Multi-Scale Finite Volume Method for Reservoir Simulation
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Solution Overview
Problem
Current multi-scale methods for reservoir simulation fail to accurately model nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces, neglecting essential physical mechanisms like capillary pressure and gravity, which are crucial for realistic fluid flow predictions in petroleum reservoirs.
Innovation Solution
A multi-scale finite-volume (MSFV) method is developed to address these limitations by treating flow and transport separately using a fully implicit sequential algorithm, decomposing the pressure field into elliptic, buoyancy/capillary, and inhomogeneous components, and employing dual-grid basis functions to compute the elliptic component, allowing for flexible accommodation of compressibility, capillary pressure, and buoyancy effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional multi-scale methods are used for reservoir simulation, then computational efficiency is improved, but accuracy of modeling nonlinear immiscible three-phase compressible flow with gravity and capillary forces deteriorates
Solution Approach 1:
The patent segments the pressure field into distinct components: an elliptic component solved using multi-scale finite-volume method for computational efficiency, and separate buoyancy/capillary and inhomogeneous components handled through operator splitting. This segmentation allows each component to be treated with appropriate numerical methods, maintaining both efficiency and accuracy for complex three-phase flow with gravity and capillary forces.
Solution Approach 2:
The patent introduces operator splitting as an intermediary technique to decouple the coupled pressure-saturation system into separate elliptic and hyperbolic components. This intermediary approach enables independent treatment of different physical mechanisms (capillary pressure, buoyancy, compressibility) while maintaining overall system accuracy and computational efficiency.
2Reliability
If detailed reservoir discretization is used to improve model reliability, then prediction accuracy improves, but computational complexity and required algorithms increase
Solution Approach 1:
The patent applies local quality by computing dual basis functions only in regions where heterogeneity and nonlinearity are significant, rather than uniformly across the entire domain. The multi-scale finite-volume method dynamically adapts the level of detail in different regions, maintaining high accuracy in critical areas while reducing computational complexity in homogeneous regions.
Solution Approach 2:
The patent changes the mathematical parameters and formulation of the governing equations to separate elliptic and hyperbolic components, allowing different numerical treatment strategies. This parameter transformation enables the use of efficient multi-scale methods for the elliptic pressure component while handling saturation and transport separately, reducing overall algorithmic complexity.
3Reliability
If black oil modeling with three-phase flow is implemented, then physical realism improves, but numerical stability and convergence difficulty worsen
Solution Approach 1:
The patent segments the nonlinear three-phase flow equations into separate elliptic pressure equations and hyperbolic saturation equations. By solving the pressure field first through multi-scale finite-volume method and then using operator splitting to handle saturation separately, the method maintains physical realism of black oil modeling while improving numerical stability through decoupled solution steps.
Solution Approach 2:
The patent performs preliminary action by solving the elliptic pressure component before the hyperbolic saturation component in a sequential manner. This preliminary resolution of the pressure field provides stable boundary conditions for subsequent saturation calculations, preventing convergence issues and improving numerical stability throughout the iterative process.
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
This approach provides an efficient algorithm for simulating fluid flow in subterranean reservoirs, improving the accuracy of pressure and saturation predictions, and enabling the simulation of complex fluid behaviors in heterogeneous formations, thereby enhancing the reliability of petroleum reservoir models.
Implementation Method 1
A MSFV method is used to compute the basis functions of the elliptic component, which captures long range interactions in the pressure field
Implementation Method 2
The general solution of the pressure is decomposed into an elliptic part, a buoyancy/capillary force dominant part, and an inhomogeneous pant with source/sink (wells) and accumulation
Implementation Method 3
The general solution of the pressure is decomposed into an elliptic part, a buoyancy/capillary force dominant part, and an inhomogeneous pant with source/sink (wells) and accumulation
Implementation Method 4
A velocity field is reconstructed on the fine-scale using primal basis functions
Implementation Method 5
This MSFV method has been proven to be accurate for strongly heterogeneous problems
Data Source
AI summary
A multi-scale finite-volume (MSFV) method simulates nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces. Consistent with the MSFV framework, flow and transport are treated separately and differently using a fully implicit sequential algorithm. The pressure field is solved using an operator splitting algorithm. The general solution of the pressure is decomposed into an elliptic part, a buoyancy/capillary force dominant part, and an inhomogeneous part with source/sink and accumulation. A MSFV method is used to compute the basis functions of the elliptic component, capturing long range interactions in the pressure field. Direct construction of the velocity field and solution of the transport problem on the primal coarse grid provides flexibility in accommodating physical mechanisms. A MSFV method computes an approximate pressure field, including a solution of a course-scale pressure equation; constructs fine-scale fluxes; and computes a phase-transport equation.