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Mud Hydraulics Fundamentals 49

c = Δp d1 (2.76)
m
q 1
or

c = Δp d2 (2.77)
m
q 2
Spreadsheet c & m-Values.xls attached to this book can be used for esti-
mating the c and m values for Bingham plastic fluids. In field operations,
the values of c and m can be determined with the following procedure:
1. At the current hole depth, before tripping out to change the bit,
circulate the drilling fluid at two flow rates (q 1 , q 2 ) with the bit off
bottom and record pump pressures (p p1 , p p2 ) at the two corresponding
rates. The flow rates should be selected to reflect the range of flow rate
to be used while drilling with the next bit.
2. When the bit is pulled out to surface, connect the bit to the kelly dir-
ectly, circulate the drilling fluid at the same two flow rates (q 1 , q 2 ), and
record two pump pressures. These two pump pressures approximate
pressure drops (Δp b1 , Δp b2 ) across the bit nozzles at the given flow
rates.
3. Determine the parasitic pressures at the two flow rates by
(2.78)
Δp d1 = p p1 − Δp b1

(2.79)
Δp d2 = p p2 − Δp b2

Determine the values of c and m in the flow rate range by Eqs. (2.75) and
(2.76).

2.3.3 Surge and Swab Pressure
When a drill string is run in a hole, it forces drilling fluid up the annulus
and out of the flow line. At the same time, the mud immediately adja-
cent to the pipe is dragged downhole. The resulting piston effect gener-
ates a surge pressure that is added to the hydrostatic pressure. Excessive
surge pressures can increase the wellbore pressure to such a degree that it
can lose circulation. Conversely, when a drill string is pulled out of a
hole, fluid flows down the annulus to fill the resulting void. This causes a
suction effect, generating a swab pressure that can lower the differential
pressure and possibly bring formation fluid into the borehole.