Abstract
In this work, we investigate the sensitivity of a family of multi-task Deep Neural Networks (DNN) trained to predict fluxes through given Discrete Fracture Networks (DFNs), stochastically varying the fracture transmissivities. In particular, detailed performance and reliability analyses of more than two hundred Neural Networks (NN) are performed, training the models on sets of an increasing number of numerical simulations made on several DFNs with two fixed geometries (158 fractures and 385 fractures) and different transmissibility configurations. A quantitative evaluation of the trained NN predictions is proposed, and rules fitting the observed behavior are provided to predict the number of training simulations that are required for a given accuracy with respect to the variability in the stochastic distribution of the fracture transmissivities. A rule for estimating the cardinality of the training dataset for different configurations is proposed. From the analysis performed, an interesting regularity of the NN behaviors is observed, despite the stochasticity that imbues the whole training process. The proposed approach can be relevant for the use of deep learning models as model reduction methods in the framework of uncertainty quantification analysis for fracture networks and can be extended to similar geological problems (for example, to the more complex discrete fracture matrix models). The results of this study have the potential to grant concrete advantages to real underground flow characterization problems, making computational costs less expensive through the use of NNs.
Highlights
Analysis of underground flows in fractured media is relevant in several engineering fields, e.g., in oil and gas extraction, in geothermal energy production, or in the prevention of geological or water-pollution risk, to mention a few
We consider two Discrete Fracture Networks (DFNs), DFN158, and DFN395, generated with respect to the characterization of Section 2.1.2; the total number of fractures n is equal to 158 and 395 for DFN158 and DFN395, respectively, and the number of outflux fracture m is equal to 7 and 13 for DFN158 and DFN395, respectively. For each of these two DFNs, we train three different Neural Networks (NN) with architectures Aα for each α = 1, 2, 3 and with respect to the two training configurations β = 1 and β = 2; we have a total number of six trained NNs, one for each (α, β) combination, for both DFN158 and DFN395
We proposed an analysis for the characterization of a family of Deep Neural Networks (DNN) with multi-task architecture Aα trained to predict the exiting fluxes of a DFN given the fracture transmissivities
Summary
Analysis of underground flows in fractured media is relevant in several engineering fields, e.g., in oil and gas extraction, in geothermal energy production, or in the prevention of geological or water-pollution risk, to mention a few. Underground flow simulations using DFNs can be, a quite challenging problem in the case of realistic networks, where the computational domain is often characterized by a high geometrical complexity; in particular, fractures and traces can intersect, forming very narrow angles, or can be very close to each other. These complex geometrical characteristics make the creation of the mesh a difficult task, especially for numerical methods requiring conforming meshes. Other approaches can be found in [18,19,20,21]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
