1HNMR relaxation and rock permeability

0016-7037/92/SKXl

Geochimica d Cosmochimica Acta Vol. 56, pp. 2947-2953 Copyright 0 1992 Pqamon Press Ltd. Printed in U.S.A.

+ .OU

LETTER

‘HNMR relaxation and rock permeability JOHN R. VOGELEY’ and CARL 0. MOSES~ Department of Earth and Environmental Sciences, Williams Hall 3 1, Lehigh University, Bethlehem, PA 18015 USA (Received February 7, 1992; accepted in revised form May 15, 1992)

Abstract-We investigated the relationships among permeability (k), porosity (4), and ‘HNMR (proton nuclear magnetic resonance) relaxation rate in sandstones with the objective of learning more about the connections between the chemical processes that influence ‘HNMR relaxation in a pore-filling aqueous solution and the permeability of the rock. We found that k is a well-correlated function of ‘HNMR relaxation time T, ( r2 = 0.79, N = 113); the correlation between k and a bivariate function of T, and 4 (c#~T:) is slightly better (r ’ = 0 86). Furthermore, permeability is a robust function of TI or ( 44T:); neither relationship is significantly influenced by the range ofporosity in the samples. In contrast, the relationship between permeability and porosity is degraded if low-porosity (4 < 10%) rocks are excluded from the calibration. The common influence of the mineral-solution interface on both k and T1, mediated by the alteration of viscosity and motion of water molecules, is responsible for the observed functional relationships and the relative insensitivity of those relationships to 4. We expect that both T, and observed k can be modified by changes in solution composition that alter the mineral-solution interface. We do not expect much paramagnetic stimulation of relaxation (shortening of T, ) by Fe( III)bearing solid phases in the pore, but more work is required to fully address this point. INTRODUCTION THE INVESTIGATION of fluid migration through porous media has a long history, driven by applications such as water quality and supply, metamorphic petrology, hydrocarbon exploration and production, waste disposal, and industrial processes. The primary property of a porous medium that influences fluid movement is its permeability ( length2). Darcy’s Law gives 3 = -k$73 for relating fluid flow (si, m s-l) to the driving “force” of pressure drop (Vz, kg mm2 sm2 = Pa m-l), permeability (k, m2 = 1.01 X lOI darcy), and viscosity (q, kg m-’ s-’ = 10 poise) ( HUBBERT, 1940). In a “Darcian” permeability measurement for a sample of porous medium, k is computed from measured values of flow and pressure drop and a tabulated value of bulk viscosity for the fluid as a function of temperature and composition, as follows:

The sign convention in Eqn. ( 1) corresponds to flow (ii > 0) in the direction of decreasing pressure (q < 0). Equation ( 1) applies to flow under certain restricted conditions, e.g., steady-state, laminar flow; see HUBBERT ( 1940) or FREEZE and CHERRY( 1979) for further discussion. Our experimental conditions were such that flow was parallel to the gradient, and we assumed isotropic flow. With these restrictions in

’ Present address: Blasland, Bouck, and Lee, Raritan Plaza III, Fieldcrest Avenue, Edison, NJ 08837, USA. 2 Corresponding author.

mind, we have dropped the vector notation of Eqn. ( 1) for the remainder of this letter. Permeability is usually defined as a property of the solid matrix of a porous medium and as independent of the porefilling fluid phase. According to this definition, permeability is a function of the abundance and geometry of flow channels that are connected between the measurement points. The abundance of flow channels is reflected in the measurement of porosity, but geometric considerations that go beyond a simple measure of porosity and suggest the style of channel connectivity include the distributions of surface area and cross section of the channels. In this letter, we address the question of whether a measurement of k may not also depend on solution composition owing to the influence of solution composition on interactions at the boundary between the solid matrix and the solution. Our reasoning is based on the need, when applying Eqn. (l), to know I), which is known for bulk solutions but not for pore-filling solutions. Our hypothesis is that qpors # sulk. The relationship between ‘HNMR (proton nuclear magnetic resonance) measurements and petrophysical properties (e.g., pore size distributions, the ratio of pore surface area to pore volume (A,/ V) , and permeability) has received considerable attention (e.g., L~RENand ROBINSON,1970; SENTURIA and ROBINSON, 1970; SCHMIDTet al., 1986; DASHENet al., 1987; KENYONet al., 1988; HOWARD~~al., 1990). ‘HNMR relaxation has also been important in building an understanding of the structure and dynamics of homogeneous aqueous solutions (e.g., HERTZ, 1973 ) , and our overall goal is to use relaxation to investigate structure and dynamics in pore-filling solutions. The objective for this preliminary inquiry was to analyze the relationships among permeability,

2948

J. R. Vogeleyand C. 0. Moses

porosity, and ‘HNMR relaxation time ( T, ) from the geochemical point of view. Our analysis confirms the conclusions of previous studies, but our discussion extends those conclusions by suggesting a geochemical connection between T, and k that accounts for both their correlation and the apparent insensitivity of that correlation to both porosity and the presence of paramagnetic solid phases. EXPERIMENTAL METHODS

0

Sandstone Samples This investigation was focused entirely on sandstones. Cores (0.9 cm diameter and 2-4 cm length) were cut from rock samples with a water-lubricated coring bit. Our experiments utilized fifteen cores from three different sandstone formations (Table 1). Permeability We pumped 0.5 M NaCl longitudinally through a core using an HPLC pump (Waters 5 10) at a constant flow rate in the range 0.19.9 mL min-’ (v = 0.03 X IO-’ to 2.7 X lo-’ m SK’for our cores). Fluid pressure was monitored at the flow cell, and we obtained Vp for several flow velocities. According to Eqn. ( I), a plot of log Vp vs. log vn should have a slope of I and an intercept of -log k: logVp=logun-logk.

log vg (kg m se2) FIG. 1.Permeability measurement; run 2 on Berea sample I. The slope should be 1 (cf. Eqn. 2). The dashed line is fit to all of the data: r = 0.9935, slope = 0.875, and intercept = 12.37. Data were rejected, beginning with the highest value of log YV,until 0.95 5 slope 2 1.05. The solid line is fit to the accepted data: r = 0.9987, slope = 0.966, and intercept = 12.96. Permeability was calculated for each accepted data pair according to Eqn. ( 1) .

in the fluid (g L-l); y = 0.001 L cmm3 and converts C to units consistent with p):

(2) vF

To avoid taking the log of negative numbers, we reversed the sign convention of Eqn. ( I ) so that Vp > 0. We used the expectation slope = 1 to constrain our data to those measurements that conformed to Eqn. (2) and, thereby, Eqn. ( 1). We rejected all data collected at Vp greater than the lowest Vp that caused the slope of Eqn. (2) to deviate from 1.OO(20.05) for a given core (e.g., Fig. 1). After rejecting any nonconforming data, we calculated, from Eqn. ( I ), a k for each conforming (v, Vp) pair collected during an experiment on a given core and then calculated a mean permeability for that experiment. We assumed that n was 1.05 X lo-’ kg m-i SK’ (WEAST, 1972). Most experiments were replicated. Note that we only used Eqn. (2) for a simple check on data consistency; Eqn. ( 1) wasusedto compute the k values that we report. Porosity For the purposes of this study, porosity (&; F = flow; NORTON and KNAPP, 1977) was the ratio ofthe volume offluid flowing under the conditions of our experiments ( VF) to the bulk volume ( VB)of a rock. We determined Va by measuring the displacement of a 0.5 M NaCl-saturated core in the same solution. The determination of VF(= mass of pore-filling fluid/density of fluid) required correction for the mass of NaCl that precipitated in the pores when the 0.5 M NaCl-saturated core (mass = m,) was dried at 60°C in a vacuum oven (Eqn. (3), in which md was the mass of the dry core, pa”,.,is the fluid density ( 1.019 g cm- r ), and C,, is the concentration of salt

Table 1. Sandstone

cleverly

Deadwood

Source

Berea,OH

RedHills, WY

Deadwood, SD

(ward’s x47E7030) qllaltzite 0.1 - 0.2

1’ minerals

q”m pl@cl~S.C chlorite

2’ minerals

calcite iron oxide

mm1- mdv

PflUld - ( rcsd,1 .

red orthoqu~te 0.2 - 0.4 qm

iron oxide q@Q=

glauconitic sand 0.3 - 0.5 qum calcite g,lauconite q”m

(3)

We subjected the cores to repeated saturation-desiccation cycles to test for alteration of $r by the technique. All measurements of mass and volume were replicated, and mean porosities were calculated for each core.

‘HNMR Relaxation ‘HNMR relaxation refers to the processes involved in perturbing the equilibrium nuclear magnetization (M) of protons in a static magnetic field. At equilibrium, M, = Ma (let z be parallel to the static field, and MOis the net sample magnetization at equilibrium). The sample is perturbed by a pulse of radio frequency (rf) energy orthogonal to z. The pulse of rfenergy tips the net sample magnetization out of parallel alignment with the z-axis, which yields M, < MO.After the pulse ends, M,(t) increases as it relaxes back to MO (Eqn. (4), where R, is the longitudinal relaxation rate coefficient and RI = T;‘): dMz(f) dt

-

= R,(M, - M,(r)).

Values for the longitudinal relaxation time coefficient T, were computed by fitting a single exponential solution of Eqn. (4) (Eqn. 5 ) to seven to eleven (7, MZ) inversion-recovery data pairs (x--7-r/2 pulse sequence; DEROME, 1987; SLIGHTER,1990): = MO exp g

(

Berea

Chin size (mm)

=

M.(T)

samples.

F0illUti0n

Descliption

rejecteddata

6.0, . , , , , , , , , I -7.0 -6.7 -6.4 -6.1 -5.8 -5.5

1

T, was measured for 0.5 M NaCl solution (pH 5.6) both as bulk solution (i.e., no rock present) and as a pore-filling solution in the same cores for which the permeability was determined. We also measured T, in bulk solutions of 0.1-20 mg L-’ Fe( III) or Mn( II) (up to -360 PM) from nitrate salts dissolved in 0.5 M NaCl and acidified (pH 3) with HCI. Rock samples were not exposed to these acidified solutions. Neither the pore-filling fluids nor the bulk solutions were deaerated, and we assume that all solutions were saturated with dissolved oxygen at Pe = 2 1 kPa (0.21 bar). Solutions or saturated cores were placed in 1.Ocm od thin-walled NMR sample tubes (Wilmad) and analyzed in a 90 MHz NMR spectrometer (JEOL FX90Q) using the external D2 lock.

HNMR relaxation rate and the permeability of sandstones

2949

RESULTS In several permeability determinations, the slope of the least-squares regression line fit to Eqn. (2) deviated substantially from the expected value of 1.O, but only at the highest flow rates and pressures (Fig. 1) . We attributed the nonconforming data to clogging of the pore network, leakage around the core, or other violations of Eqn. ( 1). After outlier rejection, repeated experiments on individual cores proved to be very consistent (Fig. 2; Table 2). We had selected 0.5 MNaCl as the pore-filling fluid based on our expectation that a high ionic strength solution would reduce the possibility of damaging the pore network by mobilizing clay or other fine particles. The repeated saturateddesiccation cycles revealed no general trend in the 4~ measurements on a core, so we report the mean 4~ for each core (Table 2). The lack of any trend suggests that the pore network was not altered by the measurement technique. T, measurements for pore-filling 0.5 MNaCl ranged from 0.320-0.757 s (Table 2). Coefficients of variation (CV = standard deviation/mean X 100%) for T1 measurements in the pore&lling solutions ranged from 3- 1 1%, with a typical value -7%. The T, measured for bulk 0.5 M NaCl without added metals (pH 5.6) was 2.73 s. The CV for T, measurements in this solution ( 1.5% ) was typical of the bulk-solution TL measurements. In the bulk 0.5 M NaCl solutions with either Mn(II) or Fe(II1) added (pH 3), T, decreased with increasing concentration of the paramagnetic metal ion. The TI values obtained for the higher concentrations were comparable to the T, values obtained for the pore-filling fluids in the sandstones (Fig. 3). In undertaking regression and correlation analyses to quantify the relationships among porosity, ‘HNMR relaxation, and permeability, we used our data plus the data of KENYON et al. ( 1988) (Fig. 4). The latter data set is more extensive ( 102 cores from fifteen sandstones) than our own and covers a wider range in 4, T, , and k. The T, values in the data set of KENYON et al. ( 1988) were obtained on a 10 MHz NMR instrument in contrast to our 90 MHz instrument, and their T, values were computed by a “stretched exponential” fit to the inversion-recovery data, which, according to the argument of KENYON et al. (1988), may be

8.0 1 7.5

Bena 4.2

A

Baea4.3

b %

BeEi

1

Beta

2

3/35 s/M,

-13.087 (0.031) -13.360 (0.043)

19.4 (0.8) -

0.402 0.341

Baa Beara

3 4

4/46 3/54

-13.433 (0.018) -13.123 (0.024)

18.8 (1.3) -

0.341 0.338

Cleverly

1 2

l/14 -

-12.900 (0.046)

20.1 (1.2) 18.2 (1.2)

0.320 -

Cleverly

3

3/40

-12.173 (0.024)

Cleverly Cleverly Cleverly

3b 4 5 1 2

3/36 1116 l/15 2/18 3/45

-12.192 -12.133 -12.291 -12.178 -12.349

3

2/34

-12.887 (0.018)

4 5

2/21 -

-11.997 (0.024) -

c10vcr1y

DcadWOOd

Deadwood WWOCd DdWOOd

Deadwood

(0.035) (0.030) (0.064) (0.067) (0.075)

-

-

20.0 (0.7) -

0.398 0.474 0.757 0.697 0.539

18.4 (1.4) 19.5 (1.7)

0.680 -

hunber of permeabilitytneasotemeotnuts/numberof accepted data pairs for the repotted value of log k bthenumberin parenthesesis the 95% confidence interval

a more physically relevant representation

of the distribution of relaxation times that corresponds to a distribution of pore sizes (Eqn. 6):

DISCUSSION Consistency of Data Despite the instrumental difference and the difference in data reduction methods, Fig. 4 shows that our results are superimposable on those of KENYON et al. ( 1988). A stretched-exponential fit requires more (7, M,) pairs over a wider range of T than we collected, so a direct comparison of our T, values with those of KENYON et al. ( 1988) may not be totally valid. Nevertheless, we have estimated, based on modeling inversion-recovery data fit to single (Eqn. 5)) stretched (Eqn. 6), and double (Eqn. 6a) exponential rep resentations, that if our T1 values were determined from stretched-exponential representations, they would be shifted

1 2.5

-I

‘i

log P (m?

3.0

0 Betra4.1 q

sample core N’

Ilr,

E

$J 7.0 &

s” 6.5

6.01”. -7.0

, , , , , , , . , -6.1 -6.4 -6.1 -5.8 -5.5 log VT ( kg

m sT2)

FIG. 2. Three separate permeability measurement runs on Rerea sample 4. Only accepted data are shown. For each run, r > 0.99; for runs 1, 2, and 3, slopes are 1.04, 1.02, and 1.02, while intercepts are 13.26, 13.29, and 13.37, respectively.

6

l&l

2t%

3t!lO

4itO

concentration (j&I) FIG. 3. Relaxation time (T,) measurements in bulk 0.5 A4 NaCl solutions ( pH = 3; solid line: Fe; dashed line: Mn). The height of the stippled region at lower left indicates the range of T, values obtained for pore-filling 0.5 M NaCl solutions ( pH = 5.6).

2950

J. R. Vogeleyand C. 0. Moses log k (In*)

- -16

o data fmm Kenyon et al. .

data from this study

FIG. 4. Exploded diagram of three-dimensional log &-log T,-log KENYON et al. ( 1988) (0, X). Data for samples with bF i 10%are indicated by X. Each straight line is a least-squares fit to the data (see Table 3). The gray lines are 95% confidence intervals for predicted values failing on the k space with data from this study (0) and from

straight lines.

toward slightly shorter values (-0.5 log T, units), which would shift our data to the left in Fig. 4. M,(T)=M,,exp(~)+~~,*exp(~).

(6a)

Such a shift does not lead us to believe that there is any important discrepancy between our data and those of KENYON et al. ( 1988); in fact, such a shift may actually improve the superimposability of the two data sets. The double-exponential representation (Eqn. 6a), which fits inversion-recovery data about as well as the stretched exponential (I&NYON et al., 1988)) may be very useful in investigations where two populations of protons relaxing at different rates can be postulated (KORRINGA et al., 1962); but fitting it, like the stretched exponential, requires a wide range of T and about three times as many data points as we collected for each measurement. There is a clear need to resolve the question of which representation of inversion recovery data is most physically relevant to pore-filling fluids, but such a discussion is beyond the scope of this contribution. Establishing the &T,-k

Relationship

We began our analyses by asking whether k is a univariate or bivariate function of & or T, . Linear plots (not shown) suggested geometric models of the form k = AD, where A E { @F, T, } and @> 1. Accordingly, we transformed the measurements to logarithmic space, i.e., log k = p log A (Fig. 4). Comparison of univariate models shows that if we interpret individual correlation coefficients ( r*) as the amount of variability for which a predictor accounts, log G$Faccounts for about 68% of the variability in log k, while log T, accounts

for about 79%. We incidentally observe that log & and log T, are correlated weakly (Table 3; log & accounts for - 5 1% of variability in log T, ). The bivariate model, log k = /32 log & + /3, log T, + PO, where j30is a constant, is a slight improvement over the univariate model with log T, (Table 4). The parameters flz and 0, are statistically identical to the values predicted on theoretical grounds (4 and 2, respectively) by BANAVARand SCHWARTZ( 1987). We thus agree with the conclusion of KENYONet al. (1988) that log k = f[log (q$T:)] in sandstones (Fig. 5 ) . The large exponent (4) for & and the weak individual correlation between log $JFand log T,, however, led us to question the relative importance and robustness of & and T, as predictors of k. KENYON et al. ( 1988) concluded that knowledge of T, is much more important than knowledge of #+ in accurately predicting k, and we can add that log k = f[ log (6°F T:)] and log k = f[ log ( T,)] are less sensitive to the range of porosity than is log k =f[log (&z)] . Although 10% is an arbitrary demarcation between relatively high and low porosity rocks, Fig. 4 shows that in the available data set, there is a clear break between samples with log &greater or less than 1.O. When we excluded data for the samples with & < 10% (ten data points), log & became a substantially weaker predictor of log k (Table 3), accounting for less than 5 1% of the variability in log k. Similarly, after excluding samples with & < lo%, the correlation between log & and log T, became much weaker ( - 30% of variability; Table 3). On the other hand, when the samples with I$~< 10% were excluded, the variability in log k for which log T, accounted dropped only from 79 to 74%. Neither the slope nor the intercept of the regression line for log k = f(log T,) was significantly altered by excluding the low-porosity samples (Table 3). The bivariate log k predictor, log ((b$T:), was also altered only slightly by excluding the low-porosity samples; the variability in log k for which log (&T:) accounted dropped from 86 only to 82% (Table 5 ). The Effects of Pamnagnetic

Materials

We know that paramagnetic solutes stimulate relaxation (Fig. 3) but we know little about the effect of paramagnetic solutions in pores or paramagnetics in the solid phase. Petrographic examination of our samples revealed an abundance of Fe( III)-bearing surface coatings. Such phases would, how-

Table 3. Least-squares fit parameters for different univariate models of the relationships among k. &, and TI. model

r

intercept

all aiza, N = 113 log k = f(log #,J logk=f(logT,) log eF =f(logT,)

0.8239 0.8883 0.7108

exclude samples with log k =f(log &) log k = f(log T,) log @=ffOogT,)

$F < 10%. N = 103 0.7133 -25.09 0.8576 -11.46 0.5514 1.35

-24.00 -11.35 1.40

slopes

8.43 (0.914) 2.64 (0.079) 0.207 (0.0007)

9.30

(1.59)

2.42 (0.078) 0.119 (0.0004)

humber in parentheses is variance of the slope (sbz)

2951

HNMR relaxation rate and the permeability of sandstones Table5. Parameters for fitting log k =f[log($~4,1’T,z)1.

Table4. Pwameters for fiaing logk=&log@F+/3, IogT, +& ,

Bo

Bz”

r

B,”

alldota,N=113 0.9295 -16.94

3.98 (0.51)

excludesampleswith & c 10% 0.9047 -17.55 4.50 (0.67)

0.9294

1.82 (0.15)

%e

ever, be expected to have very low solubility in solutions of pH 5.6. Assuming no complexing ligands other than OHand Cl-, we used PHREEQE (PARKHURST et al., 1982) to estimate the solubility of Fe( III),,,, controlled by amorphous Fe(OHh (the most soluble Fe(II1) solid phase but not necessarily the phase present), in the 0.5 MNaCl, pH 5.6, porefilling solution to be - 10-5.9 M. The effect of Fe( III),,, at such low concentrations on ‘HNMR relaxation is insignificant (Fig. 4). The concentration of Fe( II)(,) would be negligible in these aerobic solutions. The contributions of different relaxation mechanisms to the total or observed rate of relaxation are additive (Eqn. 7, in which T;L is the contribution from the kth mechanism) : Tl,‘ot-ed

= 2 T;kl.

(7)

k

If one of the terms in Eqn. (7) were a contribution from paramagnetic interactions, we would expect a variation in Tl,‘Clbsc&in linear proportion to the abundance of the paramagnetic species. We would not expect paramagnetic abundance to be generally correlated with permeability, so any paramagnetic contribution to Tl,bbservd should degrade the correlation between log k and log T, . Owing to the strength of the observed correlation between log k and log T, , in spite of no effort to account for paramagnetic abundance, we suggest that solid-phase paramagnetics had a negligible effect on relaxation in our investigation and probably most similar investigations of ‘HNMR relaxation in porous rocks. Alternatively, variable paramagnetic stimulation of relaxation may account for some of the variability in T, measurements that does not correspond to variability in k. The approach of

s”

-14 -16 -18 -20 -2

-1

0

1

2

3

4

5

-16.62

0.940

(0.009)

e.rclude samples with $p c 10%. N = 103 0.9040 -16.78 0.988 (0.012)

N = 103 1.88 (0.14)

‘the number in parentheses is thestandard error

*

slope’

inrenxpt

all data,N = 113

6

lo&$q2) FIG. 5. Log k predicted by log (&T:). The straight line is a leastsquares fit to the data (see Table 5). The gray lines are 95% confidence intervals for predicted values falling on the straight line.

number in parentheses is tlx standard error

KORRINGA

et al. ( 1962), which gives a double exponential solution (Eqn. 6a) for inversion recovery data, may be useful in future efforts to resolve the role of paramagnetic surface phases. Implications for Geochemical and Hydrogeologlc Studies of Sandstones

One would expect the size of pore “throats” or connecting channels with a narrower dimension than the pores to have a larger influence on permeability than the size of the pores themselves, while relaxation should be sensitive mainly to the pore size (more accurately, the pore size distribution). That expectation is based, however, on a schematic understanding of pore network geometry that may be unrealistically oversimplified; and, as we have shown here, relaxation rates yield very good correlations with permeability that are only slightly improved by considering porosity. We infer from this that k and T, may both be more sensitive to interactions of the fluid with the pore network’s surfaces than to the network’s porosity. This interpretation makes good sense, however, only if the pore surface can be shown to locally alter viscosity, which influences both relaxation rate and fluid flow and is, therefore, the key to understanding the mechanism underlying their correlation. If surface alteration of viscosity can be shown, we would have to reinterpret a permeability measurement as a manifestation of a surface influence on fluid viscosity in addition to being a manifestation of the pore system connectivity. HORN and SMITH ( 1990) and ISRAELACHVILI ( 1986) have suggested that the viscosity of a thin film of aqueous solution on a silicate surface is not very different from the viscosity of the same solution in bulk (no more than - 5% greater at the surface). It is possible that their measurements, made with thin films on very smooth surfaces, may not be pertinent to the pore environment with water molecules several tens of pm away from a rough mineral surface. Even if viscosity reduction is as little as 5%, however, it may still contribute to a diminished T, . According to the Bloembergen, Purcell, and Pound (BPP; BLOEMBERGEN et al., 1948) theory of relaxation, T;’ = f( 7). The BPP theory also stipulates that T;’ is stimulated by interactions between a given proton and its “partner” proton in the water molecule and between the proton and a “neighbor” proton on another water molecule that diffuses into the given proton’s proximity (Eqn. 8; cf. Eqn. 7): Globserved = K’panner + Tl,‘neight.,r.

(8)

2952

J. R. Vogeley and C. 0. Moses

In bulk solution at 298 K, Tl,baRner = 0.263 s-’ and = 2.77 s (compare TK’ne’~~r = 0.0978 s-’ , giving T,, obaewed our bulk-solution Tl of 2.73 s). If we add a term for the “partner” and the “neighbor” with 5% greater 17,we have K’obsemed = 0.263 + 0.276 + 0.0978 + 0.1027, giving T 1,observed = 1.35 s. In making this illustrative calculation, we have obviously given “high viscosity” water a weight equal to that of any porewater that behaves like bulk water. Nevertheless, our calculation demonstrates that allowing a contribution from greater viscosity decreases Tl from its bulk value and that, given equal weight, a 5% increase in n yields a -50% decrease in T, . Further investigation is required to establish the appropriate weighting; but we submit that, owing to diffusive exchange between the “high viscosity” water close to the mineral surfaces of the pore and the porewater more distant from the pore surface, the increased viscosity will be experienced by most of the water molecules in a pore during a T’ measurement (the maximum diameter of a pore for this statement to be true is limited by difhtsion rates and is on the order of 100 pm). Even so, it may be that a 5% increase in viscosity is inadequate to account for all of the decrease in Tl (from -3 to -0.5 s). If this proves to be the case, we will have to determine whether the 5% value is too low for pores in sandstones or if there are additional relaxation-stimulating mechanisms at work in pores. Candidates for such mechanisms include reactivity at the electrified interface between the porebounding mineral surfaces and the solution. For example, hydration of the surface (both physisorbed and chemisorbed water; see DAVISand KENT, 1990) and the reduced dielectric constant of water near the interface (promoting cation hydration and hydrolysis; see MULLA, 1986) would be expected to generally reduce the mobility of water molecules at the interface and, according to the BPP theory, reduce Tl . As we argued above, diffusion of molecules between regions of the pore where behavior approaches that of bulk water and the interfacial region has the effect of stimulating relaxation in some large fraction (perhaps essentially all) of the samples’ protons during the Tl measurement. An important geochemical consideration pertinent to relaxation stimulation by the surface would be the influence of solution composition (both ionic strength generally and specific properties of different solutes) on the character of the electrified interface with respect to altering the motion of water molecules. SCHMIDTet al. ( 1986) demonstrated that a ten-fold increase in concentration of an NaCl solution did increase T, in a porous sandstone, which is consistent with expectations based on the BPP theory and the “thinning” of the electrical double layer in the higher ionic strength solution. If viscosity is altered by the properties of the electrified interface, we expect it to be manifested in a permeability measurement as well as the T, measurement, and we expect that permeability measurements with different solutions will yield different values. It is already established that, at least for very low porosity rocks, wettability, which depends on solution composition, influences permeability (LEE et al., 1991) . SCHEIDE~~GER ( 1974)reviews a group of investigations that demonstrated permeability increases when the ionic strength of the solution was increased, he categorizes these observations as anomalies with respect to Darcy’s Law and

demonstrates a modification that accounts for electro-osmotic effects and the mineral-solution interface. The general form of the modification is ki = k’ + \6k,,, 1, where k, is the truly intrinsic permeability in the absence of electrical effects, k’ is the apparent or measured permeability, and 6k,,,, is the electro-osmotic effect on permeability. Increased k’ should thus be expected for a solution of increased concentration because (6k,,, 1 decreases. More modem measurements of this effect, coupled with the effect of solution composition on ‘HNMR relaxation in pore solutions, are needed to unify our geochemical understanding of the correlation between Tl and permeability. As we continue our investigations of pore-filling solutions, we are pursuing two specific lines of inquiry. There exists a conceptual framework for interpreting ‘HNMR relaxation data from homogeneous solutions and for interpreting the effects of a confining geometry (mainly cells in biological materials and micelles in solution but also porous rocks) on relaxation. That framework needs to be transferred to the geochemical domain, where we are interested in heterogeneous solutions and a confining geometry with a reactive surface (MOSES, in prep.). In addition, we are performing experiments to determine the effect of solution composition on permeability and the power of a mineral surface to stimulate relaxation. The results of those experiments may help us to refine the correlation between Tl and k, but more importantly, we expect them to help us to better understand the geochemical dimensions of permeability and to understand how the structure and dynamics of an aqueous solution are altered in the pore environment. CONCLUSIONS

1) In addition to verifying the conclusion of KENYON et al. (1988) that log (c$:T:) can be calibrated to predict log k in sandstones, our analysis shows that log Tl alone performs almost as well as log (4°F T:); the robustness of log +r alone as a predictor of either log k or log Tl is severely compromised when low-porosity rocks are excluded from the calibration dataset, and the robustness of neither log Tl alone nor log ( 4°FT :) as predictors of log k is markedly degraded by excluding low-porosity rocks. solid phases are 2) Low-solubility paramagnetic-bearing likely to contribute little relaxation stimulation in the pore environment. Further work is warranted to verify this conclusion. 3) In the pore environment, mineral-water interactions alter the viscosity ofthe pore-filling solution (compared to bulksolution viscosity) and the mobility of water molecules. Our argument suggests an opportunity for mineral-water interface geochemistry to influence the measurement of rock physical properties such as permeability. It also indicates that ‘HNMR relaxation can be used to investigate other geochemical processes in pore-filling solutions as it has been used in bulk solutions. Acknowledgments-We gratefully acknowledge the influence of con-

versations with J. Howard, W. Kenyon, and C. Straley and interactions with W. Anderson, B. Carson, N. Foster, and K. Kellar. Funding was provided by Lehigh University. We appreciate the constructive comments on the manuscript by W. Fyfe, J. Howard, D. Norton,

HNMR relaxation rate and the permeability of sandstones and an anonymous reviewer, which were instrumental in guiding our revisions. Editorial handling: G. Faure

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