Valentina Bondar

The Analysis and Interpretation of Water-Oil Ratio Performance in

Petroleum Reservoirs

12 January 2001

Texas A&M UniversityHarold Vance Department of

Petroleum Engineering

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

• 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.

Objective

• 20 Wells in the North Robertson Unit (West Texas)

• 8 Wells in the West White Lake Field (South Louisiana)

Introduction

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

Steady-State WOR Model

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Linear log(krw/kro) versus Sw rorww kk

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1

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Conventional WOR Analysis

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ww qq

qf

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w

q

qWOR

Np

fw

Conventional WOR Analysis

log(fw) versus Np

fw = 1

Conventional WOR Analysis

log(fw) versus Np

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

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bpss m

Pseudosteady-State WOR Model

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Blasingame and Lee

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Pseudosteady-State WOR Model

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Pseudosteady-State WOR Model

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Pseudosteady-State WOR Model

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Pseudosteady-State WOR Model

log(fw) versus Np

fw tw to

Pseudosteady-State WOR Model

log(fw) versus Np

Pseudosteady-State WOR ModelResults from the PSS WOR modelversus the field production data

10-3

10-2

10-1

100

60,00040,00020,0000

Cumulative Oil Production, Np, STB

Legend: NRU 1102 fw Function

fw Exponential Np Model

fw pss Model

fw = 3.7x10-2

exp(6.86841x10-5

Np)

Np, mov = 48,000 STB

Fra

cti

on

al F

low

of

Wa

ter

(fw=

qw/(

qw+

qo))

Pseudosteady-State Model:

fw=1/(1 + ( - 16.423 + 1.0064x10-1

tw)/(20.654 + 2.53111x10-2

to))

Variables:to = Np/qo, tw = Wp/qw

Pseudosteady-State WOR Model

log(fw) versus Np

10-2

10-1

100

101

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late

d W

ate

r-O

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ati

o (

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10-2

10-1

100

101

Measured Water-Oil Ratio (WOR = qw/qo)

Unit Slope Line

Pseudosteady-State WOR ModelResults from the PSS WOR modelversus the field production data

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

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

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)

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

Analysis of WOR Data

Analysis of WOR Data

log(qo) and log(qw) versus t

qo=0

Analysis of WOR Data

qo versus Np

fo=0

Analysis of WOR Data

fo versus Np

fw = 1

Analysis of WOR Data

log(fw ) versus Np

Np=145,000 STB

X-function = -5.6

@ fw = 0.99

Analysis of WOR Data

Ershagi’s X-plot

X = ln((1/fw)-1)-1/fw

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

Analysis of WOR Data

1/fw=1

Analysis of WOR Data

1/fw versus Np

1/qo

Np /qo

Analysis of WOR Data

1/qo versus Np/qo

)/(/ opo qNbaq 1

po bNaq 1

0oq bNp /1

Reciprocal of qo versus oil material balance time

Analysis of WOR Data

bNp1

b

Analysis of WOR Data

1/qo versus Np/qo

Np,mov = 164,500 STB

0.20

0.15

0.10

0.05

0.00

Rec

ipro

cal

of

Oil

Rat

e, 1

/qo,

1/S

TB

/Day

8,0006,0004,0002,0000

Oil Material Balance Time (Np/qo), days

1/qo = 1.5927x10-2 + 5.6306x10

-6(Np/qo) 1/STB/D

Np, mov = 177,600 STB

Legend: NRU 104 1/qo Function

1/qo Linear (Np/qo) Model

Analysis of WOR Data

1/qo versus Np/qo

Np,mov = 164,500 STB

Analysis of WOR Data

fwc versus Np

Comparison of the estimated Np values

Analysis of WOR Data

Method Np value,STB

Method Np value,STB

1 log(qo) versus t 86,800 5 1/fw versus Np 86,800

2 qo versus Np 86,800 6 1/qo versus Np/qo 86,800

3 fo versus Np 86,800 7 Ershagi’s X-plot 145,000

4 log(fw) versus Np 86,800 8 Log(fwc) versus Np 95,000

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)

Analysis of WOR Data

Analysis of WOR Data

WOR versus (Np+Wp)

Analysis of WOR Data

fo versus (Np+Wp)/(qo+qw)

Analysis of WOR Data

WOR and WOR' versus (Np/qo)

Analysis of WOR Data

WOR integral and integral-derivative versus (Np/qo)

• Introduction

• Conventional WOR Analysis (Steady-State WOR Model)

• Pseudosteady-State WOR Model

• Analysis of WOR

• Conclusions and Recommendations

Outline

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

Conclusions

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

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.

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.

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.

Conclusions (cont.)

• 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.

Recommendations

Valentina Bondar

The Analysis and Interpretation of Water-Oil Ratio Performance in

Petroleum Reservoirs

12 January 2001

Texas A&M UniversityHarold Vance Department of

Petroleum Engineering