PGE 323
Test #1
Open notes
February 14, 2006
Pope
1.
(30%) In homework#1, you did a mass balance for singlephase flow in a permeable
medium using cylindrical coordinates.
(a) Starting with the equation
(
29
(
29
(
29
(
29
(
29
(
29
(
29
r
z
t
t
t
r
z
r
z
r
r
z
z
r
r z
r
r z
r
z
U
r
r
U
z r
U
t
z r
r
U
r
r
U
z r
U
t
θ
+∆
θ
θ
+∆
+∆
θ+∆θ
∆θ∆ ∆ φρ
 ∆θ∆ ∆ φρ =
∆θ∆
ρ
+ ∆θ∆ ρ
+ ∆ ∆ ρ
∆
 ∆θ∆
+ ∆
ρ
+ ∆θ∆ ρ
+ ∆ ∆ ρ
∆
show in detail how to get the differential mass balance equation
(
29
(
29
(
29
(
29
r
z
1
1
r
U
U
U
0
t
r r
z
r
θ
φρ +
ρ
+
ρ
+
ρ
=
⇒∏
•
θ
(b) Starting with the mass balance from part (a) and assuming Darcy's law, derive the
diffusivity equation for ideal gas in terms of pressure squared (neglect gravity).
2.
(40%) Assume the solution for point sources and sinks applies to this problem.
(a) Make a sketch showing how to model two vertical wells completed over different
depths, which means the interval over which each well is perforated is different.
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This note was uploaded on 05/15/2011 for the course PGE 323 L taught by Professor Johns during the Spring '10 term at University of Texas.
 Spring '10
 Johns

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