stochastic and well optimization modeling - · pdf filestochastic and well optimization...
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Stochastic and Well Optimization Modeling to Evaluate Injection Potential
of a California Oilfield
Stochastic and Well Optimization Modeling to Evaluate Injection Potential
of a California Oilfield
Jeffrey A. Anderson and Russell C. Fontaine, Geomega Inc.
Allan Hunter and Dallas Tubbs, ChevronTexaco
Jeffrey A. Anderson and Russell C. Fontaine, Geomega Inc.
Allan Hunter and Dallas Tubbs, ChevronTexaco
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Modeling Study ObjectivesModeling Study Objectives
Determine subsurface injection capacity of the aquifer.
Determine optimum number of wells, location, and rate for prospective injection field.
Quantify long-term impacts of injection on adjacent oil reservoir.
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Numerical Modeling Flow ChartNumerical Modeling Flow Chart
Model developmentModel development
Steady-state stochastic modelSteady-state stochastic model
Transient verificationTransient verification
Well optimizationWell optimization
Particle trackingParticle tracking
DoneDone
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Model DevelopmentModel Development
Data set
Geology model
Mock-up to FDM model
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Map with Well Data Map with Well Data
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3D Geology Block Model3D Geology Block Model
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Numerical Model SetupNumerical Model Setup
Aerial extent and boundaries
Lateral and vertical discretization
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Numerical Model Grid on the Base mapNumerical Model Grid on the Base map
No flow
No flow
Constant heads
Flow direction
Specified flux
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Numerical Model Layer AssignmentsNumerical Model Layer Assignments
Layer
1
2
3
4
5
Layer
1
2
3
4
5
silt #1silt #1
sand #1sand #1
silt #2silt #2
sand #2sand #2
silt #3silt #3
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Stochastic ModelingStochastic ModelingK Distribution - uniform
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3
Random multiplier
f(x)
Silt Conductivity - Log uniform
0
0.5
1
1.5
-5 -4 -3 -2 -1
log K (ft/d)
f(x)
Monte Carlo 1,000 times
Results RSS<100,000
N Bound High
N Bound Middle
N Bound LowFault Conductance - Log uniform
0
0.5
1
1.5
-6 -5 -4 -3 -2 -1 0
log C (ft/d)
f(x)
North Boundary CHs - Uniform
0
0.5
1
1.5
0 200 400 600 800
heads(ft)
f(x)
857,2493.2857,2493.2
784,050.7784,050.7
710,852.1710,852.1
637,653.6637,653.6
561,455.1561,455.1
49,256.649,256.6
Su
m o
f sq
uar
esS
um
of
squ
ares
Realization numberRealization number00 200200 400400 600600 800800 10001000
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Model Predicted Sand #2 Pressure Distribution for North Boundary Middle
Model Predicted Sand #2 Pressure Distribution for North Boundary Middle
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Pressure vs Time for North Boundary Middle Transient Check
Pressure vs Time for North Boundary Middle Transient Check
300300
500500
00 100100 200200 300300
Pre
ssu
re (p
sia)
Pre
ssu
re (p
sia)
300300
500500
0 100 200 300
Pre
ssu
re (p
sia)
Pre
ssu
re (p
sia)
750750
850850
950950
00 100100 200200
Pre
ssu
re (p
sia)
Pre
ssu
re (p
sia)
ObservedComputed
423-3423-3 484-2484-2
173B-33173B-33
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800800
1,0001,000
00 400400 800800 1,2001,200 1,6001,600
Time (days)Time (days)
Pre
ssu
re (p
sia)
Pre
ssu
re (p
sia)
Pressure vs Time for North Boundary Middle, Four Year Prediction
Pressure vs Time for North Boundary Middle, Four Year Prediction
Obs173b_psiaObs173b_psia
Obs Well7_psiaObs Well7_psia
Obs Well11_psiaObs Well11_psia
north of the fault: middle north boundary case with no additional injection
Pressure constraint = 960 psia, hydrostatic
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Well Optimization Well Optimization
Use MODOFC code
Initial design of injection disposal field
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Optimization ProblemOptimization Problem
Optimization is a general mathematical technique for finding the maximum or minimum value of a function subject to constraints.
To solve this problem we seek the point where the derivative equals zero.
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Optimization ProblemSetup
Optimization ProblemSetup
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Well Optimization Pressure Distribution and Particle Tracking Results
Well Optimization Pressure Distribution and Particle Tracking Results
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Summary and ConclusionsSummary and Conclusions
73,700 BWPD injection potential over 4 yrs, 3,700 BWDP additional, without exceeding pressure constraints.
Cost effective method to evaluate subsurface injection. Study completed for less cost than installation of one pressure observation well.
Quantify uncertainty and optimal well placement/injection rates.
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