**Where:**

PHIe = effective porosity (fractional)

U = photoelectric absorption cross section (barns/cm3)

UH = photoelectric absorption of hydrocarbon (barns/cm3)

UMA = photoelectric absorption of matrix rock (barns/cm3)

USH = photoelectric absorption of shale (barns/cm3)

UW = photoelectric absorption of water (barns/cm3)

Vsh = volume of shale (fractional)

Note - 1 barn = 1*10^- 24 square centimeters - pretty small cows!
**
3: DENSSH = PHIDSH * KD1 + (1 - PHIDSH) * KD2**

4: USH = PESH * DENSSH

5: DENS = PHID * KD1 + (1 - PHID) * KD2

**
6: Uma = (PE * DENS - Vsh * USH) / (1 - PHIe - Vsh)**

**Where:**

DENS = density log reading (gm/cc)

DENSSH = density log reading in 100% shale (gm/cc)

PE = photoelectric cross section (barns/cm3)

PESH = photoelectric cross section in 100% shale (barns/cm3)

PHIe = effective porosity (fractional)

U = photoelectric absorption cross section (barns/cm3)

UH = photoelectric absorption of hydrocarbon (barns/cm3)

Uma = computed matrix photoelectric absorption cross section (barns/cm3)

USH = photoelectric absorption of shale (barns/cm3)

UW = photoelectric absorption of water (barns/cm3)

Vsh = volume of shale (fractional)

COMMENTS

The Uma values can be used in crossplots with matrix density (DENSma), to determine lithology
fractions in a two or three mineral model.

**
**

* Matrix Density vs Matrix Cross Section Crossplot
for Lithology*

**
****
****
Rock Volume from PE
Density Neutron Models**

The
PE values can be linearly interpolated between any two assumed
end points of a two mineral model in the usual way.

7: Min1 = (PE - PE2 - Vsh * PESH)
/ (PE1 - PE2)

8: Min2 = 1.00 - Min1

**This
is the ONLY lithology model that works in gas zones, since PE
is not affected by gas. All methods that use density, neutron
or sonic are invalid in gas zones.**

**The
Uma values can also be linearly interpolated between any two
assumed end points of a two mineral model in the usual way.**

9: Min1 = (Uma - UMA2 - Vsh *
USH) / (UMA1 - UMA2)

10: Min2 = 1.00 - Min1

**DENSma and Uma values can be linearly triangulated between any
three assumed end points of a three mineral model in the usual
way.**

11: D = (Uma * (DENS2 - DENS1) + DENSma * (UMA1 - UMA2)

+ UMA2 * DENS1 - UMA1 * DENS2) / (UMA1 * (DENS3 - DENS2)

+ UMA2 * (DENS1 - DENS3) + UMA3 * (DENS2-DENS1))

12: E = (D * (DENS3 - DENS1) - DENSma + DENS1) / (DENS1 - DENS2)

13: Min1 = MAX(0, 1 - D - E) /
(MAX(0, 1 - D - E) + MAX(0, D) + MAX(0, E))

14: Min2 = MAX(0, E) / (MAX(0, 1
- D - E) + MAX(0, D) + MAX(0, E))

15: Min3 = (1 - Min1 - Min2)

**Where:**

PHIe = effective porosity from any method (fractional)

PE = measured PE log value of rock mixture

PE1 = PE of first mineral (fractional)

PE2 = PE of second mineral (fractional)

Min1 = relative volume of first mineral (fractional)

Min2 = relative volume of second mineral (fractional)

Min3 = relative volume of third mineral (fractional)

Vsh = volume of shale (fractional)

Uma = computed UMA value of rock mixture

UMA1 = UMA of first mineral (fractional)

UMA2 = UMA of second mineral (fractional)

UMA3 = UMA of third mineral (fractional)

DENSma = computed matrix density value of rock mixture

DENS1 = matrix density of first mineral (fractional)

DENS2 = matrix density of second mineral (fractional)

DENS3 = matrix density of third mineral (fractional)

**COMMENTS:
**

The relative Vmin values must be multiplied by
Vrock to get absolute values of V1, V2, V3. Vrock = 1- PHIe -Vsh..

**NUMERICAL
EXAMPLE:**

1.
Assume data as follows:

PE = 1.68 barns/cm3

DENS = 2.20 gm/cc

PHIN = 0.27

U = 1.68 * 2.20 = 3.69

Uma = 1.68 * 2.20 / (1 - 0.27) = 5.20

**Both
PE and Uma are close to the quartz values. If
it is dolomitic sandstone, assume:**

Vsh = 0.10

PHIe = 0.24

Uqrtz = 4.79

Udolo = 9.00

**
Min1 = (5.20 - 9.00) / (4.79 - 9.00) = 0.90**

Mun2 = 1.00 - 0.90 = 0.10

Vrock
= 1 - 0.10 - 0.24 = 0.66.

Vmin1 = 0.90 * 0.66 = 0.60

Vmin2 = 0.10 * 0.66 = 0.06

The
rock matrix is 90% quartz, 10% dolomite, but 34% of this is made
up of porosity and shale, so the actual volumes of matrix rock
are reduced by this amount.

**
**
**
**
**MATRIX
**
ROCK PARAMETERS

**
**