Chapter 2. Volumetric Gas Reservoir Engineering

Transcription

1 Chater 2 Volumetrc as Reservor ngneerng

2 References (B) Dake, L.P., Fundamentals of Reservor ngneerng, revsed edton, lsever Scentfc B.V., Amsterdam, the Netherlands, 200. (C) Craft, B.C., and Hakns, M.F., Revsed by Terry, R.., Aled Petroleum Reservor ngneerng, Second edton., Prentce Hall, ngleood Clffs, Ne Jersey, 99. (A) Abdus Satter, hulam M. Iqbal, James L. Buchalter, Practcal nhanced Reservor ngneerng: Asssted th Smulaton Softare, PennWell, Tulsa, OK

3 as PVT as s one of a fe substances hose state, as defned by ressure, volume and temerature (PVT) One other such substance s saturated steam. 3

4 The equaton of state for gas Classcal deal gas la Classcal non-deal gas la Cubc quatons of State van der Waals equaton of state Redlch-Kong equaton of state Soave modfcaton of Redlch-Kong Peng-Robnson equaton of state llott, Suresh, Donohue equaton of state 4

5 The equaton of state for an deal gas V nrt (.3) (Feld unts used n the ndustry) [] sa; V[] ft 3 ; T [] O R absolute temerature n [] lb m moles; nthe number of lb m moles, one lb m mole s the molecular eght of the gas exressed n ounds. R the unversal gas constant [] sa ft 3 / (lb m mole 0R) q (.3) results from the combned efforts of Boyle, Charles, Avogadro and ay Lussac. 5

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7 Note: In ths text Darcy cm 2 or Darcy 0-8 cm 2 or Darcy 0-2 m 2 2 µm In other book Darcy cm 2 Darcy m 2 Darcy 2 µm

8 Non-deal gas la V nzrt (.5) Where z z-factor gas devaton factor suercomressblty factor comressblty factor V a V z Actual volume of n moles of gas at T and Ideal volume of n moles of gas at T and P P z f ( P, T, comoston) comoston γ g secfc gravty( ar ) 8

9 Determnaton of z-factor There are three ays to determne z-factor : (a)xermental determnaton (b)the z-factor correlaton of standng and katz (c)drect calculaton of z-factor 9

10 (a) xermental determnaton n moles of gas atm; Treservor temerature; > VV 0 VnzRT z for atm >4.7 V 0 nrt n moles of gas >atm; Treservor temerature; > VV VnzRT Vz(4.7 V 0 ) V z z 4.7V By varyng and measurng V, the sothermal z() functon can readly be obtaned. 0 sc sc V T 0 V zt z V V sc 0 0

11 Requrement: (b)the z-factor correlaton of standng and katz Knoledge of gas comoston or gas gravty Naturally occurrng hydrocarbons: rmarly araffn seres C n H 2n+2 Non-hydrocarbon murtes: CO 2, N 2 and H 2 S as reservor: lghter members of the araffn seres, C and C 2 > 90% of the volume.

12 The Standng-Katz Correlaton knong as comoston (n ) Crtcal ressure (P c ) Crtcal temerature (T c ) of each comonent ( Table (.) and P.6 ) Pseudo crtcal ressure (P c ) Pseudo crtcal temerature (T c ) for the mxture P T c c Pseudo reduced ressure (P r ) Pseudo reduced temerature (T r ) Fg..6;.7 z-factor n n T P c c P r T T T P P c r c const.(isothermal) 2

13 3

14 (b )The z-factor correlaton of standng and katz For the gas comoston s not avalable and the gas gravty (ar) s avalable. The gas gravty (ar) ( γ g ) fg..7, 8 Pseudo crtcal ressure (P c ) Pseudo crtcal temerature (T c ) 4

15 (b )The z-factor correlaton of standng and katz Pseudo reduced ressure (P r ) P r P P c Pseudo reduced temerature (T r ) T T T r c const.(isothermal) Fg.6.7 z-factor The above rocedure s valded only f munty (CO 2,N 2 and H 2 S) s less then 5% volume. 5

16 (c) Drect calculaton of z-factor The Hall-Yarborough equatons, develoed usng the Starlng-Carnahan equaton of state, are.2(t ) Prte z (.20) y here P r the seudo reduced ressure 2 t/t r ; T r the seudo reduced temerature ythe reduced densty hch can be obtaned as the P soluton of the equaton as folloed: + (90.7t 242.2t y + y + y ( y) (t ) 2 r te + (4.76t 9.76t t 3 ) y y ( t) 4.58t 3 ) y 0 (.2) 2 Ths non-lnear equaton can be convenently solved for y usng the smle Neton-Rahson teratve technque. 6

17 (c) Drect calculaton of z-factor The stes nvolved n alyng thus are: makng an ntal estmate of y k, here k s an teraton counter (hch n ths case s unty, e.q. y 0.00 substtute ths value n q. (.2);unless the correct value of y has been ntally selected, q. (.2) ll have some small, non-zero value F k. (3) usng the frst order Taylor seres exanson, a better estmate of y can be determned as here y k + y k df F k k dy (.22) df k y + 4y 4y + y 2 3 (29.52t 9.52t + 9.6t y dy ( y) ) ( t) + ( t)(90.7t 242.2t t ) y (.23) (4) teratng, usng eq. (.2) and eq. (.22), untl satsfactory convergence s obtaned(5) substtuton of the correct value of y n eq.(.20)ll gve the z-factor. (5) substtutng the correct value of y n eq.(.20)ll gve the z-factor. 7

18 The equaton of state for real gas The equaton of Van der Waals (for one lb mole of gas a ( + )( V b) RT (.4) 2 V here a and b are deendent on the nature of the gas. The rncal draback n attemtng to use eq. (.4) to descrbe the behavor of real gases encountered n reservors s that the maxmum ressure for hch the equaton s alcable s stll far belo the normal range of reservor ressures 8

19 Peng-Robnson equaton of state here V m s molar volume, here, ω s the acentrc factor of the seces R s the unversal gas constant. In olynomal form: ZPV/(RT) s comressblty factor. 9

20 Alcaton of the real gas equaton of state V nzrt (.5) quaton of state of a real gas Ths s a PVT relatonsh to relate surface to reservor volumes of hydrocarbon. () the gas exanson factor, Vsc volume of n moles of gas at s tan dard condtons V volume of n moles of gas at reservor condtons Real gas equaton for n moles of gas at standard condtons nzsc RTsc scvsc nzsc RT V sc sc sc Real gas equaton for n moles of gas at reservor condtons nzrt V nzrt V > nzsc RTsc Vsc sc nzsc RTsc Tsc 59.6 ρ ( note : zsc > V nzrt surface nzrtsc volume/reservor ztsc zt 4.7 volume [] SCF/ft 3 or STB/bbl [ ] zt ) 20

21 xamle Reservor condton: P2000sa; T80 0 F( )639.60R; z0.865 > surface volume/reservor or SCF/ft 3 or STB/bbl OIP Vφ( S ) 2

22 22

23 23

24 (2) Real gas densty m nm m ρv ρ V V here nmoles; Mmolecular eght) ρ nm nzrt MP zrt ρ gas M z gas gas P RT at any and T For gas For ar ρ ρ gas ar γ g M M gasp ρ gas zgasrt M ar ρ ar z RT M gas gas z z gas ar ar RT RT M M gas ar Z Z gas ar γ g ( M ( M ) Z ) Z gas ar 24

25 (2) Real gas densty γ g ( M ( M ) Z ) Z gas ar At standard condtons z ar z gas ρ gas γ g n general ρ ar γ g 0.6 ~ 0.8 (a) If s knon, then or, γ M gas γ g ρ gas γ g ρ ar g (b) If the gas comoston s knon, then γ g here M gas M M ar gas M gas (.28) ρ gas γ g ρ ar M gas n M ( ρ ) lbm ar sc ft 3 25

26 (3)Isothermal comressblty of a real gas V nzrt V nrtz[ + nrt 2 ] nzrt V nrtz ( note : z z V nzrt 2 + nrt f ( )) z V nzrt ( z z ) V ( z z ) C g V V [ V ( V z z )] C g z z C g snce.24, fg..9 >> z z 26

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28 xercse. - Problem xercse. as ressure gradent n the reservor () Calculate the densty of the gas, at standard condtons, hose comoston s lsted n the table -. (2) hat s the gas ressure gradent n the reservor at 2000sa and 800F(z0.865) 28

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30 30

31 () Molecular eght of the gas M n M. 5 snce gas or from γ g ρ ρ gas ar xercse. -- soluton - M gas γ g ρ gas γ ρ 3 ρ gas ( lbm ft ) VM ρ m V g ar V nzrt nmzrt M zrt ( lbm mzrt ft 3 ) At standard condton ρ PscM z RT ( lbm ft ) gas sc sc 3

32 xercse. -- soluton -2 (2) gas n the reservor condtons V nzrt VM nmzrt mzrt ρ m V M zrt ( lbm ft ) ( ) 32

33 ρgd xercse. -- soluton -3 d ρgdd d dd lbm slug ρg (6.45 )32. 2 ft 3 2 ft 32.2lbm s slug ft ft 2 s lb f 6.45 ft 3 lbf ft ft lb f n ft 2 ft 44n s ft 33

34 as Materal Balance: Recovery Factor Materal balance Producton OIP (IIP) - Unroduced gas (SC) (SC) (SC) Case :no ater nflux (volumetrc deleton reservors) Case 2:ater nflux (ater drve reservors) 34

35 Volumetrc deleton reservors -- No ater nflux nto the reservor from the adjonng aqufer as ntally n lace (IIP) or Intal gas n lace(iip) Orgnal gas n lace (OIP) [] Standard Condton Volume Vφ( s c here ) [ ] Materal Balance (at standard condtons) Producton IIP - Unroduced gas (SC) (SC) (SC) z T SCF [ ] SCF / ft 3 (.33) Where / IIP n reservor volume or reservor volume flled th gas HCPV 35

36 Volumetrc deleton reservors (.34) [ ] sn ft SCF zt ce. : const T T note z z T z zt (.35) z z factor ery re as deleton durng stage any at ery re gas fractonal the here cov cov z z z

37 In q.(.33) HCPV const.? HCPV const. because:. the connate ater n reservor ll exand 2. the gran ressure ncreases as gas (or flud) ressure declnes 37

38 here ~ ) ( ) ( (.3) P d FP d P FP OP + (.36) ) / ( ) ( f dv dv d HCPV d + HCPV n reducton a to leads ater of anson sgn negatve volume ore ntal V volume ater connate ntal V f ex " "

39 39 ( ) d V c dv V V c V V c P V V c f f f f f f f f f f f f ) ( ore vol. P P P P V f

40 V c V dv d c V ( FP) V V d dv d FP FP V f FP FP FP FPgas ressure FP V FP FP FPgas ressure 40

41 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) c f c ntal t c f c ntal ntal t c f c c ntal t ntal c f c c c c c c c c c f f f S c S c S c S c S c S S c d S c d S S c d S S S S HCPV S PV V S S HCPV PV V Snce d V c d V c HCPV d d

42 42 ( ) ( ) dfference th comutng S c S c S and s c s c For S c S c S c S c c f c c f c f c c f c.3% ; 0 3 (.33) 6 6

43 /z lot From q. (.35) such as In z (.35) z z z z z v. s Ya+mx y z x lot 0 m /RF.0 z A straght lne n /z v.s lot means that the reservor s a deleton tye a z /z Abandon ressure ab 0 /z 43

44 Water drve reservors If the reducton n reservor ressure leads to an exanson of adjacent aqufer ater, and consequent nflux nto the reservor, the materal balance equaton must then be modfed as: Producton IIP - Unroduced gas (SC) (SC) (SC) - (HCPV-W e ) Or - (/ -W e ) here We the cumulatve amount of ater nflux resultng from the ressure dro. Assumtons: No dfference beteen surface and reservor volumes of ater nflux Neglect the effects of connate ater exanson and ore volume reducton. No ater roducton 44

45 Water drve reservors(th ater roducton) here (We* W )/ reresents the fracton of the ntal hydrocarbon ore volume flooded by ater and consders ater roducton, and s, therefore, alays less then unty. 45 ( ) B W W e (.4) ) ( W B W z z e

46 Water drve reservors (th no ater roducton) snce 46 (.4) W z z e < W e n ater flux reservors > z z Comarng z z n deleton tye reservor

47 Water drve reservors (th no ater roducton) z (.4) z W e In eq.(.4) the follong to arameters to be determned and W e Hstory matchng or aqufer fttng to fnd W e Aqufer model for an aqufer hose dmensons are of the same order of magntude as the reservor tself. W e cw Where Wthe total volume of ater and deends rmary on the geometry of the aqufer. ΔPthe ressure dro at the orgnal reservor aqufer boundary 47

48 Water drve reservors The materal balance n such a case ould be as shon by lot A n fg., hch s not sgnfcantly dfferent from the deleton lne For case B & C n fg.(.30) >Chater 9 48

49 Bruns et. al method Ths method s to estmate IIP n a ater drve reservor From q. (.40) such as e a e e e e e e W or W or W W W W W (.40) ) ( a or e W s lot as functon of Note: / (/z)/( /z )

50 Bruns et. al method ( or a ) s lot as functon of W e The result should be a straght lne, rovded the correct aqufer model has been selected. The ultmate gas recovery deends both on () the nature of the aqufer,and (2) the abandonment ressure. The rncal arameters n gas reservor engneerng: () the IIP (2) the aqufer model (3) abandonment ressure (4) the number of roducng ells and ther mechancal defne 50

51 Hydrocarbon hase behavor 5

52 Hydrocarbon hase behavor 52

53 Hydrocarbon hase behavor C >D > Resdual saturaton (flo ceases) Lqud H.C deosted n the reservor Retrograde lqud Condensate >F Re-vaorzaton of the lqud condensate? NO! Because H.C remanng n the reservor ncrease Comoston of gas reservor changed Phase enveloe shft S drecton Thus, nhbtng re-vaorzaton. Condensate reservor, t. c, roducng Wet gas (at scf) Dry gas njecton untl dry gas break through occurs n the roducng ells Kee above de t. Δ small dslace the et gas 53

54 quvalent gas volume The materal balance equaton of eq(.35) such as z z Assume that a volume of gas n the reservor as roduced as gas at the surface. If, due to surface searaton, small amounts of lqud hydrocarbon are roduced, the cumulatve lqud volume must be converted nto an equvalent gas volume and added to the cumulatve gas roducton to gve the correct value of for use n the materal balance equaton. 54

55 quvalent gas volume If n lb m mole of lqud have been roduced, of molecular eght M, then the total mass of lqud s nm γ ρ o ( lqud volume) here γ 0 ol gravty (ater ) ρ densty of ater (62.43 lb m /ft 3 ) n γ M γ 62.4 M lbm V 3 ft 3 ( ft ) 0 0 oρ Vo 62.4γ 0V0 62.4γ 0V0 n M ( bbls) ft bbl γ 0N n here M nrt γ 0N RT Vsc M sc γ N 5 0 Vsc.33 0 M quvalent gas volume ( lbm / lbm mole) M sc sc N 3 [ ] bbls γ 0N M 4.7 N [ ] bbls 55

56 Condensate Reservor The dry gas materal balance equatons can also be aled to gas condensate reservor, f the sngle hase z-factor s relaced by the,so-called,to hase z-factor. Ths must be exermentally determned n the laboratory by erformng a constant volume deleton exerment. Volume of gas scf, as charge to a PVT cell PP ntal ressure (above de ont) TT r reservor temerature 56

57 Condensate Reservor decreases by thdra gas n stages from the cell, and measure gas Untl the ressure has droed belo the de ont Z 2 hase z (.46) ' ' (.35) z z z ' z The latter exerment, for determnng the sngle hase z-factor, mlctly assumes that a volume of reservor fluds, belo de ont ressure, s roduced n ts entrely to the surface. 57

58 Condensate Reservor In the constant volume deleton exerment, hoever, alloance s made for the fact that some of the flud remans behnd n the reservor as lqud condensate, ths volume beng also recorded as a functon of ressure durng the exerment. As a result, f a gas condensate samle s analyzed usng both exermental technques, the to hase z-factor determned durng the constant volume deleton ll be loer than the sngle hase z- factor. Ths s because the retrograde lqud condensate s not ncluded n the cumulatve gas roducton n equaton(.46), hch s therefore loer than t ould be assumng that all fluds are roduced to the surface, as n the sngle hase exerment. 58

59 Chater 2 Volumetrc as Reservor ngneerng Home ork.0;.; 3.3;

60 油層工程 蘊藏量評估 體積法 物質平衡法 衰減曲線 油層模擬 壓力分析 ( 隨深度變化, 或壓力梯度 ), 例如, 求氣水界面 物質平衡法 井壓測試分析 ( 暫態 ) ( 求 k s re xf 氣水界面 地層異質性 ) Pressure buldu Pressure dradon 水驅計算 (ater drve) 60

61 Flud Pressure Regmes The total ressure at any deth eght of the formaton rock + eght of fluds (ol, gas or ater) [] s/ft * deth(ft) 6

62 Densty of sandstone Flud Pressure Regmes 2.7 gm 2.2lbm ( cm) 3 3 cm 000gm ( ft) 3 68 lbm ft slug 32.7lbm 5.22 slug ft 3 62

63 Pressure gradent for sandstone Pressure gradent for sandstone D ρ gd ρ g lbf ft 3 2 lbf ft lbf ( s / ft) ft ft 44n n ft 63

64 Overburden ressure Overburden ressure (OP) Flud ressure (FP) + ran or matrx ressure (P) OPFP + P In non-solated reservor PW (ellbore ressure) FP In solated reservor PW (ellbore ressure) FP + P here P <P 64

65 Normal hydrostatc ressure In a erfectly normal case, the ater ressure at any deth Assume :() Contnuty of ater ressure to the surface (2) Salnty of ater does not vary th deth. [] sa P ω dp ( ) ater D dd s/ft for ure ater dp ( ) ater dd dp s/ft for salne ater ( ) ater > dd 65

66 dp dd Abnormal hydrostatc ressure ( No contnuty of ater to the surface) Pω ( ) ater D C [] sa Normal hydrostatc ressure c 0 Abnormal (hydrostatc) ressure c > 0 Overressure (Abnormal hgh ressure) c < 0 Underressure (Abnormal lo ressure) 66

67 Condtons causng abnormal flud ressures Condtons causng abnormal flud ressures n enclosed ater bearng sands nclude» Temerature change ΔT + ΔP +25 s n a sealed fresh ater system» eologcal changes ulftng; surface eroson» Osmoss beteen aters havng dfferent salnty, the sealng shale actng as the sem ermeable membrane n ths onc exchange; f the ater thn the seal s more salne than the surroundng ater the osmoss ll cause the abnormal hgh ressure and vce versa. 67

68 Are the ater bearng sands abnormally ressured? If so, hat effect does ths have on the extent of any hydrocarbon accumulatons? 68

69 Hydrocarbon ressure regmes In hydrocarbon ressure regmes dp ( ) ater dd s/ft dp ( ) ol dd 0.45 s/ft dp ( ) gas dd 0.35 s/ft

70 Pressure Kck Ol and Water 5000 P 2265 P o 235 P(sa) ol 5200 P 2355 P o 2385 ater OWC D5500ft P P o 2490 P 2535 Deth(ft) P P P P P P P P o o o 0.45 * D + 5 [ ] sa n ater zone ( at D 5600 ft ) 0.45 * sa ( at D 5500 ft or at OWC ) 0.45 * ( at D 5500 ft or at OWC ) * D + C o or C o * 5500 P o 0.35 * D n ol zone ( at D 5200 ft ) 0.35 * sa ( at D 5200 ft ) 0.45 * sa ( at D 5000 ft ) 0.35 * sa ( at D 5000 ft ) 0.45 * sa sa 70

71 ressure kck-gas and ater 5000 P 2265 P g 2450 P(sa) as 5200 P 2355 P g 2466 D5500ft WC P P g 2490 P 2535 ater Deth(ft) P 0.45* D + 5 n ater zone P ( at P ( at P ( at g P ( at g P ( at P ( at g P ( at D 5600 ft) 2535sa D 5500 ft WC) 2490 sa D 5500 ft WC) 2490 or C P g g 0.08* D + C * * D n gas zone D 5000 ft) 0.08* s D 5200 ft) 2355sa D 5000 ft) 0.08* sa D 5000 ft) 2265 sa g 7

72 ressure kck-gas, ol and ater D5300ft D5500ft OC ol OWC as P 2265 P g 2396 P 2355 P g 242 P 2400 P o P g 2420 P 2445 P o 2455 P P o 2490 P 2535 P(sa) ater Deth(ft) ( at ( at D 5500 ft OWC) 2490 sa ( at D 5500 ft OWC) 2490 sa o 0.45* D + 5 n ater zone o 0.35* D n ol zone ( at o ( at ( at ( at ( at ( at ( at D 5600 ft) 2535s or 0.35* D + C C o 565 D 5400 ft) 0.35* sa ( at D 5400 ft) 0.45* sa ( at D 5300 ft OC) 0.35* sa o g o g g D 5300 ft OC) 0.45* sa D 5300 ft OC) ( at or 0.08* D D 5200 ft) 0.08* sa D 5200 ft) 2355sa D 5000 ft) 0.08* sa D 5000 ft) 2265 sa g C g o D 5300 ft OC) 2420 sa * D + C g 72

73 Pressure Kck 5000x Ps 2369Ps P PgP0 2385Ps OC OWC OIL AS OC (5200ft) OWC (5500ft) PgP2490Ps Water D 5500x Assumes a normal hydrostatc ressure regme Pω 0.45 D + 5 In ater zone at 5000 ft Pω(at5000) sa at OWC (5500 ft) Pω(at OWC) sa 73

74 Pressure Kck 5000x Ps 2369Ps P PgP0 2385Ps OC OWC OIL AS OC (5200ft) OWC (5500ft) PgP2490Ps Water D 5500x In ol zone Po 0.35 x D + C at D 5500 ft, Po 2490 s C sa Po 0.35 D at OC (5200 ft) Po (at OC) sa 74

75 Pressure Kck In gas zone Pg 0.08 D (sa) at 5000 ft Pg sa 75

76 Pressure Kck D 2265Psa hydrostatc ressure P P0P 2490Psa OIL Water AS OWC OC D 2450Psa P as ressure gradent PgP2490Psa Water AS WC In gas zone Pg 0.08 D + C At D 5500 ft, Pg Pω 2490 sa C C 2050 sa Pg 0.08 D At D 5000 ft Pg 2450 sa 76

77 WC error from ressure measurement Pressure 2500 sa Pressure 2450 sa at D 5000 ft at D 5000 ft n gas-ater reservor n gas-ater reservor WC? WC? Sol. Sol. Pg 0.08 D + C Pg 0.08 D + C C C sa 2050 sa Pg 0.08 D Pg 0.08 D Water ressure Pω 0.45 D + 5 Water ressure Pω 0.45 D + 5 At WC Pg Pω At WC Pg Pω 0.08 D D D D + 5 D 5635 ft (WC) D 5500 ft (WC) 77

78 Results from rrors n WC or OC or OWC WC or OC or OWC locaton affectng volume of hydrocarbon OOIP affectng OOIP or OIP affectng develoment lans 78