Semi-Analytical Pressure Transient Solver for Fractured Reservoirs
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Solution Overview
Problem
Current methods for characterizing subterranean formations, such as pressure transient tests, face challenges in accurately estimating reservoir parameters, especially in naturally fractured reservoirs where available analytical solutions are limited, and conventional models like the Warren and Root dual-porosity model are not suitable for all fracture distributions.
Innovation Solution
A semi-analytical pressure transient solver is introduced to model pressure response for arbitrarily distributed fractures, allowing for the analysis of pressure and pressure derivative responses in reservoirs with fractures of varying conductivity, and global sensitivity analysis is used to identify key parameters that can be estimated from well test data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional models like the Warren and Root dual-porosity model are used, then analysis is simplified, but accuracy is reduced for naturally fractured reservoirs with arbitrary fracture distributions
Solution Approach 1:
The patent transitions from conventional dual-porosity models with fixed assumptions to a semi-analytical solution that incorporates variable fracture conductivity parameters. By changing the parameter representation from uniform to spatially varying conductivity, the model achieves both arbitrary fracture distribution capability and maintained analytical tractability through integral transform methods.
Solution Approach 2:
The patent segments the fracture system into discrete conductivity zones or elements, allowing different fracture regions to have different conductivity characteristics. This segmentation enables accurate representation of complex fracture networks while maintaining computational efficiency through superposition principles in the semi-analytical framework.
2Productivity
If available analytical solutions are used, then computational efficiency is maintained, but applicability to naturally fractured reservoirs is limited
Solution Approach 1:
The semi-analytical solution developed in the patent serves multiple functions: it handles arbitrary fracture distributions, variable fracture conductivity, different boundary conditions, and various well configurations within a single unified framework. This universal approach replaces the need for multiple specialized analytical solutions while maintaining computational efficiency through integral transform techniques.
Solution Approach 2:
The patent introduces integral transforms (Laplace and Hankel transforms) as mathematical intermediaries that bridge between the complex partial differential equations governing fluid flow in fractured reservoirs and analytically solvable forms. These transform methods enable the solution of arbitrary fracture configurations while preserving computational efficiency, acting as a mediator between physical complexity and mathematical tractability.
Data Source
AI summary
Method for using sensitivity analysis to inform the design and performance of a well test are provided. In one embodiment, a method includes providing a reservoir model of pressure transient behavior and performing a sensitivity analysis to identify an input parameter of the reservoir model that can be estimated from pressure transient test data collected from a well location. This method also includes using the results of the sensitivity analysis to design a pressure transient well test for measuring the identified input parameter. Other methods and systems are also disclosed.