PGE 323L
Test#1
Open notes
February 26, 2009
Pope
1. (10%) Darcy's law for multiphase flow in a permeable medium can be written as
follows:
(
29
rj
j
j
j
j
k
u
k
P
g
D
= 
ρ
�
�
μ
r
r
where j can be any phase such as water, oil or gas.
(a) Is Darcy's law valid for unsteady state flow?
(b) Is Darcy's law valid for compressible flow?
(c) Is Darcy's law valid for an anisotropic permeable medium?
(d) Is Darcy's law valid if all three phases are flowing simultaneously?
2. Assume single phase flow of a gas at residual water saturation.
(a) 20% Derive a mass balance for the gas in cylindrical coordinates
(b) 15% Derive a diffusivity equation for the gas assuming a diagonal permeability tensor
(c) 5% The diffusivity equation has the gas density in it. What is the most common
method that reservoir engineers use to model the gas density?
3. (a) 15% Explain when you would use the solution for line sources and sinks and when
you would uses the solution for point sources and sinks. Your explanation should include
sketches illustrating examples. Your sketches should include pathlines, isopotential
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 Spring '10
 Johns
 Fluid Dynamics, Darcy, sweep efficiency, areal sweep efficiency, volumetric sweep efficiency

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