Petroleum Engineering 311
EXAM 1
February 22, 2006
Name: ___________________________
Section: ________
THIS EXAMINATION CONSISTS OF TWO PARTS
Part I has eight completion questions worth five points each. Write the answer in the
space provided.
Part II consists of six 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. One hand-written sheet of personal notes may be
used, and must be turned in with the exam.
Questions are not permitted during the examination. Check the number of questions in
examination booklet before beginning work.
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.
STATEMENT OF ACADEMIC INTEGRITY
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
standard gravitational acceleration
g = 9.80665* m/s2
gravitational conversion constant
gc = 32.174
lb m.ft
lb f .s 2
density of water at standard conditions w = 1.0 g/cm3 = 62.4 lbm/ft3
molar mass of air
Mair = 28.97 lbm/lbmmole
absolute thermodynamic temperature
o
Universal gas constant
R = 10.732
R = oF + 459.67
psia  ft 3
lb mol o R
m
1.4696* x 10+1
psi per atm
1.01325 x 10+6
dyne/cm2 per atm
4.356*
x 10+4
ft2 per acre
3.048*
x 10-1
m per ft
1.2*
x 10+1
in per ft
4.5359
x 10-1
kg per lbm
1.0*
x 10-3
Pas per cp
1.0*
x 10-2
dynes/cm2 per cp
5.614583
4.2*
x 10+1
ft3 per bbl
gal per bbl
NOTE: An asterisk (*) follows each number which expresses an exact definition.
2
PART I
Part I consists of eight completion questions worth five points each. Write the answer
in the space provided. Define and explain the following quantities and terms. Use
equations, words, and/or sketches in your definitions and explanations.
1.
Porosity.
2.
Effective Porosity.
3
3.
Permeability.
4.
Pore compressibility.
4
5.
Non-Darcy Flow.
6.
Real gas pseudopressure (m(p)).
5
7.
List the conditions and assumptions for the integrated, steady-state form of
Darcy’s Law for horizontal, radial flow of an incompressible liquid.
8.
Describe the operation of a neutron porosity log.
6
PART II
Part II consists of six 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.
9.
Make a sketch of the apparatus Darcy used to study linear flow of water through
sand packs. Indicate inlet and outlet and show the height of the sand and difference in
fluid heads (using water manometers) for a significant flow rate.
7
10.
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 density
of 0.85 g/cm3), the sample weight is 145.23 grams. When it is immersed in kerosene,
the measured sample weight is 90.23 grams. Calculate the porosity (fraction) and the
matrix density (g/cm3).
8
11.
What is the ratio of improvement in production rate qnew/qold after injecting steam
into a cylindrical heavy oil reservoir to reduce oil viscosity, if rw = 1 ft, rh = 100 ft, and re =
300 ft? (rh is the radius of the heated zone). Assume the oil viscosity inside the heated
zone is 2 cp and the oil viscosity outside the heated zone is 100 cp. Assume steady
state flow with formation permeability, wellbore pressure and pressure at the external
boundary (re) the same for both cases.
9
12.
Find the constant (and its units) to convert the Darcy equation for linear,
horizontal flow
kAp
q
L
Convert from Darcy units to the following units: q in cm3/s, k in millidarcies, A in in2, p in
psia,  in cp, and L in inches.
10
13.
A water well drains a cylindrically shaped reservoir for which you have the
following data:
drainage area
formation thickness
radius of well bore
porosity
permeability
viscosity
pressure at external radius
pressure at the well bore radius
formation volume factor (Bw)
10 acres (external radius = 372.4 ft)
10 ft
0.25 ft
25 %
100 millidarcy
1.0 centipoise
1000 psia
100 psia
1.02 RB/STB
Calculate the steady-state flow rate in stock tank barrels per day (STB/D).
11
14.
Consider a cube of reservoir rock 1 ft on a side having a matrix permeability of
100 md and four 0.01 inch diameter cylindrical channels that traverse the rock as
shown below. Calculate the average permeability of the rock when flow is linear, and in
the direction of the channels.
12
EQUATION PAGE
General Isothermal compressibility equation
c
1  V 
 
V  p  T
Generalized Darcy equation
vs 
q
k d
gZ
; Z+; and D is a unit conversion constant

; where   p 
A
 ds
D
Darcy equations for incompressible liquid flow
horizontal,
linear form,
unit system p  p1  p 2
darcy
dipping,
linear form,**
Δp  p1  p 2
q
kAp
q
L
qC
oil field
kA  p gsin  

  L
D 
D  1.01325x10 6
kAp
L
kA  p gsin  

  L
D 
D  144  g c
qC
C  11271
.
x 10 3
horizontal,
radial form,
p  p e  p w
q
2khp
ln re rw 
qC
khp
ln re rw 
C  7.0818 x 10  3
** Note that negative gravity term is for  increasing counter-clockwise. For
upward flow (dZ/ds > 0), 0 <  < 180. For downward flow (dZ/ds < 0),
-180 <  < 0.
Permeability of a cylindrical channel
k  C d2
where C  20.4 x 10 9
md
in. 2
Permeability of a fracture
k  C w2
where C  54.4 x 10 9
md
in. 2
13