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# PE 7023 Advanced Production Design

PE 7023 Advanced Production Design

Homework Assignment #1

Single-phase Liquid Inflow Performance Relationship (IPR) is given with the following equation:

where, ππΜππ is the average reservoir pressure, πππ€π€π€π€ is the bottom-hole flowing pressure, πππ π π π  is the liquid flow rate at standard conditions, and π½π½ is the productivity index.

Single-phase Liquid Outflow Performance Relationship (OPR) is given below for vertical upward flow assuming an incompressible liquid and constant friction factor, ππ.

where, πππ π π π π π  is the separator pressure, πππ€π€π€π€ is the bottom-hole flowing pressure, πππ π π π  is the liquid flow rate at standard conditions, ππ is the acceleration gravity of Earth, πππ π  is the unit conversion factor, πΏπΏ is the depth of the well, πππΏπΏ is the density of the liquid and ππ is the diameter of the tubing. Grouping the constant parameters, Eq. 2 can be written as

Question:

1. Perform nodal analysis and find the solution point using the following input data:
 πππ π π π π π 100 psig ππππ 5000 psig π½π½ 5 bbl/D/psi π΄π΄π΄π΄π΄π΄ 25 o πΏπΏ 8000 ft ππππππππππππ 0.02 - ππππππππππππ π΄π΄πΌπΌ 2.5 in
1. Plot nodal analysis plot taking bottom hole as the node
2. Plot nodal analysis plot taking wellhead as the node (Hint: rewrite Equations (1) and (2) for wellhead pressure πππ€π€β)
2. Develop an analytical expression for the stability of the Nodal Analysis Equilibrium Solution applying new stability analysis.
3. Write a computer code using a programming language of your choice to determine if the solution is stable or unstable
4. Run your computer code to check for stability:
1. By varying J and keeping B constant (Arbitrarily define the range for J)
2. 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)
5. Present your stability results on a J vs. B (or variable of your choice included in the definition of B) map
6. Discuss your results. What do you see? Please provide your interpretation.
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