Pseudosteady-State Flow Relations for a Radial System from Department of Petroleum Engineering Course Notes (1997)

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Transcription:

Pseudoseady-Sae Flow Relaions fo a Radial Sysem fom Deamen of Peoleum Engineeing Couse Noes (1997)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

(Deivaion of he Pseudoseady-Sae Flow Relaions fo a Radial Sysem)

Illusaions of Pseudoseady-Sae Pefomance in Radial Flow Sysems fom Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady-Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986)

(Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady-Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986))

(Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady-Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986))

(Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady-Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986))

(Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady-Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986))

Pessue Tends fom Deamen of Peoleum Engineeing Couse Noes (01)

Pessue Disibuions: Soluions Seady-Sae Soluion: w e All elaions given in FIELD unis. q 141. scb ln( / w ) kh q 141. scb ln( e / ) kh [ wf fom] [ e fom] Radius of Invesigaion: Full Soluion: (q sc =consan) D 1 141. kh ( qb i ) inv -.434x10 k c 1 E 1 4 D D 1 E 1 4 ed D D ed ex 4 ed D D ed 1 4 ex 4 ed D (Vaious Noes)

Pessue Disibuions: Tansien Flow Pessue, sia 05 000 1975 1950 195 1900 1875 1850 185 Radial Pessue Disibuion (Lee ex Fig. 1.7) Pessue Dawdown and Buildu Cases E1(x) Soluion = 1000 h i = 000 sia 0.1 h 1 h 10 h 100 h 1000 h = 100 h = 10 h = 1 h = 0.1 h = 0.1 h 1 h 10 h 100 h 1000 h e = 3000 f Legend: D_DD(, _ 1Em1 h) D_DD(, _ 1E0 h) D_DD(, _ 1E1 h) D_DD(, _ 1E h) D_DD(, _ 1E3 h) D_BU(,_+_ D_ 1Em1 h) D_BU(,_+_ D_ 1E0 h) D_BU(,_+_ D_ 1E1 h) D_BU(,_+_ D_ 1E h) D_BU(,_+_ D_ 1E3 h) 1800 1775 1.E-01 1.E+00 1.E+01 1.E+0 1.E+03 1.E+04 Radial Disance, f Pessue Disibuions fo Tansien Radial Flow Noe he effec of he dawdown. Noe ha he buildu essue ends eace las dawdown end. Recall ha all measuemens ae a he wellboe, we canno "see" in he esevoi ou analyses ae infeed fom wellboe measuemens. (Vaious Noes)

Pessue Disibuions: Pseudoseady-Sae The hysical conce of he PSEUDOSTEADY-STATE FLOW condiion is defined as he condiion whee he essue a all oins in he esevoi changes a he same ae. Mahemaically, his condiion is given by: d [ (, )] consan d (Vaious Noes)

Pessue Disibuions: Pseudoseady-Sae Conce: (essue changes a he same ae a all oins in he esevoi) d d Resevoi Pessue Schemaic: consan (Vaious Noes)

Pseudoseady-Sae Flow: Summay of Relaions ( - wf ) Flow Relaions: (Cicula Resevoi) ( - wf ) Flow Relaions: ( = 0.57716 Eule's consan) Time-Deenden Pseudoseady-Sae Flow Relaions: ) ( ) ( 1 ln ) ( 141. s kh qb w e w w w e e wf Fomulaio n) (Geneal 1 4 ln 1 141. Resevoi) (Cicula 4 3 ln 141. s C A e kh qb s kh qb A w wf w e wf c V qb s kh qb c V qb kh qb w e i wf w e w e i 5.615 4 3 ln 141. 5.615 4 3 ) ( ) ( 1 ln 141. (Vaious Noes)

Fom: Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady- Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986). Pseudoseady-Sae Flow: Illusaive Behavio k inv.434x10 - c Figue : Resevoi Pessue Disibuion Consan Rae Tansien Flow Dawdown. (Vaious Noes)

Fom: Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady- Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986). Pseudoseady-Sae Flow: Illusaive Behavio - k inv.434x10 c Figue 7: Resevoi Pessue Disibuion Consan Wellboe Pessue Tansien Flow Dawdown. (Vaious Noes)

Fom: Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady- Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986). Pseudoseady-Sae Flow: Illusaive Behavio - k inv.434x10 c Figue 5: Resevoi Pessue Disibuion Consan Rae Pos- Tansien Flow Dawdown, Homogeneous Resevois. (Vaious Noes)

Fom: Blasingame, T.A.: Vaiable-Rae Analysis: Tansien and Pseudoseady- Sae Mehods of Ineeaion and Alicaion, M.S. Thesis, Texas A&M Univesiy (1986). Pseudoseady-Sae Flow: Illusaive Behavio k inv.434x10 - c Figue 57: Resevoi Pessue Disibuion Consan Wellboe Pessue Pos-Tansien Flow Dawdown, Homogeneous Resevois. (Vaious Noes)

Resevoi Pessue Tends: Quesions o Conside Q1. Why sudy "esevoi essue ends?" A1. We can no measue essue in he esevoi only a he wellboe (o sandface). In ode o esimae he behavio in he esevoi, we mus use "model-based" essue disibuions. Q. Isn' he use of a simle model oo limiing? A. Acually, no. Simle models ae exemely consisen, and as such, even when "wong," he "end" behavio is yically quie ee-senaive. Q3. Wha is he "adius of invesigaion?" A3. Fo he infinie-acing adial flow case, he adius of invesigaion is he oin in he esevoi whee he logaihm of adius equaion (saigh line) inesecs he iniial esevoi essue. I is a ficiious oin, bu i eesens he "heoeical" locaion of he fon of he essue disibuion fon. inv.434 x 10 k c (Vaious Noes)

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