IMPLEMENTATION OF CARBON ISOTOPE SUBROUTINE TO COMPUTER PROGRAM
PHREEQE AND THEIR APPLICATION TO C -14 GROUND -WATER DATING
Song -lin Cheng and Austin Long
Laboratory of Isotope Geochemistry, Department of Geosciences,
University of Arizona, Tucson, Arizona 85721
Abstract
The age of ground water is defined as the
length of time the
Among the methods for
water has been isolated from the atmosphere.
the
most
ground water dating,
C -14 is the most commonly used and
The concentration of C -14 in dissolved
studied tool.
intensively
in
processes
inorganic carbon can change as a result of chemical
nature, hence, an adjustment factor Q is included in the age equation.
-Xt
A = QAo(e
)
for
this adjustment
models have been proposed to account
factor. Among those models, the mass transfer -balance approach is the
rigorous method. Wigley, Plummer, and Pearson (1978) formulated
most
Various
a mass balance equation to calculate the evolution of C -13 and C -14 in
and
natural water systems closed to soil CO2 gas. Deines, Langmuir,
chemical- isotopic
equilibrium
of
dual
used a set
(1974)
Harmon
soil
CO2
calculate changes of C -13 in systems open to
to
equations
This study implements these two models as a subroutine and adds
gas.
Thorstenson,
isotope mixing equations to PHREEQE (Parkhurst,
carbon
and Plummer, 1980), which is a computer program for general hydrogeocalculations. With this program package, it is now possible
chemical
composisimulate the evolution of chemical and carbon isotopic
to
systems.
C
-14,
of
ground
water
from
open
to
closed
including
tions,
factors
for
allow much improved inferences of Q
These simulations
radiocarbon ground -water dating.
Introduction
The age of ground water is defined as the length of time that
water has been isolated from the atmosphere. Various models lead
estimates of ground water. Darcy's law combined with a conto
age
tinuity expression describes the rate of ground -water movement, hence,
distance
to
the
ground water can be deduced from the
the
age
of
and
the
accumulation of
Decay of radionuclides
recharge area.
decay products are time -dependent, and therefore, the age
radioactive
can
be
calculated from the decay law and the accumulation rate of
radioactive decay products. Many radioactive decay series (such as
amino
racemization of
such as
reactions
uranium series), chemical
the
(
121
acids), and isotope exchange reactions (such as the oxygen isotope exchange reaction between sulfate ion and water), take a rather
long
period of
time to reach equilibrium. Thus, it is possible to calculate an age
by
the degree of disequilibrium.
The
presence or
absence of
certain anthropogenic products, such as
freon
and
the
tritium pulse produced by thermonuclear bomb testing from 1952 through
the mid- 1960's, may classify the age of the water in terms of younger
older
or
than
the time the product
first existed in nature. Each
dating system has
its own advantages,
disadvantages,
and
limitations,
and
a
detailed discussion and comparison of
these
dating
schemes
is
outside the scope of this research.
Davis and Bentley
(1982) presented a detailed review of ground -water dating.
Among those dating methods, the systematics of carbon -14 are the
most
commonly used and the most intensively studied tool for
dating
ground water.
When recharge water migrates into the ground and
is
isolated
from the
influence of atmospheric CO2 gas,
it
longer
no
acquires radiocarbon from the atmosphere, and therefore, the carbon -14
activity of the water declines.
Because all
radioactive decay
processes
obey the first order decay law, in principle, the
age
of
ground water is calculable from the radiocarbon concentration of
the
water (A)
by
assuming an intial radiocarbon concentration (Ao). A
proper model must, of couse, not only assume the correct initial C -14
activity at zero age, but also consider all chemical processes
that
may have altered the C -14 activity in the aquifer.
all
Commonly,
non -radioactive
processes
appear as a single factor (Q) in the age
equation
.
-at
A = QAo(e
)
where "X" and "t" are the decay constant of radiocarbon and the age of
water,
respectively. The factor "Q" is nearly always less
the
than
one, and consequently has the effect of decreasing the calculated age.
Due to
the complexity of carbon geochemistry, several models of
varying complexity are available which allow estimates of the factor
"Q".
This paper reviews the foremost models and presents a more comprehensive and generally applicable alternative.
Carbon Geochemistry In The Ground -Water System
Carbon exists mainly as CO2 gas
in the
atmosphere and soil air.
Methane may be present in fairly reducing environments.
Inorganic
carbon species, such as H2CO3, (HCO3) -, and (CO3) - -, in fresh and sea
water have
their
origin
in both the atmosphere and
lithosphere.
Dissolution of CO2 gas in water generates hydrogen ions, which may
dissolve carbonate minerals in contact with the water.
Aqueous
inorganic carbon may precipitate in the aquifer as carbonate minerals.
Those dissolved
inorganic carbon (DIC) species buffer the pH of the
aqueous
solution by redistributing their relative concentrations
and
hence play an important role in controlling chemical composition of
water.
In a system consisting of CO2 gas, water, and carbonate mineral
(calcite, for example), the following equations symbolize reactions among the phases:
122
CO
H O
+
2
2
ll
++
*
CaCO
+ H CO
3(s)
2
+ 2HCO
Ca
=
3
3
*
where H CO
2
= H CO
2
3
+ CO
3
2(aq)
The molar
concentrations and isotopic compositions of these species
are
quite different in a system open to a CO2 gas reservoir than in a
closed
system, and therefore, it is necessary to examine the two systems
separately.
Both conditions are relevant to most ground water
recharge areas.
CO2 gas dissolves in water as CO2(aq). About 0.3 or 0.4% of the
aqueous CO2 associates with water molecules to form carbonic acid
(H20O3).
Additional carbonate species form as a result of subsequent
dissociation of carbonic acid. Because it is difficult to separate
aqueous
carbon dioxide from carbonic acid, they are normally treated
The equilibrium conas
one
species and are represented as H2CO3 *.
stants
for the major DIC species at 25 °C together with their corresponding reactions are listed below ( Stumm and Morgan, 1981).
H20
CO
===
CO
2(gas)
CO
logK
+ H O
2(aq)
H CO
=
2
2
+
H CO
2
H
=
2
+
=
H
H
= -2.8
(2)
= -3.5
(3)
= -6.3
(4)
H2CO3
-
logK
3
=
3
logK
+ HCO
3
HCO
logK
3
3
*
(1)
-
+ HCO
3
H CO
= -1.5
H
2(aq)
+ CO
1
= -10.3 (5)
logK
3
2
The above equations
clearly indicate that the relative concentrations
of DIC species are controlled by the partial pressure of CO2
gas
and the pH of the solution.
Any reaction that changes the pH of
the
solution will
change the carbon speciation in the solution as
well.
In a system open to a CO2 gas reservoir, the activity of carbonic acid and aqueous CO2 are controlled solely by the partial pressure
of
CO2 gas and are independent of the solution pH, while in a
closed system, they are a function of solution pH and concentration of
dissoved
total
inorganic carbon. Because each DIC species
fractionates carbon isotopes differently, open and closed systems produce
not
only distinctive DIC species distribution and concentrations, but
Therealso distinctive
carbon isotopic compositions in the water.
fore,
it
is clear that identifictit ¡on of the type of system is the
first step in understanding the carbon geochemistry of
indispensable
and consequently in dating ground water by radiocarbon systemwater,
atics.
Brief Review of Carbon -14 Ground -water Dating Models
radiocarbon ground -water
first
the
Since the publication of
dating model (Munnich,1957), accumulation of knowledge and sharing of
in the scientific community have increased the quality of
new ideas
review
this
To facilitate discussion,
dating
systematics.
these
existing models according to the fundamental
the major
classifies
chemical reactions upon which each model is based.
Munnich (1957) initiated carbon -14 ground -water dating and recognized the contribution of radiocarbon -free carbon in ground -water sysThe following reaction illustrates the dilution effect of fossil
tem.
carbonate, i.e. radiocarbon -free carbonate
:
++
XCaCO
+ XH O -- ZXHCO
+ (X+Y)CO
2
2
3
+ XCa
+ YCO
3
2
various
of
above reaction, X and Y are the numbers of moles
In
the
carbon
sources involved in the reaction. According to this reaction,
the adjustment factor (Q) for correcting the dilution effect, i.e. the
ratio of carbon originating from biogenic COZ to total carbon in the
water,
is equal to (X +Y) /(2X +Y). According to this model, the minimum value of Q occurs when Y =0, i.e. when dissolved COZ is completely
Analytically,
consumed by dissolving radiocarbon -free CaCO3, Q =0.5.
adjustment factor Q equals to: ((mH2CO3 + 0.5mHCO3 -) / (mH2CO3 +
the
which is a value easily obtainable in a field measurement.
mHCO3 -)),
isotopic redoes not consider chemical and
this model
Obviously,
equilibrium between COZ gas and the dissolved inorganic carbon after
dissolution of calcite, and therefore, it contains the assumption that
the calcite dissolution occurred in a system closed to a COZ gas
all
reservoir.
reaction path in a CO2- waterthe
oversimplifies
This model
In reality, calcite is likely to dissolve in water in
calcite system.
any
chemical
In addition,
both open and closed system conditions.
redistribute
reaction that generates or consumes hydrogen ions will
and
the
relative concentrations of aqueous carbonate species,
the
will
concentrations
of
bicarbonate
and
carbonic
acid
measured molal
from the model values of 2X and Y, respectively. The carbonic
differ
acid may also attack non -carbonate minerals, such as silicates, in the
aquifer and generate bicarbonate totally originated from carbonic acid
(equation 6). Many reactions, such as oxidation of pyrite or organic
generates hydrogen ions. These hydrogen ions not only change
debris,
speciation of aqueous carbonate, but may also attack calcite and
the
inactive (containing no carbon -14) bicarbonate ions (equation
release
7)
.
+
Na +A1
NaAlSi O +2H O+4C0
3
+ H
3
(6)
3
++
+
CaCO
-
+4HCO
+3SiO
2(aq)
2(aq)
2
8
+3
-- Ca
(7)
+ HCO
3
124
same
reaction path as Munnich's model, several
the
Based on
1964,
1959, Ingerson and Pearson,
and
al,
(Brinkmann et
authors
1967) used stable carbon isotopes as a measure of dilution of
Tamers,
carbon isotopic
compoin
ground water. Because the
radiocarbon
in limestone and soil gas are highly variable, this method is
sitions
not very reliable.
Wallick (1973) applied a chemical- isotopic model to the semi -arid
His model assumes that all calcite dissolved in the
Tucson basin.
also
the influence of CO2 gas reservoir. Mook (1976)
water without
proposed a chemical- isotopic model to calculate a Q factor. This model
Reardon
that all calcite dissolved in the unsaturated zone.
assumes
used
the
chemical
(1978)
and Fontes and Garnier (1979)
and Fritz
the water sample to infer the amount
of
calcite
characteristics of
Typically, they assumed that all Ca ++ and Mg ++ came from
dissolved.
the dissolution of carbonate minerals, SO4 -- came from the dissolution
gypsum,
and Na +, after correcting for the contribution of NaCl,
of
Therefore, they estireleased to the water by Na + /Ca ++ ion exchange.
mated the amount of calcite dissolved as follows
:
calcite dissolved = total molality of
(Ca + Mg - SO4 + Na -C1)
mathematics of these models implies that all calcite dissolved in
the closed system conditions.
The
The models discussed above consider only simple dissolution of
carbonate minerals. The Reardon and Frtiz (1978) and Fontes and Gar (1979) models consider precipitation of carbonate minerals in a
nier
is
The common occurrence of secondary calcite
very
restricted way.
clear evidence that precipitation of calcite is very common in nature.
Smith et al (1975) studied the Chalk aquifer of the London basin and
concluded that the heavy carbon isotopic composition is due to the
probable concurrent dissolution and precipitation of calcite. However, they used a simple dissolution model to adjust the radiocarbon age
the ground water. Wigley (1976) formulated a one - input- one -output
of
equation to calculate carbon isotopic commass -balance- mass -transfer
position of water resulting from concurrent dissolution and precipitaof carbonate minerals. He applied this model to the Chalk aquition
fer of the London basin and found that the age of the ground water may
up to 10,000 years younger than Smith et al reported. Wigley conbe
that: "Ignoring mineral precipitation, or neglecting isotopic
cluded
fractionation during precipitation, may lead to estimates of }4C ages
which are many thousands of years too old. ".
derived a general mass (1978)
Plummer, and Pearson
equation to calculate the evolution of carbon
isotopes, including radiocarbon, in a natural water system closed to a
CO2 gas reservoir. Unlike Wigley's one -input- one -ouput model, Wigley equation can handle one or more than one input and
Plummer- Pearson's
The user must supply the amount of mass transoutput simultaneously.
and define the reaction path based on knowledge of the particular
fer
However, the calculation of concurrent dissolution and preaquifer.
cipitation in a multi- component, multi -phase system is a very complicated matter, and requires a computer program such as PHREEQE.
Wigley,
balance -mass- transfer
dating models is to estiof radiocarbon ground -water
One goal
mate the initial condition, i.e. the chemical and carbon isotopic composition, including radiocarbon content, of the water in the aquifer
125
the onset of closed system conditions.
These initial compositions
depend on many variables in the open system,
especially,
partial
isotopic composition of CO2 gas and pH of
the water.
pressure and
Ignoring the open system effects may lead to an unjustified estimation
the adjustment factor (Q) in radiocarbon ground -water dating. Beof
cause
the application of Wigley- Plummer -Pearson's equation is limited
to systems closed to a CO2 gas reservoir, an additional procedure must
model
reactions
the
in the open system. Despite the limitations of
mass -balance- mass -transfer
approach,
it is the most rigorous
method
for
radiocarbon ground -water dating. Deines, Langmuir, and Harmon
(1974)
proposed the first radiocarbon dating method
that
considers
open system effects. These authors used a set of dual chemical- isotopic
equations to calculate the isotopic and chemical compositions of
water
in
a
The C -14 modeling
system open to a CO2 gas reservoir.
approach presented here has combined in tandem the Deines
et
al's
(1974) dual chemical- isotopic equations for the open system condition,
and
the Wigley -Plummer -Pearson's
equation
for
the
closed system
condition
into a suitable computer program which we believe to be the
ideal tool for dating ground water by radiocarbon systematics.
at
Implementation Of Carbon Isotope Subroutine - CSOTOP
The evolution of chemical and isotopic composition (including
of
aqueous
carbon is strongly reaction -path dependent.
Hydrogeochemistry of ground water varies from aquifer to aquifer.
A
reaction that
is
negligible in one aquifer could be an important
reaction
in
another ground -water system. An ideal model for
radiocarbon ground -water dating should provide the flexibility to allow the
user
to define the reacton path, which would require the convenience
and
speed of a computer program. This model should also consider the
open system effect. Mixing is a common mechanism in many ground -water
systems.
Besides the mixing ratio, the carbon isotopic composition of
the mixture is not only a function of the carbon isotopic compositions
of
the
end members in the mixture, it is also a function of carbon
concentrations of the end members as well.
carbon -14)
PHREEQE
by Parkhurst, Thor is a FORTRAN IV program written
stenson,
and Plummer in 1980. This program can simulate most hydro geochemical
reactions,
such as dissolution,
precipitation, mixing,
redox reaction, and a combination of these reactions. By implementing
Deines
al's
and Wigley-Plummeret
equations for the open system,
Pearson's equation for the closed system as a subroutine to PHREEQE,
it
is
possible to simulate the hydrogeochemistry and carbon isotope
evolution of natural water from open to closed systems. The
subroutine CSOTOP utilizes the result of the mass transfer and speciation of
solutes calculated by the main program PHREEQE to calculate the carbon
isotopic composition of
the final solution and the precipitation/
outgassing phases. This program- subroutine allows the user to model
evolution of hydrogeochemistry and carbon isotopes of water along
the
radiocarbon
probable reaction paths without the restriction of most
ground -water
dating models. Rigorous interpretation of carbon hydro geochemistry and more precise adjustment for radiocarbon age of ground
water
is possible. The next section discusses the implementation of
this subroutine and mixing equations and their application.
-
126
The Open System.
When COZ gas dissolves in water, hydration and subsequent poly aqueous
protic dissociation result in many aqueous carbon species
The equilibrium relationship between
(HCO3) -, (CO3) - -.
H2CO3,
COZ,
COZ gas and the aqueous inorganic carbons are listed above (Eqs. 1 to
:
5)
.
inorganic carbon species has a different
Each of these aqueous
an
In
fractionation
factor with respect to COZ gas.
isotope
carbon
open system, the COZ in the gas phase is assumed to be an infinite reThe carbon isotopic ratio (R) of the COZ gas will therefore
servoir.
not
carbon
change as a result of isotopic exchange with the aqueous
from water under open
If a carbonate mineral precipitates
species.
the carbon isotopic composition of the gas phase
system conditions,
contols the carbon isotopic composition of the carbonate mineral. The
following equations express the carbon isotope fractionation
factors
(a)
of
aqueous inorganic carbon species and calcite with respect to
COZ gas.
= R
a
/ R
= R
a
/ R
(COZ gas)
(HCO3 -)
1
/ R
= R
a
(CO2 gas)
(H2CO3 *)
0
= R
a
c
(COZ gas)
(CO3--)
Z
/ R
(COZ gas)
(calcite)
1Z
13
where, R =
(
C)
/
C)
(
is a function of temperature.
factor
The isotope fractionation
linear
regression to
and Harmon (1974) applied
Langmuir,
Deines,
analyze both the measured and computed fractionation factors reported
following temperature- dependent
literature. They found the
in
the
expressions for the above carbon fractionation factors
:
6
1000xlna
=
(0.0063x10 /T
=
(1.099 x10 /T
=
(0.87
=
(1.194 x10 /T
Z
)
- 0.91
)
- 4.54
)
- 3.4
)
- 3.63
0
6
1000xlna
2
1
6
1000xlna
Z
x10 /T
2
6
1000x1na
Z
c
where
T = temperature in Kelvin.
127
isotopic compositions of
Because of lack of data,
the
carbon
species in ion pairs are assumed to be the same as the corcarbonate
responding bare ions. Equation 8 is a simple mass balance expression
the
for
calculating the carbon isotope fractionation factor between
total dissolved inorganic carbon (DIC) and the CO2 gas.
a
(E (mC
=
DIC /COZ gas
)) / (total DIC)
x a
where, mC
(8)
i /COZ gas
i
molal concentration of aqueous
inorganic carbon species i.
=
i
Because the pH of the solution affects
the speciation of DIC,
to
a
each aqueous
carbon species fractionates carbon isotopes
different degree, any reaction that changes the pH of the solution may
change
the
carbon isotopic composition of the aqueous
solution as
well. Dissolution of carbonate mineral in the open system affects the
ion.
carbon
isotopic composition of the water by consuming hydrogen
The carbonate's carbon isotopic composition, including carbon -14, has
no effect on the carbon isotopic composition of the water.
and
excellent
Craig (1954)
is an
demonstrated that the
following
fractionation
carbon -14
calculation of
for
the
the
approximation
factor
.
2
(A
=
a
i,14
) / (A
)
= ((R
COZ gas
i
where, A , A
i
) /(R
(9)
))
COZ gas
i
CO2
= radioactivities of carbon -14 in
species or phase i, and CO2 gas.
i,14
= carbon -14 fractionation factor of
relative to CO2
species or phase
a
i
gas
isotopic
fractionation
This
relationship allows
one to calculate
activity in the water in a manner similar to
on
carbon -14
effects
isotopic ratio of stable carbon (Eq. 8).
solution or carbonate
fractionation
factor between
Once the
to CO2 gas is known, by the definition of 6C -13 notation (Eq.
mineral
10), the 6C -13 values of water and precipitating carbonate mineral can
be calculated from equations 11 and 12, respectively.
13
C = (R(sample)/R(standard) - 1)x1000
ö
12
13
where R =
C)
(
( 10 )
/
(
C)
13
13
C
=
water
)x6
(a
total DIC /CO2 gas
C
COZ gas
+ 1000x(a
)
total DIC /COZ gas
128
- 1000
(11)
13
13
C
min.
=
)x6
(a
C
CO2 gas
min. /CO2 gas
+ 1000x(a
)
- 1000
(12)
min. /CO2 gas
The Closed System.
When
water is
the
isolated
from the direct influence of a CO2
reservoir,
the
carbon -14 clock starts
and different
ticking,
physicochemical
processes
operate in the closed system environment.
The
gas -water
equilibrium reaction, which is dominant in the open
system conditions, is replaced by mineral dissolution -precipitation as
the main reaction that affects the carbon isotopic composition of the
water.
gas
Wigley- Plunmer- Pearson's ( Wigley et al, 1978) mass- balance -massequation (Eq. 13) is the most rigorous and general mathematransfer
tical
treatment for the evolution of both stable and radioactive car-
bon isotopes in natural water.
It allows the researcher to define the
reaction path. The computer program PHREEQE can model the amount
of
Equation 13 is adequate for
mass transfer
along the reaction path.
most
cases. However, two special situations require modification of
First, if "O" equals "I ", Equation 14 should replace
equation.
the
13.
"B"
Second, if "I" is zero, i.e. no input carbon,
is
Equation
incalculable and the solution requires a general equation for 0 input,
M outputs. This study derives an equation (15) for this case.
*
BR - R
(BI/(O - I))
*
=
(BRo - R )(mC/mCo)
(13)
where R = average carbon isotopic ratio of inputs.
mCo, Ro = initial total DIC and carbon
isotopic ratio of the solution.
mC, R
= final total DIC and carbon
isotopic ratio of the solution.
O = total carbon output rate relative
to reference output rate
I
= total carbon input rate relative
to reference output rate.
B =
+ ((a - O) /I)
1
= composite fractionation factor of
the total output phases relative
to the solution
*
BR - R
*
= (BRo - R )exp(- BT /mCo)
(14)
where T = total carbon input.
(k -1)
R /Ro = (mC /mCo)
(15)
where k = ä /O.
129
To derive
the general
form (Eq. 13), these authors assumed that
the
relative amount of input and output phases,
the
fractionation
are
conand
the carbon isotopic ratio of the input phases
factor,
stant.
As discussed by the authors: "In general, the appropriateness
of
assumption must be considered separately for each case:
althis
it
will certainly be reasonable whenever the total reaction
though
progress
is
Hence, when in doubt, one should simulate the
small. ".
reaction path with many small steps, which is possible by the computer
program PHREEQE.
The carbon isotope subroutine, CSOTOP, uses the mean
values
of the initial and final carbon isotopic fractionation factors
between phases in each step.
The Carbon Isotopic Composition Of A Mixture.
isotopic compositions of end members and the
Other than carbon
mixing ratios, the carbon isotopic composition of the mixture is also
a
function of carbon concentrations of the end members. For example,
1:1
mixing of end member A (SC- 13 = -10 o /oo)
a
and end member
B
(SC -13 =0
o /oo)
may not be -5 o /oo. The stable isotopic composition
the activity of radiocarbon in the mixture can be calculated from
and
16
and
17, respectively. Equation 18 shows
the
relationship
Eqs.
between stable and radioactive carbons in the mixture and clearly
indicates a linear relationship betweeen them.
13
13
13
C
f((Ab
B
12
12
f((Ab
xC /W )
)
xC /W )
B B
14
+ (1-0(A
C) xC
C) xC
A A
14
C)
)
B
14
f(A
+ (1-f)((Ab
A A A
M
B
B
(17)
_
M
+ (1-f)C
fC
A
B
= ((R
- R )/((A
B
C)
A
-
B
(A
C) ))x(A
A
C) R
A B
-
(A
C)
-
M
14
14
14
((A
14
14
14
M
B
(16)
12
C
R
B
=
M
(A
xC /W )
)
A A A
M
R
xC /W ) + (1-f)((Ab
)
C) R
B A
) /((A
14
C)
-
B
(A
C)
)
(18)
A
where, subscripts A, B, M
= end members A and B, and the mixture.
14
A
C, R
12
Ab
= carbon -14 activity and stable carbon
isotopic ratio.
13
,Ab
= isotopic abundances of carbon -12 and
carbon -13.
= fraction of end member A in the mixture.
C = carbon concentration.
W = atomic, weilgt of carbon.
f
Examples Of Simulation
To illustrate how this program- subroutine simulates evolution of
and carbon isotopic compositions of water in a ground -water
chemical
this
study choose the following reaction path
river
water
system,
in
open
the
equilibrates with soil CO2 gas and dissolves calcite
system conditions.
It then migrates into the aquifer and becomes isolated
from the influence of the soil CO2 gas reservoir.
In the aquifer
and under closed system conditions, it reacts with the reactants
(calcite, dolomite, alkali feldspar) to reach calcite equilibrium, and
then
to dolomite equilibrium, while maintaining calcite equilibrium.
The water remains in equilibrium with kaolinte at all time.
:
Because the dolomite
saturation
index of the water increases
steadily along the proposed reaction path, it is an indicator of reaction progress.
Figures 1 and 2 summarize the simulation.
The partial
pressure of soil CO2 gas is generally much higher
than in the atmosphere (0.00033 atm.). Parada, Long, and Davis (1983)
measured the CO2 content in soil zones in various recharge areas of the
Tucson basin.
The mean and standard deviation of 15 measurements from
nine
sites at different times of the day and season are 1.41 + 1.27 %
at
CO2
a total gas pressure of 1 atm. Deletion of two measurements
higher
than one standard deviation from the mean brings the mean and
standard deviation down to 0.97 + 0.52 %. Despite the multitude of
depth,
and
factors
controlling soil gas pCO2, such as season, soil
the value 1 + 0.5 % of COZ gas seems to be a good
vegetation cover,
for
recharge areas of the semi -arid Tucson basin.
range
Figure
1
that
variation in partial pressure of soil CO2 gas change
the
shows
carbon -14 activity and the chemical
relationship between initial
composition of the water. The uncertainty in initial carbon -14 activresults
in
an
error
ity
caused by + 0.5 % of soil CO2 gas
in
initial radiocarbon content by up to + 4 pmc (percent
estimation of
moden carbon). When the water reaches calcite equilibrium, concurrent
dissolution of carbon -bearing reactants and precipitation of calcite
the dilution effect of carbon -14 activity in the water, and
increases
results in higher slopes on Figures 1 and 2.
of the water, which is affected by water -rock interaction
in the open system, will affect the amount of CO2 gas dispCO2
dissolved inin
the water and hence the concentration of
solved
(DIC).
For the same recharge water, a lower calcite
organic carbon
The pH
and
saturation index at the beginning of the closed system condition would
reactant to dissolve to reach calcite equilibrium, and
require more
hence higher dilution effect from dissolution of inactive (containing
no
carbon -14) reactant (Figure 2). However, Figure 2 also shows that
when
the water
reaches
calcite saturation, the reaction path is
essentially independent of the initial calcite saturation index at the
onset of the closed system condition.
The combination of pH and pCO2 determines
the concentration of
aqueous
The
first
inorganic carbon in the open system conditions.
step of radiocarbon ground -water dating is to find out this inorganic
carbon concentration at the end of the open system conditions.
The
importance of these open system effects should be clear from the above
simulations.
Ignoring precipitation of carbon -bearing minerals will
result in an unjustified estimation of the carbon -14 adjustment factor
Q.
131
110-
100-
4-0.5%
REAC ON
PATH
* S.I.(CALCITE) =0
70
-3
0
í
i
S.I.(DOLOMITE)
Figure 1. The evolution of radiocarbon activity and the saturation
dolomite of the water initially equilibrated with
index of
soil air of various pCO2 (i + 0.5 % of CO gas in i atm. of
text.
in the
The reaction pat Fi is described
soil air).
The starting point of each curve is the onset of closed
system condition. The S.I.(calcite) at the starting point
point is -0.5.
132
1107.0
-LO
7.32 } pH
0.0 } Sl(CALCITE)
7.16
-0.5
100-
o-
9 0-
.4-
REA
8080
ION
PAT
70 rt
-3
S.I.(DOLOMITE)
Figure 2. The evolution of radiocarbon activity and the saturation
initial
dolomite of the water with various
index of
the
onset
of
the
closed
calcite
at
saturation indices of
described
in
the
path
is
system condition. The reaction
is
the
onset
of
curve
each
The starting point of
text.
system
is
in
the
open
The
pCO2
closed system condition.
0.01 atm. (i.e. 1 % in 1 atm. of soil air).
133
Summary And Conclusions
water is
isotopic composition of natural
Chemical and carbon
carbon
strongly reaction -path dependent. Due to the complexity of
use
geochemistry, most existing carbon -14 ground -water dating models
This
simplified reaction paths and therefore limit their usefulness.
implements a carbon isotope subroutine - CSOTOP and carbon isostudy
This program tope mixing equations to the computer program PHREEQE.
the
evolution of
user
to
simulate
allows
the
package
subroutine
chemical and carbon isotopic compositions of water from open to closed
along a user -defined reaction path. With enough knowledge
systems
about an aquifer and a density of sample points high enough to observe
hydrochemical
changes, this simulation allows rigorous
significant
water
interpretation of chemical and carbon isotopic compositions of
carbon -14
ground -water
and
therefore a more reliable estimation of
age.
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