state of the art and outlook for future development
TRANSCRIPT
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Society of Petroleum EngineersSPE 2001–2002 Distinguished Lecturer Program4 July 2002
Reservoir Fluid Properties State of the Art and Outlook for
Future Development
!"#$
Dr. Muhammad Al-MarhounKing Fahd University of Petroleum & MineralsDhahran, Saudi ArabiaE-mail: [email protected]
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OutlineOutline% Introduction% State of the Art% Determination of PVT properties%% Problems related to Problems related to PVT
&& Experimentation & CalculationsExperimentation & Calculations& Data smoothing & smoothing & Correlations
% Artificial neural networks%% PVT ReportingPVT Reporting% Conclusions
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IntroductionIntroductionFluid Properties
The study of the behavior of vapor and liquid in petroleum reservoirs as a function of pressure, volume, temperature, and composition
Importance of PVT Properties& Determination of hydrocarbon reserves& Reservoir and simulation studies& Design of production facilities
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State of the Art
& Graphical correlations are reduced to equations& Correlations have been improved& Fluid classification in reservoirs is defined & Laboratory analyses have been standardized & Chemical analyses of petroleum are made
available & EOS is utilized to calculate gas-liquid equilibria
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Determination of PVT propertiesDetermination of PVT properties
& Laboratory measurements using:' Bottom hole sample' Recombined surface sample
& Equation of state with appropriate calibrations& Empirical correlations with appropriate range
of application& Artificial neural networks models
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Problems related to Problems related to experimentationexperimentation
''Reservoir process Reservoir process presentation''Physical trends of lab dataPhysical trends of lab data
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Reservoir process presentationReservoir process presentation& Lab tests do not duplicate reservoir process
&Petroleum engineers consider liberation process in reservoir approaches differential
& Liberation process around well is considered flash
&Actual process is neither flash nor differential
&A combination test may be closest to the reservoir process
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Phase transition in oil reservoirPhase transition in oil reservoirZone A: above pbZone B: below pb, flashZone C: differential
AB
Well
Reservoir
C
Separator
OilGas
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Typical trends of good lab dataTypical trends of good lab data
1.29
1.30
1.30
1.30
1.31
1.31
1500 2000 2500 3000 3500
Pressure
Vo
&Good experimental P-V data should follow physical trend. 'Volume decreases with P'Co decreases with P
' decreases with PdpdC o−
-1.54E-09
-1.53E-09
-1.53E-09
-1.52E-09
-1.52E-091500 2000 2500 3000 3500
Pressure
Slop
e of
Co
0.00
0.00
0.00
0.00
0.00
0.00
1500 2000 2500 3000 3500
Pressure
Co
T
o
oo p
VV
C
∂∂
−=1
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Abnormal CAbnormal Coo trendtrend
1.35
1.36
1.36
1.37
1.37
1.38
1500 2000 2500 3000 3500
Pressure
Vo
&Co should decrease with pressure
-2.67E-10
-2.66E-10
-2.65E-10
-2.64E-10
-2.63E-10
-2.62E-10
-2.61E-101500 2000 2500 3000 3500
Pressure
Slop
e of
Co
0.00
0.00
0.00
0.00
0.00
0.00
0.00
1500 2000 2500 3000 3500
Pressure
Co
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Abnormal CAbnormal Coo derivative trendderivative trend
1.21
1.22
1.22
1.23
1.23
1.24
1.24
1500 2000 2500 3000 3500 4000
Pressure
Vo
& should decrease with pressure
dpdC o−
-1.69E-10
-1.69E-10
-1.69E-10
-1.69E-10
-1.69E-10
-1.69E-10
-1.69E-101500 2000 2500 3000 3500 4000
Pressure
Slop
e of
Co
0.00
0.00
0.00
0.00
0.00
0.00
1500 2000 2500 3000 3500 4000
Pressure
Co
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Problems related to calculationsProblems related to calculations
Adjustment of differential data of differential data as an exampleas an example
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Adjustment of differential data of differential data to separator conditions to separator conditions --Why?
&Rs and Bo obtained by differential liberation are not the same as Rs and Bo obtained by flash liberation
&Oil leaving reservoir is flashed to separator, therefore Rs and Bo should be determined by a flash process
&Flash liberation does not cover whole range of interest, therefore differential data are corrected
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Current adjustment methodCurrent adjustment method--PropertiesProperties!At lower pressure formation volume factor, Bo
might read a value less than 1
0.90
1.00
1.10
1.20
1.30
1.40
0 500 1000 1500 2000 2500
Pressure
Bo
Bo-typicalBo
t d
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Current adjustment methodCurrent adjustment method--PropertiesProperties!At lower pressure, the solution gas-oil ratio, Rs
extrapolates to negative values.
-200.00
0.00
200.00
400.00
600.00
0 500 1000 1500 2000 2500
Pressure
R s
Rs-typicalRs
t d
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Current adjustment methodCurrent adjustment method--PropertiesProperties
! Current adjustment method does not honor density atbubble point under reservoir conditions
ob
gsoob B
Rx γγγ
41018.2 −+=
0.71862650.738444γob
0.83430.8448γo
0.80240.9336γg
526526Rs
1.2891.289Bob
Flash Liberation
Adjusted Differential
Property
! The same crude under the same reservoir conditions, but different densities
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Adjustment methods of oil FVF
& Current Adjustment of Bo
obd
obfodo B
BBB =
& Suggested Adjustment
( )obfodnobfo BBcBB −+=
)/()( odnobdodobd BBBBc −−=
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Oil FVF
0.9
1
1.1
1.2
1.3
1.4
0 500 1000 1500 2000 2500
Pressure, psia
Oil
FVF
DifferentialCurrentSuggested
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Adjustment methods of solution GOR
& Current Adjustment of Rs
obd
obfsdsbdsbfs B
BRRRR )( −−=
& Suggested Adjustment
( )sbdsbfsds RRRR =
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Solution GOR
-100
0
100
200
300
400
500
600
0 500 1000 1500 2000 2500
Pressure, psia
Solu
tion
GO
RDifferentialCurrentSuggested
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Adjustment methods methods of gas relative density
& Current Adjustment of γg
gdg γγ =
& Suggested Adjustment
)(1 gfgdgfg n
d γγγγ −+=−
)/()(111 −
−−=ngdgdgdgdd γγγγ
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Gas relative density
0.6
0.8
1
1.2
1.4
1.6
1.8
0 500 1000 1500 2000 2500
Pressure, psia
Gas
rela
tive
dens
ity
DifferentialCurrentSuggested
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Adjustment methods methods of oil relative density
& Current Adjustment of γo
odo γγ =
& Suggested Adjustment
)( ofodofo c γγγγ −+=
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Oil relative density
0.832
0.834
0.836
0.838
0.84
0.842
0.844
0.846
0 500 1000 1500 2000 2500
Pressure, psia
Oil
rela
tive d
ensit
y DifferentialCurrentSuggested
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Live oil relative density
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0 500 1000 1500 2000 2500
Pressure, psia
Live
oil
rela
tive d
ensit
y DifferentialCurrent Suggesed
o
gsoor B
Rx γγγ
41018.2 −+=
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Problems related to Problems related to Smoothing experimental dataSmoothing experimental data
SmoothingSmoothing relative total volume data relative total volume data as an exampleas an example
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SmoothingSmoothing relative total volume datarelative total volume data
% To obtain P-V data, conduct a flash liberation experiment on a gas-oil mixture at a constant temperature
% Data analysis defines& volume & pressure at bubble point
& FVF above pb & total FVF below pb
% The experimental data as reported are accompanied by measurement errors. Therefore, the data are usually smoothed
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YY--function propertiesfunction properties
1
2
3
4
5
6
0 1000 2000 3000 4000 5000
Pressure
Tota
l Rel
ativ
e Vo
lum
e
volumeY-fun value
&Only the experimental data at pressures below pb are utilized to obtain pb
&Bubble point volume is not corrected
&Y-Correlation with an error in the bubble point volume may yield a straight line but with the wrong pb
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YY��Function plotFunction plot
1
2
3
4
5
6
0 1000 2000 3000 4000 5000
Pressure
Tota
l Rel
ativ
e V
olum
e volumecurve-1curve-2Y-fun valueYF
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Smoothing Smoothing relative total volume datarelative total volume data
& Current
paavvvppp
ybbt
b21/)(
/)(+=
−
−=
& Suggested: add x-function beside y-function
paapppvvvx
bb
bob43/)(
/)(+=
−−
=
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XX--Y Function plotY Function plot
1
2
3
4
5
6
0 1000 2000 3000 4000 5000
Pressure
Tota
l Rel
ativ
e V
olum
e volumecurve-1curve-2XY-CurveXY
YF 1944.5 1.2637XY 2014.2 1.262208
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Problems related to Problems related to correlationscorrelations
''Correlation applicationCorrelation application''Properties of correlationsProperties of correlations''Physical trends of correlationsPhysical trends of correlations''Pitfalls of least square methodPitfalls of least square method
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Correlation applicationCorrelation application
Correlations normally used to determine:Correlations normally used to determine:%% BubbleBubble--point pressure, point pressure, Pb
%% Solution gasSolution gas--oil ratios, oil ratios, RRss
%% Density of liquidsDensity of liquids%% Oil FVF, BOil FVF, Bob ob & total FVF, B& total FVF, Btt
%% Adjustment of BAdjustment of Bobob and and RRss
%% Oil compressibility, COil compressibility, Coo
%% Oil viscosity, Oil viscosity, µµoo ,, µµaa , , µµll
%% Interfacial tension, Interfacial tension, σσ
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Properties of correlationsProperties of correlations
% Correlations typically match employed experimental data, with deviations less than a few percent
% When applied to other fluids, a much higher deviations are observed
% If fluids fall within the range of tested fluids, an acceptable accuracy can be expected
% Fluid composition could not be explained by gross properties
% Errors in some PVT correlations are not acceptable
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Physical trends of correlationsPhysical trends of correlations
Trend tests are to check whether the performance of correlation follows physical behavior or not:
' Trend tests on predicted values
' Trend tests on errors
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Correlation with two equationsCorrelation with two equations
1.250
1.275
1.300
1.325
1.350
1.375
1.400
10 20 30 40 50 60
Oil API Gravity
Oil F
VF
StandingMarhounVazquez & Beggs
&Modeling physical properties with two equations might produce non-physical trend
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Correlation with nonCorrelation with non--physical constraintphysical constraint
1.2
1.25
1.3
1.35
1.4
1.45
0.4 0.6 0.8 1 1.2 1.4 1.6
Gas Relative Density (Air=1.0)
Oil F
VF
StandingMarhounVazquez & Beggs )( gapi γγ
&Restriction of correlation model gives non-physical trend
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Correlation with limited dataCorrelation with limited data
500
1000
1500
2000
2500
60 110 160 210 260
RESERVOIR TEMPERATURE F
Pb, p
si
StandingVazquezMarhounDokla & Osman
&Correlation development for limited data will give a good fit, but might lead to non-physical trend
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Trend Tests on Error: Effect of API On BTrend Tests on Error: Effect of API On Bobob
0
5
10
15
20
25
30
11.4<API<22(23)
22<API<30(39)
30<API<35(26)
35<API<40(56)
40<API<45(33)
45<API<59.2(20)
Oil API Gravity
Erro
r in
Bo
StandingVazquez & BeggsMarhoun
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Trend Tests on Error: Effect of GRD On BTrend Tests on Error: Effect of GRD On Bobob
0
5
10
15
20
25
30
0.525 - 0.7(23)
0.7- 0.75(25)
0.75-0.8(24)
0.8-0.85(24)
0.85-0.9(22)
0.9 - 1.0 (27)
1.0-1.25(30)
1.25-1.7(21)
Gas Relative Density (Air=1.0)
Err
or in
Bo
Vazquez & BeggsStandingMarhoun
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Pitfalls of least square methodPitfalls of least square methodUsed to estimate the regression coefficients in model
)( xfy =
% Basic assumption of LSM is the independent variable x is determinate, i.e. it has no error
% But x and y involve measurement errors, therefore
% Do not rely entirely on a method when its basic assumption is violated
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Comparison of the �Best fit line�
Min y-error LSM
Min x & y-error
0 10 20 30
0.01
0.1
1
10
100
1000
40
Property
y
x
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Pitfalls of logarithmic equivalencePitfalls of logarithmic equivalence
logarithmic equivalent used to linearize equations% Given the problem% Use the logarithmic equivalent
xnky logloglog +=
nkxy =
50.0419.03
8.022.51yx
% Apply LSM to minimize error% Compare errors Σδ2
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Comparative error analysisError using logarithmic equivalent
)(log)(log givenyestimatedy −=δError using original values
)()( givenyestimatedy −=δΣδ2
(original problem)
Σδ2
(logarithmic equivalent)
nkMethod
13.90.568383.360.474 Iterative100.20.020982.0962.224LSM
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Artificial neural networksArtificial neural networks''DefinitionDefinition''AdvantagesAdvantages''Problems & ChallengesProblems & Challenges
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Artificial neural networksArtificial neural networks
A mathematical model that can acquire artificial intelligence. It resembles brain in two respects by( Acquiring knowledge through learning
process ( Storing knowledge through assigning
inter-neuron connection strengths known as weights
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Neural network architectureNeural network architecture
INPUTHIDDEN
API
Rs
γg
T
OUTPUT
Bob
Pb
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ANN AdvantagesANN Advantages
( Model function does not have to be known
( ANN learns behavior by self-tuning its parameters
( ANN has the ability to discover patterns
( ANN is fast-responding systems and provides a confident prediction
( ANN can accept more input to improve accuracy; such continuous enrichment or �knowledge� leads to more accurate predictive model
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ANN Problems & ChallengesANN Problems & Challenges
% Design of ANN:
( Number of hidden layers
( Number of neurons in each hidden layer
( Learning constant to control speed of training
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ANN Problems & ChallengesANN Problems & Challenges
% Generalization Vs. Over Fitting
( New training algorithms (cross validation)
( Hybrid systems (expert systems)
( Number of adjustable weights is large which is not justified unless the PVT data is huge
% Is the neural network the ultimate solution?
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PVT ReportingPVT Reporting
'Typical PVT report'PVT report shortcoming'Suggested improvement
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Typical PVT Report
& Sampling information& Hydrocarbon analysis of reservoir fluid& Oil compressibility& Pressure volume relationship (smoothed data)& Differential liberation & Separator tests & Hydrocarbon analysis of lab flashed gases& Liquid and gas viscosity data& Mixture density
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PVT ReportPVT Report-- Shortcoming
% Reports smoothed results only
% Does not include raw data
% Does not verify data consistency
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PVT Report -Suggested improvement
%Raw data reporting&Pressure volume (experimental data) &Differential liberation (experimental data)&Viscosity (experimental data)
%Data consistency&Mixture density calculation & verification&Co calculation & verification
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ConclusionsConclusionsMore improvement in the following areas:
%% Problems related to experimentationProblems related to experimentation&Reservoir process presentation
&&Physical trends of lab dataPhysical trends of lab data
%% Problems related to calculationsProblems related to calculations&Adjustment of differential data
% Problems related to Problems related to data smoothingsmoothing&Y-function
&XY-function
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ConclusionsConclusions%% Problems related to correlationsProblems related to correlations
&Physical trends of correlations
&&Pitfalls of least square methodPitfalls of least square method
% Artificial neural networks&Design of ANN
&Over Fitting
%% PVT ReportingPVT Reporting&Raw data reporting
&Data consistency
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Final CommentFinal Comment
There are challenges in addressing these
problems, but there are untapped scientific
tools as well.
We explored these challenges and
examined possible solutions.
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Thank YouThank You
!"#$