Time scale of hydrothermal water-rock reactions in Yellowstone National Park based on radium isotopes and radon

We have measured ²²⁴Ra (3.4 d), ²²⁸Ra (5.7 yr), and ²²⁶Ra (1620 yr) and chloride in hot spring waters from the Norris-Mammoth Corridor, Yellowstone National Park. Two characteristic cold-water components mix with the primary hydrothermal water: one for the travertine-depositing waters related to the Mammoth Hot Springs and the other for the sinter-depositing Norris Geyser Basin springs. The Mammoth Hot Springs water is a mixture of the primary hydrothermal fluid with meteoric waters flowing through the Madison Limestone, as shown by the systematic decrease of the (²²⁸Ra/²²⁶Ra) activity ratio proceeding northward. The Norris Geyser Basin springs are mixtures of primary hydrothermal water with different amounts of cold meteoric water with no modification of the primary hydrothermal (²²⁸Ra/²²⁶Ra) activity ratio. Using a solution and recoil model for radium isotope supply to the primary hydrothermal water, a mean water-rock reaction time prior to expansion at 350°C and supply to the surface is 540 years assuming that 250 g of water are involved in the release of the radium from one gram of rock. The maximum reaction time allowed by our model is 1150 years.