Page 179 - Air and gas Drilling Field Guide 3rd Edition

170 CHAPTER 7 Reverse Circulation Models

For USCS units, in Equation (7-12), the specific weight of fresh water is 62.4
3
lb/ft . For SI units, in Equation (7-12), the specific weight of fresh water is the
3
density of fresh water, 1000 kg/m , multiplied by the acceleration of gravity in
2
the SI units 9.81 m/sec . The average specific gravity of sedimentary rocks is
approximately 2.7. If igneous or metamorphic rocks are to be drilled, average
values of 2.80 and 3.00, respectively, can be used [5].
The total weight rate of flow, _ w t , inside the drill string and flowing from the
bottom of the well to the surface is
_ w t ¼ _ w g þ _ w m þ _ w s : (7-13)

The drilling mud and the rock cutting solids are assumed to not change volume
when pressure is changed (note that if the liquid phase fluid is oil, the
volume changes with pressure can be taken into account). However, the air (or
gas) does change volume as a function of pressure change and, therefore, as a
function of depth. Thus, the specific weight of the gas at any position inside the drill
string is

PS g
g ¼ ; (7-14)
g
R e T av
where T av is the average temperature of the gas over a depth interval ( R, K).

This average temperature term is determined by taking the average of the sum
of the geothermal temperatures at the top and bottom of the depth interval.
The geothermal temperature at depth t h is determined from the approximate
expression
t h ¼ t r þ bH; (7-15)

where t r is the average annual atmospheric reference temperature ( F, C), t h is

the geothermal temperature at depth ( F, C), and b is the geothermal tempera-

ture gradient ( F/ft, C/m).
The reference surface geothermal temperature, t r , is assumed to be the tem-
peratures given in Tables 5-1a and 5-1b for sea level and various elevations above
sea level. These temperatures represent North American midlatitude year-round
averages. It is assumed that these temperatures also represent an average constant
of 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, or 0.018 C/m. The temperature at depth can

be expressed as absolute temperatures using the following:
T h ¼ T r þ bH; (7-16)
where T r is the reference atmospheric temperature ( R, K). Once the reference

temperature is changed to absolute, no other changes need to be made in
Equation (7-16).