Page 484 - Petrophysics

452 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

The pressure at the drainage boundary is obtained from Equation 7.106:
I
2,7202 + (43,895) ( 0.5 = 2,723 psia
?

)

which is only 3 psia higher than the average reservoir pressure.

TURBULENT FLOW OF GAS

As the velocity of the gas flowing through the porous rock is increased,
i.e., the well is produced at higher flow rate, deviation from Darcy's
law is observed. Various explanations for this deviation are presented
in the literature [30-451. The generally accepted explanation of this
phenomenon is attributed to Wright, who demonstrated that, at very
high velocities, the deviation from Darcy's law is due to inertial effects
followed by turbulent effects [28, 321. Actually, this phenomenon was
observed by Reynolds in 1901 for flow in pipes [35]. Hubbert demon-
strated that the transition from laminar flow to turbulent flow in porous
media covers a wide range of flow rates [36].

LINEAR TURBULENT FLOW

The quadrangle relationship suggested by Forchheimer is generally
found to be acceptable for expressing fluid flow under both laminar
and turbulent conditions [41]. For horizontal, steady-state flow, this
equation is:

(7.108)

where: p = pressure, atm.
L = length, cm.
pLs = viscosity of fluid, cP.
k = permeability, Darcy.
v = velocity, cm/sec.
p = density of fluid, g/cm3.
p = turbulence or non-Darcy factor, atm-sec2/g.

If p is given in atm-sec2/g use the following expression to convert it
to ft-':

p(ft-l) = p( atm - sec2 ) x 3.0889 x lo6