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Related Concept Videos

Poisson's Ratio01:23

Poisson's Ratio

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Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Design Example: Flow of Oil Through Circular Pipes01:25

Design Example: Flow of Oil Through Circular Pipes

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Understanding fluid flow behavior through pipes is critical in fluid mechanics, especially in applications like oil transportation through pipelines. Hagen-Poiseuille's law provides an exact solution derived from the Navier-Stokes equations for steady, incompressible, and laminar flow within a circular pipe. Hagen-Poiseuille's law helps determine the necessary pressure drop across a pipeline section by determining parameters like pipe length, radius, oil viscosity, and the desired...
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Major Losses in Pipes01:28

Major Losses in Pipes

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When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions — whether laminar or turbulent — and the specific physical properties of the fluid and pipe.
Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to...
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Prediction of Poisson's ratio for a petroleum engineering application: Machine learning methods.

Fahd Saeed Alakbari1, Syed Mohammad Mahmood2,3, Mohammed Abdalla Ayoub4

  • 1Centre of Advanced Process Safety (CAPS), Universiti Teknologi PETRONAS, Seri Iskandar, Perak, Malaysia.

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This study developed an accurate Gaussian process regression (GPR) model to predict static Poisson

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Area of Science:

  • Petroleum Geoscience
  • Geomechanics
  • Data-driven Modeling

Background:

  • Static Poisson's ratio (νs) is critical for fracture pressure (FP) calculations in petroleum engineering.
  • Laboratory determination of νs is time-consuming and costly, driving the need for alternative methods.
  • Existing data-driven models for νs lack the accuracy and physical relationship insights required for critical applications.

Purpose of the Study:

  • To develop a reliable and accurate data-driven model for predicting static Poisson's ratio (νs).
  • To enhance model robustness by incorporating physical behavior alongside data-driven insights.
  • To evaluate the impact of improved νs prediction on fracture pressure (FP) determination accuracy.

Main Methods:

  • Developed and evaluated nineteen common machine learning methods using a large dataset (1691 samples).
  • Selected and enhanced the best-performing model, Gaussian Process Regression (GPR), with trend analysis.
  • Compared the enhanced GPR model against published methods for both νs prediction and subsequent FP calculations.

Main Results:

  • The enhanced GPR model achieved a coefficient of determination (R2) of 0.95 and an average absolute percentage relative error (AAPRE) of 2.73% for νs prediction.
  • GPR demonstrated accurate input-output relationships and superior precision across all practical ranges, confirmed by cross-plotting and error analyses.
  • The GPR model significantly reduced the residual error in fracture pressure (FP) determination from 87% to 26%.

Conclusions:

  • The proposed enhanced GPR model provides a highly accurate and robust method for predicting static Poisson's ratio (νs).
  • This improved νs prediction capability leads to a substantial increase in the accuracy of fracture pressure (FP) calculations.
  • The GPR model's ability to capture physical trends makes it a valuable tool for critical petroleum engineering applications.