2. Petrophysicist Role
• Petrophysics is the study of rock properties and
their interactions with fluids (gases, liquid
hydrocarbons, and aqueous solutions).
• Petrophysicist is considered to be responsible for
integration of all available data from wireline
logging together with core analysis data in order
to generate a complete picture for the reservoir
in hand.
• Petrophysicist is responsible for generating field
study based on wireline logs to be provided
further for the geologists and reservoir engineers
to work on the static and dynamic modeling.
3. Archie Equation
• Archie Equation is the most famous equation used
by petrophysicists to determine the water saturation
in the reservoir in hand.
• Considered to be effective in clean reservoirs.
• Used by petrophysicists and log analysts in manual
interpretation to have a quick look evaluation.
• Presence of any shale content within the reservoir
decreases the reliability of the water saturation
calculated by Archie Equation.
• Using Archie in shaly reservoirs of high resistivity
generates high water saturation values should be
corrected further on the CPI log.
4. Extracting Archie Equation
• Resistivity Index:
• Considering Rt is the true resistivity of the reservoir,
and Ro is the resistivity of the reservoir fully saturated
with water,
RI = Rt / Ro, Where RI is the resistivity Index.
• If the reservoir is fully saturated with water, then the
true resistivity should be the same as the Ro value.
(SW)n = Ro/Rt
(SW) n = 1 / RI
(n) Is the saturation exponent
5. (SW)n =
𝑹 𝒐
𝑹𝒕
=
𝑭 𝑹𝒘
𝑹𝒕
Extracting Archie Equation
• (F) The Formation Factor of
the reservoir is characterized
by two factors, the tortuosity
and the porosity.
F =
𝒂
𝝓 𝒎
Where (a) is Tortuosity Factor,
(𝝓) is the porosity
and (m) is the saturation exponent
Where (Rw) is
the water resistivity
And
(Rt) is the true resistivity
Resistivity of Brine
Water Ro = F * Rw
The saturation equation
will be
6. Extracting Archie Equation
(SW)n =
𝒂 ∗𝑹𝒘
Ф 𝒎
∗
𝑹𝒕
• The generalized equation that had come from study of 152 core of
oil producing sandstone reservoirs indicated that (m) = 2, (n) = 2
and (a) equal (0.81) in sand with porosity higher than 0.15 and (1) in
carbonate and low porosity sand, while the other parameters are all
could be detected from the logs, then finally the following general
equation has been the standard Archie Equation.
(SW)2 =
𝒂 ∗𝑹𝒘
Ф 𝟐
∗
𝑹𝒕 Or
SW =
𝒂 ∗𝑹𝒘
Ф 𝟐
∗𝑹𝒕
Simple Archie Equation
Archie Equation
7. Humble Equation
• Humble Plot was the first graphical attempt to solve
the water saturation equation.
• This equation was extracted based on core plugs,
where F vs. ϕ were plotted on a chart, and the following
formation factor parameters were obtained,
F = 0.62 / ϕ2.15
• This Equation later simplified with the known formation
factor, which is extensively used in sandstone formations
F = 0.81 / ϕ2
10. Determining the Archie
Equation Parameters
• Total Porosity: The ratio of the volume of all pores to
the bulk volume of the rock. (ϕt = Vp/VB)
• Effective Porosity: The ratio of only the
interconnected pores to the bulk volume of the
rock.
• (m) is the cementation exponent that differs
according to the degree of cementation.
• (n) is the saturation exponent that is determined
from special core analysis.
• (a) is the tortuosity factor depends on the path that
the fluid will flow through.
11. Determining the Archie
Equation Parameters
Bulk Volume of the Rock
Rock Matrix Porosity Fluids
Bulk Volume = 1
VM+Φt =1
VM = 1-Фt
BVW = Sw* Ф
12. Determining the Archie
Equation Parameters
Shale Volume
What is the
difference between
water saturation
(Sw) and Bulk
Volume of Water
(BVW)?
Rock with shale content
13. Water Saturation and Bulk
Volume Water
• Water saturation is the amount of water in
relation to the pore spaces only.
• Bulk Volume of Water is volume of the water in
relation to the total bulk volume of the rock.
Sw= BVW/ϕeffФT = VP / VB
BVW = Sw * ϕeff
14. Example
• A rock with true resistivity around 20 ohm.m has
been encounteredin Bahariya Formation in
Western Desert with porosity ranging from 0.20 to
0.25, Determine the water saturation within this rock
if the water resistivity is 0.035 ohm.m?
15. • A sandstone rock with 30% porosity and 10 ohm.m
resistivity, What is the water saturation of this rock if
the water resistivity is 0.12 and derive the bulk
volume of water?
Example
16. How to detect the
lithology and the zone of
interest?
18. Detecting the Lithology from
the D-N Crossplot
Ρb = 2.4 g/cc
ФN = 0.20
Ρb = 2.38 g/cc
ФN = 0.165
0.20 L.St.
0.20
L.St or S.S ??
19. Calculating Porosity in the
Formation
• In order to calculate the porosity of the formation, it
is necessary to have an idea about how to detect
the lithology, how to read the logs, and the most
important thing, How to feel the wireline logs and
visualize the formation?
• Moreover, the log analyst as well as the
petrophysicist should have an idea about the
equations that will lead him to give a quick look
evaluation for the reservoir in hand.
20. Calculating Porosity in the
Formation
• Calculating porosity from the density curve
ϕD =
STUV W SX
STUV W SY
𝜌mat is the matrix density
S.S = 2.65
L.St = 2.71
Dol. = 2.847
Bulk Density
Porosity From Density
Fluid Density
Fresh = 1
Salt = 1.1-1.2
21. Calculating Porosity in the
Formation
27.5 %
Determine the
porosity from
density curve
if the ρb curve
reads around
2.4 g/cc?
22. Calculating Porosity in the
Formation
• Calculating porosity from the Sonic curve
ϕS =
`VTUV W`Vabc
`VTUVW`VY
𝛥𝑇mat is the matrix Transit Time
S.S = 55.5 µs/ft.
L.St = 47 µs/ft.
Dol. = 43 µs/ft.
Sonic Reading
Porosity From Sonic
• Primary Porosity Could be calculated from
sonic curve in conjunctionwith the density and
neutron curves.
Fluid Transit time
Fresh = 189 µs/ft.
Salt = 185 µs/ft.
23. Calculating Porosity in the
Formation
10.7 %
Determine the
porosity from sonic
curve if the 𝛥tlog
curve reads around
70 µs/ft.?
24. Calculating Porosity in the
Formation
• Calculating porosity from the Neutron curve
ϕN = Reading of the neutron curvePorosity From Neutron
• The higher the porosity of the formation, as well as the
hydrogen content, the higher the neutron curve
value.
• Interpret the high value of the neutron curve in the
shale beds?
25. Calculating Porosity in the
Formation
26 %
Determine the
porosity in
sandstone from
neutron curve if
the ФN curve reads
around 18% in
limestone scale?
26. Calculating Porosity in the
Formation
• Calculating the total porosity from the curves within
hand
φT =
ϕklϕmlϕn
o
Total Porosity
φT =
ϕklϕn
p
Or
Or
φT =
ϕklϕn
p
For Gas
Intervals
27. Example
• In the following log example, determine the interested
zones, calculate the porosity, detect the resistivity, then
determine the water saturation within the zones of
interest if the water resistivity of the same formation was
detected from water sample and the results were
around 0.03 ohm.m?
29. Detecting the Water
Resistivity
• Water resistivity is the most important parameter in
Archie equation, and plays very important role in
the equation.
• Inaccurate water resistivity value results in totally
unreliable water saturation and wrong true bulk
volume of water.
• Water resistivity could be determined through
different equations and methods, the most easiest
and fastest one is from the porosity with resistivity
value in the clean water zone.
30. Methods of Detecting the
Water Resistivity
• Form Archie Equation, in a clean 100% water
interval with high porosity.
• If the cementation exponent is known from core
analysis, this will typically enhance the accuracy of
water resistivity value. Otherwise use the standard
(m) value as usual.
Rw =
ФT
∗qV
U
31. Methods of Detecting the
Water Resistivity
• Form Picket Plot, which is considered to be an
integration between the reversed Archie Equation
and the crossplot.
• This crossplot has to be in coherent with the value
calculated from the reversed Archie Equation
(more or less the same).
Rw =
ФT
∗qV
U
32. Methods of Detecting the
Water Resistivity
• Form Picket Plot, which is considered to be an
integration for the reversed Archie Equation with
crossplot.
Rt
33. Methods of Detecting the
Water Resistivity
• From a water sample salinity value measured in
the lab. This is considered the best method.
• Water resistivity calculated from the logs using true
resistivity. There could be some errors due to the
influence of the mud on log readings.
• Analogues if no water zone available in the well.
35. Methods of Detecting the
Water Resistivity
• From SP Log, we can determine the Water Resistivity
value using the following equation
• Kc = Temperature coefficient = - (61 + 0.133 T degF)
• Rmfe= Resistivity of mud filtrate (When Rmf @ 75° F > 0.1,
then Rmfe = Rmf x 0.85.
• When Rmf @ 75°F < 0.1, use Schlumberger Chart SP-2 to
find Rmfe.
• SSP = Static Spontaneous Potential.
SSP = -Kc Log
qTYr
qsr
37. Methods of Detecting the
Cementation Exponent Value
• Form Picket Plot, (m) is the slope of the line that
detecting the Rw value.
38. Methods of Detecting the
(m) Value
• From Special Core Analysis.
• A log-log plot of F vs. ϕ yields a
straight line that can be extrapolated
to ϕ =1 to find (a) value. The slope
of the line is –m (Due to that
Log ϕ always will be with (–
value) .
• A best fit line drawn through the
points intersects the representing ϕ
=1. at a value of 1.4 then a=1.4
.The slope of the line is -1.8, so
m=1.8.
• (a) value is detected at the point of
the intersection between the drawn
line and (X = 1)
a value
m= -Y/X
39. • These methods were discussed extensively and
finally it is found that in order to use a specific (m)
value but the standard one, there must be a core
taken in the field under observation.
• Different (m) values affect the water saturation
dramatically and lead to completely unreliable
petrophysical interpretation, while difference in (a)
or (n) values does not affect the water saturation as
much as (m).
Methods of Detecting the
(m) Value
40. • References:
• SLB log interpretation principles & application
• SLB Chart book 2009
• Zaki Bassiouni, Theory,Measurement,and
Interpretation of Well Logs
