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7/29/2019 Analysis Errors Historical Use of Archie Equations
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UJCI>T
Analysis of Errors in HistoricalUse of Archie's Parameters
O. FASESAN, F. AWOLUSI, L. R. HEINZETexas Tech University
Abstract
While it is common knowledge that tbe valucs ofArchie's pa
rameters 'a' , 'm ' and 'n ' may vary for sandstone reservoirs at
difTerent conditions - consolidatedlunconsolidated, water-wet/
oil-wet, pore geometry, degree of spbericity, elay content and in
situ depositional environment - the values of a = 1, m = 2 and n= 2 have been linked bistorically with Archie 's equations. Statis
tically, these values were assumcd as the population mean when
used in calculations, but the magnitude of errors associated with
their use is often neglected. This study shows how a sample of
data drawn from experimental and analytical methods determine
Archie's parameters. Well logs from sandstone reservoirs are
used to draw statistical inferences about the population charac
teristics ofArcbie's parameters in sandstone reservoirs. This also
shows the magnitude of relative error possible when m = 2 and
n = 2 are used to compute water saturation and formation res istivity factors.
lntroductionThc 1942 landmark publication by Gus Archie titled, "Thc
Electrical Resistivity Log as an Aid in Determining Some Reser
voir Characteristics•'(l) introduced new parameters relevan! lo de
scribing reservoirs using we ll logs and set standard parameters for
the identification of permeab le zones within a reservoir.
Basically, Archic's experimcnts involved measuring the po
rosity and electrical resistivity of numerous shale-free sandstone
corcs from the Gulf Coast by saturating them with brine of salini
ties ranging from 20 to 100,000 ppm ofNaC I. Archie 's work establishcd the following relationships:
RF=_!L
Rw .............. ................ ........ ................................... ............. .. .......... ( 1)
whereR0
is the resistivity ofthe rock fully saturated with brine and
R is thc fom1ation water resistivity. F is termcd the formation re
si;tivity factor and is a measure of the effect of formation on the
path ofe lectrical curren! trave ling through the c lectrolytic brine in
the rock pore system. The plot ofF against porosity (4>) on log-log
sea les revealed a linear trend equivalen! to:
F =_!_
$"'······························· ············································· ······················· (2)
The 'm' parameter representsth
e trend's
negati
ve slope.
In deriving the above expression, Archic force-fitted a line to
hi s formation resistivity factor against porosity data such that F =
1.0 at 100% porosity. A replica ofArchie's or iginal plot using elean
sandstone cores is s hown in Figure l. This was however deemed
unnecessary as other research works revealed that when a line is
fittcd to formation res istivity factor against porosity, the intercept
at 100% porosity would not always derive one, but can be greateror lcss than one. Winsauer et aiP>, for exa mple, duplicatcd Ar
cbic's experiments witb sandstone cores from a wide range of res
ervoirs and arrived at:
F = 0.62$2 . 15
....................... ......................................................................... (3)
Thu s, the genera l form of Archie's formation resistivity factor
is expressed as:
= ~$m
......................... .......................................................................... (4)
Winsauer lirst rcferred to Archie's 'm ' parameter as tl1e cemen
tation factor, while 'a ' would later be referred to as the tortuosity
factor.
Archie, again, cons idered partially saturated bydrocarbon
bearing shale-free sandstones and proposed a second factor called
the resistivity indcx (/) that would further increase the rock's resis
tivity. He expressed this as:
l=!lRo ·········· ··················· ·· ········ ··············· ·· ·· ····· ·········•······· ··· ··· ·············· (5)
...
ob"'..
~u;
'üiQl
a:e.!:!'la
e.f 0.1L - -- -- - -- - - - - - - ----1
1 10 100
Porosity
FIGURE 1: Plot of formation resistivity factor against porosity.
PEER REVIEWEO PAPER ("REVIEW ANO PUBLICATION PROCESS" CAN BE FOUND ON OUR WEB SITE)
June 2007, Volume 46, No. 6 57
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