Tom BLASINGAME Texas A&M U. Slide 1

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1 Slide 1

2 Factors Which Affect Relative Permeability Slide 2

3 "Bundle of Tubes" Capillary Pressure Concept p c (S w =1) (largest tube) "Bundle of Tubes" Concept: Uniform tubes constant capillary pressure, 1:1 relative permeability. Distribution of tubes capillary pressure distribution. Distribution of tubes relative permeability distribution. From: Gates, J. l. and Templaar-Lietz, W.: "Relative Permeabilities of California Cores by the Capillary Pressure Method," API Drilling and Production Practices (1950) Slide 3

4 Examples: (Gates and Templaar-Lietz) High permeability samples (low capillary pressure). Gates and Templaar-Lietz models for relative permeability. From: Gates, J. l. and Templaar-Lietz, W.: "Relative Permeabilities of California Cores by the Capillary Pressure Method," API Drilling and Production Practices (1950) Slide 4

5 Concept Models for Phases in a Given Pore Size Distribution: Water always occupies the smallest pores (water-wet system). Gas always occupies the largest pores (non-wetting). Oil is the "intermediate" phase in this rendering. From: Standing, M.B.: "Notes on Relative Permeability Relationships," Course Notes, Trondheim, Norway (1978). Slide 5

6 From: Keelan, D.: "Special Core Analysis," Core Laboratories Report (1982). Slide 6

7 Influence of "End Effects:" S w 1 as p c 0. Solution 1: Higher flowrates (i.e., higher phase velocities). Solution 2: "End pieces" (extensions of the core used to "move" the end effects away from the point of measurement). From: Richardson, J.G, Kerver, J.K., Hafford, J.A., and Osoba, J.S.: "Laboratory Determination of Relative Permeability," Trans. AIME (1951) 195, Slide 7

8 Influence of Flowrate and Core Length: Effect of flowrate (i.e., pressure drop) is minor. Effect of core length (average trends) appears relatively minor. Relative permeability is relatively insensitive to flowrate. From: Richardson, J.G, Kerver, J.K., Hafford, J.A., and Osoba, J.S.: "Laboratory Determination of Relative Permeability," Trans. AIME (1951) 195, Slide 8

9 Influence Core Length: Core Lengths = 7.23 cm, 4.75 cm, and 2.30 cm. Absolutely permeability is 115 md. The shorter core length case shows the most distortion. Length effects are generally assumed to be minor. From: Richardson, J.G, Kerver, J.K., Hafford, J.A., and Osoba, J.S.: "Laboratory Determination of Relative Permeability," Trans. AIME (1951) 195, Slide 9

10 k ro (S wi ) Influence of Viscosity Ratio: Theoretically, no effect. Although based on data, this particular work is more of a cartoon. Note that residual oil saturation (S or ) is approximately 30 percent. Endpoint k rw is very low (approximately 10 percent). S wi S or k rw (S or ) From: Keelan, D.: "Special Core Analysis," Core Laboratories Report (1982). Slide 10

11 Brooks/Corey/Burdine Relative Permeability Relation and Type Curve Matching of Relative Permeability Data (Self-Study for your reference) Slide 11

12 Key Equations: Brooks-Corey-Burdine k r and p c Models Purcell-Burdine relative permeability model: Brooks-Corey-Burdine k r and p c equations: (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 12

13 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 13

14 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 14

15 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 15

16 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 16

17 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 17

18 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 18

19 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 19

20 (Relative Permeability Type Curve Matching using the Brooks and Corey Model) Slide 20