Optimization of lift gas allocation in a gas lifted oil field

as non-linear optimization problem

Authors:• Roshan Sharma (Høgskolen i Telemark)• Kjetil Fjalestad (Statoil research center)• Bjørn Glemmestad (Høgskolen i Telemark)

1

Main Contents• Description about the Norne oil field

• Problem descriptiono Why optimization is necessary?o Increased Profit!

• How to do optimization?o Non-linear optimization problem (general method)o Hill Climbing method (Industrial friendly)

• Discussion on simulation results

• One time steady state optimization enough?

• Conclusion.2

Schematic of Norne Oil Field in North Sea

Gas Distribution pipeline

Crude Oil gathering pipeline

3

Why optimization of gas distribution is necessary?

• If oil wells were identical: distribute gas equally

• However, PI (Productivity index) are different for five oil wells.

푤 = 푓(푤 , … )

PI4 > PI1 > PI2 > PI3 >PI5

4

• First principles modeling• Each well with 4

states

Why optimization of gas distribution is necessary?Gas Lift Performance curve

• Oil production as a function of gas injection• Distribute gas in an optimal way which leads to MAXIMUM

total oil production.5

How to perform optimization?

• Non-linear optimization problem.

• Hill climbing method.

Two methods:

Control part:• Maintain pressure in gas distribution

manifold to 200 bar.

• Manipulate the flow rates through injection valves.

Optimization hierarchy

Cascade control structure6

Non-linear optimization problem• Formulation of objective function

풇 풘품풂풊 =

푷푰풊풎풂풙 푷풓풊 − 푷풄 +

풘품풂풊 × ퟑퟔퟎퟎ

푵ퟔ푪풗 풖ퟏ풊 풀ퟏ풊

ퟐ

흆품풑−흆품풂풊 품푳풂풗풍

풊

ퟏퟎퟓ +

풘품풊풏풋풊 × ퟑퟔퟎퟎ푲풊풀ퟐ풊

ퟐ

흆품풂풊−흆풐품푳풓풗풍

풊 ,ퟏퟎퟓ ,ퟎ

ퟑퟔퟎퟎ

ퟓ

풊 ퟏ

풌품풔풆풄

Subject to linear equality constraint

풘품풂풊

ퟓ

풊 ퟏ

= 풘품풄

and the boundsퟎ.ퟑퟐퟑ ≤ 풘품풂

풊 ≤ ퟏퟏ.ퟔퟔ풌품풔풆풄

• Solver: ‘fmincon’ from MATLAB optimization toolbox

Maximize:

7

Simulation results

40 50 60 80 100 120

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

time[hr]

gas

flow

rate

into

ann

ulus

wga

[kg/

sec]

gas flow rate into annulus

well 1well 2well 3well 4well 5

40 60 80 100 120

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

time[hr]

gas

flow

rate

into

ann

ulus

wga

[kg/

sec]

gas flow rate into annulus

well 1well 2well 3well 4well 5

Without optimization

With optimization turned ‘ON’ at t = 50 hours

4.2% increase

8

How often to perform optimization?

• One time optimization is sufficient if:• We only consider the total gas supply as input disturbance• and with cascade control structure operated in parallel.

• Further investigation necessary if other sources are taken as disturbance to the system.

9

Hill Climbing method• Gas flow rates changed manually in smaller steps

iteratively.o Industrial friendly method

10

Simulation results for hill climbing

40 60 80 100 120

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

time[hr]

gas

flow

rate

into

ann

ulus

wga

[kg/

sec]

gas flow rate into annulus

well 1well 2well 3well 4well 5

Without optimization

With optimization turned ‘ON’ at t = 60 hours

4.5% increase

40 60 80 100 120 140

0.8

1

1.2

1.4

1.6

1.8

2

2.2

time[hr]

gas

flow

rate

into

ann

ulus

wga

[kg/

sec]

gas flow rate into annulus

well 1well 2well 3well 4well 5

11

Comparison and Conclusion

• Hill climbing does not require mathematical modelo Free from modeling errors

• Normal operation has to be disrupted for performing tests using hill climbing.

• If good model is available, general non-linear optimization method can equally provide good results.

Comparison

Conclusion• Total oil production was increased by about 4.2 %• Both methods of optimization show successful results.

12

Thank You

13