Page 92 - Introduction to Petroleum Engineering

76 PROPERTIES OF RESERVOIR ROCK
The units for Equation 4.17 are as follows:

Term Description Units

q s Gas flow rate at standard conditions (60 °F, 14.7 psia) SCF/D
k Permeability Millidarcies (md)
h Thickness ft
2
m(p ) Real gas pseudopressure at external boundary psi /cp
e
m(p ) Pressure in well (inside boundary) psi /cp
2
w
T r Reservoir temperature °R (Rankine temperature)
r w Well radius (inside boundary) ft
r Radius of external boundary ft
e
4.3 RESERVOIR HETEROgENEITY aND PERMEabIlITY

Rock formations are quite heterogeneous. In pieces of sandstone, bedding planes
are usually visible at a scale of 1–5 mm, looking somewhat like the lines in a piece
of wood. These bedding planes are visible because of variations in grain size and
composition. These variations lead to variations in porosity and permeability. In
addition to these small‐scale variations, variations at larger scale also occur and are
often seen in road cuts through sedimentary formations. In this section, features of
permeability heterogeneity are considered.

4.3.1 Parallel Configuration
Consider linear flow through two parallel layers of porous material with permeabil-
ities, thicknesses, and length as shown in Figure 4.4. The inlet pressure is the same
for both layers. Similarly, the outlet pressure is the same for both layers. The total
flow rate is the sum of the flow rates for the two layers. Using Darcy’s law, we
calculate the average permeability for the two layers as

kh + kh
k ave = 11 22 (4.18)
h + h 2
1
This result can be generalized to multiple layers as follows:
∑ kh
k = i ii (4.19)
ave h
∑ i i
Equation 4.19 holds for linear and radial flow.

4.3.2 Series Configuration
Consider linear flow through two porous materials in series with permeabilities,
lengths, and thickness as shown in Figure 4.5. In this case, the flow rate is the
same in each serial segment. The total pressure drop is the sum of the pressure