Tom BLASINGAME Texas A&M U. Slide 1
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1 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Slide 1
2 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Slide
3 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow Relations fo a Radial System fom Deatment of Petoleum Engineeing Couse Notes (1997) Slide 3
4 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 4
5 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 5
6 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 6
7 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 7
8 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 8
9 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 9
10 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 10
11 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi (Deivation of the Pseudosteady-State Flow Relations fo a Radial System) Slide 11
12 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Illustations of Pseudosteady-State Pefomance in Radial Flow Systems fom Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986) Slide 1
13 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 13
14 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 14
15 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 15
16 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 16
17 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pessue Tends fom Deatment of Petoleum Engineeing Couse Notes (01) Slide 17
18 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pessue Distibutions: Solutions Steady-State Solution: w e All elations given in FIELD units. q 141. scb ln( / w ) kh q 141. scb ln( e / ) kh [ wf fom] [ e fom] Radius of Investigation: Full Solution: (q sc =constant) D E 1 kh ( qb 4t D D i 1 E 1 ) 4t ed D t D ed ex 4t ed D inv -.434x10 D ed k c 1 ex 4 4t ed D t t Slide 18
19 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pessue Distibutions: Tansient Flow Pessue, sia Radial Pessue Distibution (Lee text Fig. 1.7) Pessue Dawdown and Buildu Cases E1(x) Solution t = 1000 h i = 000 sia 0.1 h 1 h 10 h 100 h 1000 h t = 100 h t = 10 h t = 1 h t = 0.1 h t = 0.1 h 1 h 10 h 100 h 1000 h e = 3000 ft Legend: D_DD(, t_ 1Em1 h) D_DD(, t_ 1E0 h) D_DD(, t_ 1E1 h) D_DD(, t_ 1E h) D_DD(, t_ 1E3 h) D_BU(,t_+_ Dt_ 1Em1 h) D_BU(,t_+_ Dt_ 1E0 h) D_BU(,t_+_ Dt_ 1E1 h) D_BU(,t_+_ Dt_ 1E h) D_BU(,t_+_ Dt_ 1E3 h) E-01 1.E+00 1.E+01 1.E+0 1.E+03 1.E+04 Pessue Distibutions fo Tansient Radial Flow Note the effect of the dawdown. Note that the buildu essue tends etace last dawdown tend. Recall that all measuements ae at the wellboe, we cannot "see" in the esevoi ou analyses ae infeed fom wellboe measuements. Radial Distance, ft Slide 19
20 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pessue Distibutions: Pseudosteady-State The hysical concet of the PSEUDOSTEADY-STATE FLOW condition is defined as the condition whee the essue at all oints in the esevoi changes at the same ate. Mathematically, this condition is given by: d [ (, t)] constant dt Slide 0
21 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pessue Distibutions: Pseudosteady-State Concet: (essue changes at the same ate at all oints in the esevoi) d d Resevoi Pessue Schematic: constant Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 1
22 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow: Summay of Relations ( - wf ) Flow Relations: (Cicula Resevoi) ( - wf ) Flow Relations: ( = Eule's constant) Time-Deendent Pseudosteady-State Flow Relations: ) ( ) ( 1 ln ) ( 141. s kh qb w e w w w e e wf Fomulatio n) (Geneal 1 4 ln Resevoi) (Cicula 4 3 ln 141. s C A e kh qb s kh qb A w wf w e wf t c V qb s kh qb t c V qb kh qb t w e i wf t w e w e i ln ) ( ) ( 1 ln 141. Slide
23 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow: Illustative Behavio inv -.434x10 k ct t Figue : Resevoi Pessue Distibution Constant Rate Tansient Flow Dawdown. Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 3
24 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow: Illustative Behavio k ct Figue 7: Resevoi Pessue Distibution Constant Wellboe Pessue Tansient Flow Dawdown. inv.434x10 - t Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 4
25 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow: Illustative Behavio k ct Figue 5: Resevoi Pessue Distibution Constant Rate Post- Tansient Flow Dawdown, Homogeneous Resevois. inv -.434x10 t Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 5
26 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Pseudosteady-State Flow: Illustative Behavio Figue 57: Resevoi Pessue Distibution Constant Wellboe Pessue Post-Tansient Flow Dawdown, Homogeneous Resevois. inv -.434x10 k ct t Fom: Blasingame, T.A.: Vaiable-Rate Analysis: Tansient and Pseudosteady-State Methods of Inteetation and Alication, M.S. Thesis, Texas A&M Univesity (1986). Slide 6
27 Petoleum Engineeing 60 Fluid Flow in Petoleum Resevois Fundamental Flow Lectue 4 Pseudosteady-State Flow in a Cicula Resevoi Resevoi Pessue Tends: Questions to Conside Q1. Why study "esevoi essue tends?" A1. We can not measue essue in the esevoi only at the wellboe (o sandface). In ode to estimate the behavio in the esevoi, we must use "model-based" essue distibutions. Q. Isn't the use of a simle model too limiting? A. Actually, no. Simle models ae extemely consistent, and as such, even when "wong," the "tend" behavio is tyically quite eesentative. Q3. What is the "adius of investigation?" A3. Fo the infinite-acting adial flow case, the adius of investigation is the oint in the esevoi whee the logaithm of adius equation (staight line) intesects the initial esevoi essue. It is a fictitious oint, but it eesents the "theoetical" location of the font of the essue distibution font. inv.434 x 10 k c t t Slide 7
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