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

analysis errors historical use of archie equations

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