Lagrangian Transport Simulator for Stimulation Design
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Solution Overview
Problem
Current numerical models for stimulation treatments in subterranean formations, such as hydraulic fracturing and acidizing, face complexity in accurately simulating the transport of multiple materials like proppants, acids, and fibers due to the need for fine resolution in space and time, especially in unconventional reservoirs with multiple geological layers, limiting their ability to optimize well productivity.
Innovation Solution
A method using a Lagrangian approach with particle-in-cell (PIC) algorithms and methods of characteristics to simulate the transport of materials during stimulation treatments, allowing for the calculation of physical quantity distributions within the stimulated flow domain, enabling the determination and preparation of an optimal stimulation treatment design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical models with fine resolution are used to accurately simulate material transport, then simulation accuracy is improved, but computational complexity increases
Solution Approach 1:
The simulation domain is segmented into discrete computational cells or elements, allowing the complex transport problem to be broken down into manageable segments. Each segment can be solved independently using the Lagrangian approach, reducing overall computational complexity while maintaining accuracy through proper segmentation of the flow domain.
Solution Approach 2:
The patent transforms the traditional Eulerian fixed-grid approach into a Lagrangian moving-grid approach, fundamentally changing the reference frame parameter. This parameter change allows the simulation to naturally adapt to material movement without requiring fine spatial resolution, thereby reducing computational complexity while preserving simulation accuracy.
2Device complexity
If traditional numerical models are used for multiple material transport, then model simplicity is maintained, but simulation accuracy deteriorates
Solution Approach 1:
The patent introduces a Lagrangian reference frame as an intermediary between the fixed computational grid and the moving materials. This intermediary allows accurate tracking of multiple materials (proppants, acids, fibers) through the use of material-specific velocity fields and concentration equations, achieving high simulation accuracy without requiring complex multi-phase flow models.
3Productivity
If high resolution simulation is performed for unconventional reservoirs, then treatment optimization is improved, but computational resources required increase
Solution Approach 1:
The patent implements a dynamic simulation approach where the computational grid moves with the materials rather than remaining fixed. This dynamic Lagrangian approach efficiently captures the evolving concentration distributions of multiple materials during stimulation treatment, enabling treatment optimization without requiring excessive computational resources for static fine-grid resolution.
Data Source
AI summary
A method of stimulating a subterranean formation includes acquiring stimulation treatment input data, simulating a transport of at least one material transport present in a stimulation treatment design with a transport simulator model, determining and preparing the treatment design and performing the stimulating treatment according to the selected treatment design. As recited, simulating includes assuming that for each time stage of the stimulation treatment a velocity field for the at least one material transport and a stimulated flow domain geometry are known and calculating at each time stage the distribution of at least one physical quantity of the at least one material transport using a Lagrangian approach.