Problem 1
The permeability of a reservoir is constant and estimated to be equal to 750 mD. The reservoir pressure is 3200 psi, the formation thickness 40 m, and oil viscosity 10 cP. A well with diameter 6 inch is drilled through the reservoir, which resulted the well to be damaged and consequently its permeability is reduced to 50 mD. At distance 500 m away from the well, the reservoir pressure remains constant.
a. Calculate the oil flow rate into the well (bbl/D), if the bottomhole(well) pressure is 1800 psi.
b. What is the value of skin factor?
Problem 2
A reservoir contains five layers with the following properties.
| Layer # |
h(ft) |
k(mD) |
| 1 |
15 |
15 |
| 2 |
35 |
80 |
| 3 |
5 |
235 |
| 4 |
2 |
1500 |
a. Calculate the average horizontal permeability for horizontal flow.
b. Calculate the vertical permeability for vertical flow.
c. Explain what kind of depositional environment do you envision for this reservoir
Problem 3
Derive the constant the linear form of Darcy equation in the oilfield unit system:
Q = -1.127 x 10-3 kA/μ[ΔP/ΔL]
And state the units of the various parameter involved. What does the negative sign on the right hand side term of the flow rate equation imply?
Problem 4
For the simplified capillary tube model:
a. Derive an expression for the model porosity. Explain any discrepancy from expected realistic porosity values.
b. Derive a relationship between the formation permeability, k, the porosity and capillary tube radii R. Hint: Equate the flow rate in a porous medium obtained from Darcy and Poiseuille laws.