Tom BLASINGAME Texas A&M U. Slide 1

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1 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 1

2 From: Jorden, J.R. and Campbell, F.L.: Well Logging I Rock Properties, Borehole Environment, Mud and Temperature Logging, SPE Monograph Series, SPE Richardson, TX (1984). Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 2

3 From: Keelan, D.K. and Marschall, D.M. "Fundamentals of Core Analysis," Core Laboratories, Inc., Dallas (1972,79,89). Tom BLASINGAME Texas A&M U. Slide 3

4 From: Lake, L.W. and Carroll, H.B., Jr.: Reservoir Characterization, Academic Press, Inc. Harcourt Bruce Jovanovich, Publishers, New York (1986). Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering." Tom BLASINGAME Texas A&M U. Slide 4

5 From: Keelan, D.K. and Marschall, D.M. "Fundamentals of Core Analysis," Core Laboratories, Inc., Dallas (1972,79,89). Tom BLASINGAME Texas A&M U. Slide 5

6 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Nelson Pore Size/Molecule Size Chart Each green line is x10 SMALLER scale. Perspective: The concept of pores and pore throats begins to break down at these scales. The flow path can be as small as molecular diameters (or less). Issues: How do the fluids move? Darcy flow? Dispersion (gases)? Knudsen flow? How are the fluids stored? In the organic matter? Adsorbed? Another mechanism? Question(s): How small are pores in shale gas? Note that the size of the pores is on the order of times the size of the fluid molecule. From: Nelson, P.H Pore-Throat Sizes in Sandstones, Tight Sandstones, and Shales. AAPG Bulletin 93 (3): Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 6

7 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 7

8 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Gas Flow v y v x Gas Slippage Kundt, A. and Warburg, E.: "Über Reibung und Wärmeleitung verdünnter Gase, " Poggendorfs Annalen der Physik und Chemie (1875), 155, 337. Florence "Proxy" Permeability: Compute "proxy" permeability for each individual gas species. Lighter species experience higher "proxy" permeability. In this concept proxy permeability increases with drawdown. Knudsen "microflow" model (Modified from Karniadakis and Beskok, 2002). From: Freeman, C.M., Ilk, D., Moridis, G.J., and Blasingame, T.A.: "A Numerical Study of Performance for Tight Gas and Shale Gas Reservoir Systems" paper SPE presented at the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 4 7 October Florence, F.A., Newsham, K., Rushing, J.A., and Blasingame, T.A.: "Improved Permeability Prediction Relations for Low Permeability Sands," paper SPE presented at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium held in Denver, CO, U.S.A., April Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 8

9 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 9

10 Air CO 2 H 2 From: Klinkenberg, L. J.: "The Permeability of Porous Media to Liquids and Gases," API Drilling and Production Practices, , Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 10

11 From: Keelan, D.K. and Marschall, D.M. "Fundamentals of Core Analysis," Core Laboratories, Inc., Dallas (1972,79,89). Tom BLASINGAME Texas A&M U. Slide 11

12 1000 From: Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," AAPG Bulletin, May 1950, v. 34, p Permeability (md) Porosity (Percent) Tom BLASINGAME Texas A&M U. Slide 12

13 From: Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," AAPG Bulletin, May 1950, v. 34, p Tom BLASINGAME Texas A&M U. Slide 13

14 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts From: Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," AAPG Bulletin, May 1950, v. 34, p a. Crossplot of formation (resistivity) factor versus permeability (F = a/ m ). Porosity Model: Permeability Model: F R R o w a m F R R Equating the Models: Solving for k: a m B k A o w 1/ B k A B A m a This exercise suggests that permeability and porosity are related by a power law relation this observation is only true for uniform pore systems. k b. Crossplot of formation (resistivity) factor versus permeability (F = A/k B ). Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 14

15 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts b. Appalachian samples permeability is approximated as a power law function of porosity. Legend: Thin Sections (photomicrographs) A. Upper shoreface ( = 0.207, k = 46.5 md) Vinton Cty, OH. B. Lower shoreface ( = 0.085, k = 3.43 md) Hocking Cty, OH. C. Tidal channel ( = 0.066, k = md) Carroll Cty, OH. D. Tidal flat ( = 0.053, k = md) Portage Cty, OH. E. Fluvial ( = 0.087, k = 15.3 md) Kanawha Cty, WV. F. Estuarine ( = 0.068, k = md) Preston Cty, WV. a. Thin sections of Lower Silurian Sandstones, Appalachian Basin (US). c. Attempt to correlate Morrow samples by deposition similar to Appalachian samples. From: Castle, J.W. and Byrnes, A.P.: "Petrophysics of Lower Silurian Sandstones and Integration with The Tectonic- Stratigraphic Framework, Appalachian Basin, United States," Bull., AAPG (2005) 89, Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 15

16 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Pape et al Fractal Model for Permeability: k a a2 a3 a. Pape concept model plot based on a fractal pore distribution. Some concern regarding the additive structure of the model (this seems to be a simplistic reduction of the fractal concept). b. Legend for the Pape concept model plot. Note that there are several quite different data sets shown, yet the "structure" of the correlation appears consistent. From: Pape, H., Clauser, C., Iffland, J.: "Permeability Prediction Based on Fractal Pore-Space Geometry," Geophysics (1999) Vol. 64, (September-October 1999), Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 16

17 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts Beard and Weyl Data: Morrow Data: (selected) a. Data from Beard and Weyl, and Morrow et al. These are unconsolidated sand samples. b. Log-log plot of k/d 2 versus extraordinary agreement given data quality (note slope 8). From: Beard, D.C. and Weyl, P.K.: "Influence of Texture on Porosity and Permeability of Unconsolidated Sand," Bull., AAPG (1973) 57, Morrow, N.M, Huppler, J.D., and Simmons III, A.B: "Porosity and Permeability of Unconsolidated, Upper Miocene Sands From Grain-Size Analysis," J. Sed. Pet. (1969) Vol. 39, No. 1, Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 17

18 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts From: Jorden, J.R. and Campbell, F.L.: Well Logging I Rock Properties, Borehole Environment, Mud and Temperature Logging, SPE Monograph Series, SPE Richardson, TX (1984). Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 18

19 Petroleum Engineering 620 Fluid Flow in Petroleum Reservoirs Petrophysics Lecture 1 Introduction to Porosity and Permeability Concepts 1.E+00 East Texas Tight Gas Sand Correlation Line k_eos Model 1.E+03 1.E Permeability Correlation Calculated Permeability (md) 1.E-01 1.E-02 1.E-03 1.E-04 1.E-04 c c max 1.E-03 1.E-02 1.E-01 Measured Permeability (md) a. Correlation plot of calculated versus measured permeability. East Texas (US) tight gas example. Correlation relation for this case. k=f(,s w ) k a( c) b ( b exp[ c 1 8) c2 S c3 w ] 1.E+00 Permeability (md) 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-02 1.E-01 Porosity (fraction) 1.E+00 Depth (ft) b. Log-log correlation plot of k versus. The correlation function yields an envelope E-04 1.E-03 1.E-02 Permeability (md) 1.E-01 c. Correlation plot of depth versus log(k). Correlation appears to be excellent. From: Siddiqui, A., Ilk, D., and Blasingame, T.A.: "Towards A Characteristic Equation for Permeability," paper SPE presented at the 2008 Eastern Regional Meeting, Pittsburgh, PA, October Tom BLASINGAME t-blasingame@tamu.edu Texas A&M U. Slide 19

20 From: Fancher, G.H., Lewis, J.A., and Barnes, K.B.: "Some Physical Characteristics of Oil Sands," Pa. State College, Min. Ind. Exp. Sta. Bull. 12 (1933), Tom BLASINGAME Texas A&M U. Slide 20

21 From: Cornell, D., and Katz, D.L.: "Flow of Gases Through Consolidated Porous Media," Ind. and Eng. Chem. (1953), 45, Tom BLASINGAME Texas A&M U. Slide 21

22 From: Lake, L.W. and Carroll, H.B., Jr.: Reservoir Characterization, Academic Press, Inc. Harcourt Bruce Jovanovich, Publishers, New York (1986). Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering." Tom BLASINGAME Texas A&M U. Slide 22

23 From: Lake, L.W. and Carroll, H.B., Jr.: Reservoir Characterization, Academic Press, Inc. Harcourt Bruce Jovanovich, Publishers, New York (1986). Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering." Tom BLASINGAME Texas A&M U. Slide 23

24 From: Lake, L.W. and Carroll, H.B., Jr.: Reservoir Characterization, Academic Press, Inc. Harcourt Bruce Jovanovich, Publishers, New York (1986). Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering." Tom BLASINGAME Texas A&M U. Slide 24

25 From: Lake, L.W. and Carroll, H.B., Jr.: Reservoir Characterization, Academic Press, Inc. Harcourt Bruce Jovanovich, Publishers, New York (1986). Weber, K.J.: "How Heterogeneity Affects Oil Recovery." Tom BLASINGAME Texas A&M U. Slide 25

26 From: Keelan, D.K. and Marschall, D.M. "Fundamentals of Core Analysis," Core Laboratories, Inc., Dallas (1972,79,89). Tom BLASINGAME Texas A&M U. Slide 26