Reservoir Petrophysics Introduction to Geology

Transcription

1 Natural Gas Engineering Reservoir Petrophysics Introduction to Geology T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX Slide 1

2 Geology: Basic Porosity Types Fabric Selective: Porosity (and permeability are functions of deposition and digenesis. Not Fabric Selective: Fractures, etc. Porosity and permeability may (or may not) be a function of deposition and diagensis. Slide 2

3 Geology: Basic Porosity Types Sandstones Features: Note intergranular porosity ("conventional reservoir concept). Clays can cause significant degradation of porosity. Slide 3

4 Geology: Sandstone Depositional Systems a. Various sandstone depositional sequences note the "transport" system evolves basinward. From: Reservoir Sandstones Berg (1986). b. These schematics illustrate similarity in depositional processes and also give insight into heterogeneity. Sandstone Reservoirs: Depositional sequences are well-established/accepted. Turbidite reservoirs are probably of most current interest. Slide 4

5 Geology: Carbonate Depositional Sys. and k From: Carbonate Reservoir Characterization Lucia (1999). a. Crossplot of permeability versus porosity (logarithmic scales). In-cludes particle size as a variable. b. Permeability-porosity profiles for various carbonate depositional sequences. Carbonate Reservoirs: Permeability/Porosity Character Porosity and permeability often weakly correlated in carbonates. Permeability in carbonates most often dependent on diagenetic processes. Slide 5

6 Petrophysics: Effect of Small-Scale Heterogeneities Weber Example Core: Laminated Aeolian sandstone. Thin beds (<1 cm) are common. Some laminations have zero permea-bility (influence on vertical flow?). General Considerations: Core-scale heterogeneities may or may not affect overall reservoir performance (depends on continuity). Attempts to correlate small-scale heterogeneities are likely to fail, except for isolated samples. Issues: How do such features affect: Pressure transient behavior (well test time scale events)? Pseudosteady-state behavior (production time scale events)? Solutions for increasing reservoir exposure? (hydraulic fracturing?) From: Weber, KJ.: "How Heterogeneity Affects Oil Recovery from Reservoir Characterization, Academic Press, Inc.-Harcourt Bruce Jovanovich, Publishers, New York (1986) (Edited by: Lake, L.W. and Carroll, H.B., Jr.). Slide 6

7 Petrophysics: Example k WPA, k PTA with k log mean Well TM-1E/Porosity Distribution with Depth (Upper Naricual) Well TM-1E/Permeability Distribution with Depth (Upper Naricual) Depth, ft Probability (Frequency/n) Porosity, fraction Well TM-1E/Permeability Histogram (Upper Naricual) Well TM-1E (Upper Naricual -- n = 354) Statistics for k Median log(k) = Mean log(k) = Standard deviation = Mean k = 20.9 md Depth, ft Permeability, k, md Logarithm of permeability, log(md) From: Medina, T.: Characterization of Gas Condensate Reservoirs Using Pressure Transient and Production Data-Santa Barbara Field, Monagas, Venezuela, M.S. Thesis Texas A&M University (May 2003). Permeability Comparison: Santa Barbara Field (Venezuela) Major conclusion is that these data due not appear to be correlated. High permeability values probably "overweigh" k log mean estimate. k PTA values higher than k WPA, but we have only 3 (three) k PTA values. Slide 7

8 Reservoir Scale Issues: Halderson Schematics Reservoir Scaling Issues? NANO or ATTO From: Simulator Parameter Assignment and the Problem of Scaling in Reservoir Engineering Halderson (1986). a. (Haldorsen) Four conceptual scales associated with porous media averages. b. (Haldorsen) Volume of investigation of a pressure build-up test and cross section indicating large-scale internal heterogeneities. Slide 8

9 Geology/Petrophysics: Questions to Consider Q1. Validity of correlations of petrophysical data? A1. These will always be "local" correlations, difficult to extend or extrapolate across depositional systems. Q2. Role of geology in PTA? A2. Must consider geology in general, but particularly for cases where the following reservoir models are employed: Linear sealing or leaky faults. (any geologic evidence?) Bounded reservoir system. (geologic or petrophysical evidence?) Naturally fractured/dual porosity reservoir. (any geologic evidence?) Multilayered reservoirs. (geologic or petrophysical evidence?) Q3. Correlation of k core with k PTA? A3. Always a comparison of "apples and oranges" due to: Sample size. Saturation/mobility issues. (core data are extremely localized) (k core evaluated using gas at low pressures) Q4. Effect of reservoir heterogeneity on PTA? A4. Interesting question volume-averaging appears to dominate the estimate of permeability obtained from PTA. Attempts to estimate permeability "distributions" will be non-unique and/or overly simplified. Slide 9

10 Natural Gas Engineering Reservoir Petrophysics Flow in Porous Media T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX Slide 10

11 Flow Concepts: Concepts for Fluid Flow in Porous Media Concept: "Tortuous paths" Darcy flow. Concept: Perfect paths. Poiseuille flow. How to reconcile? Slide 11

12 Flow Concepts: Klinkenberg Effect Liquid Flow: Governed by "viscous flow." Analog = Poiseuille flow. "Zero-slip" at wall concept. Gas Flow: Molecules "slip" at wall. Gradient is lower than expected. Computed permeability higher. Results MUST be corrected. Slide 12

13 Flow Concepts: High-Velocity Flow in Porous Media Slide 13

14 Flow Concepts: Klinkenberg Effect H 2, Air, and CO 2 Issues: Smaller molecules = more severe Klinkenberg effect. The Klinkenberg effect can be derived and is a subset of "Knudsen Flow." Slide 14

15 Petrophysics: Low/Ultra-Low Permeability Issues (Nelson) Simply Put: Molecules of fluid are on the same order of size as pores. Very different flow behavior than traditional "Darcy's Law." Also affects phase behavior (i.e., composition, density, temperature, and pressure relations). Definition of "unconventional" reservoirs. Nelson, P.H. "Pore-throat Sizes in Sandstones, Tight Sandstones, and Shales, AAPG Bulletin, V. 93, no. 3 (March 2009), pp Slide 15

16 Petrophysics: Permeability Characterization/Correlation From: The Fundamentals of Core Analysis Keelan (1972). a. "Cartoon" of k air versus illustrates k=a exp(b ). b. "Cartoon" of k air versus S wi illustrates the influence of pore throat structure. From: API Drilling and Prod. Prac. Bruce and Welge (1947). Permeability Characterization/Correlation: Permeability = f(, composition, texture, grain size, sorting, etc.). Simplified correlations for permeability will only be of "local" use. Slide 16

17 Petrophysics: k = a exp[b ] (Schematic Trends) Sketched Trends: Increase in porosity increase in permeability (obvious). k = a exp[b ]??? This does not seem intuitive (statistics)? What about: k = A B What about other variables? Slide 17

18 Petrophysics: k = a exp[b ] (Archie Trends) Permeability (md) 1000 Sketched Trends: Similar to previous schematic plot. This is the "original" presentation by Archie (to the best of our knowledge, this is the first plot of log(k) versus ). There are many other variables: Grain sizes Sorting Texture Angularity These variables can not be directly quantified. Porosity (Percent) Slide 18

19 Petrophysics: Archie k- -F Relations Archie Results: Porosity: F = a/ m This result "makes sense" (i.e., volume of the room is proportional to the volume of the electrolyte). Permeability: F = A/k B This result DOES NOT "make sense" (i.e., the size of the door is proportional to the volume of the room???). Slide 19

20 Petrophysics: Archie k- -F Relations 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 k A B 1/ B A m k a This exercise suggests that permeability and porosity are related by a power law relation this observation is only true for uniform pore systems. b. Crossplot of formation (resistivity) factor versus permeability (F = A/k B ). Slide 20

21 Petrophysics: Porosity-Permeability Power Law Relation 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, Slide 21

22 Petrophysics: Fractal Model for Permeability (Pape) 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), Slide 22

23 Petrophysics: Influence on and k (Unconsolidated Sand) 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, Slide 23

24 Petrophysics: and k (Power Law Relation) 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 Permeability (md) 1.E+01 1.E+00 1.E-01 Depth (ft) E-02 1.E-04 1.E-04 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 8) c2 c c exp[ c3 max c1 Sw ] 1.E+00 1.E-03 1.E-04 1.E-05 1.E-02 1.E-01 Porosity (fraction) 1.E+00 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. Towards a Characteristic Equation for Permeability, M.S. Theses, Texas A&M University (May 2008). Slide 24

25 Petrophysics: Early Concepts for Flow in Porous Media 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), Orientation: Possibly one of the most important sequences of experimental results in Petroleum Engineering. Observations: Do you see "Darcy's Law?" Is it a good idea to formulate pressure drop as a "friction factor" for flow in porous media? What would you do? Comment: Note that this approach is not perfect, ALL trends should overlay if the friction factor and Reynolds number are properly defined. Reformulate? Slide 25

26 Petrophysics: Cornell-Katz Relation for High-Velocity Flow Formulation: Cornell and Katz appear to have chosen appropriate definitions for Reynolds number and friction factor. Are all of these vari-ables "measurable?" Observations: Excellent conformance for all cases? The curved and flat portions are for "Forchheimer" flow (pressure gradient is proportional to velocity squared). Comment: Non-linear, requires numerical solutions. Slide 26

27 Natural Gas Engineering Reservoir Petrophysics (End of Lecture) T.A. Blasingame, Texas A&M U. Department of Petroleum Engineering Texas A&M University College Station, TX Slide 27