## 2 Materials and Methods
### Chemical Analyses  
A non-filtered subsample of the fluid which was extracted from freezing reactor was used to measure pH (uncertainty of \(\pm\)0.01 pH units, WTW inoLab-pH7110) and specific conductivity (\(\pm\)0.1 \(\upmu\)S cm\({}^{-1}\), Consort C830). The rest of the 15 mL was filtered through a 0.45 \(\upmu\)m Minisart(r) (Fisher Scientific, Illkirch-Graffenstaden, France) syringe filter. In the <0.45 \(\upmu\)m filtrates, the DOC and DIC were analyzed by high-temperature catalytic oxidation using TOC-VCSN, Shimadzu(r) ([PERSON], Kyoto, Japan), with an uncertainty of \(\pm\) 2% and a detection limit of 0.1 mg L\({}^{-1}\). The DIC was measured after sample acidification with HCl, and the DOC was analyzed in the acidified samples after sparging with C-free air for 3 min at 100 mL min\({}^{-1}\) as non-purgeable organic carbon (NPOC). The internationally certified water samples (MISSISSIPPI-03) were used to check the validity and reproducibility of the analysis. The UV-absorbance of the water samples was measured using a 10 mm quartz cuvette on a CARY-50 UV-Vis spectrophotometer (Varian, Belrose, Australia) to assess the aromaticity of pore fluids via specific UV absorbance (SUVA\({}_{254}\)). Major cations, Si, P, and \(\sim\)40 trace elements (TE) were measured in He and Ar operating modes, with a quadrupole ICP-MS Agilent 7500 ce (Agilent Technologies, Santa Clara, CA, USA). Indium and rhenium (approximately 3 \(\upmu\)g L\({}^{-1}\)) were used as internal standards to correct for instrumental drift and eventual matrix effects. The appropriate corrections for oxide and hydroxide isobaric interferences were applied for the Rare Earth Elements (REE). Three in-house standard solutions (1, 10, and 100 \(\upmu\)g L\({}^{-1}\) of each element in 2% HNO\({}_{3}\)) were measured every 10 samples. The data tables present the results for the elements, exhibiting a good agreement (\(\pm\)10%) between the certified or recommended values and our measurements, or for cases in which we obtain a good reproducibility (the relative standard deviation of our various measurements of standards lower than 10%), even if no certified or recommended data are available. During ICP MS analysis, the SLRS-5 international standard [51; 52] was measured at the beginning of the analytical session and after each 20 samples to assess the external accuracy and sensitivity of the instrument. All certified major (Ca, Mg, K, Na, Si) and trace elements (Al, As, B, Ba, Co, Cr, Cu, Fe, Ga, Li, Mn, Mo, Ni, Pb) and all naturally-occurring REEs (La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb, Lu, Sb, Sr, Th, Ti, U, V, Zn) concentrations of the SLRS-5 standard and the measured concentrations agreed, with an uncertainty of 10-20%. The agreement for Cd, Cs, and Hf was between 30 and 50%. For all major and most trace elements, the concentrations in the blanks were below analytical detection limits (\(\leq\)0.1-1 ng L\({}^{-1}\) for Cd, Ba, Y, Zr, Nb, REE, Hf, Pb, Th, U; 1 ng L\({}^{-1}\) for Ga, Ge, Rb, Sr, Sb; \(\leq\)10 ng L\({}^{-1}\) for Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As). Some rare elements, such as Sn, Nb, W, TI, Ta, and Bi, which were not certified in the reference materials, were also measured, but their concentrations were presented only in the case when three independent subsamples provided a <20% agreement.