PARTE TERCERA
D.- LA DISTENSIÓN
II.- CUESTIONES RELACIONADAS CON EL DESARME
a:
ARCHIE’S EQUATION
Water saturation (Sw) of a reservoir's uninvaded zone is calculated by the Archie (1942) formul
R
ntion temperature
ction or Deep Laterolog corrected for φ = poro
a = tortu m = cem n = satu
of a formation's flushed zone (Sxo) is also based on the Archie equation, but two e cha rate resistivity, Rmf, in place of formation water resistivity, Rw, and
ne res invaded zon
Sw = water saturation of the uninvaded zone Rw = resistivity of formation water at forma Rt = true formation resistivity (i.e., Deep Indu invasion)
sity
osity factor entation exponent ration exponent
Water saturation
variables ar nged: mud filt
flushed zo istivity, Rxo, in place of un e resistivity, Rt.
R
xo⋅ φ
OH.27S = water saturation of the flushed zone
Rmf = resistivity of the mud filtrate at formation temperature
Rxo = shallow resistivity from a very shallow reading device, such as Laterolog-8, Microsp
φ = porosity
a = tortuosity factor
m = cementation exponent n = saturation exponent
Water saturation of the flushed zone (Sxo) can be used as an indicator of hydrocarbon moveability. For example, if the value of Sxo is much larger than Sw, then hydrocarbons in the flushed zone have probably been moved or flushed out of the zone nearest the borehole by the invading drilling fluids (Rmf).
APPARENT WATER RESISTIVITY, Rwa
Details of the Rwa technique are in the scanning and quicklook section.
An Archie water saturation can also be calculated from the ratio of the Rwa values.
Where:
xo
herically Focused Log, or Microlaterolog
n
Openhole Interpretation
Where the cementation exponent, n, in the equation above is assumed to be 2.A shortcut to the saturation calculation, used as a scanning aid, is:
(Rwa zone/Rwa min
(Rwa zone/Rwa minimum) = 4 yields Sw = 0.50;
R zone/R minimum) = 5 yields Sw = 0.45.
PLOTS
Details of the Pickett plot technique are shown in the Determining water resistivity section.
The water saturation of a point plotting away from the water-bearing line on the Pickett plot can be determined by the equation:
imum) = 3 yields Sw = 0.58;
In practice, this means reading the resistivity of the point (Rt) and the resistivity of the water-bearing line (Ro) at the same porosity value as the point, estimating a v
OH.29
alue for saturation exponent, n, and making the calculation.
70 100 70 100
0.10 1.00 10.00
0.01 0.10 1.00 10.00
0.01 100.00
y porosity, ty, nsitnsit
True resistivity, Rt True resistivity, Rt
Openhole Interpretation
SHALY SAND ANALYSIS
from logs, it became clear that there were limitations to the method, especially in formations rly literature r of modifications were made ters) to account for those Not long after the work of Archie and others in devising a method to quantify water saturation containing shale and/or clay, and commonly referred to as “shaly sands”. The ea
tended to refer to the formations as containing “shale”, and a numbe to Archie’s equation which used shale volume (among other parame effects.
Effects of clays and shales on logging measurements.
Measurement Effect
Spontaneous Potential, SP Decrease in magnitude with respect to the shale baseline.
Gamma Ray Increased radioactivity, shown as less movement away from the nearby shale values than an equivalent clean sand.
Sonic A sonic porosity higher than the actual formation porosity due to the higher traveltime of the clays/shales.
Neutron A neutron porosity higher than the actual formation porosity due to the water which is part of the clay structure, and which is adsorbed on the clay surfaces.
Density A density porosity which is higher than the actual formation porosity due to the generally lower matrix densities of most clay
the y.
minerals. If the matrix density of the clay is close to that of formation matrix, there will be little or no effect on porosit Resistivity A decrease in resistivity when compared to an equivalent clean
formation, due to the conductivity of the clay.
This will produce a calculated water saturation which is greater than the actual formation water saturation. (Archie’s equation assumes that all conductivity is from the formation water, and that the formation matrix is completely non-conducting.)
After the shale corrected porosity has been determined, the water saturation can be calculated. A ariety of techniques are briefly introduced below. As with Arc equation, the substitution of Rmf for Rw and Rxo as Rt will yield calculations of Sxo instead of Sw.
1950’s
The automatic compensation technique. It used the resistivity and sonic logs with Archie’s quation. Since the presence of shale caused the porosity, φS, to read too high and the resistivity,
t, to read too low, one compensated for the other in the saturation equation:
v hie’s
ith the advent of the density log, the dispersed clay model gained popularity. In this model, the density was assumed to respond only to the liquid-filled porosity, while the sonic was affected by
e clays, with the difference, q, being the fraction of the intergranular space filled with clay:
1 W th
Openhole Interpretation
φ
Sand the saturation given by:
q
became popular, many of which are still being used.
include
= 0.35 in the Rocky Mountains.
(
sh)
shshThe Dual Water method is perhaps the most widely used of those techniques w
OH.35
hich go beyond the shale volume methods. This method is more fully described in Dewan (1983) and Bassiouni sands, and the apparent water resistivity, Rwa, in the sand of interest is calculated.
he total (shale corrected) water saturation of the formation is:
(1994). The bound and free water resistivities are determined from nearby shales and clean T
Openhole Interpretation
b
w 7.49
( )
( )
2
wb 1 R R
b S −
=
The effective water saturation of the formation is:
wb wb wt
we S
S S S
−
= −
1 7.50
nd the volumetric fraction of hydrocarbo
A ns is:
(
wt)
t h
= φ 1 − S
φ
7.51here
rosity (from the neutron and density).
W
φ = total pot
Appendix
This section contains three listings: References with comments, an Annotated Bibliography, and Links of Interest.
The charts illustrated in this document were taken from the following sources. A copyright citation immediately follows each figure.
Western Atlas Logging Services, 1985, Log Interpretation Charts, Rev. 12/95; Baker Atlas, Houston, Texas.
Halliburton Energy Services, 1994, Log Interpretation Charts, Third Printing, Houston, Texas.
Schlumberger, 1998, Log Interpretation Charts; Schlumberger Wireline and Testing, SMP-7006, Sugar Land, Texas.
The Tool Diagrams in each measurement section were taken from the Halliburton website in late 1999 and early 2000. They are intended to give the reader a general idea of the configuration and size of a “typical” logging tool of the particular measurement type. At the time that the figures were copied, the website was open to all interested parties. At present (Fall of 2003), much of the information on the website is open only to registered users. See www.halliburton.com