valentina bondar the analysis and interpretation of water-oil ratio performance in petroleum...
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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
)/ln(. we rrp
B
khq
1
2141
1oo
ww
B
B
Linear log(krw/kro) versus Sw rorww kk
f
1
1
Conventional WOR Analysis
ow
ww qq
qf
o
w
q
qWOR
• Introduction
• Conventional WOR Analysis (Steady-State WOR Model)
• Pseudosteady-State WOR Model
• Analysis of WOR
• Conclusions and Recommendations
Outline
pssbmt
pq
bpss m
Pseudosteady-State WOR Model
mbtAhc
B
rCe
A
kh
B
q
p
twA
2339.0
4ln6.70
2
Blasingame and Lee
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
Ca
lcu
late
d W
ate
r-O
il R
ati
o (
ps
s m
od
el)
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
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
)/(/ opo qNbaq 1
po bNaq 1
0oq bNp /1
Reciprocal of qo versus oil material balance time
Analysis of WOR Data
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
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
• 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