reservoir characterization from production and injection ... · reservoir characterization from...

Reservoir Characterization From Production and Injection Fluctuations

Larry W. LakeThe University of Texas at Austin

[email protected]

Outline

• Introduction• The Model• Applications of the Model

– Synthetic Fields (Synfields)

– Field Applications• Uses of the Model• Validation

Prior and Current Work

• Belkis Refunjol

• Jorge S’Antana Pizarro

(Petrobras)

• Isolda Griffiths (Shell)

• Alejandro Albertoni (Nexen)

• Pablo Gentil (ENI)

• Ali Al-Yousif (Aramco)

• Danial Kaviani (TAMU)

• Thang Bui (TAMU)• Xming Liang

• Morteza Sayarpour (Chevron)

• Sami Kaswas (Exxon)

• Tom Edgar, ChE

• Leon Lasdon, IROM

• Jerry Jensen (U.Calgary)• Alireza Mollaei, PGE• Ahn Phoung Nguyen, ChE• Fei Cao, PGE• Jacob McGregor, PGE• Jong Suk Kim, ChE• Wenle Wang, PGE

PastPresent

What others say about modeling…

• Bratvold and Bickel…Two types– Verisimilitude- the appearance of reality– Cogent- enables decisions

• Haldorsen….the progress of ideas– Youth= simple, naïve– Adolescence=complex, naïve– Middle age=complex, sophisticated– Maturity= simple, sophisticated

Hypothesis

• Characteristics of a reservoir can be inferred from analyzing production and injection data only

Boundary Conditions

• Must be injection project

• Rates are most abundant data type

• Rates must vary

• No geologic model required

• Everything done in a spreadsheet

Outline




q(t) = q(t0)e−(

t− t0τ

)+ I(t) 1− e

−(t− t0τ

)⎛

⎝

⎜⎜

⎞

⎠

⎟⎟− ctVp( ) pwf,t − pwf,0

t − t0

⎡

⎣⎢⎢

⎤

⎦⎥⎥

1− e−(

t− t0τ

)⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

CRM Continuity Equation

ctVpdpdt

= i(t) − q(t)

dq(t)dt

+1τ

q(t) = 1τ

i(t) − Jdpwf

dt

τ =ctVp

J

Ordinary Differential Equation:

Continuity:

Solution:

q(t)i(t)

BHPInjectionPrimary

q(t) = J p − pwf( )Production Rate:

Signal Response

Production response to an injection signal

Connectivity

τij = 1 dayfij = 0%

Connectivity

τij = 1 dayfij = 100%

Connectivity

τij = 6 daysfij = 100%

Connectivity

τij = 6 daysfij = 65%

Capacitance-Resistance Model (CRMT)

( ) k

tt

kk Ieeqq ⎟⎠⎞⎜

⎝⎛ −+=

Δ−Δ−−

ττ 11

τ

q(t)I(t) JVc pt=τ

Time constant

f2j

f6j

f4j

f3j

f5j

jτf1j

f11f12

f13

I6

I1I2

I3

I4I5

qj(t)

Capacitance-Resistance Model (CRMP)

( ) ik

n

iij

tt

kjjk Ifeeqqi

jj ∑=

Δ−Δ−

− ⎟⎠

⎞⎜⎝

⎛ −+=1

1 1 ττ

j

ptj J

Vc⎟⎟⎠

⎞⎜⎜⎝

⎛=τ

11

≤∑=

pn

jijf

Time constant

Inter-well connectivity or gain

Drainage volume around a producer

Capacitance-Resistance Model (CRMIP)

Ii(t)

qj(t)

fij

τij

ij

ptij J

Vc⎟⎟⎠

⎞⎜⎜⎝

⎛=τ

11

≤∑=

pn

jijf

Time constant

Inter-well connectivity or gain

( )∑=

Δ−Δ−

− ⎥⎦

⎤⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛ −+=i

ijijn

iikij

tt

kijjk Ifeeqq1

1 1 ττ

Steady-State Connectivity Map

0

0

0

0

0

0 20 40 60 80 100

ProducerWater InjectorCarbon Dioxide Injector 0 1,000 ft

Better CO2 Performance

Interwell ConnectivityTwo Equally Viable Solutions

Transient Interwell Connectivity After 10 days

Transient Interwell Connectivity After 2 years

Transient Interwell Connectivity After 4 years

Transient Interwell Connectivity 4 years <<

Gains >0.5

Mature West Texas Waterflood

Injector

Producer

Gains > 0.5

Gains >0.4


Injector

Producer

Gains >0.3


Gains > 0.3Injector

Producer

Gains >0.2

Mature West Texas WaterfloodGains > 0.2

Injector

Producer

Mature West Texas WaterfloodR-squared

Producer Number

Time Constants

Reservoir A

Producer 184 – Good Fit

R2 = 0.961

err = 0.146Bbl/day

Month

Producer 127 – Good Fit

R2 = 0.696

err = 0.037

outliers

Bbl/day

Month

Producer 74 – Poor Fit

R2 = -1.03

err = 0.143

Bbl/day

Month

Producer 201 – Poor Fit

R2 = 0.793

err = 6.58Bbl/day

Month

CRM: Oil Fractional-Flow Model

fo(t) =qo

qo + qw=

11+ WOR(t)

qo(t) = fo(t)q(t)

fo(t) = 1

1+ a CWI(t)( )b

log 1fo(t)

− 1⎛

⎝⎜⎞

⎠⎟= loga + blog CWI(t)( )

Outline




Future Injection

• Historic Period – 131 Active Injectors• Prediction Period – 97 Active Injectors• Injection has been concentrated in fewer wells (37

injectors shut-in)• 27.3% of historic field injection from injectors shut-

in throughout prediction period

Optimal Injection and Predicted Oil Production for the Field

0 20 40 60 80 100 120 140 160 180 2002

3

4

5

6x 10

4

Month

bbl/d

ay

HistoricOptimal

0 20 40 60 80 100 120 140 160 180 200500

1000

1500

2000

2500

3000

Month

bbl/d

ay

Historic Oil ProductionPredicted Oil ProductionExtrapolated Oil Production

Injection Shares

Injector Number

Percent of Total

Production Shares

P112 P195

Producer Number

Percent of Total

Gardner Hype Curve

The Gardner Group40Jim Honefenger (P.E. Moseley & Associates, Inc.)

Outline




Validation

Just how do we scientifically validategeoscience hypotheses?

Remember:

Characteristics of a reservoir can be inferred from analyzing production and injection data

only

Recognizing testable hypotheses can be subtle and requires practice. To do it, ask “how would one test this

hypothesis”.

– If the duck is lighter than this woman, then she is a witch.

Synfield Cases

• Heterogeneity• Large compressibility• Fractures• Barriers• Anisotropy• Partial completions• Large shut in times• Changing BHP• All agree with imposed geology

Validation

Field Injectant Independent Data AgreeWith Data

Synfields Water Simulation Very well

Characteristics of a reservoir can be inferred from analyzing production and injection data only

Retrodiction

Validation



Synfields Water Retrodiction Very well


Chihuido Field

• Good correlation• Inferred faults are in yellow•Gains and time constants reproduce known geological features

Validation




Chuido Water Faults from seismic Reasonably


SWCF Flow Capacity

75167519

7523

7524

From Al-Yousef (2006)

Homogeneous

Validation





SWCFU Water Anecdotal fractures Reasonably


North Sea Field II

Validation






NSF II Water Structure Well


North Buck Draw Comparison

• CM τ correlates with tracer breakthrough time

0

5

10

15

20

300 5 10 15 20 25 35Tracer Breakthrough Time (months)

Spea

rman

or C

M T

ime

(mon

ths)

SpearmanCMLinear (CM)

Validation



Snyfields Water Retrodiction Very well



NSF II Water Structure Well

NBDU Gas Tracer data Fairly well


Williston Basin Field

Validation



Snyfields Water Retrodiction Very well



NSF I Water Structure Well

NBDU Gas Tracer data Fairly well

Will. Basin Water Acoustic impedance Reasonably


Future Work• Working spreadsheet

– Couple to GAMS– Excel vs. MATLAB– Multiplotting (visualization)

• Integrate with DA/VOI approaches• Propagating error/uncertainty• More validation (oil in tank)• Extend to primary recovery• Fluid allocation studies (conformance)• Optimize to produce more oil• Add EOR model(s)

Remove outliers

Maximize NPV of future oil recovery

Warm start Gainfit

Removeinactive wells

Remove gainsbased on distance

Remove smallgains

Gainfit #2 Calculate residualsand replace outliers Gainfit #3

Gainfit #1

Fracfit #1 Calculate residualsand remove outliers Fracfit #2

Reservoir model

Model Fit and Prediction Algorithm

~2.5 hrs computation

time

Remove outliers


Warm start Gainfit



Remove smallgains


Gainfit #1


Reservoir model


<1 min computation

time

Remove outliers


Warm start Gainfit



Remove smallgains


Gainfit #1


Reservoir model


<10 min computation

time

Appraisal and Conceptual

AnalysisGATE GATEEvaluate

Alternatives GATE

Define Selected

AlternativeGATEExecute Operate

Inevitable Dis-

appointment

Portfolio Optimization

Uncertainty Updating

Concept Selection & Development Optimization

Real Options

Portfolio Management and Project Selection

Addressing Risks Throughout the E&P Asset Lifecycle

VOI; Impact of Estimates & Methods

Financial Risk Management

Cost and Schedule Estimating; Execution Risk Management

HSE Risk Management

Real-Time Optimization and Risk Management

Valuing Price Forecasts

Capital Allocation w/

Uncertain Arrivals

FUTURE:Life Cycle

Assessments

Contracting Strategies

(lump sum v cost plus?)

MPD & Blowouts;

Drlg Safety; Offshore

Spills

Simple Model Development

Gain MapInjector

Producer

P210

I 58

P103

Producer 210 (large distance)

093.0882.0R 2

==

err

Bbl/day

Producer 103 (skipped over)

110.0635.0R 2

==

errBbl/day

Injector Number

Lost Injection

1− fij

j=1

Np∑

CRM Fit – Total Field

R2 = 0.956Bbl/day

Month

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