1

Why

do

we

need

Art

ifici

al L

ift?

Gor

don

Kap

pelh

off

2

PR

OD

UC

ED

FLO

WR

AT

E

WE

LL O

UT

FLO

WR

ELA

TIO

NS

HIP

WE

LL I

NF

LOW

(IP

R)

SU

RF

AC

E P

RE

SS

UR

EA

t Wel

lhea

d

Pw

fP

wf

WE

LL F

AC

E

PR

ES

SU

RE

Res

ervo

ir P

ress

ure-

Pr

Req

uire

d P

o to

pro

duce

des

ired

rate

Req

uire

d P

o to

pro

duce

des

ired

rate

Po

Typ

ical

Oil

Wel

l –T

wo

Par

ts

Par

t 1 –

The

Wel

l

Par

t 2 –

The

Res

ervi

or

3

Pr

Pw

f

Pw

hP

sep

� ���P

PI

P

Q� ���

P

� ���P

0

500

1000

1500

2000

2500

3000

3500

050

010

0015

0020

0025

0030

0035

0040

0045

00

Pro

duct

ion

rate

, ST

B/D

Flowing bottomhole pressure, psi

Tubi

ng C

urve

Po

Par

t 1 –

The

Wel

l

Par

t 2 –

The

Res

ervi

or

4

Dep

th

Pre

ssur

e

Pw

h=

? Po

= ?

Pr=

?P

art 1

–T

he W

ell

Par

t 2 –

The

Res

ervi

or

5

Wel

l Bor

e F

luid

Cal

cula

tions

As

we

can

see

from

the

form

ula’

s th

e m

ost r

elev

ant

para

met

er to

wel

l bor

e ca

lcul

atio

n is

pre

ssur

e. T

here

fore

we

will

spe

nd s

ome

time

look

ing

at th

e ba

sics

of w

hat

pres

sure

is.

Wha

t is

pres

sure

?

Wha

t is

For

ce?

6

Wel

l Bor

e F

luid

Cal

cula

tions

In e

nglis

hun

its:

Mas

s =

lbm

Acc

eler

atio

n =

gra

vity

In E

nglis

h U

nits

lbm

= lb

f

Thi

s is

not

the

case

in m

etric

uni

ts

7

Wel

l Bor

e F

luid

Cal

cula

tions

We

have

dis

cuss

ed fo

rce

–w

hat i

s pr

essu

re?

Pre

ssur

e =

Am

ount

of f

orce

ove

r a

spec

ified

are

a

Thi

s is

ver

y im

port

ant i

n no

t onl

y un

ders

tand

ing

a w

ell,

but

desi

gnin

g ar

tific

ial l

ift. B

ecau

se a

s w

e ha

ve s

een

the

wel

l is

only

con

cern

ed w

ith p

ress

ure,

not

forc

e.

8

Wel

l Bor

e F

luid

Cal

cula

tions

Wha

t exe

rts

mor

e fo

rce?

a. 1

000

ft of

wat

er in

2 3

/8”

tubi

ngb.

100

0 ft

of w

ater

in 2

7/8

” tu

bing

Wha

t exe

rts

mor

e pr

essu

re?

a. 1

000

ft of

wat

er in

2 3

/8”

tubi

ngb.

100

0 ft

of w

ater

in 2

7/8

” tu

bing

9

Wel

l Bor

e F

luid

Cal

cula

tions

As

stat

ed p

ress

ure

is fo

rce

over

a s

peci

fic a

rea,

or:

P =

F /

A

In e

nglis

hun

its w

hen

deal

ing

with

pre

ssur

e no

rmal

ly th

e un

itsus

ed a

re:

F =

lbf

A =

in2

Pre

ssur

e =

lbf/i

n2(k

now

as

a ps

i)

10

Whe

n de

alin

g w

ith fl

uid

in a

tube

wha

t is

the

stan

dard

Pre

ssur

e ca

lcul

atio

n?

P =

For

ce/A

rea

Are

a =

πx

(ID

of T

ubin

g/2)

2=

ID A

rea

For

ce =

Mas

s x

Acc

eler

atio

n

Mas

s =

vol

ume

of fl

uid

x de

nsity

Vol

ume

of F

luid

= ID

Are

a x

HA

ccel

erat

ion

= g

ravi

ty

For

ce =

ID A

rea

x H

x d

ensi

ty x

gra

vity

P =

(ID

Are

a x

H x

den

sity

x g

ravi

ty)/

ID A

rea

= ρ

x g

x h

11

P =

ρ ρρρx

g x

h

For

pur

e w

ater

the

engl

ish

units

are

as

follo

ws:

ρ ρρρ=

62.3

lbm

/ft3

As

men

tione

d 1

lbm

= 1l

bf at

sta

ndar

d gr

avity

So

ρ ρ ρ ρ x

g fo

r w

ater

=

62.

3 lb

f/ft3

Gra

dien

t pre

ssur

e is

pre

ssur

e di

vide

d by

hei

ght

Rea

rran

ging

the

form

ula

P/h

=

ρ ρρρx

g

So

ther

efor

e th

e pr

essu

re g

radi

ent f

or w

ater

is 6

2.3

lbf/f

t3

Doe

s th

at lo

ok r

ight

?

12

We

know

that

P =

psi

= lb

f/ i

n2

We

know

that

1 ft

= 1

2 in

Wat

er G

rad

= 6

2.3

lbf/f

t3

= 6

2.3

lbf

x 1

ft

x 1

ft

(ft3

)

12 in

12 in

= 0

.433

__l

b f__

(in2

x ft)

= 0

.433

psi

/ft

Doe

s th

at s

ound

rig

ht?

13

So

for

Pur

e W

ater

P(p

si)

= 0

.433

x h

(ft)

For

all

othe

r flu

ids

we

use

spec

ific

grav

ity =

sg

Sg

= d

ensi

ty o

f a fl

uid

/ den

sity

of p

ure

wat

er

The

refo

re th

e st

anda

rd in

Eng

lish

is:

P(p

si)

= 0

.433

x s

g x

h(ft)

14

Spe

cific

Gra

vity

Ofte

n sp

ecifi

c gr

avity

com

es in

the

form

of

AP

I, to

cov

ert

the

follo

win

g is

use

d:

sg =

141.

5

131.

5+A

PI

Whe

n tw

o liq

uids

of d

iffer

ent d

ensi

ty m

ake

one

fluid

, the

Spe

cific

gra

vity

is c

alcu

late

d as

follo

ws:

Sp

. G

r. =

wf o

+×

()

γγ

×)

(o

fw

15

For

mul

as S

o fa

r

sg =

141.

5

131.

5+A

PI

Sp

. G

r. =

wf

o+

×(

)γ

γ×

)(

of

w

P(p

si)

= 0

.433

x s

gx

h(ft)

Pre

ssur

e du

e to

flui

d:

AP

I to

sg:

Com

posi

te s

g:

16

Exe

rcis

e 1a

Oil

Den

sity

:

30 A

PI

Wat

er c

ut:

0%W

ater

Den

sity

:1.

026

sgP

res:

3765

psi

gP

whe

ad:

100

psia

PI:

10 s

tb/d

/psi

Bo:

1.33

rb/

stb

TV

D:

9183

feet

Fin

d P

outfl

owfo

r th

e ab

ove

cond

ition

s(a

ssum

e no

fric

tion)

17

Exe

rcis

e 1b

Oil

Den

sity

:

30 A

PI

Wat

er c

ut:

30%

Wat

er D

ensi

ty:

1.02

6 sg

Pre

s:37

65 p

sig

P w

head

:10

0 ps

iaP

I:10

stb

/d/p

siB

o:1.

33 r

b/st

bT

VD

:91

83 fe

et

Fin

d P

outfl

owfo

r th

e ne

w w

ater

cut

18Wel

l Per

form

ance

Pre

ssur

e gr

adie

nt p

lots

Dep

th

Pre

ssur

eP

o (0

%)

Po

(30%

)P

wh

Po

(30%

) R

equi

red

for

100

psi

wel

lhea

d pr

essu

re =

376

1 ps

i

Po

(0%

)Req

uire

d fo

r 10

0 ps

iw

ellh

ead

pres

sure

= 3

582

psi

19

For

this

cou

rse

we

are

goin

g to

mak

e th

e as

sum

ptio

n th

at fl

uid

alw

ays

flow

s fr

om h

igh

pres

sure

tow

ard

low

pre

ssur

e.

Som

e of

you

may

rec

ogni

ze th

at th

is is

not

exa

ctly

tr

ue.

The

exa

ctly

true

exp

ress

ion

is fl

uid

alw

ays

flow

s fr

om h

igh

pote

ntia

l tow

ard

low

pot

entia

l.

Wel

l Pro

duct

ivity

20

The

diff

eren

ce b

etw

een

"pre

ssur

e" a

nd "

pote

ntia

l" is

th

e el

evat

ion

(or

heig

ht)

and

the

elev

atio

n po

tent

ial c

an b

e ca

lcul

ated

from

the

equa

tion

−−

ρ ∗

g *

h.

We

have

alre

ady

seen

how

pr

essu

re in

crea

ses

with

the

dept

h in

a c

olum

n of

flui

d.

6"

14.7

psi

14.9

psi

Wel

l Pro

duct

ivity

21

Inflo

w –

Dar

cy’s

Exp

erim

ents

The

rel

atio

nshi

p be

twee

n pr

essu

re a

nd F

low

rate

was

firs

t st

udie

d ex

tens

ivel

y by

the

scie

ntis

t Hen

ry D

arcy

(1

803-

1858

).H

e cr

eate

d pr

essu

re d

iffer

entia

ls a

cros

s a

poro

us m

edia

and

m

easu

red

the

resu

lting

flow

rat

es th

at r

esul

ted

from

thos

e pr

essu

res.

His

exp

erim

ents

res

ulte

d in

wha

t is

now

kno

wn

as ‘

Dar

cy’s

La

w’ (

1856

) an

d ar

e th

e be

nchm

ark

for

perm

eabi

lity.

In

fact

, th

e un

it of

per

mea

bilit

y is

cal

led

the

‘Dar

cy’ (

D).

P0

P1

Dire

ctio

n of

Flo

wPer

mea

ble

Med

ium

: A

rea,

Len

gth,

Per

mea

bilit

yF

luid

Pro

pert

ies:

Vis

cosi

ty, V

olum

e F

acto

r

22

Dar

cy’s

Law

For

gen

eral

flow

thro

ugh

poro

us M

edia

:

01

**

()

*

kA

PP

QL

µ−

=

But

we’

re w

orki

ng w

ith o

il re

serv

oirs

, not

gen

eral

po

rous

med

ia…

23

Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Pw

f

Pr

Pr

Pr Q

=?

Res

ervo

ir O

uter

"dr

aina

ge"

boun

dary

Flu

id F

low

Flu

id F

low

Flui

d Fl

ow

Fluid Flow

Flui

d Fl

ow

24

Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

For

the

syst

em ju

st d

escr

ibed

, Dar

cy's

Law

look

s lik

e:

qo

= flo

w r

ate

k

o=

effe

ctiv

e pe

rmea

bilit

yh

= e

ffect

ive

feet

of p

ay

µ µµµo

= av

erag

e vi

scos

ityP

r=

rese

rvoi

r pr

essu

re

P

wf

= w

ellb

ore

pres

sure

re=

drai

nage

rad

ius

r

w=

wel

lbor

e ra

dius

Bo

= fo

rmat

ion

volu

me

fact

or

Not

e: (

Pr

-P

wf)

is th

e dr

awdo

wn

pres

sure

qk

hP

P

Br

o

or

wf

oo

e

w

=7.

08 x

10

S

-3 ln

()

µr

25Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

If w

e m

ake

the

assu

mpt

ion

that

ko,

h, r

e, r

w, B

o a

nd

µοar

e co

nsta

nt fo

r a

part

icul

ar w

ell t

he e

quat

ion

beco

mes

:

qk

kP

P

kk

o

1r

wf

54

6

7

=ln

kk2

3k

k8

()

Sim

plify

ing.

..

qK

PP

or

wf

=−

()

26Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Q -

Flow

Rat

e (B

PD

)

Pre

ssur

e -

PS

I Inte

rcep

t = P

r

Slo

pe =

-1/

K

0

0

Pw

f

27Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

The

Pro

duct

ivity

Inde

x (P

I) is

equ

al to

the

flow

ra

te d

ivid

ed b

y th

e "d

raw

dow

n":

PI

q o=

PP r

wf

−(

)

PI

xq o

=P

P rw

f−

()

28Exa

mpl

eD

arcy

's L

aw fo

r ra

dial

flow

into

a w

ellb

ore:

Con

side

r th

e fo

llow

ing

exam

ple:

Pr=

2,3

00 p

si, a

nd

Pw

f=

1,2

00 p

si @

qo

= 1

,150

bpd

Wha

t is

the

Pro

duct

ivity

Inde

x (P

I) o

f the

wel

l?

PI =

23

00

-12

00

()

11

50

= 1

.046

bbl

/day

/psi

29Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Wha

t is

the

max

imum

flow

rat

e th

e w

ell w

ill p

rodu

ce?

T

he m

axim

um fl

ow r

ate

occu

rs a

t the

max

imum

dr

awdo

wn

(Pw

f = 0

).

PI

=q m

ax 0

P r−

()

orq m

ax

P rP

I=

x

23

00

x1.

046

= 2

40

6 B

PD

q ma

x=

30Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

The

str

aigh

t-lin

e P

I wor

ks g

reat

for

sing

le p

hase

flui

d (i.

e. w

ater

, oil,

or

wat

er/o

il*)

flow

ing

into

a w

ellb

ore,

but

w

hat h

appe

ns if

gas

com

es "

out o

f sol

utio

n" in

the

rese

rvoi

r?

* E

ven

thou

gh w

ater

and

oil

are

two

sepa

rate

pha

ses,

th

ey a

re c

onsi

dere

d si

ngle

pha

se s

ince

they

are

bot

h liq

uid.

31Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Wha

t hap

pens

whe

n th

e ga

s co

mes

out

of s

olut

ion?

D

arcy

's la

w w

orks

just

as

wel

l for

a s

ingl

e ph

ase

gas

as it

doe

s fo

r a

sing

le p

hase

oil.

Let's

look

qua

litat

ivel

y at

wha

t will

hap

pen

to th

e flo

w

rate

of g

as.

qk

hP

P

Br

g

gr

wf

gg

e

w

=7.

08 x

10

0.75

-3 lnµ

r

32

Gas

will

beg

in

to fo

rm h

ere

Pr

Pr

Pre

ssur

e dr

ops

as w

em

ove

tow

ard

the

wel

lbor

eP

b

33Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Q -

Flow

Rat

e (B

PD

)

Pre

ssur

e -

PS

I

00

Pw

f

Gra

phic

ally

it w

ould

look

like

this

:

Pr

< P

b

Dar

cy's

law

pred

icte

dQ

max

Act

ual

Qm

ax

34

We

use

inst

ead

Vog

el's

IPR

cur

ve.

The

equ

atio

n is

:

whe

re q

o(m

ax)

is th

e m

axim

um fl

ow r

ate

the

wel

l ca

n pr

oduc

e.

Inflo

w P

erfo

rman

ce R

elat

ions

hip

-IP

R:

Q(m

ax)

=1

-0.

2-

0.8

2

Pwf r

PQ

Pwf r

P

35

Con

side

r ou

r pr

evio

us e

xam

ple…

Pr=

2,30

0 ps

iP

wf=

1,20

0 ps

i @ q

o=

1,15

0 bp

d

Inflo

w P

erfo

rman

ce R

elat

ions

hip

-IP

R:

36

Firs

t we

need

to c

alcu

late

Q/Q

max

:

Inflo

w P

erfo

rman

ce R

elat

ions

hip

-IP

R:

Q(m

ax)=

1 -

0.2

-0.

82

1200

2300

1200

2300

1150

-bpd

= 1

696

bpd

Q(m

ax)

=1

-0.

2-

0.8

2

Pwf r

PQ

Pwf r

P

Q(m

ax)

=Q

=

0.67

8

0.67

8T

hen…

37

Com

pare

this

to th

e Q

max

we

got f

rom

Dar

cy's

equ

atio

n of

240

6 bp

d. T

he w

ell h

as lo

st 7

10 b

pd (

~-30

%)

in c

apab

ility

due

to g

as

inte

rfer

ence

.

Inflo

w P

erfo

rman

ce R

elat

ions

hip

-IP

R:

Vo

gel vs

. P

I fo

r g

iven

test

po

int

0

50

0

10

00

15

00

20

00

25

00

05

00

10

00

15

00

20

00

25

00

30

00

Q (

bp

d)

Pwf (psi)

38

We

saw

that

we

coul

d us

e D

arcy

's la

w w

hen

gas

was

not

a

prob

lem

(P

wf >

Pb)

.

We

also

saw

how

to u

se V

ogel

's IP

R fo

r ca

ses

whe

re P

wf <

P

b.

Wha

t abo

ut a

cas

e w

here

Pr

is a

bove

Pb

and

Pw

fis

less

th

an P

b?

Com

bine

d IP

R

39

All

we

have

to d

o in

this

cas

e is

use

Dar

cy's

law

for

Pr

> P

wf >

Pb

and

Vog

el's

IPR

for

the

port

ion

whe

re P

b >

Pw

f > 0

.

Let's

say

, for

our

pro

blem

, we

have

a P

b of

180

0 ps

i.

Gra

phic

ally

it w

ould

look

like

:

Com

bine

d IP

R

40Com

bine

d IP

R:

0

500

1000

1500

2000

2500

050

010

0015

0020

00

Flo

w R

ate

-B

PD

Pre

ssur

e -

psi

Pr=

2300

Pb=

1800

We

use

a st

raig

ht li

ne P

I abo

ve P

b

We

use

VO

GE

L be

low

Pb

Qto

t-m

ax =

Qb

+ Q

v

Qv

Qb

Qb

= P

I x (

Pr-

Pb)

Qv

= P

I x P

b / 1

.8

Pw

f =0

.125

x P

b {-

1+[8

1-80

(q-q

b)/(

qtm

x-qb

)]^.

5}

41

Vog

el's

rel

atio

nshi

p w

orks

rea

sona

bly

wel

l for

wat

er

cuts

bel

ow 5

0%.

For

hig

her

wat

er c

uts,

a m

etho

d ha

s be

en d

evel

oped

w

hich

take

s an

arit

hmet

ic a

vera

ge o

f the

PI a

nd IP

R

equa

tions

to y

ield

a "

com

posi

te IP

R“.

For

a g

iven

PW

F, t

here

fore

, Com

posi

te p

redi

cts

mor

e flo

w th

an V

ogel

but

less

flow

than

str

aigh

t-lin

e P

I.

Com

posi

te V

ogel

IPR

:

42

q o(m

ax)

Flo

w R

ate

-B

PD

Pre

ssur

e

Wat

er P

I

Oil

IPR

Com

posi

teIP

R

q w(m

ax)

q t(m

ax)

�F

inal

ly, w

e ca

n co

nsid

er b

oth

com

bine

d (s

trai

ght-

line

plus

cur

ve)

and

com

posi

te o

n th

e sa

me

IPR

.

�G

raph

ical

ly it

wou

ld lo

ok li

ke th

is, w

here

qtis

the

com

posi

te fl

ow:

Com

posi

te a

nd C

ombi

ned

IPR

:

The

“S

kin”

effe

ct(v

an E

verd

inge

n&

Hur

st)

Ski

n is

a w

ellb

ore

phen

omen

on, t

hat c

ause

s an

add

ition

al p

ress

ure

drop

in

the

near

-wel

lbor

e re

gion

:

Sh

k

Bq

S hkq

po

oo

oosk

inµ

πµ2.

141

2)

(=

=∆

44Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

In s

ome

case

s, th

e P

I can

als

o be

impr

oved

slig

htly

by

acid

izin

gor

frac

turin

g. A

cidi

zing

clea

ns u

p "s

kin"

on

the

perf

orat

ions

and

can

impr

ove

poro

sity

in li

mes

tone

re

serv

oirs

by

mak

ing

larg

er h

oles

for

oil f

low

.

Ski

n D

amag

eA

cid

Bef

ore

Afte

r

45Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Fra

ctur

ing

can

also

impr

ove

perm

eabi

lity

by m

akin

g la

rge

crac

ks n

ear

the

wel

lbor

e.

Bef

ore

Afte

r

46Dar

cy's

Law

for

radi

al fl

ow in

to a

wel

lbor

e:

Why

is r

emov

ing

skin

so

impo

rtan

t?

skin

47Wel

l Per

form

ance

Pre

ssur

e gr

adie

nt p

lots

Dep

th

Pre

ssur

eP

o (0

%)

Po

(30%

)P

wh

Po

(30%

) R

equi

red

for

100

psi

wel

lhea

d pr

essu

re =

376

1 ps

i

Po

(0%

)Req

uire

d fo

r 10

0 ps

iw

ellh

ead

pres

sure

= 3

582

psi

Thi

s is

out

flow

Now

let’s

incl

ude

inflo

w

Pre

s

48

If th

e de

sire

d flo

w r

ate

is 1

000

BP

D d

o w

e ne

ed a

rtifi

cial

lift?

Cal

cula

te P

wfa

t 100

0 B

PD

49

Rem

embe

r ou

r D

ata

-E

xerc

ise

1aO

il D

ensi

ty:

30

AP

IW

ater

cut

:0%

Wat

er D

ensi

ty:

1.02

6 sg

Pre

s:37

65 p

sig

P w

head

:10

0 ps

iaP

I:10

stb

/d/p

siB

o:1.

33 r

b/st

bT

VD

:91

83 fe

et

Fin

d P

wfat

a fl

ow ra

te o

f 100

0 B

PD

(ass

ume

no fr

ictio

n)

50Wel

l Per

form

ance

Pre

ssur

e gr

adie

nt p

lots

Dep

th

Pre

ssur

eP

res

Po

(0%

)P

o (3

0%)

Pw

h

Po

(30%

) R

equi

red

for

100

psi

wel

lhea

d pr

essu

re =

376

1 ps

i

Po

(0%

)Req

uire

d fo

r 10

0 ps

iw

ellh

ead

pres

sure

= 3

582

psi

Pw

fava

ilabl

e at

100

0 B

PD

=

366

5 ps

i

Pw

f

51

HO

W?

Art

ifici

al L

ift

Pre

ssur

e

or

gas

lift t

he w

ell

Intr

oduc

ea

pum

p to

red

uce

Pw

f

52

Art

ifici

al L

ift O

ptio

ns

ES

P-C

reat

es h

ead

(� ���

P)

to lo

wer

Pw

f

GA

S L

IFT

-R

educ

es fl

uid

colu

mn

grad

ient

to lo

wer

Pw

f

PC

P-C

reat

es h

ead

(� ���

P)

to lo

wer

Pw

f

JET

PU

MP

-pro

vide

s pr

essu

re d

rop

in v

entu

rito

low

er

Pw

f

RO

D P

UM

P-I

nter

mitt

ently

suc

ks fl

uid

from

wel

l bor

e lo

wer

ing

Pw

f

ALL

INC

RE

AS

E D

RA

WD

OW

N T

O P

RO

DU

CE

FLO

W

53

Cash Flow Cash Flow

Tim

eT

ime

Art

ifici

al

Art

ifici

al

Lift

Lift

••M

ake

good

wel

ls b

ette

rM

ake

good

wel

ls b

ette

r

••G

ener

ate

mor

e re

venu

e ea

rlier

in th

e lif

e G

ener

ate

mor

e re

venu

e ea

rlier

in th

e lif

e of

a p

roje

ctof

a p

roje

ct

Fie

ld D

evel

opm

ent

54

Cash Flow Cash Flow

Tim

eT

ime

Art

ifici

al

Art

ifici

al

Lift

Lift

Pro

duct

ion

Pro

duct

ion

Opt

imiz

atio

nO

ptim

izat

ion

••D

ata

enab

led

syst

ems

Dat

a en

able

d sy

stem

s

••In

form

atio

n to

dec

isio

n m

aker

sIn

form

atio

n to

dec

isio

n m

aker

s

Pro

duct

ion

Opt

imiz

atio

n

EN

D o

f MO

DU

LE O

ne