Production Analysis Reserves Estimation in Unconventional Reservoirs New Rate-Time Relations

Transcription

1 Naural Gas Engineering Producion Analysis Reserves Esimaion in Unconvenional Reservoirs New Rae-Time Relaions T.A. Blasingame, Texas A&M U. Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX Slide 1

2 SPE Exponenial vs. Hyperbolic Decline in Tigh Gas Sands Undersanding he Origin and Implicaions for Reserve Esimaes Using Arps' Decline Curves D. Ilk, Texas A&M Universiy A.D. Perego, Anadarko Peroleum Corp. J.A. Rushing, Anadarko Peroleum Corp. T.A. Blasingame, Texas A&M Universiy Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX Slide 2

3 SPE : Inadequacy of Arps' Rae Relaions ASSUMPTION: The Arps decline parameer, b, defines he decline behavior... REALITY: Difficul o idenify he correc b-parameer during he early decline period grealy impacs reserve esimaes. SPE (2008) Exponenial vs. Hyperbolic Decline in Tigh Gas Sands Undersanding he Origin and Implicaions for Reserve Esimaes Using Arps' Decline Curves. D. Ilk, Texas A&M U., J.A. Rushing and A.D. Perego, Anadarko Peroleum, and T.A. Blasingame, Texas A&M U. a. (Semilog plo) Producion forecas of a igh gas well. b. (Log-log plo) Producion forecas of a igh gas well. Slide 3

4 SPE : Definiions of Rae Funcions Rae Funcion Definiions: Loss Raio: 1 q D dq/ d Derivaive of Loss Raio: b d d 1 D d d Exponenial and Hyperbolic Rae Relaions: D con Cause and Effec: q i q dq/ d i Hyperbolic relaion is mis-applied o ransien daa. Wha is he "characerisic behavior" of he D and b-parameers? Evaluae coninuously using daa. or or D b con q dq dq d dq q 1 D (Exponenial Decline) (Hyperbolic Decline) q exp[ D ]; or b q [1 bd ] i i (1/ b) Slide 4

5 SPE : "Power-Law Exponenial" Rae Resul Observed Behavior of he "Decline" Parameer [D()]: D dq 1 n D ndˆ (1 ) i q d D A B Solving for Flowrae [q()] Using he D() Relaion: q qˆ i exp[ D Dˆ i n ] Solving for he "Hyperbolic" Parameer [b()]: b ndˆ i (1 n) n [ ndˆ i D (1 n) ] 2 Slide 5

6 SPE : q-d-b Plo Small WF Tigh Gas Well Discussion: Small "Waerfrac" Gas Well Liquid loading effecs are obvious in he laer porion of he flowrae daa. The onse of he boundary-dominaed flow regime is observed. We observe a very good mach of he flowrae daa using D =0. Slide 6

7 SPE : q-d-b Plo Large WF Tigh Gas Well Discussion: Large "Waerfrac" Gas Well Erraic rae behavior caused by liquid loading is seen a lae imes. Ousanding maches of he compued D- and b-parameers wih he power-law exponenial model are observed. Slide 7

8 Developmen: Rae Decline Model Type Curves We conver he "power-law exponenial" rae decline model ino a dimensionless form. q qˆ i exp[ D Dˆ i n ] q Dd ~ exp[ D Dd n Dd ] Slide 8

9 Developmen: Rae Decline Model Type Curves We develop ype curves using he dimensionless form of he "power-law exponenial" rae decline model. ~ n qdd exp[ D Dd Dd ] Slide 9

10 Field Example: Tigh Gas Well Discussion: Tigh Gas Well (Bossier) Excellen mach of he daa wih he ype curve for n=0.2 his yields an upper bound for he reserves ( 5.34 BSCF). The lower bound for he reserves (G p,max ) is esimaed by he second ype curve mach. ~ D 10 Slide 10

11 SPE A Simple Mehodology for Direc Esimaion of Gas-in-place and Reserves Using Rae-Time Daa N.L. Johnson, Texas A&M Universiy S.M. Currie, Texas A&M Universiy D. Ilk, Texas A&M Universiy T.A. Blasingame, Texas A&M Universiy Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX nahalie.johnson@pe.amu.edu Slide 11

12 Developmen: q g -G p Relaion Quadraic rae-cumulaive producion relaion can be rearranged o yield a ploing funcion as: q q 1 D gi g D i i Gp Gp 2 G The ploing funcion (q gi -q g )/G p versus G p yields an inercep in he x-axis of 2G i.e., use o esimae G. Slide 12

13 Developmen: q g -G p Relaion Boundary-dominaed flow regime can be idenified using he -parameer hrough he modificaion of he rae-cumulaive producion relaion: G p G 1 q q 1 2 g gi G G p 2 The ploing funcion, versus G p /G has a diagnosic value in esablishing he boundary-dominaed flow regime (i.e., = 2 as q g 0 and G p G). Slide 13

14 Developmen: q g -G p Relaion The ploing funcions q g /q gi versus G p /G and q g versus G p are used in conjuncion wih he previous ploing funcions o yield he bes esimae for G. q gi, D i, G parameers are calibraed using he ploing funcions. We ierae on all plos unil he bes mach is obained. Slide 14

15 Field Example: Tigh Gas Well a. Ploing Funcion 1: (Tigh Gas Well) (q gi -q g )/G p vs G p Plo (Caresian scale). b. Ploing Funcion 2: (Tigh Gas Well) "" Diagnosic Plo reverse soluion for he -parameer (Caresian scale). c. Ploing Funcion 3: (Tigh Gas Well) Model Validaion Plo q g /q gi versus G p /G (Caresian scale). d. Ploing Funcion 4: (Tigh Gas Well) Model Validaion Plo q g (daa and model) versus G p (log-log forma). Slide 15

16 SPE Decline Curve Analysis for HP/HT Gas Wells: Theory and Applicaions D. Ilk, Texas A&M Universiy J.A. Rushing, Anadarko Peroleum Corp. T.A. Blasingame, Texas A&M Universiy Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX Slide 16

17 Orienaion: Rae-Time Relaion From: Knowles R.S Developmen and Verificaion of New Semi-Analyical Mehods for he Analysis and Predicion of Gas Well Performance. M.S Thesis, Texas A&M Universiy, College Saion, Texas. Ansah, J., Knowles, R.S., and Blasingame, T.A A Semi-Analyic (p/z) Rae- Time Relaion for he Analysis andpredicion of Gas Well Performance. SPEREE. 3 (6): Rae-Time Relaion: Discussion: Rae-Time Gas Flow Relaion (Knowles e al.) Basis is he linearizaion of he nonlinear " g c g " erm (Ansah, e al.). D-funcion and b-funcion are formulaed using he definiions for lossraio and he derivaive of he loss-raio. q D Dd D ((1 p wd wd 4p 2 wd ) (1 p exp[ p wd Dimensionless D-funcion (D D ): 1 dq D Dd D qdd ddd pwd(1 pwd (1 ( p 1 (1 p wd wd Dd )exp[ p ] wd pwd)exp[ p )exp[ p wd wd Dd Dd ]) Dd ]) 2 ["Loss-Raio"] b-funcion (b): ["Derivaive of Loss-Raio"] b d d Dd wd qdd ( dqdd/ ddd ) 2exp[ pwd b (1 p (1 p Dd wd ] (1 p )exp[ p 2 wd wd ) Dd ]) 2 ]) Slide 17

18 Orienaion: Rae-Cumulaive Producion Relaion From: Knowles R.S Developmen and Verificaion of New Semi-Analyical Mehods for he Analysis and Predicion of Gas Well Performance. M.S Thesis, Texas A&M Universiy, College Saion, Texas. Ansah, J., Knowles, R.S., and Blasingame, T.A A Semi-Analyic (p/z) Rae- Time Relaion for he Analysis andpredicion of Gas Well Performance. SPEREE. 3 (6): Rae-Cumulaive Producion Relaion: 2 1 GpD G 2 pd Dimensionless D-funcion (D D ): dqdd D dgpd ["Loss-Raio"] b-funcion (b): ["Derivaive of Loss-Raio"] Discussion: Rae-Cumulaive Gas Flow Relaion The definiion of he loss-raio can be re-cas in erms of rae and cumula-ive producion. A quadraic relaionship exiss beween rae and cumulaive producion. qdd DD ( 1 GpD) b qdd d 1 dgpd ( dqdd/ dgpd) GpD G pd b 2 2 ( GpD 1) 2 2/ (1 p wd ) Slide 18

19 Orienaion: Analysis Mehodology Discussion: Mehodology The main goal is o mach he daa wih he model using he definiions for he q-d-b funcions during he boundary-dominaed flow regime. b-funcion 0.5 for high drawdown cases (almos consan behavior). Slide 19

20 Field Example: HP/HT Tigh Gas Well p i = psia and T R = 260 o F Field Example: Applicaion of he Mehodology 3.5 years of daily daa are available for a hydraulically fracured well compleed in a HP/HT gas reservoir. Well clean-up effecs, liquid-loading, and operaional changes are observed in he daa rends. The flowrae daa are reviewed prior o analysis; and any erroneous/ redundan daa poins are removed. The half-slope rend is eviden in he rae-inegral derivaive funcion. Slide 20

21 Field Example: HP/HT Tigh Gas Well a. q g versus G p (Caresian plo). b. D-funcion versus (Caresian plo). c. b-funcion versus (Caresian plo). d. q g versus (Semilog plo). e. D-funcion versus (Semilog plo). f. b-funcion versus (Semilog plo). Field Example: Applicaion of he Mehodology For he compuaion of D- and b-parameer daa funcions we remove he oulying daa poins; hen we perform he numerical differeniaion. Our analysis using he proposed semi-analyical relaion provides a gas-in-place esimae of approximaely 8.0 BSCF. Slide 21

22 Field Example: HP/HT Tigh Gas Well Field Example: Applicaion of he Mehodology Reasonable maches of he D-funcion wih he daa using he semianalyical model is achieved (pos-ransien flow only). The maches of he b-funcion daa wih he semi-analyical model are problemaic daa indicae no unique characerisic behavior. Compuaion of he b-parameer daa funcion is severely affeced by facors such as liquid loading. Slide 22

23 Field Example: HP/HT Tigh Gas Well Field Example: Applicaion of he Mehodology We observe a good mach of he flowrae daa wih he model (excep for he early ime daa affeced by "cleanup"). The "power-law exponenial" model yields G p,max 8.0 BSCF. Gas-in-place esimaes are consisen comparing he mehods we used. Slide 23

24 SPE Hybrid Rae-Decline Models for he Analysis of Producion Performance in Unconvenional Reservoirs D. Ilk*, Texas A&M U./DeGolyer and MacNaughon S.M. Currie, Texas A&M U./Devon Energy Corp. D. Symmons, Consulan J.A. Rushing, Apache Corp. T.A. Blasingame, Texas A&M Universiy *DeGolyer and MacNaughon Dallas, TX Slide 24

25 Sreched Exponenial Funcion: Kohlrausch (1854) Observed Behavior of Decline Parameer (D): D dq 1 (1 n) q d ndˆ i Solving for Flowrae: q qˆ i exp[ Dˆ Lieraure: Kohlrausch (1854). Phillips (1996). Kisslinger (1993) Decays in randomly disordered, chaoic, heerogeneous sysems (e.g. relaxaion, afershock decay raes, ec.). i n ] Valkó (2009) q( ) qˆ i exp[ ( / ) Jones (1942) and Arps (1945) q( ) q o n Do exp 100 ( m ] 1 1) m (Sreched Exponenial Funcion) Slide 25

26 Sreched Exponenial Funcion: q( ) q( ) qˆ n i i1 exp[ Dˆ q i i n exp[ a i ] ] (Sreched Exponenial Funcion) Discussion: Sreched Exponenial Funcion Single, double and four exponenials are used o approximae he daa using linear leas squares. Sreched exponenial funcion can be described as a linear superposiion of exponenial decays. Slide 26

27 Rae-Time Equaions: Theoreical Consideraions Rae-Time Relaion: q Dd ((1 p wd 4p 2 wd ) (1 p exp[ p wd wd Dd )exp[ p ] wd Dd Conclusions: Theoreical jusificaion for hyperbolic decline relaion for gas flow? b = 0.5 for high drawdown cases (p wf /p i 0.05). ONLY valid for BOUNDARY- DOMINATED FLOW REGIME. Exponenial decline a very lae imes. ]) 2 (Theoreical Consideraions) Discussion: Rae-Time Gas Flow Relaion (Knowles e al.) Basis is he linearizaion of he nonlinear " g c g " erm (Ansah e al.). D-funcion and b-funcion are formulaed using he definiions for lossraio and he derivaive of he loss-raio. See Ansah e al. (2000), Knowles e al. (1999), and Ilk e al. (2009) for more deails. Slide 27

28 Diagnosics: q,cp -Derivaive ()-Derivaive: Well Tes Analysis (Hosseinpour-Zoonozi e al. 2006) p d ( ) d ln( p) d ln( ) 1 p dp ()-Derivaive: Modificaion for his work (for consan pressure) q, cp ( ) d ln( q) d ln( ) q dq d d ( q-cp -derivaive) Discussion: Srong diagnosic characer of he q,cp -derivaive funcion. Holly Branch igh gas field producion daa exhibi similar characerisic behavior. Early ime daa are affeced by "non-reservoir" effecs. Slide 28

29 Diagnosics: q,cp -Derivaive Shale Gas Field C Shale Gas Field D Shale Gas Field A Shale Gas Field B (q-cp-derivaive) Slide 29

30 Field Example: Mexico Gas Well (Mexico Gas Well) Discussion: Fracured verical gas well wih 43 years of producion. Slide 30

31 Field Example: Mexico Gas Well (Mexico Gas Well) Discussion: Boundary-dominaed flow regime is apparen a lae imes. Slide 31

32 Field Example: Shale Gas Well (Field D) (Shale Gas Well) Discussion: Horizonal well wih muliple fracures wih 340 days of producion. Slide 32

33 Field Example: Shale Gas Well (Field D) (Shale Gas Well) Discussion: Ousanding daa qualiy provides remarkable characer. Slide 33

34 Rae-Time Equaions: Comparison [Knowles A-1] (All Models) Discussion: Rae-Time Models Rae-ime models decrease he uncerainy in reserves esimaes. Slide 34

35 Naural Gas Engineering Producion Analysis Reserves Esimaion in Unconvenional Reservoirs New Rae-Time Relaions (Summary) T.A. Blasingame, Texas A&M U. Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX Slide 35

36 Summary: New rae-ime relaions which uilize power-law, hyperbolic, sreched exponenial and exponenial componens are proposed o model rae-ime behavior. The basis for he proposed relaions is daa characerisics. The proposed rae-ime models are cenered on he sreched exponenial funcion. We include power-law componen for approximaing early-ime behavior and hyperbolic and exponenial componens for represening lae ime behavior. A variey of field examples using producion daa acquired from igh and shale gas reservoir sysems are presened. (Summary) Slide 36

37 Conclusions: Coninuous evaluaion of he D-parameer (based on he definiion of loss-raio) indicaes power-law behavior for almos all analyzed cases in low o ulralow permeabiliy reservoirs. The only excepion is he Mexico well wih more han 40 years of producion daa available where he effecs of boundary-dominaed flow regime are being esablished. The power-law behavior of he D-parameer daa rend yields he sreched exponenial funcion. (Conclusions) Slide 37

38 Conclusions: The sreched exponenial funcion is rigorous and effecive in modeling he behavior of producion daa. Modeling he lae-ime behavior wih differen funcional forms migh reduce he uncerainy associaed wih producion exrapolaion. The compued q,cp -derivaive daa funcions for wells producing in he same field indicaes ha he well compleion and geology are he primary facors affecing well performance for wells in unconvenional reservoirs. (Conclusions) Slide 38

39 Naural Gas Engineering Producion Analysis Reserves Esimaion in Unconvenional Reservoirs New Rae-Time Relaions (End of Lecure) T.A. Blasingame, Texas A&M U. Deparmen of Peroleum Engineering Texas A&M Universiy College Saion, TX Slide 39