One-Dimensional Fluid Flow Model for Well System Simulation
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Solution Overview
Problem
Current fluid flow models in well systems are limited in accurately simulating multi-dimensional, unsteady fluid flow and fluid displacement processes, particularly during fracture treatments, due to computational complexity and the need for more efficient simulation methods that can account for miscible and immiscible fluid interactions.
Innovation Solution
The development of one-dimensional fluid flow models that integrate governing equations over cross-sections, using finite difference, finite volume, or finite element methods, to reduce computational costs and enable faster simulations, while accounting for the distinct properties of composite fluids formed in mixing zones through effective diffusion coefficient models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-dimensional, unsteady fluid flow models are used to accurately simulate fluid displacement during fracture treatments, then simulation accuracy is improved, but computational complexity and cost increase
Solution Approach 1:
The patent segments the fluid flow domain into distinct regions (e.g., wellbore, fracture, reservoir) and applies different modeling approaches to each segment. The wellbore is modeled with one-dimensional equations while the fracture and reservoir use multi-dimensional models, allowing accurate simulation of fluid displacement without the computational burden of fully multi-dimensional modeling throughout the entire system.
Solution Approach 2:
The patent transitions from fully multi-dimensional fluid flow models to one-dimensional models by integrating the governing equations over the cross-section of the flow path. This dimensional reduction maintains the essential physics of fluid displacement while significantly reducing computational complexity and enabling faster simulations.
2Productivity
If one-dimensional flow models are used to reduce computational costs, then productivity is improved, but measurement precision of fluid displacement may deteriorate
Solution Approach 1:
The patent introduces an effective diffusion coefficient parameter that captures the essential physics of fluid displacement in a simplified one-dimensional framework. This parameter, derived from the multi-dimensional governing equations through cross-sectional integration, allows the one-dimensional model to accurately represent fluid displacement behavior while maintaining computational efficiency.
Solution Approach 2:
The patent creates a simplified one-dimensional representation of the complex multi-dimensional fluid flow system by integrating the governing equations over the cross-section. This copying approach retains the key physical processes (convection, diffusion, dispersion) while reducing the computational domain to a single spatial dimension, enabling faster simulations with acceptable accuracy.
3Measurement precision
If composite fluid properties are accounted for in mixing zones, then simulation accuracy is improved, but model complexity increases
Solution Approach 1:
The patent applies different fluid property characteristics to different regions of the flow system. In mixing zones where multiple fluids interact, the model uses composite fluid properties (effective diffusion coefficients, mixed viscosities) that reflect the local conditions. In single-phase regions, simpler fluid properties are used, allowing accurate representation of fluid interactions without uniformly complex modeling throughout the entire system.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
These models allow for more computationally efficient and accurate simulations of fluid flow and displacement in well systems, improving the prediction and analysis of fluid behavior during treatments, such as hydraulic fracturing, by reducing complexity and enhancing the simulation of miscible and immiscible fluid interactions.
Implementation Method 1
the fluid flow model can include an effective diffusion coefficient that can be based on a difference between properties of the first fluid and the second fluid
Data Source
AI summary
In some aspects, a one-dimensional flow model is generated. The one-dimensional flow model can represent flow of a first fluid and a second fluid in a flow path in a well system environment. The one-dimensional flow model comprises an effective diffusion coefficient model for a composite fluid volume comprising the first and second fluids. The effective diffusion coefficient model calculates an effective diffusion coefficient for the composite fluid volume based on a difference between the respective densities and viscosities of the first fluid and the second fluid.