Use of Streamline Flow Diagnostics for

Injection and Production Rate Allocation

Optimization

Shusei Tanaka

November, 2014

Background

2/19

• Determining optimal injection/production rates to maximize NPV is challenging

Heterogeneous geological reservoir

Reallocate well rate to sweep bypassed oil

• Rate reallocation algorithm needs to be fast and robust

Requires a number of simulations

Handle waterflood, EOR…

Improve NPV under multiple constraints

• Diagnose efficiency of the well

How much ‘Inj-1’ contributes to field NPV?

- Improve oil production rate

- Works only after breakthrough

SL-Based Flow Rate Allocation Optimization:

Previous Study

3/19

• Use of Well Allocation Factors (WAFs): [Thiele et. al, 2003]

Well Allocation Factor map [SPE84080]

[SPE113628]

- WAFs by offset oil production of well-pair

• Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009]

Norm Wt. - 0

Aft

er

2 y

ears

Aft

er

5 y

ears

Aft

er

10 y

ears

Base

Base Improved

Norm Wt. - 0

Aft

er

2 y

ears

Aft

er

5 y

ears

Aft

er

10 y

ears

Base

- Control well rate to have equivalent

‘breakthrough’ time

- Increase well rate of high WAFs

Decrease

Increase

Decrease

Decrease

Decrease

Increase

- Improves sweep efficiency- Works only before breakthrough

- Improve oil production rate

- Works only after breakthrough

SL-Based Flow Rate Allocation Optimization:

Previous Study

4/19

• Use of Well Allocation Factors (WAFs): [Thiele et. al, 2003]

Well Allocation Factor map [SPE84080]

[SPE113628]

- WAFs by offset oil production of well-pair

• Equalize arrival time of injection fluid: [Al-Hutali et. al, 2009]

Norm Wt. - 0

Aft

er

2 y

ears

Aft

er

5 y

ears

Aft

er

10 y

ears

Base

Base Improved

Norm Wt. - 0

Aft

er

2 y

ears

Aft

er

5 y

ears

Aft

er

10 y

ears

Base

- Control well rate to have equivalent

‘breakthrough’ time

- Increase well rate of high WAFs

Decrease

Increase

Decrease

Decrease

Decrease

Increase

- Improves sweep efficiency- Works only before breakthrough

• Fast

• Not robust

• Does not optimize NPV

Motivation and Objective

5/19

• Previous study of SL-based waterflood optimization does not optimize NPV and limited applicability

• Study objective:

Propose a new NPV-based flow diagnostics

Develop a streamline-based rate allocation method to optimize NPV

Apply model to Brugge benchmark case

Brugge field: multiple well and constraints [SPE 119094]

Streamlines

Proposed Optimization Method:

Overall Workflow

6/19

2. Trace Streamlines and Find connection map

3. Calculate NPV diagnostic plot

4. Reallocate flow rate of unconstrained well

via ‘efficiency’

1. Run simulation model

‘Value’ and ‘NPV’ of a Streamline

7/19

Injector

Producer

𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞𝑠𝑙

𝑛𝑜𝑑𝑒

𝑆𝑜𝑏𝑜𝑅𝑜 ∆𝜏

𝑁𝑃𝑉𝑠𝑙 = 𝑞𝑠𝑙

𝑛𝑜𝑑𝑒

𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉

𝑝𝑟𝑑

𝑛𝑜𝑑𝑒

∆𝜏 > 𝑡𝑟𝑠𝑚

Hydrocarbon value (Maximum possible revenue)

NPV along SL (Prospected revenue)

• Hydrocarbon value and NPV along Streamline from time T to reservoir life, trsm

𝑷𝑽 = න𝟎

𝒔

𝑨 𝝃 𝝓 𝝃 𝒅𝝃 = න𝟎

𝒔𝒒𝒔𝒍𝝓 𝒔

𝒖𝒕(𝒔)𝒅𝝃 = 𝒒𝒔𝒍න

𝟎

𝒔 𝝓 𝒔

𝒖𝒕(𝒔)𝒅𝝃

= 𝒒𝒔𝒍𝝉

𝜏 𝜉 0=𝑠 𝜙 𝑠

𝑢𝑡(𝑠)𝑑𝜉

Pore volume:

Time-of-Flight (TOF):

Pore volume × Saturation × FVF × Price

Discount rate Reservoir life

I1 I2 I3

I6

I5

I7 I8

NPV-based Efficiency of Streamline

P1 P2

P3 P4 P5

P6 P7

8/19

HCIP, integrate along SL

NPV, integrate along SL, only reservoir life time

𝐻𝐶𝐼𝑃𝑠𝑙 = 𝑞𝑠𝑙

𝑛𝑜𝑑𝑒

𝑆𝑜𝑏𝑜𝑅𝑜 ∆𝜏

𝑁𝑃𝑉𝑠𝑙 = 𝑞𝑠𝑙

𝑛𝑜𝑑𝑒

𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉

𝑝𝑟𝑑

𝑛𝑜𝑑𝑒

∆𝜏 > 𝑡𝑟𝑠𝑚

𝑒𝑠𝑙 =𝑁𝑃𝑉𝑠𝑙𝐻𝐶𝐼𝑃𝑠𝑙

• Efficiency of a SL

• Streamline efficiency by hydrocarbon value and NPV using economic values

I4

I1 I2 I3

I6

I5

I7 I8

NPV-based Efficiency of Well Pair

P1 P2

P3 P4 P5

P6 P7

9/19

𝑁𝑃𝑉𝑝𝑎𝑖𝑟 =

𝑠𝑙

𝑁𝑃𝑉𝑠𝑙

𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 =

𝑠𝑙

𝐻𝐶𝐼𝑃𝑠𝑙

• Well pair efficiency by hydrocarbon value and NPV

𝑒𝑝𝑎𝑖𝑟 =𝑁𝑃𝑉𝑝𝑎𝑖𝑟𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟 HCIP

NPVHCIP and NPV,

integrate by SL bundle

• Well pair efficiency

I4

NPV-Based Flow Diagnostics

10/19

I1 I2 I3

I6

I5

I7 I8

P1 P2

P3 P4 P5

P6 P7

𝑒𝑝𝑎𝑖𝑟

=𝑁𝑃𝑉𝑝𝑎𝑖𝑟

𝐻𝐶𝐼𝑃𝑝𝑎𝑖𝑟

5-connection from Inj-4 pairv

pairr

HCIP (Normalized)

NP

V (N

orm

aliz

ed)

𝑰𝟒𝐆𝐨𝐨𝐝

𝑷𝟒

𝑰𝟒𝐏𝐨𝐨𝐫

𝑷𝟕

NPV-based diagnostic plot

I4

(𝑁𝑃𝑉,𝐻𝐶𝐼𝑃 are normalized by field maximum 𝐻𝐶𝐼𝑃)

MCERIN

PV

(Norm

aliz

ed)

Streamline-based Rate Allocation:

A New Approach

𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤 = 𝑞𝑝𝑎𝑖𝑟

𝑜𝑙𝑑𝑒𝑝𝑎𝑖𝑟ҧ𝑒𝑓𝑖𝑒𝑙𝑑

𝑞𝑤𝑒𝑙𝑙 = 𝑟

𝑝𝑎𝑖𝑟

𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤

ത𝐞𝐟𝐢𝐞𝐥𝐝

decrease rate

Increase rate

Before update After update

Total value (Normalized)

11/19

MCERIN

PV

(Norm

aliz

ed)

Total value (Normalized)

Streamline-based Rate Allocation:

A New Approach

decrease rate

Increase rate

Before update After update

• Advantages:• Dynamically visualize efficiency of the injector and producer

• Able to propose ‘better’ well rate by post processing

12/19

𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤 = 𝑞𝑝𝑎𝑖𝑟

𝑜𝑙𝑑𝑒𝑝𝑎𝑖𝑟ҧ𝑒𝑓𝑖𝑒𝑙𝑑

𝑞𝑤𝑒𝑙𝑙 = 𝑟

𝑝𝑎𝑖𝑟

𝑞𝑝𝑎𝑖𝑟𝑛𝑒𝑤

ത𝐞𝐟𝐢𝐞𝐥𝐝

13/19

• 3 years of waterflood, 8 injectors and 7 producers• Constraint: Field water injection/production 2500 [rb/day], min/max BHP per well• Relative oil, water price = 1, -0.2 $/bbl, Discount rate = 10%• Compare developed model with 3 approaches:

• Uniform injection (Uniform), Well allocation factors (WAFs), Equalize Arrival Time (EqArrive), Developed model (SLNPV)

Permeability Field Initial Oil Saturation SLs by Uniform Injection

I1 I2 I3

I6

I5

I7 I8

P1 P2

P3 P4 P5

P6 P7

I4

Demonstration: 2D Multi-well Case

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

0 180 360 540 720 900 1080

Net

Pre

sen

t V

alu

e [

$]

Time [Days]

SLNPVEqArriveWAFsUniform

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

0 180 360 540 720 900 1080

Net

Pre

sen

t V

alu

e [

$]

Time [Days]

SLNPVEqArriveWAFsUniform

14/19

Recovery Factor Net Present Value

2D Multi-well: Recovery and NPV

SLNPV:

Maximum NPV at 2 years

2.5 times of uniform injection

0.0

0.1

0.2

0.3

0.4

0 180 360 540 720 900 1080

Re

cove

ry F

acto

r [-

]

Time [Days]

SLNPVEqArriveWAFsUniform

15/19

Result of Saturation Distribution:

Uniform Injection and SLNPV

SLNPVUniform injection

: at 0.5 yrs

Reduced injection

Increased injection

High water saturation

High oil saturation

NPV-Based Flow Diagnostics

2D Multiwell Example

16/19

𝑁𝑃𝑉𝑝𝑎𝑖𝑟 =

𝑠𝑙

𝑞𝑠𝑙

𝑛𝑜𝑑𝑒

𝑆𝑜𝑏𝑜𝑅𝑜 + 𝑆𝑤𝑏𝑤𝑅𝑤 ∆𝜏 ∙ 1 + 𝑑 −𝜏/365 ∉

𝑝𝑟𝑑

𝑛𝑜𝑑𝑒

∆𝜏 > 𝑡𝑟𝑠𝑚

InjectorP/I 1 2 3 4 5 6 7 8

1 96879 45170 0 38964 0 0 0 0

2 0 26458 25571 0 0 0 0 0

3 77264 0 0 49230 0 40210 0 0

4 0 54433 0 53080 0 0 0 0

5 0 66903 80531 0 78445 0 0 18356

6 0 0 0 19642 0 -4292 5050 0

7 0 0 0 4419 18840 0 -6175 -21328

Pro

du

cer

Predicted NPV, until end of the simulation

I1 I2 I3

I6

I5

I7 I8

P1 P2

P3 P4 P5

P6 P7

I4

17/19

Oil Saturation and Well Location

• Constraints:- Field water injection qt <= 20,000 bbl/d- Well flow rate qti <= 6000 bbl/d- Producer BHP > 100 psi, Injector BHP < 6000 psi

• Simulation Model:- Synthetic water flooding - 20 producers, 10 injectors- 20 years of simulation- Relative oil, water price = 1, -0.2 $/bbl

Brugge Benchmark Model

Streamlines by Sw

SLN

PV

Un

ifo

rm In

ject

ion

Streamlines by Injector

Example of SLs: After 10 Years

Not sweep aquifer region

Sweep aquifer region

Increased Inj-Prd

connection

18/19

0.00

0.04

0.08

0.12

0.16

0.20

0 1200 2400 3600 4800 6000 7200

Re

cove

ry F

acto

r [-

]

Time [Days]

SLNPVEqArriveWAFsUniform

0.E+00

5.E+06

1.E+07

2.E+07

2.E+07

3.E+07

3.E+07

4.E+07

0 1200 2400 3600 4800 6000 7200

Net

Pre

sen

t V

alu

e [

$]

Time [Days]

NPVEqArriveWAFsUniform

Recovery Factor Net Present Value

Recovery Factor and NPV

Injection Rate Production Rate

Updated Well Rate by SLNPV

0

1000

2000

3000

4000

5000

6000

7000

0 1200 2400 3600 4800 6000 7200

Pro

du

ctio

n R

ate

[b

bl/

day

]

Time [Days]

BR-P-1 BR-P-2BR-P-3 BR-P-4BR-P-5 BR-P-6BR-P-7 BR-P-8BR-P-9 BR-P-10BR-P-11 BR-P-12BR-P-13 BR-P-14BR-P-15 BR-P-16BR-P-17 BR-P-18BR-P-19 BR-P-20

0

1000

2000

3000

4000

5000

6000

7000

0 1200 2400 3600 4800 6000 7200

Inje

ctio

n R

ate

[b

bl/

day

]

Time [Days]

BR-I-1 BR-I-2BR-I-3 BR-I-4BR-I-5 BR-I-6BR-I-7 BR-I-8BR-I-9 BR-I-10

19/19

• Have developed a new SL-based rate allocation method to improve recovery considering NPV

• Proposed a new diagnostic plot to visualize the relative value and efficiency of a well in the asset

• Results in greater NPV compared to prior streamline-based rate allocation methods

• Can be applied to IOR/EOR simulation study with any commercial simulator by post processing

Conclusions

20/19