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Density Calculation


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Can you please provide the equations and reference that GWB uses to calculate the density of a solution from TDS and temperature? I'm trying to understand how GWB includes these variables in the calculation. Additionally, does the calculation change if the solution is not dominantly Na-Cl, but is, say, dominantly Ca-SO4 or Mg-SO4?





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Hi Morgan,


Density is calculated from a correlation developed by Phillips et al. 1981 for NaCl solutions. The correlation uses the temperature, pressure (which corresponds to the principal temperatures in the thermo dataset), and salinity of the fluid.


The program normally figures density as that of an NaCl solution with the same TDS (which it calculates by adding the masses of solutes) as the fluid in question, at the temperature of interest. With the command “density = chlorinity” you can tell the program to instead use the density of an NaCl solution of equivalent chlorinity. Please see 5.15, density, in the GWB Reference Manual for more information.


Phillips, S. L., A. Igbene, J. A. Fair and H. Ozbek, 1981, A technical databook for geothermal energy utilization. Lawrence Berkeley Laboratory Report LBL-12810, 46 p.
Hope this helps,
Brian Farrell
Aqueous Solutions LLC
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  • 3 years later...

Hi, I am using GWB 12.0.6. These are the results obtained by Spec8:

          Temperature =  13.9 C    Pressure =  1.013 bars
          pH =  7.997
          Ionic strength      =    0.005059 molal
          Charge imbalance    =   -0.000267 eq/kg (-3.873% error)
          Activity of water   =    0.999995
          Solvent mass        =      1.0000 kg
          Solution mass       =      1.0003 kg
          Mineral mass        =     0.00000 kg
          Solution density    =    1.021    g/cm3
          Solution viscosity  =    0.012    poise
          Chlorinity          =    0.000132 molal
          Dissolved solids    =         291 mg/kg sol'n
          Elect. conductivity =      326.08 uS/cm (or umho/cm)
          Hardness            =      164.64 mg/kg sol'n as CaCO3
            carbonate         =      164.64 mg/kg sol'n as CaCO3
            non-carbonate     =        0.00 mg/kg sol'n as CaCO3
          Carbonate alkalinity=      172.96 mg/kg sol'n as CaCO3
          Water type          =    Ca-HCO3
          Bulk volume         =        980. cm3
          Fluid volume        =        980. cm3
          Mineral volume      =       0.000 cm3
          Inert volume        =       0.000 cm3
          Porosity            =        100. %
          Permeability        =        98.7 cm2

Water is fresh (TDS = 291 mg/kg sol'n), so I am very surprised to obtain a calculated density of 1.021 g/cm3. This latter value is typical of seawater or an NaCl brine. Indeed, using PHREEQC and density calculation by Pizer.dat dataset, I have obtained Density (g/cm³)  =   0.99950.
Thank you.

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Density of electrolyte solutions is not calculated in most geochemical modeling programs. It's secondary in importance to species distributions, saturation indices, and so on, but it's our opinion that a simple calculation is better than nothing. The Phillips correlation described above, which is the default method for GWB12 and older releases, was designed for geothermal applications, so it works best at higher temperatures and salinities. The correlation is known to be valid for NaCl solutions from 10 < T < 350 °C, 0.25 < m < 5 molal, and P < 50 MPa and greater than the fluid’s vapor pressure. Your fluid is outside (below) the range of valid salinities and very close to the lower T limit.

GWB14 by default uses the Batzle-Wang method (Batzle, M. and Z. Wang, 1992, Seismic properties of pore fluids. Geophysics 57, 1396–1408) for calculating density. It was fit over the range 20 < T < 350 °C and 0 < m < 8 molal, so it works better over a range of conditions. I checked a NaCl fluid of the same ionic strength and temperature as your fluid in GWB14.0.1 and calculated a density of 0.998 g/cm3.

PHREEQC's method is quite new. It requires a large number of parameters, but it looks interesting.


Brian Farrell
Aqueous Solutions


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