Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network

Xu，Rui1; Zhang，Dongxiao2; Wang，Nanzhe3

2022-10-01

10.1016/j.jhydrol.2022.128321

JOURNAL OF HYDROLOGY   Impact Factor & Quartile

0022-1694

1879-2707

We build surrogate models for dynamic 3D subsurface single-phase flow problems with multiple vertical producing wells. The surrogate model provides efficient pressure estimation of the entire formation at any timestep given a stochastic permeability field, arbitrary well locations and penetration lengths, and a timestep matrix as inputs. The well production rate or bottom hole pressure can then be determined based on Peaceman's formula. The original surrogate modeling task is transformed into an image-to-image regression problem using a convolutional encoder-decoder neural network architecture. The residual of the governing flow equation in its discretized form is incorporated into the loss function to impose theoretical guidance on the model training process. As a result, the accuracy and generalization ability of the trained surrogate models are significantly improved compared to those of fully data-driven models. They are also shown to possess flexible extrapolation ability to permeability fields with different statistics. The surrogate models are used to conduct uncertainty quantification considering a stochastic permeability field, as well as to infer unknown permeability information based on limited well production data and observation data of formation properties. Results are shown to be in close accordance with those of traditional numerical simulation tools, but computational efficiency is dramatically improved.

Convolutional neural network Inverse problem Subsurface flow Surrogate modeling Theory-guided machine learning Uncertainty quantification

SCI ; EI

English

Corresponding

Engineering ; Geology ; Water Resources

Engineering, Civil ; Geosciences, Multidisciplinary ; Water Resources

WOS:000862505600004

ELSEVIER

20223612699912

Computation theory ; Computational efficiency ; Convolution ; Convolutional neural networks ; Decoding ; Machine learning ; Network architecture ; Network coding ; Stochastic models ; Stochastic systems ; Uncertainty analysis

Information Theory and Signal Processing:716.1 ; Computer Theory, Includes Formal Logic, Automata Theory, Switching Theory, Programming Theory:721.1 ; Data Processing and Image Processing:723.2 ; Artificial Intelligence:723.4 ; Control Systems:731.1 ; Probability Theory:922.1 ; Systems Science:961

ENGINEERING

2-s2.0-85137165561

Scopus

1.Department of Mathematics and Theories,Peng Cheng Laboratory,Shenzhen,Guangdong,518055,China
2.National Center for Applied Mathematics Shenzhen (NCAMS),Southern University of Science and Technology,Shenzhen,Guangdong,518055,China
3.College of Engineering,Peking University,Beijing,100871,China

Xu，Rui,Zhang，Dongxiao,Wang，Nanzhe. Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network[J]. JOURNAL OF HYDROLOGY,2022,613.

Xu，Rui,Zhang，Dongxiao,&Wang，Nanzhe.(2022).Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network.JOURNAL OF HYDROLOGY,613.

Xu，Rui,et al."Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network".JOURNAL OF HYDROLOGY 613(2022).