Agreement DE-FC26-02NT15342, Seismic Evaluation of ...

ε - y i + 〈w, x i 〉 + b ≤ 0 if α i > 0 (15)
In conjunction with an analogous analysis on α * i we have
max {-ε + y i - 〈w, x i 〉 | α i < C or α * i > 0} ≤ b ≤ (16)
min {-ε + y i - 〈w, x i 〉 | α i > 0 or α * i < C} (17)
(*)
If some α i ∈ (0, C) the inequalities become equalities. Then the b term can be
calculated by choosing any i.
Calculation of water saturation log
We applied the following steps in calculation of water saturation log:
1. Calculate shale percentage with Gamma ray log;
2. Convert shale percentage to different lithology;
3. Determine input parameters (water and gas density, water resistivity) according to
depth, temperature, and resistivity of water saturated sand zone;
4. Solve saturation and porosity for different lithology.
Shale percentage (Vsh) can be calculated from Gamma ray log according to equation
(18):
GR − GR
sand
Vsh = (18)
GR − GR
shale
Here GR is the reading from Gamma ray log; GR sand is the Gamma ray reading from sand
zone; and GR shale is the Gamma ray reading from shale zone. In our following examples,
when shale percentage is 50% and above, we consider this interval as shale; and when the
shale percentage is below 50%, we consider this interval as sand.
We also need calculate porosity and water saturation of reservoir For porous sand
reservoir water saturation (S w ) can be calculated by the Archie’s law (…..):
S
w
=
0 .81 / φ
R
t
2
×
where Rw is resistivity of formation brine. The formation resistivity (R t ) of sand zones
can be read directly from the resistivity log. Bulk density is usually calculated from grain
density and fluid density:
ρ = ( 1 − φ ) ρ ρ φ (20)
ma +
Where ρ ma is the grain density and ρ f is the fluid density. Fluid density can be expressed
by gas density and water density (Here the fluid in our reservoir consists only gas and
water):
ρ
f
= S
w
ρ
w
+ ( 1 − S
w
) ρ (21)
g
Where ρ w is the water density and ρ g is the gas density. With equation (19), (20), and
(21), porosity can be expressed as:
f
sand
R
w
(19)
Agreement DE-FC26-02NT15342, Seismic Evaluation of Hydrocarbon Saturation 22