Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf ·...
Transcript of Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf ·...
![Page 1: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/1.jpg)
Sections 1.1 – 1.3
Rock Physics SeminarAlejandra Rojas
February 6th, 2009
![Page 2: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/2.jpg)
OutlineIntroduction
Velocity –Porosity relations for mapping porosity and facies
Fluid substitution analysis
![Page 3: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/3.jpg)
1.1 Introduction
“ Discovering and understanding the seismic‐to‐reservoir relations has been the focus of rock physics research”
![Page 4: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/4.jpg)
1.2 Velocity – Porosity relations
Classical models:Wyllie time averageRaymer ‐ Hunt ‐ GardnerRaiga – ClemenceauCritical porosity
![Page 5: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/5.jpg)
Bounds: framework for V‐φ models
For each constituent:1. Volume fraction2. Elastic moduli
3. Geometric arrangement Avseth et al., 2005
Upper and lower bounds
![Page 6: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/6.jpg)
Elastic boundsVoigt and Reuss:‐ Simplest bounds
Hashin‐Shtrikman: ‐ Best bounds for an isotropic mixture without specifying geometric arrangement.‐ Applicable to more than 2 phases.
1 1
, ,n n
v i i v i ii i
K x K xμ μ= =
= =∑ ∑
1 11/ / , 1/ /
n n
r i i r i ii i
K x K xμ μ= =
= =∑ ∑
KHS+ = f (Ki, µmax, Xi)
KHS‐ = f (Ki, µmin, Xi)
µHS+ = f (µi, µmax, Kmax, Xi)µHS‐ = f (µi, µmin, Kmin, Xi)
Upper and lower bounds depend on how different the constituents are.
![Page 7: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/7.jpg)
Voigt‐Reuss vs. Hashin‐Shtrikman
Watt, Davies, and O’Connell, 1976
![Page 8: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/8.jpg)
Using bounds to describe diagenesis
suspensions
Newly deposited clean sand
Compaction cementingdiagenesis
Avseth et al., 2005
![Page 9: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/9.jpg)
Diagenetics vs. depositional trends
Suspension line
Diagenetictrend
Depositional trend
Porosity
Porosity is controlled by sedimentation (sorting and clay content)
Porosity is controlled by diagenesis(cementation, compaction, pressure solution)
Han’s relations
clay
Avseth et al., 2005“Diagenesis is the stiffest way to reduce porosity”
![Page 10: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/10.jpg)
Diagenetics vs. depositional trends
Diagenetictrend
Depositional trend
Porosity
Each line has constant depth but variable texture, sorting, clay content.
Porosity is controlled by diagenesis(cementation, compaction, pressure solution)cl
ay
Avseth et al., 2005“Diagenesis is the stiffest way to reduce porosity”
Cleaner sands
![Page 11: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/11.jpg)
Factors affecting velocitiesP and S velocities depend greatly on porosity.
Porosity can be estimated from impedance.
Clay increases VP/VS ratio (consolidated sands).
Clay stiffens rock (unconsolidated sands).
Pore shape cause variable V‐φ trends (crack‐like aspect ratio has similar signature than high clay content and poor sorting)
![Page 12: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/12.jpg)
1.3 Fluid Substitution“How seismic velocity and impedance depend on pore fluids”
2 fluid effects:Change in rock bulk density
Change in rock compressibility
Kφ
“Seismic fluid sensitivity is determined by a combination of porosity and pore‐space stiffness”
![Page 13: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/13.jpg)
1.3 Fluid SubstitutionHow to do fluid substitution?R: follow the steps in page 18.
How to calculate fluid properties? R: Use Batzle and Wang (1992) formulas to calculate fluid moduli.
How to approximate dry rock condition?R: air‐filled rock with a pore pressure of 1 bar (don’t use just gas).
How to relate Gassmann’s equations and ultrasonic measurements?R: use dry ultrasonic velocities and saturate them using Gassmann
equations.
How to obtain mineral moduli for complex rocks?R: Compute upper and lower bounds of the mixture of minerals and take the
average. Or use Berryman and Milton equation.
How to deal with mixed saturation? R U D i ( 6) ff ti fl id ti ( )
![Page 14: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/14.jpg)
1.3 Fluid Substitution• Valid for seismic frequencies.
• Not appropriate for ultrasonic velocities, heavy oils and tight sands reservoirs.
• Valid for isotropic rocks
• Valid for uniform distribution of fluid
Rock modulus with patchy saturation can be approximated by using Voigt average to estimate effective fluid properties. Avseth et al., 2005
![Page 15: Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas ...rpl.uh.edu/pdf/section1_rojas.pdf · Sections 1.1 –1.3 Rock Physics Seminar Alejandra Rojas February 6th, 2009. Outline](https://reader033.fdocuments.net/reader033/viewer/2022042309/5ed6688675f83015187a927a/html5/thumbnails/15.jpg)
Influence of clay content on velocity‐porosity relationship at a constant confining pressure (50 MPa). Distinct trends for shaly sand and for shale are schematically superposed on experimental data on sand‐clay mixture. From Dominique Marion, 1990, Ph.D. dissertation, Stanford University. ~ Data are from Yin, et al., 1988, and Han, 1986.