Page 58 -

Mud Hydraulics Fundamentals 35

The critical Reynolds number N Rec in the annulus is calculated as follows:
1

8ð2 × 0:8 + 1Þ 1−0:2638
N Rec = = 2,737
0:8 × 0:0767
Since N Re < 2,737, laminar flow exists in the annular space.

2.3.2 Pressure Loss
For drilling fluid to flow through the circulating system, it must over-
come frictional forces between the fluid layers, solid particles, pipe wall,
and borehole wall. The pump pressure corresponds to the sum of these
forces:

(2.45)
p p = Δp s + Δp dp + Δp dc + Δp mt + Δp b + Δp dca + Δp dpa
where
p p = pump pressure, psi or kPa
Δp s = pressure loss in the surface equipment, psi or kPa
Δp dp = pressure loss inside drill pipe, psi or kPa
Δp dc = pressure loss inside drill collar, psi or kPa
Δp mt = pressure drop inside mud motor, psi or kPa
Δp b = pressure drop at bit, psi or kPa
Δp dca = pressure loss in the drill collar annulus, psi or kPa
Δp dpa = pressure loss in the drill pipe annulus, psi or kPa
If the total frictional pressure loss to and from the bit is called the
parasitic pressure loss Δp d , then
(2.46)
Δp d = Δp s + Δp dp + Δp dc + Δp dca + Δp dpa
and (if no mud motor used)

(2.47)
p p = Δp b + Δp d
For a given fluid type, flow regime, and type of conduit (in pipe or
annulus), all the components of the parasitic pressure loss can be calcu-
lated with the same pressure loss equation.
The surface equipment consists of a standpipe, a rotary hose, a swivel,
and a kelly pipe. Table 2.1 shows the inner diameter and length of each
for some typical combinations. In field applications, the total pressure loss