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MODELLING HEAT LOSSES IN A TAR SAND FORMATION DURING THERMALRECOVERY PROCESSES

BY

NMEGBU, G.C.J., DUNE, K.K. AND JACKCREECE LABOMIE G.Dept. of Petro e!" E#$%#eer%#$, R%&er' St(te U#%&er'%t) of S*%e#*e (#+ Te* #o o$), PortH(r*o!rt.

He(t o''e' to (+-(*e#t for"(t%o#' -eop(r+% e t e eff%*%e#*) of t er"( re*o&er)

oper(t%o#'. Pre+%*t%#$ t e'e e#er$) o''e' %' %"port(#t %# t e +e'%$# of ( t er"( re*o&er)

pro-e*t. T e *('e 't!+) %' ( 'te("f oo+ pro-e*t / ere e(t o''e' fro" ( t(r '(#+

for"(t%o# %' "(t e"(t%*( ) "o+e e+ 0('e+ o# pert%#e#t (''!"pt%o#'. T e e(t o''

"o+e /(' +e&e ope+ !'%#$ t e (/ of *o#'er&(t%o# of e#er$), /%t e(t e#er$) (' (

f!#*t%o# of t e propert%e' of t e t(r '(#+ for"(t%o# (#+ t e e(t1*(rr)%#$ f !%+. So !t%o#'

of t %' "o+e /ere o0t(%#e+ !'%#$ t e MATLAB 'oft/(re. Se#'%t%&%t) (#( )'e' re&e( e+

t (t t e r(te of e(t o'' to t e (+-(*e#t 'tr(t( %#*re('e+2+e*re('e+ +epe#+%#$ o# t e

&(r%(t%o# of t e 'te(" (#+ t(r '(#+ for"(t%o# propert%e'. A &(r%(t%o# of 'o"e propert%e'

(+ #o '%$#%f%*(#t effe*t o# t e r(te of e(t o''e'. T !', %t %' &%t( %# (+&(#*e to $(t er

(+e3!(te %#for"(t%o# e'pe*%( ) of t e t(r '(#+ for"(t%o# 'o (' to prep(re (# %#-e*t%o#

f !%+ / o'e propert%e' /o! + "%#%"% e e(t o''e' to t e *(p (#+ 0('e ro*4'. T %' /o! +

%#*re('e t e "o0% %t) of t e o% (#+ e5te#+ t e %&e of t e pro+!*t%o# /e 6'7.

PREDICTING HEAT LOSSES

T e t er"( re*o&er) "et o+ *o#'%+ere+ %# t %' 't!+) %' 'te("f oo+%#$. He(t o''e' fro"

t e for"(t%o# (&e re"(%#e+ ( perpet!( * ( e#$e to petro e!" e#$%#eer'. It (' e+ to

re+!*t%o# %# t e te"per(t!re of 'te(", / %* re&ert' t e pro*e'' to /(terf oo+%#$. 8

A++%t%o#( ), t e '/eep (re( of t e re'er&o%r %' '"( (' *o"p(re+ to t e e#t%re &o !"e of

t e re'er&o%r, re'! t%#$ %# o/er o% "o0% %t) r(t%o'. T !', ( ot of re'e(r* (' 0ee# +o#eto pre+%*t e(t o''e' %#to (+-(*e#t for"(t%o#'.

P(* e*o (#+ F(ro!3 A % 9 for"! (te+ ( *o"pre e#'%&e "(t e"(t%*( "o+e of 'te("

%#-e*t%o# %#to ( re'er&o%r to %#* !+e ( '%"! t(#eo!' *( *! (t%o# of t e 'te(" pre''!re (#+

3!( %t). T e "o+e ("o#$'t ot er t %#$' too4 %#to (**o!#t e(t o''e' 0) r(+%(t%o#,

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*o#+!*t%o# (#+ *o#&e*t%o# (#+ *o#'%'te+ of t/o *o!p e+ #o#1 %#e(r +%ffere#t%( e3!(t%o#'

t (t /ere 'o &e+ %ter(t%&e ).

:o ot!4 %# ; (+opte+ t e *o#*ept of o&er( e(t tr(#'fer *oeff%*%e#t to repre'e#t t e e(t

o'' fro" ( re'er&o%r %#to t e (+-(*e#t 'tr(t( (#+ +e&e ope+ ( #e/ (ppro(* %# / %* e propo'e+ t (t t e o&er( e(t tr(#'fer *oeff%*%e#t %' #ot *o#'t(#t, !# %4e ot er *o#*ept',

0!t * (#$e' /%t re'pe*t to t%"e for pro*e''e' '!* (' ot /(ter or 'te(" %#-e*t%o#, or

I#1'%t! *o"0!'t%o#.

S !" (#+ H()#e' < +e&e ope+ ( "o+e to *( *! (te t e tr(#'fer of e(t %#to 6(#+ fro"7 t e

*(p (#+ 0('e ro*4', (#+ #e*e''(r% ) t e te"per(t!re +%'tr%0!t%o# %# t e ro*4'. T e

pr%#*%p( of '!perpo'%t%o# /(' (pp %e+ %# t %' "et o+ +!e to %t' '%"p %*%t) (' (# effe*t%&e

'o !t%o# "et o+, (#+ *o"p!ter 'tor($e (#+ t%"e.

U# %4e "o't "(t e"(t%*( "et o+' 0('e+ o# t e fro#t( +%'p (*e"e#t of o% 0) 'te("

o&er t e f! t %*4#e'' of (# o% '(#+, %# / %* 'o !t%o#' /ere !'!( ) +%'p ()e+ (' *!r&e'

t (t re (te t e per*e#t($e of tot( e(t ret(%#e+ %# t e o% o#e to ( +%"e#'%o# e'' t%"e=

V$e >' ? "et o+ of e(t re3!%re"e#t' for 'te(" f oo+' !t% % e' e3!(t%o#' for %#e(r e(t

f o/ fro" (# %#f%#%te p (#e, / %* (' pro&e# to 0e "ore (**!r(te. A t o!$ t %' "et o+

'pe*%f%*( ) +e( ' /%t pro&%+%#$ (**!r(te e't%"(te' %# *('e' '!* (' for t e ! t%"(te e(t

re3!%re"e#t' (#+ for +e'%r(0 e ret!r#' of e(t %#-e*t%o#, t e) (re !'ef! for e't%"(t%#$ (

e(t o''e'.

C %! (#+ T (4!r @ +e&e ope+ ( /e 0ore e(t o'' (#+ pre''!re 6 HAP7 "o+e . It

*o#'%+er' t e %#-e*t%o# of 'te(" or %3!%+ /(ter %#to ( +%re*t%o#( /e !#+er %#-e*t%o#

*o#+%t%o#'. T e "o+e *(# pre+%*t e(t o''e' !#+er * (#$%#$ %#-e*t%o# *o#+%t%o#'. T e

%#-e*t%o# r(te, pre''!re, te"per(t!re (#+ 'te(" 3!( %t) (t t e /e e(+ "() * (#$e /%t

t%"e. T e '!perpo'%t%o# pr%#*%p e %' !'e+ to +eter"%#e t e r(te of e(t o''e' (#+,

! t%"(te ), t e 0otto"1 o e *o#+%t%o#' of t e f !%+.

F(ro!31A % +e&e ope+ ( "o+e 0('e+ o# "('' (#+ "o"e#t!" 0( (#*e' %# t e /e 0ore

(#+ o# e(t 0( (#*e %# t e /e 0ore (#+ '!rro!#+%#$ "e+%(, %# / %* e(t o'' to t e

'!rro!#+%#$ f!#*t%o#' /(' tre(te+ &%$oro!' ).

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A0+!rr( "(# et ( propo'e+ ( "o+e for %#e(r (#+ r(+%( re'er&o%r $eo"etr%e' %# / %*

ot (#+ *o + /(ter /ere %#-e*te+ %#to poro!' "e+%(.

I# repre'e#t%#$ 'te(" pro*e'' /%t &(*!!" "o+e ', Ste$e"e%er et ( '%"! (te+ *(p (#+

0('e ro*4 e(t o''e' 0) *e"e#t%#$ 1%# $ ('' p (te' to$et er /%t * e(r '% %*o# pott%#$*o"po!#+. Before t e *e"e#t (' (r+e#e+, t e p (te' (re o(+e+ to e5tr!+e e5*e''

*o"po!#+, e(&%#$ o# ) ( t %# *e"e#t ()er. T %' t %# ()er ( o/' '!ff%*%e#t t er"(

e5p(#'%o# to (&o%+ *r(*4%#$ of t e 0 o*4' +!r%#$ t e t er"( e5per%"e#t.

STATEMENT OF THE PROBLEM

A "(-or 'et0(*4 of t e 'te("f oo+ pro*e'' %' e(t o''e' to t e (+-(*e#t for"(t%o#' %.e.

*(p (#+ 0('e ro*4'. Pre+%*t%#$ e(t o''e', /%t t e (%+ of "(t e"(t%*( "o+e ', ' ( 0e pre'e#te+ %# or+er to *o#'%+er t e f(*tor' t (t *o#tr%0!te to "ore o''e' (#+ o/ t e) "()

0e &(r%e+ to "(4e ( 'te("f oo+ pro*e'' "ore effe*t%&e.

MATHEMATICAL MODEL DEVELOPMENT

Basic Assumptions

T e fo o/%#$ pert%#e#t (''!"pt%o#' /ere "(+e for t e "(t e"(t%*( +e'*r%pt%o# of e(t

o''e' +!r%#$ 'te(" %#-e*t%o#' for t e t er"( re*o&er) of o% fro" t(r '(#+'

8. T e re'er&o%r %' o"o$e#eo!' (#+ of *o#'t(#t t %*4#e''.

9. Ste(" %' %#-e*te+ (t ( *o#'t(#t r(te, te"per(t!re, pre''!re (#+ 3!( %t). It %'

e%t er '(t!r(te+ or !#+er1'(t!r(te+ 0!t #ot '!per1'(t!r(te+.

;. Ste(" f o/' !#%for" ) %#to t e p() o#e (#+ %# t e %#e(r +%re*t%o# o# ). T e

'te(" fro#t %' (''!"e+ to 0e &ert%*( 'p(##%#$ t ro!$ t e e#t%re p().

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@. V(r%(t%o# of t e %#-e*te+ 'te(" 3!( %t) %# t e &ert%*( +%re*t%o# %' #e$ %$%0 e.

. I#%t%( ), t e 0o!#+%#$ for"(t%o#' (re (t t e '("e te"per(t!re (' t e re'er&o%r.

. He(t o''e' %#to t e *(p (#+ 0('e ro*4' (re e3!( .

. T e "o+e +oe' #ot *o#'%+er f !%+ f o/.

Mode De!e opment

Co#'%+er%#$ (# e e"e#t( &o !"e of t e t(r '(#+ for"(t%o# (' ' o/# %# f%$.8, t e e#er$) 0( (#*e for e(t f o/ %# (#+ o!t of t e &o !"e %' $%&e# 0)

lossesout in QQQ

= 8

F%$. 8 E e"e#t( &o !"e of t(r '(#+

He(t tr(#'fer %#to t e t(r '(#+ for"(t%o# o**!r' 0) *o#+!*t%o# (#+ *o#&e*t%o#. T !' t er(te of e(t %#-e*t%o#

inQ

%' $%&e# 0)

convectioninconductioninin QQQ 7676

+= 9S%"% (r ), e(t e(&e' t e e e"e#t( &o !"e t ro!$ *o#+!*t%o# (#+ *o#&e*t%o# to t e(+-(*e#t for"(t%o#'. M(t e"(t%*( ),

out Q

%' $%&e# 0)

lossesconvectionout conductionout out QQQQ

++= 7676 ;

T e r(te of e(t 'tore+, storageQ

%' $%&e# 0)

f r storage QQQ +=

' (/ of *o#+!*t%o#, 88 /e(&e for Qout

88S!0't%t!t%#$ E3!(t%o#' , 8 (#+ 88 %#to e3!(t%o# 8, /e (&e

89M(4%#$Q losses t e '!0-e*t of t e for"! (,

8;U'%#$ T() or>' e5p(#'%o# 'er%e' to e5p(#+ E3. 8;, /e (&e

+

=

+9

9

dxT d

x! xT

!dxdT

! x xo

8