A hydrogeophysical model for relations between electrical and hydraulic properties of aquifers

Journal o f Hydrology, 79 (1985) 1--19

1

Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

[2] A HYDROGEOPHYSICAL MODEL FOR RELATIONS BETWEEN ELECTRICAL AND HYDRAULIC PROPERTIES OF AQUIFERS

O. MAZA~ l , W.E. KELLY 2 and I. LANDA 3

1Geophyzika N.E., Geologicka 2, 152 O0 Praha 5 -- Barraandov (Czechoslovakia) 2Department o f Civil Engineering, University o f Nebraska, W348 Nebraska Hall, Lincoln, NE 68588-0531 (U.S.A.) 3Geofond, Kostelni 26, 1 70 O0 Praha 7 --Holesovice (Czechoslovakia) (Received August 22, 1984; revised and accepted February 11, 1985)

ABSTRACT Mazad, O., Kelly, W.E. and Landa, I., 1985. A hydrogeophysical model for relations between electrical and hydraulic properties of aquifers. J. Hydrol., 79: 1--19. Factors influencing relations between electrical and hydraulic properties of aquifers and aquifer materials are discussed. Both direct and inverse relations are shown to be possible and to exist. A general hydrogeophysical model is outlined for aquifer--scale relations which are shown to depend primarily on two factors: the character of the material--level relationship; and the mutual relation between the direction of groundwater flow, aquifer layering, and hydrogeophysical conditions in the aquifer.

INTRODUCTION

The purpose of this paper is to present an analysis of the basis for relationships between aquifer hydraulic and electrical properties leading to a general hydrogeophysical model for such relationships; attention will be limited to aquifers possessing percolation hydraulic conductivity. Surface electrical measurements are widely used for qualitative estimates of aquifer properties b u t their applications in quantitative studies remain controversial. Two of the reasons are a lack of a clear understanding of what causes correlations and problems in interpreting electrical sounding results.

PREVIOUS WORK

Surface resistivity methods are routinely used by engineers and geohydrologists to obtain qualitative aquifer information. Since the late 1960s resistivities determined from surface measurements have been used to estimate aquifer properties including yield, hydraulic conductivity, and transmissivity; this review will concentrate on these applications. 0022-1694/85/$03.30

© 1985 Elsevier Science Publishers B.V.

Vincenz (1968) obtained a good positive correlation between surface resistivities and well yield. Worthington (1975) reported an inverse correlation between corrected formation factor and intergranular permeability. Ungemach et al. (1969) correlated transmissivities determined from the results of six pumping tests in the Rhine aquifer with transverse resistances. Croft (1971) used data from Jones and Bufford (1951) to develop a relation between permeability and formation factor; Croft used this relationship to estimate transmissivities from borehole resistivity measurements. Scarascia (1976) used electrical soundings to estimate transmissivities in Italy. Kelly (1977) and Kosinski and Kelly (1981) correlated saturated thickness resistivities with hydraulic conductivities obtained from pumping tests in southern R h o d e Island. Maz~C and Landa (1979) analyzed data from Czechoslovakia and concluded that relations between aquifer transmissivities and either transverse resistance or longitudinal conductance are possible for both direct and inverse material--level correlations between resistivity and hydraulic conductivity. Table 1 gives definitions for transverse resistance, longitudinal conductance, transmissivity, and leakance. The first two are layer parameters for electrical flow perpendicular and parallel to the layering, respectively, while the latter are for hydraulic flow parallel and perpendicular to the bedding. Heigold et al. (1979) presented data from Illinois showing an inverse correlation between resistivity and hydraulic conductivity. Similarly, Plotnikov {1972) reported an inverse correlation for twenty measurements from Kirgizia in the Soviet Union. Niwas and Singhal (1981) reanalyzed data presented by Kelly (1977) emphasizing the use of transverse resistances rather than resistivities. Mel'kanovitskii et al. (1981) reviewed correlations reported by Russian investigators. As a first approximation relations between resistivity and hydraulic conductivity were found to be linear on a log-log plot. Generally a monotonic increase of hydraulic conductivity with resistivity is observed although the authors indicate that peaks in this relation have sometimes been observed. A theoretical basis for the log-log relationship is presented b u t the authors conclude that empirical field correlations are usually needed. The results reported appear to involve mainly alluvial deposits in which the percentage of clay is controlling the correlation. Although the authors caution about the effects of variations in the mineralization of the groundwater they use transverse resistance and resistivity in the reported correlations. Allessandrello and Lemoine (1983) report that field data from several alluvial basins in France show a log-log relation between hydraulic conductivity and apparent formation factor. They note that based on Archie's law and the known relation between hydraulic conductivity and porosity an inverse correlation between formation factor and hydraulic conductivity is expected; however, this is not what is generally found in the field. Figure 1 summarizes field relations reported in terms of hydraulic conductivity and formation factor and Fig. 2 those reported in terms of transmissivity and transverse resistance.

TABLE 1 Definitions of hydraulic and electrical layer parameters

Electrical Transverse resistance

T

=

hip i

2.

=

pt H

i=l

Longitudinal conductance

hi

S "~

H

i= 1 Pi

PL

Hydraulic

Transmissivity

TH

=

~

hiKi

:

KLH

i=l

~ Ki i=1 hi

Leakance

\,

I(~ f .

Kt H

/ I

Allessondrelto

ond

2

KOSln~k~ o n d

Kelly

(1~8~)

3

Shockley

Gorber

[ l g 5 3 ) . c | . Fig.3

~, Croft

~c~2

E o

\

! o

ond

Le M o L n e

{ IgI~3 )

[1971 )

5

HePgold e t

6

PIOtnlkOV

7 8

Moz6~.

g

Worthington

OI. et

(Ig7~I

ql(lg72)

Mozd~ o n d Londo [ l g T g l Qnd

[19751

observed .....

(19791

LClndo

by

c o m p u t e d by or

deduced

from

~ ld ~ i i"

'\

\, ,

,

,

,

,

,'-, 10 FormQlion

100

foctor

F. F, ( - ]

Fig. 1. Reported relations between hydraulic conductivity and aquifer formation factor.

Pfannkuch (1969) discussed factors that should be considered in developing quantitative relations between electrical transport and viscous flow parameters. In particular Pfannkuch argued that for predicting porosities from resistivity measurements, true formation factors should be used. True

104

UngemGch

et al

(Ig6g)

/

observed by compu ~e(~ by or deduced from

Kelly ~tg81) 10: computed

by Niwas and

%

/;x

#

lo 2

j

Maz6~ and Landa

.4

/

/"

/

/

~ ,tg,~,.y..

/

101 100

7

/

/

/

/ 10(]0 10000 Transversat resistance T (ohm m 2 ]

30000

Fig. 2. Reported relations between transmissivity and transverse resistance.

formation factors are those that would be measured if the soil grains were perfect insulators. For all the field relations reported apparent formation factors rather than true formation factors are reported. Based on laboratory results presented by Biella et al. (1983) it can be concluded that for clay-free unconsolidated sediments with pore waters at specific conductances of 300 #ohms and above the difference is slight. The relationship between formation factor and hydraulic conductivity used by Croft was for constant porosity. In the field, porosity, grain size and grain-size distribution may vary systematically at least in some geologic environments. In general finer sediments tend to deposit at higher porosities, all other factors the same. Urish (1978, 1981) used an assumed in-situ density grain-size correlation and Pfannkuch's expression to demonstrate probable relations between apparent formation factor and hydraulic conductivity. Contradictory information is available on systematic variations of porosity and grain size with lithology in unconsolidated deposits. Graton and Fraser (1935) studied a wide variety of sediment types and showed qualitatively the tendency for porosity to decrease with increasing grain size. Shockley and Garber (1953) reported on an extensive study by the United States Army Corps of Engineers on Mississippi River sands. They showed a correlation

0,12

O,10

E 0.08

U

oo6 ~J

~

0.04

0 02 (Colcu|oted from Shockiey and Gather, 1953] .00

I

34

36

i

i

38

i

i

40

i

I

42

Natural Porosity (%) Fig. 3. In-situ variation o f hydraulic c o n d u c t i v i t y and porosity.

between peak grain size and density. Figure 3 is replotted from their results assuming that the peak diameter and the median diameter are equivalent. Such relations can be developed from results obtained by testing in surface exposures as well as by undisturbed borehole sampling. Theoretically, grain size has not influence on porosity for uniform sized sediments which varies only with the packing arrangement of the grains (Lohman, 1972). Keys and MacCary (1971) point out in their manual on borehole geophysics that in much of the literature on hydrogeophysics, " p o r o s i t y " is mentioned without definition or without the modifying terms " t o t a l " or "effective". For fine-grained sediments with significant percentages of clay the differences between the two porosities could be substantial; on the contrary, for coarse-grained sediments the difference is negligible. For homogeneous sediments where hydraulic conductivity is dependent primarily on effective porosity an inverse correlation between formation factor and hydraulic conductivity is found. If systematic variations of porosity and hydraulic conductivity occur -- specifically decreasing porosity with increasing hydraulic conductivity -- then formation factor will correlate directly with hydraulic conductivity. If resistivity changes are controlled by variations in percent clay, then resistivity can again correlate directly with hydraulic conductivity. In the general case, both direct and inverse correlations should be allowed for depending on the type of aquifer.

In the glacial aquifers of Rhode Island heterogeneity rather than homogeneity is the rule. Kelly (1977) found that electrically, the entire aquifer thickness could in m a n y cases be considered as a single layer although the aquifers are normally macroscopically anisotropic due to layering which is not evident in the sounding curve. In situations where the aquifer rests on resistive bedrock, the longitudinal conductance of the aquifer layer is the parameter defined by the sounding curve. Curves were interpreted to obtain aquifer longitudinal resistivities which were used in correlations with hydraulic conductivity. The transverse resistances used in correlations were actually longitudinal resistivities multiplied by the estimated saturated thicknesses. Since both resistivity values and the hydraulic conductivities require interpretation of data from field tests both are subject to error. Also as Mazh~ and Landa (1979) and Maza5 et al. (1978) point out, correlations will be affected by the degree of aquifer heterogeneity. They determined the useful limits of field correlations between hydraulic conductivity and resistivity and between transmissivity and transverse resistance or longitudinal conductance allowing for the effects of disturbing factors. They discussed the accuracy of hydrogeologic parameters estimated from geoelectric parameters using the law of error propagation. For correlations between hydraulic conductivity and resistivity the error in estimated hydraulic conductivity increases as: (a) the slope of the regression line increases from 0 to 90 degrees -- the direct correlation, but decreases as the slope increases from 90 to 180 d e g r e e s - the inverse correlation; (b) the length D of the regression line; and (c) the standard error in resistivity and hydraulic conductivity measurements. The error in estimating transmissivity depends on variations in aquifer thickness and on the length of the regression line (D) for the investigated area. The error is a minimum for a constant aquifer thickness for any slope, and for a slope of one (optimum correlation) for any thickness.

BASIS FOR ELECTRICAL--HYDRAULICCORRELATIONS Correlations between aquifer scale parameters have been obtained for a range of geohydrologic environments but the basis for and limitations of observed correlations have n o t been well-defined. Aquifer--scale correlations depend on several factors including a material--level relation which can be established at the laboratory or sample scale. The material--level relationship will indicate the type of field correlation to be expected; direct or inverse. Urish (1981) ran a series of laboratory tests on clay-free glacial sediments from southern Rhode Island and showed that Pfannkuch's expression adequately described laboratory resistivity--hydraulic conductivity data. With estimates of in-situ effective porosity -- hydraulic conductivity variations such as Shockley and Garber (1953) reported for the Mississippi River sediments, a material--level relation between electrical and hydraulic

0.~

E

u

I->

Q Z 0

0,01

Z

Compu/ed horn Shockley ond Gather Oofo

0.001

J

io FORMAT ION FACTOR

Fig. 4. Computed hydraulic conductivity--formation factor relation.

properties can be developed. Such relations incorporate the limitations of the empirical correlation between hydraulic conductivity and porosity. Figure 4 is computed from Shockley and Garbers data (Fig. 3) and Pfannkuch's relation; the sands are assumed to be clay-free. Ideally, such a relation should be developed from laboratory or possibly field measurements on undisturbed samples; however, this is very difficult to do and has not been reported for unconsolidated sediments. This is quite easily done for cores of consolidated materials and has been done by several researchers {Barker and Worthington, 1973). The important consideration for unconsolidated sediments is not the exact material--level relation which will vary from area to area but its form and a satisfactory explanation of its cause. Maza~ and Landa (1984) point out that derived field relations between electrical and hydraulic parameters depend on: (a) the accuracy of the geoelectric parameters determined from the field measurements, usually sounding curves; (b) the accuracy of the hydraulic parameters determined from pumping tests or other less reliable methods; (c) the form of the regression equation; and (d) the reliability of the regression equation, Determination of geoelectrical parameters is made more difficult by the fact that almost all sedimentary aquifers are anisotropic and characterized by an average longitudinal resistivity in the direction parallel to the layering and an average transverse resistivity normal to the bedding. The average transverse resistivity is always greater than the average longitudinal resistivity; this is completely analogous to the average hydraulic

conductivities parallel and perpendicular to the bedding. The properties of an anisotropic aquifer cannot be directly determined from a sounding curve. Interpretation of a sounding curve yields an average resistivity and an equivalent thickness if the layer is thick enough to be distinguished on the sounding curve. The average resistivity is the geometric mean of the average longitudinal and transverse resistivities and the thickness is the actual thickness times the coefficient of anisotropy which is always greater than one. If the aquifer layer is thin relative to the thickness of the overburden then it is only possible to determine the total longitudinal conductance or transverse resistance from the sounding curve. This is the situation most frequently encountered in practice. To determine average longitudinal resistivity or transverse resistivity it is necessary to have an independent measure of the actual thickness throughout the study area. All interpretation procedures for vertical electrical soundings (VES) assume a horizontally layered medium which is frequently only a crude approximation of reality. Aquifers are frequently heterogeneous, and may be layered heterogeneous or the scale of the heterogeneities may be such that the aquifer behaves as a single heterogeneous layer. The scale of the heterogeneities relative to the sounding curve and pumping test complicate interpretation and may make the usual assumptions for interpretation invalid. The determination of transmissivity and hydraulic conductivity is strongly influenced by the test method chosen. The choice of the test m e t h o d depends on the resources available and the hydrogeological conditions. Under very complex conditions even a well-instrumented, carefully conducted pumping test may not yield unambiguous estimates. All methods are subject to certain errors. The form of the regression curve may be rectangular or curved and is usually represented with an appropriate regression equation. In general, the preference has been for the rectangular form either log-log or semi-log. Careful attention must be paid to the reliability of the regression equation relating hydraulic and geoelectrical parameters; the reliability depends on a certain minimum number of measurements. To determine the minimum number, the m e t h o d of successive analysis {Smirnov and Dunin-Barkovskii, 1968) should be applied and strictly observed.

EXAMPLES Kosinski and Kelly (1981) correlated resistivity results for four-layer sections where the longitudinal conductance was the unique parameter. Since the aquifer is clearly layered, average longitudinal resistivities were reported. Sounding curves used by Kosinski and Kelly were obtained in the Beaver and Chipuxet River aquifers. In the lower Wood River area conditions are such that at some locations the average transverse resistivity of the

I0,000

•

ond

(1981)

~l,ooc

r

Iz a. I00 Q.

I0

I

I

t

I0

~00

1,000

AB/(m)

Fig. 5. Comparison of sounding curves. Transverse

resistivity hi pI izl ~-- hi i=l

Pt =

Longtudinal Kt

PL =

P,

electrical h=

Kt

i:l ~.

h~

i:l

Pl

anisotropy

X. = . ~ ' P . ~ t "

h2 ,'

resistivity

PL

mean

t'L

resistivity

KL h3

K3

P"=

~

Transverse h4

hydraulic ~--

K,

=

Longitudinal KL =

Fig. 6. Layered models.

=

i:l

PvEs conductivity

hi

hydraulic - - ~ h,

conductivity

10 aquifer section is obtained. Conditions where the transverse resistance is measured occur when the aquifer rests on a thickness of less-permeable material rather than directly on bedrock. Under these conditions five layers can often be distinguished on the sounding curve and the transverse resistance and under favorable conditions the thickness and average transverse resistivity of the aquifer layer can be determined. Ungemach et al. (1969) correlated resistivity results obtained from threelayer geoelectric soundings where the upper layer comprises the topsoil and unsaturated zone, the middle layer is the aquifer and the basement is shale. Figure 5 shows some typical curves. In this case an estimate of the transverse resistance may be obtained using approximate methods. This is a K-type curve and Heigold et al. reported that their results were also obtained from K-type curves (Keller and Frischnecht, 1966). Allessandrello and Lemoine (1983) correlated formation factors and hydraulic conductivities. The middle curve in Fig. 5 is taken from their paper. They used automatic interpretation techniques to obtain layer resistivities. In this case the aquifer again rests on a less-resistive basement. In all these cases a direct field correlation was obtained and although no information on the underlying material--level relation was reported it would be expected to be positive. In the cases where the aquifer lies between lessresistive layers the average transverse resistivity is obtained and used in correlations. Ungemach et al. used the transverse resistance which would be satisfactory only if the material--level correlation is linear which does not appear to be generally the case.

DISCUSSION Aquifer layers in the field are recognized as being both heterogeneous and anisotropic. Kelly and Reiter (1984) presented the results of a study of the influence of anistropy on field correlations using simple layered models. Figure 6 shows the layered model which assumes horizontal groundwater flow with vertical electrical flow in the transverse case and horizontal flow in the longitudinal case. Definitions of terms used in the discussion to follow are given in Fig. 6 and Table 1. Correlations between average hydraulic conductivity and both average transverse resistivity and average longitudinal resistivity were examined. A direct linear material--level relationship between hydraulic conductivity and resistivity does not represent the general case but it will be assumed to describe the influence of anisotropy. For a direct linear relationship the relationship between average hydraulic conductivity and average longitudinal resistivity can be shown to involve the hydraulic anisotropy; plotted linearly, the slope is a function of aquifer anisotropy. Plotted on log-log paper the relation is a series of parallel lines, with the intercept a function of anisotropy. If the material--level relationship is linear on a log-log plot which

11

i--

L~

×

LL Kx

HUNDREDS

THOUSANDS

AOUIFER RESISTIVITY

Ohm m

Fig. 7. Computed model relation between average hydraulic conductivity and average longitudinal resistivity (from Kelly and Reiter, 1984).

is the more general form (Mazh6 and Landa, 1979), points with equal anisotropy appear to cluster along parallel lines. If anisotropy is ignored, points will scatter above the material---level relationship. Figure 7, after Kelly and Reiter, shows this scatter for the nonlinear material--level relationship and a range of hydraulic anisotropies from 1 to 7. These results suggest that field-scale relationships will exhibit considerable scatter unless anisotropy is constant. For the case of a linear material--level relationship the relationship between average hydraulic conductivity and average transverse resistivity would follow the same material--level relationship; there would be no influence of aquifer anisotropy. For the nonlinear material--level relationship Kelly and Reiter showed that there would be a slight influence of aquifer anisotropy. Figure 8 shows the relationship between average hydraulic conductivity and average transverse resistivity for the same range of anisotropies as in Fig. 7. In this case the scatter is reduced and the averaged relationship is effectively independent of anisotropy.

12

u

r~ ~9

>2=

u-

I

,7'

HUNDREDS

THOUSANDS

AOUIFER RESISTIVITY

Ohm

m

Fig. 8. Computed model relation between average hydraulic conductivity and average transverse resistivity (Kelly and Reiter, 1984).

Theoretical relations between average hydraulic conductivity if the flow is parallel or perpendicular to the bedding and the average longitudinal or transverse resistivity were also calculated by Maza5 and Landa (1984}. They considered two models. The first model of a sandy-clay horizontally layered aquifer with horizontal groundwater flow was computed assuming the resistivity of the sand layers was 1000 ohm m and that of the clay layers was 1 0 o h m m with corresponding hydraulic conductivities of 1 c m s -1 and 1 x 10 .3 cm s -1 respectively. The average hydraulic conductivity was calculated for flow parallel to the bedding. Clay content was calculated based on the ratio of the total thickness of clay beds to the total thickness of clay and sand beds. Analysis of the above results (Fig. 9a) indicate that for this type of aquifer the direct material--level relationship is preserved at the field level; however, the form of the relationship is generally curved. The best approximation to a linear relationship is obtained for the transverse resistivity as a measure of the mean resistivity and the worst for the longitudinal resistivity. The second model was calculated for a vertically

13

Q

o 2O 410

I°C l

b

IO 0

-0 ,

i PL

60 70

,?

/

Scheme:

80

. :

~

,o

/

k-

',/X

> I-

El

z

99

Z 0 u

i.-i

Z

~

o*1

Scheme :

ui

u

z0 '

KL

30 4O ~0 60

>I IO ~

~0

.'8

99.9

-

102 RESISTIVITY

I 399"99 (ohm.m)

IOO

io I

io z RESISTIVITY

103

(ohm.m) 5

ANISOTROPY

(-)

El

ANISOTROPY

6

(-)

Fig. 9. Relations between hydraulic conductivity, clay content, coefficient of anisotropy and resistivity.

layered aquifer with alternate layers of sand and clay (Fig. 9b). The same parameter values were assumed as for the horizontally layered model. The results indicate the same direct relationship except that the best approximation to linearity is obtained for the vertical hydraulic conductivity and the longitudinal resistivity. As for the horizontally layered case, an acceptable correlation exists between the hydraulic conductivity parallel to the bedding and the mean resistivity. The worst correlation is between the transverse resistivity and hydraulic conductivity. These results will be generalized in the next section. Which resistivity to use in correlations will depend on the location of the aquifer relative to nonproducing strata and the properties of those layers. The most favorable condition is where the aquifer layer is relatively thick and rests directly on conductive bedrock. However, where the aquifer is thin or where multiple aquifers exist it may not be possible to determine aquifer resistivity but only its transverse resistance. Relatively thick and thin are

14 used in the sense of layer detectability on a sounding curve (Keller and Frischnecht, 1966). Transverse resistances can be used directly in correlations with aquifer transmissivities. For the general case of a nonlinear material--level relationship these involve aquifer thickness; if the aquifer thickness is not constant, scatter would be seen in the field relationship. For a direct material--level relationship the best field relationships will be developed where the aquifer is relatively thick and is situated between layers with low resistivities. Ungemach et al. (1969) appear to have encountered nearly ideal conditions in the Rhine aquifer. In southern Rhode Island the best locations would be where the water table is shallow and the unsaturated zone consists of silty material with the aquifer in turn overlying less resistive material. These conditions are not generally encountered and the field relationships were influenced accordingly. For cases where aquifer transverse resistivity and thicknesses can be estimated from sounding curves, good correlations with aquifer hydraulic conductivity and transmissivity are possible. When only the aquifer transverse resistance can be determined, and the material--level relation is direct, only an estimate of the transmissivity can be made. When the longitudinal resistivity of the aquifer is measured, anisotropy will influence field correlations and good relations will be possible only if aquifer anisotropy is relatively constant. If only the longitudinal conductances of the aquifer can be determined it will be possible to estimate transmissivity only if the inverse material--level relationship exists ( M a z ~ and Landa, 1979). GENERAL HYDROGEOPHYSICALMODEL The general hydrogeophysical model should account for the following: (a) The material--level correlation occurs for fundamentally different reasons for clay-free aquifers such as pure sand and gravel, aquifers where the clay is dispersed in a sandy matrix, and aquifers where the clay occurs primarily in layers. (b) Hydraulic conductivity correlates with grain size and effective or total porosity in clay-free sediments and with clay content in clayey sediments. (c) Resistivity at the material--level is a function primarily of porosity in clay-free sediments and of clay content and porosity in clayey sediments. (d) Resistivity at the aquifer scale is controlled by the material--level relationship and the geometrical characteristics of the aquifer. For an isotropic clean sand aquifer there is no difference between the interpreted mean resistivity, the longitudinal resistivity and the transverse resistivity. Similar results are valid for clayey aquifers where the clay occurs in a sand matrix; at the material--level resistivity is a function of the percentage of clay and porosity (Desbrandes, 1968). In layered anisotropic aquifers all three of the resistivities differ although they may be related approximately; the mean resistivity obtained from the sounding curve is approximately equal to the average longitudinal resistivity.

15

£ompuled ~()er Worthington 10 6

I sediments

IO 5

0

E ~

--

. . . .

11975]

for woler resist,vily

~o = ~ 105.A p 2 ~o ...oqui|er

reslstlvlly ( o h m m )

A ,..mOtrix

¢e$1stwdy

1"/.

P ...effective

(ohm.m)

porosdy [ * / o ]

FOr A < ] ~ ) o h m m

5°/°~

:voriollon$

sn go ore ¢nolnly

c o n t r o l l e d by voriQhons

"o

~w=lOo~n m

depends

in A where A

on cloy conlen(

I0 'Io

For A > l S 0 o h m m ' vorlotlon.~, in ~o o#e rt~oinly controlled by vorll3t*ons In P

~o~T--- -1- ~

100

101

Jo./.

~,0o/, 50 %

102

10 ] A[ohm

10~'

105

105

m)

Fig. 10. Relations between aquifer resistivity, matrix resistivity, and effective porosity.

10O

.

.

.

.

.

.

.

.

.

.

//

, // X

o °

%,'

_ik

/

<./,'

\o1,t ~

,, ,.. J ' o , f "

_

0

20

30 60 Porosity P [ ° / o ]

... m e a n

--~ ..

ranges

values

of v a l i d i t y

50

60

/\

/ ~_to"4

~6 s

10

x.,z

oc

~

/

_

10

\

-% 101 10 Resishvlly

103 10 ¢ £ robin.m)

general

trends

specdlc

trends p e r t i n e n t

1135

to d i f f e r e n |

rock

lype

Fig. 11. Relations between hydraulic conductivity, porosity and resistivity for different sediment types.

(e) Besides the form of the material--level relationship -- rectilinear or curved -- the characteristic o f the proportionality either direct or inverse plays a dominant role. Figures 1 0 - - 1 2 show this in slightly different ways. The first way is shown in Fig. 10. It can be concluded that for clayey aquifers (A < 180 o h m m) the resistivity and corresponding hydraulic conductivity are controlled by clay content. For more sandy aquifers

16

"~ 102

/

-1

\\

161

A

10 3 104

/

~d~ 106

,,(

107 108

\

x 169

02 06 10 lZ. 18 2 0 Coefhcienl of potos4ty 6 [ - ] ] / ~

index of plestlcdy ( proporhone~ Io cloy content } generel Irend ( po,nts with mQxqmum Curvaldre of ~pecltlc trends connected ) specdf~c trenas perlinenl to different rock type

10

30 102 ~eslshvdy

I0 ] 104 {~ [ ohm m ]

i05

", X\

11mils Of preCllCQ[ VOlhal~leS

0

meen ot r e s , s h , d y I*P

value~,

where P.,. porosdy

Fig. 12. Relations between hydraulic conductivity, porosity, resistivity, and plasticity index.

(A > 1 8 0 o h m m) the resistivity and hydraulic conductivity are controlled primarily by variations in porosity. The second way is illustrated in Fig. 11 adapted from Chouker (1970). The general relation has a direct proportionality to the grain size and hence to rock type giving rise to a direct material--level relationship. However, within a particular lithology characterized by a certain grain size, variations in hydraulic conductivity are due primarily to porosity and an inverse material--level relationship is observed. The third way is based on the adaption of the Maslov and Nesterov graph in Maksimov (1959) and involves plasticity index (Myslivec, 1970) and the resistivity properties (Mares et al., 1983). The graph (Fig. 12) makes it possible to estimate hydraulic conductivity using plasticity index which is closely related to percentage of clay and the specific clay minerals present, and to resistivity. In this case the plasticity index serves as the indicator of grain size. (f) To estimate hydraulic conductivity from resistivity it is first necessary to determine resistivity from a sounding curve. If because of equivalence for T with K- and Q-type curves or S for H- and A-type curves it is only possible to determine T or S, then it is only possible to estimate the transmissivity. The reliability of transmissivity estimates depend on the character of the material--level relationship and on the variations of aquifer thickness in the surveyed area. Provided that the relationship is linear the accuracy in determining transmissivity is greater for a direct material--level relationship under T equivalence (K or Q types of VES curves) and for an inverse material-level relationship greater under S-equivalence (H- or A-type curves). In the opposite cases the accuracy is substantially less.

17 (g) In anisotropic aquifers characterized by alternating sand and clay layers the choice of the most convenient geoelectrical parameter to obtain optimum correlation with hydraulic conductivity depends on the direction of flow relative to the layering. If flow is parallel to the bedding the best correlation is obtained between the hydraulic conductivity parallel to the bedding and the average transverse resistivity (Fig. 9a). If flow is normal to the bedding then the best correlation is obtained between the hydraulic conductivity normal to the bedding (always the minimum value) and the average longitudinal resistivity (Fig. 9b). This case could occur when it is the hydraulic conductivity of an aquifer that is being sought. In both cases an acceptable correlation is obtained between the hydraulic conductivity parallel to the bedding and the mean resistivity. The determination of either parameter depends on the hydrogeophysical conditions of the aquifer and the adjacent layers as already discussed.

CONCLUSIONS Factors affecting relations between the geoelectric and hydraulic properties of aquifers have been discussed in detail. It can be concluded that the reliability of relations between electrical and hydraulic aquifer parameters depends primarily on two factors: the character of the material--level relationship; and the mutual relation between the direction of groundwater flow, layering and the hydrogeophysical conditions in the aquifer. The sources of errors in determining the basic geoelectric and hydraulic parameters in a set of measurements were analyzed. The necessity of applying a statistical criterion for determining the minimum number of parametric points was stressed. It was concluded that both direct and inverse material--level relationships can exist depending on the rock type and the character of the hydraulic conductivity. Inverse relationships can be expected when porosity controls variations in hydraulic conductivity and other factors such as grain size, sorting, and clay c o n t e n t are relatively constant. Direct relationships appear to be controlled by inverse correlations between grain size and porosity or inverse correlations between clay content and hydraulic conductivity. A general hydrogeophysical model was used to demonstrate that at the aquiferscale a variety of relations may be expected.

REFERENCES

Allessandrello, E. and Lemoine, Y., 1983. D~termination de la perm~abilit~ des alluvions partir de la prospection 41ectrique. Bull. Int. Assoc. Eng. Geol., 26-27; 357--360. Barker, R.D. and Worthington, P.F., 1973. Some hydrogeophysical properties of the Bunter Sandstone of Northwest England. Geoexploration, 11: 151--170.

18 Biella, G., Lozej, A. and Tabacco, I., 1983. Experimental study of some hydrogeophysical properties of unconsolidated porous media. Ground Water, 21 (6) : 741--751. Chouker, F., 1970. Methodische und theoretische Untersuchungen fiir geophysikalischen Grundwasser Erkundung. Freiberg. Forschungsh., C 271, p. 235. Croft, M.G., 1971. A method of calculating permeability from electric logs. In: Geological Research, 1971. U.S. Geol. Surv., Prof. Pap. 750-B, pp. B265--B269. Desbrandes, R., 1968. Th~orie et Interpretation des Diagraphies. Inst. Franc;ais du Petrole, Paris. Graton, L.C. and Fraser H.J., 1935. Systematic packing of spheres with particular relation to porosity and permeability. J. Geol., 43: 785--909. Heigold, P.C., Gilkeson, R.H., Cartwright, K. and Reed, P.C., 1979. Aquifer transmissivity from surficial electrical methods. Ground Water, 17 (4): 338--345. Jones, P.H. and Bufford, T.B., 1951. Electric logging applied to ground-water exploration. Geophysics, 16 (1): 115--139. Keller, G.V. and Frischnecht, F.L., 1966. Electrical methods in geophysical prospecting. Pergamon, New York, N.Y., p. 517. Kelly, W.E., 1977. Geoelectric sounding for estimating aquifer hydraulic conductivity. Ground Water, 15 (6): 420--424. Kelly, W.E., 1980. Porosity permeability relationships in stratified glacial deposits (ABS). EOS, 61 (17): 232. Kelly, W.E. and Reiter, P.E., 1984. Influence of anisotropy on relations between aquifer hydraulic and electrical properties. J. Hydrol., 74: 311--321. Keys, W.S. and MacCary, L. 1971. Application of borehole geophysics to water-resources investigations. In: Techniques of Water-Resources Investigations of the USGS. p. 126. Kosinski, W.K. and Kelly, W.E., 1981. Geoelectric soundings for predicting aquifer properties. Ground Water, 19 (2): 163--171. Lohman, S.W., 1972. Groundwater hydraulics. USGS Prof. Pap. 708, p. 70. Maksimov, V.M., 1959. Information Manual for Hydrogeologists. Nedra, Moscow. p. 836 (in Russian). Mares, S., Karous, M., Landa, J., M a z ~ , O., Miiller, K. and Miillerova, J., 1983. Geophysical methods in hydrogeology and engineering geology. SNTL, Praha, p. 197 (in Czech). Martinello, E., 1978. Groundwater exploration by geoelectrical methods in southern Africa. Bull. Eng. Geol., 15 (1): 113--124. MazhS, O. and Landa, I., 1979. On determination of hydraulic conductivity and transmissivity of granular aquifers by vertical electric sounding. J. Geol. Sci., 16: 123--139. (in Czech ) Mazh(~, O. and Landa, I., 1984. General model for correlations between hydraulic and resistivity parameters in saturated granular aquifers. Methodical Man. (in Czech). M a z ~ , O., Landa, I. and Skuthan, B., 1978. Information capacity of some geoelectrical methods applied to hydrogeological surveys. Proc., 23rd Geophysical Symposium, Varna, Bulgaria. Mel'kanovitskii, I.M., Baisarovich, M.N., Bobrinev, V.I. and Pavlova, T.A., 1981. Estimation of transmissibility of clastic deposits from the value of transverse resistivity. Water Res., 7 : 123--132 (translation). Myslivec, A., 1970. Soil Mechanics. SNTL, Praha, p. 388 (in Czech). Niwas, S. and Singhal, D.C., 1981. Estimation of aquifer transmissivity from Dar-Zarrouk parameters in porous media. J. Hydrol., 50: 393--399. Page, L.M., 1968. Use of the electrical resistivity method for investigating geologic conditions in Santa Clara County, CA. Ground Water, 6 (5): 31--40. Pfannkuch, H.O., 1969. On the correlation of electrical conductivity properties of porous systems with viscous flow transport coefficients. Proc. of the IAHR First International Symposium. Fundamentals of Transport Phenomena in Porous Media, Haifa, pp. 42-54.

19 Plotnikov, N.I., 1972. Geophysical Methods in Hydrology and Engineering Geology. Nedra, Moscow, 294 pp. (in Russian). Reiter, P.F., 1981. A computer study of the correlations between aquifer hydraulic and electric properties. M.S. Thesis, University of Rhode Island, Kingston, R.I. Scarascia, S., 1976. Contributions of geophysical methods to the management of water resources. Geoexploration, 14: 265--266. Shockley, W.G. and Garber, P.K., 1953. Correlation of some physical properties of sand. Proc. Third Int. Conf. on Soil Mechanics and Foundation Engineering, 1 : 203--206. Smirnov, N.S. and Dunin-Barkovskii, I.V., 1968. Course of Theory of Probability and Mathematical Statistics. Nedra, Moscow, 380 pp. (in Russian). Ungemach, P., Mostaghimi, F. and Duprat, A., 1969. Essais de determination du coefficient d'emmagasinement en nappe libre application a la nappe alluvial du Rhin. Bull. Int. Assoc. Sci. Hydrol., XIV (3): 169--190. Urish, D.W., 1978. A study of the theoretical and practical determination of hydrogeological parameters in glacial sands by surface geoelectrics. Ph. D. diss., University of Rhode Island, Kingston, R.I. Urish, D.W., 1981. Electrical resistivity--hydraulic conductivity relationships in glacial outwash aquifers. Water Resour. Res., 17 (5): 1401--1407. Vincenz, S.A., 1968. Resistivity investigations of limestone aquifers in Jamaica. Geophysics, 33 (6): 980--994. Worthington, P.F., 1975. Quantitative geophysical investigations of granular aquifers, Geophys. Surv., 3: 313--366. Worthington, P.F., 1976. Hydrogeophysical equivalence of water salinity, porosity and matrix conduction in arenaceous aquifers. Ground Water, 14 (4): 224--232.