Multi-grid Finite Element Model for Coupled Fluid Flow and Heat Transfer

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Solution Overview

Problem

Current methods for predicting subterranean formation stress states and deformation paths in oil and gas reservoirs are limited by the availability of data, especially in complex geometries and nonlinear time-dependent formations, and struggle to accurately model fully coupled compositional fluid flow and heat transfer in nonlinearly deforming rocks.

Innovation Solution

A method using multi-grid finite element simulations, which involves collecting raw data, generating coarse or fine scale petrophysical and geomechanical models, and creating a multi-grid finite element simulation model to analyze subterranean formations, enabling the modeling of complex geometries and nonlinear behaviors.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If traditional finite difference methods are used for reservoir modeling, then the method is well-established and easier to implement, but it cannot accurately model complex geometries and nonlinear time-dependent formations

Engineering Contradiction:

Improvemodeling accuracy for complex geometriesVSAvoidcomputational model complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent replaces traditional finite difference mechanical grid systems with finite element mesh systems that can adapt to complex geometries. The finite element method uses continuous displacement fields and shape functions to model deformation, substituting the rigid grid structure of FDM with a flexible mesh that conforms to arbitrary boundaries and nonlinear formation characteristics.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent implements dynamic adaptive mesh refinement where the finite element mesh can be refined or coarsened based on local solution characteristics and deformation gradients. This allows the model to dynamically adjust computational resolution in regions of high stress concentration or complex geometry while maintaining coarser resolution elsewhere, balancing accuracy and computational efficiency.

Inventive Principle:

Principle #15Dynamics

2Measurement precision

If fully coupled compositional flow modeling is implemented, then the accuracy of predicting stress state and deformation path improves, but the computational time and complexity increase significantly

Engineering Contradiction:

Improveprediction accuracy of stress stateVSAvoidcomputational time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent segments the fully coupled compositional flow model into modular finite element formulations for different physical processes (mass conservation, momentum balance, energy equation, constitutive relationships). Each module can be independently formulated and assembled into the global system, allowing for efficient numerical implementation and potential parallelization while maintaining full coupling capability.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent employs numerical techniques such as implicit time integration schemes and iterative solvers that adapt parameters like time step size and convergence criteria based on solution behavior. This allows the model to maintain high accuracy for stiff nonlinear problems while reducing computational effort in regions or time periods where solutions are more benign.

Inventive Principle:

Principle #35Parameter changes

3Manufacturing precision

If fine scale modeling is used to capture detailed formation properties, then the resolution and accuracy of the model improves, but the computational resources and data requirements increase

Engineering Contradiction:

Improvemodel resolutionVSAvoidcomputational resource requirements

Core Design Contradiction:

Manufacturing precisionVSDevice complexity

Solution Approach 1:

Inventive Principle:

Principle #15Dynamics

4Ease of operation

If loose coupling schemes are used for fluid flow and solid deformation, then the computational simplicity is maintained, but the accuracy for nonlinear and time-dependent formations deteriorates

Engineering Contradiction:

Improvecomputational simplicityVSAvoidsolution accuracy for nonlinear formations

Core Design Contradiction:

Ease of operationVSReliability

Solution Approach 1:

The patent merges the fluid flow and solid deformation problems into a single fully coupled finite element system. Rather than solving separate equations sequentially, the formulation integrates mass conservation, momentum balance, and constitutive relationships into a unified set of nonlinear equations that are solved simultaneously at each time step, capturing the bidirectional coupling effects essential for nonlinear formations.

Inventive Principle:

Principle #5Merging (Combining)

Data Source

PatentUS8255195B2N-phasic element method for calculating a fully coupled response of multiphase compositional fluid flow and a system for uncertainty estimation

Publication Date: 2012.08.28 GEOSCALE

AI summary

In an exemplary embodiment, a method is disclosed for developing an N-phasic finite element model for performing fully coupled analyses of multi-phase compositional fluid flow and heat flow in nonlinearly deforming porous solid media with time-dependent failure. The method can include formulating a finite element model of the behavior of a coupled solid-fluid formation, having complex geometry and behavior, and applying the model to derive the response of the formation in the form of one or more displacement fields for the solid phases and one or more pressure fields for the fluid phases in a zone of interest in a formation. In an exemplary embodiment, a system is disclosed for estimating the uncertainties in the derived displacement and pressure field solutions for the response of the fully coupled solid-fluid phases.