Gas-Lift Optimization in Satellite Wells...OptIntro 1/31 Gas-Lift Optimization in Satellite Wells Eduardo Camponogara Department of Automation and Systems Engineering Federal University

OptIntro 1 / 31

Gas-Lift Optimization in Satellite Wells

Eduardo Camponogara

Department of Automation and Systems EngineeringFederal University of Santa Catarina

October 2016

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Summary

Motivation

Problem Formulation

Santos Multi-Reservoir Production System

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Motivation

Summary

Motivation

Problem Formulation


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Motivation

Motivation: production from mature fields

Young oil field

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Motivation


Mature oil field (without artificial lifting)

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Motivation


Mature oil field (with artificial lifting)

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Motivation


Gas-lift system

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Motivation


60% of Brazilian oil fields are gas-lifted

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Problem Formulation

Summary

Motivation

Problem Formulation


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Problem Formulation

Practical Application

Petrobras bundled:

I An in-house well simulator (Marlim)

I Algebraic Modeling Languages (GAMS and AMPL)

I Optimization solvers (CPLEX, Gurobi, and CBC)

in a software package denominated BR-SIOP. It is available in Infogridplatform to run on a computer cluster.

Remarks:

I The baseline version of BR-SIOP optimizes daily production ofplatforms that operate with gas-lifted satellite wells.

I It is the most common configuration in Campos Basin.

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Problem Formulation

Practical Application

Petrobras bundled:

I An in-house well simulator (Marlim)

I Algebraic Modeling Languages (GAMS and AMPL)

I Optimization solvers (CPLEX, Gurobi, and CBC)

in a software package denominated BR-SIOP. It is available in Infogridplatform to run on a computer cluster.

Remarks:

I The baseline version of BR-SIOP optimizes daily production ofplatforms that operate with gas-lifted satellite wells.

I It is the most common configuration in Campos Basin.

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Problem Formulation

BR-SIOP GLC

I Mathematical model for gas-lift optimization of satellite wells inoffshore operations.

I Model implemented in BR-SIOP, Petrobras.

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Problem Formulation

FPSO Cidade de Santos

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Problem Formulation

FPSO Cidade de Santos

FPSO Santos produces from two reservoirs, Tambau and Urugua.

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Problem Formulation

Sets

I N : set of production wells.

I P iwh: breakpoints for well-head pressure of well i .

I Qigl: breakpoints for gas-lift injection rate of well well i .

I Ri : breakpoint pairs considering well-head pressure and lift-gas rate forwell i , P i

wh ×Qigl, including naturally flowing conditions.

I Ri+: breakpoint pairs not considering naturally flowing conditions,P i

wh × {Q igl \ {0}}.

I Ri0: breakpoint pairs considering only zero gas-lift injection rate,P i

wh × {0}.

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Problem Formulation

Sets







wh × {Q igl \ {0}}.


wh × {0}.

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Problem Formulation

Sets







wh × {Q igl \ {0}}.


wh × {0}.

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Problem Formulation

Sets







wh × {Q igl \ {0}}.


wh × {0}.

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Problem Formulation

Sets







wh × {Q igl \ {0}}.


wh × {0}.

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Problem Formulation

Parameters

I q̂ io(whpi , qigl): oil rate from well i , at well-head pressure whpi and

lift-gas injection qigl.

I gor i : gas-oil ration for well i .

I wcut i : water cut.

I qigl,min: minimum lift-gas injection rate.

I qigl,max: maximum lift-gas injection rate.

I whpimin: minimum pressure.

I whpimax: maximum pressure.

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Problem Formulation

Parameters









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Problem Formulation

Parameters









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Problem Formulation

Parameters









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Problem Formulation

Parameters

I ql,max: Liquid handling capacity of the platform.

I qw,max: Water handling capacity of the platform.

I qflare,max: Limit for gas flaring.

I qflare,min: Minimum rate for gas flaring.

I qgtc: Gas compression capacity.

I qturbine: Gas demand for electric turbine.

I qmaxexp : Maximum rate for gas exportation.

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Problem Formulation

Parameters








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Problem Formulation

Parameters








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Problem Formulation

Parameters

I (t ilb and t iub) are two parameters that impose conditions on welloperations:

I (0, 0) forces well i to be closed during the optimization process.I (0, 1) allows the optimization algorithm to decide whether to

operate well i or not.I (1, 1) forces well i to be producing.I (1, 0) not a viable setting.

I enablei allows well i to operate without gas-lift injection, naturallyflowing production.

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Problem Formulation

Parameters





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Problem Formulation

Parameters





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Problem Formulation

Variables

Platform Variables:

I qgas−prod: total gas produced.

I qgas−lift: total gas allocated for injection.

I qexp: total gas exported.

I qflare: total gas flared.

Well i ’s Variables:

I qio: oil production rate from well i .

I qig: gas production rate from well i .

I qiw: water produced from well i .

I qigl: lift-gas injected.

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Problem Formulation

Variables

Platform Variables:

I qgas−prod: total gas produced.

I qgas−lift: total gas allocated for injection.

I qexp: total gas exported.

I qflare: total gas flared.

Well i ’s Variables:

I qio: oil production rate from well i .

I qig: gas production rate from well i .

I qiw: water produced from well i .

I qigl: lift-gas injected.

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Problem Formulation

Variables

I whpi : well i ’s head pressure.

I t i : well activation, 1 if well is active, 0 otherwise.

I t igl: glc operation, 1 if gas is injected, 0 otherwise.

I t isurg: assumes value 1 if well is naturally flowing, 0 if operated withlift-gas injection.

I κiq: auxiliary SOS2 variable.

I κip: auxiliary SOS2 variable.

I µip,q: weighting variable for piecewise-linear approximation.

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Problem Formulation

Variables








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Problem Formulation

Variables








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Problem Formulation

Problem Formulation

Cascading objectives:

1. f1 = max∑i∈N

qio: oil production maximization.

2. f2 = min qflare: gas flare minimization.

3. f3 = min∑i∈N

qigl: gas-lift injection minimization.

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Problem Formulation

Problem Formulation


1. f1 = max∑i∈N



3. f3 = min∑i∈N


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Problem Formulation

Problem Formulation


1. f1 = max∑i∈N



3. f3 = min∑i∈N


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Problem Formulation

Platform Constraints

Platform constraints:

I qgas−prod =∑

i∈N qig

I qgas−lift =∑

i∈N qigl

I qexp = qgas−prod − qflare − qturbine

I qgas−prod + qgas−lift − qflare ≤ qgtc

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Problem Formulation



I qgas−prod =∑

i∈N qig

I qgas−lift =∑

i∈N qigl



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Problem Formulation



I qgas−prod =∑

i∈N qig

I qgas−lift =∑

i∈N qigl



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Problem Formulation



I qgas−prod =∑

i∈N qig

I qgas−lift =∑

i∈N qigl



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Problem Formulation



I qexp ≤ qmaxexp

I qflare,min ≤ qflare ≤ qflare,max

I∑

i∈N(qio + qiw

)≤ ql,max

I∑

i∈N qiw ≤ qw,max

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Problem Formulation



I qexp ≤ qmaxexp


I∑

i∈N(qio + qiw

)≤ ql,max

I∑


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Problem Formulation



I qexp ≤ qmaxexp


I∑

i∈N(qio + qiw

)≤ ql,max

I∑


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Problem Formulation



I qexp ≤ qmaxexp


I∑

i∈N(qio + qiw

)≤ ql,max

I∑


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Problem Formulation

Well ConstraintsConstraints on each well i ∈ N :

qio =

∑(p,q)∈Ri

+

µip,q · q̂ i

o(p, q) +∑

(p,q)∈Ri0

µip,q · q̂ i

o(p, q)

qig = rgo i · qi

o

qiw =

bsw i

1− bsw i· qi

o

whpi =∑

(p,q)∈Ri+

µip,q · p +

∑(p,q)∈Ri

0

µip,q · p

qigl =

∑(p,q)∈Ri

+

µip,q · q

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Problem Formulation


qio =

∑(p,q)∈Ri

+

µip,q · q̂ i

o(p, q) +∑

(p,q)∈Ri0

µip,q · q̂ i

o(p, q)

qig = rgo i · qi

o

qiw =

bsw i

1− bsw i· qi

o

whpi =∑

(p,q)∈Ri+

µip,q · p +

∑(p,q)∈Ri

0

µip,q · p

qigl =

∑(p,q)∈Ri

+

µip,q · q

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Problem Formulation


qio =

∑(p,q)∈Ri

+

µip,q · q̂ i

o(p, q) +∑

(p,q)∈Ri0

µip,q · q̂ i

o(p, q)

qig = rgo i · qi

o

qiw =

bsw i

1− bsw i· qi

o

whpi =∑

(p,q)∈Ri+

µip,q · p +

∑(p,q)∈Ri

0

µip,q · p

qigl =

∑(p,q)∈Ri

+

µip,q · q

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Problem Formulation


qio =

∑(p,q)∈Ri

+

µip,q · q̂ i

o(p, q) +∑

(p,q)∈Ri0

µip,q · q̂ i

o(p, q)

qig = rgo i · qi

o

qiw =

bsw i

1− bsw i· qi

o

whpi =∑

(p,q)∈Ri+

µip,q · p +

∑(p,q)∈Ri

0

µip,q · p

qigl =

∑(p,q)∈Ri

+

µip,q · q

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Problem Formulation


qio =

∑(p,q)∈Ri

+

µip,q · q̂ i

o(p, q) +∑

(p,q)∈Ri0

µip,q · q̂ i

o(p, q)

qig = rgo i · qi

o

qiw =

bsw i

1− bsw i· qi

o

whpi =∑

(p,q)∈Ri+

µip,q · p +

∑(p,q)∈Ri

0

µip,q · p

qigl =

∑(p,q)∈Ri

+

µip,q · q

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Problem Formulation


t igl · qigl,min ≤ qi

gl ≤ qigl,max · t igl

t i · whpimin ≤ whpi ≤ whpi

max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg

t i = t igl + t isurg

t ilb ≤ t i ≤ t iub

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Problem Formulation





max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg



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Problem Formulation





max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg



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Problem Formulation





max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg



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Problem Formulation





max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg



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Problem Formulation





max · t i

∑(p,q)∈Ri

+

µip,q = t igl

∑(p,q)∈Ri

0

µip,q = t isurg



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Problem Formulation

SOS2 Constraints

To impose the piecewise-linear approximation of the production functions, foreach well i ∈ N :

κip =

∑q∈Qi

gl\{0}

µip,q, ∀p ∈ P i

wh

κiq =

∑p∈P i

wh

µip,q, ∀q ∈ Qi

gl \ {0}

and

(µip,q)(p,q)∈R i

0, (κi

p)p∈P iwh

and (κiq)q∈Qi

gl\{0} are SOS2

and

enablei ≤ t isurg

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Problem Formulation

SOS2 Constraints


κip =

∑q∈Qi

gl\{0}


wh

κiq =

∑p∈P i

wh

µip,q, ∀q ∈ Qi

gl \ {0}

and

(µip,q)(p,q)∈R i

0, (κi

p)p∈P iwh

and (κiq)q∈Qi

gl\{0} are SOS2

and

enablei ≤ t isurg

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Problem Formulation

SOS2 Constraints


κip =

∑q∈Qi

gl\{0}


wh

κiq =

∑p∈P i

wh

µip,q, ∀q ∈ Qi

gl \ {0}

and

(µip,q)(p,q)∈R i

0, (κi

p)p∈P iwh

and (κiq)q∈Qi

gl\{0} are SOS2

and

enablei ≤ t isurg

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Summary

Motivation

Problem Formulation


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Santos Basin

Santos Basin is a very large, multi-reservoir oil field.

Features:

I 300 Km off the coast.

I Several reservoirs: Gas,Post-Salt, and Pre-Salt.

I 5 operational FPSOs,27 to be commissioned.

I Shared drainage andprocessing facilities.

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Santos Basin: Production System

MEXILHAO

GAS

GAS

FPSO ANGRA

GAS

OIL

OIL

GAS

PIPELINE

FPSO SANTOS

OIL

OIL

ONSHORE

TERMINAL

OFFSHORE SANTOS BASIN

SAO PAULO

PARATY

I Several production units sharing resources, facilities and goals.

I High content of CO2 in gas produced from Pre-Salt reservoirs.

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Challenges:

I Several production unitssharing resources, facilitiesand goals.

I Dynamically evolvingproduction infrastructure.

=⇒

Needs for ProductionOptimization:

I General models forproduction units.

I Models of shared resources.

I Coordination of productionand control.

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Challenges:

I Several production unitssharing resources, facilitiesand goals.

I Dynamically evolvingproduction infrastructure.

=⇒

Needs for ProductionOptimization:

I General models forproduction units.

I Models of shared resources.

I Coordination of productionand control.

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Santos Basin: Future Production System

MEXILHAO

FPSO

GAS

FPSO ANGRA

GASGAS

OIL

OIL

FPSO

GAS

PIPELINE

FPSO SANTOS

30 FPSOs

��

��

ONSHORE

TERMINAL

OFFSHORE SANTOS BASIN

NEW TERMINAL

I New subsea gas pipeline.

I 27 FPSOs to be commissioned.

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Gas-Lift Optimization in Satellite Wells

I End!

I Thank you for your attention.

Gas-Lift Optimization in Satellite Wells...OptIntro 1/31 Gas-Lift Optimization in Satellite Wells Eduardo Camponogara Department of Automation and Systems Engineering Federal University

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