Mathematical modeling of the excessive 234U formation in groundwater

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Abstract

Excess of uranium-234 in natural water (ratio 234U/234U > 1 in comparison to the equilibrium value as 1 by activity) correlates with global climate variations, increasing during warm and decreasing during cold periods. The hurricane disequilibrium of 234U/234U >> 10 are found in groundwater. Based on mathematical models, it is shown that such anomalies are the result of a geologically long stay of aquifers in a frozen state in the past and the subsequent melting of ground ice with the formation of “revived” water. Non-freezing film moisture present in permafrost rocks make a decisive contribution to the formation of hurricane 234U excess.

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About the authors

I. V. Tokarev

Science Park, St. Petersburg State University

Author for correspondence.
Email: i.tokarev@spbu.ru
Russian Federation, Dekabristov per., 16, V.O., St. Petersburg, 199155

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Supplementary files

Supplementary Files
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2. Fig. 1. Conceptual scheme of groundwater enrichment with uranium‑234 in the framework of a one‑stage model of radiokinetic separation [19, 21, 36].

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3. Fig. 2. Change in the ratio 234U/238U (curve 1, scale on the left) and the time of establishment of radioactive equilibrium in pore water (curve 2, scale on the right) depending on the size of the elementary grain at concentrations of uranium in the matrix [U]MATR = 3 micrograms/g, [U]PORE = 3 ng/g and the recoil track length is 234Th / = 55 nm (adapted from [24] and calculated according to the model [29]).

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4. Fig. 3. Shapes and sizes of cavities that occur at the site of the alpha particle track during etching. The track is located: a — normal to the nearest face, b — at 45° to the nearest face. The numbers around the curves are the duration of etching. The calculated grid is not shown for ease of visualization. 10

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5. Fig. 4. Fragment of the grain grid model for Monte Carlo calculations: on the left is the option “matrix + tracks”, on the right is the option “matrix + tracks + microfractures". 1 — pores containing gravitational water or ice; 2 — mineral matrix (hydraulically impermeable k = 10-10 m/day); 3 — tracks; 4 — micro-fractures (contacts of mineral individuals, gas-liquid inclusions, microcracks, etc.); 5 — boundaries of the first kind (HVC = const, HB = const and C0 = 0); 6 — the direction of movement of gravitational water through the pores. The calculated grid is not shown for visualization convenience.

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6. Fig. 5. One—stage model — calculation options for 234U/238U at the exit from the model with a stationary flow of pore moisture: a — “matrix + tracks”, b — “matrix + tracks + microfractures”; parameter W/R ‑ the ratio of the volume of filtered water to the volume of grain; the numbers near the curves — the ratio D TRACK/D MATRIX; black dashed the line is an equilibrium ratio of 234U/238U = 1 (the geometry of the model in Fig. 4, the track density is 0.012 µm/mm2, the grain matrix is hydraulically impermeable k = 10-10 m/day, there is no film moisture).

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7. Fig. 6. Calculation option 234U/238U in pore water for a two—stage model: a — in the absence of film moisture, b - in the presence of film moisture in MMGP; parameter W/R — the ratio of the volume of filtered water to the volume of grain; the numbers near the curves are the ratio DTRACK/D MATRIX; the rest of the symbols are in Fig. 5.

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