Horizontal Drilling | What is a horizontal drilling?

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Horizontal Drilling, Horizontal Wells, Horizontal Well, Directional and Horizontal Drilling

Build Curve Design

There are four basic build curve designs used in bringing a well from vertical to horizontal:

single build (Figure 1)

Single build, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 1**

simple tangent (Figure 2)

Simple tangent, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 2**

Complex tangent (Figure 3)

Complex tangent, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 3**

Ideal (Figure 4)

Ideal Build Curve, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 4**

The equations for designing these curve types are easy to derive, and are summarized below (Schuh, 1989).

From Figure 5 (Circular arc),

Circular arc build curve design, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 5**

$L_{c}= \dfrac{\theta _{i}-\theta _{i-1}}{BR}$ (1)

$\Delta H_{b}= R_{b}\cdot \left ( \cos\theta_{i-1}-\cos \theta_{i} \right )$ (2)

$\Delta V_{b}= R_{b}\cdot \left ( \sin \theta_{i-1}-\sin \theta_{i} \right )$ (3)

where

L_c = length of curved section

R_b = build curve radius

BR = build rate angle

ΔH_b = horizontal displacement of build curve section

ΔV_b = vertical displacement of build curve section

θ_i, θ_i−1 = inclination angles at stations i and i−1, respectively, on build curve

The straight section required to hit a sloping target (Figure 6) is

Sloping target, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 6**

$L_{s} = \dfrac{\Delta H_{s}}{\sin \theta_{s}}$ (4)

$\Delta H_{s}= \dfrac{\Delta V_{s}}{\cos \theta _{s}-\cos \theta _{tr}}$ (5)

where

L_s = length of straight section

ΔH_s = horizontal displacement of straight section.

ΔV_s= height to target slope.

θ_s, θ_tr = straight section and target angles, respectively.

s = straight

tr = target

The build rate angle required to hit a sloping target (Figure 7) is

$BR = \dfrac{57.3}{V_{tr}}\cdot \left ( \sin \theta _{i} - \sin \theta _{i -1} +\dfrac{\cos \theta _{i}\cdot \cos \theta _{i-1}}{\tan \theta _{tr}}\right )$ (6)

where

BR = build rate

V_tr = vertical height from target

The build rate angle, Build Curve Design, Horizontal Wells, Directional and Horizontal Drilling, Directional Drilling — **FIGURE 7**

$\Delta H = \dfrac{57.3}{BR}\cdot \left ( \cos \theta _{i-1}-\cos \theta _{i} \right )$ (7)

$\Delta V_{tr} = \dfrac{57.3}{BR}\cdot \left ( \sin \theta _{i}-\sin \theta _{i-1}+\dfrac{\cos \theta _{i}\cdot \cos \theta_{i-1} }{\tan \theta_{tr}} \right )$ (8)

$\Delta V = \dfrac{57.3}{BR}\cdot \left ( \sin \theta _{i}-\sin \theta _{i-1} \right )$ (9)

The tool face angle required for the second build is

$\phi _{tf}= \cos^{-1} \dfrac{BR_{1}}{BR_{2}}$ (10)

The dog-leg severity is

$DL = \left ( \theta _{i} -\theta _{i-1}\right )\cdot \left ( \dfrac{BR_{1}}{BR_{2}} \right )$ (11)

The azimuth change is

$\alpha = \left ( 57.3\cdot \tan \phi _{tf} \right )\cdot \ln \left [ \dfrac{\tan\left ( \dfrac{\phi _{1}}{2} \right ) }{\tan \left ( \dfrac{\phi_{i-1}}{2}\right )} \right ]$ (12)