Numerical study of H${}_2$, CH${}_4$, CO, O${}_2$ and CO${}_2$ diffusion in water near the critical point with molecular dynamics simulation

Abstract

Diffusion coefficient of H${}_2$, CH₄, CO, O${}_2$ and CO₂ in water near the critical point (600-670K, 250atm) is numerically investigated using Molecular Dynamics (MD) simulation. Main factors determining diffusion coefficient are discussed. Arrhenius behavior of temperature can be divided into two separate parts which are subcritical region and supercritical region. The activation energy has a huge difference between two regions. Diffusion coefficient has a negative power relation with density of water through logarithmic plot. Viscosity of water has effects on diffusion coefficient by a combination with temperature that term 1/T$\eta$ has a quadratic relation with diffusion coefficient. A new empirical equation to predict diffusion coefficient in water near the critical point is developed in which the effect of solute gas and solvent water is separated to the pre-factor ${\mathit{A}}_0$ and the second part ${\mathit{F}}_w$. ${\mathit{A}}_0$ is a unique constant for different solutes and ${\mathit{F}}_w$ considers temperature, density and viscosity of water. It successfully predicts diffusion coefficient near the critical point for all solute gases and average absolute relative deviation is only 7.65%. Compared to other equations, our equation shows the best accuracy and simplicity for extension and modification.

Introduction

Diffusion is one of the most important properties among transport properties of binary mixtures [1], [2], [3], [4]. It is characterized by diffusion coefficient of solute in solvent. Diffusion in water at infinite dilution has been of great interest to scientific and engineering researches for years, yet it is not fully clear and understood. Diffusion in water is essential for mass transfer through boundary layer and concentration distribution at different time and position [5]. There are several equations to predict diffusion coefficient in water at room temperature [6], [7], [8]. However, diffusion coefficient at higher temperature neat the critical point is lacking in discussion, let alone the accurate equation to predict diffusion coefficient in water near the critical point.

The critical point of water is the end point of a phase equilibrium curve where at this point, defined by a critical temperature $T_{\mathrm{c}}=647$ K and a critical pressure $P_{\mathrm{c}}=218$ atm, liquid and gas phase boundaries vanish and they all become one supercritical phase [9]. Around the critical point, thermal and physical properties encounter a dramatic change which may lead to the same dramatic change in mass transfer and reaction pathway. To figure it out, accurate diffusion coefficient is needed in finding the relation between diffusion and reaction and microscopical mechanics of diffusion-controlled reaction [10].

From subcritical to supercritical, water has transformed from liquid-like to gas-like in a way. Diffusion coefficient in gas, which can be estimated theoretically, is about 10⁻⁵ m²/s [11]. To a first approximation, diffusion coefficient in gas is inversely proportional to pressure. It varies with the 1.5–1.8 power of temperature and in a more complicated fashion with factors such as molecular weight. Diffusion coefficient in liquid, which cannot be reliably estimated, is about 10⁻⁹ m²/s. The range of diffusion coefficient is remarkably small. The reasons for this narrow range are that the viscosity of simple liquid like water varies little, and that diffusion coefficient is only a weak function of solute size.

Normally, diffusion coefficient in water at room temperature is estimated through experiments. For example, Witherspoon and Saraf [12] used the capillary-cell method to measure diffusion coefficient of methane, ethane, propane and n-butane in water from 24.8 to 42.6 °C. Ferrell and Himmelblau [13] did measurements of laminar dispersion in a capillary to determine diffusion coefficient of hydrogen and helium dissolved in water over the temperature range of 10 to 55 °C. A statistical analysis of experiments indicated that diffusion coefficient could be related to the absolute temperature by a semiempirical correlation. With the development of computer, MD simulation is an alternative way to investigate physical and chemical properties in recent years [14], [15]. Martins et al. [16] predicted diffusion coefficient of chlorophenols in water by MD simulation. They correlated mutual diffusion coefficient by the well-known Wilke–Chang equation. Michalis et al. [17] obtained diffusion coefficient of the first five n-alkanes in water at infinite dilution from MD simulation. It is shown that the diffusion coefficient of methane and n-butane obey the Stokes–Einstein equation. Moultos et al. [18] employed MD simulation for the calculation of diffusion coefficient of CO₂ in water. They examined different force-field combinations and found that EPM2-TIP4P/2005 was the most accurate. Zhang and Yang [19] studied structure and diffusion properties of ethanol/water mixture at 298.15 K and atmospheric pressure by MD simulation. The effect of the distinct diffusion coefficient to the mutual diffusion coefficient has been evaluated and discussed. Xiao [20] investigated hydrogen diffusion in supercritical water. However, diffusion coefficient in water near the critical point has not been reported. Besides, there is not accurate empirical equation to predict diffusion coefficient in water near the critical point. Due to the experimental limits, MD simulation is a proper way to investigate diffusion coefficient in water near the critical point.

In this work, diffusion coefficients of ${\mathrm{H}}_2$, CH₄, CO, ${\mathrm{O}}_2$ and CO₂ in water near the critical point are computed by MD simulation at 600–670 K, 250 atm. The main physical and thermal factors influencing diffusion coefficient are investigated to figure out the relation between specific factor and diffusion coefficient. By developing an empirical equation, influencing factors are divided into two parts and diffusion coefficient is accurately predicted near the critical point. The paper is organized as follows. In Section 2, the computation and simulation details are introduced. In Section 3, results are discussed. At last, conclusions are made.