The classic Dual Formation Model provides a familiar FORMATION VOLUMETRIC MODEL for log analysists, logging engineers, logging tool designers, reservoir managers, geologists, and upper management to better understand a reservoir's composition and hydrocarbon content. Five formation volume fractions are used: (1) matrix, (2) free water, (3) hydrocarbons, (4) clay, and (5) bound water. These volume fractions sum to unity and are subject to constraints imposed by the model itself. (See below).
LVFPM is a nuclear micro-geophysical Forward Model: given a formation's specific minerals, fluids, pore sizes, and volume fractions (also summing to unity), LV(F)PM computes classical neutron and gamma ray physical parameters that are routinely used by logging tool designers and other experts to determine porosity, water saturation, and hydrocarbon content from logging tool responses. While LV(F)PM volume fractions also sum to unity, there are a large number of component volume fractions that consist of (a) specific minerals, fluids, and gases and their chemical formulae, (b) their grain or fluid densities, and (c) the actual volume fractions of all; these components are specified to reside in the pores, not in the pores, or in both. These volume fractions do sum to unity but are not otherwise subject to constraints, unless as imposed by the user's input choices.
Programs LVPM.exe (fixed user-specified pore size) and LVFPM.exe (variable pore size at user-specified fractal dimension) are operated in “HET”, "PARA", or "PERP" modes for two separate formations.
The five volumetric components of the Dual Formation Model are pictured above. Program LV(F)PM CAN offer modeling for two such formations; both will generally contain instances of all five components. Program LV(V)PM MAY ALSO provide modeling of a much larger class of formations not subject to constraints inposed by the Dual Formation Model.
The equation just below shows the unity relation that the five DFM components must always satisfy. Program L(F)PM treats both its formations independently and the user will always be forced to strictly obey the unity relationships for all its volume fractions.
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.