Page 159 - Air and gas Drilling Field Guide 3rd Edition

150 CHAPTER 6 Direct Circulation Models

3
3
specific weight of the fresh water (lb/ft , N/m ), and k is the penetration rate
(ft/sec, m/sec).
For USCS units, in Equation (6-12), the specific weight of fresh water is 62.4 lb/
3
ft . For SI units, in Equation (6-12), the specific weight of fresh water is the density
3
of fresh water, 1000 kg/m , multiplied by the acceleration of gravity in the SI units
2
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 in the annulus from the bottom of the well to
the surface is
_ w t ¼ _ w g þ _ w m þ _ w s : (6-13)
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 in the
annulus is

PS g
g ¼ ; (6-14)
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 geo-
thermal temperature at depth, t h , is determined from the approximate
expression
t h ¼ t r þ b H; (6-15)

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 isassumedtobethe 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 deep soil or rock temperatures near the surface of the earth
at the elevations given in the table. The value of the geothermal gradient con-
stant 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 b H; (6-16)