Exponential Integral Functions
Spreadsheet
25 rows x 3 columns
| A | B | C | |
|---|---|---|---|
| 1 | Exponential Integral Ei(x) | ||
| 2 | Positive Arguments | ||
| 3 | x = 0.5 | 0.4542199049 | |
| 4 | x = 1.0 | 1.895117816 | |
| 5 | x = 1.5 | 3.301285449 | |
| 6 | x = 2.0 | 4.954234356 | |
| 7 | x = 3.0 | 9.933832571 | |
| 8 | x = 5.0 | 40.18527536 | |
| 9 | |||
| 10 | PTA Application | ||
| 11 | tD/rD2 | Ei(-1/(4*tD/rD2)) | Ln approx |
| 12 | 0.1 | -0.02491491787 | -1.493490732 |
| 13 | 0.5 | -0.5597735948 | 0.1159471806 |
| 14 | 1 | -1.044282634 | 0.8090943611 |
| 15 | 5 | -2.467898489 | 2.418532274 |
| 16 | 10 | -3.136508403 | 3.111679454 |
| 17 | 25 | -4.037929577 | 4.027970186 |
| 18 | 100 | -5.416747321 | 5.414264547 |
| 19 | |||
| 20 | Negative Arguments | ||
| 21 | x = -0.1 | -1.822923958 | |
| 22 | x = -0.5 | -0.5597735948 | |
| 23 | x = -1.0 | -0.2193839344 | |
| 24 | x = -2.0 | -0.04890051071 | |
| 25 | x = -5.0 | -0.001148295591 |
Description
Demonstrate the exponential integral (Ei) function used in pressure transient analysis and well test interpretation.
Exponential Integral (Ei):
- Ei(x) = integral from -inf to x of (e^t / t) dt
- Critical for line-source well solutions
- Used in calculating pressure drawdown and buildup
PTA Applications:
- Ei(-1/(4*tD/rD^2)) appears in the line-source solution
- For tD/rD^2 > 25, can use logarithmic approximation
How to use this blueprint
- In Excel, go to the Petroleum Office ribbon tab and click Blueprint Manager
- Search for Exponential Integral Functions
- Click on the blueprint to preview the spreadsheet template
- Click Insert to place it into your worksheet. Modify the input values to match your data.