Page 97 - Introduction to Petroleum Engineering

ACTIVITIES 81
4.3 A core sample is 3 in. long. The flow path through the core can be observed by
injecting dye into the core and then slicing the core into thin sections which can
be studied under the microscope. Estimate the tortuosity of the core if the
length of the flow path is approximately 4 in. and assume the flow path is con-
fined to flow along a two‐dimensional surface. Note: Tortuosity is the actual
length of the flow path divided by the length of a linear flow path.
4.4 a. The superficial velocity of a core is approximately 1 ft/day. What is the
interstitial velocity if the core has 20% porosity?
b. Effective permeability to oil is 100 md and absolute permeability is
200 md. What is the relative permeability to oil?
4.5 Hall’s correlation relates porosity to formation compressibility using the
relation

1 782. 
c =  0 438  ×10 −6
.
f
 φ 
where ϕ = porosity (fraction) and c = formation compressibility (1/psi). Use
f
Hall’s correlation to estimate formation compressibility at 18% porosity.
Remember to include units.
4.6 A reservoir has three layers. Each layer has a thickness of 1 ft and the following
permeabilities:

Layer Permeability (md)

1 126
2 4
3 35

a. What is the arithmetic average of permeability?
b. What is the harmonic average of permeability?
C. Use these values to estimate the Dykstra–Parsons coefficient for a log-
normal permeability distribution.
4.7 A cylindrical sandstone core sample has a length of 3 in. and a diameter of
0.5 in. The core is dried and weighed. The dried core weighs 25.0 g. The core is
then saturated with freshwater. The water‐saturated core weighs 27.5 g. What is
the porosity of the sandstone core? Neglect the weight of air in the dried core
and assume the density of water is 1 g/cc at laboratory temperature and pressure.
4.8 a. Suppose a well flows 600 STBO/D at a pressure drawdown of 25 psia.
Calculate the productivity index of the well. Recall that production rate is
equal to productivity index times pressure change.
b. What pressure drawdown is required to produce 100 STBO/D if the pro-
ductivity index for a well is 0.23 STBO/D/psi?