11 History Matching

History Matching

History Matching

Calibrating the Dynamic Model 

DYNAMIC MODEL

DYNAMIC MODEL

Well/Facilities Well/Facilities Model Model Near Wellbore Near Wellbore Peror!ance Models Peror!ance Models "#scaled "#scaled $eser%oir $eser%oir Model Model Preli!inary Preli!inary Dyna!ic Dyna!ic Model Model Calibrated Calibrated Dyna!ic Dyna!ic Model Model Pro&ected Pro&ected $eser%oir $eser%oir Peror!ance Peror!ance Field Field Econo!ic Econo!ic Model Model O#ti!i'ed O#ti!i'ed $eser%oir $eser%oir De%elo#!ent De%elo#!ent Plan Plan

Integrated $eser%oir (t)dy

History Matching

History Matching

*he #rocess o ad&)sting the reser%oir *he #rocess o ad&)sting the reser%oir

descri#tion )ntil the #rod)ction and

descri#tion )ntil the #rod)ction and

#ress)res #redicted by the dyna!ic !odel #ress)res #redicted by the dyna!ic !odel

!atch the historical #rod)ction and

!atch the historical #rod)ction and

#ress)res+ #ress)res+

I!#ortance o History Matching

I!#ortance o History Matching

•

• A !odel !)st be able to re#rod)ce #astA !odel !)st be able to re#rod)ce #ast

#rod)ction and #ress)re #eror!ance

#rod)ction and #ress)re #eror!ance

beore ,e can )se it to #redict )t)re beore ,e can )se it to #redict )t)re #eror!ance ,ith acc)racy+

#eror!ance ,ith acc)racy+

•

• Li!itations- Li!itations- Calibrated Calibrated !odels !odels !ay !ay notnot

reliably #redict )t)re #eror!ance )nder reliably #redict )t)re #eror!ance )nder o#erating conditions that are s)bstantially o#erating conditions that are s)bstantially dierent ro! those )sed in

Plan History Match

•

$e%ie, ob&ecti%es o integrated st)dy

•

Deine ob&ecti%es o history !atch

•

Deter!ine .)ality o history !atch

)ality o History Match Needed

•

For lo, #ress)re gas reser%oirs0 !atch

!ay need to be ,ithin 123 #si

•

For high #ress)re gas reser%oirs0

!atch ,ithin 34 #si !ay be ade.)ate

•

In general0 the tolerances or the !atch

sho)ld be at least   as tight as the

acc)racy desired or #ro&ections+

$eser%oir Data

• Collect reser%oir data

• $e%ie, data or consistency and acc)racy

• $an5 a%ailable reser%oir data according to

)ncertainty

• Esti!ate !ost li5ely %al)e0 e6#ected range

Preli!inary (i!)lation $)ns

• 7rid sensiti%ity 2 Is the grid ine eno)gh

to !eet the st)dy ob&ecti%es8

• *i!e ste# sensiti%ity 2 Are the ti!e ste#s

s!all eno)gh to ca#t)re the reser%oir res#onse o interest8

• Para!eter sensiti%ity 2 What #ara!eters

Peror! History Match

• 7eneral g)idelines

 – Where%er #ossible0 )se con%entional

reser%oir engineering !ethods to get initial esti!ates or #ara!eters

 – Loo5 or #ara!eters ,hich ha%e eects that

are inde#endent o any other )n5no,n #ara!eters0 and !atch those irst

 – Proceed ,ith the !atch ro! gross o%erall

beha%ior to detailed beha%ior o indi%id)al ,ells

(elect $es#onse to be Matched

• Field,ide a%erage reser%oir #ress)re

• Field,ide #rod)ction rates

• Field,ide 7O$0 WO$

• Well #ress)res

• Well rates

• Well 7O$0 WO$

(elect Para!eters to 9ary to

Obtain Match

• History !atching can only #ro%ide esti!ates

o reser%oir #ara!eters ,hich ha%e an aect on the reser%oir res#onse+

• Identiy i!#ortant #ara!eters 2 those ,hich

are )ncertain and   ,hich aect the reser%oir res#onse to be !atched+

• $e%ie, res)lts o #ara!eter sensiti%ity st)dy

to deter!ine ,hich o the )ncertain data ite!s ha%e the !ost inl)ence on the beha%ior being !atched+

A##ly Classical $eser%oir

Engineering Methods

• *o g)ide #ara!eter changes ,hile history

!atching- – "se Darcy:s la, to esti!ate

#er!eability changes

 – "se to esti!ate reser%oir #ore

%ol)!e

 – "se #ress)re transient theory

 5A .; t # c .; <=> + 4 9 ,  t # #

E6a!#le 1

• 7i%en the ollo,ing esti!ates o drainage

area0 or!ation #er!eability0 and altered 'one #er!eability0 #eror! a history !atch )sing classical reser%oir engineering

calc)lations to g)ide the !atch+

Drainage area ?3 acres

Per!eability =3 !d

E6a!#le 1

(ol)tion

Man)al History Match 2 (e!ilog 7ra#h

or Matching *ransient ;eha%ior

>444 >434 >144 >134 ><44 ><34 4+41 4+1 1 14 144 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed First *rial (+ L+ obs (+ L+ si!

Man)al History Match 2 Cartesian

7ra#h or Matching Pore 9ol)!e

==44 =>44 =344 =@44 =44 =B44 =?44 >444 >144 ><44 >=44 4 <4 >4 @4 B4 144 1<4 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed First *rial (+ L+ Obs (+ L+ (i!

• (ince the %arying #er!eability aects only

the linear #ortion o the se!ilog #lot0 ,hile %arying drainage area aects only the linear #ortion o the Cartesian #lot0 ,e can change #er!eability and drainage area si!)ltaneo)sly+

E6a!#le =

(ol)tion

• *he slo#e o a se!ilog #lot o ,ellbore

#ress)re %s ti!e sho)ld be in%ersely #ro#ortional to the #er!eability+ *o get a ne, #er!eability esti!ate0 ,e calc)late the se!ilog slo#es o the obser%ed and si!)lated res#onse-cycle  / #si B > >1@4 >1?< !_obs cycle  / #si 3 + < > > + >441 > + >11< !_si!

• We can then obtain a ne, esti!ate o #er!eability-or  obs si! si! obs ! ! 5 5 !d > + 1<1 B 3 + < =3 ! ! 5 5 obs si! si! obs

• *o obtain a ne, drainage area esti!ate0

,e calc)late the slo#es o the obser%ed and si!)lated res#onse on a Cartesian gra#h-day  / #si = + > 144 4 =>3 >1B< !_obs day  / #si 4< +  144 4 ==3@ >43B !_si!

• *his slo#e sho)ld be in%ersely

#ro#ortional to #ore %ol)!e or drainage

area+ *h)s0 ,e can calc)late a ne,

drainage area

esti!ate-or 

obs si! si! obs ! ! A A acres @ + 13< = + > 4< +  ?3 ! ! A A obs si! si! obs

Man)al History Match 2 Matching

*ransient ;eha%ior0 *rial <

>444 >434 >144 >134 ><44 ><34 4+41 4+1 1 14 144 *i!e0 days    W  e    l    l    b  o   r   e   #   r   e   s   s   )   r   e Obser%ed (econd *rial

Man)al History Match 2 Matching

$eser%oir Pore 9ol)!e0 *rial <

==44 =>44 =344 =@44 =44 =B44 =?44 >444 >144 ><44 >=44 4 <4 >4 @4 B4 144 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed (econd *rial

Man)al History Match 2 Matching

*ransient ;eha%ior0 *rial =

• At this #oint0 ,e ha%e e6cellent !atches or

#er!eability and reser%oir %ol)!e0 as sho,n by the slo#es o the rele%ant gra#hs+

• Changing the altered 'one #er!eability sho)ld ca)se

a )nior! shit in the #ress)re res#onse+

• *o esti!ate the change necessary in altered 'one

#er!eability0 ,e !)st !a5e another si!)lation r)n to deter!ine its eect on the #ress)re res#onse+

• We choose to !a5e the ne6t r)n ,ith the altered 'one

#er!eability the sa!e as that o the or!ation0 5a 

Man)al History Match 2 Matching

*ransient ;eha%ior0 *rial =

>444 >434 >144 >134 ><44 ><34 >=44 4+41 4+1 1 14 144 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed (econd *rial *hird *rial

Man)al History Match 2 Matching

$eser%oir Pore 9ol)!e0 *rial =

=44 =B44 =?44 >444 >144 ><44 >=44 4 <4 >4 @4 B4 144 *i!e0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed (econd *rial *hird *rial

• *he total   #ress)re dro# across the altered

'one is in%ersely #ro#ortional to the #er!eability in the 'one+ It can be sho,n that the additional #ress)re dro# d)e to a lo,er #er!eability in the altered 'one is #ro#ortional to

5

1

5

1

a

• *h)s0 ,e ha%e or  si! obs si! a obs a # # 5 1 5 1 5 1 5 1 si! a si! obs obs a 5 1 5 1 # # 5 1 5 1

• *hereore0 5 1 5 1 5 1 # # 5 1 si! a si! obs obs a !d >1 + 1< > + 1<1 1 > + 1<1 1 14 1 = + @< 1 + >? 1 5 1 5 1 5 1 # # 1 5 si! a si! obs obs a

Man)al History Match 2 Final Match0

(e!ilog 7ra#h

>444 >434 >144 >134 ><44 ><34 4+41 4+1 1 14 144 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed Final Match

Man)al History Match 2 Final Match0

Cartesian 7ra#h

=34 =B44 =B34 =?44 =?34 >444 >434 >144 >134 ><44 ><34 4 <4 >4 @4 B4 144 *i!e 0 days    W  e    l    l    b  o  r   e   #   r   e   s   s   )   r   e Obser%ed Final Match

Match 7ross $eser%oir ;eha%ior 

• *he irst ste# in a history !atch is to !atch

the o%erall gross reser%oir beha%ior+

• D)ring this #hase0 the o%erall reser%oir

%ol)!e and the gross distrib)tions o #er!eability and #orosity ,ill be deter!ined+

• Oten0 this #hase o a st)dy can be cond)cted

)sing a coarse grid !odel0 #ro%iding s)bstantial sa%ings in engineering and co!#)ter ti!e+

Match A%erage Press)re Le%els

• (#eciy total reser%oir #rod)ction rate or

each ,ell+

• 9ary reser%oir %ol)!e0 total co!#ressibility0

a.)ier storati%ity and trans!issibility to obtain !atch+

• Match o%erall reser%oir a%erage #ress)re+

• $estrict the !atch to #ri!ary #rod)ction

• It !ay be hel#)l to !atch only that

#rod)ction occ)rring #rior to or!ation o ree gas in the reser%oir+

Match Press)re 7radients to

Establish Flo, Patterns

• 9ary inter,ell #er!eability and net #ay to

obtain !atch

• Match reser%oir #ress)re gradients

• In areas e6#eriencing #se)dosteady state

lo,0 )se Darcy:s la, to esti!ate changes in #er!eability necessary to obtain

!atch-

#

5A

$e%ie, Press)re Match

•

;eore #roceeding ,ith the !atch0 the

#ress)re !atch !)st be re%ie,ed to

ens)re that the correct a!o)nt o l)ids

are being #rod)ced ro! the !odel+

Match Contact Mo%e!ents and O%erall

7O$0 WO$0 and W7$ Peror!ance

•

9ary #er!eability stratiication

Match Detailed $eser%oir ;eha%ior 

• Ater !atching the o%erall gross reser%oir

beha%ior0 the ne6t ste# is to !atch !ore detailed reser%oir beha%ior+

• D)ring this #hase0 the distrib)tions o

#er!eability and #orosity ,ill be reined+

• I a coarse grid ,as )sed to !atch the

gross reser%oir beha%ior0 it !ay be

necessary to de%elo# a ine grid !odel at this #oint+

Match $egional Peror!ance

• Match #ress)res and #ress)re gradients

by %arying #er!eability

• Match 7O$0 WO$0 W7$ by %arying area

#se)dorelati%e #er!eabilities or

Match

Indi%id)al Well Peror!ance

• Change ,ell PI to !atch lo,ing #ress)res

static #ress)res sho)ld be !atched ,hile !atching regional beha%ior

• Change ,ell #se)dorelati%e #er!eability

A)to!atic History Matching

• A)to!atic history !atching is the #rocess

o a)to!ating the !atching #rocess+

• *he engineer s#eciies the #ara!eters to

%ary to obtain a !atch0 and the res#onse to be !atched+

• A co!#)ter #rogra! is then gi%en the tas5

o inding the %al)es o the !atch

#ara!eters ,hich gi%e the best history !atch+

When to "se A)to!atic History

Matching

• *o reine !atch obtained by !an)al history

!atching

• Ater identiying the !ost i!#ortant )n5no,n

#ara!eters

• A)to!atic history !atching !ethods ,or5

better and r)n aster ,hen gi%en a s!aller n)!ber o #ara!eters to !atch

• Do not incl)de #ara!eters ,hich ha%e little or

no eect on the desired res#onse+ (o!e

!ethods !ay ail entirely or )nderdeter!ined #roble!s