Page 298 - Air and Gas Drilling Manual

Chapter 7: Reverse Circulation Models 7-7
t + β
=
t
H
h
r
where t r is the reference temperature (˚F),
t h is the geothermal temperature at depth (˚F), (7-15)
β is the geothermal gradient constant (˚F/ft).
The reference surface geothermal temperature is assumed to be the temperatures
given in Table 4-1 for sea level and various elevations above sea level. These
temperatures represent North American mid latitudes year round averages. It is
assumed that these temperatures also represent an average constant deep soil or rock
temperatures near the surface of the earth at the elevations given in the table. The
value of the geothermal gradient constant is determined from temperature logs of
offset wells and other geophysical data. An average value of the geothermal gradient
that can be used when the actual gradient has not been determined is 0.01˚F/ft. The
absolute reference surface geothermal temperature is
T = t + 459 67. (7-16)
r
r
where T r is the absolute reference temperature (˚R). The absolute geothermal
temperature at the bottom of the depth interval is
T = t + 459 67 (7-17)
.
h h
where T h is the absolute bottomhole temperature (˚R). The absolute average
temperature, T av, over the depth interval is given by
T + T
T av = o h (7-18)
2
The relationship between the weight rate of flow of the gas and the specific
weight and volumetric flow rate of gas at any position inside the drill string is given
by
˙ w = γ Q = γ Q (7-19)
g g g
Substituting Equations 7-6 and 7-14 into the two terms on the right side of
Equation 7-19 gives a relationship between the known specific weight and
volumetric flow rate at the surface and the specific weight of volumetric flow rate at
any position inside the drill string. This is
PS PS
g
Q g = Q (7-20)
R T g R T av
Solving Equation 7-20 for Q yields