History-Matching of Imbibition Flow in Multiscale Fractured Porous Media Using Physics-Informed Neural Networks (PINNs)

TL;DR

To the best of the knowledge, the proposed PINNs-based workflow is the first to offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements.

Abstract

We propose a workflow based on physics-informed neural networks (PINNs) to model multiphase fluid flow in fractured porous media. After validating the workflow in forward and inverse modeling of a synthetic problem of flow in fractured porous media, we applied it to a real experimental dataset in which brine is injected at a constant pressure drop into a CO2 saturated naturally fractured shale core plug. The exact spatial positions of natural fractures and the dynamic in-situ distribution of fluids were imaged using a CT-scan setup. To model the targeted system, we followed a domain decomposition approach for matrix and fractures and a multi-network architecture for the separate calculation of water saturation and pressure. The flow equations in the matrix, fractures and interplay between them were solved during training. Prior to fully-coupled simulations, we proposed pre-training the model. This aided in a more efficient and successful training of the coupled system. Both for the synthetic and experimental inverse problems, we determined flow parameters within the matrix and the fractures. Multiple random initializations of network and system parameters were performed to assess the uncertainty and uniqueness of the results. The results confirmed the precision of the inverse calculated parameters in retrieving the main flow characteristics of the system. The consideration of multiscale matrix-fracture impacts is commonly overlooked in existing workflows. Accounting for them led to several orders of magnitude variations in the calculated flow properties compared to not accounting for them. To the best of our knowledge, the proposed PINNs-based workflow is the first to offer a reliable and computationally efficient solution for inverse modeling of multiphase flow in fractured porous media, achieved through history-matching noisy and multi-fidelity experimental measurements.

Figures (19)

• Figure 1: A schematic of the core and the applied boundary conditions, as well as the distribution of fractures in the core.a) The simplified geometry of the matrix-fracture system and the impacting boundary conditions, c) The spatial distribution of the matrix and fracture collocation points, in three-dimensions (left), and x-y projection (right), c) the mathematical notations in fractures
• Figure 1: The impact of 3D convolutional kriging on the in-situ water saturation data. a) The applied weighting kernel, b) A comparisons of the saturation distribution before and after kriging at two different times
• Figure 2: A schematic of the applied PINNs-based computational workflow.a) the cross-sectional view of the porosity distribution in the experimental data, b) The model architecture; separate networks for the state variables of matrix and fracture systems, c) The architecture of each NNs, d) The proposed step-wise learning strategy, e) The spatial distribution of the matrix and fracture collocation points.
• Figure 2: The results of history-matching using coupled finite-difference numerical simulations, and Nelder-Mead (NM) optimization. The history-matching continued for around 100 NM iterations. a) The MAE in the matched RF, b) The estimated $\bar{\Lambda}$ curve compare to the expected true value, c) The total run-time versus NM iterations, d) the performance (1: run-time, 2: NMAE in the estimations) of PINNs, and FD-NM history-matching tools are compared.
• Figure 3: The collocation points used for solving the problem under study. The color of the points demonstrate the corresponding time for each point in the range $t=1-10^6$ sec. a) The collocation points at the boundary conditions of inlet (y=0) and outlet (y=L) faces (940 spatial points), b) The collocation points corresponding to the non-flowing boundary condition at $r=r_{c}$ (8630 spatial points), c) The collocation points corresponding to the fracture (4103 spatial points), d) The collocation points corresponding to the matrix (23500 spatial points). The matrix collocation points with distance less than 0.0006 m from the fracture collocation points have been removed. e) the observational data points used in the data loss: 1) RF points, 2) points with the measured injected volume, and 3) spatiotemporal points of the in-situ $s_w$ measured using CT-scan.