LLNL_AQUEOUS_MODEL_PARAMETERS
This keyword data block
is used to define aqueous model parameters for the Lawrence Livermore National
Laboratory aqueous model. The parameters are the temperature-dependent values
of the Debye-Hückel A , B , and B -dot parameters
and the expression for the activity coefficient of aqueous carbon dioxide as a
function of temperature and ionic strength. The LLNL_AQUEOUS_MODEL_PARAMETERS
data block is used in the database file llnl.dat , which is the only
context in which it can be used.
Example
data block
Line 0: LLNL_AQUEOUS_MODEL_PARAMETERS
Line 1: -temperature
Line 2: 0.0100 25.0000 60.0000 100.0000
Line 2a 150.0000 200.0000 250.0000 300.0000
Line 3: -dh_a
Line 4: 0.4939 0.5114 0.5465 0.5995
Line 4a: 0.6855 0.7994 0.9593 1.2180
Line 5: -dh_b
Line 6: 0.3253 0.3288 0.3346 0.3421
Line 6a: 0.3525 0.3639 0.3766 0.3925
Line 7: -bdot
Line 8: 0.0374 0.0410 0.0438 0.0460
Line 8a: 0.0470 0.0470 0.0340 0.0000
Line 9: -co2_coefs
Line 10: -1.0312 0.0012806
Line 10a: 255.9 0.4445
Line 10b: -0.001606
Explanation
Line
0: LLNL_AQUEOUS_MODEL_PARAMETERS
LLNL_AQUEOUS_MODEL_PARAMETERS
is the keyword for the data block. No other data are input on the keyword line.
-temperature
--Begins a block of data that defines a temperature grid. Values of the other
parameters are specified at each of the temperatures in the grid. Optionally, temperature
, temperatures , or -t [ emperatures
].
list_of_temperatures
--Temperatures, °C, for the temperature grid. Any number of temperatures can be
given, but values of the parameters defined by -dh_a , -dh_b
, and -bdot must be defined for each temperature.
-dh_a
--Begins a block of data that defines the Debye-Hückel A parameter at
each temperature in the temperature grid. Optionally, adh , dh_a
, -a [ dh ], or -d [
h_a ].
dh_a_values
--Values of Debye-Hückel A for each temperature in the temperature
grid.
-dh_b
--Begins a block of data that defines the Debye-Hückel B parameter at
each temperature in the temperature grid. Optionally, bdh , dh_b
, -b [ dh ], or -dh_b .
dh_b_values
--Values of Debye-Hückel B for each temperature in the temperature
grid.
-bdot
--Begins a block of data that defines the Debye-Hückel B -dot
parameter at each temperature in the temperature grid. Optionally, bdot
, b_dot , -bdo [ t ], or -b_
[ dot ].
dh_bdot_values
--Values of Debye-Hückel B -dot for each temperature in the
temperature grid.
-co2_coefs
--Begins a block of data that defines the parameters in the expression for the
activity coefficient of CO 2 (aq) as a function of temperature and
ionic strength. Optionally, c_co2 , co2_coefs
, -c [ _co2 ], or -c [
o2_coefs ].
Notes
The Lawrence Livermore
National Laboratory aqueous model (Daveler and Wolery, 1992) uses this
expression for the log (base 10) of an activity coefficient: 
, where 
is
the Debye-Hückel A parameter corresponding to -dh_a ,
is the Debye-Hückel B
parameter corresponding to -dh_b , 
is the Debye-Hückel B- dot
parameter corresponding to -bdot , 
is the hard core diameter, which is
specific to each aqueous species, and I is the ionic strength. The LLNL_AQUEOUS_MODEL_PARAMETERS
data block defines 
, 
, and 
as
functions of temperature. A temperature grid is defined with -temperatures
and values of each of these parameters are specified at each point in the
temperature grid. For a given simulation temperature, values of the parameters
are interpolated linearly between points on the temperature grid. The
ion-specific parameter 
is defined in the SOLUTION_SPECIES data block with the
identifier -llnl_gamma .
The activity
coefficient of aqueous carbon dioxide is defined as a function of ionic
strength based on the parameterization of Drummond (1981). The formula for the
natural log of the activity coefficient is 
,
where T is temperature in kelvin; I is ionic strength; and C
, F , G , E , and H are defined in order
with the -co2_coefs identifier. The activity coefficient
calculated from this formula can be applied to specific neutral species by
using the identifier -CO2_llnl_gamma in the SOLUTION_SPECIES data block.