Deep Learning of Two-Phase Flow in Porous Media via Theory-Guided Neural Networks

SPE Journal ◽  
2021 ◽  
pp. 1-19
Author(s):  
Jian Li ◽  
Dongxiao Zhang ◽  
Nanzhe Wang ◽  
Haibin Chang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Expert Knowledge ◽  
Initial Conditions ◽  
The Other ◽  
Phase Flow ◽  
Scientific Theories ◽  
Two Phase ◽  
Collocation Points ◽  
Oil Water

Summary A theory-guided neural network (TgNN) is proposed as a prediction model for oil/water phase flow in this paper. The model is driven by not only labeled data, but also scientific theories, including governing equations, boundary and initial conditions, and expert knowledge. Two independent neural networks (NNs) are built in the TgNN for oil/water phase flow problems, with one approximating pressure and the other approximating saturation. The two networks are connected by loss functions, which include a data mismatch term, as well as theory-guided terms. The desired parameters in NNs are trained by a certain optimization algorithm to decrease the value of the loss function. The training process uses a two-stage strategy as follows: (1) after one of the two NNs obtains a satisfactory result, parameters in the network with better performance are fixed in calculating the nonlinear terms and (2) the other NN continues to be trained until satisfactory performance is also obtained. The proposed TgNN offers an effective way to solve the coupled nonlinear two-phase flow problem. Numerical results demonstrate that the proposed TgNN achieves better accuracy than the traditional deep neural network (DNN). This is because the governing equation can constrain spatial and temporal derivatives, and other physical constraints (i.e., boundary and initial conditions, expert knowledge) can make the outputs more scientifically consistent. The effect of sparse data (including labeled data and collocation points) is tested, and the results show that more labeled data and collocation points lead to improved long-term prediction performance. However, the TgNN can also be successfully trained in the absence of labeled data by merely adhering to the above-mentioned scientific theories. In addition, several more complicated scenarios are tested, including the existence of data noise, changes in well condition, transfer learning, and the existence of different levels of dynamic capillary pressure. Compared with the traditional DNN, TgNN possesses superior stability with the guidance of theories for the considered complex situations.

Prediction of Two-Phase Heat Transfer Coefficients in a Horizontal Pipe for Different Inclined Positions With Artificial Neural Networks

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Najmeh Sobhanifar ◽  
Ebrahim Ahmadloo ◽  
Sadreddin Azizi
Keyword(s):  
Neural Network ◽  
Heat Transfer ◽  
Experimental Data ◽  
Neural Networks ◽  
Two Phase Flow ◽  
Reynolds Numbers ◽  
Phase Flow ◽  
Transfer Coefficients ◽  
Two Phase ◽  
Heat Transfer Coefficients

This paper presents the application of artificial neural network (ANN) in prediction of heat transfer coefficients (HTCs) of two-phase flow of air–water in a pipe in the horizontal and slightly upward inclined (2, 5, and 7 deg) positions. For this purpose, the superficial liquid and gas Reynolds numbers and the inclination of the pipe were used as input parameters, while the HTCs of two-phase flow were used as output parameters in training and testing of the multilayered, feedforward, backpropagation neural networks. In this present study, experimental data were taken from literature and then used for the ANN model. The superficial liquid and gas Reynolds numbers ranged from 740 to 26,100 and 560 to 47,600 for water and air, respectively. The mean deviations against experimental data were determined for the model. Results showed that the network predictions were in very good agreement with the experimental HTC data, whereas the correlation showed more deviations. Finally, results showed that the accuracy between the neural network predictions and experimental data was achieved with mean relative error (MRE) of 2.92% and correlation coefficient (R) that was 0.997 for all datasets, which suggests the reliability of the ANNs as a strong tool for predicting HTCs with two-phase flows.

N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Valerii Dmitrienko ◽  
Sergey Leonov ◽  
Mykola Mezentsev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
The Other ◽  
Proximity Function ◽  
Input Information ◽  
Proximity Measures ◽  
The One ◽  
True Values

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other).  For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b). Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.

A Combined Eulerian and Lagrangian Method for Prediction of Evaporating Sprays

2002 ◽  
Vol 124 (3) ◽  
pp. 481-488 ◽  
Author(s):  
M. Burger ◽  
G. Klose ◽  
G. Rottenkolber ◽  
R. Schmehl ◽  
D. Giebert ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Lagrangian Method ◽  
Phase Flow ◽  
Two Phase Flows ◽  
Two Phase ◽  
Lagrangian Methods ◽  
Eulerian Method ◽  
Lagrangian Modeling

Polydisperse sprays in complex three-dimensional flow systems are important in many technical applications. Numerical descriptions of sprays are used to achieve a fast and accurate prediction of complex two-phase flows. The Eulerian and Lagrangian methods are two essentially different approaches for the modeling of disperse two-phase flows. Both methods have been implemented into the same computational fluid dynamics package which is based on a three-dimensional body-fitted finite volume method. Considering sprays represented by a small number of droplet starting conditions, the Eulerian method is clearly superior in terms of computational efficiency. However, with respect to complex polydisperse sprays, the Lagrangian technique gives a higher accuracy. In addition, Lagrangian modeling of secondary effects such as spray-wall interaction enhances the physical description of the two-phase flow. Therefore, in the present approach the Eulerian and the Lagrangian methods have been combined in a hybrid method. The Eulerian method is used to determine a preliminary solution of the two-phase flow field. Subsequently, the Lagrangian method is employed to improve the accuracy of the first solution using detailed sets of initial conditions. Consequently, this combined approach improves the overall convergence behavior of the simulation. In the final section, the advantages of each method are discussed when predicting an evaporating spray in an intake manifold of an internal combustion engine.

Sign in / Sign up

Export Citation Format

Share Document