Chapter 2
Modeling Concepts
Mobility Weighting
Calculation of fluid flow between blocks requires knowledge of the mobilities across block boundaries,
calculation of the proper mobility which is heavily dependent on saturations is difficult because it
depe

1. True or False: For each statement, circle True or False. (1 Point per question; 10 points
total)
The well mixed tank assumption states that all properties in each grid
cell are homoeneous and the uids are well mixed.
True One advantage of Window mo

PETE 4056
Numerical Simulation of Improved Recovery Processes
Exam #1
February 27, 2012
Name
INSTRUCTIONS:
RULES:
Read each question thoroughly and carefully before attempting an
answer. Start with the easiest problems. Work on each problem. Budget
your t

PETE 4056
Numerical Simulation of Improved Recovery Processes
Exam #1
February 21, 2011
Name
INSTRUCTIONS:
RULES:
Read each question thoroughly and carefully before attempting an
answer. Start with the easiest problems. Work on each problem. Budget
your t

Slides 09
Aquifers
Less information is known about aquifer properties than about the reservoir itself,
this lends itself to added difficulty when modeling an aquifer. The three primary
methods of modeling an aquifer are analytical aquifers, numerical aqui

Slides 09
Transmissibility
Nearly every simulator has a term named transmissibility. It may be defined
differently in different simulators but serves roughly the same purpose. It is
designed to allow better respresentation of and control over flow between

Slides 06
Well Treatment
In simulation wells appear as source/sink terms distributed over the entire block. The pressure of the
block does not equal the pressure in the well, they are related through a well model accounting for
geometry of the well, the b

Slides 05
Relative Permeability
For a porous medium saturated by more than one fluid each fluid has its own relative permeability
value proportional to the saturation of that fluid. While more than one fluid is present no fluid will
have a permeability eq

Slides 05
Reservoir Fluid Properties
Below Bubble-Point:
-Reservoir processes simulated by differential vaporization
-Bottomhole to stock tank simulated by separator test
Above Bubble-Point:
-Reservoir processes simulated by flash vaporization
-Bottomhole

1-D Multiphase Flow General Equation
Tx Mo
1
i+
2
Tx
i
1
2
1
i+
2
[ ( P o P o ) o g ( Di+1D i) ] +T x M o
i+1
i
yz
=
kx
x
(
1
i+
2
k ro
o B o
( )
Mo =
i
)
i
1
i
2
1
i
2
[ ( P o Po ) o g ( Di1Di ) ] +q o =
k x=
1
2
i1
i
i
x y z
t
x i + x i 1
x i x i+1

Example Well Index and Well Treatment
1. A well in the middle of a single gridblock is shown below. For this well determine
the well index for a simulation with generic values of x and y where x y.
Assume you have information as would be available from a

Errors
Accuracy: how closely computed value(s) agree with the true value
Precision: how closely computed values agree with each other
True value = Approximation + Error
Roundoff Error: arise when a quantity is not represented exactly. The two major
facets

Example Transmissibility and Mobility
Consider the three block 1D system shown below and determine the upstream
weighted transmissibility and mobility for flow between blocks i-1 and i and flow
between blocks i and i+1.
Pi1> P i> Pi +1
Transmissibility is

Example 2: 1-D Diffusivity Equation Iteratively by Gauss-Seidel
Consider the following 1-D arrangement:
Here block 1 represents the outermost gridblock and block 6 contains the wellbore
and is considered to have the same pressure as the well flowing press

Example 1: Solving 1-D Diffusivity Equation by Directly Gaussian
Elimination
The 1-D diffusivity equation is given by:
2 P c t P
=
kx t
x2
Using central differences allows approximation of the partial derivatives:
P f i +12 f i + f i1 P32 P2 + P1
=
=
2

Numerical Simulation of Improved Recovery Processes February
Exam #1
PETE 4056
Gn"/ B ?
2lr20ll
1KE
Name
INSTRUCTIONS:
Read each question thoroughly and carefully before attempting an
answer. Start with the easiest problems. Work on each problem. Budget
y