## Wednesday, December 8th, 2010

### Quantifying Pore Pressure through Modeling the Elastic Stage of Shale Compaction

#### James T. Krushin, Consulting Geologist/Petrophysicist

### Abstract

Traditionally, geologists use the shallow, inelastic-dominated,
exponential loss of porosity from the near surface to predict porosity
at depth and infer overpressure. This calibration to shallow high
porosity mud fails to properly model compaction at depths and
temperatures important in oil and gas drilling, where the porosity of
the shale is elastic.

Shales lose porosity through compaction.
More specifically, the components of compaction are mechanical, governed
by effective stress; thermal, associated with increasing temperature
due to the geothermal gradient, and chemical, such as the
smectite-to-illite transformation. In addition to the components of
compaction, the variables of CEC (cation exchange capacity) and the
specific exchangeable cation (Na is believed to be the most dominatant
species in the subsurface) also affect shale porosity. The salinity of
the depositional fluid only affects shallow, inelastic shale porosity
and is not further discussed.

Techniques that have been used to
study clays and soils are applied to the bulk properties of shale.
Desorption water vapor isotherms of Na exchanged pure clays, clay
mixtures, and shales help to quantify the interrelationship of the
variables and components that control elastic shale porosity. These
isotherms show that the amount of water per gram of dry sample (water
content) increases with increasing CEC (cation exchange capacity) for a
given relative humidity (p/p

_{o}). Plotting p/p

_{o} vs.
mass of water normalized by meq (meq is a unit of CEC measurement)
results in a general mechanical compaction curve when a thermodynamic
equation (Kelvin equation) is used to convert p/p

_{o} to
effective overburden stress. Note that this general mechanical
compaction curve is referenced to the temperature of the isotherms,
about 75ºF. Additional thermal effects on porosity are quantified via
another technique and thermodynamic transformation.

The effects
of diagenesis (i.e. smectite-to-illite) and variable mineralogy are
incorporated in the compaction model via the bulk CEC parameter,
calculated from well logs using a refined published algorithm. Pore
pressure is calculated from the effective stress equation after all the
compaction components and variables controlling shale porosity are
accounted for.

CEC is strongly correlated to the total specific surface area - SSA (m

^{2}/g)
for shales, soils, and clays. The shale’s average water thickness
(average pore size radius) can be calculated from SSA and porosity. The
commonly used, shaly sand Dual Water model adds insight into shale pore
water electrical conductivity as it relates to the distance from the
shale surface (i.e., average water thickness). The authors of the Dual
Water model conclude that where this average water thickness is less
than or equal to 6.2 angstroms, the electrical conductivity of this
bound water (Stern Layer) is a function of temperature and Qv (meq/CEC)-
which is just another form of the previously mentioned, mass of water
normalized by meq.

Interpretation of an onshore Gulf Coast well
shows that below about 1500 ft. (TVD), the average water thickness for
the shales is less than 6.2 angstroms and the decrease in water
thickness is fairly linear. Above 1500 ft., the average water thickness
increases exponentially upward. The 1500 ft. delineates the shallow
inelastic compaction, dominated by the unrecoverable loss of large
pores, from the deeper elastic compaction. The electrical resistivity
of the elastic stage of compaction is modeled using a simple Archie’s
equation, that is, the electrical resistivity of the shale is a product
of the Formation Factor (F) and Stern layer resistivity. Multiple
linear regression analysis shows that F varies with effective stress,
porosity and CEC.

A review of this compaction model shows that
all shales have the same average water thickness per SSA (or similar
values of - Qv, or mass of water per meq) for a given state of effective
stress and temperature. The shales differ in porosity for a given
state of stress and temperature because of the variability of the
shales’ bulk CEC (or SSA). This conclusion is supported by other
researchers working within the realm of soil science, groundwater, and
civil engineering..

### Speaker Biography

**James T. Krushin** is a consulting geologist/petrophysicist working
both domestically and internationally in the spectrum of single-well
interpretations, integrated field studies, and company appraisals for
the past 12 years. Prior to working as a consultant, Jim worked for 15
years at Amoco Production Company in Houston, TX and Tulsa, OK in
exploration and exploitation. His recent interests include quantifying
reservoirs, seals, pore pressure, and, obviously, shales.

He has
both a BS and MS degree in geology from the University of Pittsburgh
and also is a graduate of Amoco’s Petrophysics Training Class XXIV,
where his research topic was the petrophysical properties of shale. Jim
is a member of SEG and a 30 year member of the AAPG.

### References

Krushin, J. T., 2005, Quantifying shale porosity- A thermodynamically based, predictive model which includes the effects of mechanical compaction, temperature, mineralogy, and chemical diagenesis: Gulf Coast Association of Geological Societies Transaction, v. 55, p. 401-414.

Krushin, J. T., 2008, A compaction-based pore pressure model for shales: Gulf Coast Association of Geological Societies Transaction, v. 58, p. 575-586.