BAKER HUGHES - Drilling Fluids Reference Manual

PRESSURE PREDICTION AND CONTROL
The “d” Exponent
The “d” exponent method of detecting and predicting the magnitude of pressure abnormalities
while drilling is a useful tool in some areas. Improvement in plotting techniques has refined the
method to the extent that pressure gradients in many areas can routinely be predicted with an
accuracy of approximately 0.010 to 0.025 psi/ft, the equivalent of 0.2 to 0.5 lb m /gal of fluid
weight. The value of formation pressure information during drilling operations is readily
apparent. Properly utilized, this information can reduce the incidence of blowouts and
significantly reduce the use of unnecessarily heavy fluids, thereby increasing penetration rate
and reducing drilling costs. Preparation of the “d” exponent plots is uncomplicated and requires
no special equipment. The required information – penetration rate, rotary rpm, weight on bit,
and hole diameter – is routinely available at the wellsite.
In 1965, Bingham suggested that the relationship between penetration rate, weight on bit,
rotary speed, and bit diameter can be expressed by the following general equation,
where,
R = penetration rate
R ⎡W
⎤ = K
N ⎢
⎣ D ⎥ ⎦
N = rotary speed
K = a constant
W = weight on bit
D = hole diameter
d = exponent.
In 1966, Jorden and Shirley of Shell Oil Company introduced the “d” exponent concept. Earlier
investigators had established the inverse relationship between penetration rate and the pressure
differential between the fluid column and the formation. Jorden and Shirley advanced the idea
that while drilling normally pressured formations with constant fluid weight, the pressure
differential increases with depth and decreases as abnormally pressured formations are
encountered. Under constant drilling conditions and uniform rock properties, these changes in
differential pressure result in gradually decreasing penetration rate through normally pressured
formations and an increase in penetration rate through abnormally pressured formations. Thus,
if it were possible to hold the entire drilling variables constant, a simple plot of penetration rate
versus depth could be used as a pressure detection tool.
Similarly, if all variables other than rotary speed, weight on bit, and hole size are held constant,
the relationship between the “d” exponent in the Bingham equation and pressure differential
would show recognizable trends when the “d” exponent is plotted versus depth. Solving
Bingham's equation for “d” and adding constants to permit use of common oilfield units,
Jorden and Shirley introduced the “d” exponent equation,
d
d =
R
log
60N
12W
log
6
10 D
BAKER HUGHES DRILLING FLUIDS
REFERENCE MANUAL
REVISION 2006 12-13