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48 Part I Liquid Drilling Systems

Illustrative Example 2.7 (Continued )
In the open-hole/drill collar annulus:

v = 300 = 4:59 ft/s
2 2
2:448ð8:5 − 6:75 Þ
N Re = 5,218, N Rec = 2,737, N Re < N Rec , turbulent flow
C = 0:5589

a
−0:2638
= 0:008
f a = 0:0767ð0:5589 × 5,218Þ
2
Δp f = 0:008 × 0:6684 × 10:5 × 7:48 ð450Þ = 18 psi
2 2 2
1421:22 × ð0:708 − 0:563Þ × ð0:708 − 0:563 Þ
The total system pressure loss is
Δp d = 491 + 204 + 42 + 21 + 18 = 776 psi = 5,279 kPa

The Generalized Pressure Loss Model
The total parasitic pressure loss in a drilling circulation system includes
the frictional pressure loss in the surface equipment Δp s , frictional pressure
losses in the drill pipe Δp dp and drill collars Δp dc , and frictional pressure
losses in the drill collar annulus Δp dca and the drill pipe annulus Δp dpa .If
each term of the parasitic pressure loss is computed for the usual case of
turbulent flow, examining the equations for turbulent flow yields
Δp d = cq m (2.74)

where m is a constant that theoretically has a value near 1.75 for turbu-
lent flow, and c is a constant that depends on the mud properties and
wellbore geometry. Considering that laminar flow may exist in some
annular sections, the constant m may take a value less than 1.75.
The values of c and m can be estimated by matching the calculated
m
pressure losses with the model Δp d = cq at two flow rates. At a given
depth of interest, suppose pressure losses at flow rates q 1 and q 2 are calcu-
lated as Δp d1 and Δp d2 , respectively. The values of c and m in the flow
rate range can be determined by

Δp d2
log
Δp d1
m = (2.75)
q 2
log
q 1