Page 87 - Introduction to Petroleum Engineering

PERMEABILITY 71

answer
Pore volume = initial volume of water = 2.95 ml
Oil saturation = 2.10 ml/2.95 ml = 0.712
Water saturation = (2.95 ml – 2.10 ml)/2.95 ml = 0.288
Alternatively S = 1 – S = 0.288
w o

4.1.3 Volumetric analysis
The volume of oil in place V in a reservoir with bulk volume V can be expressed
B
o
with quantities introduced in this chapter:
φ
V = VS o (4.8)
o
B
If A is the areal extent of the reservoir and h its thickness, then
φ
V = Ah S o (4.9)
o
As written, Equations 4.8 and 4.9 give the volume of oil at reservoir conditions.
To obtain oil volume at stock tank conditions, the formation volume factor for oil
B must be included:
o
φ
Ah S
V = o (4.10)
o
B o

Example 4.3 OIP in a Square Mile
In the Sanish field of North Dakota, the porosity is 0.06 and the oil saturation
is 75%. The formation is 30 ft thick. What is the oil in place in STB in a square
mile? The oil formation volume factor is 1.5 RB/STB.
answer

)
2
φ
)( .
.
Ah S (5280 ft) (30 ft)(0060 75 1 Bbl
V = o = = 44500000STB
o
/
.
.
B o 15 RB STB 56 ft 3
4.2 PERMEabIlITY
The concept of permeability was developed by Henry Darcy in the early 1800s while
studying the flow of water through sand filters for water purification. Darcy found
that flow rate is proportional to the pressure change between the inlet and outlet
of the porous medium. Darcy’s relationship between flow rate and pressure change,
now known as Darcy’s law, states that flow rate q of a fluid of viscosity μ is related
to pressure drop ∆p by the equation
kA
q = – ∆ p (4.11)
µ L