Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Copyrigh 23, IFP Energies nouvelles DOI:.256/ogs/2222 Vol. 69 (24), No. 2, pp. 37-37 A Siple Approach o Dynaic Maerial Balance in Gas-Condensae Reservoirs M. Heidari Sureshjani*, S. Gerai and M.A. Eadi IOR Research Insiue, NIOC, 22 Negar S., Vanak Sq., Tehran - R.I. d Iran e-ail:.heidari.su@gail.co - sgerai@gail.co - eadi@nioc.rd.ir * Corresponding auhor Résué Une approche siple pour un équilibre dynaique des aières dans des réservoirs de gaz-condensa Lors de calculs radiionnels d équilibre de aières, des données de pression de puis feré son uilisées pour déeriner une pression oyenne du réservoir, andis que des echniques récenes n exigen pas que le puis soi feré e uilisen à la place des données de valeur de pression de puis en écouleen. Ces éhodes, connues sous le no d équilibre dynaique de aières, son développées pour un écouleen onophasique (huile ou gaz) dans les réservoirs. Touefois, l uilisaion de elles éhodes pour des réservoirs de condensas de gaz peu générer des erreurs significaives en aière de prédicion de pression oyenne du réservoir du fai de la ransgression de l hypohèse de phase unique dans de els réservoirs. Au cours de ravaux précédens, une éhode desinée à l analyse de données de producion dans les réservoirs de condensas de gaz a éé développée. La éhode exigeai un aux de producion de gaz sandard, un rappor gaz-huile de producion, une pression de puis en écouleen, des données de CVD (Consan Volue Depleion) e des courbes de peréabilié relaive. Le présen aricle présene une nouvelle echnique n ayan pas besoin des courbes de peréabilié relaive e de la pression du puis en écouleen. Par cee éhode, le rappor gaz-huile de producion es inerpolé à parir des données R v en foncion de la pression p dans le ableau de CVD e la pression correspondane es localisée. Le paraère p/z p es alors évalué en des poins de pression déerinés e il es racé en foncion de n p qui fore une ligne droie. La naure de ce racé es elle que son exrapolaion au poin où p/z p = donnera le nobre de oles iniial en place. En ean p i /z p,i (paraère connu) e un n i esié dans l équaion d équilibre de aières, une pression oyenne de réservoir peu êre déerinée. La éhode repose sur une hypohèse principale selon laquelle la région, où à la fois les phases gazeuses e le condensa son obiles, es de diensions négligeables par rappor au réservoir. L approche es pluô siple e les calculs son beaucoup plus faciles que dans le cadre des ravaux précédens. Elle procure un ouil d ingénierie praique pour des éudes indusrielles puisqu elle exige des données qui son généraleen disponibles lors d opéraions norales de producion. Touefois, elle n es applicable que lorsque la pression oyenne de réservoir approche la pression de poin de rosée e chue plus bas que celle-ci. La éhodologie es validée en uilisan des données synhéiques de producion provenan de plusieurs exeples. De plus, la éhode es évaluée par le biais d une esiaion de la pression oyenne de réservoir e du gaz d origine en place à parir de données de chaps réels. Les résulas onren un assez bon accord en aière de gaz en place pour ce chap enre cee nouvelle éhode e le calcul voluérique. Absrac A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs In radiional aerial balance calculaions, shu-in well pressure daa are used o deerine average reservoir pressure while recen echniques do no require he well o be shu-in and use insead flowing well pressure-rae daa. These ehods, which are known as dynaic aerial balance, are developed
38 Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Vol. 69 (24), No. 2 for single-phase flow (oil or gas) in reservoirs. However, uilizaion of such ehods for gas-condensae reservoirs ay creae significan errors in predicion of average reservoir pressure due o violaion of he single-phase assupion in such reservoirs. In a previous work, a ehod for producion daa analysis in gas-condensae reservoirs was developed. The ehod required sandard gas producion rae, producing gas-oil raio, flowing well pressure, CVD daa and relaive pereabiliy curves. This paper presens a new echnique which does no need relaive pereabiliy curves and flowing well pressure. In his ehod, he producing oil-gas raio is inerpolaed in he vaporized oil in gas phase (R v ) versus pressure (p) daa in he CVD able and he corresponding pressure is locaed. The paraeer pressure/wo-phase deviaion facor (p/z p ) is hen evaluaed a he deerined pressure poins and is ploed versus produced oles (n p ) which fors a sraigh line. The naure of his plo is such ha is exrapolaion o poin where p/z p = will give iniial oles in place. Puing iniial pressure/iniial wo-phase deviaion facor (p i /z p,i ) (known paraeer) and esiaed iniial oles (n i ) ino he aerial balance equaion, average reservoir pressure can be deerined. A ain assupion behind he ehod is ha he region where boh gas and condensae phases are obile is of negligible size copared o he reservoir. The approach is quie siple and calculaions are uch easier han he previous work. I provides a pracical engineering ool for indusry sudies as i requires daa which are generally available in noral producion operaions. However, i is only applicable when average reservoir pressure approaches dew poin pressure and falls below i. The ehodology is validaed using synheic producion daa for several exaples. In addiion, he ehod is evaluaed hrough esiaion of average reservoir pressure and original gas in place fro acual field daa. The resuls show a fairly good agreeen in gas in place obained fro he new ehod and ha of voluerically calculaed value for his field. NOMENCLATURE B Foraion volue facor b pss Paraeer defined by Equaion (3) c Copressibiliy G Iniial gas in place h Reservoir hickness k Absolue pereabiliy k rg Gas relaive pereabiliy k ro Oil relaive pereabiliy Single-phase pseudopressure p Two-phase pseudopressure n Moles n p Produced oles p Pressure p Reference pressure p dew Dew poin pressure q gsc Sandard volueric gas flow rae q Molar gas flow rae r e Reservoir exernal radius r w Wellbore radius R p Producing gas-oil raio R s Soluion gas in oil phase R v Vaporized oil in gas phase S Sauraion Tie acr Maerial balance pseudoie Two-phase pseudoie a,p acr,p z z p μ ρ ρ gsc ρ osc Subscrips eff g ave. i o w wf INTRODUCTION Two-phase aerial balance pseudoie Deviaion facor Two-phase deviaion facor Viscosiy Molar densiy Molar densiy of gas coponen a sandard condiions Molar densiy of oil coponen a sandard condiions Effecive wih respec o iniial waer sauraion Gas phase Average Iniial Oil phase Waer phase Well flow Maerial balance calculaions are perfored during he producion life of he reservoirs o deerine hydrocarbon in place. This inforaion is crucial for reservoir anageen and decision aking for field developen. The reserves can be deerined using volueric ehod, aerial balance ehod and/or producion decline echniques. Aong hese ehods, he aerial balance is acceped o be he os accurae way for esiaing original hydrocarbon in place.
M. Heidari Sureshjani e al. / A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs 39 There is a basic assupion behind aerial balance calculaions which considers he reservoir o be depleed in a ank-ype anner, i.e. he pressure dependen properies across he reservoir are evaluaed a an equivalen pressure which is he average reservoir pressure. The pressure dependen properies could be fluid and rock properies. The volue expansion of rock and fluid should be known as a funcion of pressure o accoun for heir volue changes when balancing oal ass enering and oal ass exiing he reservoir. For volueric dry gas reservoirs, a siple plo of p/z evaluaed a average reservoir pressure versus cuulaive gas producion fors a sraigh line saring fro iniial pressure, p i /z i, going o original gas in place. Deviaions fro he sraigh line are due o exernal recharge or offse drainage. For volueric gas-condensae reservoirs, a plo of p/z p calculaed a average reservoir pressure versus cuulaive produced oles of fluids gives iniial oles in place and uliaely iniial gas in place. To prepare such a plo, average reservoir pressure us be known as a funcion of ie. Tradiionally, saic ess are ipleened a several poins during he producion life of he wells which requires he well o be shu-in for cerain ie inervals. Consequenly, here will be loss of producion and eergence of addiional coss associaed wih he operaions. Quie ofen, he duraion of shu-in is no long enough (especially in igh foraions) o direcly easure he average reservoir pressure and exrapolaion echniques are needed. This can resul in an addiional proble due o possible wrong inerpreaions and iproper ess knowing ha he ess and inerpreaions are uch ore difficul for gas-condensae reservoirs. In addiion, for condiions of asphalene precipiaion in wellbore during shu-in ie, he saic pressure daa canno be acquired. In 998, he concep of Flowing aerial balance was inroduced by Maar and McNeil (998). In a flowing aerial balance procedure, he flowing well pressure daa along wih he cuulaive producion (consan rae producion) are analyzed o deerine original fluid in place and average reservoir pressure. The iporan feaure of his echnique is ha i does no require he well o be shu-in (no need o saic ess). Insead of average reservoir pressure daa, i uses flowing well pressure daa which are norally available in producion operaions. Thus i provides a very pracical ool for esiaing hydrocarbon (oil or gas) in place. The ehod was furher exended o he case of variable well rae condiions known as Dynaic aerial balance (Maar and Anderson, 25). For variable well rae condiions, he flow ie us be replaced by Maerial Balance Tie (Blasingae and Lee, 986; Palacio and Blasingae, 993). In his work, we show ha he ehods of dry gas reservoirs for dynaic aerial balance of gas-condensae syses ay inroduce enorous errors in esiaion of average pressure and gas in place and his is due o presence of wo phases in a gas-condensae reservoir. The auhors recenly developed a ehod for esiaing original gas in place and average reservoir pressure of gascondensae reservoirs wih he analysis of well producion daa (Heidari Sureshjani and Gerai, 2). They proposed a boundary doinaed flow equaion and wo-phase aerial balance pseudoie for gas-condensae syses and coupled he wih a aerial balance equaion o esiae gas in place and average reservoir pressure hrough an ieraive procedure. However, he ehod has soe pracical liiaions. I needs relaive pereabiliy daa which ay no be always available o reservoir engineers and even if available, i is soehow uncerain inforaion which ay no be a represenaive one for he wo-phase flow region. Furherore, he calculaions were o soe exen coplex. In he curren sudy, we presen a very siple echnique which is uch easier, alhough less accurae, han he previous ehod. I does no need relaive pereabiliy curves and flowing well pressure daa for analysis. DRY GAS DYNAMIC MATERIAL BALANCE For gas wells producing under variable pressure-rae condiions, average pseudopressure can be deerined fro he following equaion (Maar and Anderson, 25): where: ave. () = wf () + q ()b pss () Once ave. is deerined, average pressure can be inerpolaed fro he PVT able of p versus. The paraeer p/z p is hen evaluaed a he deerined average pressure and is ploed versus G p which fors a sraigh line. Exrapolaion of his plo o poin where p/z p = will give iniial gas in place, as he following equaion deonsraes: In case ha b pss is no known (r e and k eff h are no known), he following boundary doinaed flow equaion can be used o deerine his paraeer (Palacio and Blasingae, 993): where: i b p p Gp = z z G q pss acr = 2πk ave. wf eff p = ρ dp μ p re 3 ln h r 4 i = b GB c pss + μ gicgi μ c q d ( τ) τ μg g = q () w gi gi gi acr (2) (3) (4) (5) (6)
3 Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Vol. 69 (24), No. 2 Fro he inercep of a linear plo of ( i wf ) / q versus acr, b pss can be obained. Also, fro he slope of his plo G can be deerined. 2 GAS-CONDENSATE DYNAMIC MATERIAL BALANCE 2. Previous work For a well locaed in he cener of a cylindrical gas-condensae reservoir, we can use he following flowing aerial balance equaion proposed by Fevang and Whison (995) and furher invesigaed by Heidari Sureshjani and Gerai (2): where: p,ave. () = p,wf () + q gsc ()b pss (7) Paraeer b pss is he sae as Equaion (3) excep k eff should be replaced by k. The boundary doinaed flow equaion for gas-condensae reservoirs is given as follows (Heidari Sureshjani and Gerai, 2): In Equaion (9), he wo-phase aerial balance pseudoie is expressed as: where a,p is wo-phase pseudoie and is defined as: ap, p p wf ( Swi ) = bpss + q GB p, i, p, i acr, p gsc gi = p krg k B B R ro = + dp s p μg g μ o o acr, p (8) (9) () () Fro Equaion (9), i is seen ha a plo of: ( p,i p,wf )/q gsc versus acr,p should yield a sraigh line when boundary doinaed flow is reached. Fro he slope and inercep of his line, G and b pss can be esiaed, respecively. However, a,p which is required in calculaion of acr,p is a funcion of average reservoir pressure. Therefore, an auxiliary equaion, which is aerial balance equaion, is needed. I is wrien as (Hagoor, 988; Vo e al., 99): p z dew p, i ap, qgsc ( τ) dτ = q p S B p = z p p p ave. pi gsc d So B R + s o n p n (2) Coupling he above equaions and going hrough an ieraive procedure will yield average reservoir pressure and original gas in place. g g i pave. 2.2 Presen Approach In his secion a siple approach is inroduced for esiaing average reservoir pressure and original gas in place and his is he purpose of his sudy. The ain siplificaion underlying he ehod is ha we can divide he reservoir ino wo pars. The flow behavior in he inner par, where wo phases are flowing, is assued o be seady-sae i.e. he olar percenage of coposiions enering his region is equal o ha of enering he well bore a a cerain ie. The fluid inside he ouer region, where oil phase is iobile, is assued o have average properies which are evaluaed a average reservoir pressure and his par is depleed in a ank-ype anner. The locaion of he inerface boundary of hese wo regions is no necessarily consan. Since he flow in he inner region is seady-sae and he oil phase in he ouer region is iobile, he depleion behavior of he ouer region can be siulaed wih a CVD es. However, he aerial balance assues he enire reservoir o be a single cell and siulaes he enire reservoir by CVD es. This will no inroduce a considerable error because he size of seady sae region is sall copared o he ouer par. Knowing ha he inner par is seady sae, he soluion oil-gas raio in he enering gas o his par is equal o he producing oil-gas raio a each ie (Fevang and Whison, 995; Mo, 23). Therefore, we inerpolae he producing oil-gas raio in he R v versus p daa in he CVD able and locae he corresponding pressure. This pressure poin is a rough esiaion of average reservoir pressure a ha ie. We evaluae p/z p a he deerined pressure poins and plo i versus n p which fors a sraigh line. The naure of his plo is such ha is exrapolaion o poin where p/z p = will give iniial oles in place. The produced oles are relaed o sandard gas flow rae and producing gas-oil raio using he following equaion: q gsc np = qgscρgsc + ρosc (3) R d p To esiae iniial gas in place, we use he following equaion: ni G = (4) ( ρgsc + ρoscrvi ) Puing p i /z p,i (known paraeer) and esiaed n i ino Equaion (2), we can deerine average reservoir pressure as a funcion of ie. The procedure is suarized as follows: locae he pressures in CVD able where well producing oil-gas raio is equal o R v in CVD es; calculae p/z p using he obained pressure daa in he previous sep. Plo p/z p versus n p. Exrapolae his line o he poin where p/z p =, he corresponding n p is regarded as iniial oles in place; subsiue p i /z p,i and esiaed n i ino Equaion (2) o calculae average reservoir pressure. In he above procedure, he required producion daa are q gsc and R p (no need for p wf ).
M. Heidari Sureshjani e al. / A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs 3 3 VERIFICATION To verify he presened ehod, several synheic producion daa have been generaed using fine grid coposiional siulaions. The posiive coupling and inerial effecs have been acivaed in he siulaor. The generaed producion daa were analyzed wih he oulined procedure o obain gas in TABLE Basic reservoir properies Thickness () Well bore radius (). Reservoir exernal radius () Porosiy (fracion).2 Pereabiliy (d) 2 Forchheier paraeer for (/) 2.7864 9 Forchheier paraeer for (/).7732 9 place and average reservoir pressure. We used wo differen fluids which are wih axiu liquid dropou of 3.7% and wih axiu liquid dropou of 27.33%. Also wo ses of iiscible relaive pereabiliy daa were considered. Table shows basic reservoir properies. Tables 2 and 3 provide he key fluid properies and coposiions of fluids, respecively. In Table 4, inforaion of iiscible relaive pereabiliy daa is given. Toally four TABLE 2 Key reservoir PVT properies Iniial pressure (bar) 2 26 Dew poin pressure (bar) 88.2 257.278 Reservoir eperaure ( C) 93.333 93.333 Maxiu CVD liquid dropou (%) 3.7 27.33 Iniial soluion oil in gas (S 3 /S 3 ).4535.56958 6 6 2.5 2. 2. q gsc (S 3 /day).5. q gsc (S 3 /day).5..5.5 5 5 a) b) 5 5 2 6 4.5 6 5 4. 3.5 4 q gsc (S 3 /day) 3. 2.5 2..5 q gsc (S 3 /day) 3 2..5 2 4 6 8 2 4 6 c) d) Figure Gas flow rae for a) se A and ; b) se A and ; c) se B and ; d) se B and. 8
32 Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Vol. 69 (24), No. 2 TABLE 3 Mixure overall coposiions C 83.2 78 C4 3 2 C7 3. 7.2 C.4.4 C4.3.4 cases are analyzed which are ade based on differen cobinaions of he considered fluids and relaive pereabiliy daa. Figures and 2 show gas producion rae and producing gas-oil raio, respecively. In Figure 3, p/z p is evaluaed a he pressure poins calculaed in he way as TABLE 4 Key reservoir iiscible relaive pereabiliy properies Iniial waer sauraion (%) 25 6 Criical oil sauraion (%) 3 24 Maxiu oil sauraion (%) 75 84 Gas relaive pereabiliy a iniial waer sauraion.84258.8 Gas relaive pereabiliy a criical oil sauraion.557569.4 Oil relaive pereabiliy a axiu oil sauraion.834773.8 enioned in he firs sep of he oulined procedure and is ploed versus n p. Figure 4 copares he esiaed average reservoir pressure and siulaed values. I is seen ha he esiaed values show very good ach wih he siulaed poins. 4 7 4 6 6 5 R p (S 3 /S 3 ) 5 4 3 2 R p (S 3 /S 3 ) 4 3 2 5 5 a) b) 5 5 2 4 5. 4 3. R p (S 3 /S 3 ) 4.5 4. 3.5 3. 2.5 2. R p (S 3 /S 3 ) 2.5 2..5..5.5. 2 4 6 8 2 4 6 c) d) Figure 2 Producing gas-oil raio for a) se A and ; b) se A and ; c) se B and ; d) se B and. 8
M. Heidari Sureshjani e al. / A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs 33 2 p/z p versus n p Exrapolaed line 3 25 p/z p versus n p Exrapolaed line 5 2 p/z p (bar) p/z p (bar) 5 5 Esiaed iniial oles in place 5 Esiaed iniial oles in place a).5..5 2. 2.5 n p (kgole) 8 b).5..5 2. 2.5 3. n p (kgole) 8 2 p/z p versus n p Exrapolaed line 3 25 p/z p versus n p Exrapolaed line 5 2 p/z p (bar) p/z p (bar) 5 5 Esiaed iniial oles in place 5 Esiaed iniial oles in place c).5..5 2. 2.5 n p (kgole) 8.5..5 2. 2.5 3. d) n p (kgole) 8 Figure 3 Plo of p/z p evaluaed a he pressures calculaed in he firs sep of procedure versus cuulaive ole producion for a) se A and ; b) se A and ; c) se B and ; d) se B and. TABLE 5 Esiaed G (MMMS 3 ) for synheic exaples Value Presen approach Previous ehod Esiaed Error Esiaed Error 5.555 5.8636 5.55 5.5672.22 6.29 6.669 6.3 6.659 3.56 6.226 6.5773 5.72 6.2994.25 7.448 7.458 5.86 6.6948 4.97 Error = Esiaed value True value / True value Table 5 suarizes he rue values, esiaed values and errors for deerinaion of G using he presen approach and also he previous ehod. As can be seen fro his able, he inroduced errors using he presen approach are higher han hose of he previous ehod. However, hey are ye reasonable for engineering pracices. 4 DISCUSSION The ain advanage of he curren ehod copared o he previous one is is sipliciy and he requireen for iniu inpu daa. Gas producion rae, producing gas-oil raio and PVT inforaion are usually available o reservoir engineers. However, synheic exaples reveal ha he inroduced errors using his ehod are a lile higher han hose of he previous work. In addiion, in he forer work we could be able o deerine a paraeer called b pss which would give us soe addiional inforaion (such as skin) abou he reservoir. I is noed ha he given procedure in his
34 Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Vol. 69 (24), No. 2 2 Siulaed Esiaed 25 Siulaed Esiaed Average reservoir pressure (bar) 5 5 Average reservoir pressure (bar) 2 5 5 a) 5 5 b) 5 5 2 2 Siulaed Esiaed 25 Siulaed Esiaed Average reservoir pressure (bar) 5 5 Average reservoir pressure (bar) 2 5 5 c) 2 4 6 8 d) 2 4 6 8 Figure 4 Average reservoir pressure for a) se A and ; b) se A and ; c) se B and ; d) se B and. Coparison of proposed procedure and nuerical siulaion. sudy is unable o analyze early par of producion daa (when average reservoir pressure is higher han dew pressure) while in he previous work as he pressure response reached he boundary, a plo of noralized wo-phase pseudopressure versus wo-phase aerial balance pseudoie would for a sraigh line and G could be deerined fro he slope of his line. In suary, no one can conclude which ehod is superior o anoher as each of which ay be applicable in differen siuaions. Likewise any oher ehod, he enioned ehod has is liiaions. One liiaion is is inabiliy o analyze he producion daa when average reservoir pressure is considerably higher han dew poin pressure (early par of daa). However, he p/z p daa end o for a sraigh line as he reservoir pressure approaches dew poin pressure and falls below i. In anoher word, we us observe variaion of producing gas-oil raio and his happens when condensae is fored in he bulk of he reservoir. The unusable early daa are disinguished as a curved par in p/z p plos and are ignored. This behavior can be observed in Figure 3. If he producing ie is no long enough o observe a sraigh line, i would be a proble using his ehod. The duraion of his period is long for large reservoirs and for reservoirs wih significan difference beween iniial pressure and dew poin pressure. Forunaely, he dry gas approach can be used for early ie of producion provided ha sandface pressure reains above dew poin pressure. For analyzing producion daa of dry gas reservoirs, a plo of noralized single-phase pseudopressure versus aerial balance pseudoie will for a sraigh line in boundary doinaed flow period and fro he
M. Heidari Sureshjani e al. / A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs 35 ( i - wf )/q (bar.day)/(cp. 3 ).35.3.25.2.5 Calculaed daa True line A his ie p wf reaches p dew Cuulaive gas producion (MMMscf) 4 35 3 25 2 5 5 Well X2 Well X3. 5 5 Maerial balance pseudoie (day) Figure 5 Noralized single-phase pseudopressure versus aerial balance pseudoie. Deviaion occurs fro rue sraigh line as he sandface pressure approaches dew poin pressure and falls below i. 2 2 3 4 Tie (year) Figure 6 Cuulaive gas producion of wells X2 and X3. 35 Well X2 3 slope of his line G can be esiaed. In a gas-condensae reservoir, such a plo deviaes fro he sraigh line as he sandface pressure reaches dew poin pressure and he deviaion becoes very severe as ie goes by. To observe such behavior, r e has been doubled in case and so ha such behavior can be clearly observed. Deviaion fro he sraigh line can be seen in Figure 5. As shown in his figure, he dry gas approach works bes in he region where sandface pressure is sill above dew poin pressure. For reservoirs wih saller r e, his region ay be very sall and soeies unrecognizable. We conclude ha in he early par (for ies when p wf > p dew ) of he regions where he proposed siple approach is unusable, he dry gas approach ay be applicable. In he period when p wf is below p dew and reservoir pressure is sill above p dew, neiher dry gas approach nor he inroduced ehod can be used for analysis of producion daa in gas-condensae reservoirs. 5 APPLICATION TO A FIELD EXAMPLE To deonsrae he applicabiliy of he ehod, we have analyzed he producion daa of gas-condensae field X. Several wells have been drilled in his field bu here were only wo acive wells naed X2 and X3. For soe periods of ie, he wells have been closed following 2 years of producion. Figures 6 and 7 show he cuulaive gas producion and producing gas-oil raio for hese wells. Using he above described procedure, p/z p versus n p is ploed for boh wells and a sraigh line is fied o he obained poins, as indicaed 25 2 5 2 3 4 a) Tie (year) R p (Mscf/bbl) 45 Well X3 4 35 3 25 2 5 2 3 4 b) Tie (year) R p (Mscf/bbl) Figure 7 Producing gas-oil raio of a) well X2; b) well X3.
36 Oil & Gas Science and Technology Rev. IFP Energies nouvelles, Vol. 69 (24), No. 2 55 55 5 Well X2 p/z p versus n p Exrapolaed line 5 45 Well X3 p/z p versus n p Exrapolaed line p/z p (psia) 45 p/z p (psia) 4 35 4 p/z p exrapolaed o n i = 5.5 8 lbole 3 p/z p exrapolaed o n i = 8 8 lbole 35 25 5 5 a) n p (lbole) 7 b) 2 3 4 n p (lbole) 8 Figure 8 Plo of p/z p evaluaed a he pressures calculaed in he firs sep of procedure versus cuulaive ole producion for a) well X2, b) well X3. in Figure 8. I should be noiced ha he early fla par of daa in Figure 8b should be ignored in sraigh line fiing. Alhough producing gas-oil raio daa are soewha scaered, we sill can deec a general increasing rend. Acually we should noice ha producion daa are low qualiy, noisy and unconrolled daa which are gahered over he years. Therefore, preliinary reaens and daa viabiliy us be perfored before analysis. A good discussion abou such asks has been perfored by Ilk e al. (2). In he repored producing gas-oil raio daa for his field, we can siply ignore few daa poins which show errible deviaion fro he ajoriy of he daa. Eliinaing such daa causes exrapolaed lines in Figure 8 o be less hazardous han wha appears a he firs look. For line fiing we have disregarded soe of he daa bu here in he figures all daa poins are shown. Afer eliinaing such daa, we have deerined wo sraigh lines which presen lower bound and upper bound for esiaing gas in place. In anoher word, we are dealing wih a region enclosed beween hese lines raher han a unique line. Then, we considered a line which is exacly in he cener of he deerined lower and upper bound lines and his is he line ha we finally choose o deerine gas in place, as ploed in Figure 8. The obained gas in place values for drainage volues of wells are G X2 = 28 MMMscf and G X3 = 32 MMMscf. The oal gas in place of he field is he suaion of hese wo values which is G = 5 MMMscf. The calculaed G wih he use of volueric ehod for his field is known o be G = 568.88 MMMscf which is in good agreeen wih he esiaed value using he enioned procedure. Engineering ehods for esiaing reservoir paraeers always have soe degree of uncerainy and he proposed ehod here is no differen. Acually no one can clai ha any specific ehod gives he exac answer. Tha is why reservoir engineers should no rely only on one ehod and oher sources of inforaion us be eployed along wih he used analysis ehod. Since he size of he sudied reservoir is raher sall and he wells have produced for a long ie, we have assued ha he drainage volues of he wells cover he enire reservoir pore volue conaining hydrocarbon. In realiy, he wells ay inerfere and no-flow boundaries igh be displaced. However, lieraure reveals Average pressure (psia) 6 55 5 45 4 Drainage volue of well X2 Drainage volue of well X3 Reservoir 2 3 4 Tie (year) Figure 9 Average pressure for drainage volue of well X2, X3 and enire reservoir.
M. Heidari Sureshjani e al. / A Siple Approach o Dynaic Maerial Balance for Gas-Condensae Reservoirs 37 ha he assupion of considering fixed no-flow boundaries works well in any cases and i is he basis of any analyical ehods which are already in use for producion analysis. Using such assupion, we can siply add gas in place inside drainage volue of each well o obain oal gas in place. The agreeen beween he obained gas in place and ha of he voluerically calculaed one confirs he validiy of his assupion. Figure 9 shows he calculaed average pressure for drainage volues of wells X2 and X3 and reservoir as well. To obain average pressure of he reservoir, we used a siple weighing using he esiaed gas in place and average pressures for drainage volues of wells X2 and X3. CONCLUSIONS A siple ehod was presened o deerine original gas in place and average reservoir pressure in gas-condensae reservoirs. The ehod uses flowing well daa (gas producion rae and producing gas-oil raio) and here is no need o shu-in he well o deerine average reservoir pressure. I provides a pracical engineering ool for indusry sudies as i requires daa which are generally available in noral producion operaions. The ehod was used o analyze synheic producion daa and i was observed ha he inroduced errors were reasonable. I was also observed ha he early producion daa canno be analyzed using he proposed ehod bu dry gas approach works well for analysis of early par of such daa. The inroduced ehod was furher applied o a real gas-condensae field exaple. The obained gas in place using he enioned procedure was in agreeen wih he voluerically calculaed value for his field. REFERENCES Blasingae T.A., Lee W.J. (986) Variable-Rae Reservoir Liis Tesing, SPE paper 528, presened a he Perian Basin Oil and Gas Recovery Conference, Midland, TX, 3-4 March. Fevang Ø., Whison C.H. (995) Modeling Gas-Condensae Well Deliverabiliy, SPE 377, Annual Technical Conference and Exhibiion, Dallas, 22-25 Ocober. Ilk D., Anderson D.M., Sos G.W.J., Maar L., Blasingae T.A. (2) Producion-Daa Analysis-Challenges, Pifalls, Diagnosics, SPE Reserv. Evalu. Eng. 3, 3, 538-552. Hagoor J. (988) Fundaenals of Gas Reservoir Engineering, Elsevier, Aserda. Heidari Sureshjani M., Gerai S. (2) A New Model for Modern Producion Decline Analysis of Gas-condensae Reservoirs, J. Can. Perol. Technol. 5, 7/8, 4-23. Maar L., McNeil R. (998) The Flowing Gas Maerial Balance, J. Can. Perol. Technol. 37, 2, 52-55. Maar L., Anderson D. (25) Dynaic Maerial Balance (Oil or Gas-in-place wihou shu-ins), Paper Peroleu Sociey 25-3, presened a he Peroleu Sociey s 6h Canadian Inernaional Peroleu Conference, Calgary, Albera, Canada, 7-9 June. Mo R. (23) Engineering Calculaions of Gas-Condensae-Well Produciviy, SPE Reserv. Eval. Eng. 6, 5, 298-36. Palacio J.C., Blasingae T.A. (993) Decline Curves Analysis Using Type Curves: Analysis of Gas Well Producion Daa, SPE 2599, presened a he 993 SPE Rocky Mounain Regional/Low Pereabiliy Reservoirs Syposiu, Denver, CO, 2-4 April. Vo D.T., Jones J.R., Caacho-V R.G., Raghavan R. (99) A Unified Treaen of Maerial Balance Copuaions, SPE 2567, CIM/SPE Inernaional Technical Meeing, Calgary, Canada -3 June. Final anuscrip received in February 22 Published online in January 23 Copyrigh 23 IFP Energies nouvelles Perission o ake digial or hard copies of par or all of his work for personal or classroo use is graned wihou fee provided ha copies are no ade or disribued for profi or coercial advanage and ha copies bear his noice and he full ciaion on he firs page. Copyrighs for coponens of his work owned by ohers han IFP Energies nouvelles us be honored. Absracing wih credi is peried. To copy oherwise, o republish, o pos on servers, or o redisribue o liss, requires prior specific perission and/or a fee: Reques perission fro Inforaion Mission, IFP Energies nouvelles, fax. +33 47 52 7 96, or revueogs@ifpen.fr.