Multicomponent Diffusion Coefficients Research Articles

Measurement of Effective Hydrogen-Methane Gas Diffusion Coefficients in Reservoir Rocks

Summary If hydrogen is stored in depleted gas fields, the remaining hydrocarbon gas can be used as cushion gas. The composition of the backproduced gas depends on the magnitude of mixing between the hydrocarbon gas and the hydrogen injected. One important parameter that contributes to this process of mixing is molecular diffusion. Although diffusion models are incorporated in the latest commercial reservoir simulators, effective diffusion coefficients for specific rock types, pressures, temperatures, and gas compositions are not available in the literature. Thus, laboratory measurements were performed to improve storage performance predictions for an underground hydrogen storage (UHS) project in Austria. An experimental setup was developed that enables measurements of effective multicomponent gas diffusion coefficients. Gas concentrations are detected using infrared light spectroscopy, which eliminates the necessity of gas sampling. To test the accuracy of the apparatus, binary diffusion coefficients were determined using different gases and at multiple pressures and temperatures. Effective diffusion coefficients were then determined for different rock types. Experiments were performed multiple times for quality control and to test reproducibility. The measured binary diffusion coefficients without porous media show a very good agreement with the published literature data and available correlations based on the kinetic gas theory (Chapman-Enskog, Fuller-Schettler-Giddings). Measurements of effective diffusion coefficients were performed for three different rock types that represent various facies in a UHS project in Austria. A correlation between static rock properties and effective diffusion coefficients was established and used as input to improve the numerical model of the UHS. This input is crucial for the simulation of backproduced gas composition and properties which are essential parameters for storage economics. In addition, the results show the impact of pressure on effective diffusion coefficients, which impacts UHS performance.

Transport Properties of Carbohydrates: Towards the Minimization Toxicological Risks of Cobalt and Chromium Ions

The influence of oligosaccharides (α-cyclodextrin, β-cyclodextrin and γ-cyclodextrin), and a polysaccharide, sodium hyaluronate (NaHy), on the diffusion of aqueous solutions of cobalt and chromium chlorides has been investigated. Cobalt and chromium are constituents of metal alloys for biomedical use, including dental prostheses. Thus, the release of these ions in the human body can lead to harmful biological effects. The interaction of metal ions with saccharides might have information on the role of mouthwashes in preventing these effects. This interaction has been assessed by measuring multicomponent intermolecular diffusion coefficients at 298.15 K. It has been found that β-cyclodextrin has the highest interaction towards cobalt and chromium ions. This work will contribute to unveiling the mechanisms responsible for transport by diffusion in aqueous solutions, and, therefore, mitigating the potential toxicity inherent to those metal ions.

The unexpected weirdness of rate-based simulation of some high-pressure column operations

Diffusion is the process by which molecules move. One way to model multicomponent diffusion is with a version of Fick’s law: (J) = - [D] d(c)/dz where [D] is a matrix of multicomponent diffusion coefficients. [D] is the product of two other matrices, one of which involves partial derivatives of the fugacity or activity coefficients. It is usually the case that all of the elements on the main diagonal of [D] have a positive value. Wambui Mutoru and Firoozabadi (2011, 2012) showed that CO2-rich and N2-rich hydrocarbon systems could have main diagonal elements of [D] that are negative. Using rate-based column simulations, we have found that these negative main diffusion coefficients readily occur in some high-pressure distillation operations. We investigate these processes in more detail and explore the consequences for the design and operation of columns in which this phenomenon is predicted to occur.

Salt-induced diffusiophoresis of a nonionic micelle: Roles of salting out and proximity to surfactant cloud point

• Salt-induced diffusiophoresis is the migration of a colloidal particle in water caused by a salt concentration gradient. • Tyloxapol micelle was identified as model particle with surface properties governed by polyethylene glycol (PEG) chains. • Na 2 SO 4 was chosen because it is a common salt and a strong salting-out agent according to Hofmeister series. • Gradient of Na 2 SO 4 drives micelle diffusiophoresis from high to low salt concentration due to PEG preferential hydration. • Near surfactant cloud point, diffusiophoresis becomes dominant mechanism responsible for micelle transport. Salt-induced diffusiophoresis is the migration of colloidal particles in water caused by salt concentration gradients. A widespread example of colloidal particles is represented by those with interfacial properties governed by polyethylene glycol (PEG) functionalities. Since salting-out salts strongly affect PEG-water interactions, their gradients are expected to generate diffusiophoresis of PEG-based particles. In this work, diffusiophoresis of nonionic micelles of tyloxapol, a polyoxyethylene surfactant, was characterized in the presence of Na 2 SO 4 . Specifically, multicomponent-diffusion coefficients were measured at 25 °C for the ternary tyloxapol-Na 2 SO 4 -water system using Rayleigh interferometry. These transport data, together with measurements of cloud points and dynamic-light-scattering diffusion coefficients, were used to determine the effect of salt concentration on micelle mobility, salt-induced micelle diffusiophoresis and salt osmotic diffusion induced by micelle gradients. It was found that gradients of Na 2 SO 4 induce micelle diffusiophoresis from high to low salt concentration. Moreover, diffusiophoresis becomes the dominant mechanism responsible for micelle transport near surfactant cloud point due to increase in both micelle size and osmotic compressibility with salt concentration. A hydration model was employed to theoretically describe salt salting-out effect on micelle diffusiophoresis and salt osmotic diffusion. This work is the first report showing salt-induced diffusiophoresis of a neutral PEG-based colloidal particle and characterizing its magnitude near miscibility gaps.

Accurate and efficient calculation of multicomponent thermal diffusion coefficients and partial thermal conductivity based on kinetic theory

The calculation of the multicomponent thermal diffusion coefficients and partial thermal conductivity of polyatomic gas mixtures, with large numbers of components, based on the Kinetic Theory of Gases is revisited. The terms involving inelastic collisions and relaxation times for various internal degrees of freedom are considered, in addition to the classical Chapman-Enskog expressions. For polar gases, the resonant exchange of rotational energy is also accounted for. The present work is the natural extension of the algorithms shown in Combust. and Flame 163 (2016) 540-55 for the calculation of the Fick’s law multicomponent diffusion coefficients, of which it makes use.This work presents a new iterative algorithm for the calculation of the multicomponent thermal diffusion coefficients and partial thermal conductivity. This new algorithm has been implemented in the C++ library MuTLib (Multicomponent Transport Library), available for the transport properties calculations in third party applications and included in the additional material of this publication. The algorithm performance improvements are shown in two different flames: a hydrogen premixed flame and a methane diffusion flame. The results are successfully compared against the library package EGLib (Ern-Giovangigli Library, which considers the same physical effects as this work), and to the well known mixture averaged approximation.

Correct definition of internal energy at the phenomenological construction of model of multicomponent continuous medium by methods of nonequilibrium thermodynamics

Taking into account the methods of thermodynamics of irreversible processes using the Onsager principle, a model of a multicomponent continuous medium is constructed, the internal energy of which is "free" of the kinetic energy of diffusion. The model is designed for an imperfect continuous medium with chemical reactions in the field of conservative external forces. Generalized StefanMaxwell relations are obtained, which represent a system of hydrodynamic equations of motion of a mixture with true inertial forces. The proposed thermodynamic technique made it possible to obtain a number of algebraic relations known from the kinetic theory of gases for the transfer coefficients, relating, in particular, the coefficients of multicomponent diffusion with binary diffusivitys, thermal diffusion ratios with thermal diffusion coefficients and multicomponent diffusion coefficients, true (molecular) thermal conductivity coefficient for multicomponent mixture with partial thermal conductivity coefficient, which indicates their versatility. The results obtained are intended for modeling not only liquid imperfect solutions, but also gas-dust mixtures with a finely dispersed dust component.

Modeling of single-particle char combustion under O2/H2O conditions: Effects of temperature and steam concentration

In this study, the single-particle char-O2/H2O combustion kinetic model was modified based on the one-dimensional unsteady mass and heat transfer equation coupled with the Maxwell–Stefan multicomponent diffusion coefficient. Numerical simulations of char-O2/H2O combustion at different reaction temperatures and H2O concentrations were performed. The simulation results show that the average temperature of a char particle decreases with increasing H2O concentration, and the particle temperature is higher in the inner layer than in the outer layer. Without H2O, O2 consumption in the boundary layer accounts for 50% of the total O2 consumption at different temperatures. Higher temperatures and H2O concentrations promote competition for O2 by homogeneous reactions in the boundary layer. Char-O2/H2O combustion is simultaneously controlled by O2 external diffusion and internal diffusion. Control by O2 internal diffusion is hardly affected by the H2O concentration. The contribution of the gasification reaction to carbon consumption increases with increasing temperature and H2O concentration. Increasing the H2O concentration three-fold from 5% increases the contribution of the gasification reaction to carbon consumption 1.96-fold at 1373 K, but only 1.25-fold at 1673 K.

Fick and Maxwell-Stefan Diffusion Coefficients in the Ternary Liquid Mixture of Acetone-Methanol-Chloroform

Fick diffusion coefficients are calculated by means of molecular simulation for liquid mixtures containing acetone, methanol and chloroform at 1 atm and 298 K for different compositions. For this means, Maxwell-Stefan (MS) diffusion coefficients were calculated using physical properties of the components and thermodynamic factors, Γ, using three different models of Wilson, NRTL and UNIQUAC. Because of the lack of experimental data for Fick diffusivities for ternary system, the validity of the model was tested by comparing Fick diffusivities obtained for binary subsystems with experimental data for acetone- chloroform system. The results were in good agreement. So the Fick coefficients, Maxwell-Stefan diffusion coefficient and the thermodynamic factors were predicted for the ternary mixture as well as its binary subsystems by molecular simulation in a consistent manner. The presented ternary diffusion data should facilitate the development of aggregated predictive models for diffusion coefficients of polar and hydrogen-bonding systems and allows for an efficient and consistent prediction of multicomponent Fick diffusion coefficients from molecular models.

Multicomponent Fickian solution-diffusion model for osmotic transport through membranes

Osmotically-assisted membrane processes (OAMP) are separation technologies that leverage osmotic gradients to recover water from brine. Accurate modeling of the solute-coupling effects for transmembrane transport is integral to the development and subsequent optimization of OAMP unit operations. In the literature, multicomponent transport in OAMP is commonly linearized, and species fluxes are computed using binary solution-diffusion theory and then superposed. However, recent publications highlight the large predictive errors associated with such an approach as the transport coupling between species is ignored. In this paper, we demonstrate that significant improvements in multicomponent species fluxes can be obtained when solute-coupling interactions are incorporated. Here, we present a multicomponent solution-diffusion model, by extending the binary solution-diffusion model with multicomponent diffusion theory. When multicomponent diffusion coefficients are available, we find that the average absolute deviation (AAD) of the model decreased from 21.0% to 3.0% for 7 unique combinations of forward osmosis processes involving ternary mixtures. In the absence of data for multicomponent diffusion coefficients, we demonstrate that the multicomponent model can regress the impact of transport coupling on water and solute fluxes, using excess solute permeabilities. For the case of H2O-NaCl-EtOH forward osmosis process, the AAD of the solution-diffusion model is shown to decrease from 66.1% to 7.2% for NaCl concentrations from 0.0 to 1.5 M and EtOH mass fractions from 0.0 to 0.5. These values are extended to analyze the implications on the thermodynamic and membrane area requirements of the desalination systems employing OAMP.

Direct Measurement of Aqueous Mercury(II): Combining DNA-Based Sensing with Diffusive Gradients in Thin Films.

A highly specific DNA-functionalized hydrogel sensing layer was integrated with the diffusive gradients in thin films (DGT) technique for the direct determination of aqueous mercury(II). The DNA-functionalized layer in the DGT unit exhibited both high affinity (complexation constant Kc = 1019.8 at 25 °C) and high binding capacity (9.5 mg Hg disk-1) toward Hg2+. The diffusion coefficient for Hg2+ complexed with common inorganic ligands was an order of magnitude higher than that for Hg2+ complexed with natural dissolved organic matter: 9.0 × 10-6 versus 9.8 × 10-7 cm2 s-1 at 25 °C. The performance of the DNA-DGT sensor was further assessed under variable pH (3-10) and temperature (5-40 °C) conditions, as well as across a range of hydrochemically diverse artificial and natural freshwaters. The observed effects of the environmental and solution compositional variables on Hg2+ binding to the DNA in the sensing layer were successfully accounted for by equilibrium speciation calculations and temperature-corrected, multicomponent diffusion coefficients for aqueous Hg(II). The results therefore support the use of the DNA-DGT sensor as an alternative to traditional sampling and analysis methods for measuring aqueous Hg(II) concentrations down to the nanomolar level in freshwater environments.

Stratification of polymer mixtures in drying droplets: Hydrodynamics and diffusion.

We study the evaporation-induced stratification of a mixture of short and long polymer chains in a drying droplet using molecular simulations. We systematically investigate the effects of hydrodynamic interactions (HI) on this process by comparing hybrid simulations accounting for HI between polymers through the multiparticle collision dynamics technique with free-draining Langevin dynamics simulations neglecting the same. We find that the dried supraparticle morphologies are homogeneous when HI are included but are stratified in core-shell structures (with the short polymers forming the shell) when HI are neglected. The simulation methodology unambiguously attributes this difference to the treatment of the solvent in the two models. We rationalize the presence (or absence) of stratification by measuring phenomenological multicomponent diffusion coefficients for the polymer mixtures. The diffusion coefficients show the importance of not only solvent backflow but also HI between polymers in controlling the dried supraparticle morphology.

Vanadium Transport through Cation and Anion Exchange Membranes

Transport of redox active molecules across the separator in a flow battery represents an important source of inefficiency and electrolyte-imbalance-induced capacity fade [1]. This transport can occur by diffusion, migration, and convection, with driving forces that change as cells are charged and discharged. The negative electrolyte in a vanadium redox flow battery, for example, contains V2+ and V3+ in proportions that depend on state of charge, but these species are absent from the positive side, leading to ever present concentration driving forces for diffusion across the separator. Migration alternately enhances and diminishes crossover since the electric field in the membrane orients in opposite directions during charge and discharge. Finally, hydraulic and osmotic pressure differences between the positive and negative electrolytes cause solvent flow that carries redox ions.Rigorous theoretical treatment of transport across membranes in flow batteries with concentrated-solution theory is complicated by the large number of species. For example, Nafion in a vanadium redox flow battery may contain: V2+, V3+, VO2+, VO2 +, H+, HSO4 -, SO4 2-, H2O, and fixed SO3 - anions (8). The number of multicomponent diffusion coefficients required to characterize a systems is , where n is the number of species present (after accounting for species coupled by rapid chemical equilibrium). The n multicomponent diffusion coefficients define one conductivity, transference numbers or ratios, , and diffusion coefficients of neutral combinations of species. The experimental and theoretical complexities associated with the multicomponent framework when many species are present motivates exploration of the applicability of the simpler, but less generally valid dilute-solution framework. In particular, we seek to understand how well do the relationships between diffusion coefficients, transference numbers, and conductivity predicted by dilute solution theory hold in practical membranes exposed to application-relevant electrolyte solutions? Do transference numbers predicted from conductivity and permeability measurements agree with independently measured values?Figure 1 shows measured transference numbers for the four vanadium ions relevant to flow batteries in N211 and N212 as blue and red squares, respectively. The measurements were made using a cell with three membranes and four flow compartments [2, 3]. Good agreement between the two data sets is apparent. The averages of the N211 and N212 values are plotted as crosses and reported in boxes to the right of the symbols. Transference numbers for V(IV) and V(V) are approximately an order of magnitude lower than transference numbers for V(II) and V(III). The grey squares with blue and red perimeters are the transference numbers calculated from the formula using measured conductivities and permeabilities. The average calculated values are given to the left of the data symbols, to facilitate comparison with the measured values. The measured and calculated transference numbers agree in magnitude, and no systemic differences are evident. The calculated transference number for V(III) appears to be off the experimental trend with one exception: a relatively large transference number is calculated for V(III) because it has a charge number of 3. The disagreement between the measured and calculated transference numbers for V(III) could arise from ion pairing effectively lowering the charge number. The calculated transference numbers are higher for V(II) and V(III) than V(IV) and V(V) because their permeabilities are higher while their conductivity is lower. All these results indicate the value of the study: dilute solution theory accurately predicts transference numbers for all species except perhaps V(III) in Nafion, and this deviation from the model for V(III) may inform the solvated behavior of V(III) ions.AcknowledgementsThis work was supported as part of the Joint Center for Energy Storage Research, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences. The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357.

Impact of rock properties and wettability on Tertiary-CO2 flooding in a fractured composite chalk reservoir

This study presents the experimental and numerical evaluation of tertiary-CO2 flooding (CF) using reservoir and outcrop composite chalk at reservoir conditions. We were able to reproduce the results of composite core flooding experiment and our findings show the considerable effect of rock properties and wettability on the tertiary-CO2 flooding.In our experiments, we place the composite reservoir chalk core vertically in the core-holder with the total length of 45 cm and average diameter of 3.74 cm. The composite core consists of six core plugs of 7.5 cm each and include a centralized axial hole that represents the single fracture with the diameter of 0.6 cm. The whole core plugs are sampled from the reservoir formation in North-Sea-Chalk-Field (NSCF) and are saturated with NSCF stock tank oil (STO) and synthetic connate water. Once reservoir conditions are established, the sea water is injected from the bottom of the core holder and the STO is produced from the top. After no additional produced oil is observed, water flooding (WF) is stopped and CO2 is then injected from the top and the hydrocarbon streams are produced from the bottom of the fracture. The whole core flooding is operated at constant reservoir conditions of 258 bara and 110 °C, representative of NSCF reservoir conditions. Two different chalks, one from the reservoir formation (Exp-3C) and the other from outcrop (Exp-2C) are used in this study to investigate the effect of wettability during tertiary CO2 flooding. A comprehensive compositional numerical simulation with a tuned equation of state (EOS) was developed to model the experiments. Best match for the WF experiments was achieved mainly through tuning the oil-water capillary pressure and reducing the oil relative permeability data. Although the final tuned capillary pressure and relative permeability data were different, we observe similar water saturation at the end WF experiments for Exp-3C and Exp-2C.The tertiary CF lab results were reproduced by numerical model mainly by tuning the multi-component diffusion coefficients. The produced water during CF was successfully modeled by taking the hysteresis effect into account in water-oil capillary pressure data. We also observe that although the final water saturation at the end of WF is comparable, performance of tertiary CO2 flooding for each experiment is different. The reservoir chalk experiment shows higher oil recovery during the tertiary CO2 injection.

Numerical Investigation on Heat and Mass Transfer of Volatile Flammable Gases Within the Nuclear Reactor Containment

Abstract Diffusion of volatile flammable species in the air can cause a fire risk within the nuclear reactor containment. However, computational prediction on species concentration distributions remains significantly difficult due to a shortage of multicomponent diffusion coefficients. In this work, considerable effort has been made to calculate concentration distributions of formaldehyde and benzene vapor volatilized from radiation-proof coatings of reactor containment walls. For this purpose, a numerical model is proposed to simulate species transport and concentration distributions due to full multicomponent diffusion and thermal diffusion. Meanwhile, the in-house UDFs' source code is programmed for solving diffusivities and essential thermophysical properties. After compiling and linking the source code with the numerical model, a pressure-based SIMPLE algorithm is imposed for pressure–velocity coupling calculations. Computational results indicate that concentration distributions are highly dependent on the fluid motion as well as potentially flammable areas decrease gradually with increased ventilation rates. Also, primary and secondary vortices are symmetrically distributed about the vertical centerline of the reactor containment as well as triangular secondary vortices can significantly suppress concentrations of formaldehyde and benzene vapor at the bottom portion of the containment. Finally, excellent agreement is observed between computational results and analytical solutions.

Multicomponent mutual diffusion in the warm, dense matter regime.

We present the formulation, simulations, and results for multicomponent mutual diffusion coefficients in the warm, dense matter regime. While binary mixtures have received considerable attention for mass transport, far fewer studies have addressed ternary and more complex systems. We therefore explicitly examine ternary systems utilizing the Maxwell-Stefan formulation that relates diffusion to gradients in the chemical potential. Onsager coefficients then connect the macroscopic diffusion to microscopic particle motions, evinced in trajectories characterized by positions and velocities, through various autocorrelation functions (ACFs). These trajectories are generated by molecular dynamics (MD) simulations either through the Born-Oppenheimer approximation, which treats the ions classically and the electrons quantum-mechanically by an orbital-free density-functional theory, or through a classical MD approach with Yukawa pair-potentials, whose effective ionizations and electron screening length derive from quantal considerations. We employ the reference-mean form of the ACFs and determine the center-of-mass coefficients through a simple reference-frame-dependent similarity transformation. The Onsager terms in turn determine the mutual diffusion coefficients. We examine a representative sample of ternary mixtures as a function of density and temperature from those with only light elements (D-Li-C, D-Li-Al) to those with highly asymmetric mass components (D-Li-Cu, D-Li-Ag, H-C-Ag). We also follow trends in the diffusion as a function of number concentration and evaluated the efficacy of various approximations such as the Darken approximation.

Upscaling of CO2 injection in a fractured oil reservoir

The purpose of this study is to present the numerical evaluation of the upscaling of secondary and tertiary CO2 flooding at reservoir pressure and temperature. In all simulation cases, CO2 is injected from the top of the fracture in a fracture-matrix block system and displaces oil toward the bottom of the block. Our numerical models provide comprehensive sensitivity analyses that are proved to be important for the upscaling of CO2 injection from lab to reservoir scale. In addition, we address the scale dependency of the diffusion mechanism in a large matrix-fracture domain.In our earlier studies, we have conducted a significant number of reservoir-condition CO2 flood experiments by employing fractured core systems and North Sea reservoir oil. Our experimental and numerical studies are proved to be useful to investigate the complex physical phenomena affecting the efficiency of CO2 injection in oil recovery from a fracture reservoir. The height of the core plugs used in our experiments varies from 7 to 28 cm while the fracture spacing varies between ∼4 cm and 12 cm. In all cases, we find the important role of diffusion mechanism in increasing oil recovery in a fracture-matrix system at the lab scale. However, the field matrix block size is often 1-to-2 orders of magnitude larger than that in the lab scale. Recovery mechanisms are significantly affected by the matrix dimension. For instance, the impact of diffusion mechanism on oil recovery may alter with the size of the matrix block and the fracture spacing. This highlights the importance of upscaling from lab to the field scale that is addressed in this study.We employ a compositional reservoir simulation with a developed equation of state (EOS) to model CO2 injection in a fracture-matrix system at reservoir conditions. In all the numerical simulations, the single-porosity (SP) model consists of a single axial fracture with a typical fracture aperture of 1 mm. The SP model also contains a single matrix block that feeds the producer through fracture next to it. The dimension of the fracture-matrix block varies in the SP models to account for the scale dependency of the results. In our modeling framework, we assume a network of open fractures that are homogenously distributed in the reservoir and links the oil in the matrix to the production wells. We initialize the matrix with the North-Sea-Chalk-Field (NSCF) live oil and the fracture with the injected gas (CO2). The whole displacement process is operated at the constant reservoir conditions of 3750 psia and 110 °C, representing typical NSCF reservoir conditions. Prior to conducting simulations, we successfully tune EOS parameters against the extensive PVT data, sampled from a specific fractured NSCF reservoir. The tuned EOS model assures the proper estimation of the complex phase and volumetric properties for CO2 and oil mixtures at reservoir conditions. In addition, the multi-component diffusion coefficients that are tuned using experimental data are employed as input parameters for the compositional simulations.We study the effect of several key parameters on oil recovery; e.g. matrix block size, fracture spacing, CO2 injection rate, density difference, vaporization and the diffusion. The results show that the mass transport is mainly dominated by diffusion in the lab scale which is not the case for the large matrix block size. Finally, we test the accuracy of the dual-porosity (DP) model against the SP model at various displacement conditions. Results show that when diffusion and vaporization are significant the DP model fails to predict the results of the SP reservoir model.Our findings are an important step towards modeling the tertiary-CO2 flooding in an actual fracture-chalk system. We also provide some important inputs that are necessary for upscaling tertiary-CF from a lab-scale into a field-scale reservoir model.

Impact of pressure on tertiary-CO2 flooding in a fractured chalk reservoir

The purpose of this study is to present the numerical and experimental evaluation of tertiary-CO2 flooding (CF) at high operating pressure and temperature conditions. In this study, water flooding is followed by CO2 injection into an outcrop chalk core with a centralized fracture. Our validated numerical models reproduce the results of core flooding experiments.The experiments used an outcrop core which is vertically placed in the core-holder with the total length of 28 cm and the diameter of 12.3 cm. The axial “fracture” is represented by a centralized hole with the diameter of 2.2 cm. We utilize the Wood's Metal technique to initially saturate the chalk core with the North-Sea-Chalk-Field (NSCF) live oil. The core sample is aged to restore the original chalk wettability at the operating conditions. Then, the water flooding (WF) is performed by injecting brine from the bottom of the fracture and producing the oil from the top. After no additional produced oil is observed, the WF is stopped. A “shut-in” period follows, which allows preparing the rig for tertiary-CO2 flooding. CO2 is then injected from the top and the hydrocarbon streams are produced from the bottom of the fracture. The whole core flooding is operated at constant reservoir conditions of 300 bara and 110 °C, which is higher than the initial NSCF reservoir pressure (258 bara and 110 °C). This allows us to investigate the efficiency of the tertiary-CF at a higher operating pressure condition.We employ a compositional reservoir simulation with a developed equation of state (EOS) to model the experiment. An automated history matching procedure is developed to match the experimental results. The modeling workflow is capable of taking into account the significant vaporization effect observed during CF when the rich-CO2 enters the three-phase separator.We accurately model the WF experiment through tuning the oil-water capillary pressure and relative permeability data. The numerical model is capable of reproducing the CF lab results by employing the best match multi-component diffusion coefficients. Moreover, we successfully model the excessive water production during CO2 injection by taking into account the hysteresis effect in water-oil capillary pressure and relative permeability.Comparing these results with our previous work at lower reservoir pressure shows the positive effect of pressure on increasing the efficiency of the tertiary-CF in recovering more oil from a matrix-fracture system. Also, the tuned capillary pressure and relative permeability during WF indicate an active imbibition drive and a strongly water-wet system. Our findings are an important step towards modeling the tertiary-CO2 flooding in an actual fracture-chalk system.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan–Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman–Enskog procedure using Sonine polynomial expansions. The modified Stefan–Maxwell relations are used for the description of ambipolar diffusion in the Earth’s ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

Impact of variation in multicomponent diffusion coefficients and salinity in CO2-EOR: A numerical study using molecular dynamics simulation

CO2 injection in depleted or partially depleted oil reservoirs entails a three phase flow system governed by physical processes such as molecular diffusion and solubility. Using numerical modelling, the aims of this paper are two-fold. (i) We investigate the impact of variations in the magnitude of diffusion of CO2 into oil on dissolution of CO2 in brine, and quantify the sensitivity of the simulation outputs (recovery factor and amount of CO2 stored in water and oil phases) by use of different sets of diffusion coefficients throughout the simulation based on the variations in the compositions of the fluids. (ii) We investigate whether CO2 dissolution in brine in a water-flooded system will be a competing or limiting factor for enhanced oil recovery by molecular diffusion of CO2 into oil. To this end, we use molecular dynamics (MD) simulation to determine composition-dependent diffusion coefficients for a multicomponent fluid system in a synthetic fractured reservoir that undergoes CO2 injection. In total we consider 5 components interacting in the reservoir model, namely, CO2, CH4, C4H10, C6H14 and C10H22. The fracture-matrix interaction is simplified with the dual-porosity assumption. Our results show that (i) molecular diffusion not only enhances oil recovery but also enhances CO2 dissolution in water. The enhancement, nevertheless, depends on the values of the multicomponent diffusion coefficients and may exhibit an optimal condition for dissolution due to the impact of CO2 diffusion and entrapment into matrix oil. (ii) The amount of CO2 stored in oil is strongly affected by variation in molecular diffusion coefficients (we observe up to %13 difference). (iii) The results show that there is 4% discrepancy between estimates of the recovery factor for simulation cases that are run with different values of diffusion coefficients. Therefore it is important to account for compositions-dependent diffusion coefficients in simulation of CO2-enhanced oil recovery processes.

New phenomenological model of multicomponent gas diffusion

A new phenomenological model is proposed for diffusion of multicomponent gas mixtures. Obvious general structural relations between the mass diffusion fluxes and the gradients of gas mixture components are obtained within the framework of the model in the case of the multicomponent diffusion coefficients expressed in terms of the “intrinsic” diffusion coefficients of individualmixture components. The molecular mean free path model can be used to estimate the latter.