Petroleum Engineering 603
MIDTERM EXAM
October 24, 2002
Name:_________________________________________
You may use one sheet of handwritten equations, attach to exam when turned in.
You may use a calculator.
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:
____________________________________
1
Beginning with the Continuity Equation, derive the Diffusivity Equation for single
phase reservoir flow of an ideal gas, considering pressure squared (p2) to be the
dependent variable.
After completing the derivation, answer the following two questions:
 Were any nonlinear terms neglected? If so, describe them.
 What parts of the diffusivity term (ct/k) are expected to be nonlinear for reservoir
flow of an ideal gas
Continuity Equation:

   
   u = t
Diffusivity Equation – Ideal Gas:
2
   ct   p
2 p 2 = 

 k  t
 
 
2
3
Consider reservoir flow of a slightly compressible, single phase fluid, in a horizontal,
1-D, linear reservoir.
a) Show the partial differential equation that describes fluid flow for this reservoir
geometry, using Wattenbarger’s usual oilfield units [Unit Conversion
Constant = 0.00633]. List the units of each term of the partial differential equation.
b) For each of the following flow solutions to the partial differential equation, show
examples of the initial conditions and boundary conditions, expressed in equation
form. For all cases, consider constant rate production for the left edge boundary
condition.
 Transient (Infinite Acting)
 Steady State
 Pseudosteady State
c) For each of the following flow solutions, discuss the reservoir flow conditions under
which each solution would be applicable to analysis of field data.
 Transient (Infinite Acting)
 Steady State
 Pseudosteady State
4
5
The following sketch shows the dimensions of two adjacent reservoir simulation
gridblocks (block centered grid). Calculate the water flow rate and direction between
gridblocks, using single point upstream relative permeability (in units of scf/day), for:
Gridblock 1 Gridblock 2
p
Sw
Z
krw
Pcow
Bw
w
w/144
k
100 ft
1910.0
0.60
-5610.0
0.08
23.0
1.024
0.3350
0.48
100.0
1950.0 psia
0.80
-5615.0 ft, subsea
0.20
20.0 psia
1.020 rcf/scf
0.3360 cp
0.48 psia/ft
100.0 md
100 ft
100 ft
1
2
20 ft
6
7
Consider single phase flow of water containing a polymer. We will assume that the
polymer flows with the water and also adsorbs onto the rock. Assume the
concentration of polymer in the water phase to be C units [mass of polymer/volume of
water] and adsorption of polymer onto the rock surface is Ĉ units [mass of
polymer/rock volume].
Starting from first principles, derive a gridblock material balance equation for polymer
mass. You may neglect diffusion of polymer in the water.
[Hint: The polymer can be treated like a tracer except: it adsorbs onto the rock surface,
and does not diffuse in the water]
8
9
10