Diffusivity Equations (Governing Flow Relations)
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1 Diffusiviy Equains (Gvernin Fl Relains) Thmas A. lasiname, Ph.D., P.E. Dearmen f Perleum Enineerin Texas A&M Universiy Cllee Sain, TX (USA) blasiname@amu.edu Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 1
2 Diffusiviy Equains (Gvernin Fl Relains) Diffusiviy Equains: "la Oil" (> b ) "Sluin-Gas Drive" (valid fr all, referened fr < b ) "Dry Gas" (> d ) Mulihase Fl Orienain Diffusiviy Equains (il, as, mulihase fl) Slide
3 Diffusiviy Equains la Oil (> b ) Diffusiviy Equains fr a la Oil: Slihly Cmressible Liquid: (General Frm) φ ( ) + Slihly Cmressible Liquid: (Small and frm) φ Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 3
4 Diffusiviy Equains la Oil and vs. ehavir f he and variables as funins f ressure fr an examle bla il ase. Ne behavir fr > b bh variables shuld be nsidered be "arximaely nsan" fr he sae f develin fl relains. Suh an assumin (i.e., and nsan) is n an abslue requiremen, bu his assumin is fundamenal fr he develmen f "liquid" fl sluins in reservir enineerin. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 4
5 Diffusiviy Equains la Oil vs. ehavir f he variable as a funin f ressure examle bla il ase. Ne he "jum" a b, his behavir is due he as exansin a he bubblein. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 5
6 Diffusiviy Equains Sluin-Gas Drive (< b ) Diffusiviy Equains fr Sluin-Gas Drive: (< b ) Oil Pseudressure Frm: (Auns fr and ) φ Oil Pseudressure Definiin: ( n is any referene ressure) 1 [ ] d n base Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 6
7 Diffusiviy Equain Sluin-Gas Drive 1/( ) vs. ( b 5000 sia, T175 De F) 1 [ ] d n base "Sluin-Gas Drive" Pseudressure Cndiin: (1/( ) vs. ) Cne: IF 1/( ) nsan, THEN il seudressure NOT required. 1/( ) is NEVER "nsan" bu des n vary sinifianly ih. Oil seudressure alulain sraihfrard, bu rbably n neessary. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 7
8 Diffusiviy Equains Sluin-Gas Drive ( ) vs. ( b 5000 sia, T175 De F) a, 1 n 0 ( ) [ ] d ( ) "Sluin-Gas Drive" Pseudressure Cndiin: (( ) vs. ) Cne: IF ( ) nsan, THEN il seudime NOT required. ( ) is NEVER "nsan" UT, il seudime uld be very diffiul. Oher evidene suess ha inrin ( ) variane is aeable. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 8
9 Diffusiviy Equains Sluin-Gas Drive Mbiliy/Cmressibiliy (Camah) Camah-V., R.G. and Rahavan, R.: "undary- Dminaed Fl in Sluin-Gas-Drive Reservirs," SPERE (Nvember 1989) "Sluin-Gas Drive" ehavir: (( /λ ) vs. ime) Observain: ( /λ ) nsan fr > b and laer, fr < b. f nsan bu rbably valid fr any rduin/ressure senari. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 9
10 Diffusiviy Equains Hisrial Ne Eviner-Musa Cne (194) Why n use liquid seudressure? Eviner and Musa (194) ne ha: The indefinie ineral may be evaluaed, as as dne fr he -hase sysem, and he ressure disribuin may be deermined. Hever, i ill be suffiien fr he alulain f he rduiviy far nsider nly he limiin frm... (i.e., he nsan rery liquid relain). Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 10
11 Slide 11 Orienain Diffusiviy Equains (il, as, mulihase fl) Diffusiviy Equains Dry Gas Relains (ase Relains) Diffusiviy Equains fr a "Dry Gas:" General Frm fr Gas: Diffusiviy Relains: Pseudressure/Time: Pseudressure/Pseudime: Definiins: Pseudressure: Pseudime: φ z z φ ] [ a n ) ( φ d z z base n [ ] d n a ) ( ) ( 1 0
12 Diffusiviy Equains Dry Gas Pseudime Cndiin ( vs., T00 De F) a n 0 1 ( ) [ ] d ( ) "Dry Gas" Pseudime Cndiin: ( vs. ) Cne: IF nsan, THEN seudime NOT required. is NEVER nsan seudime is alays required (fr liquid eq.). Hever, an enerae numerial sluin fr as ases (n seudime). Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 1
13 Slide 13 Orienain Diffusiviy Equains (il, as, mulihase fl) Diffusiviy Equains Dry Gas Relains Diffusiviy Equains fr a "Dry Gas:" Relains Frm Full Frmulain: Frm Arximain: ) ( ) ( )] [ln( ) ( z φ ) ( ) ( φ
14 Diffusiviy Equains Dry Gas Cndiin ( z vs., T00 De F) z n base z d "Dry Gas" PVT Preries: ( z vs. ) Cne: IF ( z) nsan, THEN -variable valid. ( z) nsan fr <000 sia. Even ih numerial sluins, frmulain uld n be arriae. Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 14
15 Slide 15 Orienain Diffusiviy Equains (il, as, mulihase fl) Diffusiviy Equains Dry Gas Relains Diffusiviy Equains fr a "Dry Gas:" Relains Frm Full Frmulain: Frm Arximain: z φ ) ( ln φ
16 Diffusiviy Equains Dry Gas Cndiin (/( z) vs., T00 De F) z n base z d "Dry Gas" PVT Preries: (/( z) vs. ) Cne: IF /( z) nsan, THEN -variable is valid. /( z) is NEVER nsan seudressure required (fr liquid eq.). frmulain is never arriae (even if eneraed numerially). Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 16
17 Slide 17 Orienain Diffusiviy Equains (il, as, mulihase fl) Diffusiviy Equains Mulihase Case -Frm Relains (Perrine-Marin) Gas Equain: Oil Equain: Waer Equain: Mulihase Equain: s s s s S R S R S R R φ S φ S φ λ φ Cmressibiliy Terms: d dr d d s + 1 d dr d d s + 1 d d 1 f S S S λ + +
18 Diffusiviy Equains (Gvernin Fl Relains) End f Mdule Thmas A. lasiname, Ph.D., P.E. Dearmen f Perleum Enineerin Texas A&M Universiy Cllee Sain, TX (USA) blasiname@amu.edu Orienain Diffusiviy Equains (il, as, mulihase fl) Slide 18
Tom BLASINGAME Texas A&M U. Slide 1
Fundamenal Fl Lecure 7 The Diffusiviy Equain fr Mulihase Fl Slide 1 Fundamenal Fl Lecure 7 The Diffusiviy Equain fr Mulihase Fl Slide Fundamenal Fl Lecure 7 The Diffusiviy Equain fr Mulihase Fl Slide 3
Diffusivity Equation
Perleum Enineerin 34 Reservir Perfrmane Diffusiviy Equain 13 February 008 Thmas A. lasiname, Ph.D., P.E. Dilhan Il Dearmen f Perleum Enineerin Dearmen f Perleum Enineerin Texas A&M Universiy Texas A&M
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