PE 7023 Advanced Production Design
PE 7023 Advanced Production Design
Homework Assignment #1
Singlephase Liquid Inflow Performance Relationship (IPR) is given with the following equation:
where, ππΜ ππ is the average reservoir pressure, πππ€π€π€π€ is the bottomhole flowing pressure, πππ π π π is the liquid flow rate at standard conditions, and π½π½ is the productivity index.
Singlephase Liquid Outflow Performance Relationship (OPR) is given below for vertical upward flow assuming an incompressible liquid and constant friction factor, ππ.
where, πππ π π π π π is the separator pressure, πππ€π€π€π€ is the bottomhole flowing pressure, πππ π π π is the liquid flow rate at standard conditions, ππ is the acceleration gravity of Earth, πππ π is the unit conversion factor, πΏπΏ is the depth of the well, πππΏπΏ is the density of the liquid and ππ is the diameter of the tubing. Grouping the constant parameters, Eq. 2 can be written as
Question:
 Perform nodal analysis and find the solution point using the following input data:
ππ_{π π π π π π }
100
psig
ππ_{ππ}
5000
psig
π½π½
5
bbl/D/psi
π΄π΄π΄π΄π΄π΄
25
o
πΏπΏ
8000
ft
ππππππππππππ
0.02

ππππππππππππ π΄π΄πΌπΌ
2.5
in
 Plot nodal analysis plot taking bottom hole as the node
 Plot nodal analysis plot taking wellhead as the node (Hint: rewrite Equations (1) and (2) for wellhead pressure πππ€π€β)
 Develop an analytical expression for the stability of the Nodal Analysis Equilibrium Solution applying new stability analysis.
 Write a computer code using a programming language of your choice to determine if the solution is stable or unstable
 Run your computer code to check for stability:
 By varying J and keeping B constant (Arbitrarily define the range for J)
 By varying B and keeping J constant (Arbitrarily define the range for B. You can change any parameter included in the definition of B to have a meaningful B range)
 Present your stability results on a J vs. B (or variable of your choice included in the definition of B) map
 Discuss your results. What do you see? Please provide your interpretation.
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