11 History Matching

History Matching Calibrating the Dynamic Model 

Integrated $eser%oir (t)dy DYNAMIC MODEL Well/Facilities Model

"#scaled $eser%oir Model

Near Wellbore Peror!ance Models

Preli!inary Dyna!ic Model

Pro&ected $eser%oir Peror!ance

Field Econo!ic Model

Calibrated Dyna!ic Model

O#ti!i'ed $eser%oir De%elo#!ent Plan

History Matching *he #rocess o ad&)sting the reser%oir descri#tion )ntil the #rod)ction and #ress)res #redicted by the dyna!ic !odel !atch the historical #rod)ction and #ress)res+

I!#ortance o History Matching •

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A !odel !)st be able to re#rod)ce #ast #rod)ction and #ress)re #eror!ance beore ,e can )se it to #redict )t)re #eror!ance ,ith acc)racy+ Li!itationsCalibrated !odels !ay not reliably #redict )t)re #eror!ance )nder o#erating conditions that are s)bstantially dierent ro! those )sed in the calibration+

Plan History Match •

$e%ie, ob&ecti%es o integrated st)dy

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Deine ob&ecti%es o history !atch

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Deter!ine .)ality o history !atch necessary to !eet ob&ecti%es

)ality o History Match Needed •

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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

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

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$an5 a%ailable reser%oir data according to )ncertainty Esti!ate !ost li5ely %al)e0 e6#ected range o %al)es

Preli!inary (i!)lation $)ns •

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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 ha%e the !ost eect on the ans,ers8

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  –

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(elect $es#onse to be Matched •

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

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Field,ide #rod)ction rates

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Field,ide 7O$0 WO$

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Well #ress)res

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Well rates

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Well 7O$0 WO$

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Arri%al ti!es

(elect Para!eters to 9ary to Obtain Match •

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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,

.;

5A # 

to esti!ate

#er!eability changes  –

"se

9#

%ol)!e  –

4+.; # ,  ct t

to esti!ate reser%oir #ore

"se #ress)re transient theory

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

Altered 'one #er!eability

14 !d

E6a!#le 1 (ol)tion

Man)al History Match 2 (e!ilog 7ra#h or Matching *ransient ;eha%ior >134   s   e   r   #   e   r   o    b    l    l >144   e    W

>434

Obser%ed First *rial (+ L+ obs (+ L+ si!

>444 4+41

4+1

1 *i!e 0 days

14

144

Man)al History Match 2 Cartesian 7ra#h or Matching Pore 9ol)!e >=44 >144 >444   e   r   )   s =?44   s   e   r   # =B44   e   r   o    b    l    l =44   e    W=@44

Obser%ed First *rial (+ L+ Obs

=344

(+ L+ (i!

=>44 ==44 4

4

@4 *i!e 0 days

B4

144

11?<

>1@4 >

>11< +>

B #si / cycle

>441 +> >

3 4 144

>+= #si / day

!si!

>43B ==3@ 4 144

+4< #si / day

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*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!ateAobs A si!

!si! !obs

Aobs

A si!!si! !obs

or  ?3

+4< >+=

13134   s   e   r   #   e   r   o    b    l    l >144   e    W

>434

Obser%ed (econd *rial

>444 4+41

4+1

1 *i!e0 days

14

144

Man)al History Match 2 Matching $eser%oir Pore 9ol)!e0 *rial < >=44 >144 >444   e   r   )   s =?44   s   e   r   # =B44   e   r   o    b    l    l =44   e    W=@44

Obser%ed (econd *rial

=344 =>44 ==44 4

4

@4 *i!e 0 days

B4

144

Man)al History Match 2 Matching *ransient ;eha%ior0 *rial = •

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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 5 a  1 !d+

Man)al History Match 2 Matching *ransient ;eha%ior0 *rial = >=44

>134   e   r   o    b    l    l   e    W>144

Obser%ed >434

(econd *rial *hird *rial

>444 4+41

4+1

1 *i!e 0 days

14

144

Man)al History Match 2 Matching $eser%oir Pore 9ol)!e0 *rial = >=44

>144   )   s   s   e   r   # >444   e   r   o    b    l    l   e    W=?44

Obser%ed (econd *rial *hird *rial

=B44

=44 4

4

@4 *i!e0 days

B4

144

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*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

1 5a

1 5

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*h)s0 ,e ha%e 1 5a

1 5

1 5a

1 5

1 5a

1 5

obs

#obs # si!

si!

or 

obs

#obs 1 # si! 5 a

1 5

si!

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*hereore0 1 5a

5a

#obs 1 # si! 5 a

obs

1 5

1 obs

#obs 1 # si! 5 a

1 5

si!

1 5

>?+1 1 @134   s   e   r   #   e   r   o    b    l    l >144   e    W

>434

Obser%ed Final Match

>444 4+41

4+1

1 *i!e 0 days

14

144

Man)al History Match 2 Final Match0 Cartesian 7ra#h >134 >144   e   r   )   s >434   s   e   r   # >444   e   r   o    b    l    l =?34   e    W=?44

Obser%ed Final Match

=B34 =B44 =34 4

4

@4 *i!e 0 days

B4

144

Match 7ross $eser%oir ;eha%ior  •

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*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 •

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(#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+

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

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

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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 •

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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

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9ary area #se)dorelati%e #er!eabilities

Match Detailed $eser%oir ;eha%ior  •

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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 •

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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 #er!eability stratiication

Match Indi%id)al Well Peror!ance •

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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 c)r%es to !atch ,ell 7O$0 WO$0 W7$

A)to!atic History Matching •

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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 •

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*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