Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model...

99
Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin [email protected]

Transcript of Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model...

Page 1: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Capacitance Resistance Model Update

Larry W. Lake

The University of Texas at Austin

[email protected]

Page 2: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Outline

• Introduction

• The Model

• Validation

• Updates of Technology

Page 3: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Prior and Current Work

• Belkis Refunjol

• Jorge S’Antana Pizarro (Petrobros)

• Isolda Griffiths (Shell)

• Alejandro Albertoni (Nytec)

• Pablo Gentil (Galp)

• Ali Al-Yousif (Aramco)

• Danial Kaviani (TAMU)

• Thang Bui (TAMU)

• Xming Liang

• Morteza Sayarpour (Chevron)

• Sami Kaswas (ExxonMobil)

• Daniel Weber (Shell)

• Tom Edgar, ChE

• Leon Lasdon, IROM

• Tad Patzek, PGE

• Alireza Mollaei, PGE

• Anh Phoung Nguyen, ChE

• Fei Cao, PGE

• Wenle Wang, PGE

• Jong Suk Kim, ChE

Past Present

Page 4: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

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

Page 5: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Hypothesis

• Characteristics of a reservoir can be

inferred from analyzing production

and injection data only

Page 6: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Boundary Conditions

• Must be injection project

• Rates are most abundant data type

• Rates must vary

• No geologic model required

• Input, output in a spreadsheet

Page 7: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Outline

• Introduction

• The Model

• Validation

• Updates of technology

Page 8: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

q(t) q(t0)e(

t t0

) I(t) 1 e

(t t0

)

ctVp

pwf,t pwf,0

t t0

1 e(

t t0

)

CRM Continuity Equation

ctVp

dp

dt i(t) q(t)

dq(t)

dt

1

q(t)

1

i(t) J

dpwf

dt

ctVp

J

Ordinary Differential Equation:

Continuity:

Solution:

q(t) i(t)

BHP Injection Primary

q(t) J p pwf

Production Rate:

Page 9: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu
Page 10: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Signal Response

Production response to an injection signal

Connectivity

τij = 1 day

fij = 0%

Connectivity

τij = 1 day

fij = 100%

Connectivity

τij = 6 days

fij = 100%

Connectivity

ij = 6 days

fij = 65%

Page 11: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Capacitance-Resistance Model (CRMT)

k

tt

kk Ieeqq

11

q(t) I(t) J

Vc pt

Time constant

Page 12: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

f2j

f6j

f4j

f3j

f5j

jf1j

f11 f12

f13

I6

I1

I2

I3

I4 I5

qj(t)

Capacitance-Resistance Model (CRMP)

ik

n

i

ij

tt

kjjk Ifeeqqi

jj

1

1 1

j

pt

jJ

Vc

11

pn

j

ijf

Time constant

Inter-well connectivity or gain

Drainage volume

around a producer

Page 13: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Capacitance-Resistance Model (CRMIP)

Ii(t)

qj(t)

fij

ij

ij

pt

ijJ

Vc

11

pn

j

ijf

Time constant

Inter-well connectivity or gain

i

ijij

n

i

ikij

tt

kijjk Ifeeqq1

1 1

Page 14: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.5

Mature West Texas Waterflood

Injector

Producer

Gains > 0.5

Page 15: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.4

Mature West Texas Waterflood

Injector

Producer

Page 16: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.3

Mature West Texas Waterflood

Gains > 0.3 Injector

Producer

Page 17: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.2

Mature West Texas Waterflood

Gains > 0.2

Injector

Producer

Page 18: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Outline

• Introduction

• The Model

• Validation

• Updates to technology

Page 19: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Validation

How do we scientifically validate

geoscience hypotheses?

Remember:

Characteristics of a reservoir can be inferred

from analyzing production and injection data

only

Page 20: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

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.

Page 21: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Validation

Field Injectant Independent Data Agree

Synfields Water Simulation Very well

Snyfields Water Retrodiction Very well

Chuido Water Faults from seismic Reasonably

SWCFU Water Anecdotal fractures Reasonably

NSF I Water Structure Well

NBDU Gas Tracer data Fairly well

Will. Basin Water Acoustic impedance Reasonably

SELU Water Oil in tank Maybe

Characteristics of a reservoir can be inferred from

analyzing production and injection data only

Page 22: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Outline

• Introduction

• The Model

• Validation

• Updates to Technology

Page 23: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Updates to Technology

• Input data screening (Cao, 2011)

• New graphical methods (Wang, 20110

• Integrated CRM (error intervals) (Kim, 2011)

• Extension to primary recovery (Nguyen, 2011)

• Extension to subsidence problem (Wang, 2011)

Page 24: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Possible Data Problems

• Missing flowing

pressures, flow rates

• Unexplained

discontinuous changes

• Inconsistencies with

rates, pressures

• Wrong water

production data

• Unknown operational

changes

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50 60 70 80 90pro

duct

ion r

ate

(rb/d

ay)

Time, month

Example 1

oil production

total production

water production

gas production

Page 25: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Data Issues Remedies

• Get to know data set

• Replace with averages

• Restart CRM

• Outlier detection

• Fill in blanks with CRM

Page 26: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Remove outliers

Maximize NPV of future oil recovery

Warm start

Gainfit

Remove

inactive wells Remove gains

based on distance

Remove small

gains

Gainfit #2 Calculate residuals

and replace outliers Gainfit #3

Gainfit #1

Fracfit #1 Calculate residuals

and remove outliers Fracfit #2

Reservoir

model

Model Fit and Prediction Algorithm

~2.5 hrs

computation

time

Page 27: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Remove outliers

Maximize NPV of future oil recovery

Warm start

Gainfit

Remove

inactive wells Remove gains

based on distance

Remove small

gains

Gainfit #2 Calculate residuals

and replace outliers Gainfit #3

Gainfit #1

Fracfit #1 Calculate residuals

and remove outliers Fracfit #2

Reservoir

model

Model Fit and Prediction Algorithm

<1 min

computation

time

Page 28: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Remove outliers

Maximize NPV of future oil recovery

Warm start

Gainfit

Remove

inactive wells Remove gains

based on distance

Remove small

gains

Gainfit #2 Calculate residuals

and replace outliers Gainfit #3

Gainfit #1

Fracfit #1 Calculate residuals

and remove outliers Fracfit #2

Reservoir

model

Model Fit and Prediction Algorithm

<10 min

computation

time

Page 29: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Updates to Technology

• Input data screening (Cao, 2011)

• New graphical methods

• Integrated CRM (error intervals)

• Extension to primary recovery

• Extension to subsidence problem

Page 30: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Well connectivity for time interval 11/06/2006-

07/29/2007

P1

P2

P3

P4

P5

P6 P7

P8

P9

P10

P11

P12

P13

P14 P15

P16

P17

P18

P19

P20

P21

P22

P23

P24

P25

P26

P27 P28

P29

P30

P31

P32

P33

P34

P35

P36

P37

P38

P39

P40 P42 P43

P44

P45

P46

P47

P48

P49

P50

P51

P52

P53

P54 P55

P56

P57

P59

P60 P61

P62 P63

P64 P65

P66

P67

P68

P71

P72

P73

P74

P75

P76

P77

P78

P79

P80

P81

P82

P84

P85

P86

P88

P89

P91

P93

P94

P95

P96

P97

P98

P99

P100

P101 P102

P103 P104

P105

P106

P107

P108

P109

P110

P111

P112

P115

P116

P117

P118

P119

P120

P121

P122

I1

I2

I3

I4

I6

I7

I14

I15

I18

I19 I21

I22 I23

I24

I25

I26

I28

I29

I30

I31

I32

I33

I34

I35

I36

I37

I38

I39

I40

I41

I42

I43

I44

I45

I46

I47 I48

I49

I50

I51

I52

I53

I54

I55

I56

I57

I58

I59 I61

I62

I63

I64

I65

I66

I67

I68

I69

I70

I71

I75

I76

I77

I78

I79

I80

I81

I82

I83 I84

I85

I86

I87

I88 I89

I90 I91

I92 I93 I94

I95

I96

I97

I98 I99

I100

I101

I102 I103

I104

I105

I106

I107

I108

I109

I110

I111

I112

I113

I115

0.85 - 1

0.75 - 0.85

0.65 - 0.75

0.55 - 0.65

0.45 - 0.55

0.35 - 0.45

0.25 - 0.35

0.15 - 0.25

0 - 0.15

•For gain>0.2

Page 31: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•Gain vector sum for time interval 11/06/2006-

07/29/2007

Page 32: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

5

10

15

30

210

60

240

90

270

120

300

150

330

180 0

Gain Orientation from 11/06/2006-07/29/2007

5

10

15

20

30

210

60

240

90

270

120

300

150

330

180 0

Gain Orientation from 08/13/2007-06/29/2008

5

10

15

30

210

60

240

90

270

120

300

150

330

180 0

Gain Orientation from 06/29/2008-06/28/2009

Gain Orientation Histogram

for Different Time Periods

Page 33: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Updates to Technology

• Input data screening (Cao, 2011)

• New graphical methods

• Integrated CRM (error intervals)

• Extension to primary recovery

• Extension to subsidence problem

Page 34: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Integrated Capacitance Resistive Model for

Primary Recovery

HYPOTHESIS In primary recovery, reservoir properties such as pore

volume, reservoir pressure, productivity index, producer-

producer interaction can be inferred from production data

ADVANTAGES A quick, simple diagnostic tool for engineer

No additional cost

No well shut-in required as to measure productivity

index, reservoir pressure

OUTCOME Reservoir property estimates (volume, pressure, etc.)

Future production forecast

Support production planning (number of wells, production

rate schedule, producing life)

Page 35: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR Model

•Reservoir 3

•Reservoi

r 2 •Reservoi

r 1

•Well

1

•Well

2

•Well

3

•Known - Production rates –

q

• - Bottom hole

pressure – Pwf

• - Initial average

pressure – Pi(0)

• - Cumulative

production - Np

i

pi

i

iwfiipt

i

i

i

ipt NPPVcqJ

Vc)0()(

•Unknown - Pore Volume

– Vp

• - Productivity

Index – J

•Assumption: ct is

constant

•Assumptions

•No gas

•No volatile oil

•No aquifer

Page 36: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR Model Validation

• ICR has been tested to on different fields to consider the effects of Field size Permeability Initial oil saturation Heterogeneity Number of producers, producers start at different times

Page 37: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR results – CMG synthetic field

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

4.0E+07

4.5E+07

12/6/1999 3/15/2000 6/23/2000 10/1/2000 1/9/2001 4/19/2001

Dynamic pore volume Vp (bbl)

P1

P2

P1+P2

Actual pore volume 37.7e6 bbl

Page 38: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR Case Study – Oman field

•Estimated dynamic pore volumes

•Estimated productivity index over time

Page 39: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Updates to Technology

• Input data screening (Cao, 2011)

• New graphical methods

• Integrated CRM (error intervals)

• Extension to primary recovery

• Extension to subsidence problem

Page 40: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Contents

Synfield-1 (Streak case) Confidence limits by linear regression

Synfield-2 (Complete sealing barrier)

Synfield-3 (Partially sealing barrier)

Synfield-4 (Wells in random locations)

• ICR Model Applied on Synfields:

• Summary

• Future Work

•40

• CRM Introduction

•Application of the ICR

model for Secondary

Recovery

Page 41: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

• qjk, Iik, and pwf,jk are assumed to be constant over the time step

length (t)

• qj0 is the actual production rate of producer j at k=0

- Fully model driven

• Parameters to be determined by nonlinear regression are

- fij is the connectivity between injector i and producer j

- j is the time constant of producer j

- Jj is the productivity index of producer j

Nonlinear CRMP (CRM-Producer

Based)

1

/ /

( 1)ˆ ˆ 1j j

j kjknit t wf wf

jk j k ij ik j j

i

p pq q e e f I J

t

•(4)

•Weight on the rate at previous time

•Weight on the injection signals at current time

•41 •Application of the ICR

model for Secondary

Recovery

Page 42: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

• Least Mean Squares(LMS) parameters estimation

(5)

• Constraints

for all i (6)

for all i and j (7)

Equation 7 ensures that injected water does not adversely affects the

reservoir production.

Objective Function and Constraints of CRM

2

1 1

ˆmint Pn n

obs

jk jk

k j

z q q

1

1jn

ij

j

f

, 0ij jf

•42 •Application of the ICR

model for Secondary

Recovery

Page 43: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

CRMP vs. ICR model

•43

• using cumulative

quantities

• using instantaneous

quantities

1

/ /

( 1)ˆ ˆ 1j j

j kjknit t wf wf

jk j k ij ik j j

i

p pq q e e f I J

t

-3.00E+06

-2.00E+06

-1.00E+06

0.00E+00

1.00E+06

2.00E+06

3.00E+06

50 70 90

To

tal w

ate

r in

jec

ted

or

liq

uid

p

rod

uc

ed

(rb

)

Time periods (month)

Independent variables used for the ICR model

W4

-Np4

W1

W2

W3

W5

0

500

1000

1500

2000

2500

3000

50 60 70 80 90 100

Wate

r in

jecti

on

rate

s (

rb/d

ay)

Time periods (month)

Independent variables used for the CRMP

I1

I2

I3

•* Reservoir barrel

(rb)

•Application of the ICR

model for Secondary

Recovery

0

, 0 , ,

1

ink k k

p j j jk j ij i j j wf j wf j

i

N q q f CWI J p p

•where

• NP,j is the cumulative total liquid

production from a producer j

• CWIi is the cumulative water injection

into a injector i

Page 44: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Schematics of Convex Function with Constraints which form Convex Sets

Convex optimization problem: Minimize: f(x1,x2)

Subject to: gi(x1,x2) ≤ 0 i=1, 2, … , m

f(x1,x2)

x2 x1

•Global minimum

•without constraints

•Global minimum

•With constraints

•g1(x1,x2

)

•g2(x1,x2

) •g3(x1,x2

)

•g4(x1,x2

)

Page 45: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Streak Case – Inverted 5-Spot Pattern

•2480 ft

• Square reservoir (2480 ft by 2480 ft)

• 5 water injectors & 4 producers

• Isotropic and homogeneous reservoir

• - except 2 high permeability channels

• Water flood for 100 months (8.33 years)

• Fitting periods from 58th to 100th month

• Number of fitting periods is 42

• Radial distance limit of 4000 ft

• CRMP used

•45

•2480 ft

•(Same example as in Sayarpour, 2008)

•Application of the ICR

model for Secondary

Recovery

Page 46: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR Model Results ICR model is comparable to the CRMP

•46

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

I01 I02 I03 I04 I05

fi1

P01-fi1

fi1_nonlinear

fi1_linear_Np

0.00

0.05

0.10

0.15

0.20

0.25

I01 I02 I03 I04 I05

fi2

P02-fi2

fi2_nonlinear

fi2_linear_Np

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

I01 I02 I03 I04 I05

fi3

P03-fi3

fi3_nonlinear

fi3_linear_Np

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

I01 I02 I03 I04 I05

fi4

P04-fi4

fi4_nonlinear

f4_linear_Np

•Application of the ICR

model for Secondary

Recovery

Page 47: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ICR Model Results ICR model is comparable to the CRMP

•47 •Application of the ICR

model for Secondary

Recovery

0

5

10

15

20

25

30

P1 P2 P3 P4

Tau

s (

day)

Time Constants

Tau_CRMP Tau_ICR

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P1 P2 P3 P4

R2

Fit Qualities

R2_CRMP R2_ICR

fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)

P1 (j=1) 0.8961 0.5926 0.1981 0.2515 0.1625 5.16

P2 (j=2) 0.0357 0.0351 0.0402 0.2047 0.0330 13.64

P3 (j=3) 0.0199 0.1808 0.0856 0.0400 0.1660 12.27

P4 (j=4) 0.0586 0.1992 0.6634 0.5511 0.5929 10.60

Page 48: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•48

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

3.50E+06

4.00E+06

50 60 70 80 90 100

Np

(rb

)

Time period (month)

P01

Data

Linear_Npk0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

50 60 70 80 90 100

Np

(rb

)

Time period (month)

P02

Data

Linear_Npk

0.00E+00

1.00E+05

2.00E+05

3.00E+05

4.00E+05

5.00E+05

6.00E+05

7.00E+05

8.00E+05

50 60 70 80 90 100

Np

(rb

)

Time period (month)

P03

Data

Linear_Npk0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

3.00E+06

50 60 70 80 90 100

Np

(rb

)

Time period (month)

P04

Data

Linear_Npk

ICR Model Results NP(t) vs time

•Application of the ICR

model for Secondary

Recovery

Page 49: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•49

ICR Model Results q(t) vs time

•Application of the ICR

model for Secondary

Recovery

Page 50: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

95% Confidence Intervals – ICR Model Narrow error bars show the estimates are trustworthy

•50 •Application of the ICR

model for Secondary

Recovery

• Confidence limits calculated by the linear model (ICR) is smaller than

those calculated by the nonlinear model (CRMP).

Page 51: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•51

95% Confidence Intervals – ICR Model Narrow error bars show the estimates are trustworthy

•Application of the ICR

model for Secondary

Recovery

0

5

10

15

20

25

30

P1 P2 P3 P4

Ta

us

(d

ay) Time Constants

Tau_CRMP Tau_ICR

Page 52: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•52

Synfield-2: Complete Sealing Barrier

•Application of the ICR

model for Secondary

Recovery

fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)

P1 (j=1) 1.0000 0.0000 0.0000 0.0000 0.0000 8.359

P2 (j=2) 0.0000 0.0000 0.9995 1.0000 0.0000 33.04

P3 (j=3) 0.0000 0.7461 0.0001 0.0000 0.5002 25.98

P4 (j=4) 0.0000 0.2539 0.0005 0.0000 0.4996 22.89

•ICR parameters for Synfield-2

•Synfield-2 is a homogeneous isotropic reservoir (k=50

md and =0.2) and consists of three compartments that

do not communicate to each other because of the

presence of fault seals.

• The ICR model is able to detect the presence of

no-flow boundaries.

Page 53: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•53

Synfield-2: Complete Sealing Barrier q(t) vs time

•Application of the ICR

model for Secondary

Recovery

Page 54: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•54

Synfield-3: Partially Sealing Barrier

•Application of the

ICR model for

Secondary Recovery

•ICR parameters for Synfield-3

fij I1 (i=1) I2 (i=2) I3 (i=3) I4 (i=4) I5 (i=5) j (day)

P1 (j=1) 0.0326 0.4670 0.0409 0.0827 0.1257 27.79

P2 (j=2) 0.6286 0.0737 0.3560 0.4568 0.1410 13.84

P3 (j=3) 0.1000 0.3550 0.1717 0.1470 0.3659 13.45

P4 (j=4) 0.2388 0.1043 0.4314 0.3135 0.3674 13.40

•Synfield-3 is a homogeneous isotropic reservoir

(k=50 md and =0.2) with a partially sealing barrier

(navy diagonal blocks).

The presence of transmissibility barrier could be

inferred by low gains calculated from the ICR model.

Page 55: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•55

Synfield-3: Partially Sealing Barrier q(t) vs time

•Application of the

ICR model for

Secondary Recovery

Page 56: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•56

Synfield-4: Wells in Random Locations

•Application of the ICR

model for Secondary

Recovery

•Synfield-4 is a homogeneous isotropic reservoir (k=50 md

and =0.2).

Page 57: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•57

Synfield-4: Relationship between the

interwell-distance and interwell-

connectivity (gain)

•Application of the ICR

model for Secondary

Recovery

The results show that as the distance between interwell-pairs increases, the well

connectivity tends to decrease.

fij = -0.0003(ft-1)*dij (ft)+ 0.402 for 110 ft < dij < 959 ft

Distance (ft) fij (ICR) fij(CRMP)

110 0.5409 0.5321

198 0.4294 0.4091

260 0.1968 0.2977

310 0.4837 0.2868

388 0.2401 0.2314

426 0.2068 0.2010

426 0.2751 0.2510

442 0.1270 0.1418

493 0.0444 0.1646

510 0.3100 0.4077

527 0.2742 0.2643

543 0.3502 0.3413

576 0.1253 0.1250

650 0.2059 0.2369

677 0.1246 0.1226

745 0.0861 0.1439

806 0.2895 0.2504

815 0.2756 0.2323

860 0.2457 0.1878

959 0.1687 0.1722

y = -0.0003x + 0.402 R² = 0.3681

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1000 1200

f ij

Distance between well-pair (ft)

Gains vs Distance (CRMP)

fij_CRMPLinear (fij_CRMP)

y = -0.0003x + 0.401 R² = 0.2487

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1000 1200

f ij

Distance between well-pair (ft)

Gains vs Distance (ICR Model)

fij_ICRLinear (fij_ICR)

Page 58: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•58

Synfield-4: q(t) vs time

•Application of the ICR

model for Secondary

Recovery

Page 59: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Updates to Technology

• Input data screening (Cao, 2011)

• New graphical methods

• Integrated CRM (error intervals)

• Extension to primary recovery

• Extension to subsidence problem

Page 60: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Comparison of Actual and Model

Subsidence

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0 365 730 1095 1460 1825

Su

rface s

ub

sid

en

ce

(ft

)

Average subsidence vs. time

Actual average cumulative

subsidence

Model average cumulative

subsidence

•Elapsed days between 12/31/2003-9/16/2008 (days)

Page 61: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

• Dr. Edgar (Principal advisor)

• Dr. Lake (Co-advisor)

• Lab mates

Acknowledgment

•61

• This work was supported by the

sponsors of the Center for Petroleum

Asset Risk Management (CPARM) at UT

Austin

•Application of the ICR

model for Secondary

Recovery

Page 62: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

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)

Page 63: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gardner Hype Curve

The Gardner Group 63 Jim Honefenger (P.E. Moseley & Associates, Inc.)

Page 64: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Validation

Field Injectant Independent Data Agree

Synfields Water Simulation Very well

Snyfields Water Retrodiction Very well

Chuido Water Faults from seismic Reasonably

SWCFU Water Anecdotal fractures Reasonably

NSF I Water Structure Well

NBDU Gas Tracer data Fairly well

SELU Water Oil in tank Msybe

Characteristics of a reservoir can be inferred from

analyzing production and injection data only

Page 65: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Williston Basin Field

Page 66: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

ObjectiveÊfunction actualÊrate modelÊrate 2

FittingÊwindow

Producers

F fittingÊwindow,modelÊparameters

öqj t qj t;modelÊparameters 2

ttFirst

tLast

j1

Np

modelÊparameters

CRMT

j, fij CRMP

ij, fij CRMIP

fittingÊwindow int ervalÊwithÊnoÊexternalÊchanges

Basic Definitions

Page 67: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

RProducer

2 1ScatterÊofÊproducerÊrateÊaboutÊmodel

ScatterÊofÊproducerÊrateÊaboutÊmean

Basic Definitions

R j2

fittingÊint erval

1

öqj t qj t;modelÊparameters 2

ttFirst

tLast

öqj t qj 2

ttFirst

tLast

Page 68: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Steady-State Connectivity Map

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Better CO2

Performance

Page 69: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Interwell Connectivity

Two Equally Viable Solutions

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 70: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 10 days

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 71: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 30 days

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 72: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 90 days

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 73: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 180 days

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 74: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 365 days

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 75: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 2 years

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 76: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

After 4 years

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 77: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Transient Interwell Connectivity

4 years <<

0

20

40

60

80

0 20 40 60 80 100

Producer

Water Injector

Carbon Dioxide Injector 0 1,000 ft

Page 78: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.5

Mature West Texas Waterflood

Injector

Producer

Gains > 0.5

Page 79: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.4

Mature West Texas Waterflood

Injector

Producer

Page 80: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.3

Mature West Texas Waterflood

Gains > 0.3 Injector

Producer

Page 81: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gains >0.2

Mature West Texas Waterflood

Gains > 0.2

Injector

Producer

Page 82: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Mature West Texas Waterflood

0 50 100 150 200 250-1.5

-1

-0.5

0

0.5

1

Producer Number

R-squared Value

R-squared

Producer Number

Page 83: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

•109,252

•103,042

•Confidence band

for regression

line

•39,956 bbl •~

$2,800,000

Oil Rate vs. Cumulative Oil Production

Page 84: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Producer 184 – Good Fit

0 20 40 60 80 100 12020

40

60

80

100

120

140

160

180

200

Month

bbl/day

Historic Total Production

Modeled Total Production

R2 = 0.961

err = 0.146 Bbl/

day

Month

Page 85: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Producer 127 – Good Fit

0 20 40 60 80 100 1200

100

200

300

400

500

600

Month

bbl/day

Historic Total Production

Modeled Total Production

R2 = 0.696

err = 0.037

outliers

Bbl/

day

Month

Page 86: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Producer 74 – Poor Fit

0 20 40 60 80 100 1200

20

40

60

80

100

120

140

160

180

Month

bbl/day

Historic Total Production

Modeled Total Production

R2 = -1.03

err = 0.143

Bbl/

day

Month

Page 87: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Producer 201 – Poor Fit

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

Month

bbl/day

Historic Total Production

Modeled Total Production

R2 = 0.793

err = 6.58

Bbl/

day

Month

Page 88: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Gain Map

712000

714000

716000

718000

720000

722000

724000

726000

728000

475000 480000 485000 490000 495000 500000

ft

ft

Injector

Producer

P210

I 58

P103

Page 89: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Producer 210 (large distance)

0 20 40 60 80 100 1200

100

200

300

400

500

600

Month

bbl/day

Historic Total Production

Modeled Total Production

093.0

882.0R 2

err

Bbl/

day

Page 90: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

0 20 40 60 80 100 1200

50

100

150

Month

bbl/day

Historic Total Production

Modeled Total Production

Producer 103 (skipped over)

110.0

635.0R 2

errBbl/

day

Page 91: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

0 20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Injector Number

Fraction of Injection Lost

Injector Number

Lost Injection

1 f

ijj1

Np

Page 92: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Time Constants

1

10

100

1000

10000

100000

1

11

21

30

42

56

75

87

10

1

11

1

12

3

13

3

14

2

15

3

16

3

17

5

18

4

19

5

20

5

21

6

22

5

23

4

Producer Number

Tim

e C

on

sta

nt

(da

ys

)

...

.... Before Outlier Removal

After Outlier Removal

Reservoir A

Page 93: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

CRM Fit – Total Field

0 20 40 60 80 100 1202.5

3

3.5

4

4.5

5

5.5

6x 10

4

Month

bbl/day

Historic Injection

Historic Total Production

Modeled Total Production

R2 = 0.956 Bbl/

day

Month

Page 94: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

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

Page 95: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Appraisal and

Conceptual

Analysis

GATE GATE Evaluate

Alternatives GATE

Define

Selected

Alternative

GATE Execute 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

Page 96: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Optimal Injection and Predicted Oil Production for

the Field

0 20 40 60 80 100 120 140 160 180 200 2

3

4

5

6 x 10

4

Month

bb

l/d

ay

Historic

Optimal

0 20 40 60 80 100 120 140 160 180 200 500

1000

1500

2000

2500

3000

Month

bb

l/d

ay

Historic Oil Production

Predicted Oil Production

Extrapolated Oil Production

Page 97: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Injection Shares

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

3.5

Injector Number

Percent of Total Field Injection

Historic Share

Predicted Share

Injector Number

Percent of

Total

Page 98: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

Producer Number

Percent of Field Oil Production

Historic Share

Predicted Share

Production Shares

P112 P195

Producer Number

Percent of

Total

Page 99: Larry W. Lake The University of Texas at Austin Larry Lake ... · Capacitance Resistance Model Update Larry W. Lake The University of Texas at Austin Larry_Lake@mail.utexas.edu

Retrodiction