Page 497 - Petrophysics

TURBULENT FLOW OF GAS 465

SOLUTION

The values of J1 and 52 are first calculated from Equations 7.125a and
b, respectively. By substituting values of p, A, p, L, and Ap, one finds:

JI = 2.115 X lop5

and:

52 = 1415.38

Substituting these values of J1 and 52 into Equation 7.125, one obtains
the following expression for the function J(qm):

Table 7.2 shows the assumed values of Repr and the corresponding
values of qm from Equation 7.118, or:

(7.130)

Table 7.2 also shows the values of the function J(Qm) obtained from
Equation 7.129. A semilog plot Of J(qm) vs. qm, as shown in Figure 7.11,
yields a mass flow rate value of 3.3 x lop4 (lb,/sec) at J(qm) = 0. To
change this mass flow rate to volumetric flow rate, the following
expression is used:

(7.131)

At an average pressure of 3.9 atm, the density is 4.64 x 10@ g/s, and
the volumetric flow rate is calculated from Equation 7.13 1:

3.3 x io-*

= 2.205 x 10-3 x 4.64 x 10-3 = 32.25 cm3/s

Substituting the values of qm at J(qm) = 1, i.e., 3.3 x10p4 lb,/s, and
JZ = 1,415.38 into Equation 7.130 yields a Reynolds number of 0.467.
Using the recommendation in step 8 of the procedure yielded no
significant change of the mass flow rate.