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Flashcards

Rock physics

Vanerahal English 41 cards

Velocity P and S equation

Cards in this deck (41)

  1. 1Velocity P and S equationVelocity P and S equation
  2. 2Bulk modulusThe bulk modulus, K is the extent to which a material can withstand isotropic squeezing. Imagine an amount of material subjected to an isotropic pressure P1. Now let the isotropic pressure
    increase to a pressure P2. The material will compress from its initial vol v1 to a new smaller vol v2.
  3. 3Bulk modulus Equationwhere D(P) is the change in pressure, and Dv is the change in volume. Thus DP is the change in pressure that causes Dv change in volume.Bulk modulus Equation
  4. 4Effect of fluid saturation on Bulk modulusK is significantly less in a gas
    filled porosity than brine
    filled porosity
  5. 5Shear ModulusThe shear modulus, "mu" is the extent to which a material can withstand shearing
    Imagine an amount of material subjected to a isotropic pressure P1. Now apply a shear stress Ps to one side of the sample. The material will shear to the new shape, and its overall length 'll increase from l1 to l2.
  6. 6Shear modulus equation and variables (Change in shape no change in volume)Gives info only about the rock matrix
    Fluid filled pores have little effect on Shear Modulus. In fluids μ = 0.    Shear modulus equation and variables (Change in shape no change in volume)
  7. 7Poisson's ratioIs the negative ratio of transverse to axial strain. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression
  8. 8Poisson's ratio relationship with Vp/vsPoisson's ratio relationship with Vp/vs
  9. 9Poisson's ratio IIIPoisson's ratio III
  10. 10Determining a rock’s velocity and density from its constitute parts Effective elastic media or Effective medium theory? PART 1Seismic reflection amp and TWT depends on Vp, Vs, and density
    Vp and Vs depend on Bulk, shear and density (Again)
    How Bulk, Shear and density vary with Porosity, Lithology, Pore structure and pore fluid content.
  11. 11AIM Effective elastic mediaTo estimate or predict the effective elastic moduli of a mixture of grains and pores theoretically
  12. 12Effective elastic media What three things should be specified?1. Individual elastic moduli of constituent minerals and fluids
    2. Volume fractions of the constituent materials
    3. Structure of the pore space – rock frame
  13. 13Effective elastic media From the three things that have to be defined wich is the hardest to deal with?Structure of the pore space
  14. 14Effective elastic media If we specify only the volume fractions and the constituent moduli, the best we can do is to predict...the upper and lower bounds on the moduli of the composite rock.:
    1. Use theory to estimate upper and lower bounds of the elastic moduli
    2. Bounds are robust
    3. Data points outside these bounds suggests you have made a large
    mistake in vol fraction or matrix
  15. 15Effective elastic media Well logs are useful for... ??They provide information about volume of the constituents and their elastic moduli BUT bad for determine rock frame geometry of the pores etc.
  16. 16TWO ways to calculate these upper and lower bounds...Voigt – Reuss Bounds
    Voigt - Reuss Hill
    Hashin-Shtrikman bounds
  17. 17Voigt - Reuss boundsVoigt - Reuss bounds
  18. 18Voigt - Reuss hill averageit is an estimate of the modulus calculated from a simple average of the Voigt (upper) and Reuss (Lower) bounds (not a range)
    Mvrh = Mv + Mr / 2
  19. 19Hashin-Shtrikman bounds Physical interpretationPhysical interpretation:
    Assembly of spheres each
    with the same volume
    fraction of fluid and
    grain.
  20. 20Hashin-Shtrikman boundsGive the narrowest range of elastic moduli bounds without specifying anything about the rock frame geometry
  21. 21Hashin-Shtrickman Bounds EquationsHashin-Shtrickman Bounds Equations
  22. 22Hashing Shtrikman Bounds. for contrasting mineralsHashing Shtrikman Bounds. for contrasting minerals
  23. 23Hashin-Shtrikman USESTo compute the estimated range of average mineral modulus for a mixture of
    mineral grains.
    To compute the upper and lower bounds for a mixture of mineral and pore fluid.
  24. 24Hashin - Shtrikman LIMITATIONSThe bounds described in this section apply under the following conditions:
    Each constituent is isotropic, linear, elastic.
    The rock is isotropic linear elastic.
  25. 25Voigt reuss USESTo compute the estimated range of average mineral modulus for a mixture of
    mineral grains.
    To compute the upper and lower bounds for a mixture of mineral and pore fluid.
  26. 26Voigt - Reuss LimitationsThe methods described in this section presuppose that each constituent is isotropic.
    linear, elastic.
  27. 27Voigt - Reuss - Hill average ASSUMPTIONS AND LIMITATIONSThe result is strictly heuristic (experimental, trial and error)
    Several authors have shown
    that the average of these bounds can be a useful and sometimes accurate
    estimate of rock properties.
    ***The rock is isotropic.
  28. 28Velocity - Porosity relationshipsVelocity - Porosity relationships
  29. 29Velocity-Porosity relationships GRAPHSVelocity-Porosity relationships GRAPHS
  30. 30Velocity porosity model Voigt - Reuss bound Compaction, diagenesis -> Depth ... Decrease in sorting -> Increase in ... SuspensionsVelocity porosity model Voigt - Reuss bound Compaction, diagenesis -> Depth ... Decrease in sorting -> Increase in ... Suspensions
  31. 31If the porosity increases Vp and Vs? In sandstones, clay causes...Decreases
    In consolidated sst clay decreases Vel and increasesVp/Vs.
    In unconsolidated rocks clay can sometimes stiffen the rock.
  32. 32What happens when the fluid is changed within the rock?The bulk density changes
    The Bulk modulus changes (change in rock compressibility)
    The shear modulus is zero for fluids
  33. 33Kdry low and high is associated with...?Low -> Microcracks, poorly consolidated rocks
    High -> Well-cemented rocks, no micro-cracks -> Stiff rocks
  34. 34For a dry rock bulk modulus relationship1/Kdry = 1/Kmat + (Phi)/Kphi
    Kphi -> pore space, rock frame bulk modulus
    Kmat = bulk of the grains or the matrix
    Kdry = dry rock bulk
  35. 35Basic assumptions of Gassmann's equation1. The rock is isotropic
    2. Valid at Low frequencies
    3. All pores are interconnected
    3. Pores filled with frictionless fluid
    4. Rock-fluid system closed
    5. Pore fluid does not interact with the rock frame (to soften or harden it)
  36. 36Fluid substitution Workflow Part I1. You need measured Vp,Vs and density
    2. From Vp and Vs equation isolate K and Mu for fluid 1 and 2
    3. For rocks filled with fluid 1 and 2 get the Gassmann equation, isolate the term Kdry/Kmat-Kdry and equalise both eqs.
  37. 37Fluid Substitution Part 24. NB Mu1 = Mu2
    5. With the density equation get the equation for both fluids 1 and 2 and as the matrix is the same equalise both equations to find the density for rock saturated 2 as a function of density saturated 1
  38. 38Fluid Substitution Part 2 PRINTEDFluid Substitution Part 2 PRINTED
  39. 39Fluid substitution workflow PART 36. Calculate the Vp and Vs velocities as a function of K2 Mu2 Rho2 (that are dependent on the previous fluid 1)
  40. 40Pore fluid properties for Gassmann's equation As pore pressure increases... As temperature increases... What happen to Bulk and Density for fluids?As pore pressure increases most fluids' density and bulk modulus INCREASES
    The density and bulk modulus of fluids in reservoirs DECREASES
  41. 41Empirical relationships for Vp and Vs SANDSTONESEmpirical relationships for Vp and Vs SANDSTONES

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Flashcards on Rock physics, created by Vanerahal on 17/04/2015.
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Vanerahal
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