The diagenesis model in Parageo allows to capture the macroscopic effects of diagenetic reactions on sediment properties (e.g. porosity, permeability, strength, compressibility, stifness, etc.) and pore pressure. In such model:

 

•Diagenesis_data structure is used to define each diagenetic reaction that may be assigned to any Matreial_data

•Any Material_data may have assigned multiple reactions with cumulative effects

•Reaction rates are temperature driven

•Each reaction is defined by a maximum diagenetic porosity loss (the maximum diagenetic porosity loss for a given material will be the sum of the maximum diagenetic porosity loss of each assigned reaction)

•The diagenetic overprint on geomechanical properties is directly related to the diagenetic porosity reduction for each reaction

 

This model therefore allows a given material to be assigned a diagenetic reaction that occurs at shallow depths where the temperature is realtively low (e.g. early carbonate cementation) and a reaction triggered at higher temperatures (e.g. Smectite-Illite transformation). Note that the target of this model is to allow representation of the macroscopic diagenetic effects on sediments and pore pressure for evolutionary modelling over geological time scales. Thus for the sake of simplicity and applicability the actual stoichiometry and the mass balance of a given reaction is not considered. This facilitates model calibration to data that may be retrieved from the field (e.g. well log trends).

 

Thus the porosity in ParaGeo is then:

 

 

Where is the reference/depositional porosity defined in Material_data, is the change in porosity due to mechanical compaction and is the change in porosity due to diagenesis which is the sum of the porosity change of the diagenesis reactions assigned to the material described as:

 

 

 

The model has several components, some of which may be optional (e.g. you may or may not consider cementation in a given diagenetic reaction). Such components are described below. Note that for the sake of simplifiying notation in the formulas they are described for a given considered reaction (i.e. avoiding the continuous specification of the subscript ).

 

 

Reaction model

The reaction model defines the function and parameters controlling the rate of porosity change ( ) for the defined reaction. There are two laws currently implemented:

 

Power law

 

The power law introduces an initiation threshold temperature above which the reaction starts to occur. Thus for then:

 

 

Where is the pre-exponential factor, is the current temperature, is the maximum diagenetic porosity change for the reaction, is the current diagenetic porosity change for the reaction and and are the exponents.

 

 

Exponential law

 

The exponential law is always active and defined as:

 

 

Where is the activation energy in [J· mol-1] and is the gas constant in [J· K-1· mol-1]

 

 

 

Compaction model

 

The compaction model defines the effect of the diagenesis in the sediment strength, compressibility and stiffness. There different models available are:

 

Enhanced pc

In this model a diagenetic plastic volumetric strain which contributes to increasing the strength of the material (via an increase in ) is calculated for the considered reaction as:

 

 

Where is a multiplication factor defining the portion of the diagenetic porosity loss for the considered reaction that will contribute to the calculation of the diagenetic volumetric plastic strain. Then the plastic volumetric strain used to compute the hardening law (and hence compute ) is split into the mechanical and diagenetic contributions as:

 

 

 

Enhanced hardening

 

This model considers an increase in in an identical manner than the "Enhanced_pc" model as well as a reduction in sediment compressibility via a reduction in (which defines the slope of the Normal Compression Line) and increase in sediment stiffness via a reduction in (which defines the slope of the unloading/reloading line). This is formulated as:

 

  and  

 

Where and are the initial values defined for mechanical compaction (non-diagenetically modified material) and and are the maximum change in the respective variables due to the diagenetic overprint of the considered reaction.

 

 

 

Cementation model

 

Cementation of minerals in the pore spaces creates bonds between the sediment grains. This macroscopically results in an increase in tensile strength which is formulated as an increase in as:

 

 

Where is the initial reference value and is the maximum increase in tensile strength due to the considered diagenetic reaction.

 

 

 

Flow rule

 

The flow rule defines whether the non-mechanical (diagenetic) compaction is uniaxial, hydrostatic or anything in between.  This is defined via an input parameter named "Compaction_direction_factor" that takes value 0.0 for the uniaxial case and 1.0 for the hydrostatic case. This parameter has a large influence on the horizontal effective stress evolution due to diagenesis (and therefore on the stress path) where the higher the number the larger the reduction in horizontal effective stress (thus a relatively large reduction in horizontal stress is expected for the hydrostatic case). This will be explained in detail in the Diagenesis Model Behaviour page.