Physics-Encoded Learning for DAS-Based Flow Allocation: A Comparative Study

Abstract

Abstract Distributed Acoustic Sensing (DAS) has become an important surveillance technology for injection and production wells because it enables dense acoustic measurements along the wellbore using fiber-optic sensing channels. Each DAS channel behaves as a distributed strain-sensitive acoustic measurement over a finite gauge length, recording broadband acoustic disturbances generated by flow-induced vibrations. The resulting high-resolution spatial and temporal measurements provide a rich dataset that can support a wide range of applications, including flow allocation, event detection, completion-integrity monitoring, flow-assurance diagnostics, production surveillance, and well testing. Despite these capabilities, quantitative interpretation of DAS data, particularly for flow allocation, remains challenging. Conventional workflows often depend on high signal-to-noise ratios, long spatial apertures, transient low-frequency events, or calibration against controlled measurements. Such requirements can limit applicability in field operations because calibration conditions may change with time, drift from actual downhole conditions, or fail to capture the complexities of multiphase flow and completion heterogeneity. Here, we present a physics-encoded neural network (PeNN) framework for estimating downhole flow parameters from acoustic measurements. The proposed method combines physics-informed preprocessing, multi-domain feature extraction, and a neural network architecture in which prior physical knowledge is embedded directly into the model structure. The preprocessing workflow includes de-drifting, denoising, sound-transmission-loss compensation, attenuation-informed frequency-wavenumber filtering, noise matching, phase-based stacking, and data standardization. Extracted features include time-domain, spectral, higher-order spectral, cepstral, frequency-wavenumber, and spatial-wavelet descriptors. The proposed PeNN model encodes physical relationships, such as turbulent-flow behavior, noise-logging relationships, and mechanistic constraints, directly into the model layers. This structure is designed to improve generalization, reduce dependence on large, labeled datasets, and support the transition from instance-based learning to continuous learning. The workflow is further extended through federated learning, enabling local assets to train models on site while sharing only model updates with a central server. To demonstrate the effectiveness of the proposed framework, a synthetic injection-well case study was developed using computational fluid dynamics simulations of a 2.5 m water-injection section with two injection zones. The proposed PeNN model was compared with a conventional neural network of identical architecture but without embedded physical constraints. Results showed that the physics-encoded model required approximately 2.5 times fewer labeled training samples to achieve comparable prediction performance under sparse-label conditions.