The effect of salinity on the maximum thermal gradient of a hydrothermal system at hydrostatic pressure

TLDR

A mathematical model was used to calculate temperature‑depth relations of Na‑Ca‑K‑Cl brines in a vein system at hydrostatic pressure, approximating vapor‑saturated NaCl–H₂O solutions based on available data. The model shows steeper thermal gradients in saline brines than in pure water, with isotherm depths in 5–25 wt % NaCl brines being 92–63 % of those in H₂O, enabling estimation of crystal‑growth depths and informing geothermal brine behavior.

Abstract

The effect of salinity on the temperature-depth relations of a brine of constant composition, enclosed in a vein system, but freely connected to the surface, and everywhere at the boiling point for the hydrostatic head, was calculated by using a mathematical model. The Na-Ca-K-Cl brines which are found in thermal springs and in fluid inclusions in ore minerals were approximated by the available data for vapor-saturated NaCl-H 2 O solutions. In general, the results are similar to those calculated by D. E. White in 1968 for H 2 O, except that the gradients are steeper because of the increase in density and the decrease in vapor pressure caused by the dissolved salt. As a practical rule, the depth to an isotherm in a 5, 10, 15, 20, and 25 wt percent NaCl brine system is, respectively, 92, 84, 77, 70, and 63 percent (+ or -2 percent) of the depth to the same isotherm in an H 2 O system. From the data presented, the minimum depth to the growth site of crystals containing fluid inclusions which indicate boiling of the brine can be estimated. Among other applications, these results are useful toward the understanding of the behavior of brines in geothermal areas which may or may not contain compositional stratification.