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 (m²/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.