Petroleum Engineering 311
EXAM 4
May 9, 2006
Name: ___________________________
Section: ________
THIS EXAMINATION CONSISTS OF TWO PARTS
Part I has ten completion questions worth five points each. Write the answer in the
space provided.
Part II consists of five problems worth ten points each. Grading will be on the basis of
approach and answers. Work out the answer in the space provided. SHOW ALL
WORK and STATE ALL ASSUMPTIONS.
This examination is CLOSED BOOK. Three hand-written sheets of personal notes may
be used, and must be turned in with the exam.
Questions are not permitted during the examination.
examination booklet before beginning work.
Check the pages in the
Do not fold or unstaple the examination booklet.
Time allotted for the examination is 120 minutes.
When you have completed the examination, read and sign the statement below, then
turn in the examination booklet.
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I pledge that I have neither given nor received aid in completing this examination. I
have followed the strictures of the Texas A&M University Aggie Code of Honor during
this examination.
Signature:
________________________________
Date:
________________________________
1
CONSTANTS & CONVERSION FACTORS
density of water at standard conditions
g = 9.80665* m/s2
.
lb ft
gc = 32.174 m. 2
lb s
f
3
w = 1.0 g/cm = 62.4 lbm/ft3
molar mass of air
Mair = 28.97 lbm/lbmmole
absolute thermodynamic temperature
o
Universal gas constant
psia  ft 3
R = 10.732
lb mol o R
standard gravitational acceleration
gravitational conversion constant
R = oF + 459.67
m
4.356*
x 10
+4
2
ft per acre
1.01325 x 10+6
dyne/cm2 per atm
1.01325 x 10+5
Pa per atm
x 10+1
psi per atm
1.4696
ft3 per bbl
5.614583
4.2*
x 10+1
1.01325 x 10+8
gal per bbl
darcy per cm2
1.0*
x 10-2
dynes/cm2 per cp
1.0*
x 10-3
Pas per cp
3.048*
x 10-1
m per ft
1.2*
x 10
in per ft
4.5359
x 10-1
kg per lbm
NOTE: An asterisk (*) follows exact conversion factors.
2
EQUATION PAGE
Generalized Darcy equation
vs  
k d
k  dp g dZ 
  
; Z+
 ds
  ds D ds 
Darcy equations for incompressible liquid flow
unit system
darcy
horizontal,
linear form,
p  p1  p 2
dipping,
linear form,
p  p1  p 2
kAp
q
L
q
qC
oil field
darcy
kAp
L
q
kA  p gsin  

  L
D 
D  144  g c
qC
qC
2khp
ln re rw 
khp
ln re rw 
C  7.0818 x 10  3
horizontal,
linear form
horizontal,
radial form
Tsc kA  p12  p 22 


q sc 
p sc T zL  2 
Tsc
2kh  p12  p 22 


q sc 
p sc T zln re rw   2 
q sc  C
oilfield
kA  p gsin  

  L
D 
D  1.01325 x10 6
C  11271
.
x 10 3
Darcy equations for real gas flow
unit system
horizontal,
radial form,
p  p e  p w

Tsc kA 2
p1  p 22
p sc T zL

q sc in scf / d
C  3.1641 x 10
C  1.9881 x 10  2
Linear, serial flow
Lj
L

k
j kj
kh   k j h j
j
Land’s Trapping Constant – Standing
C
1
1
 *
*
S gr
S gi
3

Tsc
kh
p12  p 22
p sc T zln re rw 
q sc in scf / d
3
Linear, parallel flow
Critical Gas Saturation  Zero :
q sc  C

1.
What quantities must be measured to determine effective porosity?
2.
Explain the Helium Porosimeter method of porosity determination.
3.
Determination of porosity from well logs. For the three porosity logs discussed:
Name of the
well log?
What quantity is measured Relationship of the measured quantity to porosity?
by the logging tool?
4
4.
What is the procedure to determine absolute permeability from core plugs using a liquid?
5.
gas?
What factors can affect the laboratory determination of absolute permeability using a
6.
Determination of water saturation.

Give a qualitative definition of water saturation.

Give a quantitative definition of water saturation (Sw). Define all terms.
5
7.
Explain the retort distillation method for determining water saturation in the laboratory
including analysis of data.
8.
Suppose the relative permeability relationship for the water-oil system of a preferentially
water-wet oil reservoir is shown at right. What is
the relative permeability to oil (krow) when the
water saturation is 0.60, given the following
saturation history?



The initial water saturation was 0.3
The oil was originally produced by rock and
fluid expansion drive, and the water saturation
remained constant at 0.3
The oil is now being produced by
waterflooding, and the injected water has
displaced some oil, so that the water saturation
is now 0.60
6
Water-Oil System
1.0
Krw
0.8
Krow
0.6
Kr
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Water Saturation
0.8
1.0
9.
Determine the value of the cementation factor, m for the following data:
Sample
14A
31A
48A
77B
Porosity
0.162
0.195
0.067
0.120
Formation
Resistivity Factor
40.7
31.6
191.2
81.3
Clearly label the axes of your graph.
1000
100
10
0.01
1
0.1
10. Consider the gas/water
relative permeability data
graphed at right. Assuming the
irreducible water saturation is
0.15 and the critical gas
saturation is zero, determine:
1.0
0.8
krg
0.6
a. Trapping constant, C.
0.4
b. Residual gas saturation for a
reservoir with initial water
saturation of 0.50.
0.2
0.0
0.0
0.2
0.4
0.6
Water Saturation
7
0.8
1.0
Part II. Work out the answer in the space provided. Show details of your work and clearly
identify your answer. Grading will be on the basis of approach and answers.
11.
Find the constant and its units required to convert the Darcy equation for radial,
horizontal flow
q
2khp
ln re rw 
to the following unit system: q(gallons/min), k(md), h(ft), p(psi), and (Pa s). Note the constant
is 2 and dimensionless for Darcy’s units.

8
12.
A core sample is cleaned and dried for porosity measurement. The dry weight of the
sample is 131.76 grams. After it is completely saturated with kerosene (with a density of 0.85
g/cm3), the sample weight is 145.23 grams. When the kerosene saturated sample is immersed in
kerosene, the sample weight is 90.23 grams. Calculate the porosity (fraction) and the matrix
density (g/cm3).
9
13.
Horizontal, isothermal, linear flow of a gas at moderate pressure, is given by the pressuresquared form of Darcy’s Law (for Darcy units),
q sc 
Tsc kA  p12  p 22 

.
Tp sc μzL  2 
If flow is measured at T = Tsc and a relatively low pressure, so that z  1, then plotting
q sc  p sc
p12  p 22
as shown below allows permeability of the porous media to be
Y
versus X 
A
2L
determined from the slope of the graph, if viscosity is known.
Graph to Determine Permeability from Slope
Y (ft^3 psi)/(day ft^2)
2500000
2000000
1500000
1000000
500000
0
0
10000
20000
30000
40000
50000
60000
X (psi^2/ft)
Determine the permeability of the porous media from the above graph if the gas is has a viscosity
of 0.020 cp, Tsc = 60 oF, and psc = 14.65 psia.
10
14.
The water-oil relative permeability data at
right were determined for a water-wet sandstone as
a function of its water saturation (kbase = kabs).
Calculate the ratio of the volumetric production
rate of water to oil at surface conditions when the
well is completed in the transition zone where Sw =
0.6 and Sg is negligible.
kr vs Sw
1
kro
0.8
0.6
kr
0.4
Assume the absolute permeability is 100 md; the
fluid properties are o = 3.4 cp, w = 0.68 cp,
Bo = 1.20 rb/stb, and Bw = 1.05 rb/stb; and the
flow potential gradients and cross-sectional flow
areas are equal for both water and oil.
q
NOTE: Production rate at surface conditions is ,
B
where
q is the rate at reservoir conditions, and
B is the formation volume factor.
11
krw
0.2
0
0
0.2
0.4
0.6
Sw
0.8
1
15.
A limestone formation has matrix porosity of 0.10
and matrix permeability of one millidarcy (md).
However, it contains three vertical fractures per foot,
each 0.03 inches wide (shown as dashed lines) per cubic
foot.
The permeability in md of a single fracture is given by, k
= 54.0 x 109 b2, where b is the width of the fracture in
inches.
What fraction of the storage capacity of the rock is in the fractures and what is the average
permeability of the rock, assuming flow parallel to the fractures?
12