Modified Athy-Law Compaction to Account for Porosity Generation and Preservation from Kerogen Conversion in
Terzaghi-Like Models of Petroleum Source Rocks*
Matthias Cremon1, Alan K. Burnham1, Yimin Liu1, and Alexandre Lapene2
Search and Discovery Article #42062 (2017)**
Posted May 8, 2017
*Adapted from oral presentation given at AAPG Annual Convention & Exhibition, Houston, Texas, April 2-5, 2017
**Datapages © 2017 Serial rights given by author. For all other rights contact author directly.
1
Energy Resources Engineering, Stanford University, Stanford, California (aburnham@stanford.edu)
2
Total E&P USA, Palo Alto, California
Abstract
A new algorithm is proposed and calibrated for assessing the effect of organic matter on compaction, porosity generation, and porosity
preservation in organic-rich fine-grained sediments at various maturities. The algorithm involves the addition of simple terms to the Athy-Law
exponent relating porosity to effective stress in Terzaghi-like compaction models, which are often used in basin and petroleum systems models
to calculate expulsion of water and petroleum from source rocks. The central concept in these models is that porosity is related to the difference
between vertical lithostatic pressure and pore pressure, and pore pressure is calculated from a simple permeability model, either 0D or 1D. The
new model presented here is empirical and requires calibration for the source rock of interest. It considers that because kerogen is softer than
most inorganic grains, when in high concentration, it can lead to lower rock porosity prior to catagenesis. This part of the model was calibrated
for the Green River Formation using log data at 600-700 m that shows porosity decreasing from 15-25% to about 7% as the kerogen volume
fraction increases from negligible to 50 vol%. In addition, the new model was designed to consider that preservation of porosity created from
kerogen conversion can be related to its geometric shape and the ductility of the surrounding mineral grains. Model results are shown for the
ranges of residual kerogen porosities observed in source rocks. The model has been incorporated into TRESORS, a 0D simulator of source rock
maturation and expulsion at both laboratory and geological conditions.
References Cited
Athy, L.F., 1930, Density, porosity and compaction of sedimentary rocks: American Association of Petroleum Geophysicists Bulletin, v. 14, p.
1-24.
Braun, R.L., A.K. Burnham, 1992, PMOD: a flexible model of oil and gas generation, cracking, and expulsion, Org. Geochem., v. 19, p. 161-
172.
Burnham, A.K., 2017, Porosity and permeability of Green River oil shale and their changes during retorting, Fuel, v. 203, p. 208-213.
Chen, Z., and C. Jiang, 2016, A revised method for organic porosity estimation in shale reservoirs using Rock-Eval data: Example from
Duvernay Formation in the Western Canada Sedimentary Basin, AAPG Bull., v. 100, p. 405-422.
Fishman, N.S., H.A. Lowers, P.C. Hackley, R.J. Hill, and S.O. Egenhoff, 2012, Porosity in shales of the organic-rich Kimmeridge Clay
Formation (Upper Jurassic), offshore United Kingdom: AAPG Annual Convention and Exhibition, Long Beach, CA, April 22-25, 2015. Search
and Discovery Article #50620. (2012). Website accessed April 18, 2017.
http://www.searchanddiscovery.com/pdfz/documents/2012/50620fishman/ndx_fishman.pdf.html
Hantschel, T., and A.I. Kauerauf, 2009, Fundamentals of basin and petroleum systems modeling: Chapter 2, Springer-Verlag.
Horsrud, P., 2001, Estimating mechanical properties of shale from empirical correlations: SPE Drilling & Completion, June, p. 68-73.
Reeder, S.L., R.J. Kleinberg, B. Vissapragada, M. Macklus, M.M. Herron, A.K. Burnham, and P. Allix, 2013, A multi-measurement core-log
integration for advanced formation evaluation of oil shale formations: A Green River Formation case study: Petrophysics, v. 54, p. 258-273.
Smith, J.W., H.E. Thomas, and L.G. Trudell, 1968, Geologic factors affecting density logs in oil shale: SPWLA 9th Annual Logging
Symposium, New Orleans, LA, June, Paper P, 1-17.
Sone, H., and M.D. Zoback, Mechanical properties of shale-gas reservoir rocks - Part 2: Ductile creep, brittle strength, and their relation to the
elastic modulus: Geophysics, v. 78, p. D393-D402.
Terzaghi, K., 1923, Die Berechnung der Duerchlassigkeitsziffer des Tones im Verlauf der hydrodynamischen Spannungserscheinungen: Szber
Akademie Wissenschaft Vienna, Math–naturwissenschaft Klasse IIa, v. 132, p. 125-138.
Thomas, G.W., 1966, Some effects of overburden pressure on oil shale during underground retorting: Soc. Petrol. Eng. Jour., March, p. 1-8.
Tisot, P.R., and H.W. Sohns, 1970, Structural response of rich Green River oil shales to heat and stress and its relationship to induced
permeability: J. Chem. Eng. Data, v. 15, p. 425-434.
Tisot, P.R., 1967, Alterations in structure and physical properties of Green River oil shale by thermal treatment, J. Chem. Eng. Data, v. 12, p.
405-411.
White, J.A., A.K. Burnham, and D.W. Camp, 2017, A thermoplastic model for oil shale, Rock Mech. Rock Eng., v. 50, p. 677-688.
Modified Athy-Law Compaction to Account for Porosity
Generation and Preservation from Kerogen Conversion in
Terzaghi-Like Models of Petroleum Source Rocks
A A P G A C E , H OUSTON, T X , 2 - 5 A PRIL 2 0 1 7
PRESENTED BY M . C R E M O N , A . K . B U R N H A M , Y. L I U , AND A. LAPENE
S T A N F O R D U N I V E R S I T Y, S T A N F O R D C A , AND T O TA L E & P R & D , P A U F R A N C E
Common compaction modeling laws
Athy (1930): Terzaghi (1923):
Exponential decline of Exponential decline of porosity
porosity with depth with effective stress (P L-P)
PH P PL
Examples from Hantschel and Kauerauf, Fundamentals of Basin and Petroleum Systems Modeling, Springer, 2009
2
Key questions for modeling porosity evolution
How does porosity evolve in mixtures of brittle and ductile
materials?
Clay and kerogen are more ductile than quartz, silicates, and carbonates
Related to the classical discussion of whether kerogen is load bearing or pore filling
How does the porosity evolve with kerogen conversion?
Conversion of kerogen to oil and gas creates void space amounting to 20-80 % of the
kerogen volume depending on Hydrogen Index
How much of this generated porosity is lost immediately and during subsequent burial?
Note: The initial discussion uses Athy’s law as an example with the understanding that
compaction in the absence of organic matter is more complicated than a single exponential
3
Green River Formation porosity depends
strongly on organic content
Parachute Creek Member
Porosity
Depth, feet
L3 Aquifer
Parachute
TOC, wt%
Creek
Garden Gulch
Garden
Gulch
Quartz & 4
Feldspar
Adjusting Athy’s Law for organic content
𝑛)
𝜑 = 𝜑0 𝑒 −𝑎𝑑/(1−𝑘 0.30
R1 Zone
R1 Zone calc
0.25
𝜑 is porosity R0-L0 zone
𝑑 is depth R0-L0 zone calc
0.20
𝑎 is a compaction coefficient
Porosity
𝑘 is kerogen volume fraction
𝑛 is an organic grain 0.15
compaction correction
0.10
Interval Depth, ft 𝜑0 𝑎 𝒏 0.05
R1 2014-2135 0.6 0.0011 0.5
0.00
R0-L0 2135-2250 0.5 0.0016 0.7 0.0 0.2 0.4 0.6
Kerogen volume fraction (𝑘)
5
Kerogen reduces porosity because it is softer
2.5 20
Uniaxial compressive strength, MPa
0.8+1.3*exp(-gpt/12)
Young's modulus, GPa
2.0 16 6.5+9.5*exp(-gpt/12)
0.076(304.8/DTCO)3.23
1.5 12 0.77(304.8/DTCO)2.93
1.0 8
0.5 4
kerogen is 50 vol%
0.0 0
0 5
10 10
20 15
30 20
40 25
50 0 5
10 10
20 15
30 20
40 25
50
TOC, wt% TOC, wt%
DTCO is the sonic log compressional wave arrival time; gpt = gal/ton 2TOC
Asymptotic limit of Young’s modulus is the same as for high-density polyethylene 6
Clay-quartz mixtures have analogous
enhanced compaction
Ductility of clay enables
more deformation and
compaction under lithostatic
load corresponding to
~6600 ft of burial
From Linked-In PSA
Webinar #5 by Rob Lander
of UT Austin
7
Clay has a smaller effect on porosity than
kerogen for the Green River Formation
Clay mineral content determined by Schlumberger ELAN
Clay is uncorrelated to anti-correlated with kerogen content depending on
depth interval
Porosity correlates weaker with clay than kerogen content
Parameter fits including both kerogen and clay content are negligibly
better than for kerogen alone
porosity = (a + b*clay)*exp(-c*kerogen)+d
8
Kerogen conversion modifies Athy’s Law
Kerogen conversion creates porosity
20-80% of kerogen volume, depending on HI
A large fraction has pore diameters less than 100 nm
Does this porosity cause a positive deviation from Athy’s law?
It will not if the porosity is easily filled by rearrangement of surrounding mineral grains
It will if the porosity is stable due to mineral bridges
Compaction likely depends on ductility of mineral matrix (Fishman et al., 2012)
Compaction efficiency likely depends on kerogen geometry (globular versus lenticular)
Why do we care? Compaction likely affects expulsion efficiency
Generation of oil and gas increases organic volume by only ~20% at generation T & P
Sorption capacity of kerogen may depend on applied lithostatic load
Expulsion may depend on hydrocarbon saturation level of pore fluids (relative permeability)
9
Porosity generated is calculated simply from
mass and volume balance
Generated porosity
𝜑 k = R×(Ki/i -Kr/r) = R× Ki(1/i -fr/r)
R = density of rock
Vitrinite reflectance, %Ro
i = density of immature kerogen
r = density of residual kerogen} 1.6
3.0 2.0 1.0
Ki = mass fraction of immature kerogen density = 1.7 0.46×H/C
inertinite
anthracite
Kr = mass fraction of residual kerogen = fr×Ki 1.4
density, g/cm3
vac resid
fr = mass fractional conversion of immature to
delayed petcoke
bituminous coal
alginite
mature kerogen 1.2
vitrinite
bitumenite
1.0
0.8
0.4 0.6 0.8 1.0 1.2 1.4
H/C ratio
10
Measured and calculated porosities agree
well for low applied stress
Thomas 1966 1000 psig
0.6 AMSO cores 2400psi Unconfined
AMSO cores 3 psig swelling?
swelling?
Porosity, fraction Retorted LETC
Raw LETC
compaction
Retorted (calc) at 16 MPa
0.4
Raw (calc) From
Burnham
Thomas says (2017)
15% compaction
0.2 for 70 gpt
Lineis isfrom
Line from CH-1
CMR loglog
for AMSO well CH-1
0
00 5 10
20 15 20
40 25 30
60 35 40
80
TOC, wt%
Grade, gal/ton 11
Mature source rock porosity is largely within
residual organic matter
From Sone and Zoback (2013) From Chen and Jiang (2016)
Duvernay,
Canada
oil-wet gas
dry gas
wet gas
Rock
oil-wet gas
12
Athy’s Law corrected for additional porosity
from kerogen conversion
−𝑎𝑑/(1−𝑘𝑖 𝑛)
𝜑 = 𝜑0 𝑒 + 𝜑𝑘𝑒 −𝑏𝑑 0 15
1,000
𝜑 is porosity
𝜑0 is initial porosity at burial
2,000 63
𝜑𝑘 is porosity from kerogen decomposition
Temperature, C
𝑑 is depth
87
Depth, m
𝑎 is a mineral porosity compaction coefficient 3,000
𝑘𝑖 is initial kerogen volume fraction Basic Athy Law 121
(perhaps labile kerogen only) 4,000
𝑛 is an organic grain compaction correction Ductile kerogen
𝑏 is a kerogen porosity compaction coefficient 5,000 modification 135
Add porosity from
6 wt% Type I kerogen 12.6 vol% 6,000
kerogen conv 159
35% converted to residual kerogen 3.3 vol% Compactable
Single first-order reaction organic porosity
𝜑0 = 0.6; 𝑎=0.0008; 𝑛=0.5; 𝑏=0.0002 7,000
0 0.1 0.2 0.3
Porosity
13
Alternate and additional approaches provide
better agreement for complex systems
Use effective stress instead of depth
Include a fracture pressure relief valve
Include a residual irreducible baseline porosity
Example:
𝑛)
𝜑 = 𝜑0 𝑒 −𝐾𝜀 (𝑃𝐿 −𝑃)/(1−𝑘𝑖 + 𝜑𝑘 𝑒 −𝐾𝑘 (𝑃𝐿 −𝑃) + 𝜑𝑖𝑟
1992
𝜑𝑘 is porosity from kerogen conversion
𝐾 is a mineral compaction coefficient
𝐾𝑘 is a kerogen compaction coefficient
𝜑𝑖𝑟 is the irreducible porosity
P is the pore pressure
PL is the lithostatic pressure
From Braun and Burnham (1992) PH is the normal hydrostatic pressure
14
Summary and Conclusions
Ductility of kerogen causes greater compaction for richer source rocks
Similar to observations by others for clay in quartz matrices
CMR and other logging tools can be used to gather much more data than laboratory
measurements to better discern trends and calibrate appropriate models
Unambiguous trends were observed for the Green River Formation in the Piceance Basin
and used to calibrate a simple enhanced-compaction model
Generation of porosity from kerogen decomposition is well known but
preservation is not well quantified
Data in the literature is relatively sparse with large scatter
Others have suggested that ductility of mineral matrix dominates porosity preservation
Several empirical functional forms were suggested for modeling preservation and
compaction but await better data for calibration
These effects have been incorporated into the in-house single-cell
compositional kinetics-fluid flow-geomechanics computer code
TRESORS currently under development through TOTAL E&P R&D
15
ACKNOWLEDGEMENTS
This work has been financially supported by TOTAL S.A. through
STEMS project, a research collaboration between TOTAL S.A.
and Stanford University.
The authors would like to thank TOTAL S.A. for its financial
support.
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