Hydraulic Fracture Analysis

Introduction

The Pipeline HUB is home to many tools and calculators. The following user’s manual will outline calculations that cover design, construction, operations, and integrity. The HDD PT User’s Guide presents information, guidelines, and procedures for use during design, construction, operations, and integrity tasks for field or office applications. Horizontal Directional Drilling (HDD) is for professionals involved in the design, engineering, and installation of pipelines and utilities by horizontal directional drilling.

The HDD module provides a means to generate high-level drill designs and/or check and analyze existing designs you may encounter in the field. The underlying mathematical models and technical procedures are based on the latest HDD technology and are following current regulations, standards, and recommended practices. The HDD module provides standard stress and pull force analysis for steel, drilling fluid, and pressure analysis, and addresses the installation of cables in conduits.

Mud Management

Inadvertent returns of the drilling fluid to the surface are often a significant issue for HDD installations. Even though the drilling fluid is usually a non-toxic fluid containing mainly fresh water and 1% to 3% bentonite, accidental surface returns can be detrimental. The risk of inadvertent returns can be reduced by proper HDD design and good drilling practices.

Hydro-fracture occurs in non-fissured cohesive soils when the pressure gradient in the borehole exceeds the formation pressure gradient. This happens when the drilling fluid pressure exceeds the strength and confining stress of the surrounding soils. Under these conditions, the pressure fractures the soil around the borehole wall and allows the drilling fluid to escape the annulus. The likelihood of this occurring is often modeled with the cavity expansion model

The cavity expansion model can be used to calculate the estimated maximum allowable drilling fluid pressure in a borehole. The risk of hydrofracture can be evaluated by calculating the maximum allowable pressure with the following cavity expansion equation (often referred to as the Delft Equation). The minimum required pressure needs to be considerably lower than the maximum allowed pressure to reduce the chance of hydrofracture.

Initial Ground Water Pressure:

\mu = \gamma_{\text{water}} (h_w)

\mu = \gamma_{\text{water}} (h_w)

𝛾_{𝑤𝑎𝑡𝑒𝑟} = Unit weight of water above the groundwater (lb/ft3)
ℎ_𝑤 = Depth of the bore below groundwater elevation (ft)

Unit Weight of Soil Below Groundwater Elevation:

\gamma_w = \gamma_{\text{soil}} – \gamma_{\text{water}}

\gamma_w = \gamma_{\text{soil}} - \gamma_{\text{water}}

γ_soil = Unit weight of soil above the groundwater (lb/ft3)

Radius of Plastic Zone:

R_{\text{pmax}} = \frac{h_{\text{total}}}{2}

R_{\text{pmax}} = h_{\text{total}}

h_total = Height of Ground Surface at Point of Interest (ft)

Effective Stress:

\sigma_0=\gamma_w\cdot h_{total}

\sigma_0=\gamma_w\cdot h_{total}

Cavity Expansion Model

Maximum Allowable Mud Pressure:

P_{\text{max1}} = \mu +( \sigma_0(1 + \sin\varphi) + c.\cos\varphi +c.\cot\varphi)\left[ \left( \frac{R_0}{R_{\text{pmax}}} \right)^2 +\frac{\sigma_0.\sin\varphi + c.\cos\varphi} G\right]^{{ \frac{-\sin\varphi}{1+\sin\varphi}}} – c.\cot\varphi \~\P_{\text{max2}} = \mu + (\sigma_0(1 + \sin\varphi)) \left[ \left( \frac{R_0}{R_{\text{pmax}}} \right)^2 + \frac{ \sigma_0\sin\varphi}{G} \right] ^{{{\frac{-\sin\varphi}{1+\sin\varphi}}}}\~\ P_{\text{max3}} = \mu + \sigma_0 + c

P_{\text{max1}} = \mu +( \sigma_0(1 + \sin\varphi) + c.\cos\varphi +c.\cot\varphi)\left[ \left( \frac{R_0}{R_{\text{pmax}}} \right)^2 +\frac{\sigma_0.\sin\varphi + c.\cos\varphi} G\right]^{{ \frac{-\sin\varphi}{1+\sin\varphi}}} - c.\cot\varphi \\~\\P_{\text{max2}} = \mu + (\sigma_0(1 + \sin\varphi)) \left[ \left( \frac{R_0}{R_{\text{pmax}}} \right)^2 + \frac{ \sigma_0\sin\varphi}{G} \right] ^{{{\frac{-\sin\varphi}{1+\sin\varphi}}}}\\~\\ P_{\text{max3}} = \mu + \sigma_0 + c

φ = Soil friction angle (degree)
R₀ = Borehole radius (inch)
C =Cohesion coefficient (lb/ft2)
G = Shear modulus of soil (lb/ft2)

Safety factor when applied is used to the Maximum Allowable Mud Pressure. A safety factor of 1.5 for sands or 2.0 for clays could be used to determine the maximum pressure at the critical location (Delft, 1997).

Pmax with Safety Factor (SF)

Minimum Required Mud Pressure:

v := \frac{Q}{0.785(\text{bore}{diameter} – d{\text{pipe}})^2}\~\P_{\text{min}} = \gamma_{\text{mud}}.h_{\text{total}} + L_{\text{bore}} \left{ \left[ \frac{\mu_{p1}.v}{(\text{bore}{diameter} – d{\text{pipe}})^2} \right] + \left[ \frac{\tau_y}{\text{bore}{diameter} – d{\text{pipe}}} \right] \right}

v = \frac{Q}{2.448(\text{bore}_{diameter}^2 - d_{\text{pipe}}^2)}\\~\\P_{\text{min}} = \gamma_{\text{mud}}.h_{\text{total}} + L_{\text{bore}} \left\{ \left[ \frac{\mu_{p1}.v}{(\text{bore}_{diameter} - d_{\text{pipe}})^2} \right] + \left[ \frac{\tau_y}{\text{bore}_{diameter} - d_{\text{pipe}}} \right] \right\}

ϒ_mud = Unit weight of drilling fluid (lb/gal)
L_bore = Distance from the rig entry point (ft)
bore_diameter = Borehole diameter (inch)
d_pipe = Drill or pipe product outside diameter (inch)
µ_p1 = Viscosity of drilling fluid (cP)
τy = Yield point of drilling fluid (lb/100ft2

Average Soil Layer Model

The Average Soil layer model is also called as the Average Delfts model and is useful in evaluating the stress induced in the bore profile due to different layers of soil materials.  

In this situation calculate the initial effective stress (σo) for each soil layer and add them together to get the initial effective stress at the point of interest.

There are 3 variations of the model available in HDD PowerTool

Contact Layer

This approach use the soil weight of the layer of soil around the borehole as this will have the greatest influence since the pressures are highest near the bore in calculating the total effective stress.

Here strata IV is closest to the bore profile and hence soil weight of the highlighted layer will be used to calculate  total effective stress.

Average Soil Weight

In this approach the effective stress is evaluated using the average soil weight of the individual soil layers. Once effective stress of each layer is calculated they are added to obtain the total effective stress (σo).

Weighted Average

The soil friction angle, cohesion, and shear modulus can also change with the various soil conditions. The values for these variables can be used as a weighted average in this approach to provide a convenient and provide conservative results.

In the example approach below to calculate shear modulus, we  assume the layer of soil around the borehole will have the greatest influence since the pressures are highest near the bore. So we have weighted the layer at 85% (0.85) and the rest of the layer accordingly.

The same approach can be applied for all the soil properties (soil friction angle, cohesion, soil weight and shear modulus) in the Average Soil Layer model.

Input Parameters (Single Point)

• Borehole Diameter [inch]
• Drill or Pipe Product Outside Diameter [inch]
• Unit Weight of Drilling Fluid [lb/gal]
• Mud Flow Rate [gal/min]
• Yield Point of Drilling Fluid [lb/100ft2]
• Viscosity Drilling Fluid [cP]
• Height of Ground Surface at Point of Interest [ft]
• Height of Water Table at Point of Interest [ft]
• Height of Standing Water at Point of Interest [ft]
• Height from Point of Interest to Surface at HDD Entry Point [ft]
• Distance from the entry Point [ft]
• Soil Type
• Soil Friction Angle [degree]
• Soil Cohesion [lb/ft2]
• Soil Shear Modulus [lb/ft2]
• Unit Weight of Soil [lb/ft3]
• Unit Weight of Water [lb/ft3]

Outputs/Reports (Single Point)

• Initial Ground Water Pressure [lb/ft2]
• Unit Weight of Soil Below Groundwater Elevation [ [lb/ft3]
• Radius of Plastic Zone [ft]
• Effective Stress [lb/ft2]
• Maximum Allowable Mud Pressure [psi]
• Minimum Allowable Mud Pressure (HDD Consortium) [psi]

Input Parameters (Multiple Point)

• Borehole Diameter [inch]
• Drill or Pipe Product Outside Diameter [inch]
• Unit Weight of Drilling Fluid [lb/gal]
• Mud Flow Rate [gal/min]
• Yield Point of Drilling Fluid [lb/100ft2]
• Viscosity Drilling Fluid [cP]
• Unit Weight of Water [lb/ft3]

Outputs/Reports (Multiple Point)

• Station
• Distance from the Rig Site
• Maximum Allowable Mud Pressure
• Minimum Required Mud Pressure
• Borehole Stability Analysis
  • Plot/Graph
  • Expanded Version

References

• Willoughby, David (2005). Horizontal Directional Drilling, McGraw-Hill, New York, ISBN 0-87814-395-5. v.
• Willoughby, David, Training – Horizontal Directional Drilling, TTI, November 2016
• HDD Consortium. (2001). Horizontal directional drilling, good practices guidelines, HDD Consortium.
• Horizontal Directional Drilling Training Manual, Horizontal Drilling International, February 1999
• Skonberg, Eric R. II. Muindi, Tennyson M. (2014). Pipeline Design for Installation by Horizontal Directional Drilling, American Society of Civil Engineers. Horizontal Directional Drilling Design Guideline Task Committee.
• “Installation of Pipelines by Horizontal Directional Drilling”, PRCI Report PR-227-9424
• Nayyar, Mohinder L. (1992). Piping Handbook, 6th Edition, McGraw-Hill, New York, NY.
• AWWA (2006), PE Pipe Design and Installation, M55, American Water Works Association, Denver, CO
• ASTM (1962), PPI Handbook

FAQ