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Table 7 Parameters used in the water–rock interaction model (Ku et al. 1992)
From: Water–rock interactions in the Bruchsal geothermal system by U–Th series radionuclides
Symbol | Parameter | SI units |
|---|---|---|
\(A\) | Specific activity of a dissolved radionuclide | Bq kg−1 |
\(A^{*}\) | Specific activity of a dissolved radionuclide originated from diffusional flux | Bq kg−1 |
\(A_{a}\) | Specific activity of an adsorbed radionuclide | Bq kg−1 |
\(\overline{A}\) | Specific activity of a radionuclide in solids | Bq kg−1 |
\(C\) | Concentration of a dissolved radionuclide | atoms kg−1 |
\(C^{i}\) | Initial concentration of a dissolved radionuclide | atoms kg−1 |
\(D_{m}\) | Diffusion coefficient of a radionuclide | m2 s−1 |
\(F\) | Diffusional flux of a nuclide into larger fractures | Bq m−2 |
\(e_{Ra}\) | Radium recoil efficiency relative to 222Rn | – |
\(\varepsilon_{i}\) | Recoil efficiency for nuclide i | – |
\(\phi\) | Porosity of the aquifer | – |
\(k_{1}\) | First-order adsorption rate constant | s−1 |
\(k_{2}\) | First-order desorption rate constant | s−1 |
\(k_{p}\) | First-order precipitation rate constant | s−1 |
\(k_{w}\) | First-order dissolution rate constant | s−1 |
\(K\) | Dimensionless distribution coefficient | – |
\(K_{d}\) | Distribution coefficient | L kg−1 |
\(\lambda\) | Radioactive decay constant of radionuclide | s−1 |
\(M_{b}\) | Mass of brine | kg m−3 |
\(M_{r}\) | Mass of rock | kg m−3 |
\(P\) | Supply rate of radionuclide to brine | Bq kg−1 |
\(P_{d}\) | Supply rate of radionuclide to brine by desorption | Bq kg−1 |
\(P_{r}\) | Supply rate of radionuclide to brine by alpha-recoil | Bq kg−1 |
\(P_{r}^{*}\) | Supply rate of radionuclide to brine by alpha-recoil in consideration of diffusional flux | Bq kg−1 |
\(P_{w}\) | Supply rate of radionuclide to brine by dissolution process | Bq kg−1 |
\(Q\) | Supply rate of radionuclide by water flow | Bq kg−1 |
\(r\) | Recoil distance | m |
\(R_{f}\) | Retardation factor due to adsorption and desorption | – |
\(R_{f}^{*}\) | Retardation factor due to precipitation as well as adsorption and desorption | – |
\(\rho_{b}\) | Fluid density | kg m−3 |
\(\rho_{s}\) | Density of aquifer solid | kg m−3 |
\(S\) | Surface area of solids, expressed as area of solid per volume of fluid contacting the solids | m2 m−3 |
\(S_{a}\) | Scavenging rate of radionuclide from brine by adsorption to rock surfaces | Bq kg−1 |
\(S_{p}\) | Scavenging rate of radionuclide from brine by co-precipitation with minerals | Bq kg−1 |
\(\tau_{b}\) | Transit time of brine in the aquifer | s |
\(\tau_{p,i}\) | Mean time for nuclide i in solution to precipitate in minerals | s |
\(\tau_{w,i}\) | Mean time for leach nuclide i from solid phases | s |
\(w_{f}\) | Fracture width | m |
\(v_{f}\) | Advection velocity of fracture fluid | m s−1 |
\(x\) | Distance | m |
\('\) | Superscript referring to radioactive parent | – |