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Mud Hydraulics Optimization 91

The flow rate, however, should never be reduced below the minimum
flow rate q min required to lift cuttings. The minimum flow rate q min should
be maintained, and larger nozzles should be used in the subsequent depth to
maintain pump pressures less than p max . Nozzles should then be sized not
honoring the optimum pressure ratio as follows. First, calculate the parasitic
pressure losses using

Δp d = cq m (4.22)
min
Second, the allowable pressure drop at the bit is calculated by

(4.23)
Δp b = p max − Δp d
Finally, the total nozzle area is calculated by
ρ
r ffiffiffiffiffiffiffiffi
A T = 0:00912q min (4.24)
C d Δp b

If the maximum nozzle velocity criterion is employed, Eq. (2.87) indi-
cates that the nozzle velocity is maximum when the pressure drop at the
bit is maximum. To maximize the pressure drop at the bit, the parasitic
pressure losses need to be minimized. For given well geometries and fluid
properties, the parasitic pressure can be minimized with the minimum
flow rate corresponding to the minimum annulus velocity required to lift
cuttings. Based on this theory, bit nozzles are sized as follows.
First, calculate the parasitic pressure losses using

Δp d = cq m (4.25)
min
Second, the allowable pressure drop at the bit is calculated by

(4.26)
Δp b = p max − Δp d
Finally, the total nozzle area is set to be
ρ
r ffiffiffiffiffiffiffiffi
A t = 0:00912q min (4.27)
C d Δp b

4.3.3 Application Examples
This section illustrates the applications of hydraulics models in drilling
hydraulics design and calculations of surge, swab, and critical running
speeds using commercial software.