petroleum engineering 620 — fluid flow in petroleum …€¦ · factors which affect relative...
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Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
Factors Which AffectRelative Permeability
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — 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) 285-302.
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
"Bundle of Tubes" Capillary Pressure Concept
● "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.
pc(Sw=1)(largest tube)
From: Gates, J. l. and Templaar-Lietz, W.: "Relative Permeabilities of California Cores by the Capillary Pressure Method," API Drilling and Production Practices (1950) 285-302.
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
●Examples: (Gates and Templaar-Lietz)■High permeability samples (low capillary pressure).■Gates and Templaar-Lietz models for relative permeability.
From: Standing, M.B.: "Notes on Relative Permeability Relationships," Course Notes, Trondheim, Norway (1978).
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
●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: Keelan, D.: "Special Core Analysis," Core Laboratories Report (1982).
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
From: Richardson, J.G, Kerver, J.K., Hafford, J.A., and Osoba, J.S.: "Laboratory Determination of Relative Permeability," Trans. AIME (1951) 195, 187-196.
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
● Influence of "End Effects:"■Sw → 1 as pc → 0.■Solution 1: Higher flowrates (i.e.,
higher phase velocities).■Solution 2: "End pieces" (exten-
sions 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, 187-196.
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
● 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, 187-196.
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
● 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: Keelan, D.: "Special Core Analysis," Core Laboratories Report (1982).
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
● Influence of Viscosity Ratio:■Theoretically, no effect.■Although based on data, this
particular work is more of a cartoon.
■Note that residual oil saturation (Sor) is approximately 30 percent.
■Endpoint krw is very low (approximately 10 percent).
Sorkrw(Sor)Swi
kro(Swi)
Brooks/Corey/BurdineRelative Permeability Relation
andType Curve Matching
of Relative Permeability Data
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Self-Study — for your reference)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
●Purcell-Burdine relative permeability model:
●Brooks-Corey-Burdine kr and pc equations:
Key Equations: Brooks-Corey-Burdine kr and pc Models
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability
(Relative Permeability Type Curve Matching using the Brooks and Corey Model)
Petroleum Engineering 620 — Fluid Flow in Petroleum ReservoirsPetrophysics Lecture 5 — Relative Permeability