PE 212E Rock Properties Mustafa Onur Given Date: March 02, 2007 Due Date: March 09, 2007 Subject: Permeability Homework No: 4 Problem 1: A cylindrical horizontal core sample (see the following figure) was subjected to the following linear flow test conditions. Compute the sample’s permeability in cm 2 , darcy, and md. L = 10.0 cm., μ = 1.0 cp, diameter (d) = 2 cm, q = 12 cc/min. (Hint: you need to use a Table of unit conversion factor. You can ask our photocopy center for conversions factors document, I have also put a short-one in course web page, see conversion factors.pdf) . flow l-direction l l = 0 l 2 =10 q =12 cc/min p 1 =44.1 psig p 2 =0 psig Problem 2: What linear pressure gradient is required to cause a flow of 0.10 cc/sec of 5 cp fluid through a rock (assume horizontal system, i.e., z´ is perpendicular to flow direction) having a permeability of 50 md and an area of 5 cm 2 ? Problem 3: For a linear flow, Darcy’s law in oil field units is written as ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ θ ρ + μ × − = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ ρ − μ × − = − − sin 144 10 127 . 1 144 10 127 . 1 3 3 c c g g dl dp k dl z d g g dl dp k v Assume a channel reservoir that is inclined at 30o from horizontal and the pressure at the left end of the channel is 1000 psia. Find the pressure 2500 ft away going in the uphill direction if the fluid density is 50 lb-mass/ft 3 and the fluid is at rest. Problem 4: Consider a cylindrical sand-packed core of length 10 feet and radius 0.3 feet. Assume that water is injected at the left end l = 0 and produced at the right end (l =10 feet) with the pressure at the right end held constant at 100 psia and the pressure at the left end held constant at 150 psia. Assume that water is incompressible and water viscosity is 1 cp, and water density is 62.252 lb-mass/ft 3 . Assume that the tube may be inclined from the horizontal. In problems below we wish to flow rates in STB/D. Since the compressibility of water is very small and we will assume that water is incompressible so that the formation volume factor of water (B) is equal to 1.0. If the permeability of sand is 1000 md, find the flow rate through the sandpack under steady state flow conditions for the case where the inclination is θ = 0 o , π/4, and -π/4. Note that θ = -π/4 means that the angle from the horizontal to the l axis measured in the counter clockwise direction is (7π)/4.
Given Date: March 02, 2007 Due Date: March 09, 2007 Subject:
Permeability
Homework No: 4 Problem 1: A cylindrical horizontal core sample
(see the following figure) was subjected to the following linear
flow test conditions. Compute the samples permeability in cm2,
darcy, and md. L = 10.0 cm., = 1.0 cp, diameter (d) = 2 cm, q = 12
cc/min. (Hint: you need to use a Table of unit conversion factor.
You can ask our photocopy center for conversions factors document,
I have also put a short-one in course web page, see conversion
factors.pdf) .
flow
l-direction ll = 0 l2=10
q =12 cc/min
p1 =44.1 psig p2=0 psig
Problem 2: What linear pressure gradient is required to cause a
flow of 0.10 cc/sec of 5 cp fluid through a rock (assume horizontal
system, i.e., z is perpendicular to flow direction) having a
permeability of 50 md and an area of 5 cm2? Problem 3: For a linear
flow, Darcys law in oil field units is written as
+=
=
sin144
10127.1144
10127.1 33cc g
gdldpk
dlzd
gg
dldpkv
Assume a channel reservoir that is inclined at 30o from
horizontal and the pressure at the left end of the channel is 1000
psia. Find the pressure 2500 ft away going in the uphill direction
if the fluid density is 50 lb-mass/ft3 and the fluid is at rest.
Problem 4: Consider a cylindrical sand-packed core of length 10
feet and radius 0.3 feet. Assume that water is injected at the left
end l = 0 and produced at the right end (l =10 feet) with the
pressure at the right end held constant at 100 psia and the
pressure at the left end held constant at 150 psia. Assume that
water is incompressible and water viscosity is 1 cp, and water
density is 62.252 lb-mass/ft3. Assume that the tube may be inclined
from the horizontal. In problems below we wish to flow rates in
STB/D. Since the compressibility of water is very small and we will
assume that water is incompressible so that the formation volume
factor of water (B) is equal to 1.0. If the permeability of sand is
1000 md, find the flow rate through the sandpack under steady state
flow conditions for the case where the inclination is = 0o, /4, and
-/4. Note that = -/4 means that the angle from the horizontal to
the l axis measured in the counter clockwise direction is
(7)/4.
