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68 Part I Liquid Drilling Systems

turbulent flow is usually higher than that in laminar flow. For the pur-
pose of pump selection, assuming turbulent flow throughout the circulat-
ing system will result in conservative values of pressure losses.
This section presents the analytical method used for predicting the pres-
sure losses in the drill string and in the annulus, as well as considerations for
pressure drop at the bit. The length of the surface equipment is considered
to be a small fraction of that of the drill string. Necessary hydraulics models
were presented in Chapter 2. For directional and horizontal drilling, the
pressure losses through the MWD and LWD tools are considered to be
negligible. The pressure drop at the mud motor is considered as a specific
value between 200 psi and 600 psi, depending on motor size.
However, the pressure drop at the bit is not calculated with Eq. (2.64)
in the process of pump selection. For the optimum bit hydraulics, the
pressure drop at the bit should be selected based on the total pressure loss
in the system. According to the maximum bit hydraulic horsepower cri-
terion (see Chapter 4), the following relation should be held:

Δp b = m p p (3.1)
m + 1

where p p is the pump pressure in psi or Pa, and m is the flow rate expo-
nent. If the Blasius correlation is used for friction factor determination,
Eq. (3.2) shows m = 1.75. However, according to the maximum jet
impact force criterion (see Chapter 4), the following relation should be
held:
Δp b = m p p (3.2)
m + 2

3.3.4 The Minimum Required Pressure
The minimum required pump pressure is expressed as

(3.3)
p p = Δp d + Δp b
where

Δp d = the total frictional pressure loss (parasitic pressure)
2
in psi or N/m —that is,
n
Δp d = ∑ p fi
i=1