The first step in calculating the estimated pulling loads is to develop the input data that will be used in the calculations. This data includes the product-pipe material properties, the drilling-fluid properties, and any code or design factors that are applicable. An example of the input data required for calculating estimated pulling loads is provided in Example 6-1 later in this chapter.
Defining the Bore Path The next step is to define the bore path for the crossing. Figure 6-1 defines a typical bore path profile. The values are assigned to the variables based on the profile required to successfully cross the obstacle while reaching the required depth. The preliminary attempt at determining the values is based on the definition of the obstacle, the subsurface conditions, and the material properties of the product pipe. Using this data and the equations provided in Chapter 8, the designer can develop a combination of straight lines and curves that will cross the obstacle at the desired depth within the available overall bore length. Figure 6-2 provides an example of a designed bore path where:
L1 = 91 feet Lard = 126 feet Ls = 52 feet Larc2 = 126 feet L2 = 177 feet
148 Chapter 6 ■ HDD Stress Analysis for Steel Product Pipe
In this example the total bore length is the sum of each segment for a bore-path length of 572 feet.
Straight Sections After defining the input data and the bore path, the calculations begin with the straight section of pipe, assuming that the pipe is pulled from the left to the right (as viewed in Figure 6-2). The modeling and calculation process must be done from the pipe side to the rig side. As stated earlier, it is usually assumed that the load at point 1 is zero. When using this assumption the first calculated load is at the end of the first straight section, or point 2. Each straight section is modeled with variables as shown in Figure 6-3.
For any straight section the tension at T2 is calculated from the static force balance:
where:
T2 = the tension (or pull load) at the rig side of the straight section required to overcome the drag and friction in pounds T1 = the tension (or pull load) at the pipe side of the straight section, usually assumed to be zero, in pounds | fric\ = the friction between the pipe and soil in pounds
The +/- term is (-) if T2 is downhole, (+) if T2 is uphole, and (0) if the hole is horizontal.
where:
DRAG = the fluidic drag between the pipe and the drilling fluid in pounds
T2 = T1 +1 fric\ + DRAG ± WS * L *sin 0 Equation 6-1
where:
DRAG = the fluidic drag between the pipe and the drilling fluid in pounds
Equation 6-2
Equation 6-3
FIGURE 6-3 Straight Section where:
WS = the effective (submerged) weight of the pipe plus any internal contents (if filled with water) in foot-pounds L1 = the length of the straight section in feet n = the angle of the straight section relative to the horizontal plane (zero is horizontal and 90 degrees is vertical) ^soii = the average coefficient of friction between the pipe and soil; the recommended value is 0.21 to 0.30 (Maidla) ^ mud = the fluid-drag coefficient for steel pipe pulled through the drilling mud; the recommended value is 0.025 to 0.05 D = the outside diameter of the pipe in inches
Curved Sections Each curved section is modeled with variables as shown in Figure 6-4.
The variables that are different than those in the straight sections are:
= the radius of curvature of the curved section between points 2 and 3 in feet 0c1 = the angle of the curved section in degrees
01 = the angle from horizontal of T2 at the right end of the section in degrees
02 = the angle from horizontal of T3 at the left end of section in degrees 0 = (01 + e2)/2 in degrees
Larc1 = R1 x 0c1 in feet
The values N, N1, and N2 are the contact forces at the center, right, and left points of the section. The values fric, fric1, and fric2 are the frictional forces at the center,
150 Chapter 6 ■ HDD Stress Analysis for Steel Product Pipe right, and left points of the section. The curved sections are modeled as three-point beams. For the bent pipe to fit in the bore hole it must bend enough to place its center at a point that reflects the displacement (h):
Equation 6-4
This method is not completely accurate, however, since the objective is to determine the normal contact forces and then calculate the frictional forces, it is an acceptable estimation. The vertical component of the distributed weight and the arc length of the pipe section are used to find N. From Roark's2 solution for elastic beam deflection:
Equation 6-5
where:
arc 12
arc 12
Í • A j |
*tanh |
' U ^ |
12 J |
Larc 2 cosh Equation 6-7 Equation 6-8 Equation 6-9 Equation 6-10 E = Young's Modulus for steel (2.9 x 107 psi). t = Pipe wall thickness in inches Equations 6-5 and 6-8 both require a value for T, which is the average value of T2 and T3. This requires an iterative solution to solve for T3. One method is to change the variable T to an assumed average value and solve the problem until the required accuracy is obtained. The assumed average value of T should be within 10 percent of the actual average of T2 and T3 where the values: T = T + T and T"vg ~ Tavgassumed * 100 should be with 10 percent. If not within avg 2 T avgassumed 10 percent use a new assumed value for Tavg and solve again. Using computer programs makes this a relatively easy task. For a curved section fric becomes: The reactions at the end of the curved section are assumed to be N/2, and end friction forces are assumed to be fric/2. For positive values of N (defined as downward-acting as in Figure 6-4) the bending resistance and/or buoyancy of the pipe is sufficient to require a normal force acting against the top of the hole in order for the pipe to displace downward by an amount equal to h. Where N is negative, the submerged pipe weight is sufficient to carry the pipe to the bottom of the curved section, where an upward-acting normal force is felt at the point of contact. Regardless of the value of N, all friction values are positive, acting in opposition to T3. The estimated forces acting along the curved path of the pipeline are added as if they were acting in a straight line. As a result T3 becomes: Equation 6-12 The load at point 3 then becomes AT3 + T2 in pounds of force. Total Pulling Loads The total force (or pulling load) required to pull the pipe through the bore hole is the sum of the required force for all the straight and curved sections in the pipeline. Example 6-1 is an example of the pulling-load calculations for the HDD crossing provided in Figure 6-2. |
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