Evidence for a variable Archie porosity Evidence for a variable Archie porosity exponent exponent ““mm”” and impact on saturation and impact on saturation

calculations for Mesaverde tight gas calculations for Mesaverde tight gas sandstones: Piceance, Uinta, Green River, sandstones: Piceance, Uinta, Green River,

Wind River, and Powder River basinsWind River, and Powder River basinsRobert M Cluff, The Discovery Group Inc.Robert M Cluff, The Discovery Group Inc.

Alan P. Byrnes, Kansas Geological SurveyAlan P. Byrnes, Kansas Geological Survey1111presently with Chesapeake Energypresently with Chesapeake Energy

Stefani Whittaker, The Discovery Group Inc.Stefani Whittaker, The Discovery Group Inc.Dan Krygowski, The Discovery Group Inc.Dan Krygowski, The Discovery Group Inc.

AAPG Rocky Mountain Section meeting, Denver, ColoradoAAPG Rocky Mountain Section meeting, Denver, Colorado10 July 200810 July 2008

US DOE Project SummaryUS DOE Project SummaryDOE Contract # DOE Contract # DEDE--FC26FC26--05NT4266005NT42660

completion date 30 June 2008completion date 30 June 2008Organizations Organizations

University of Kansas Center for Research, Inc.University of Kansas Center for Research, Inc.Kansas Geological Survey, Lawrence, KSKansas Geological Survey, Lawrence, KSThe Discovery Group Inc., Denver, COThe Discovery Group Inc., Denver, CO

Principal Investigators: Alan P. Byrnes, KGS; Principal Investigators: Alan P. Byrnes, KGS; Bob Cluff, Discovery GroupBob Cluff, Discovery Group

project website is project website is http://http://www.kgs.ku.edu/mesaverdewww.kgs.ku.edu/mesaverde

Objectives of this taskObjectives of this task

Characterize Mesaverde electrical Characterize Mesaverde electrical properties as a function of porosity and properties as a function of porosity and salinitysalinity

Archie porosity (cementation) exponent Archie porosity (cementation) exponent ““mm””Investigate behavior at low porosity end Investigate behavior at low porosity end (<6%) not previously studied(<6%) not previously studiedEvaluate excess conductivity effectsEvaluate excess conductivity effects

Methods to compute accurate Sw from Methods to compute accurate Sw from logslogs

SamplingSampling

systematic systematic characterization of characterization of KmvKmv lithofacies lithofacies over entire Rocky over entire Rocky MtnMtn regionregion44 wells/6 basins44 wells/6 basinsDescribed ~Described ~7000 ft core (digital)ft core (digital)2200 core 2200 core samplessamples120120--400 advanced 400 advanced properties properties samplessamples

Green River

Wind River

Washakie

Piceance

PowderRiver

Uinta

Wyoming

Colorado

Utah

N

Permeability Permeability vsvs PorosityPorositySamples collected over a wide range of porosity and Samples collected over a wide range of porosity and permeability across 6 basinspermeability across 6 basins00--24% porosity, spanning 1 24% porosity, spanning 1 nDnD to >100 to >100 mDmD

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10 12 14 16 18 20 22 24In situ calc Porosity (%)

Klin

kenb

erg

Perm

eabi

lity

(4,0

00 p

si, m

D)

Green RiverPiceancePowder RiverUintahWashakieWind RiverlogK=0.3Phi-3.7logK=0.3Phi-5.7

ArchieArchie’’s equations equation

Swn = (a / φ m) * (Rw / Rt )

completely empirical – no theoretical basis“m” is the porosity or cementation exponent

loosely related to tortuosity of the current flow path, better thought of as electrical efficiency of the path

“n” is the saturation exponentrelated to change in conductivity path with changing saturation

Archie porosity exponentArchie porosity exponent

for a simple bundle of capillary tubes oriented parallel to current flow direction: m → 1

insensitive to cross section shape, so fractures act like capillary tubes

as porosity increases and less of it participates in the conductive path, m ↑for an “average” sandstone comprised of spherical grains, m → 2

Resistivity of a simple rock modelResistivity of a simple rock model

For rock with tortuous pores:

For straight capillary tubes: F = Ro/Rw = 1/φ

0 1Porosity (φ)

RwResistivity (Ro)∞

F = Ro/Rw = 1/φ m(after Doveton, 2005)

Capillary tube model for mCapillary tube model for mm 1.0

> 1

~2

> 2

m = 1

after Herrick & Kennedy, 1993, SPWLA Paper HH

Core measurement Core measurement of the formation of the formation

factor, F

Freq

uenc

yG

ener

ator

Res

ista

nce

Ref

eren

ceC

ell

high -Pcore holder

Cor

e P

lug

Mi c

ropi

pette

high-P fluid

brine in

Plated electrodes

electricinsulator

factor, F

A

L

Rw

Φ

Start with core plug saturated with brine of known Rw & φ

then we measure R0. F = R0/Rw.

When F and When F and φφ are plotted logare plotted log--loglog

1

10

100

1000

0.01 0.1 1

φ

m= 3m= 2

m= 1

log F = -m log φ

F

Observed porosity dependence Observed porosity dependence of of ““mm””

Empirical: m = 0.676 log Empirical: m = 0.676 log φφ + 1.22 + 1.22 RR22 = 0.63 (RMA)= 0.63 (RMA)

each salinity is differenteach salinity is different40Kppm dataset is largest and used for base case40Kppm dataset is largest and used for base casecap m at 1.95cap m at 1.95

40K ppm brine data

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 4 8 12 16 20 24

In situ Porosity (%)

In s

itu A

rchi

e C

emen

taito

n Ex

pone

nt

y = 0.5377x + 1.3313R2 = 0.6331

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

log In situ Porosity (%)

In s

itu A

rchi

e m

Dual porosity modelDual porosity modelm = log[(m = log[(φφ--φφ22))m1m1 + + φφ22

m2m2]/log ]/log φφφ φ expressed as V/Vexpressed as V/Vφφ22 = 0.0035, m1=2, m2=1; SE both = 0.11= 0.0035, m1=2, m2=1; SE both = 0.11rock behaves like a mixture of matrix porosity and cracks, with rock behaves like a mixture of matrix porosity and cracks, with cracks dominating low porosity endcracks dominating low porosity end

cap at m = 1.95 (cap at m = 1.95 (φφ ~ 16%)~ 16%)both models fit data

40K ppm brine data

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 4 8 12 16 20 24

In situ Porosity (%)

In s

itu A

rchi

e C

emen

taito

n Ex

pone

nt

both models fit data

φφ = bulk porosity= bulk porosityφφ22 = fracture porosity= fracture porosity

mm11 = matrix cementation = matrix cementation exponentexponent

mm22 = fracture cementation = fracture cementation exponentexponent

And a third way to look at it....And a third way to look at it....Why is the minimum m ~ 1.2, instead of 1?A – for a distribution of cracks of different cross-sectional area, the largest (widest) cracks will dominate the conductivityThe high tail of the distribution determines the bulk conductivity,while the rest of the cracks act like “excess”porosity that do not participate (significantly) in the conductivity. Therefore m ↑

And are the And are the ““crackscracks”” all fractures?all fractures?

Probably not..............Slot-like pores oriented preferentially parallel to bedding also act like conductive cracks

Thin parallel laminae of slightly coarser, more permeable sand will be crack-like

Salinity dependence of Salinity dependence of ““mm””tested plugs with 20K, 40K, 80K, and 200K tested plugs with 20K, 40K, 80K, and 200K ppmppm brinesbrinesNearly all cores exhibit some salinity dependenceNearly all cores exhibit some salinity dependence

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 2 4 6 8 10 12 14 16 18 20 22

Brine Conductivity (mho/m)

Cor

e C

ondu

ctiv

ity (m

ho/m

)

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

0.01 0.1 1

Brine Resistivity (ohm-m)

In s

itu A

rchi

e C

emen

tatio

n Ex

pone

nt,

(m, A

=1)

n=335

All data, all salinities All data, all salinities

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

0 2 4 6 8 10 12 14 16 18 20 22

In situ Porosity (%)

Arc

hie

Cem

enta

iton

Expo

nent

(m, a

=1)

200K

80K

40K

20K

Salinity dependence of Salinity dependence of ““mm””m = a log m = a log φ φ + b+ bintercept b drops with intercept b drops with decreasing salinitydecreasing salinityslope is ~ constantslope is ~ constant

20K ppm

y = 0.2267Ln(x) + 2.2979

R2 = 0.6619

0.00

0.50

1.00

1.50

2.00

2.50

0.000 0.050 0.100 0.150 0.200 0.250

insitu porosity (%)

Axis Title

Series1

Log. (Series1) 40K ppm

y = 0.2328Ln(x) + 2.409

R2 = 0.6547

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.000 0.050 0.100 0.150 0.200 0.250

insitu porosity (%)

Axis Title

Series1

Log. (Series1)

80K ppm

y = 0.2149Ln(x) + 2.4354

R2 = 0.5132

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.000 0.050 0.100 0.150 0.200 0.250

insitu porosity (%)

Axis Title

Series1

Log. (Series1)

200K ppm

y = 0.1621Ln(x) + 2.3222

R2 = 0.3633

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.000 0.050 0.100 0.150 0.200 0.250

insitu porosity (%)

Axis Title

Series1

Log. (Series1)

Simple procedure to compute SwSimple procedure to compute Sw

determine Rw @ Tf conventionallyPickett plots – focus on the lower porosity, wetter sandstonesproduced watersyour best guess.......

convert Rw to 75°F by chart lookup or Arps equation

Pickett Plot examplePickett Plot example

Rw = 0.306

pick m at low porosityend, where BVWirr ~ BVW

Williams PA 424Williams PA 424--3434Piceance basinPiceance basinKmvKmv above above ““top gastop gas””

Pickett plot Pickett plot RwRw 0.306 0.306 ohmmohmm @ 160@ 160°°F = 0.7 @ 75F = 0.7 @ 75°°F (9K F (9K ppmppm))

Our new procedureOur new procedurecompute m at 40K ppm from RMA regression:

m40k = 0.676 log φ + 1.22e.g. for 10% φ : m = 0.676 + 1.22 = 1.896

correct m for salinity effect bym = m40k + ((0.0118 φ – 0.355) * (log Rw + 0.758))

e.g. for 10% φ, Rw = 0.7 @ 75°Fm = 1.896 + ((0.0118 * 10 – 0.355) * (log 0.7 + 0.758))m = 1.896 + (-0.237 * 0.603) = 1.753

cap m at 1.95 (~12% porosity)

Practical impactPractical impact

Nominally, most of us use an m close to 2, but usually slightly less, for tight gas sand evaluations (e.g. 1.85, 1.90)Variable m that DECREASES with decreasing porosity leads to lower Sw’sTherefore, there is more gas in the tight rocks than we thought.Above 10% porosity there is very little difference

Example: Low porosity, wet zoneExample: Low porosity, wet zone

Moderate porosity, wetModerate porosity, wet

““HighHigh”” porosity gas zoneporosity gas zone

m is HIGHER than base case, so Sw is higher

20Kppm example, Natural Buttes20Kppm example, Natural Buttes

30K 30K ppmppm example, Wamsutterexample, Wamsutter

Summary & ConclusionsSummary & Conclusions

335 Kmv samples run at multiple salinitiesArchie porosity exponent m varies with

porosity m ↓ as porosity ↓salinity m ↓ as salinity ↓

behavior is consistent with increasing electrical efficiency with decreasing porosity, whatever the pore scale architecture

variable m model can be implemented with a simple equation relating m to porosity and formation water salinitym is constant above ~12% porosity at 1.95lowering m at 5-12% φ increases GIPsee no impact below ~5% porosity

BVWirr is typically 3-5%no longer calculate Sw’s >> 1Sw = 1 at low φ validates Rw

Visit our project websiteVisit our project website

http://www.kgs.ku.edu/mesaverdehttp://www.kgs.ku.edu/mesaverde

Questions?Questions?