Thermodynamic Correction for Salts in Variably Saturated Porous Media

Abstract

Using thermodynamic principles, the general relationship describing the equilibrium vapor content in the gas phase above a saline liquid and across a curved liquid-gas interface is developed. Since high salt concentration affects the intensive and extensive liquid properties, it is also necessary to account for these effects in liquid water content/liquid water pressure relationship curves so that experimentally derived curves for pure water may be useful for elevated salt concentrations. The appropriate thermodynamic relationships are derived to describe the salt effects on liquid and vapor properties. The resulting equations are valid for salt concentrations between zero and saturation, and for any temperatures that nominally occur in nearsurface geologic materials. Notation Variablesµ i chemical potential of the ith constituent. N i mole number of the ith constituent.the mole fraction of i in the gas. a iL the activity of constituent i in the liquid.LG surface tension at the gas-liquid interface. A LG area of the gas liquid interface. dA LG dV L the gas-liquid interface area to liquid volume ratio (or the density of gas-liquid interface).

Effects of sodium chloride on constitutive relations in variably saturated porous media

“… Edlefsen and Anderson , 1943]. However, to the authors' knowledge, no general derivation from first principles of the synergistic effects of salt and the curved interface had been accomplished prior to Burns et al [2006]. Similar thermodynamic constitutive relationships with varying amounts of detail have been defined for various purposes [ Olivella et al , 1996; Bear and Gilman , 1995; Nassar and Horton , 1989].…”

“…Burns et al consider an isothermal system for which the local equilibrium assumption applies and for which a single dissolved salt species is present in water in a porous medium that is well connected to the atmosphere. These conditions are summarized in the following assumptions [ Burns et al , 2006].…”

“…We restrict the present analysis to a single salt to enhance clarity. The resulting constitutive relations derived by Burns et al [2006] are where where the notation pressure (P), activity (a), volume (V), number of moles (N), the ideal gas constant (R), temperature (T), area (A), and surface tension (σ) are used, with superscripts to indicate which subsystem or constituent is being considered. Lowercase letters describe the constituent (water (w) or salt (h)), and the capital letters describe the phase (liquid (L) or gas (G) (see Notation section)).…”

“…Liquid volume changes with NaCl salt concentration (Figure 1); thus implies that the liquid pressure will be affected by changes in liquid volume (possibly associated with changes in salt concentration), and by changes in surface tension. Defining the unit pore volume: V pore ≡ 1 (units to be chosen on the basis of available empirical relationships), the liquid saturation may be defined as L , which represents the pressure corresponding to an equivalent saturation of salt‐free water L ≡ P L ( S L ), is a function of water geometry only (specifically, the change in liquid‐gas interfacial area with a change in liquid volume), and S L is a function of both water and salt contents [ Burns et al , 2006]. Hence L may be determined from the pressure‐saturation curves for salt‐free water.…”

“…As an example of “domination,” it is convenient to consider a slightly different form of . Taking the natural log of both sides of the equation, may be rewritten The dilute solution approximation to is given by setting a wL = X wL (i.e., the mole fraction of water in the liquid) and = , which is a constant, allowing evaluation of the integral (complete details provided by Burns [2004]). Hereafter, the integral in will be referred to as the volume correction term, and the zero‐salt liquid pressure term will be called the dilute approximation term (since the dilute approximation effectively results in the last two terms collapsing to ( P L − P 0∞ L )).…”