Neural ODE Network for Physically Constrained Reservoir Modeling
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Solution Overview
Problem
Reservoir modeling using capacitance-resistance models often produces numerous outputs that do not make physical sense, making it difficult and time-consuming to select physically feasible solutions, especially with sparse and noisy input data.
Innovation Solution
A neural ordinary differential equation network is used to model reservoir characteristics, where measured data is employed as boundary conditions to determine equation parameters, constraining the solutions within the physics of the reservoir, thereby providing physically viable outputs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If capacitance-resistance models are used for reservoir modeling, then the modeling process can be performed, but numerous outputs are produced that do not make physical sense, making selection difficult and time-consuming
Solution Approach 1:
The patent transforms the traditional capacitance-resistance model parameters into a neural network parameter space, where the model learns optimal parameters from data while being constrained by physical equations. This parameter transformation allows the model to maintain physical feasibility while improving prediction accuracy and reducing the need for manual output selection.
Solution Approach 2:
The patent replaces the traditional mechanical reservoir modeling approach with a neural network-based system that incorporates physics constraints. The neural network learns from measured data while being guided by physical equations, substituting the need for manual interpretation of multiple physical models with an automated data-driven approach that inherently respects physical laws.
2Adaptability or versatility
If traditional reservoir modeling is used, then multiple solutions can be generated, but reviewing and selecting physically feasible outputs is difficult and time consuming
Solution Approach 1:
The neural network model performs self-validation by incorporating physics constraints directly into its architecture. The model automatically filters out non-physical solutions during the prediction process, eliminating the need for manual review and selection of physically feasible outputs. The system serves itself by inherently understanding and applying physical laws.
Solution Approach 2:
The patent implements a feedback mechanism where the neural network predictions are continuously validated against physical equations and measured data. The model adjusts its predictions to satisfy physical constraints, creating a closed-loop system that automatically ensures physical feasibility without requiring external intervention for output validation.
Data Source
AI summary
Differential equations defining physics of a reservoir are modeled as a neural network. Measured data for the reservoir is used as boundary condition to calculate the different equation parameters. The result is a neural ordinary differential equation network that models reservoir characteristics (e.g., inter-well connectivities, response times for injection wells and production wells) using physics that are encoded into the network. The neural ordinary differential equation network provides a solution for the reservoir that is constrained by the physics of the reservoir.