W6157
Reservoir Engineering II
MATLAB Exercises – WS 2020/21
Prof. L. Ganzer, B. Jenei, M. Wirth
Institute of Subsurface Energy Systems
Reservoir Engineering II – MATLAB Exercises
Contents
1 Exercise 1 – Skin Factor 2
2 Exercise 2 – Fluid Pressure Regimes 3
3 Exercise 3 – Material Balance Gas 4
4 Exercise 4 – Material Balance Oil 5
5 Exercise 5 – Decline Curve Analysis 7
6 Exercise 6 – Buckley Leverett Calculation 9
1
Reservoir Engineering II – MATLAB Exercises
1 Exercise 1 – Skin Factor
For a well with a diameter of 6 inch (0.5 ft), it is known that the damaged region around the well
is 12 inches (1 ft) deep. Information about the damaged zone shows that its permeability is half of
the undamaged zone, i.e. ks = 0.5 k.
a) Calculate the skin factor for the damaged zone using the following equation:
S =
(
k
ks
1
)
ln
(
rs
rw
)
(1)
b) Calculate the effective wellbore radius using the following equation:
rweff = rw e( S) (2)
c) For another set of wells (one vertical well and one horizontal well) the following data is
available:
– Height: h = 25 ft
– Length Horizontal Well: L = 1000 ft
– Oil Formation Volume Factor: Bo = 1.06
bbl
STB
– Permeability: kv = kh = 10mD
– Viscosity of Oil: μo = 0.8cP
– Oil Fl
ow Rate: qo = 1000
STB
d
– Skin Factor: 1
– Wellbore Radius: rw = 0.25ft
– Reservoir Radius: re = 1500ft
Calculate the additional pressure drop due to skin for the vertical and the horizontal well
using the following equations:
pSv =
141.2qoμoBo
kh
S (3)
pSh =
141.2qoμoBo
kL
S (4)
d) The productivity index of a well is defined as PI = q p . Calculate the productivity index for
the vertical and the horizontal well, the following equations should help:
qv =
0.007078kh p
μoBo
(
ln rerw + S
) (5)
qh =
0.007078kh p
μoBo
(
ln 4reL +
h
LS + 0.34
) (6)
Additional Exercises:
Use the information of the well in a) and b). Change the ratio between the damaged and
undamaged formation permeability and investigate what happens to the skin factor and the
effective wellbore radius for different ratios.
Use the information of the wells in c). Investigate the influence of the skin factor on the
pressure drop for each well.
2
Reservoir Engineering II – MATLAB Exercises
2 Exercise 2 – Fluid Pressure Regimes
For a hydrocarbon reservoir the following structural data is known:
Top of the structure: 5000 ft
Gas-Oil-Contact: 5200 ft
Water-Oil-Contact: 5500 ft
Additionally, the following pressure gradients for water, oil and gas are known: