Transcript AUTOMATED IDENTIFICATION TECHNOLOGY

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
Outline
• 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
Objective
• Provide
the development of a pseudosteady-state WOR equation.
• Estimate and compare values of
"movable" oil using various straight-line
extrapolation methods.
• Introduce two new methods for estimating Np,mov.
• Perform "qualitative" analysis of oil and
water production data.
Introduction
• 20 Wells in the North Robertson Unit
(West Texas)
• 8 Wells in the West White Lake Field
(South Louisiana)
Outline
• Introduction
• Conventional WOR Analysis
(Steady-State WOR Model)
• Pseudosteady-State WOR Model
• Analysis of WOR
• Conclusions and Recommendations
Conventional WOR Analysis
Steady-State WOR Model
qw
WOR 
qo
qw
fw 
qw  qo
kh
1
q
p
141.2B
ln(re / rw )
Bw  w
1
Bo  o
Linear log(krw/kro) versus Sw
fw 
1
1  k rw k ro
Conventional WOR Analysis
log(fw) versus Np
fw
Np
Conventional WOR Analysis
log(fw) versus Np
fw = 1
Outline
• Introduction
• Conventional WOR Analysis
(Steady-State WOR Model)
• Pseudosteady-State WOR Model
• Analysis of WOR
• Conclusions and Recommendations
Pseudosteady-State WOR Model
Blasingame and Lee
p
B
4A
B
 70.6
ln 

0
.
2339
t
mb
q
kh e CArw 2
hct A
bpss
p
q 
mt  bpss
m
Pseudosteady-State WOR Model
qw
WOR 
qo
p
q 
mt  bpss
Pseudosteady-State WOR Model
WOR 
to 
Np
qo
mo t o  bpsso
mw t w  bpssw
tw 
Wp
qw
Pseudosteady-State WOR Model
WOR 
mo t o  bpsso
mw t w  bpssw
Pseudosteady-State WOR Model
log(fw) versus Np
mw
fw
mo
tw
bppsw
to
bppso
Pseudosteady-State WOR Model
log(fw) versus Np
fw
tw
to
Pseudosteady-State WOR Model
Results from the PSS WOR model
versus the field production data
Pseudosteady-State WOR Model
log(fw) versus Np
0
10
Fractional Flow of Water
(fw=qw/(qw+qo))
Np, mov = 48,000 STB
-1
10
-2
-5
Pseudosteady-State
fw =Model:
3.7x10 exp(6.86841x10
Np)
-1
-2
fw=1/(1 + ( - 16.423 + 1.0064x10 tw)/(20.654 + 2.53111x10 to))
-2
Variables:
to = Np/qo, tw = Wp/qw
10
Legend: NRU 1102
fw Function
fw Exponential Np Model
fw pss Model
-3
10
0
20,000
40,000
Cumulative Oil Production,Np, STB
60,000
Pseudosteady-State WOR Model
Results from the PSS WOR model
versus the field production data
1
Calculated Water-Oil Ratio (pss model)
10
Unit Slope Line
0
10
-1
10
-2
10
-2
10
-1
10
0
10
Measured Water-Oil Ratio
(WOR = qw/qo)
1
10
Outline
• Introduction
• Conventional WOR Analysis
(Steady-State WOR Model)
• Pseudosteady-State WOR Model
• Analysis of WOR
• Conclusions and Recommendations
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
–
–
1/fw versus cumulative oil production, Np
1/qo versus oil material balance time, to
• New techniques
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
log(qo) and log(qw) versus t
Analysis of WOR Data
qo versus Np
qo=0
Analysis of WOR Data
fo versus Np
fo=0
Analysis of WOR Data
log(fw ) versus Np
fw = 1
Analysis of WOR Data
Ershagi’s X-plot
Np=145,000 STB
X = ln((1/fw)-1)-1/fw
X-function = -5.6
@ fw = 0.99
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
1/fw versus Np
1/fw=1
Analysis of WOR Data
1/qo versus Np/qo
1/qo
Np /qo
Analysis of WOR Data
Reciprocal of qo versus oil material balance time
1 / qo  a  b(N p / qo )
1  aqo  bN p
qo  0
Np  1 / b
Analysis of WOR Data
1/qo versus Np/qo
Np  1
b
b
Analysis of WOR Data
1/qo versus Np/qo
Reciprocal of Oil Rate, 1/qo, 1/STB/Day
0.20
Np,mov = 164,500 STB
Legend: NRU 104
1/qo Function
0.15
0.10
-2
1/qo Linear (Np/qo) Model
-6
1/qo = 1.5927x10 + 5.6306x10 (Np/qo) 1/STB/D
Np, mov = 177,600 STB
0.05
0.00
0
2,000
4,000
6,000
Oil Material Balance Time N
( p/qo), days
8,000
Analysis of WOR Data
fwc versus Np
Np,mov = 164,500 STB
Analysis of WOR Data
Comparison of the estimated Np values
Method
Np value,
STB
1
log(qo) versus t
86,800
2
qo versus Np
3
fo versus Np
4 log(fw) versus Np
Method
Np value,
STB
5
1/fw versus Np
86,800
86,800
6
1/qo versus Np/qo
86,800
86,800
7
Ershagi’s X-plot
145,000
86,800
8
Log(fwc) versus Np
95,000
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
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)
Outline
• Introduction
• Conventional WOR Analysis (SteadyState WOR Model)
• Pseudosteady-State WOR Model
• Analysis of WOR
• Conclusions and Recommendations
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 investigated.
The only significant limitation of the our
model is that it does not provide a mechanism for the prediction of future production
Conclusions (cont.)
Estimation of Movable Oil
• We
•
provide a compilation of the "conventional" straight-line extrapolation methods.
These techniques should be applied
simultaneously in order to obtain consistent 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 observations 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.
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 parameters 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.
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