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Related Concept Videos

Energy Line and Hydraulic Gradient Line01:27

Energy Line and Hydraulic Gradient Line

Based on Bernoulli's equation, the energy line (EL) and hydraulic grade line (HGL) provide graphical representations of energy distribution in a fluid flow system. For steady, incompressible, inviscid flows, Bernoulli's equation is expressed as:
Isothermal Processes01:21

Isothermal Processes

A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to maintain thermal equilibrium. Processes involving phase changes like water evaporation into steam or freezing water into ice at a constant temperature are examples of Isothermal Processes.
An ideal gas can also undergo isothermal expansion or compression.
For example, consider 1 mole of an ideal gas inside an isolated cylinder at initial volume V...
Thermodynamic Potentials01:26

Thermodynamic Potentials

Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
Thermodynamic Systems01:06

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of  tea boiling in a kettle. The tea and...
Thermal expansion and Thermal stress: Problem Solving01:27

Thermal expansion and Thermal stress: Problem Solving

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
Work and Energy for Variable Forces01:10

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...

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Related Experiment Videos

A robust physics-constrained neural operator framework for efficient geothermal resource development.

Zhenqian Xue1, Jianfei Bi2, Haoming Ma3

  • 1Department of Chemical & Petroleum Engineering, University of Calgary, Calgary, AB, Canada.

Nature Communications
|May 15, 2026
PubMed
Summary
This summary is machine-generated.

A new physics-constrained neural operator framework accelerates geothermal system evaluation. This method provides accurate, physically consistent predictions for scalable geothermal energy development.

Related Experiment Videos

Area of Science:

  • Geothermal Energy Engineering
  • Computational Science
  • Artificial Intelligence in Energy

Background:

  • Efficient evaluation of geothermal systems is crucial for scalable development.
  • Conventional methods face challenges due to high computational costs and limited surrogate model generalizability.

Purpose of the Study:

  • To present a physics-constrained neural operator framework for rapid, high-resolution, and physically consistent geothermal system evaluation.
  • To enable accurate prediction of subsurface dynamics and surface energy production across diverse conditions.

Main Methods:

  • Developed a physics-constrained neural operator framework learning the solution operator of governing partial differential equations.
  • Integrated modules for power output estimation and techno-economic assessment.

Main Results:

  • Achieved an average relative error of 1.76% for reservoir predictions and 1.70% for target variables.
  • Demonstrated approximately 1,400-fold acceleration compared to conventional numerical methods.
  • Enabled consistent techno-economic assessment across multiple geothermal applications.

Conclusions:

  • The framework offers a scalable pathway for geothermal development by supporting rapid analyses.
  • Facilitates resource assessment, uncertainty quantification, and multi-objective optimization for geothermal energy.