Page 491 - Petrophysics

TURBULENT FLOW OF GAS 459

and qm is equal to:

1 g
qm = { - 4.44 + [4.4d2 + (4)(15.44)(0.85)]0.5} = 0.13 -
(2)( 1 5.44) S
To change this mass flow rate to volumetric flow rate, which is more
commonly used, the density of the fluid at some pressure must be
calculated and the mass flow divided by the fluid density. At an average
pressure p = (100 + 14.312 = 57.35 psia or 3.9 atm, the density of
the fluid [p = Mp/zRT] is equal to:

and the volumetric flow rate, q, at the average pressure is equal to:

0.13 = 28 -
cm3
4.64 x 10-3 S
FRICTION FACTOR OF POROUS ROCKS

In flow of fluids in pipes, it is important to know if the flow is laminar
or turbulent. The laminar flow regime is dominant if the fluids move
along smooth streamlines parallel to the wall of the pipe. The velocity
of the flowing fluid is virtually constant in time during laminar flow. The
turbulent flow regime is dominant if the fluid velocity at any point in
the pipe varies randomly with time. The differences between these two
flow regimes were first investigated by Reynolds. His experimental and
theoretical work showed that the nature of the flow regime in pipes
depends on the Reynolds number (Re=Dvp/y), where D is the pipe
inside diameter. In engineering practices if:

(a) Re < 2,100, flow is in the laminar region,
(b) 2,100 < Re e 4,000, the nature of the flow regime is unpredictable,
i.e., flow passed through a transition region in which both laminar
and turbulent flow regimes can be present, and
(c) Re > 4,000, the flow is fully turbulent.

The flow of gas in very rough pipes can be considered fully turbulent
because gas flows at high velocities and therefore high Re. Dimensionless
analysis of energy loss in pipe flow of gas led to the concept of the friction
factor. Moody showed that the friction factor, 2DAp/pLv2, where L is
the pipe length, is a function of Re and the relative roughness of the pipe
[43]. Using a similar approach, Cornell and Katz investigated the flow