Digital oilfield

Machine Learning Improves Accuracy of Virtual Flowmetering and Back-Allocation

In this study, the authors investigated a fully data-driven approach using artificial neural networks (ANNs) for real-time virtual flowmetering and back-allocation in production wells.


In this study, the authors investigated a fully data-driven approach using artificial neural networks (ANNs) for real-time virtual flowmetering and back-allocation in production wells. The main goal was to develop computationally efficient data-driven models to determine multiphase production rates of individual phases (gas and liquid) in wells using existing measured data in fields. The results showed that ANNs were capable of estimating multiphase flow rates accurately in both simulated and field data.


Virtual-flowmetering (VFM) methods are categorized in two types generally: physics-based models (hydrodynamical approach) and data-driven models. In the physics-based approach, multiphase flow rates are estimated by simplified hydrodynamical models using sensor data (e.g., pressure and temperature) as input parameters. The second approach is solely dependent on the available data in the field, performing statistical analysis on this data and deriving relations between input features and quantities of interest (in this case, multiphase flow rates). Such an approach requires a sufficient data set to train the models. In the context of data-driven VFM, such a data set could be obtained from periodic test-separator data or well tests.

In this study, two types of ANNs were assessed: feed-forward (multilayer-­perceptron) and recurrent [long short-term memory (LSTM)] to capture temporal dependencies. ANNs were used for real-time gas flowmetering at an individual well level using total production rates measured downstream of the combined production separators.


The feed-forward ANN is a suitable method for modeling the relations between a set of features and output parameters by functional mapping of the features in the input layer to the outputs. Fig. 1 shows a schematic of a feed-forward ANN. The relation of the input to the output parameters is found by calibrating the weights and biases in the hidden (middle) layers. Depending on the complexity of the input/output relations, the number of hidden layers, and neurons therein, could be varied. The disadvantage of feed-forward networks is their inability to identify temporal trends in the data set. 

Fig. 1—An example of a feed-forward ANN (left) and a mathematical representation of a feed-forward neural network (right).


Recurrent neural networks (RNNs) are suggested for prediction of systems in which states are changing continuously before reaching an equilibrium, or when the time-dependency of states is crucial for predicting these states. A common disadvantage of some RNNs is their inability to capture long-term dependencies in the data. Use of an LSTM network is suggested for predictions involving systems in which both short- and long-term dependencies are present. An LSTM network is composed of several units of RNN, with each unit composed of a cell with an input, output, and forget gate.

For the feed-forward neural networks, a single hidden layer was used and the number of neurons in the hidden layer was varied to find the architecture that provided optimal accuracy for flow-rate estimation. The Levenberg-Marquardt back-propagation method was used for training the feed-forward neural network.

Case Study

Simulated Data. Steady-State Gas and Liquid Flow Rates. The simulated data set for the steady-state predictions was used for training and validating the ANN model. A feed-forward neural network with one hidden layer and six neurons in the hidden layer was used for flow-rate estimation and 80% of the data set was used for training.

The results for the steady-state gas flow rate show that using only two pressure parameters as inputs for the neural network does not result in accurate estimation of gas flow rates. By including the third parameter, wellhead temperature, the prediction accuracy was increased. These results suggest that the relation of the gas mass-flow rate to the pressure difference and gas density was captured using the neural network. The steady-state liquid flow-rate results showed an accurate estimation using bottomhole and wellhead pressure together with gas flow rates.

Transient Cases. In practice, steady-state operations are rare, especially in mature wells. Therefore, rather than using steady-state data, transient data are used. For this purpose, several transient simulations were performed by changing the valve opening in time.

As a first step, the performance of a feed-forward neural network, trained on the steady-state data set in predicting the liquid rate, was evaluated. The inputs that led to the highest accuracy in predicting the steady-state liquid rates were used: bottomhole pressure, wellhead pressure, and gas flow rates. The results showed that, during the steady-state periods, the liquid flow rate could be estimated accurately; however, during the shut-in periods, the prediction was no longer accurate. Additionally, the dynamic trends of well shut-in or transients in the liquid flow rate were not captured correctly.

To increase the accuracy in production transient periods, the training of the feed-forward model was performed on the transient data. The training was performed on half of the production data, and the test was performed on the second half of the data set. The results show that the prediction was improved by including the transient data in the training. The dynamics in production were also captured correctly by the neural network. Thus, these results confirm that the relation between the pressures and gas flow rate to the liquid flow rate can be captured using a feed-forward neural network under both steady-state and transient conditions.

One of the characteristics of mature wet gas wells is the increase in liquid/gas ratio (LGR) over time. It could be seen that the LSTM network was better capable of capturing the LGR trend, and, consequently, the liquid flow rate in time.

Field Data. Daily Liquid Flow Rates. Field data of a gas well in the North Sea were used. The available data for this field include daily pressure, temperature, choke setting, and flow rates. An ANN was used to create a model predicting the liquid flow rates using all other available parameters.

Both feed-forward neural networks and RNNs were evaluated for this test case. For the feed-forward neural network, different numbers of neurons were tested; the results with 10 neurons are presented in the complete paper. For the selected field, 6.5 years of production data were available for training and testing the neural network. Half of the data set was used for training the ANN, and the second half was used for testing the ANN. Because the liquid rate was increasing in time in this field, both feed-forward and RNN networks were used for the liquid rate estimation.

The computation of the liquid flow rate using the feed-forward ­neural network underpredicted the liquid flow rate; the error of the prediction increased in time. As expected, time dependencies could not be accurately captured using the feed-forward neural network; this could be a reason for underprediction of the liquid rates. However, the results of the RNN confirmed that the increase in liquid flow rates in time was better captured with the RNN.

The last test performed on the daily averaged liquid-rate-estimation data was to assess the size of the data set required to train the model while maintaining the accuracy of future ­liquid-flow-rates estimation. For this specific field, it was found that with a limited number of data (daily data for 10 months), an accurate estimation could be made for the liquid flow rates for the next 4 months. These results confirmed that the correlation of the liquid flow rates and other measured parameters was captured accurately with the ANN model trained with limited data.

Back-Allocation. The goal of the last part of the study was to validate the ­data-driven approach by testing it with high-resolution field data to make a real-time virtual flowmeter.

A data set from a platform with four wells in the North Sea was used. On this platform, pressures, temperatures (bottomhole and topside), and gas flow rates of each well were measured hourly with the total gas flow rate. In this test, only the results for gas-flow-rate allocation is presented because of unavailability of the separator liquid levels.

Within the available data set, 300 data points (300 hours) were found in which only one of the wells was producing. The trained model, on the basis of the total flow rates, was used to predict the flow rate of this well for the period in which it was producing alone. For this prediction, other wells were assumed to be in the shut-in mode.

The mean of the relative error (error of the estimated value compared with the field value) is on the order of 1%, which indicates a relatively small drift in the estimation. The standard deviation provides a more-accurate measure of relative error, which is approximately 25% around the mean error. It can be concluded that the prediction of gas flow rate when only one of the wells is producing has a high accuracy margin with respect to the actual flow from the data set. The steady-state production rates are better predicted than the dynamic conditions.

This method could be devised as a simple computational tool trained on available data in the field. It can accurately monitor multiphase flow rates produced from each well in a real-time manner. It is suggested that this approach be tested on several fields for which reliable total liquid-flow-rate data are also available.

The results also showed that the model predictions were not greatly affected by the uncertainties in the measurement data and that this model could be used as a robust model to estimate flow rates.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 192819, “Improving the Accuracy of Virtual Flowmetering and Back-Allocation Through Machine Learning,” by Pejman Shoeibi Omrani, SPE, Iulian Dobrovolschi, and Stefan Belfroid, SPE, TNO, and Peter Kronberger and Esteban Munoz, Wintershall Noordzee, prepared for the 2018 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 12–15 November. The paper has not been peer reviewed.