CPE 327 Reservoir Engineering I
Homework #5
Due Date: 12:00 PM on April 8th (Friday), 2016
1. Two wells are located 2500 ft apart. The well pressure at the top of perforations (9332 ft subsea)
in well A is 4365 psia and at the top of perforations (9672 ft subsea) in well B is 4372 psia. The
reservoir vertical fluid gradient is 0.25 psi/ft, reservoir permeability is 245 md, and reservoir
fluid viscosity is 0.63 cp.
(a) Calculate the two pressures to a datum level of 9100 ft subsea for the two wells.
(b) In what direction is the fluid flowing between the wells?
dp
(c) What is the average pressure gradient (
) between the wells at the datum level of 9100 ft
dl
subsea?
(d) What is the apparent velocity of the fluid between the wells by using the pressure gradient
obtained from part (c)?
2. Derive the equation for the steady-state, single-phase, hemispherical flow of an incompressible fluid.
3. A well is producing 215 STB/day at a bottom-hole pressure of 2,200 psia from a formation that
consists of two strata (or layers) of 15 ft and 10 ft thick. The permeability of the 15 feet strata is
known to be 200 md and that of the 10 ft strata is unknown. The external pressure of the
reservoir is estimated to be 2500 psia. Other reservoir data are as follows:
Reservoir external radius
Well radius
Oil viscosity
Oil formation volume factor
700 feet
6 inches
3.4 cp
1.32 bbl/STB
What is the permeability of the 10 ft strata?
4. A well was given a large fracture treatment, creating a fracture that extends to a radius of about
150 ft. The effective permeability of the fracture area was estimated to be 200 md. The
permeability of the area beyond the fracture is 15 md. Assume that the flow is steady state, single
phase, and incompressible. The outer boundary at r = r = 1500 ft has a pressure of 2200 psia, and
the wellbore pressure is 100 psia (r = 0.5 ft). The reservoir thickness is 20 ft and the porosity is
18%. The flowing fluid has a formation volume factor of 1.12 bbl/STB and a viscosity of 1.5 cp.
(a) Calculate the flow rate in STB/day.
(b) Calculate the pressure in the reservoir at a distance of 300 ft from the center of the wellbore.
5. One hundred capillary tubes of 0.02 in. in diameter and 50 capillary tubes of 0.04 in. (in diameter),
all of equal length, are placed inside a pipe of 2 in. in diameter. The space between the tubes is
filled with wax so that flow is only through the capillary tubes. What is the permeability of this
“rock”?
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