Skip to content
  • Home
  • About
    • Privacy Policy
  • Categories
    • Hiking & Activities
    • Outdoor Gear
    • Regional Specifics
    • Natural Environments
    • Weather & Forecasts
    • Geology & Landform
Geoscience.blogYour Compass for Earth's Wonders & Outdoor Adventures
  • Home
  • About
    • Privacy Policy
  • Categories
    • Hiking & Activities
    • Outdoor Gear
    • Regional Specifics
    • Natural Environments
    • Weather & Forecasts
    • Geology & Landform
Posted on June 8, 2024 (Updated on July 12, 2025)

measuring fracture length and width using PKN and KGD models for hydraulic fracturing?

Energy & Resources

Decoding Fracking: Cracking the Code on Fracture Length and Width

Hydraulic fracturing, or “fracking” as it’s more commonly known, is like giving an oil or gas well a supercharge. Think of it as a way to boost production, especially in those tricky reservoirs where oil and gas just don’t flow easily. The basic idea? We pump fluid down the well at crazy-high pressure to crack open the surrounding rock, creating fractures that let the good stuff flow more freely. But here’s the million-dollar question: how do we know how big these cracks are? That’s where understanding fracture length and width comes in – it’s absolutely crucial for getting the most bang for our buck. Several models help us estimate these fracture dimensions, and among the most popular are the PKN and KGD models. They’re not perfect, mind you, but they give us valuable insights under the right conditions.

Why Fracture Geometry Matters (A Lot!)

Imagine trying to water your garden with a hose that has a kink in it. Not very effective, right? Well, the same goes for fracking. The size and shape of the fractures we create directly impact how well the well produces. Fracture length dictates how much of the reservoir we’re actually tapping into, while fracture width determines how easily fluids can flow back to the well. Get these dimensions wrong, and you’re leaving money on the table. Accurate estimation is essential for designing efficient fracturing treatments, predicting well performance, and optimizing proppant placement.

PKN Model: When Fractures Go Long (and Tall)

The PKN model, named after Perkins, Kern, and Nordgren, is your go-to when you’re dealing with fractures that are long and thin, like a stretched-out rubber band. It’s a 2D model, meaning it simplifies things by assuming the fracture height stays pretty constant. This is typical in formations where you’ve got strong layers of rock above and below that prevent the fracture from growing upwards or downwards. In essence, it assumes that the fracture is much longer than it is tall. The PKN model also works best when we can assume the rock behaves in a predictable, elastic way, and when the fluid flows smoothly, without too much turbulence.

PKN Model: The Fine Print (Assumptions)

  • Fracture length is much greater than fracture height
  • The rock behaves predictably (linear isotropic elasticity)
  • Fluid flows smoothly (laminar flow)
  • The fracture stays the same height

Crunching the Numbers: PKN Style

Alright, let’s get a little technical, but I’ll keep it simple. The PKN model gives us formulas to estimate fracture half-length ($x_f$) and the maximum width at the wellbore ($w_{w,0}$). These formulas use things like the injection rate (how fast we’re pumping fluid), the rock’s properties (Young’s modulus and Poisson’s ratio), the fluid’s viscosity (how thick it is), the fracture height, and the pumping time.

  • Fracture half-length ($x_f$):

    $\displaystyle x_f = \left( \frac{625}{512} \frac{Q_0^3 E’}{\mu h_f^4} t^4 \right)^{1/5}$

  • Maximum width at the wellbore ($w_{w,0}$):

    $\displaystyle w_{w,0} = \left( \frac{512}{625 \pi^3} \frac{\mu Q_0^2 h_f}{E’^2} t \right)^{1/5}$

    Where:

    • $Q_0$ is the injection rate.
    • $E’$ is the plane strain modulus, defined as $E’ = E / (1 – \nu^2)$, where $E$ is Young’s modulus and $\nu$ is Poisson’s ratio.
    • $\mu$ is the fluid viscosity.
    • $h_f$ is the fracture height.
    • $t$ is the pumping time.

The average fracture width ($\bar{w}$) for a PKN fracture is related to the maximum width at the wellbore: $\bar{w}= (\pi/5) w_{w}$ .

KGD Model: When Height is King

Now, let’s flip the script. The KGD model, named after Khristianovich, Geertsma, and de Klerk, is best suited for fractures where the height is the dominant factor. Think of a tall, narrow fracture, almost like a crack in a wall. This model is often used when the fracture tends to spread out vertically, either because the rock layers aren’t strong enough to contain it, or because the stresses in the earth are aligned in a way that encourages upward growth. Like the PKN model, it assumes the rock behaves elastically and the fluid flows smoothly.

KGD Model: The Fine Print (Assumptions)

  • Fracture height is much greater than fracture length
  • The rock behaves predictably (linear isotropic elasticity)
  • Fluid flows smoothly (laminar flow)

KGD: Calculating Fracture Dimensions

The KGD model also gives us ways to estimate fracture size, but the equations can get a bit hairy depending on the specific assumptions you make. A common approach involves using the Geertsma-de Klerk equation and Sneddon’s elasticity equation. For a static penny-shaped fracture without leakoff under constant net normal pressure $p_0$, the following equations apply :

  • Fracture radius (R):

    $R = \left( \frac{3 E’ Q_0 t}{8 \sqrt{\pi} K_{Ic}} \right)^{0.4}$

  • Wellbore net pressure ($p_0$):

    $p_0 = \frac{\sqrt{\pi} K_{Ic}}{2 \sqrt{R}}$

  • Wellbore fracture width ($w_0$):

    $w_0 = \frac{8 p_0 R}{\pi E’}$

    Where:

    • $E’$ is the plane strain modulus.
    • $Q_0$ is the injection rate.
    • $t$ is the pumping time.
    • $K_{Ic}$ is the fracture toughness.

PKN or KGD: How to Choose?

So, which model do you use? It all boils down to the specific situation. If you’re dealing with long, confined fractures, PKN is your friend. If you’re seeing significant height growth, KGD is the way to go.

A Word of Caution: Models are Just Models

It’s crucial to remember that these models are simplifications. They’re based on assumptions that aren’t always true in the real world. Things like variations in the rock, weird fluid behavior, and existing cracks in the formation can all throw a wrench in the works.

That’s why more advanced models exist, like pseudo-3D (P3D) and full 3D models. These can handle more complex scenarios, but they also require more data and computing power. No matter which model you use, it’s always a good idea to calibrate it with real-world data, like microseismic monitoring.

The Bottom Line

The PKN and KGD models are valuable tools for understanding fracture geometry in hydraulic fracturing. They’re not perfect, but they provide a solid foundation for making informed decisions. By understanding their assumptions and limitations, and by combining them with real-world data and more advanced techniques, we can optimize our fracturing treatments and unlock the full potential of our reservoirs.

New Posts

  • Headlamp Battery Life: Pro Guide to Extending Your Rechargeable Lumens
  • Post-Trip Protocol: Your Guide to Drying Camping Gear & Preventing Mold
  • Backcountry Repair Kit: Your Essential Guide to On-Trail Gear Fixes
  • Dehydrated Food Storage: Pro Guide for Long-Term Adventure Meals
  • Hiking Water Filter Care: Pro Guide to Cleaning & Maintenance
  • Protecting Your Treasures: Safely Transporting Delicate Geological Samples
  • How to Clean Binoculars Professionally: A Scratch-Free Guide
  • Adventure Gear Organization: Tame Your Closet for Fast Access
  • No More Rust: Pro Guide to Protecting Your Outdoor Metal Tools
  • How to Fix a Leaky Tent: Your Guide to Re-Waterproofing & Tent Repair
  • Long-Term Map & Document Storage: The Ideal Way to Preserve Physical Treasures
  • How to Deep Clean Water Bottles & Prevent Mold in Hydration Bladders
  • Night Hiking Safety: Your Headlamp Checklist Before You Go
  • How Deep Are Mountain Roots? Unveiling Earth’s Hidden Foundations

Categories

  • Climate & Climate Zones
  • Data & Analysis
  • Earth Science
  • Energy & Resources
  • General Knowledge & Education
  • Geology & Landform
  • Hiking & Activities
  • Historical Aspects
  • Human Impact
  • Modeling & Prediction
  • Natural Environments
  • Outdoor Gear
  • Polar & Ice Regions
  • Regional Specifics
  • Safety & Hazards
  • Software & Programming
  • Space & Navigation
  • Storage
  • Water Bodies
  • Weather & Forecasts
  • Wildlife & Biology

Categories

  • Climate & Climate Zones
  • Data & Analysis
  • Earth Science
  • Energy & Resources
  • General Knowledge & Education
  • Geology & Landform
  • Hiking & Activities
  • Historical Aspects
  • Human Impact
  • Modeling & Prediction
  • Natural Environments
  • Outdoor Gear
  • Polar & Ice Regions
  • Regional Specifics
  • Safety & Hazards
  • Software & Programming
  • Space & Navigation
  • Storage
  • Water Bodies
  • Weather & Forecasts
  • Wildlife & Biology
  • English
  • Deutsch
  • Français
  • Home
  • About
  • Privacy Policy

Copyright (с) geoscience.blog 2025

We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. By clicking “Accept”, you consent to the use of ALL the cookies.
Do not sell my personal information.
Cookie SettingsAccept
Manage consent

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. These cookies ensure basic functionalities and security features of the website, anonymously.
CookieDurationDescription
cookielawinfo-checkbox-analytics11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics".
cookielawinfo-checkbox-functional11 monthsThe cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional".
cookielawinfo-checkbox-necessary11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary".
cookielawinfo-checkbox-others11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other.
cookielawinfo-checkbox-performance11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Performance".
viewed_cookie_policy11 monthsThe cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. It does not store any personal data.
Functional
Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features.
Performance
Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.
Analytics
Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc.
Advertisement
Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. These cookies track visitors across websites and collect information to provide customized ads.
Others
Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet.
SAVE & ACCEPT