Molecular kinetic modelling of non-equilibrium transport of confined van der Waals fluids

A thermodynamically consistent kinetic model is proposed for the non-equilibrium transport of confined van der Waals fluids, where the long-range molecular attraction is considered by a mean-field term in the transport equation, and the transport coefficients are tuned to match the experimental data. The equation of state of the van der Waals fluids can be obtained from an appropriate choice of the pair correlation function. By contrast, the modified Enskog theory predicts non-physical negative transport coefficients near the critical temperature and may not be able to recover the Boltzmann equation in the dilute limit. In addition, the shear viscosity and thermal conductivity are predicted more accurately by taking gas molecular attraction into account, while the softened Enskog formula for hard-sphere molecules performs better in predicting the bulk viscosity. The present kinetic model agrees with the Boltzmann model in the dilute limit and with the Navier-Stokes equations in the continuum limit, indicating its capability in modelling dilute-to-dense and continuum-to-non-equilibrium flows. The new model is examined thoroughly and validated by comparing it with the molecular dynamics simulation results. In contrast to the previous studies, our simulation results reveal the importance of molecular attraction even for high temperatures, which holds the molecules to the bulk while the hard-sphere model significantly overestimates the density near the wall. Because the long-range molecular attraction is considered appropriately in the present model, the velocity slip and temperature jump at the surface for the more realistic van der Waals fluids can be predicted accurately

Molecular Simulation of Transport and Storage in Shale

Over the past few years, the production of shale hydrocarbons has seen a renewed interest both in science and industry. Indeed, these fluids today constitute a significant energy and economic stake to compensate for the scarcity of so-called conventional resources. This is due to the fact that shale gases and oils represent enormous potential resources and are present all over the world. In shales, hydrocarbons are generally contained in microporous organic nanopores: kerogen. The kerogen is both the source rock of hydrocarbons and their reservoir. In shales, the extreme confinement of fluids in organic matter, high pressure-high temperature thermodynamic condition as well as very low permeabilities, imply a significant change in the state of the fluids (present in adsorbed form) and its transport mechanisms (diffusive). In this dissertation, we studied the physical properties (adsorption, transport) of kerogen as well as its carbon dioxide sequestration potential. The characteristic scales in the shales are of the order of a nanometer, which is accessible today by molecular simulations on supercomputers or even personal computers. Therefore, we have chosen to study kerogens by molecular simulation. The objective of this work is to stimulate a fundamental research on this subject in order to understand and model the mechanisms encountered in the shales and thus to respond responsibly and sustainably to the energy challenges of the years to come. Initially, the simplified kerogen models (carbon nanochannels and nanocapillaries) are developed and transport and storage of different gases are studied. This part of research is beneficial for developing analytical models of gas transport in organic nanopores. Furthermore, kerogens with different maturities were generated by molecular dynamics simulations under thermodynamic conditions typical of this type of reservoir (338 K, 20 MPa). In our simulations, the microporous network of kerogen is created by the inclusion of dummy particles, which were deleted after kerogen structure is created. The average density of the structures of organic matter created is in agreement with the experimental results obtained on such kerogens. The density is very strongly correlated with the stacking of the kerogenic polyaromatic clusters which is a strong indicator of the coherence of the simulated structures with respect to the experiments. We were interested in the transport of hydrocarbons in the kerogen and have identified the mechanisms of mass transfer through kerogens and we have been able to predict their evolution as a function of thermodynamic conditions (composition and pressure). Based on the results, it is demonstrated that the higher the maturity of kerogen, the higher is its adsorption capability. This is in agreement with experimental results of adsorption on kerogen. Furthermore, it is shown that the permeation of fluid through the kerogen membrane can be described by a diffusive formalism. The heavier alkanes have smaller diffusion coefficients and as a result, they may trap inside organic nanopores. Multicomponent diffusion of mixtures containing water and carbon dioxide is investigated and it is shown that water and carbon dioxide have lowest diffusion coefficients compared with hydrocarbons. The diffusion coefficients of hydrocarbons increases in presence of water due to higher adsorption capability of water and filling the adsorption sites. Adsorption molecular simulations of binary mixture of methane and carbon dioxide demonstrate that carbon dioxide have higher adsorption capabilities than methane. Binary mixture diffusion simulation of these two components also shows that carbon dioxide molecules have lower diffusion coefficients compared with methane. Therefore, injection of carbon dioxide into organic matter causes the methane molecules desorb and produce.;In conclusion, this dissertation work consisted of developing models, algorithms, and methodologies to predict the properties and mechanisms governing the behavior of the organic matter contained in the shales by employing molecular simulations . This work aims to improve our understanding of this type of resources

On the transport mechanisms of fluids under nanoscale confinements

The presence of fluids confined to the nanoscale has been known for some time in nature, as observed in geological formations, e.g. light hydrocarbon fluids trapped in shale reservoirs, or in biological systems, e.g. water in aquaporins. However, it is only recently that technological advances have stimulated interest in studying fluid behaviour under such conditions in more detail, due to the disruptive potential of engineering applications at these scales. Three important characteristic lengths can be identified in these flows, namely the molecular mean free path λ (denoting the average distance travelled by particles between collisions), the diameter of fluid constituent particles σ, and the channel size L. At the microscale, λ may be become comparable to L, leading to an increased collision frequency with the confining walls rather than with other particles. In this scenario, the gas is no longer in quasi-local thermodynamic equilibrium state as assumed by continuum fluid dynamics, and the Boltzmann equation must be used to accurately describe its behaviour. At the nanoscale, where L is comparable to σ, excluded volume effects and non-locality of collisions become significant. Consequently, the Boltzmann description becomes invalid and alternative kinetic models, such as the Enskog equation, or a more fundamental approach, such as molecular dynamics simulations, must be considered. This thesis aims to contribute to the understanding of transport phenomena at the nanoscale, spanning fluid conditions from the dense to the rarefied gas, and considering different channel sizes, geometries, and surface roughnesses. In order to do so, a fluid composed of hard spheres confined between mathematical surfaces has been studied because, despite its simplicity, this model retains the essential physics of more realistic systems. Self-diffusion of atoms is the simplest transport mechanism, and yet it is not fully understood in the context of molecularly confined flows. Firstly, in this thesis, a systematic study of this process was carried out for a fluid within a slit geometry, delimited by two infinite parallel plates. One of the most distinctive features of the fluid behaviour in confined conditions is the preferential fluid structuring that occurs next to the walls, due to the limited mobility of particles in the normal direction to the wall. To clarify a source of debate in the literature, it is proved that, despite the strong fluid inhomogeneities, the self-diffusivity based on the Einstein relation can still be used to describe Fickian diffusion under molecular confinements, the latter being explicitly computed in simulations by tracking the dynamics of tagged particles. The interplay of the underlying diffusion mechanisms, i.e. molecular and Knudsen diffusion, is then identified, by differentiating between fluid-fluid and fluid-wall collisions. The key finding is that the Bosanquet formula, previously used for describing the diffusive transport of rarefied gases, also provides a good semi-analytical description of self-diffusivities for dense fluids under tight confinements, as long as the channel size is not smaller than five molecular diameters. Importantly, this allows one to predict the self-diffusion coefficient in a wide range of Knudsen numbers, including the transition regime, which was not possible before. Although diffusion is believed to dominate the fluid transport at the nanoscale, it is shown that the Fick first law fails to describe the surprising fluid behaviour that occurs within confined straight channels. For example, since Knudsen’s experimental work circa 1910, it has been known that the Poiseuille mass flow rate along microchannels features a stationary point as the fluid density decreases, referred to as the Knudsen minimum. However, when the characteristic length L is further decreased, this minimum has been reported to disappear and the mass flow rate monotonically increases over the entire range of flow regimes. Using an analytical procedure, in this work it is shown, for the first time, that this vanishing occurs because the decay of the mass flow rate, due to the decreasing density effects, is overcome by the enhancing contribution to the flow provided by the fluid velocity slip at the wall. The latter phenomena become more important in tight geometries, ultimately being capable of modifying the flow dynamics. The physical mechanisms underlying fluid slippage at walls are not well understood at the nanoscale, where dense and confinement effects add several complexities. For example, it is unclear to what extent the Navier-Stokes equations with slip boundary conditions can accurately describe the fluid behaviour under molecular confinements. Furthermore, the effects of fluid density and confinement as well as the surface properties, such as curvature and microscopic roughness, on velocity slip are not fully understood. Using a simple fluid-wall framework, it is shown that the interfacial friction coefficient, which is inversely proportional to the slip length, is linear with the peak fluid density at the wall, regardless of the nominal density, confinement ratio, and wall curvature. The peak density turns out to increase as the nominal density increases, with a mild dependence on confinement and curvature. Furthermore, the friction coefficient scales according to the Smoluchowski prefactor with respect to the influence of the accommodation coefficient, similar to the case of a rarefied gas where the same gas-surface dynamics are considered – despite the physics next to the wall are very different. Altogether, these results represent a significant step forward in understanding the mechanisms of fluid flow in molecular-scale systems, and have important implications for the design and optimisation of nanofluidic devices

THE EFFECT OF PORE SPACE ON FLUID FLOW AND PHASE BEHAVIOR IN TIGHT FORMATIONS

Unconventional resources have led to a new abundance of natural oil and gas supply all over the world over the past decade and are expected to play a vital role in the future of this industry. Despite tremendous growth of extraction technologies which increased the production of these reserve significantly, knowledge and understanding of flow and phase behavior of the fluid in unconventional resources has remained insufficiently explored. Accurate understanding of phase behavior of fluids trapped in the extremely small pores of these resources, especially shale reservoirs, is the center of attention for a lot of scholars globally. Although numerous mathematical and theoretical studies are available to explain phase behavior of confined fluids, limited number of studies attempted to explore this effect experimentally. Experimental data are invaluable in providing the deep insight needed to explain this effect, validate available models, and introduce methods of characterizations that would help with optimization of production plans. The present work is an attempt to enhance the understanding of fluid phase behavior in tight formations through experimental investigations. Microscopic effects and their macroscopic consequences that plays a crucial role in adding to the complexity of fluid phase behavior in these reservoirs are explored and explained prior to discussing modeling and experimental works. Fundamental knowledge of phase behavior and thermodynamic principals that are essential for exploring this effect and for comparing the shortcomings of established experimental approaches in phase behavior studies of conventional reservoirs are covered. A thorough review on the existing theoretical and experimental studies on the topic, considering their results and predictions, is conducted to shed more light on the need for further experimental investigation of phase behavior alterations in tight gas condensate formations. Isochoric method is an indirect high-precision way of phase transition point determination which is commonly used in other disciplines where a clear non-visual determination of phase transition of a fixed volume of fluid is needed. The present work provides an insight into using this approach in determining dew pint pressure (DPP) for gas mixtures inside and outside of the porous media. A semi-automated apparatus for measuring and monitoring equilibrium conditions along with fluid properties is designed based on the isochoric method. The apparatus provides constant volume, variable pressure (0 to 1500 psi), and variable temperature (290 to 410 K) experimental conditions. Pressure and temperature measurements are used to detect the phase transition point along the constant-mole-constant-volume line based on the change in the slope of this line at the transition point. A packed bed of BaTiO3 nanoparticles, providing a homogenous porous medium with pores of 1 to 70 nm is used as a representative nano-scale porous medium. The synthesized porous medium is very helpful in uncoupling the effect of pore size from the effect of mineralogy on the observed deviations in behavior, providing a volume more than 1000 times larger than typical nano channels. The result is a set of Isochoric lines for bulk and confined sample, plotted on the phase envelope to demonstrate the change in saturation pressure. Phase envelopes (P-T diagrams) of the same mixture using different equations of state are constructed and the accuracy of each of these equations of state in providing an experimentally detected DPP is discussed. Many attempts in explaining the shift in saturation pressures of the reservoir fluid confined in the narrow pores of unconventional reservoirs compared to those of the bulk can be found in the literature. However, there are some contradictions between the predicted behavior using different mathematical approaches. Experimental data could be substantially helpful in both validating models and improving the understanding of the fluid behavior in these formations. Contrary to what many published models predict, the results of the present work show that confinement effects shift the DPP towards higher values compared to the bulk for a fixed temperature in the retrograde region. In the non-retrograde region, however, this shift is towards lower dew point pressure values for the confined fluid compared to the bulk. Capillary condensation is identified to be the main source of the deviations observed in the behavior of fluids inside nanopores. We evaluated published models, including those based on EOS modifications, by comparing it to experimental results to provide a quantification of their accuracy in estimating saturation pressure values for the confined mixture. Future applications of the present work for directing it towards an all-inclusive theory for all reservoir fluids in unconventional formations are clearly outlined.

Comprehensive characterization of shale gas seepage in nanoscale organic-rich shales

Unlike conventional gas reservoirs, the shale gas resources are widely distributed in organic-rich shale formations with most pore sizes down to nanoscale. Such nanoscale confinement has invalidated the conventional gas transport mechanisms which are characterized by the Navier-Stokes equations. A common practice in shale reservoir simulation, which arbitrarily increases intrinsic matrix permeability to match the production data, has been proven inefficient and unreliable. This research work aims to bridge the gap in scientific understanding of the shale gas transport across the hierarchical structures of organic-rich matrix by developing different analytical and numerical models which incorporate various mechanisms in shale formations. More specifically, this work explores the qualitative and quantitative influences of the rarefaction effect, real gas effect, multilayer adsorption, surface diffusion, nano-confinement effect, and pore-structure heterogeneity on the shale gas flow. First, a new unified gas transport model is developed by modifying Bravo’s model to describe the rarefaction which is commonly in presence in nanopores. Particularly, a straight capillary tube is characterized by a conceptual layered model consisting of a viscous flow zone, a Knudsen diffusion zone, and a surface diffusion zone. To specify the contributions of the viscous flow and the Knudsen diffusion, the virtual boundary between the viscous flow and Knudsen diffusion zones is firstly determined based on Kennard’s analytical kinetics approach. Then, the model considers the real gas effect, multilayer adsorption and nano-confinement effect to quantify the density oscillation and phase behavior in confined nanopores. Meanwhile, the apparent permeability (AP) model is analytically derived and numerically simulated at core-scale. In addition, the field scale production rate is numerically calculated by coupling the nanoscale mechanisms. Furthermore, the pore-structure heterogeneity impact on production rate is studied by the fuzzy statistical method in which the Monte Carlo simulation is implemented for the sensitivity analyses of the structural parameters in the fractal model. The proposed analytical model has been successfully validated against molecular dynamic simulation and experimental flux results for five types of gases (i.e., methane, nitrogen, helium, argon, and oxygen) with the assistance of optimization methods. One of the advantages of the new unified gas transport model is its great flexibility which is capable to cover the full flow regimes. It is found that the increase of real gas viscosity can reduce the total molar flux in the inorganic pores up to 66.0%. In addition, it is observed that the pore confinement effect is of importance when the pore size is smaller than 50 nm. The apparent permeability is found to increase greatly as the adsorption layer number increases, implying that the application of Langmuir model in existing gas transport models may substantially underestimate it. Given organic nanopores, the contribution of surface diffusion is tangible when the pore size is below 150 nm and the Knudsen diffusion is negligible under high pressures. Compared with the flow mechanisms in the nanopores, it is found that the fractal dimension of the tortuosity has the largest impact on the production rate than the pore size and the fractal dimension of pore size distribution. In addition, the fuzzy statistical method can quantify the confidence interval within which the satisfactory flow rate results can be acquired. The fuzzy statistical method enables more flexibility to predict the realistic production profile with significant data fluctuations