presented as a novel method of measuring the gas volume fraction in gas/oil/water pipe flows independent of the salinity of the water component. The different response in photoelectric attenuation and Compton scattering to changes in salinity is utilized. The total attenuation coefficient is found through traditional transmission measurements with a detector positioned outside the pipe wall diametrically opposite the source. The scatter response is measured with a second detector positioned somewhere between the source and the transmission detector. The feasibility of the method is demonstrated for homogeneously mixed flows.

The Marquardt algorithm for nonlinear least squares is presented and is incorporated into the backpropagation algorithm for training feedforward neural networks. The algorithm is tested on several function approximation problems, and is compared with a conjugate gradient algorithm and a variable learning rate algorithm. It is found that the Marquardt algorithm is much more efficient than either of the other techniques when the network contains no more than a few hundred weights.