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

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.

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

Model DevelopmentModel Development

Data set

Geology model

Mock-up to FDM model

Map with Well Data Map with Well Data

3D Geology Block Model3D Geology Block Model

Numerical Model SetupNumerical Model Setup

Aerial extent and boundaries

Lateral and vertical discretization

Numerical Model Grid on the Base mapNumerical Model Grid on the Base map

No flow

No flow

Constant heads

Flow direction

Specified flux

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

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

Model Predicted Sand #2 Pressure Distribution for North Boundary Middle

Model Predicted Sand #2 Pressure Distribution for North Boundary Middle

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

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

Well Optimization Well Optimization

Use MODOFC code

Initial design of injection disposal field

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.

Optimization ProblemSetup

Optimization ProblemSetup

Well Optimization Pressure Distribution and Particle Tracking Results

Well Optimization Pressure Distribution and Particle Tracking Results

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.