Flow regime identification in formations using pressure derivative analysis with optimized window length

Patent metadata

Field	Value
Publication number	US-10941646-B2
Application number	US-201816047536-A
Country	US
Kind code	B2
Filing date	Jul 27, 2018
Priority date	Jul 28, 2017
Publication date	Mar 9, 2021
Grant date	Mar 9, 2021

Abstract

A method of investigating an earth formation. A tool having a pressure sensor is used in a borehole to collect formation fluid pressure data over time. A pressure derivative curve is generated from the formation fluid pressure data by conducting a piecewise linear regression of the data having optimal window length values L determined by calculating a derivative with respect to L of a pressure derivative value (DD), and selecting values of L where DD has a transition that departs from oscillatory behavior to gradual change. The pressure derivative is calculated with piecewise linear regression with the optimal window length values 2L. Different L values are generated for different groups of data points obtained over time. The pressure derivative is then used for flow regime determination.

First claim

The invention claimed is:

1. A method of investigating an earth formation traversed by a borehole having a wall, comprising:
locating a tool having a probe and a pressure sensor in the borehole;
contacting the borehole wall with the probe and causing fluid movement into or out of the probe;
using the pressure sensor to sense formation fluid pressure data over time;
generating a pressure derivative curve from said formation fluid pressure data by conducting a piecewise linear regression of the data having window length values 2L determined by calculating for selected pressure data points a derivative with respect to L of a pressure derivative value (DD), and selecting a value of L where DD has a transition that departs from oscillatory behavior to gradual change;
using the pressure derivative curve to identify a flow regime of the formation.

2. The method of claim 1 , wherein the selecting a value of L where DD has a transition comprises integrating an absolute value of said derivative DD and selecting a location representing a change in slope of the integral from a large value to a small value.

3. The method of claim 2 , wherein the selecting a location comprises measuring the slope of the integral.

4. The method of claim 2 , wherein the selecting comprises fitting an approximant to the integral where the approximant has a slope that may be analytically estimated at any location.

5. The method of claim 4 , wherein the approximant is a Padé approximant.

6. The method of claim 4 , wherein the approximant is calculated by a least-square optimization.

7. The method of claim 4 , wherein said selecting a location comprises selecting a location where the slope of the approximant when normalized to have equal horizontal and vertical scales is between 0.25 and 0.75.

8. The method of claim 7 , wherein the slope of the approximant when normalized is approximately 0.5.

9. The method of claim 4 , wherein the selecting comprises removing outlier values prior to said integrating.

10. The method of claim 1 , wherein said selected data points are evenly spaced in a log Δt domain, where t is the elapsed time since fluid movement is stopped at the probe.

11. The method of claim 10 , wherein L is chosen to be a fixed predetermined value for early pressure data points where derivative calculations are not sensitive to noise.

12. The method of claim 1 , wherein L is chosen to be a fixed predetermined value for early pressure data points where derivative calculations are not sensitive to noise.

13. A method of providing information about a formation useful for hydrocarbon production, comprising:
locating a tool having a probe and a pressure sensor in a borehole traversing the earth formation;
contacting a wall of the borehole wall with the probe and causing fluid movement into or out of the probe;
using the pressure sensor to sense formation fluid pressure data over time;
generating a pressure derivative curve from said formation fluid pressure data by conducting a piecewise linear regression of the data having window length values 2L determined by calculating for selected pressure data points a derivative with respect to L of a pressure derivative value (DD), and selecting a value of L where DD has a transition that departs from oscillatory behavior to gradual change; and
plotting said pressure derivative curve as a function of time.

14. The method of claim 13 , wherein the selecting a value of L where DD has a transition comprises integrating an absolute value of said derivative DD and selecting a location representing a change in slope of the integral from a large value to a small value.

15. The method of claim 14 , wherein the selecting comprises fitting an approximant to the integral where the approximant has a slope that may be analytically estimated at any location.

16. The method of claim 15 , wherein said selecting a location comprises removing outlier values prior to said integrating and selecting a location where the slope of the approximant when normalized to have equal horizontal and vertical scales is between 0.25 and 0.75.

17. The method of claim 13 , wherein said selected data points are evenly spaced in a log Δt domain, where t is the elapsed time since fluid movement is stopped at the probe.

18. The method of claim 17 , wherein L is chosen to be a fixed predetermined value for early pressure data points where derivative calculations are not sensitive to noise.

Assignees

• Schlumberger Technology Corp

Inventors

• Li Jiyao
• Ramakrishnan Terizhandur S

Classifications

• E21B49/10 Primary

  using side-wall fluid samplers or testers · CPC title

• E21B47/06 Primary

  Measuring temperature or pressure · CPC title

• E21B49/00

  Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells · CPC title