François Montel

Thermal diffusion sensitivity to the molecular parameters of a binary equimolar mixture, a non-equilibrium molecular dynamics approach

Abstract The goal of this study is to analyse how the thermal diffusion process is dependent on molecular parameters when describing a fluid mixture. To estimate the associated transport coefficient, which is the thermal diffusion factor αT, a non-equilibrium molecular dynamics algorithm has been applied on equimolar binary mixtures of Lennard–Jones (LJ) particles in supercritical conditions. Firstly, it is shown that this model is able to correctly estimate αT for simple alkane mixtures, provided there are a sufficient number of particles and long enough simulations. Then, using various mixing rules, the separate influences of the mass, the moment of inertia, the atomic diameter and the interaction strength have been studied. Results indicate that the molar fraction of the component, having the smallest mass and moment of inertia as well as the biggest radius and the strongest potential, tends to increase in the hot area. Elsewhere, simulations for various cross-interaction parameters show that αT is extremely sensitive to the intermolecular pair potential between unlike particles. Finally, results on methane/normal alkane mixtures indicate that a simple sum between the separate contributions provides a reliable evaluation of αT only when the molecular parameter ratios between the two components are close to 1.

On thermal diffusion in binary and ternary Lennard-Jones mixtures by non-equilibrium molecular dynamics

Molecular simulation appears to be an alternative to experiment for the estimation of transport and thermodynamics properties of fluid mixtures, which is of primary importance in the evaluation of the initial state of a petroleum reservoir. In this study, a non-equilibrium molecular dynamics algorithm has been applied to mixtures of Lennard-Jones spheres in order to compute the thermal diffusion process. The pertinence of such an approach to simple alkane mixtures is shown. The separate influences on the thermal diffusion of the molecular features in binary equimolar mixtures are then summarized. Simulations on binary non-equimolar mixtures have been performed as well. The results indicate an increase in the thermal diffusion process with increasing molar fraction of the lightest component. Moreover, this increase is enhanced with increasing difference in the number of carbons between the two alkanes. Then, a simple method, which yields results consistent with simulations, is proposed to predict thermal diffusion for the whole range of molar fractions starting only from the equimolar value. Finally, for ternary mixtures, the law of the corresponding states is shown to be valid when the appropriate mixing rules are applied, which allows the estimation of thermal diffusion in such mixtures from equivalent binary mixtures.

MASS EFFECT ON THERMODIFFUSION USING MOLECULAR DYNAMICS

Abstract The scope of this study is to improve the understanding of the thermal diffusion process on a microscopic scale by studying the mass effect on thermal diffusion factors. To achieve such a goal, non-equilibrium molecular dynamics simulations are performed on binary mixtures of simple Lennard–Jones spheres for a large range of thermodynamic states. Mixtures for which only the mass between species differs, up to mass ratios of 50, are analysed (isotope-like mixtures). In equimolar mixtures, it is shown that the link between the thermal diffusion factors and the ratio between the difference in masses and the sum of masses holds approximately for all states studied. In addition, it is found that this link strongly depends on density but weakly on temperature. In nonequimolar mixtures, results indicate that the effect of the mass ratio between species depends on the molar fraction. Using the data computed, a simple density-dependent correlation is proposed to quantify the mass effect in Lennard-Jones binary mixtures. Finally, it is shown that, taking into account only the mass effect, this correlation is able to provide a reasonable estimation of thermodiusion in n-pentane/n-decane mixtures, which underlines the intrinsic weakness of some of the usual thermodynamic models predicting thermodiffusion.

A molecular dynamics study of thermal diffusion in a porous medium

It is the main aim of this work to identify the microscopic origin of the perturbations brought about by a porous environment on the thermal diffusion (Soret effect) of a liquid mixture. For this purpose, nonequilibrium molecular dynamics simulations are carried out on model systems representing hydrocarbons in a porous medium. In keeping with previous simulations, a simplified model,i.e., Lennard-Jones spheres, is used for representing a methanedecane mixture, while the porosity is modeled by the inclusion of quasi-harmonic solids of various sizes and shapes. The model parameters are chosen to yield the proper order of magnitude for a silicate and its interactions with the alkanes. The model was first validated by investigating the equilibrium properties of the system. Then the thermal influence of the porous medium was evaluated and the adsorbing behaviour of the alkanes on the pores was characterized. It is found that the Soret coefficient of the equimolar mixture studied here is lowered by about 30% at 75% porosity. We find also that this reduction is strongly dependent on the structure of the porous medium.

Note: Temperature derivative of the refractive index of binary mixtures measured by using a new thermodiffusion cell

A thermodiffusion cell is developed for performing Soret experiments on binary mixtures at high pressure and in the presence of a porous medium. The cell is validated by performing experiments at atmospheric pressure. The experiments are performed by applying different temperature gradients to binary mixtures in order to determine their thermal contrast factor. These measurements provide a first demonstration of the good reproducibility of this kind of measurements upon calibration.

Thermodiffusion in multicomponent n -alkane mixtures

Compositional grading within a mixture has a strong impact on the evaluation of the pre-exploitation distribution of hydrocarbons in underground layers and sediments. Thermodiffusion, which leads to a partial diffusive separation of species in a mixture due to the geothermal gradient, is thought to play an important role in determining the distribution of species in a reservoir. However, despite recent progress, thermodiffusion is still difficult to measure and model in multicomponent mixtures. In this work, we report on experimental investigations of the thermodiffusion of multicomponent n-alkane mixtures at pressure above 30 MPa. The experiments have been conducted in space onboard the Shi Jian 10 spacecraft so as to isolate the studied phenomena from convection. For the two exploitable cells, containing a ternary liquid mixture and a condensate gas, measurements have shown that the lightest and heaviest species had a tendency to migrate, relatively to the rest of the species, to the hot and cold region, respectively. These trends have been confirmed by molecular dynamics simulations. The measured condensate gas data have been used to quantify the influence of thermodiffusion on the initial fluid distribution of an idealised one dimension reservoir. The results obtained indicate that thermodiffusion tends to noticeably counteract the influence of gravitational segregation on the vertical distribution of species, which could result in an unstable fluid column. This confirms that, in oil and gas reservoirs, the availability of thermodiffusion data for multicomponent mixtures is crucial for a correct evaluation of the initial state fluid distribution.Microgravity simulators: improving oil field assessmentsTo support oil and gas exploration, researchers sent hydrocarbon mixtures into space to obtain accurate data on how each component behaves. The group—led by Guillaume Galliero from the University of Pau and Pays de l’Adour, France—wanted to study the effect of temperature on the movement of individual hydrocarbons in mixtures under typical reservoir conditions. Eliminating the effects of gravity allowed them to collect more accurate data than has previously been obtained. The team showed that thermodiffusion has a large impact on the distribution of hydrocarbon reservoirs under the ground. They state that thermodiffusion should therefore be considered in computer models that assess analytical data collected at potential underground reservoirs. This would allow oil and gas companies to more accurately predict the suitability of the hydrocarbons at potential drilling sites.

Macroscopic model of multicomponent fluids in porous media

This article is about a macroscopic model simulating the heat and mass transfer of a fluid containing numerous species in porous media. In order to use it in the modelling of petroleum fields, the physical phenomena studied are gravitational segregation, thermal diffusion, convection and diffusion. The originality of this approach is to simulate the movement of each component in order to deduce the species distribution and mixture flow. The mass flux calculated by an entropic balance is compared with the Darcy equation to evaluate the phenomenological coefficients. After presenting the possible origins of composition variations and the ways that they are usually studied, the article describes the developments that have led to the new model and finally reports the first results obtained.

Pseudo-component Delumping for Multiphase Equilibrium in Hydrocarbon-Water Mixtures

Abstract An analytical and consistent delumping procedure is implemented for fluids of petroleum interest containing water, non-hydrocarbon gases (such as N2, CO2, and H2S) and hydrocarbon (HC) compounds. Two sorts of difficulties are associated with these fluids: they often exhibit three or more equilibrium phases, and their thermodynamics cannot be described by conventional cubic equations of state (EoS). In this work, the Søreide-Whitson modification of the Peng-Robinson EoS, in which different binary interaction parameters are used in the aqueous and non-aqueous phases, is used. The method is successfully tested on two cases in the two- and three-phase regions: one synthetic HC/N2/CO2/H2O fluid and a “real” water/reservoir fluid.

High-Pressure Acid-Gas Viscosity Correlation

Acid gases containing hydrogen sulfide (H2S) are often encountered in the petroleum industry. However, reliable experiments on their thermophysical properties in reservoir conditions, on viscosity in particular, are scarce. From a modeling point of view, H2S and carbon dioxide (CO2) are polar compounds and as such are often considered rather difficult to model accurately. In this work, we propose a correlation with a strong physical background based on a corresponding-states (CS) approach to predict the viscosity from the temperature and the density of a large variety of systems for all stable thermodynamic states (gas, liquid, and supercritical). In particular, this correlation is applicable to predict the viscosity of sour/acid-gas mixtures, whatever the thermodynamic conditions. This approach is based on the Lennard-Jones (LJ) fluid model, which has been studied extensively thanks to molecular-dynamics (MD) simulations over a wide range of thermodynamic conditions. This fluid model can be extended to deal with polar molecules such as CO2 or H2S without a loss of accuracy. First, we demonstrate that the proposed physically based correlation is able to provide an excellent estimation of the viscosity [with average absolute deviations (AADs) below 5%] of pure compounds, including normal-alkanes, CO2, or even H2S, whatever the thermodynamic conditions (gas, liquid, or supercritical). Then, using a one-fluid approximation and a set of combining rules, the correlation is applied to various fluid mixtures in a fully predictive way (i.e., without any additional fitted parameters). Using this scheme, the deviations between predictions and measurements are as low as those on pure fluids using temperature and density as inputs. The viscosity of natural- and acid-gas mixtures at reservoir conditions is shown to be very well predicted by the proposed scheme. In addition, it is shown that this correlation can also be applied to predict reasonably the viscosity of asymmetric high-pressure mixtures, even in the liquid phase. This physically based approach is easy to include in any simulation software as long as, apart from temperature and density, the only inputs--the molecular parameters of each species--can be estimated from the critical temperature and the critical volume when not known.

High Pressure Acid Gas Viscosity Correlation

Acid gases containing H2S are often encountered in the petroleum industry. However, reliable experiments on their thermophysical properties in reservoir conditions, in particular viscosity, are very scarce. From a modeling point of view H2S (and CO2) are polar compounds and are so often considered as rather difficult to model accurately. In this work, we propose a correlation based on a corresponding states approach in order to predict the viscosity of acid gas mixtures, among others, with a strong physical background. This correlation is based on the Lennard-Jones fluid model, which has been studied extensively thanks to molecular dynamics simulations over a wide range of thermodynamic conditions. This fluid model can be extended to deal with polar molecules such as CO2 or H2S without a loss of accuracy. In a first part, we demonstrate that the proposed physically based correlation is able to provide an excellent estimation of the viscosity (with average absolute deviations below 5 %) of pure compounds including normal-alkanes, CO2 or even H2S whatever the thermodynamic conditions, gas, liquid or supercritical. Then, using a one-fluid approximation and a set of combining rules, the correlation is applied to various mixtures in a fully predictive way, i.e. without any additional fitted parameters. Using this scheme, the deviations between predictions and measurements are as low as on pure fluids. The viscosity of natural and acid gas mixtures in reservoir conditions is shown to be very well predicted by the proposed scheme. In addition, it is shown that this correlation can also be applied to predict reasonably the viscosity of asymmetric high pressures mixtures even in the liquid phase. This physically based approach is easy to plug in any simulation software as long as the only inputs, the molecular parameters, are directly related to the critical temperature and volume.