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Related Concept Videos

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Energy Conservation and Bernoulli's Equation01:16

Energy Conservation and Bernoulli's Equation

Applying the conservation of energy principle or the work-energy theorem to an incompressible, inviscid fluid in laminar, steady, irrotational flow leads to Bernoulli's equation. It states that the sum of the fluid pressure, potential, and kinetic energy per unit volume is constant along a streamline.
All the terms in the equation have the dimension of energy per unit volume. The kinetic energy per unit volume is called the kinetic energy density, and the potential energy per unit volume is...
Maximizing the Directional Derivative01:25

Maximizing the Directional Derivative

The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...
Laminar Flow: Problem Solving01:24

Laminar Flow: Problem Solving

Laminar flow occurs when a fluid moves smoothly in parallel layers with minimal mixing and turbulence. In fluid mechanics, ensuring laminar flow within a pipe is essential for precise control of flow characteristics, especially in engineering applications. The key factor in determining whether flow remains laminar is the Reynolds number, a dimensionless quantity that depends on the fluid's velocity, density, viscosity, and the pipe's diameter. A Reynolds number of 2100 or lower indicates...
Turbulent Flow: Problem Solving01:09

Turbulent Flow: Problem Solving

Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
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Surface Tension and Surface Energy

When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
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Optimizing subsurface carbon-energy synergy by balancing diffusion and convection via physics-informed Bayesian

Zongfa Li1,2,3,4, Guihua Yang1,2,3,4, Maoheng Li1,2,3,4

  • 1Hubei Key Laboratory of Complex Shale Oil and Gas Geology and Development in Southern China, Wuhan, 430100, China.

Scientific Reports
|July 7, 2026
PubMed
Summary

This study introduces a physics-informed optimization framework for enhanced oil recovery and carbon sequestration in shale, improving net present value and computation speed. The new method balances diffusion and convection for efficient hybrid CO₂-N₂ huff-n-puff operations.

Keywords:
Bayesian active learningDiffusion-convection couplingGeological carbon storageNanoconfined multiphase flowPhysics-informed machine learning

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Area of Science:

  • Petroleum Engineering
  • Geoscience
  • Computational Science

Background:

  • Optimizing enhanced oil recovery (EOR) and CO₂ sequestration in shale reservoirs is complex due to competing diffusion and convection physics.
  • Existing data-driven methods lack physical fidelity, failing to address these constraints effectively.

Purpose of the Study:

  • To develop a physics-informed adaptive ensemble surrogate-assisted Bayesian optimization framework (AES-BO) for co-optimizing EOR and CO₂ sequestration.
  • To address the limitations of black-box models in handling the diffusion-convection trade-off in shale reservoirs.

Main Methods:

  • Developed AES-BO, integrating Gaussian process regression, polynomial response surface, and radial basis function networks.
  • Dynamically weighted surrogates based on real-time cross-validation error to embed physical priors.
  • Applied the framework to a field-scale shale oil model for CO₂-N₂ hybrid huff-n-puff optimization.

Main Results:

  • Achieved a global optimum net present value of $64.2 million, outperforming other methods by 2.2-2.8%.
  • Accelerated computation by up to 82.7% compared to existing techniques.
  • Enhanced recovery factor by 8.23% using CO₂ for oil mobilization and N₂ for pressure maintenance, identifying an economic limit of three huff-n-puff cycles.

Conclusions:

  • AES-BO provides a generalizable, physics-guided paradigm for intelligent design of low-carbon subsurface energy systems.
  • The framework effectively links operational decisions to fundamental transport physics for optimized EOR and sequestration.
  • Demonstrated the economic viability and enhanced efficiency of hybrid CO₂-N₂ huff-n-puff operations in shale reservoirs.