0. Lecture 21 Rosalind Archer
PETE 324
Lecture 21
Rosalind Archer

1. Analysis of Drawdown Tests
Infinite-acting radial flow in a homogenous reservoir is governed by:
This is of the form:

2. Analysis of Drawdown Tests
This implies the pressure data should form a straight line on a semilog plot.

3. Analysis of Drawdown Tests
Analysis procedure
Plot all data!
Fit a straight line to the data, remembering this solution does not account for radial flow which may distort the early time data. If the pressure derivative is also plotted it should be at a constant level during infinite-acting radial flow (m=2.303Dp’)
Use the slope of the semilog straight line (m) to determine permeability (k)
Use the value of p(1hr) [read from the semilog straight line] to determine skin (s).

4. Analysis of Drawdown Tests
If the data departs from the semilog straight line in late time in indicates the presence of boundaries:

5. Analysis of Drawdown Tests
Time can be related to radial distance in a well test via the concept of the radius of investigation:
This can be used to estimate the distance to the reservoir boundary based on the time at which the pressure data departs from the semilog straight line.

6. Analysis of Buildup Tests
Pressure buildup tests involve recording pressure data while a well is shut in after a period of flow.

7. Analysis of Buildup Tests
The pressure response for a buildup can be constructed by using superposition and the drawdown solution.
An fake injection well (located at the same location as the production well) is turned on at t = tp. It’s rate is -q.

8. Analysis of Buildup Tests
This implies a plot of pws versus (tp+Dt)/Dt should be a straight line. (Horner plot)

9. Analysis of Buildup Tests
Analysis procedure
Plot all data (p versus (tp+Dt)/Dt)
Fit straight line to middle time region (early time is distorted by wellbore storage).
Find slope (m) and extrapolation of straight line to pws(1hr)

10. Analysis of Buildup Tests
Average reservoir pressure is estimated using p* (extrapolated from the straight line on the Horner plot) using the Matthew-Brons-Hazebrok (MBH) technique (not covered).
Remember Dt =t-tp i.e. time since the well was shut-in.

11. Analysis of Buildup Tests
In practice the production time (tp) may be unknown. Rather than assuming a value for tp it is ignored. This is strictly valid if the reservoir has been produced to pseudosteady state conditions.
Miller-Dyes-Hutchinson (MDH) analyzed this situation.

12. Analysis of Buildup Tests

13. Analysis of Buildup Tests

14. Variable-Rate Tests
The pressure response of a test with a sequence of variable flow rates can also be constructed using superposition.

15. Variable-Rate Tests
It is convenient to normalise both sides of this equation by the current flowrate:

16. Variable-Rate Tests
This equation is a straight line (Odeh-Jones plot):

17. Wellbore Storage Definition of wellbore storage coefficient:
Fluid filled wellbore
Rising or falling liquid level

18. Wellbore Storage
During wellbore storage dominated flow the following pressure-time relationships hold:
Drawdown
Buildup

19. Wellbore Storage
Dimensionless wellbore storage coefficient

20. Type Curve: Pressure

21. Type Curve: Press. Derivative

22. Last Words Be consistent!
whatever is characterized as wellbore storage, radial flow etc on one plot e.g. Cartesian must be consistent with the presentation of the data on all other plots e.g. semilog/Horner.