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Brazil is the fifth largest country by area in the world, with a variety of climates in its territory. This work assesses the economic attractiveness of domestic rainwater harvesting direct feed systems, for the replacement of non-drinking water, in 148 locations of the Brazilian territory considering hourly rainfall data for the 14-year period between 2008 and 2021. The water tariff and consumption data for each location were also considered along with estimated hourly and monthly consumption patterns. With annual operating expenses at 1% of the capital expenditure and an annual discount rate of 8%, the net present value for the 14-year period is positive in only 15 locations, which are among those with the highest water tariffs in the country. The results of these base case simulations discourage the installation of domestic RWH systems in most of the Brazilian locations considered. However, the results also show that, depending on house occupancy, filtration equipment cost, water tariff, and catchment area, outcomes more favorable to the installation of RWH systems are obtained, especially in cities of Brazil's southern and southeastern regions.
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In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.
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A recently reported modification of the zeolitic-imidazolate framework-8 (ZIF-8) with partial replacement of the 2-methylimidazolate (mIm) linker with benzimidazolate (bIm), namely ZIF-7-8, is investigated with molecular simulations using a first-time reported force field. The size of the ZIF-7-8 aperture, which governs the gas-separation efficiency of this material and which has not been estimated before for this modification, is smaller than that of the original ZIF-8. The diffusivities of CO2, N2, and CH4 estimated through transition state theory calculations result in remarkably high diffusion selectivities for CO2/CH4 and CO2/N2 mixtures. This performance enhancement is investigated in terms of structural flexibility in the form of the aperture motion through extensive estimation of the effective diameter, the total effective area, and the motion of the aperture linkers, of both ZIF-8 and ZIF-7-8. Both apertures exhibit an oscillation through the rotation of the linkers, which are adjusted according to the size of the penetrant molecules the moment they pass through it. Finally, a subsequent analysis reveals that there is strong dependency of the separation performance on the bIm-to-mIm ratio: below 33% bIm incorporation, the appearance of ZIF-8-alike wide apertures decreases dramatically the size-based selectivity of the mixtures in ZIF-7-8.
RESUMEN
The influence of a zeolitic imidazolate framework (ZIF)'s metal identity on its gas separation performance is studied extensively through molecular simulations for a variety of gases. ZIF-8 is used as the original framework for alterations of different metal substitutes of the Zn2+ metal. ZIF-8 consists of cages connected by narrow apertures that exhibit flexibility through "swelling", allowing for relatively large penetrants to diffuse. Replacing the central metal atom in the basic tetrahedral unit of ZIF-8 with Cd, Co or Be results in three different structures with increasing bonding stiffness with their neighboring atoms. The metal modification approach offers a way to control the flexibility and the size of the aperture, which constitutes the main energy barrier of the penetrant's hop-like diffusion between the framework's cages. Newly developed force fields are reported and utilized here; the new frameworks are compared to the original one, in terms of the diffusivity of various gas molecules as a function of their size (from He to n-butane). The correlation of the gas diffusivity with the aperture flexibility-molecular size relation is investigated. The results reveal that the aperture flexibility-molecular size relation governs the diffusivity, which shapes a common trend along all modifications. Furthermore, a new generalized method is employed for the screening of the various modifications for specific gas separations. This method is useful to detect optimum separation performance for the various modifications: CdIF-1 (Cd) for n-butane/iso-butane mixture; ZIF-67 (Co) for propylene/n-propane and ethylene/ethane mixtures; BeIF-1 (Be) for CO2/C2H6, CO2/CH4 and CO2/N2 mixtures.
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We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior.
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We extend the SAFT-VR Mie equation of state to calculate adsorption isotherms by considering explicitly the residual energy due to the confinement effect. Assuming a square-well potential for the fluid-solid interactions, the structure imposed by the fluid-solid interface is calculated using two different approaches: an empirical expression proposed by Travalloni et al. ( Chem. Eng. Sci. 65 , 3088 - 3099 , 2010 ), and a new theoretical expression derived by applying the mean value theorem. Adopting the SAFT-VR Mie ( Lafitte et al. J. Chem. Phys. , 139 , 154504 , 2013 ) equation of state to describe the fluid-fluid interactions, and solving the phase equilibrium criteria, we calculate adsorption isotherms for light hydrocarbons adsorbed in a carbon molecular sieve and for carbon dioxide, nitrogen, and water adsorbed in a zeolite. Good results are obtained from the model using either approach. Nonetheless, the theoretical expression seems to correlate better the experimental data than the empirical one, possibly implying that a more reliable way to describe the structure ensures a better description of the thermodynamic behavior.
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Applying classical molecular dynamics simulations, we calculate the parallel self-diffusion coefficients of different fluids (methane, nitrogen, and carbon dioxide) confined between two {101Ì4} calcite crystal planes. We have observed that the molecules close to the calcite surface diffuse differently in distinct directions. This anisotropic behavior of the self-diffusion coefficient is investigated for different temperatures and pore sizes. The ion arrangement in the calcite crystal and the strong interactions between the fluid particles and the calcite surface may explain the anisotropy in this transport property.
RESUMEN
We propose a new method to calculate the diffusion coefficient within molecular dynamics simulations for either homogeneous or inhomogeneous fluids. We formulate such method by solving analytically the Smoluchowski equation for a linear potential of mean force within a thin layer with absorbing boundary conditions. The bulk, or homogeneous, fluid diffusion emerges as a particular case in this approach. We apply this method to bulk liquid water at atmospheric pressure and different temperatures using the SPC/E water force field. We show that our method gives results as accurate as the traditional Einstein-Smoluchowski method, avoiding the fitting procedure required in the traditional method. We also apply this method for molten sodium chloride showing its applicability for multicomponent systems. The water vapor-liquid interface is studied as an example of an inhomogeneous system. We calculate all the components of the diffusion tensor at the interface. We observe the same anisotropy between the perpendicular and the parallel components at the interface as it has been noted in the literature. We also calculate the perpendicular self-diffusion coefficient of methane near the calcite surface showing that this coefficient is much lower than the parallel diffusion coefficients. We believe that this new unified approach is a very promising technique for both bulk and confined media.