Page 479 - Petrophysics

RADIAL LAMINAR FLOW OF GAS 447

since f < 1, the pressure at the drainage boundary is not constant because
either the water drive is not very strong or only a fraction of the reservoir
boundary is open to water drive.

RADIAL LAMINAR FLOW OF GAS

Three approaches are available for describing gas flow through
porous rock.

If the reservoir pressure is high (p > 3000 psia), the radial flow
equations of the previous section, even though they were developed
strictly for the case of liquid flow, can be used to analyze gas flow by
converting gas flow rates from SCFD to STBD and calculating the
formation volume factor in bbl/SCF from:
ZT
Bg= 0.00504- (7.90)
P
where the gas deviation factor z is estimated at the average reservoir
pressure p , and the reservoir temperature T is expressed in OR. Using
this procedure can lead to large errors under certain conditions,
as the diffusivity equation describing liquid flow in porous rock
(Equation 7.53) was derived on the assumption that small pressure
gradients are negligible. In low-permeability gas reservoirs, however,
these gradients can be considerably high.
If the average reservoir pressure is low (p < 2000 psia), the radial
gas-flow equations can be derived in terms of the pressure-squared
function, p2. This classical approach is discussed in the next section.
If the reservoir pressure is intermediate (2000 < p < 3000 psia), the
real gas pseudo-pressure function, m(p), is more accurate than
the pressure or the pressure-squared approach. Actually, in tight
gas formations the m(p) approach must be used, especially if
the reservoir is produced at high rates. This function is defined
as [26, 271:

(7.91)

where Pb is an arbitrary base pressure, and m(p) is expressed in
psi2/cP. Equation 7.91 only accounts for changes in p and z, and
fails to correct for changes in gas compressibility, c, and kinetic
energy. When the real gas pseudopressure is used, the diffusivity
equation (7.54) becomes:

(7.92)
dr2