ANNUAL MEETING MASTER OF PETROLEUM ENGINEERING

Gonçalo Soares de Oliveira

goncalo@cepetro.unicamp.br

Integration of Geostatistical

Modeling with History Matching Global and Regional Perturbation

Case of Study

• Synthetic reservoir obtained form real well tests

• Campos Basin, Campo de Namorado

• Turbiditic reservoir

• Complex case of study :

– 25 wells

• 14 Production wells

• 11 Injector wells

• 11 years of history data

Faceis

Porosity

Global Method Regional Method

(...)

1 2 3 N

Best image

from iteration

(Secondary

image)

Collocated Cokriging

with different

correlation

coefficients; [0;1]

c=0.1 c=0.2 c=0.8

1 2 3 N

c=0.9

(...)

N 3 1 2

(...)

1 2 3 N

Regions Parameterization Selection of the best image for

each region (Secondary Image)

Collocated

Cokriging

(...)

Objective

Objective

Quality Control

TOP BASE HISTOGRAM

Once more, the values with null porosity are larger than

well tests. Which suggests that a treatment to porous

volume could me done

Quality Control

Variogram

Horizontal

(>R)

Horizontal

(<R)

Vertical

ANNUAL MEETING MASTER OF PETROLEUM ENGINEERING

Global Method GRFS

Vs.

Regional Method

Evolution of FO value

181

165

188

150

170

190

210

230

250

270

290

310

330

350

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteration

Evolution of FO

Regional Method 2

Global Method GRFS

IterationGlobal

Method GRFSRegional Method 2

1 328 328

2 290 257

3 229 194

4 225 181

5 215 172

6 216 176

7 188 180

8 208 176

9 217 170

10 230 179

11 169

12 165

13 168

Regional Method 2 gives better results in convergence speed and minimum obtained

-100

-80

-60

-40

-20

0

20

40

60

Função Objetivo - Vazão de Óleo (Qo)NA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

Oil Production Rate

-100

-80

-60

-40

-20

0

20

40

60

Função Objetivo - Vazão de Óleo (Qo)NA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

-100

-80

-60

-40

-20

0

20

40

60

Função Objetivo - Vazão de Óleo (Qo)NA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

1st Iteration

Regional

Best

Match

Global

Best

Match

Objective Function – Oil Rate (Qo)

Objective Function – Oil Rate (Qo)

Objective Function – Oil Rate (Qo)

𝐹𝑂 = 𝑃𝑎ℎ𝑖𝑠𝑡 − 𝑃𝑎

2

𝑃𝑎ℎ𝑖𝑠𝑡 ∗ 𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝐸𝑟𝑟𝑜𝑟 + 𝐶𝑒𝑃𝑎2

𝑛

𝑡=1

𝑛

𝑃𝑎=1

25

𝑃𝑜=1

Margin of Error = 10%

Po – Well (1 a 25)

Pa – Parameters (Qo, Qw, Qi, Pw)

T – time of history data

Ce – Constant to sum to the allowed

error

Water Production Rate

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

Função Objetivo - Vazão de Água (Qw)NA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

Função Objetivo - QwNA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

Função Objetivo - QwNA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

1st Iteration

Regional Best Match

Global Best Match

Objective Function – Water Rate (Qw)

Objective Function – Water Rate (Qw)

Objective Function – Water Rate (Qw)

Production Well Pressure

-30

-20

-10

0

10

20

30

40

50

60

70

Função Objetivo - Pressão (Pw)NA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

-30

-20

-10

0

10

20

30

40

50

60

70

Função Objetivo - PwNA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

-30

-20

-10

0

10

20

30

40

50

60

70

Função Objetivo - PwNA1A

NA2

NA3D

PROD005

PROD008

PROD009

PROD010

PROD012

PROD014

PROD021

PROD23A

PROD24A

PROD25A

RJS19

1st Iteration

Objective Function –Pressure (Pw)

Objective Function –Pressure (Pw)

Objective Function –Pressure (Pw)

Regional Best Match

Global Best Match

Water Injection Rate

-10

0

10

20

30

40

50

60

70

80

90

Função Objetivo - Taxa de Injeção de Água (Qi)INJ003

INJ005

INJ006

INJ007

INJ010

INJ015

INJ017

INJ019

INJ021

INJ022

INJ023

-10

0

10

20

30

40

50

60

70

80

90

Função Objetivo - QiINJ003

INJ005

INJ006

INJ007

INJ010

INJ015

INJ017

INJ019

INJ021

INJ022

INJ023

-10

0

10

20

30

40

50

60

70

80

90

Função Objetivo - QiINJ003

INJ005

INJ006

INJ007

INJ010

INJ015

INJ017

INJ019

INJ021

INJ022

INJ023

1st Iteration

Objective Function –Water Injection (Qi)

Objective Function –Water Injection (Qi)

Objective Function –Water Injection (Qi)

Regional Best Match

Global Best Match

ANNUAL MEETING MASTER OF PETROLEUM ENGINEERING

Evolution of Regional FO

Prod009

Global

Regional

-8,00

-6,00

-4,00

-2,00

0,00

2,00

4,00

6,00

8,00

10,00

12,00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional FO

Iteration

Oil Rate

Water Rate

Pressure

Regional FO

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional FO

Iteration

Oil Rate

Water Rate

Pressure

Regional FO

OF

OF

OF

OF

Global

Regional

Prod021

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional FO

Iteration

Oil Rate

Water Rate

Pressure

Regional

FO

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

40.00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional OF

Iteration

Oil Rate

Water Rate

Pressure

Regional

FO

OF

OF

OF

OF

OF

Global

Regional

Prod23A

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional OF

Iteration

Oil Rate

Water Rate

Pressure

Regional OF

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional FO

Iteration

Oil Rate

Water Rate

Pressure

Regional OF

OF

OF

Global

Regional

Prod24A

-20,00

-10,00

0,00

10,00

20,00

30,00

40,00

50,00

60,00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional OF

Iteration

Oil Rate

Water Rate

Pressure

Regional

OF

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

1 2 3 4 5 6 7 8 9 10 11 12 13

FO

Iteração

Evolução do valor de FO regional

Vazão de Óleo

Vazão de Água

Pressão

FO Região

Evolution of Regional OF

Iteration

Oil Rate

Water Rate

Pressure

Regional

OF

OF

OF

• Integration of geostatistical modelling with history matching is

an important process to optimize the reservoir model

• Regional Perturbation honours well data, histogram and

continuity

• Methodology applied is applicable in any realistic case. A

parameterization for complex geology may be necessary

• Regional Method has a convergence speed twice as fast as

Global Method

• Optimization using regional perturbation guarantees that the

minimum obtained for each region stabilizes through the

iterations

Conclusions