Chemical Modeling in Aqueous Systems - American Chemical Society

34

Application

of

Geochemical

Kinetic

D a t a to

Ground

water Systems A

Tuffaceous-Rock

System in Southern

HANS C. CLAASSEN and ART

1

Nevada

F. WHITE

Downloaded by EAST CAROLINA UNIV on January 4, 2018 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch034

U.S. Geological Survey, Denver, CO 80225 In p r i n c i p l e , the chemical composition of water recharging a l i t h o l o g i c a l l y homogeneous a q u i f e r w i l l depend upon the mineral phase present i n the a q u i f e r , the amount of d i s s o l v e d carbon d i o x i d e (H2CO3), the amount of a q u i f e r surface area (S) i n contact w i t h the h y d r a u l i c a l l y e f f e c t i v e pore volume (V), the temperature at which r e a c t i o n occurs (Τ), the contact time ( t ) , and the r e a c t i o n r a t e ( k ) . Laboratory experiments may be c a r r i e d out using s p e c i f i c l i t h o l o g i e media to determine the r a t e s of r e a c t i o n of these media w i t h water c o n t a i n i n g d i s s o l v e d carbon d i o x i d e . I f the i n t e r r e l a t i o n s h i p s of the above v a r i a b l e s can be s u f f i c i e n t l y d e f i n e d , a determination of one of the above a q u i f e r p r o p e r t i e s can be made, i f the others are known, and i f a r e p r e s e n t a t i v e water sample from the a q u i f e r i s a v a i l a b l e . O r d i n a r i l y , a q u i f e r p r o p e r t i e s are measured using h y d r a u l i c t e s t i n g techniques. These techniques y i e l d estimates of r a t e s and q u a n t i t i e s of water movement w i t h i n a given a q u i f e r and are not r e l a t e d to chemical r e a c t i v i t y . However, knowledge of the chemical r e a c t i v i t y of an a q u i f e r i s necessary, i f meaningful pre d i c t i o n s of the e f f e c t s on water q u a l i t y of wastes i n j e c t e d i n t o the a q u i f e r are to be made, because s o r p t i o n of waste m a t e r i a l s by the a q u i f e r i s u s u a l l y r e l i e d upon to reduce any p o t e n t i a l hazard. The amount of a c t i v e a q u i f e r surface i n r e l a t i o n to the s o l u t i o n volume w i t h which i t i s i n contact (S/V or σ) must be known f o r a given a q u i f e r system to p r e d i c t the e f f i c i e n c y of the a q u i f e r to m i t i g a t e the e f f e c t of waste i n t r o d u c t i o n . This σ i s unobtainable by h y d r a u l i c t e s t i n g of an a q u i f e r , but could be estimated from w a t e r - q u a l t i y data i f values of the other r e q u i r e d parameters were a v a i l a b l e . Hydrologie S e t t i n g To t e s t the above hypothesis, a system i n southern Nevada was chosen f o r which s u f f i c i e n t h y d r a u l i c and w a t e r - q u a l i t y data were a v a i l a b l e . This sytem, R a i n i e r Mesa, i s l o c a t e d about 160 km northwest of Las Vegas, Nev. The l i t h o l o g y and hydrology of 1

This is Part I of a series.

0-8412-0479-9/79/47-093-771$05.75/0 This chapter not subject to U.S. copyright Published 1979 American Chemical Society Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


772

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

R a i n i e r Mesa have been described by Thordarson (1) and are s c h e m a t i c a l l y i l l u s t r a t e d on F i g u r e 1. The caprock of the mesa i s predominantly d e v i t r i f i e d t u f f , the R a i n i e r Mesa Member of the Timber Mountain T u f f . I t s t h i c k ness v a r i e s , but i s g e n e r a l l y about 100 m, although i n s m a l l areas the u n d e r l y i n g P a i n t b r u s h Tuff crops out. The t u f f of the R a i n i e r Mesa Member has a v i t r i c b a s a l zone of chemical composition s i m i l a r to the o v e r l y i n g d e v i t r i f i e d t u f f . Underlying the R a i n i e r Mesa Member i s the v i t r i c P a i n t b r u s h Tuff w i t h a chemical composition a l s o s i m i l a r to t h a t of the o v e r l y i n g rocks. The P a i n t b r u s h i s g e n e r a l l y 200 m t h i c k and i s u n d e r l a i n by v i t r i c rocks which have undergone extensive a l t e r a t i o n to c l a y minerals and z e o l i t e s . These a l t e r e d rocks are i n f o r m a l l y r e f e r r e d to as the "tunnel beds," so named because of the many d r i f t s which have been mined i n t o R a i n i e r Mesa. Although c h e m i c a l l y s i m i l a r , these rocks are hydrologically quite dissimilar. Recharge to the R a i n i e r Mesa h y d r o l o g i e system occurs mainly through f r a c t u r e s i n the competent d e v i t r i f i e d t u f f ; some recharge may a l s o occur d i r e c t l y to the P a i n t b r u s h Tuff where i t crops out on the s u r f a c e of the mesa. The f r a c t u r e (secondary) h y d r a u l i c c o n d u c t i v i t y may be l o c a l l y very h i g h , but the average c o n d u c t i v i t y of the d e v i t r i f i e d rock i s probably low. That water which passes through the f r a c t u r e s of the d e v i t r i f i e d t u f f enters the P a i n t b r u s h T u f f , which has a r e l a t i v e l y h i g h i n t e r s t i t i a l (primary) h y d r a u l i c c o n d u c t i v i t y as determined by measurements made on core samples (1_). Continued downward movement of water i n the R a i n i e r Mesa system i s retarded by the t u n n e l beds which have both low primary and secondary c o n d u c t i v i t i e s . Thus, recharged water probably t r a v e l s r a p i d l y through the f r a c t u r e d R a i n i e r Mesa Member; perhaps more s l o w l y through the u n d e r l y i n g P a i n t b r u s h ; and even more s l o w l y through the tunnel beds. This c o n s t i t u t e s one example of a perched water body: a zone of s a t u r a t i o n above an unsaturated z o n e — i n t h i s case caused by an u n d e r l y i n g zone of low c o n d u c t i v i t y , the z e o l i t i z e d t u f f of the t u n n e l beds. In R a i n i e r Mesa, the top of the zone of s a t u r a t i o n i s i r r e g u l a r . Composite water l e v e l s measured i n d r i l l holes p e n e t r a t i n g both the P a i n t b r u s h and the t u n n e l beds i n d i c a t e that the top of the zone of s a t u r a t i o n i s i n the lower part of the P a i n t b r u s h . Data from cores (Larry Benson, Lawrence Berkeley Laboratory, Berkeley, w r i t t e n communication, 1978; 1, 2 ) , however, i n d i c a t e that other p a r t s of the P a i n t b r u s h may be n e a r l y s a t u r a t e d . I t appears that the d e v i t r i f i e d R a i n i e r Mesa Member i s unsaturated (1). An a d d i t i o n a l f e a t u r e that may i n f l u e n c e the h y d r o l o g i e system i s a g e n t l y east-northeast plunging s y n c l i n e . L i t h o l o g i e , h y d r o l o g i e , and w a t e r - q u a l i t y data suggest that f l o w i n the P a i n t b r u s h , i n a d d i t i o n to downward, may be l a t e r a l toward the synclinal axis.

Jenne; Chemical Modeling in Aqueous Systems ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

AND WHITE

Kinetic Data and Groundwater Systems


CLAASSEN

773

t5

Ο

"I "δ

PC

ο


CHEMICAL

774

M O D E L I N G IN

AQUEOUS

SYSTEMS


Water Q u a l i t y For many y e a r s , water samples have been c o l l e c t e d from seeps i n t u n n e l s , mined f o r the most p a r t i n the tunnel beds. These samples have shown one s i g n i f i c a n t c o m p o s i t i o n a l s i m i l a r i t y : h i g h percent sodium. The B-tunnel system was d r i v e n i n t o the P a i n t b r u s h T u f f , and c o n s i d e r a b l e c a l c i u m was a l s o present i n the water samples c o l l e c t e d . Some samples c o l l e c t e d from the T-tunnel system contained h i g h c o n c e n t r a t i o n s of sodium, t y p i c a l of water from the tunnel beds; other samples contained s i g n i f i c a n t calcium. These l a t t e r samples were c o l l e c t e d from regions of T-tunnel q u i t e near the s y n c l i n a l a x i s . This p r o x i m i t y r e s u l t s i n a l e s s e r t h i c k n e s s of t u n n e l beds o v e r l y i n g l o c a t i o n s nearer the a x i s , and the samples represented water which had t r a v e l e d a s h o r t e r d i s t a n c e i n the tunnel beds. The high-sodium water i s b e l i e v e d to r e s u l t from p r e c i p i t a t i o n o f , or i o n exchange r e a c t i o n s w i t h , z e o l i t e s which are present i n the tunnel beds. Furthermore, these r e g i o n s of Τ tunnel produced l a r g e water flows of more than 6 L/s, as c o n t r a s t e d w i t h the more u s u a l seeps of a few hundredths of a l i t e r per second. Benson (LBL, Berkeley, w r i t t e n commun., 1978) reported analyses of a few samples c e n t r i f u g e d from cores taken i n the P a i n t b r u s h i n the v i c i n i t y of the T-tunnel complex; these showed s i g n i f i c a n t c a l c i u m contents. F i g u r e 2 shows some of the w a t e r ^ q u a l i t y data from the R a i n i e r Mesa system p l o t t e d on a Na-Ca-K t r i l i n e a r diagram. Those samples from B- and T-tunnel systems w i t h s i g n i f i c a n t Ca contents are p l o t t e d as open c i r c l e s , and the more t y p i c a l tunnel water samples w i t h low Ca are c l o s e d circles. Laboratory experiments (3) w i t h both v i t r i c and d e v i t r i f i e d t u f f of the R a i n i e r Mesa Member have d i s c l o s e d the r a t e s and mechanism of d i s s o l u t i o n of these rocks. Many experiments were c a r r i e d out to d e f i n e the i n t e r r e l a t i o n s h i p s among pH, S/V (or σ), and temperature (Τ), i n determining the r a t e s and c a t i o n products of the r e a c t i o n s . F i g u r e 2 a l s o shows the p r o g r e s s i v e changes i n r e a c t i o n products f o r both v i t r i c and d e v i t r i f i e d rocks at an experimental pH v a l u e s i m i l a r to that at which most of the r e a c t i o n occurs i n the n a t u r a l system. The r e a c t i o n r e s u l t s have been e x t r a p o l a t e d beyond the experimental r e a c t i o n time using the relationship

where the t o t a l mass of c a t i o n M t r a n s f e r r e d from s o l i d to s o l u t i o n i n time, t , the mass t r a n s f e r r e d from s o l i d to s o l u t i o n by i o n exchange at f r e s h rock s u r f a c e , the r a t e constant a s s o c i a t e d w i t h t r a n s f e r of c a t i o n M at constant pH.


34.

CLAASSEN AND WHITE


775


CO

CO

V. Ο

ο

e

.S *o

ο Κ

Co

SS

co

Ο CO

•S-

es

•2 *ζ

ο ο Ο

csj V-

•BP


776

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

The r e l a t i o n s h i p i s derived from the p r e v i o u s l y mentioned l a b o r a t o r y experiments. Although the Q term i s a s i g n i f i c a n t d e t e r minant of t o t a l mass t r a n s f e r r e d i n the experiments using m a t e r i a l f r e s h l y disaggregated, the authors b e l i e v e that Q = 0 i n the environment of a steady-state ground-water system. The f r e s h surface has a s s o c i a t e d c a t i o n s , which are more e a s i l y removed than those w i t h i n the rock i t s e l f . These c a t i o n s are no longer a v a i l a b l e f o r removal i n a n a t u r a l ground-water system not under going l a r g e - s c a l e p h y s i c a l d i s r u p t i o n . E x t r a p o l a t i o n of the l a b o r a t o r y data to much longer times f u r t h e r presumes a continua t i o n of the same mechanism as at s h o r t e r times; f o r g l a s s e s , the assumption appears v a l i d , as nonparabolic r a t e s have not g e n e r a l l y been observed (see (3) f o r a more complete d i s c u s s i o n ) . R a t i o s of p a r a b o l i c r a t e constants s u c c e s s f u l l y p r e d i c t the i o n r a t i o s observed i n R a i n i e r Mesa ground-water samples, whereas, i f l i n e a r r a t e s would become important at longer times i n t h i s system, con gruent d i s s o l u t i o n must take p l a c e , and the d i s s o l v e d - i o n r a t i o s should r e f l e c t the composition of the s o l i d . This i s not observed i n the f i e l d data (see (3) f o r a more d e t a i l e d d i s c u s s i o n of d i s s o l u t i o n mechanisms). I t i s c l e a r that r e a c t i o n w i t h the d e v i t r i f i e d ( c r y s t a l l i n e ) t u f f of the R a i n i e r Mesa Member r e s u l t s i n water extremely h i g h i n calcium and magnesium, whereas r e a c t i o n w i t h the v i t r i c t u f f of R a i n i e r Mesa of the same chemical composi t i o n produces water of a composition s i m i l a r to that of the samples from Β and Τ tunnels b e l i e v e d to have been l i t t l e a f f e c t e d by the z e o l i t i z e d t u f f . F i e l d - d a t a c o n f i r m a t i o n of the l a b o r a t o r y r e s u l t s from r e a c t i o n of the c r y s t a l l i n e t u f f i s d i f f i c u l t , because no water samples have ever been obtained from the unsaturated R a i n i e r Mesa Member. One s p r i n g sample obtained from d e v i t r i f i e d Timber Mountain T u f f , however, i s b e l i e v e d to be r e p r e s e n t a t i v e of a system s i m i l a r to t h a t of R a i n i e r Mesa, but without the v i t r i c phase; i t s composition i s a l s o i n d i c a t e d on F i g u r e 2.


Q

The l o c a t i o n i n the geologic s e c t i o n from which the Β and Τ tunnel-complex water samples were obtained, comparison of t h e i r chemical composition w i t h data obtained from l a b o r a t o r y experiments on both v i t r i c - and c r y s t a l l i n e - t u f f , and hydrologie data from the R a i n i e r Mesa system, combine to imply that the v i t r i c m a t e r i a l ( R a i n i e r Mesa Member and Paintbrush T u f f ) of R a i n i e r Mesa i s r e s p o n s i b l e f o r the water q u a l i t y observed above the z e o l i t i z e d zone. I t i s l i k e l y that because the recharging water must f i r s t pass through the f r a c t u r e s i n the c r y s t a l l i n e t u f f of R a i n i e r Messa, at l e a s t some of the d i s s o l v e d m a t e r i a l i n the water must be derived from t h i s m a t e r i a l . The question, of course, i s not " i f , " but "how much." The development that f o l l o w s w i l l assume that the e f f e c t i s not s i g n i f i c a n t , and the probable e r r o r introduced by t h i s assumption w i l l be d e a l t w i t h l a t e r .


34.

CLAASSEN


AND WHITE

777

Chemical K i n e t i c Modeling Of The R a i n i e r Mesa System To model the c h e m i c a l - k i n e t i c e v o l u t i o n of the R a i n i e r Mesa ground water, s e v e r a l s i m p l i f y i n g assumptions and parameter estimates had t o be made. F i g u r e 1 diagrammatically i l l u s t r a t e s the R a i n i e r Mesa system, i n d i c a t i n g regions of l i t h o l o g i e and h y d r o l o g i e importance; these w i l l be discussed s e p a r a t e l y . Region 1 i s the s o i l zone (or e q u i v a l e n t ) . This i s the zone of a e r o b i c b i o l o g i c a l a c t i v i t y and the r e g i o n of h i g h p a r t i a l pressure of carbon d i o x i d e gas (Ρ„ ) r e s u l t i n g from p l a n t r e s p i r a Λ


CU2

t i o n and m i c r o b i o l o g i c a l - d e c a y mechanisms. Some of t h i s gas i s d i s s o l v e d by the r e c h a r g i n g water as i t passes through r e g i o n 1, according t o the r e a c t i o n H2O1 + C02 i=^ H2CO3 An estimate of H2CO3 i n recharge water was made from__six R a i n i e r Mesa water samples f o r which r e l i a b l e pH and HCO3 values were a v a i l a b l e . I n simple s i l i c a t e rock d i s s o l u t i o n , a l l carbonate species r e s u l t from r e a c t i o n of H C 0 w i t h the rock. Thus, HC0 + C0§"+ H C 0 at any p o i n t i n the flow path i s assumed t o be a constant. C a l c u l a t i o n s of c o n c e n t r a t i o n s of these species i n the s i x samples p r e v i o u s l y mentioned allowed c a l c u l a t i o n of H2CQ3 i n i t i a l l y a v a i l a b l e f o r r e a c t i o n . These data a r e presented i n Table I . The a r i t h m e t i c mean was used i n subsequent c a l c u l a t i o n s . The r e a c t i o n process was viewed as a s e r i e s of simple s t e p s , o u t l i n e d h e r e a f t e r . F i r s t , r e c h a r g i n g water d i s s o l v e s s o i l - z o n e CO2 t o y i e l d a t y p i c a l sample value of H2CO3 + HCO3 of .„ 2.16 χ 1 0 ~ mol/L (CO^'is n e g l i g i b l e ) . The d i s t r i b u t i o n of major carbonate species i s governed by the e q u i l i b r i u m r e l a t i o n s h i p (4): g

2

3

3

2

3

3

Kf

V = —

5

a

a

HCOi

[ 7

= 4.31 χ ΙΟ" * H C0 2

3

H +

H

][ ™3l rn -i

> H

[

H 2 C

° 1

( 1 )

'

3

Table I . — D a t a Used To Estimate Recharge Concentration of H C 0 I n T y p i c a l R a i n i e r Mesa Ground Water 2

3

T o t a l

Sample d e s i g n a t i o n

pH

carbonate — species

U12t.03 UGl U12t.03 UG3 U12n.07 Byp. U12n.02 UGl U12t main 1805 U12t main

7.18 7.40 8.04 7.31 7.83 8.21

A r i t h m e t i c mean - HCO3 + H C 0 2

3

+ CO3" i n mmol/L; CO3" i s n e g l i g i b l e .


2.14 2.36 .89 2.51 2.53 2.52 2.16

778

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

For a t o t a l carbonate species c o n c e n t r a t i o n of 2.16

X 10~

3

[HCO3] =

mol/L,

3.05

X 10

5

and

[H C0 ] 2

=

3

2.13 Χ 10*" mol/L a t 25°C. The a s s o c i a t e d pH v a l u e was c a l c u l a t e d to be 4.5. The a c t u a l temperature of recharge i s not known; 25°C was chosen because temperatures w i t h i n R a i n i e r Mesa are b e l i e v e d to range from ~ 20° to 25°C and most of the r e a c t i o n takes p l a c e under those c o n d i t i o n s . Once the recharged ground water leaves the mesa s o i l zone (region 1) where i t r e c e i v e d i t s charge of H2CO3, i t enters rocks (region 2, R a i n i e r Mesa Member, and r e g i o n 3, P a i n t b r u s h T u f f ) , where i t r e a c t s w i t h the tuffaceous a q u i f e r u t i l i z i n g only the H2CO3 d e r i v e d from the s o i l zone. This i s c a l l e d a c l o s e d system reaction:


3

( s i l i c a t e rock) (M ) + H C 0 +

2

+

3

-> ( s i l i c a t e rock) (H ) + M

+

+ HCO3

+

thus, H ions are consumed, i n c r e a s i n g the pH and b i c a r b o n a t e , and metal ions appear i n s o l u t i o n . The r e a c t i o n progress may be modeled as a s e r i e s of s t e p s , the beginning and end of each step defined by a s p e c i f i c pH change, which, i n t u r n , f i x e s concentra t i o n s of a l l major carbonate species by e q u i l i b r i u m (equation 1) and mass-balance (equation 2) r e l a t i o n s h i p s : 2.16 X

(2)

3

10" .

For the a n a l y s i s presented here, an approximation to c o n t i n u o u s l y v a r y i n g pH was_made by choosing 0.5-pH i n t e r v a l s , and the boundary v a l u e s f o r HCO3 i n Table I I were c a l c u l a t e d . Changes i n HCO3 w i t h i n each pH i n t e r v a l were then determined, these changes r e s u l t i n g from consumption of hydrogen ions from H2CO3 w i t h an, e q u i v a l e n t p r o d u c t i o n of both HCO3 and c a t i o n s , M * Because 2.08 meq/L H2CO3 i s converted to HCO3, i n a r e a c t i o n which goes from pH = 4.5 to pH = 8.0, 2.08 meq/L c a t i o n s are produced. C a t i o n compositions of s e v e r a l R a i n i e r Mesa ground-water samples are shown on F i g u r e 3, w i t h the c a t i o n composition of a sample having 2.08 meq/L t o t a l c a t i o n s i n d i c a t e d by the arrow and by the numerical values l i s t e d . The s t r a i g h t l i n e s drawn through the data p o i n t s are to f a c i l i t a t e determination of a c a t i o n composi t i o n and are not intended to imply composition changes during r e a c t i o n ; t h i s would only be t r u e i f a l l the samples represented p o i n t s along a s i n g l e f l o w path or along s i m i l a r f l o w paths. I n R a i n i e r Mesa, i t i s more probable t h a t the samples represent s i m i l a r l o c a t i o n s along a s e r i e s of d i s s i m i l a r f l o w paths, and t h e r e f o r e , i n theory, any one of the a c t u a l samples could be modeled. Instead, a s i n g l e median value was chosen as t y p i c a l . A s s o c i a t e d w i t h each pH i n t e r v a l t h e n _ i s a midpoint pH, a change i n bicarbonate c o n c e n t r a t i o n ( A J H C 0 3 p , and a set of r a t e c o n s t a n t s . These v a l u e s are presented i n Table I I . White and n+



8.0

7.5

7.0

6.5

6.0

5.5

5.0

4.5

pH interval boundary

7.75

7.25

6.75

6.25

5.75

5.25

4.75

Mean pH (reaction pH)

4

5

5

2.08x10"

1.98x10"

1.73x10"

3

3

3

1.2 3x10"

3

4

6.42x1ο-

2.56xl0"

8.80x10"

3.05x10"

3

[HC0 ~] a t boundary mol/L

9.73χ10"

4

5

2.56χ10-

4

4

5.00χ10-

5.87X10"

4

3.86x1ο-

4

5

1.68χ10"

5.75xl0"

3

A[HC0 "] mol/L

14.07

13.98

13.90

13.82

13.73

13.64

13.57

-log k Na +

2

+

2

14.54

14.54

14.54

14.54

14.54

14.54

14.54

mol/cm sec

-log k K

14.91

14.66

14.40

14.15

13.90

13.65

13.40

(25°C)

-log k Ca

Table I I . — B o u n d a r y Values and K i n e t i c Rate Constants Used i n Simulation of R a i n i e r Mesa Ground Water


2 +

14.90

14.70

14.49

14.28

14.08

13.88

13.67

-log k Mg

2 +

780

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS


Claassen (3) determined k i n e t i c r a t e constants (k . ) f o r r e l e a s e M of c a t i o n s from v i t r i c m a t e r i a l of the R a i n i e r Mesa Member. These r a t e constants are pH-dependent, because the mechanism of the r e a c t i o n i n v o l v e s d i f f u s i o n of hydrogen i o n s i n t o the g l a s s , and a corresponding (and e q u i v a l e n t ) d i f f u s i o n of c a t i o n s out; thus, c o d i f f u s i o n determines the r a t e at which c a t i o n s appear i n solution. The equation which determines the mass of any one species t r a n s f e r r e d during a given pH i n t e r v a l i s : q

= tft^nk

(3)

n +

where Π

q

i s mass of s p e c i e s Μ t r a n s f e r r e d during any pH i n t e r M v a l (at a constant pH equal to the mean pH of the i n t e r v a l ) , equivalents/1., σ i s the a q u i f e r s u r f a c e area i n cm i n contact w i t h 1 L of ground water, t . i s the time t h a t the ground water i s i n contact w i t h the a q u i f e r to produce a 0.5-pH change during r e a c t i o n i n t e r v a l , i , i n seconds, k i s the k i n e t i c r a t e constant of production of species M n+ M at the mean pH of the i n t e r v a l considered, i n moles per square centimeter per second, n+ n i s the formal charge of species M The t o t a l mass of major c a t i o n s t r a n s f e r r e d to s o l u t i o n during reaction interval, i , i s : n +

2

T. = Iq 1

M

T.=

at.

0.99

1.0

α Downloaded by EAST CAROLINA UNIV on January 4, 2018 | http://pubs.acs.org Publication Date: March 19, 1979 | doi: 10.1021/bk-1979-0093.ch034

LU

0.0

0.0

l.o Na

+

+ K

+

2.0

+ C a

2

+

Figure 3.

+ Mg

2 +

3.0

4.0

, I N MILLIEQUI V A LE NTS PER LITER

Rainier Mesa groundwater data Ο Na"* φ

1.0 N a

S

+

+ K

+

Na

Composition Of Typical Sample

+

2.0

+ C a

2

+

+ Mg

2 +

,IN

3.0

4.0

M I L L I E Q U I V A L E N T S PER LITER

Figure 4. Change in water composition of typical sample from kinetic data (no montmorillonite precipitation)

Ο £

A l l o w i n g Montmorillonite

Ca

Precipitation

I-

+

, Compos it ion Of Typical Sample

ΡΕ ζ ζ uj LU

Ο Na"* 2

•

Ca Mg

2+

Ο

ο

s

00


2

>

π

CO

786

CHEMICAL

M O D E L I N G IN

AQUEOUS

SYSTEMS

D i s c u s s i o n of R e s u l t s and Conclusions The imperfect f i t of the k i n e t i c p r e d i c t i o n s to the f i e l d data may have i t s o r i g i n i n any of s e v e r a l areas. The i n t e r v a l s of 0.5 pH u n i t s chosen are probably too l a r g e f o r constant k i n e t i c r a t e constants to be assumed, e s p e c i a l l y f o r C a and M g i n the pH range 4.75 - 6.75. This shortcoming can be e l i m i n a t e d simply by decreasing the i n t e r v a l s t o , f o r example, 0.1 or 0.01 pH u n i t . The authors have developed an expression to modify k i n e t i c r a t e constants f o r s u r f a c e - s o r p t i o n e f f e c t s . C o r r e c t i o n s to r a t e constants have not been made i n the c a l c u l a t i o n s reported here, but the experimental values f o r r a t e constants are w i t h i n a few percent of those which would be a p p r o p r i a t e f o r the R a i n i e r Mesa a q u i f e r . The b a s i c methodology reported here i s b e l i e v e d v a l i d ; only minor changes i n the computed values are expected from more precise calculations. The assumption t h a t m o n t m o r i l l o n i t e of reported composition i s being produced and i s the only a u t h i g e n i c phase i s probably only an approximation. The composition may be i n e r r o r or may vary a r e a l l y w i t h i n R a i n i e r Mesa as a r e s u l t of a r e a l v a r i a t i o n s i n water q u a l i t y . Although no z e o l i t e s or other c l a y m i n e r a l s were reported i n the b u l k of the P a i n t b r u s h T u f f , very s m a l l amounts may remain undetected by e i t h e r x-ray d i f f r a c t i o n a n a l y s i s or t h i n - s e c t i o n petrography and may a f f e c t the aqueous composition by p r e c i p i t a t i o n or by i o n exchange. I t has a l s o been assumed that the d e v i t r i f i e d R a i n i e r Mesa Member has had i n s i g n i f i c a n t e f f e c t on the water chemistry. This assumption i s supported by comparison of the observed water compo s i t i o n w i t h compositions resulting·from r e a c t i o n s of both d e v i t r i f i e d and v i t r i c m a t e r i a l w i t h water c o n t a i n i n g d i s s o l v e d carbon d i o x i d e (see F i g u r e 2 ) . I t i s obvious that at l e a s t some of the water r e c h a r g i n g R a i n i e r Mesa must pass through the d e v i t r i f i e d m a t e r i a l and that there w i l l be some i n t e r a c t i o n , but the r e s u l t s of t h i s study i n d i c a t e t h a t the i n t e r a c t i o n i s s m a l l , because s i g n i f i c a n t i n t e r a c t i o n should preclude a reasonable match to f i e l d data.


2 +

2 +

E f f e c t i v e A q u i f e r Surface Table IV and F i g u r e 5 c o n t a i n the best r e s u l t s o b t a i n a b l e w i t h i n the assumptions and approximations o u t l i n e d above. Included h

i n the t a b l e are a set of at product terms which c o n t a i n the most s i g n i f i c a n t a p p l i c a t i o n of the methodology presented here. As p r e v i o u s l y d i s c u s s e d , one of the purposes of t h i s work i s to determine the e f f e c t i v e s u r f a c e area of a q u i f e r m a t e r i a l i n contact w i t h ground water. Such a v a l u e i s unobtainable through present h y d r a u l i c - t e s t i n g techniques and i s necessary f o r v a l i d p r e d i c t i o n s to be made concerning the a q u i f e r s o r p t i o n p r o p e r t i e s from laboratory-developed s o r p t i o n data. Only the water a c t u a l l y i n contact w i t h a q u i f e r m a t e r i a l , under n a t u r a l c o n d i t i o n s of a,


34.

CLAASSEN

AND WHITE


787

can r e f l e c t the nature of surface w i t h which the waste products w i l l come i n contact. I f we consider that the match t o the t y p i c a l R a i n i e r Mesa ground-water sample presented on F i g u r e 5 i s adequate, an estimate of t o t a l residence time of the ground water w i t h i n R a i n i e r Mesa w i l l a l l o w determination of σ. Clebsch (9) presented a range f o r residence of R a i n i e r Mesa ground water of 0.8-6 years based on i t s t r i t i u m content. A p l o t of σ v s t was made using each of s e v e r a l values of σ


and the f o l l o w i n g r e l a t i o n s h i p : t = —

(see Table I V ) . σ The r e s u l t i n g curve i s presented i n F i g u r e 7. The residence time l i m i t s of 0.8 - 6 year (2.5 χ 1 0 - 1.9 χ 1 0 s) were then i d e n t i f i e d w i t h the corresponding σ values of 6.4 χ 1 0 to 2.3 χ 10 cm /L. Thordarson (1) and Benson (LBL, Berkeley, w r i t t e n commun., 1978) both d e s c r i b e the P a i n t b r u s h Tuff as p a r t i a l l y s a t u r a t e d . Core samples obtained from the lower p a r t o f the P a i n t b r u s h i n the t u n n e l complex were reported by Diment and others (2) t o have s a t u r a t i o n l e v e l s of 55-91 percent, w i t h an average of 77 percent. Benson (LBL, Berkeley, w r i t t e n commun., 1978) reported an average value f o r water s a t u r a t i o n i n the P a i n t b r u s h of 90 percent. I t would t h e r e f o r e be expected that the t o t a l a q u i f e r - p o r e surface would not be i n v o l v e d i n t r a n s p o r t o f water. As a matter of f a c t , assuming that a l l of the saturated-pore space i s e f f e c t i v e i n t r a n s m i t t i n g water, one might p r e d i c t t h a t , on the average, some where between 77 and 90 percent of the a q u i f e r surface i s i n contact w i t h p e r c o l a t i n g water. E s t i m a t i o n o f a q u i f e r σ through B.E.T. and p o r o s i t y measure ments of cores obtained from the P a i n t b r u s h Tuff i n w i d e l y s c a t t e r e d l o c a t i o n s i n R a i n i e r Mesa y i e l d e d values ranging from 8.0 χ 1 0 t o 2.3 χ 10 cm /L. Even i f the lower of the measured s a t u r a t i o n values i s used t o estimate the f r a c t i o n of surface area a c t u a l l y i n contact w i t h l i q u i d , the σ values (6.2 χ 1 0 t o 1.8 χ 1 0 cm /L) appear t o be much too high when compared w i t h the r e s u l t s of the geochemical k i n e t i c a n a l y s i s . The i m p l i c a t i o n i s t h a t , on the average, only about 3 percent of the t o t a l pore space i s e f f e c t i v e i n t r a n s m i t t i n g water, as determined by the r a t i o o f measured σ t o the σ derived from w a t e r - q u a l i t y k i n e t i c s . S t a t i n g t h i s d i f f e r e n t l y , the r o c k - s u r f a c e area apparently i n contact w i t h u n i t volume of l i q u i d i s only about 3 percent of that which would be p r e d i c t e d on the b a s i s of measurements made on s o - c a l l e d n a t u r a l - s t a t e m a t e r i a l . This discrepancy may be magnified somewhat by the f a c t that we are d e a l i n g w i t h p a r t i a l l y saturated m a t e r i a l , but none of the measurements made have i n d i c a t e d s a t u r a t i o n a t the 3 percent l e v e l . We must conclude that the major w a t e r - t r a n s p o r t i n g pores c o n s t i t u t e only a s m a l l f r a c t i o n of the t o t a l interconnected (and probably saturated) pore space. 7

8

6

6

2

7

2

7

7

2


788

MODELING IN AQUEOUS

SYSTEMS


CHEMICAL

Figure 7.

Relation between reaction time (t) and surface to volume ratio (σ) for aqueous reaction of Rainier glass



34.

CLAASSEN

AND WHITE


789

An important aspect of t h i s f i n d i n g l i e s i n i t s c o n t r i b u t i o n to understanding t r a n s p o r t of waste m a t e r i a l s i n n a t u r a l systems. Too o f t e n , p r e d i c t i o n s of the waste-sorbing p o t e n t i a l of an a q u i f e r are made on the b a s i s of l a b o r a t o r y experiments u t i l i z i n g crushed a q u i f e r m a t e r i a l which i s intended to reach e q u i l i b r i u m w i t h a waste-containing s o l u t i o n . The amount of waste removed from s o l u t i o n i s measured, and the s o r p t i o n c a p a c i t y o f the a q u i f e r m a t e r i a l i s determined as weight, o r equivalent-weight contaminant, per u n i t weight of a q u i f e r m a t e r i a l . More s o p h i s t i c a t e d e x p e r i ments may measure surface area of crushed m a t e r i a l and attempt t o r e l a t e t o g r a i n s i z e of i n - s i t u m a t e r i a l . Cores are u t i l i z e d i n such experiments only r a r e l y . None of these techniques have the p o t e n t i a l t o p r e d i c t the a q u i f e r surface area e f f e c t i v e i n remov ing waste. The techniques used i n t h i s report w i l l be r e f i n e d and f u r t h e r t e s t e d i n t h i s and other systems. Montmorillonite

Supersaturation

The c a l c u l a t i o n of m o n t m o r i l l o n i t e s a t u r a t i o n index present at the end of each 0.5-pH i n t e r v a l from the k i n e t i c a l l y generated s o l u t i o n composition and the e q u i l i b r i u m constant f o r the Aberdeen m o n t m o r i l l o n i t e was presented on Figure 6. A r a p i d increase i n s a t u r a t i o n at lower values of pH slowing a t higher pH values i s i n d i c a t e d . This behavior suggests that the r a t e o f production of s o l u b l e c a t i o n s i s greater than the r a t e at which species r e q u i r e d f o r m o n t m o r i l l o n i t e p r e c i p i t a t i o n are removed from s o l u t i o n . Note that i t has not been s t a t e d that m o n t m o r i l l o n i t e p r e c i p i t a t e s i n the c l a s s i c a l sense; that i s , as a simple c r y s t a l l i n e substance. I t i s more l i k e l y that formation of an amorphous-aluminosilicate m a t e r i a l precedes both the i n c o r p o r a t i o n of the i r o n and magnesium and the subsequent rearrangement t o form the f i n a l phase. F i g u r e 8 shows the changes i n r a t e of production of the sum of a l l c a t i o n s as the r e a c t i o n proceeds. Because the r e a c t i o n r a t e i s dependent on pH, greater r a t e s occur a t lower pH values. I t i s , however, c u r i o u s to observe the time-dependence on removal of Mg + from s o l u t i o n , and, presumably, a l s o the r a t e of p r e c i p i t a t i o n of m o n t m o r i l l o n i t e . As shown on Figure 6, m o n t m o r i l l o n i t e s a t u r a t i o n i s reached a t about 1.9 χ 10 s. P r i o r t o t h i s time, the p r e c i p i t a t i o n r a t e must be zero; t h i s i s i n d i c a t e d on Figure 8 by the v e r t i c a l arrow. Once s a t u r a t i o n has been reached, a small but f i n i t e r a t e of p r e c i p i t a t i o n i s a n t i c i p a t e d and expected t o increase as the s a t u r a t i o n index i n c r e a s e s . The r a t e s of p r e c i p i t a t i o n c a l c u l a t e d from the data of Table IV are i n d i r e c t o p p o s i t i o n to t h i s e x p e c t a t i o n ; r a t e s are i n i t i a l l y high and decrease w i t h time more r a p i d l y than the r a t e at which production of a l l d i s solved species decreases. This would i n d i c a t e that the r a t e c o n t r o l l i n g step i n the formation of m o n t m o r i l l o n i t e i s one that i n v o l v e s a species undergoing s i g n i f i c a n t change w i t h time o r r e a c t i o n progress. The most l i k e l y species i s the hydrogen i o n , or the species whose s o l u t i o n c o n c e n t r a t i o n i s c o n t r o l l e d by 2

5


790

CHEMICAL MODELING IN AQUEOUS

SYSTEMS

J


*«s "5 *§ Co

•2

1 Si Ο Ο

•2 ο ο ν α Ο

1 •Β CO

3? Ο

οό

ε


34.

CLAASSEN

AND WHITE

Kinetic

Data and Groundwater 3 +

hydrogen such as AlCOH)^ (10) o r F e (11). r e q u i r e d t o s u b s t a n t i a t e t h i s hypothesis.

Systems

791

Further work i s


Summary A technique f o r determination of e f f e c t i v e a q u i f e r surface area i n contact w i t h p e r c o l a t i n g ground water has been presented. The method u t i l i z e s laboratory-determined chemical k i n e t i c d i s s o l u t i o n data w i t h g e o l o g i c , h y d r o l o g i e , and ground-water-quality data t o y i e l d an estimate of e f f e c t i v e a q u i f e r surface area, a parameter not obtained by other techniques. A n a l y s i s of the r e s u l t s obtained f o r the R a i n i e r Mesa ground water system by a p p l i c a t i o n of the above method i n d i c a t e d that although measurements of water s a t u r a t i o n on core samples from the P a i n t b r u s h Tuff evidenced a high degree of s a t u r a t i o n (77 to 90 p e r c e n t ) , the major w a t e r - t r a n s m i t t i n g regions of the a q u i f e r c o n s t i t u t e only about 3 percent of the t o t a l , i f the p o r o s i t y i s e q u a l l y d i s t r i b u t e d . I f the regions of major h y d r a u l i c conductiv i t y are f r a c t u r e s , measurements of σ on core samples w i l l be meaningless, and the method presented here w i l l provide the only means f o r an estimate of σ. Although the P a i n t b r u s h has been described as a h y d r a u l i c system of primary p o r o s i t y , the c a l c u l a t i o n s of σ suggest that i t i s a system of secondary p o r o s i t y , which provides the major throughput. This a l l o w s f o r h i g h l y water-saturated rock, w i t h l i t t l e water movement, coupled to f r a c t u r e s or other conductive passages through which most of the water f l o w s . The e f f e c t of such a system on the t r a n s p o r t of waste can be s i g n i f i c a n t i f core data are used to p r e d i c t s o r p t i v e behavior; i n the P a i n t b r u s h T u f f , s o r p t i v e behavior i s n e a r l y two orders of magnitude lower than that p r e d i c t e d from core measure ments. R e s u l t s of experiments u t i l i z i n g crushed rock and e q u i l i b r a t i o n w i t h waste s o l u t i o n s to determine s o r p t i o n behavior cannot be e x t r a p o l a t e d to a c t u a l a q u i f e r c o n d i t i o n s , even i f B.E.T. surface area i s known. This technique has been commonly used i n the past to assess w a s t e - s t o r a g e - s i t e s a f e t y . As the primary h y d r a u l i c c o n d u c t i v i t y decreases and secondary c o n d u c t i v i t y becomes more prominent, t h i s methodology becomes l e s s and l e s s v i a b l e f o r input to modeling of waste t r a n s p o r t . The method presented i n t h i s r e p o r t should r e s u l t i n more r e a l i s t i c waste-transport modeling.

Abstract Kinetic modeling was used to estimate the effective surface area of aquifer in contact with a unit volume of ground water for a composite saturated-unsaturated groundwater system in southern Nevada. This aquifer property, not obtainable by other means, i s necessary for r e a l i s t i c modeling of solute transport i n ground water systems. The results of the kinetic modeling indicate that



792

C H E M I C A L MODELING IN AQUEOUS SYSTEMS

only a small part of the total interconnected pore space i s available for transport of water to the water table. The aquifer studied i s composed of both v i t r i c (glassy) and d i v i t r i f i e d (crystalline) volcanic tuff of nearly identical chemical com position. Comparison of laboratory and f i e l d data indicated that only the v i t r i c phase has a significant influence on ground-water composition. Laboratory determination of mass-transfer rates from the v i t r i c material to solution as functions of pH allowed a simulation of the natural water's cation composition. Simulated results were improved considerably when the model was modified to take into account precipitation of the clay mineral, montmoril lonite. Estimates of surface area per unit volume obtained from the kinetic model are about 3 percent of those obtained indepen dently from surface area measurements using the Braunauer, Emmett, and Teller (B.E.T.) equation. Literature Cited 1.

2.

3.

4. 5.

6. 7.

8.

9.

Thordarson, William, Perched ground water i n zeolitized-bedded tuff, Rainier Mesa and v i c i n i t y , Nevada Test Site, Nevada, U.S. Geol. Survey Open-file Rept., TEI-862, 93 p. (1965). Diment, W. H., Wilmarth, V. R., McKeown, F. Α., Dickey, D. D., Hinrichs, Ε. N., Botinelly, T., Roach, C. H., Byers, S. Μ., Jr., Hawley, C. C., Izett, G. Α., Clebsch, Alfred, Jr. Geological Survey investigations in the U12b.03 and U12b.04 tunnels, Nevada Test Site, U.S. Geol. Survey Open-file Rept., TEM-996, 75 p. (1959). White, A. F., and Claassen, H. C. Dissolution kinetics of s i l i c a t e rocks, application to solute modeling, in Jenne, E.A., ed., "Chemical Modeling—Speciation, Sorption, Solubility, and Kinetics in Aqueous Systems," Am. Chem. Soc., 1978 (this volume). Garrels, R. Μ., and Christ, C. L. "Solutions, Minerals and Equilibria", 450 p., Harper & Row, New York, 1965. U.S. Geological Survey, Results of exploration of Baneberry Site, early 1971, U.S. Geol. Survey Rept. USGS-474-245, NTIS, Springfield, VA, 92 p. (1974). Kittrick, J. A. Stability of montmorillonites II, Aberdeen Montmorillonite, Soil Sci. Soc. Amer., 35, 820-823 (1971). White, A. F., and Claassen, H. C. Geochemistry of ground water associated with tuffaceous rocks, Oasis Valley, Nevada, Geol. Soc. Am. Abs. 7 (7), 1316-1317 (1976). White, A. F., and Claassen, H. C. Kinetic model for the dissolution of a r h y o l i t i c glass, Geol. Soc. Am. Abs. 9, (7), 1223 (1977). Clebsch, Alfred, J r . Tritium age of ground water at the Nevada Test Site, Nye County, Nevada, C122-C125, in "Short Papers in the Geologic and Hydrologie Sciences", U.S. Geol. Survey Prof. Paper 424-C, (1961).


34.

CLAASSEN AND WHITE


793

10. Hem, J. D., Roberson, C. E., Lind, C. J., and Polzer, W. L. Chemistry of aluminum in natural water, U.S. Geol. Survey Water-Supply Paper 1827-E, 57 p. (1973). 11. Hem, J. D., and Cropper, W. H. Survey of ferrous-ferric equilibria and redox potentials, U.S. Geol. Survey Water-Supply Paper 1827-A, 55 p. (1959).


Disclaimer: The reviews expressed and/ or the products mentioned in this article represent the opinions of the author(s) only and do not necessarily represent the opinions of the U.S. Geological Survey. RECEIVED November 16, 1978.


Chemical Modeling in Aqueous Systems - American Chemical Society

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