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A Petrophysically valid Xu-White Velocity Model
Andy MayMarch 19, 2014
Rock Physics Determine the in-situ acoustic properties of
the reservoir and surrounding rocks and their fluids.
Use the properties to create an ideal seismic response, both compressional and shear. How does the seismic response change with porosity, permeability, fluid content, bed thickness, mineral content, etc.?
Slide - 2
Seismic Petrophysics
How is it done? Do a full petrophysical interpretation of the wells in the area
Use the interpretation to create a velocity (Rock Physics) model
Geophysicist supplies a depth tie of the wells to the seismic volume, a wavelet and sections through the wells
The geologist supplies the tops and info on rock variablity
The engineers supply the production characteristics of the wells
The petrophysicist uses the geophysical info to create synthetics with various rock and fluid characteristics
Together the geophysicist and the petrophysicist compare the synthetics to the seismic to help decide what can be seen and how to display it
Crossplots and cross sections are made comparing seismic properties to production and geological characteristics to quantify/verify the results
Slide - 3
Goals for the velocity (Rock Physics) model
Borehole and invasion correct the compressional and shear sonic logs
Borehole and invasion correct the density
Compute the acoustic properties and the density of the borehole and formation fluids
Compute a shear log when one was not measured
Fill gaps in both shear and compressional sonic
Solid, Non-Porous Material (Matrix)
Dry, Porous Material (Frame)
Fluid Filled, Porous Material
K0 bulk modulusU0 shear modulus
Kd bulk modulusUd shear modulus
K bulk modulusU shear modulus
Fluid Only
Kf bulk modulusUd (Uf=0) shear modulus
Mechanical Properties Notation
After Wally Souder, 2001
Processing Steps Compute “Solid Rock” density, compressional ITT, and shear ITT
using volumetric sum of petrophysical results. The “theoretical values.”
Add effective porosity to the solid values using Kuster-Toksoz
Add borehole and formation fluids to theoretical compressional sonic using the Gassman equation and Sxo
Iterate to best pore aspect ratios by converging the difference between theoretical sonic and measured sonic compressional values.
Add formation fluids to best theoretical dry frame sonic values
Porosity and Vshale Definitions
PHIT = PHIE + PHISH*VSH
Assumes that porosity is distributed proportionately between sand and shale, that is, RHOMA of shale = RHOMA of sand.
Volumetric equation
Xu and White, “Poro-elasticity of Clastic Rocks”
Petrophysical Rock Models
Defining “Shale” on logs Correlation
Env Corr GR (GRCO)0 (API) 150
Caliper (CAL)5 (in) 15
Static SP (SSP)-100 (mV) 0
Bitsize (BITSZ)5 (in) 15
De
pth
(ft)
12050
Resistivity
Apparent Rw (RWA)0.02 (ohmm) 2
True formation resistivity (RT)0.2 (ohmm) 20
RW0.02 (ohmm) 2
Deep Induction (RILD)0.2 (ohmm) 20
Raw Porosity
Env Corr Density (RHOC)1.7 (g/cc) 2.7
Env Corr Neutron (PHIN)0.6 0
Edited Sonic (DLTC)150 50
Ge
ne
ral E
ng
.
34
35
36
37
38
39
PAY0 4
12050
Porosity
Effective Porosity (PHIE)0.5 0
BVXO0.5 0
BVW0.5 0
OIL0.5 0
PHIESS0.5 0
Vshale
Volume of shale (VSH)
0 1
VSHGR0 1
VSHKTH0 1
VSHND0 1
VSHSP0 1
DOL LS SS SH
GR = 47
GR = 100 RT = .85RHOC = 2.32PHIN = 40DT = 121
Shale
Greenberg and Castanga, 1992
“VClay” is not the actual volume of clay, mineral or otherwise. It is an abstraction of dry Vsh. It has the Rhoma of sand and the velocity of dry shale.
GB 197 # 1 ST2
Elev: 72.00Correlation
Env Corr GR (GRCO)0 150 (API)
Caliper (CAL)6 16 (in)
Static SP (SSP)-80 20 (mV)
Bitsize (BITSZ)6 16 (in)
Formation Temp (FT)50 250 (degF)
THEV0 20 (ppm)
K * TH Spectral GR (PINDEX)0 50
De
pth
(ft)
7550
7600
7650
7700
7750
7800
Resistivity
Apparent Rw (RWA)0.02 2 (ohmm)
True formation resistiv ity (RT)0.2 20 (ohmm)
RW0.02 2 (ohmm)
Flushed zone resistiv ity (RXO)0.2 20 (ohmm)
Density
Env Corr Density (RHOC)1.7 2.7
Modeled Density (RHOC_G)1.7 2.7 (g/cc)
RHOC (water) (RHOC_GW)1.7 2.7
Shear
DTSMODEL500 80
Shear theoretical (DTS_T)500 80 (us/f)
Compressional
Edited Sonic (DLTC)200 60 (us/f)
DLT theoretical (DLT_T)200 60 (us/f)
DLT (water) (DLT_TW)200 60
Sw
SXOE1 0
SWE1 0
Asp ect Ratio s
ASPMAMZ0 1
ASPSHMZ0 1
PAY0 4
7550
7600
7650
7700
7750
7800
Effective Porosity
Effectiv e Porosity (PHIE)0.5 0
BVXO0.5 0
BVW0.5 0
PHIE unbounded (PHIEU)0.5 0
OIL0.5 0
SH SS VOLC LS DOL A N
Vshale
VSHSP0 1
VSHGR0 1
Vol ume of sh al e (VSH)0 1
VSHND0 1
VSHKTH0 1
VSHTH0 1
CORVSH0 1
DLT_TW Sonic when wet
DLT_TW
RHOC_GW
Correlation
Env Corr GR (GRCO)0 150 (API)
Dep
th (ft)
7450
7500
7550
7600
7650
7700
7750
7800
Resistivity
True formation resistivity (RT)0.2 20 (ohmm)
Density
Modeled Density (RHOC_G)
1.7 2.7 (g/cc)
RHOC (water) (RHOC_GW)
1.7 2.7
Env Corr Density (RHOC)
1.7 2.7 (g/cc)
Shear
Shear theoret ical (DTS_T)
900 70 (us/f)
Mud Rock Shear (DTS_CSTG)
900 70
Compressional
Edited Sonic (DLTC)200 50 (us/f)
DLT theoretical (DLT_T)200 50 (us/f)
DLT (water) (DLT_TW)200 50
Bulk Moduli
Bulk Mod shale (K_SH)0 40
Bulk Mod of solid (KMOD_M)0 40
Bulk Mod sand (K_SS)0 40
Comp HS SS Bound (KHS_SS)0 40
Comp HS SH Bound (KHS_SH)0 40
PAY0 4
7450
7500
7550
7600
7650
7700
7750
7800
Effective Porosity
Effective Porosity (PHIE)0.5 0
BVXO0.5 0
BVW0.5 0
PHIE unbounded (PHIEU)0.5 0
SH SS VOLC LS DOL AN
Sonic when wet
Sonic when wet
Density when wet
PHIEU
Correlation
Env Corr GR (GRCO)0 150 (GAPI)
Caliper (CAL)6 16 (in)
Bitsize (BITSZ)6 16 (in)
Dep
th (m
)
650
700
Resistivity
True formation resistivity (RT)0.2 20 (ohmm)
Density
Modeled Density (RHOC_G)1.7 2.7
Env Corr Density (RHOC)1.7 2.7 (g/cc)
Shear
Shear theoretical (DTS_T)900 70
DTSMC900 70
Compressional
Edited Sonic (DLTC)200 50
DLT theoretical (DLT_T)200 50
DLT (water) (DLT_TW)200 50
650
700
Effective Porosity
Effective Porosity (PHIE)0.5 0
BVXO0.5 0
BVW0.5 0
PHIE unbounded (PHIEU)0.5 0
SH SS VOLC LS DOL AN
Caliper
Measured shear
Measured AIGOM Example
After Frederic Gallice
AI Model InsituGOM Example
After Frederic Gallice
Example well Example well
Example wellExample well
China Example
After Gordon Marney
wirelinewireline
Conclusions
Petrophysical velocity modeling can improve well ties to seismic
The wet shale and effective porosity method is superior to the total porosity and dry clay method
Sonic and density logs are often bad due to borehole and invasion effects
Further Reading Keys and Xu, Geophysics, 2002. This paper incorporates all of the discussion,
criticism, and corrections to the Xu and White model that had accumulated since its introduction in 1995. The analytical model presented in this paper is very good. As Leiknes, et. al. discusses the exact Kuster and Toksoz effective medium solution in Xu and White, 1995 is flawed. The approximation is robust and of high quality.
Xu and White, 1996. " Physical Model for Shear...", Geophysical Prospecting. This summarizes their theory pretty well. Note their model is a PHIE and VSH model, ignore the references to Vclay. The equations make this clear, the text is a bit sloppy.
Leiknes, Pedersen, and Nordahl. "Examination and Application of the Sand-clay..." This paper discusses and summarizes all of the criticism of the Xu-White model in a fair way. These issues are dealt with in the Keys and Xu paper.
Batzle and Wang, 1992, “Seismic Properties of Pore Fluids.” This paper gives the equations for oil, gas, water acoustic properties. I used these in the model. The equations I use in the model for OBM are from Dr. Han and are not published.
Petrophysicists