PETE-358: Well Performance Date: July.
2021
Instructor: Dr. Prince Appiah Owusu
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QUESTIONS
1. A well is 250 ft due west of a north-south trending fault. From pressure transient
tests, the skin factor, s, of this well has been found to be 5.0. Suppose that this well
has been flowing for 8 days at 350 STB/D. Given the following reservoir and well
properties, calculate the pressure at the flowing well:
Reservoir thickness = 50 ft
Porosity = 16 %
Permeability = 25 md
Viscosity = 0.5 cp
Total compressibility = 2 E-5 psi-1
Formation volume factor = 1.13 RB/STB
Wellbore radius = 0.333 ft
Initial Reservoir pressure = 3000 psia
2. Suppose that there is a shut-in well 500 ft due north of the producing well in
Question 1. Calculate the pressure drop at the shut-in well at the end of 8 days.
3. A producing well is opened to flow at 250 STB/D for 1 day. The second day its
flow is increased to 450 STB/D and the third day to 500 STB/D. Using the following
reservoir and well properties, what is the pressure in a shut-in well 660 ft away after
the third day.
Initial Reservoir pressure = 2500 psia
Reservoir thickness = 43 ft
Porosity = 16 %
Permeability = 25 md
Viscosity = 0.44 cp
Total compressibility = 1.8 E-5 psi-1
Formation volume factor = 1.32 RB/STB
4. An oil well produces at a constant surface rate of 1500 STB/D. Estimate the
radius of investigation at:
a) 1 hr
b) 100 hrs.
Reservoir and well information are givens as follows:
Reservoir thickness = 45 ft
Porosity = 18 %
Permeability = 38 md
Viscosity = 0.7 cp
Total compressibility = 1.5 E-6 psi-1
Formation volume factor = 1.37 RB/STB
Wellbore radius = 0.25 ft
Reservoir temperature = 215 oF
Initial Reservoir pressure = 5300 psia
c) What will be the radius of investigation in parts a) and b), if the well was
flowed at 3500 STB/D?
d) What is the minimum flow time required to see a fault 1.5 km away from
the well?
5. From the test data given in the Table below, estimate the following (you may use
Excel spreadsheet to do this exercise):
a) Formation Permeability
b) Skin Factor
c) Drainage area, in Acres
6. Show that the Semi-log pressure derivative is related to the Cartesian pressure
dp dp
=t
derivative by the following: d ln t dt
7. A formation has been severely damaged during drilling with the well exhibiting a
skin factor, S, of 70. The virgin formation permeability, k, from the well test is 70
md and the formation thickness is 150 ft. The wireline logs indicate a depth of
filtrate invasion of 6 ft and it is presumed that the damage is uniform over the
invaded annulus. An acid stimulation job is being designed which will remove
formation damage to a radial depth of 3 ft from the wellbore i.e the acid dissolves
interstitial clay, polymer and mud solids and returns the permeability to the
unaltered value. Calculate the well skin factor after stimulation and the volume of
acid required for the treatment if the porosity is 0.2, residual oil saturation is 0.3
and the well radius, rw= 0.354 ft.
8.
9. Problem: A well produces 100 stb/d oil at a measured flowing bottomhole
pressure (BHP) of 1500 psi. A recent pressure survey showed that average
reservoir pressure is 2000 psi. Logs indicate a net sand thickness of 10 ft. The
well drains an area with drainage radius, re, of 1000 ft; the borehole radius is 0.25
ft. Fluid samples indicate that, at current reservoir pressure, oil viscosity is 0.5 cp
and formation volume factor is 1,5 RB/STB.
Estimate the productivity index for the tested well.
Estimate formation permeability from the tested data.
Core data from the well indicate an effective permeability to oil of 50 md. Does
this imply that the well is either damaged or stimulated? What is the apparent skin
factor?
10. An 8 ½” diameter well is damaged 30” into the formation. The permeability of
the undamaged reservoir is ten times that of the damaged zone. The following are
additional well and reservoir data:
Reservoir pressure = 5000 psia
Flowing well pressure = 4200 psia
Permeability = 50 md
Reservoir Thickness = 200 ft
Production rate = 2500 STB/D
Formation volume factor = 1.3 RB/STB
Viscosity = 0.75
a) Calculate:
i. Skin factor
ii. Skin pressure drop
iii. PI
iv. Ideal PI
v. Flow Efficiency
b) b) How will the results in part a) change if the well was stimulated such that the
damaged zone permeability is ten times that of the virgin reservoir?
11. The following data is given for an oil well that is scheduled for a drawdown test:
volume of fluid in the wellbore=180 bbl
tubing outside diameter=2 inches
production oil density in the wellbore=7.675 inches
average oil density in the wellbore=45 lb/ft3
h=50 ft, φ=15 %, rw=0. 25 ft, µo=2cp, k=30 md, s=0, ct =20×10−6psi−1,
co=10×10−6psi−1
If this well is placed under a constant production rate, calculate the dimensionless
wellbore storage coefficient CD. How long will it take for wellbore storage
effects to end
