1. Harold Vance Department of Petroleum Engineering
The Analysis and Interpretation of Water-Oil Ratio Performance in Petroleum Reservoirs
Valentina Bondar
Texas A&M University
Harold Vance Department of
Petroleum Engineering
12 January 2001

2. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

3. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

4. Objective
Provide the development of a pseudo-steady-state WOR equation.
Estimate and compare values of "movable" oil using various straight-line extrapolation methods.
Introduce two new methods for esti-mating Np,mov.
Perform "qualitative" analysis of oil and water production data.

5. Introduction 20 Wells in the North Robertson Unit (West Texas)
8 Wells in the West White Lake Field (South Louisiana)

6. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

7. Steady-State WOR Model
Conventional WOR Analysis
Steady-State WOR Model
Linear log(krw/kro) versus Sw

8. Conventional WOR Analysis
log(fw) versus Np fw
The logarithm of the water-oil ratio (WOR) or water cut (fw) functions plotted versus cumulative oil production are commonly used for evaluation and prediction of waterflood performance. This presumed log-linear relationship of WOR (or fw) and oil recovery allows extrapolation of the straight-line to any desired water cut as a mechanism for determining the corresponding oil recovery. Straight-line extrapolation methods assume that the mobility ratio is equal to unity and the plot of log (krw/kro) versus Sw is a straight line.
The plot of logarithm of water-oil ratio or water cut functions versus cumulative production6 is widely used technique for prediction and evaluation of waterflood performance. This method applies for analysis of late time WOR behavior and allows obtaining the volume of the movable oil by extrapolating the WOR straight-line trend to higher values of water cuts. The technique uses steady state flow equation
Several articles have been developed to analyze linearity of late time behavior of the WOR function and to obtain analytical solution for natural water drive and/or waterflooding mechanisms in oil production
This technique uses an equation that represents the waterflood process in a fully developed waterflood with stabilized operations. It permits calculation of water-oil relative permeability ratio (krw/kro) as a function of water saturation from production data. The estimated field relative permeability ratio curve includes reservoir properties as well as operational conditions of the field. This approach also provides an estimate oil recovery by extrapolation of the straight line to higher water cuts. In order to apply this method linear relationship between oil recovery and water cut has to be achieved thus a reservoir has to produce with water cuts greater than 50%. Np

9. Conventional WOR Analysis
log(fw) versus Np
fw = 1

10. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

11. Pseudosteady-State WOR Model
Blasingame and Lee
bpss m

12. Pseudosteady-State WOR Model
Steady state flow equation is used in all conventional WOR analysis. Our goal is to extend conventional WOR analysis to the case of pseudosteady-state flow.
The original material balance approach for boundary dominated reservoir (i.e., pseudosteady-state) with a variable rate was developed by Blasingame and Lee,7 and the following approximated solution was obtained for a circular drainage area and stabilized flow:
Recalling that WOR = qw/qo we obtain a new WOR model that does not involve assumptions of conventional steady-state equation.

13. Pseudosteady-State WOR Model

14. Pseudosteady-State WOR Model

15. Pseudosteady-State WOR Model
log(fw) versus Np mo mw
bppsw
bppso fw tw to
In order to test the presented pseudosteady-state equation production data for North Robertson Unit (NRU)10 was used. The NRU is located in Gainics County, Texas in the northern part of the Central Basin Platform of the Permian Basin.
Curve fitting analyses were conducted to determine mo, bpsso, mw, bpssw coefficients. The plot of calculated and measured values of WOR function for NRU Well 3107 is shown in the fig.1. As it can be observed a good agreement is achieved. The pseudosteady-state model is able to reproduce the trend of observed field performance even at early time of production, which can not be done by straight-line extrapolation.

16. Pseudosteady-State WOR Model
log(fw) versus Np fw tw to
In order to test the presented pseudosteady-state equation production data for North Robertson Unit (NRU)10 was used. The NRU is located in Gainics County, Texas in the northern part of the Central Basin Platform of the Permian Basin.
Curve fitting analyses were conducted to determine mo, bpsso, mw, bpssw coefficients. The plot of calculated and measured values of WOR function for NRU Well 3107 is shown in the fig.1. As it can be observed a good agreement is achieved. The pseudosteady-state model is able to reproduce the trend of observed field performance even at early time of production, which can not be done by straight-line extrapolation.

17. Pseudosteady-State WOR Model
Results from the PSS WOR model versus the field production data

18. Pseudosteady-State WOR Model
log(fw) versus Np

19. Pseudosteady-State WOR Model
Results from the PSS WOR model versus the field production data

20. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

21. Analysis of WOR Data Estimation of Movable Oil Conventional techniques
log(qo) versus production time, t
qo versus cumulative oil production, Np
fo versus cumulative oil production, Np
log(fw) versus cumulative oil production, Np
Ershagi's X-function
New techniques
1/fw versus cumulative oil production, Np
1/qo versus oil material balance time, to

22. Analysis of WOR Data Qualitative Analysis
log(fwc) versus cumulative oil production, Np
log(WORc) versus cumulative oil production, Np
log(WOR) versus total production, (Np+Wp)
log(fo) versus total material balance time, tt
WOR and WOR associated functions versus time, t (to)

23. Analysis of WOR Data Estimation of Movable Oil Conventional techniques
log(qo) versus production time, t
qo versus cumulative oil production, Np
fo versus cumulative oil production, Np
log(fw) versus cumulative oil production, Np
Ershagi's X-function
New techniques
1/fw versus cumulative oil production, Np
1/qo versus oil material balance time, to

24. log(qo) and log(qw) versus t
Analysis of WOR Data
log(qo) and log(qw) versus t

25. Analysis of WOR Data
qo versus Np
qo=0

26. Analysis of WOR Data
fo versus Np
fo=0

27. Analysis of WOR Data
log(fw ) versus Np
fw = 1

28. Analysis of WOR Data Ershagi’s X-plot X-function = -5.6 @ fw = 0.99
Np=145,000 STB
X = ln((1/fw)-1)-1/fw
The value of Np,mov obtained correspond to those determined by conventional techniques (decline curves, EUR plots, etc.). Fig.3 shows application of this technique for NRU Well 3107.
X-function = -5.6
@ fw = 0.99

29. Analysis of WOR Data Estimation of Movable Oil Conventional techniques
log(qo) versus production time, t
qo versus cumulative oil production, Np
fo versus cumulative oil production, Np
log(fw) versus cumulative oil production, Np
Ershagi's X-function
New techniques
1/fw versus cumulative oil production, Np
1/qo versus oil material balance time, to

30. Analysis of WOR Data
1/fw versus Np
1/fw=1

31. Analysis of WOR Data 1/qo Np /qo 1/qo versus Np/qo
A new method for estimating Np,mov is introduced. We suggest that 1/qo versus the oil material balance time (to=Np/qo) plot can be used to evaluate Np,mov since a linear trend was observed for all cases considered. We have an equation of straight line, which is

32. Reciprocal of qo versus oil material balance time
Analysis of WOR Data
Reciprocal of qo versus oil material balance time

33. Analysis of WOR Data b 1/qo versus Np/qo
The value of Np,mov obtained correspond to those determined by conventional techniques (decline curves, EUR plots, etc.). Fig.3 shows application of this technique for NRU Well 3107.

34. Analysis of WOR Data 1/qo versus Np/qo Np,mov = 164,500 STB
The value of Np,mov obtained correspond to those determined by conventional techniques (decline curves, EUR plots, etc.). Fig.3 shows application of this technique for NRU Well 3107.

35. Analysis of WOR Data
fwc versus Np
Np,mov = 164,500 STB

36. Comparison of the estimated Np values
Analysis of WOR Data
Comparison of the estimated Np values

37. Analysis of WOR Data Qualitative Analysis
log(fwc) versus cumulative oil production, Np
log(WORc) versus cumulative oil production, Np
log(WOR) versus total production, (Np+Wp)
log(fo) versus total material balance time, tt
WOR and WOR associated functions versus time, t (to)

38. Analysis of WOR Data
WOR versus (Np+Wp)

39. fo versus (Np+Wp)/(qo+qw)
Analysis of WOR Data
fo versus (Np+Wp)/(qo+qw)

40. WOR and WOR' versus (Np/qo)
Analysis of WOR Data
WOR and WOR' versus (Np/qo)

41. WOR integral and integral-derivative versus (Np/qo)
Analysis of WOR Data
WOR integral and integral-derivative versus (Np/qo)

42. Outline
Introduction
Conventional WOR Analysis (Steady-State WOR Model)
Pseudosteady-State WOR Model
Analysis of WOR
Conclusions and Recommendations

43. Conclusions Pseudosteady-state WOR model
We have developed a new pss WOR model for boundary-dominated reservoir behavior.
The proposed pss WOR model provides the best representation of the oil and water production data for the cases that we in-vestigated.
The only significant limitation of the our model is that it does not provide a mechan-ism for the prediction of future production

44. Conclusions (cont.) Estimation of Movable Oil
We provide a compilation of the "conven-tional" straight-line extrapolation methods. These techniques should be applied simultaneously in order to obtain consis-tent estimates of movable oil.
We proposed two new methods for estimating movable oil reserves:
1/fw versus Np
1/qo versus Np/qo

45. Conclusions (cont.) Estimation of Movable Oil
The results obtained by these new methods correspond quite well to the results obtained "conventional" WOR techniques.
Analysis of Oil and Water Production Data
We note a straight-line behavior for the fwc and WORc functions plotted versus Np. However, the extrapolation of these straight-line trends does not lead to similar result for movable oil as the "conventional" extrapolation techniques.

46. Conclusions (cont.) Analysis of Oil and Water Production Data
We have extended the diagnostic plots proposed by Chan. The following obser-vations are noted:
unit slope of the WOR and WOR integral and integral-derivative functions when plotted versus t, to, tt.
the WOR' function is typically very erratic and can not be used for routine analysis due to poor overall behavior.

47. Conclusions (cont.) Analysis of Oil and Water Production Data
We believe that the X-plot method provides no substantive advantage over the "conventional" extrapolation techniques. The extrapolation of the X-function tends to significantly overestimate the value of movable oil.

48. Recommendations
Investigate the possibility of using the proposed pss WOR model for the estimation of movable oil.
Examine a possibility to develop an analysis scheme to estimate pss parameters (bpsso, bpssw, mo, and mw). We suggest that the para-meters can be further used for reservoir analysis.
We suggest further qualitative and quantitative analysis for the various WOR trends as a function of time, cumulative production, material balance time. A”type curve" approach may be possible.

49. Harold Vance Department of Petroleum Engineering
The Analysis and Interpretation of Water-Oil Ratio Performance in Petroleum Reservoirs
Valentina Bondar
Texas A&M University
Harold Vance Department of
Petroleum Engineering
12 January 2001