Matrix Acidizing Simulation Using Complex Potential Theory
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Solution Overview
Problem
Current matrix acidizing models are limited in accurately simulating non-axisymmetric acid flow in carbonate reservoirs, which is crucial for optimizing well production as they often assume axisymmetric conditions that are not always present, leading to suboptimal treatment designs.
Innovation Solution
A computationally efficient method using complex potential theory to determine streamlines and solve acid flow along them, incorporating parameters from core flood experiments like Θr and Δpr for self-diverting acids, and optimizing treatment designs through an optimization loop with user-input parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If axisymmetric flow models are used for acid placement simulation, then the modeling process is simpler and faster, but the accuracy of predicting acid flow in non-axisymmetric conditions deteriorates
Solution Approach 1:
The patent segments the acid flow simulation into two distinct phases: a rapid axisymmetric flow field calculation that provides the overall flow pattern, and a more detailed non-axisymmetric streamline tracking that follows acid flow paths individually. This segmentation allows the system to achieve both speed (from the simplified first phase) and accuracy (from the detailed second phase).
Solution Approach 2:
The patent explicitly handles non-axisymmetric flow conditions by allowing the flow field to vary with angular position around the wellbore. The model calculates asymmetric flow patterns that reflect actual reservoir conditions, such as anisotropic permeability and uneven acid distribution, rather than forcing symmetric simplifications that reduce accuracy.
2Measurement precision
If complex potential theory is used to determine streamlines for non-axisymmetric flow, then the accuracy of acid flow modeling improves, but the computational complexity increases
Solution Approach 1:
The patent introduces complex potential theory as an intermediary mathematical tool that bridges the gap between simple axisymmetric flow calculations and detailed non-axisymmetric streamline tracking. The complex potential function serves as a mediator that encodes both the simplicity of potential flow theory and the complexity of non-axisymmetric conditions, allowing accurate modeling without requiring fully complex numerical simulations throughout.
Solution Approach 2:
The patent replaces direct numerical solution of complex non-axisymmetric flow equations with an analytical approach using complex potential theory. This substitution of mechanical/mathematical methods allows the system to handle non-axisymmetric flow without the computational burden of full numerical simulations, reducing complexity while maintaining accuracy.
3Reliability
If more acid volume is used to ensure adequate well stimulation, then the production increase target is more reliably achieved, but the treatment cost increases
Solution Approach 1:
The patent implements feedback mechanisms that continuously monitor and adjust acid placement based on real-time flow field calculations and streamline tracking. The system uses feedback from core flood experiments and reservoir models to optimize acid volume, ensuring adequate stimulation while minimizing waste. This feedback loop allows dynamic adjustment of acid volume based on actual flow conditions and wormhole propagation.
Solution Approach 2:
The patent changes key parameters such as acid concentration, injection rate, and total volume based on calculated flow field characteristics and reservoir conditions. By dynamically adjusting these parameters rather than using fixed volumes, the system achieves reliable production increases while optimizing acid consumption to reduce costs.
Data Source
AI summary
A computationally efficient general method of modeling or simulating matrix acidizing treatment when flow is not axisymmetric involves determining streamlines in the general flow field using complex potential theory to solve for the flow along the streamlines. The flow over a time step is used to model the propagation of the acid front and the creation and extension of wormholes.