Two-parameter Equation Research Articles

A new two-parameter equation for correlation and prediction of densities as a function of concentration and temperature in binary aqueous solutions

A detailed numerical analysis of the literature densities in aqueous solutions was performed in order to obtain their representation which will be simple and accurate for engineering and physical calculations, and will also be suitable for reliable predictions of densities as a function of concentration and temperature. This was achieved by introducing a new two-parameter equation for densities which includes the pure water density at a given temperature and the function F(w)=Aw+Bw2. The adjustable parameters A and B are independent of temperature and w is the mass fraction of dissolved in water substance. A and B parameters were evaluated for 643 aqueous solutions of strong and weak inorganic electrolytes, ionic liquids, organic acids, salts of organic acids, amino acids, sugars, peptides and other industrially and biologically important substances.

An investigation of different gas injection scenarios as enhanced condensate recovery method in a naturally fractured gas-condensate reservoir

In gas condensate reservoirs, when the bottom hole pressure falls below the dew point pressure condensates are formed. This causes hydrocarbon liquid saturation around the well bore region. This phenomenon is called condensate blockage or condensate banking. Condensate recovery reduction due to condensate banking near the well bore region is an important problem in gas condensate reservoirs. The common method to prevent the condensate banking is gas cycling (reinjection of produced dry gas) into the reservoir that can contribute to the condensate vaporization, thus increasing the condensate recovery factor. The objective of this study was to find a suitable replacement for gas cycling. For this purpose, an investigation on the effects of injection of different types of gases (CO2, N2, and C1) on enhance condensate recovery factor and pressure maintenance were performed. This research was done on one of the Iranian gas condensate reservoirs through a compositional simulator. The two-parameter Peng-Robinson equation of state (EOS) and Lohrenz-Bray-Clark correlation were used to model reservoir fluid properties through regression on the pressure-volume-temperature (PVT) experimental data. A fracture network was distributed over the reservoir, so a dual porosity/dual permeability model was selected for better evaluation of the fracture system. Then, various scenarios of natural depletion and CO2, N2, C1, and gas cycling injection were studied. The results showed that CO2 injection scenario being associated with the highest efficiency compared to that of other gases.

Phase behavior of an aqueous two-phase ionic liquid containing (N-butylpyridiniumtetrafluoroborate + sulfate salts + water) at different temperatures

Liquid–liquid equilibrium (LLE) data for N-butylpyridiniumtetrafluoroborate ([BPy]BF4)+sulfate salt+H2O systems have been determined experimentally at T=(298.15, 308.15, and 318.15)K. The binodal curves agree with an empirical nonlinear expression developed by Merchuk, while the tie-line data are described by the Othmer–Tobias, Bancroft, two-parameter, and Setschenow-type equations. Factors, such as salts, that affect the binodal curves are also studied. The effective excluded volume (EEV) values obtained from the bimodal models for the two systems were determined, and the salting-out capabilities of different salts follow the order of Na2SO4>(NH4)2SO4, which may be related to the Gibbs free energy of hydration of the ions (△Ghyd). Furthermore, the tie line is also discussed to evaluate the phase separation capabilities of the investigated systems. These reported data provide a significant contribution to the further study of extraction processes using ionic liquids (ILs).

Water Sorption Isotherm of Pea Starch Edible Films and Prediction Models.

The moisture sorption isotherm of pea starch films prepared with various glycerol contents as plasticizer was investigated at different storage relative humidities (11%–96% RH) and at 5 ± 1, 15 ± 1, 25 ± 1 and 40 ± 1 °C by using gravimetric method. The results showed that the equilibrium moisture content of all films increased substantially above aw = 0.6. Films plasticized with glycerol, under all temperatures and RH conditions (11%–96%), adsorbed more moisture resulting in higher equilibrium moisture contents. Reduction of the temperature enhanced the equilibrium moisture content and monolayer water of the films. The obtained experimental data were fitted to different models including two-parameter equations (Oswin, Henderson, Brunauer–Emmitt–Teller (BET), Flory–Huggins, and Iglesias–Chirife), three-parameter equations Guggenhiem–Anderson–deBoer (GAB), Ferro–Fontan, and Lewicki) and a four-parameter equation (Peleg). The three-parameter Lewicki model was found to be the best-fitted model for representing the experimental data within the studied temperatures and whole range of relative humidities (11%–98%). Addition of glycerol increased the net isosteric heat of moisture sorption of pea starch film. The results provide important information with estimating of stability and functional characteristics of the films in various environments.

Towards a cosmological neutrino mass detection

Future cosmological measurements should enable the sum of neutrino masses to be determined indirectly through their effects on the expansion rate of the Universe and the clustering of matter. We consider prospects for the gravitationally lensed Cosmic Microwave Background anisotropies and Baryon Acoustic Oscillations in the galaxy distribution, examining how the projected uncertainty of $\approx15$ meV on the neutrino mass sum (a 4$\sigma$ detection of the minimal mass) might be reached over the next decade. The current 1$\sigma$ uncertainty of $\approx 103$ meV (Planck-2015+BAO-15) will be improved by upcoming 'Stage-3' CMB experiments (S3+BAO-15: 44 meV), then upcoming BAO measurements (S3+DESI: 22 meV), and planned next-generation 'Stage 4' CMB experiments (S4+DESI: 15-19 meV, depending on angular range). An improved optical depth measurement is important: the projected neutrino mass uncertainty increases to $26$ meV if S4 is limited to $\ell>20$ and combined with current large-scale polarization data. Looking beyond $\Lambda$CDM, including curvature uncertainty increases the forecast mass error by $\approx$ 50% for S4+DESI, and more than doubles the error with a two-parameter dark energy equation of state. Complementary low-redshift probes including galaxy lensing will play a role in distinguishing between massive neutrinos and a departure from a $w=-1$, flat geometry.

Coadsorption of Human Immunoglobulin G and Bovine Serum Albumin on a p-Aminohippuric Acid Based Mixed-Mode Resin

Mixed-mode chromatography (MMC) has been developed as a cost-effective new technique for antibody purification. Nuvia cPrime (NP) is a novel MMC resin with p-aminohippuric acid as the functional ligand. The adsorption of human immunoglobulin G (IgG) and bovine serum albumin (BSA) on NP was measured, including single component adsorption at different pH and binary coadsorption at various pH values and IgG/BSA mass ratios. Typical pH-dependent adsorption behavior was found in the single component adsorption which can be described by a two-parameter equation that offered a convenient way to analyze pH effects. Moreover, a competitive and preferential adsorption of IgG to BSA was investigated in binary coadsorption. Extended Langmuir (EL) and Extended Langmuir−Freundlich (ELF) models with parameters obtained from single-component isotherms were used to describe the coadsorption behaviors of IgG and BSA at various mass ratios. The results indicated the ELF model was more suitable for IgG adsorption, while the ...

A Parametric Energy Model for Energy Management of Long Belt Conveyors

As electricity prices continue to rise, the increasing need for energy management requires better understanding of models for energy-consuming applications, such as conveyor belts. Conveyor belts are used in a wide range of industries, including power generation, mining and mineral processing. Conveyor technological advances are leading to increasingly long conveyor belts being commissioned. Thus, the energy consumption of each individual belt conveyor unit is becoming increasingly significant. This paper proposes a generic energy model for belt conveyors with long troughed belts. The model has a two-parameter power equation, and it uses a partial differential equation to capture the variable amount of material mass per unit length throughout the belt length. Verification results show that the power consumption calculations of the newly proposed simpler model are consistent with those of a known non-linear model with an error of less than 4%. The online parameter identification set-up of the model is proposed. Simulations indicate that the parameters can be identified successfully from data with up to 15% measurement noise. Results show that the proposed model gives better predictions of the power consumed and material delivered by a long conveyor belt than the steady-state models in the current literature.

Two-Parameter Fuzzy-Valued Stochastic Integrals and Equations

This article is concerned with notions of fuzzy-valued stochastic integrals driven by two-parameter martingales and increasing processes. We present their main properties and formulate next two-parameter fuzzy-valued stochastic integral equations. We establish the existence and uniqueness of solutions to such equations as well as their additional properties.

Modeling of Variably Saturated Flow in Response to Pumping from an Unconfined Aquifer: Numerical Evidence of Gravity-Delayed Drainage and Its Parameterization

AbstractA numerical model of variably saturated axis-symmetric radial flow is employed to simulate and parameterize the gravity-delayed drainage, viewing it as the vertical accretion over falling water table. Numerical experiments are conducted to simulate the head fields at advancing discrete times as pumping is sustained at the assigned well. The head fields are invoked to generate the corresponding time series of water table elevation and the accretion rate over it. Employing these time series, the optimal structure/parameters of gravity-delayed drainage equation are estimated by the least-squares approach under a variety of hydrogeologic/geometric conditions. It is revealed that generally, a two-parameter gravity-delayed drainage equation reproduces parsimoniously the accretion time series.

Comprehensive derivation of bond-valence parameters for ion pairs involving oxygen.

Published two-body bond-valence parameters for cation-oxygen bonds have been evaluated via the root mean-square deviation (RMSD) from the valence-sum rule for 128 cations, using 180,194 filtered bond lengths from 31,489 coordination polyhedra. Values of the RMSD range from 0.033-2.451 v.u. (1.1-40.9% per unit of charge) with a weighted mean of 0.174 v.u. (7.34% per unit of charge). The set of best published parameters has been determined for 128 ions and used as a benchmark for the determination of new bond-valence parameters in this paper. Two common methods for the derivation of bond-valence parameters have been evaluated: (1) fixing B and solving for R(o); (2) the graphical method. On a subset of 90 ions observed in more than one coordination, fixing B at 0.37 Å leads to a mean weighted-RMSD of 0.139 v.u. (6.7% per unit of charge), while graphical derivation gives 0.161 v.u. (8.0% per unit of charge). The advantages and disadvantages of these (and other) methods of derivation have been considered, leading to the conclusion that current methods of derivation of bond-valence parameters are not satisfactory. A new method of derivation is introduced, the GRG (generalized reduced gradient) method, which leads to a mean weighted-RMSD of 0.128 v.u. (6.1% per unit of charge) over the same sample of 90 multiple-coordination ions. The evaluation of 19 two-parameter equations and 7 three-parameter equations to model the bond-valence-bond-length relation indicates that: (1) many equations can adequately describe the relation; (2) a plateau has been reached in the fit for two-parameter equations; (3) the equation of Brown & Altermatt (1985) is sufficiently good that use of any of the other equations tested is not warranted. Improved bond-valence parameters have been derived for 135 ions for the equation of Brown & Altermatt (1985) in terms of both the cation and anion bond-valence sums using the GRG method and our complete data set.

Sorption of Cu2+ and Cd2+ from aqueous solutions by Modified and Unmodified Breadfruit Seed Hull: Isotherm Studies.

The ability of an economically cheap adsorbent material of natural origin, African breadfruit seed hull, was assessed for Cu(II) and Cd(II) ions’ adsorption from aqueous solutions. The effects of adsorbent dose, particle size and initial metal ion concentrations were investigated in a batch adsorption process. The experimental data were analyzed using five two-parameter isotherm equations (i.e., Langmuir, Freundlich, Temkin, Harkins-Jura and Halsey isotherm models). Freundlich and Halsey models provided the best description for the adsorption data while the other three models gave fairly good interpretation to the experimental adsorption data. The maximum adsorption capacity corresponding to saturation of sites (q max ), obtained from the Langmuir plots, were 7.76 and 8.06 mg g -1 for Cu(II) and Cd(II) onto the unmodified breadfruit seed hull (UBSH) and 12.67 and 13.97 mg g -1 , respectively for Cu(II) and Cd(II) adsorption onto the modified breadfruit seed hull (MBSH). The experimental results showed that there was an enhancement in the removal of the metal ions by the mercaptoacetic acid-modified breadfruit seed hull. DOI: http://dx.doi.org/10.17807/orbital.v7i3.625

Particle penetration and deposition inside historical churches

Particle sources and deposition inside two historical churches, differing in size and construction were examined. The particle concentrations indoors and outdoors were monitored for at least 10 months. The air exchange rate (AER) was determined by fitting an exponential decay curve to the recorded concentration of indoor-generated CO2. The two-parameter mass balance equation, taking into account the particle sources and sinks in the indoor environment of churches, was used to determine the particle deposition velocities and penetration factors. Large indoor and outdoor particle concentration variability helped to separate the effects of penetration and deposition losses. For example, liturgical services regularly generated high indoor particle concentrations, owing to the burning of incense. During the particle concentration decay after the services, losses due to deposition could be reliably determined, whereas the events of high outdoor aerosol concentrations with no emission of particles indoors allowed the penetration factors to be precisely determined. The minimal AER values of 0.1 and 0.3 h−1 were observed in the closed brick and wooden church, respectively. Typically, area-averaged deposition velocities for particles of diameters 0.3–1 μm or above 1 μm were 1.5·10−5 and 2.1·10−5 m/s, respectively, and were very consistent between the two churches studied in spite of the differences in their design, size, construction materials and pattern of use. Penetration factors ranged from 0.7 to 0.86.

Adsorption of Pb(II) on raw and organically modified Jordanian bentonite

AbstractA comparative study using bentonite (BT), hexadecyltrimethylammonium-modified bentonite (BT-HDTMA) and phenyl fatty hydroxamic acid-modified bentonite (BT-PFHA) as adsorbents for the removal of Pb(II) has been proposed. These adsorbents were characterized by X-ray diffraction, X-ray fluorescence, Fourier-transform infrared spectroscopy and surface area measurement. Cation exchange capacity was also determined in this study. The adsorbent capabilities for Pb(II) from aqueous solution were investigated, and the optimal experimental conditions including adsorption time, adsorbent dosage, the initial concentration of Pb(II), pH and temperature that might influence the adsorption performance were also investigated. The experimental equilibrium adsorption data were tested by four widely used two-parameter equations, the Langmuir, Freundlich, Dubinin- Radushkevich (D-R) and Temkin isotherms. The monolayer adsorption capacities of BT, BT-HDTMA and BT-PFHA for Pb(II) were 149.3, 227.3 and 256.4 mg/g, respectively. The experimental kinetic data were analysed by pseudo-first order, pseudo-second order and intraparticle diffusion kinetics models. The experimental data fitted very well with the pseudo-second order kinetic model. Determination of the thermodynamic parameters, ΔG, ΔH and ΔS showed the adsorption to be feasible, spontaneous and exothermic.

A thermodynamic study on the phase behaviour of ethanol and 2-propanol in aqueous ammonium sulphate/sodium sulphate solution

Liquid–liquid equilibrium (LLE) data for quaternary systems containing ethanol+2-propanol+salt [(NH4)2SO4/Na2SO4]+water were experimentally determined at 308.15, 318.15 and 328.15K. Binodal curves were fitted to four empirical nonlinear equations, whereas tie-lines were fitted to the Setschenow-type equation and its temperature-dependent expression as well as another two-parameter equation. All of the models were successfully correlated with the experimental data. Factors affecting the phase-forming abilities of the investigated systems were also studied, such as the temperature, mass fraction of ethanol in the alcohol mixture and type of salt. The effective excluded volume values for the studied systems also were determined to evaluate the phase separation abilities of investigated systems. These data can be used for the development and design of extraction processes utilizing such systems.

Possibilities of retention prediction in fast gradient liquid chromatography. Part 3: Short silica monolithic columns

We studied possibilities of prediction of the gradient elution data for alkylbenzenes, flavones and phenolic acids on two short octadecyl silica gel monolithic columns, namely a Chromolith Flash C18, 25×4.6mm, and a “new generation” Chromolith High Resolution C18, 50×4.6mm, in fast 1−2min gradients. With fixed short gradient times and varying gradient ranges of acetonitrile concentration in water, high flow rates of the mobile phase (3−5mL/min) could be used. The gradient elution data were predicted from four gradient models based on two-parameter and three-parameter isocratic retention equations. Various gradient retention models can be used for prediction of chromatograms and optimization of separation within a fixed gradient time. A two-parameter log−log model introduced in 1974 and a three-parameter model introduced in 1980 provided slightly more accurate prediction than the Linear Solvent Strength (LSS) semi-logarithmic two-parameter model, most frequently used in reversed-phase LC. A three-parameter model introduced in 1978 provided slightly improved accuracy of prediction of gradient data with respect to two-parameter models, in contrast to another, more recent three-parameter empirical model introduced in 2010 (which failed for gradients starting at a non-zero concentration of acetonitrile). Both a longer (5cm) and more efficient Chromolith HR column and a shorter (2.5cm) slightly less efficient Chromolith Flash column provide useful separations in fast gradients (1−2min) at high flow rates (3.5−5mL/min), especially in second dimension of two-dimensional LC×LC, in combination with HILIC separation on monolithic microcolumn in D1.

Liquid–liquid equilibria for 1-butyl-4-methylpyridinium tetrafluoroborate and inorganic salts aqueous two-phase systems

Liquid–liquid equilibria were determined at 305.15 K for aqueous two-phase systems (ATPSs) containing 1-butyl-4-methylpyridinium tetrafluoroborate + inorganic salts (NaH2PO4·2H2O, (NH4)2SO4, Na2SO4, and Na2HPO4·12H2O) + water. Four nonlinear equations were used to correlate the binodal data, and the binodal curves were used to describe and display the effect of different experimental salts on phase separation. Furthermore, a simple, two-parameter equation, along with the Othmer–Tobias and Bancroft equations, was used to correlate the tie-line data. All the results showed good agreement between the fitting equations and the experimental data. The effect of temperature on the binodal curves and tie-lines for 1-butyl-4-methylpyridinium tetrafluoroborate + Na2SO4 + water systems was studied at T = 298.15, 311.15 and 338.15 K. Additionally, the effect of Gibbs energy on the salting-out ability of the different inorganic salts was discussed. From this study, we concluded that these salting-out abilities decline in the following order: Na2HPO4 > Na2SO4 > (NH4)2SO4 > NaH2PO4. These data may be helpful for the further investigation of ATPSs based on the ionic liquid 1-butyl-4-methylpyridinium tetrafluoroborate. In summary, our study determined the basic extraction data for this aqueous two-phase system and developed a fundamental method for the further study of material separation.

Experimental Determination of Phase Equilibrium in Aqueous Two-Phase Systems Containing Ionic Liquids and Sodium Salts at Different Temperatures

The binodal curves of 1-butyl-3-methylpyridinium tetrafluoroborate ([3-MBP][BF4]) + NaH2PO4/Na2SO4 + H2O aqueous two-phase systems (ATPSs) at T = (310.15, 318.15, and 327.15) K were experimentally determined. Three nonlinear equations were fit to the binodal data. Tie-line data were fit to the Othmer–Tobias, Bancroft, two-parameter, and Setschenow-type equations. The results were consistent with the experimental data. The effective excluded volume (EEV) values were determined using the binodal model for these two systems. According to the binodal curves and tie-line data obtained at different temperatures, the effect of temperature on the ATPSs was also discussed.

Calculation of critical and engineering parameters for a supercritical water oxidation reaction system as exemplified by water-aromatic hydrocarbon binary mixtures

Approaches to the calculation of critical and engineering process parameters of the supercritical water oxidation (SCWO) of water-aromatic hydrocarbon (benzene, toluene, and phenol, which are the most hazardous chemicals contained in industrial wastewater) binary mixtures are discussed. The calculations were performed based on an example of the oxidation of 10% aqueous solutions of benzene, toluene, and phenol with the use of the Redlich-Kwong two-parameter equation of state. The critical parameters of the reaction mixture components, the parameters of the equation of state, the minimum oxygen amount required for complete oxidation, the fuel content of the reactor, the maximum values of the reaction temperature and pressure, the composition and critical parameters of the expected reaction products, etc., were calculated. The calculated critical reaction parameters can be used as control signals for an automatic control system in the development of a SCWO process for sewage destruction. The high ecological efficiency of the process was demonstrated using the bioassay testing of starting solutions and reaction products.

Refinements to the relaxation model for sound propagation in porous media

The relaxation formulation for sound propagation in porous media [D. K. Wilson, J. Acoust. Soc. Am. 94(2), 1136–1145 (1993)] was intended to provide a phenomenologically correct model with relatively simple equations. This paper presents several refinements, which connect the relaxation model more clearly to others in the literature, and clarify interpretation of the parameters. In particular, the relaxation function is applied to the dynamic tortuosity (rather than the inverse of the complex density), and the vorticity and thermal relaxation times are related directly to the length scales of Allard and Champoux [J.-F. Allard and Y. Champoux, J. Acoust. Soc. Am. 91(6), 3346–3353 (1992)]. When formulated in this manner, the relaxation and Allard-Champoux models coincide exactly in the low-frequency/small-pore and high-frequency/large-pore limits, although interpolation between these limits differs somewhat. The revised relaxation model can be readily transformed into a causal time-domain model, involving convolutions between the acoustic fields and a relaxation response function. The basic formulation has five parameters: porosity, static flow resistivity, tortuosity, and two relaxation times. A sequence of model reductions is described, leading finally to two-parameter (porosity and static flow resistivity) equations for the impedance and complex wavenumber, which provide a useful generalization of the Delany-Bazley equations.

Extending the supernova Hubble diagram toz~ 1.5 with theEuclidspace mission

We forecast dark energy constraints that could be obtained from a new large sample of Type Ia supernovae where those at high redshift are acquired with the Euclid space mission. We simulate a three-prong SN survey: a z<0.35 nearby sample (8000 SNe), a 0.2<z<0.95 intermediate sample (8800 SNe), and a 0.75<z<1.55 high-z sample (1700 SNe). The nearby and intermediate surveys are assumed to be conducted from the ground, while the high-z is a joint ground- and space-based survey. This latter survey, the "Dark Energy Supernova Infra-Red Experiment" (DESIRE), is designed to fit within 6 months of Euclid observing time, with a dedicated observing program. We simulate the SN events as they would be observed in rolling-search mode by the various instruments, and derive the quality of expected cosmological constraints. We account for known systematic uncertainties, in particular calibration uncertainties including their contribution through the training of the supernova model used to fit the supernovae light curves. Using conservative assumptions and a 1-D geometric Planck prior, we find that the ensemble of surveys would yield competitive constraints: a constant equation of state parameter can be constrained to sigma(w)=0.022, and a Dark Energy Task Force figure of merit of 203 is found for a two-parameter equation of state. Our simulations thus indicate that Euclid can bring a significant contribution to a purely geometrical cosmology constraint by extending a high-quality SN Hubble diagram to z~1.5. We also present other science topics enabled by the DESIRE Euclid observations