The Dual Formation Model provides a logging theoretic setting for the volume fractions of program LVPM as it is operated in “HET”, "PARA", or "PERP" modes for two separate formations. In the DFM, constraints are placed on the fundamental volume fractions of these two formations, and The Good Doctor, unmasked as an inveterate and incurable symbol pusher, provides the rasion d’tre for the term “Dual”, as in Dual Formation Model or in Dual Water Model. He also explores many of the fascinating algebraic properties of the Dual Formation Model.
The five volumetric components of the Dual Formation Model are pictured above. Program LVPM offers modeling for two such formations. Both will generally contain instances of all five such components.
The equation just below shows the unity relation that these five components must always satisfy. Program LVPM treats both formations independently and the user will always be prompted to strictly enforce this relationship.
In the Dual Formation Model, the total porosity includes both the liquid free water and hydrocarbons, together with the bound water:
Vsh in the Dual Formation Model is defined as the simple sum of the bound water and clay volume fractions:
The equations below define the component fluid saturations in terms of the TOTAL POROSITY. Note that the total water saturation includes the bound water !
With the effective porosity defined as above, including only the free water and the hydrocarbons, the DFM is evoked by stating the following simple proportionality:
THe Key Constraint that "evokes" the DFM
In the pdf file below, the Good Doctor demonstrates that this is equivalent to the classic ansatz of the dual water model stating that the bound water saturation is numerically equal to Vsh !! His statement here is more physically appealing and may lead to important generalizations for other formations in the future.
This report demonstrates that all five DFM component volume fractions can be obtained from just three quantities: the toal porosity, the total water saturation, and Vsh:
Note that the total water saturation is needed only to compute the free water and the hydrocarbon volume fractions. Many other interesting relationships are explored in the pdf file below.