Starting a shiny application for PTA using the Tiab’s Direct Synthesis technique (Manual parameter estimation using Log-Log Plot) for a vertical well with constant WBS and skin in an infinity-acting reservoir.
In this case we need a two columns dataset in .csv format, time in the first column and well pressure in the second one, in hours and psia.
## t pwf
## 1 0.0000 2750.00
## 2 0.0010 2748.95
## 3 0.0021 2745.62
## 4 0.0034 2744.63
## 5 0.0048 2745.49
## 6 0.0064 2741.70
The app allows get permeability, skin and well storage coefficiente with the following equations (1)
plot has a horizontal line to fit IARF data of the derivative and a unit-slope line to fit well storage data. After fit the IARG and WDS lines we can generate de analytical model using the laplace transform solutions to the diffusivity equation
Transform of the dimensionless wellbore pressure (2):
Through the stehfest numerical inverse
transformation method (1976), we can calculate dimensionless wellbore
pressure in real space. The Laplace transform method can be given by (3)
where
The variable N could be one of the even numbers from 8 to 12. In this case we use the V(i) with Stehfest parameter N = 8
| V(1) | V(2) | V(3) | V(4) | V(5) | V(6) | V(7) | V(8) |
|---|---|---|---|---|---|---|---|
| -0.3333 | 48.3333 | -906 | 5464.6667 | -14376.66667 | 18730 | -11946.6667 | 2986.6667 |
References
- Spivey, J. & Lee, J. (2013) Applied well test interpretation. Society of petroleum engineers
- Lee, J., Rollins, J. & Spivey, J. (2003) Pressure transient testing. Society of petroleum engineers
- Sun, H. (2015) Advanced Production Decline Analysis. Gulf Professional Publishing