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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