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

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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