Instantaneous Fraction Research Articles

Nature of the action of a compost from olive mill wastewater on Cu sorption by soils

Abstract The reaction of two soils that have received composted OMW as manure with Cu solutions is studied. The data were fitted into a multi‐reaction model which considers both reversible and irreversible adsorption sites, and an ‘instantaneous’ fraction. The presence of composted OMW caused a strong increase in the distribution coefficient describing the instantaneous fraction, and the disappearance of the irreversible fraction. This behaviour was attributed to blocking of some sorbing surfaces by the organics, and to new surfaces present in the compost. These effects can have some environmental significance from the viewpoint of Cu mobility.

Heterogeneous Sorption Processes in Subsurface Systems. 2. Diffusion Modeling Approaches

The pore diffusion modeling approach is often used to model the sorption of organic chemicals by natural sorbents, implicitly assuming that the physical and sorptive properties of the sorbent are homogeneous. But application of such approaches to systems with significant variations in particle size and sorption equilibrium properties maybe inappropriate ; most natural systems have such variations. A general multiple-particle class pore diffusion model that accounts for variations in physical and sorptive properties was developed and used to interpret the results of a batch sorption rate study. Results indicated that multiple-particle class models provide a more accurate representation of long-term sorption rate data than traditional single-particle class approaches, the common approach of adding an instantaneous equilibrium fraction to single-particle class models leads to model parameters that are sensitive to the range over which data is collected, and tortuosity factors obtained with multiple-particle class modeling approaches were consistent with the range of values expected based upon mechanistic reasoning.

Large-eddy simulations of turbulent reacting flows in a chamber with gaseous ethylene injecting through the porous wall

Large-eddy simulations were performed to study the turbulent reacting flows in a simulated solid-fuel combustion chamber. The time-dependent axisymmetric compressible conservation equations were solved directly without using subgrid-scale turbulence models. The combustion process considered was a one-step, irreversible, and infinitely fast chemical reaction and the pyrolizing solid fuel was simulated by gaseous ethylene injected through a porous wall for a practical range of fuel blowing velocity encountered in solid-fuel combustion chambers for the first time. The numerical code used the finite-volume technique which involved alternating in time the second-order, explicit MacCormack's and Godunov's methods. Characteristic-based boundary conditions were applied on inflow and outflow boundaries, which allowed outlet boundary conditions to be nonzero gradients and, in turn, a practical length of computational domain to be realized. The effects of combustion on the large-scale unsteady flow structure and the mean flameholder recirculation zone were documented in terms of the density contours, vorticity dynamics, streamlines, mean-velocity vector fields, temperature profiles, flame position, and fuel blowing velocity. A comparison of the distributions of instantaneous and mean mass fractions of reactants shows that the present method appropriately reveals the effects of large-scale turbulent motions on combustion. Furthermore, the present large-eddy simulations have achieved a significant improvement in predicting the mean effective reattachment length over the previous calculations incorporating with turbulence models. The physical insight regarding the decrease of the mean effective reattachment length with combustion was also addressed.

Coupled radiation and soot kinetics calculations in laminar acetylene/air diffusion flames

Radiation heat transfer from flames depends on the instantaneous soot volume fractions and temperatures. A coupled radiation and soot kinetics calculation in laminar acetylene/air and acetylenemethane/air diffusion flames is described. Transport equations for mass, momentum, gas-phase mixture fraction, enthalpy (sensible + chemical), soot mass fraction, and soot number density are solved. A simplified soot kinetics model incorporating nucleation, growth, oxidation, and agglomeration processes is used. The reaction rates in the simplified kinetics model depend on the temperature and the local concentrations of acetylene and oxygen. The major gas species concentrations are obtained from state relationships. The local temperature is obtained by solving the energy equation, taking radiation loss and gain and the energy exchanges associated with soot formation and oxidation into consideration. The radiative source/sink term in the energy equation is obtained using a multiray method. Since these flames radiate a substantial part of their energy, the kinetic rates associated with soot processes are strongly coupled to the energy equation. This strong coupling between radiation, and soot formation and oxidation processes is modeled for the first time. The results of the soot kinetics model are compared with measurements of soot volume fractions obtained using laser tomography. The agreement between measurements and predictions of soot volume fractions supports the present method. The predicted temperature profiles support the structure of strongly radiating flames discovered earlier.

Shape and extent of the void formed by a horizontal jet in a fluidized bed

AbstractThe introduction of reactant gas into a fluidized‐bed chemical reactor as a jet is a common design practice. However, the shape and extent of the void formed by a jet into a fluidized bed and the manner in which the void breaks up into bubbles have still not been described well.An experimental study of a horizontal jet into a 15 cm by 38 cm cross‐section fluidized bed was carried out using an X‐ray system. Instantaneous solid fraction averaged along 15‐cm chords across the bed were measured. The mean value and the fluctuating component of solid fraction were determined for two initial jet diameters, 0.64 and 1.27 cm, and three initial jet velocities, 23, 46 and 69 m/s. Maps of the mean solid fraction and of statistical properties of the fluctuating component show that there are three discernible regions in the jet‐influenced area of the bed. These are a coherent void, bubble trains, and a surrounding compaction zone.

Mass Transfer in Mixed Solute Osmotic Dehydration of Apple Rings

Development and verification of a model for mass transfer in osmotic dehydration of apple rings in mixed solute osmotic media is described. ‘Red Delicious’ apple rings were osmotically dehydrated in sucrose-sodium chloride solutions of 50% total solids-50% water. The sodium chloride concentration was varied at 0, 2.5, 5 and 10% by weight. The temperatures used were 20, 30, and 50° C, and contact times were 0, 1, 2, 3, and 4 h. Moisture loss (Y) was calculated as a fraction of original moisture in apple rings, and the combined solute-gain was expressed as an “equivalent molality”, C, of sucrose and sodium chloride in the liquid phase of apple rings. Both Y and C were modeled as functions of osmotic solution composition, temperature and time of contact. An empirical equation was developed to establish a relationship between the instantaneous mass fractions of sucrose and sodium chloride in apple rings. The above three equations and a fourth equation derived from mass balance on total solids originally present in apple rings, were solved simultaneously to give the ratio of instantaneous to original total mass of apple rings (mq/m0) and instantaneous mass fractions of sucrose (w2), sodium chloride (w1), and water (w4) in the apple rings. Knowing mq/m0, w1, w2, and w4, and from the knowledge of total solids originally present in the material, one can calculate the moisture loss and individual solutes-gain during osmotic contacting.

Temperature / soot volume fraction correlations in the fuel-rich region of buoyant turbulent diffusion flames

Instantaneous soot volume fractions and temperatures were measured in the fuel-rich (underfire) region of turbulent nonpremixed acetylene, propylene, ethylene, and propane flames burning in still air. Large-scale, highly buoyant, pool-like flames were considered, having characteristic residence times greater than 250 ms and burner exit Richardson numbers greater than 18. Measurements were made using an optical probe than involved laser extinction for soot volume fractions and two-wavelength pyrometry for temperatures. Strong correlations were found between soot volume fractions and temperatures for each fuel-relatively independent burner operating conditions and position in the underfire region. This behavior is supportive of the existence of nearly universal relationships between soot volume and mixture fractions in the underfire region of turbulent nonpremixed flames having large characteristic residence times. Underfire soot is largely confined to a narrow range of mixture fractions (yielding a soot spike) and temperatures. The latter observation supports approximations of constant-temperature soot layers that have been proposed in teh past for estimates of continuum radiation from soot-containing diffusion flames.

A study on solute NO3N transport in the hydrologic response by an MRF model

Abstract The results of field studies on solute transport over basin-scale distances are analyzed using the Mass-Response Function (MRF) model and its generalization proposed in this paper. The generalization proposed concerns reversible production/removal processes of solute. It is assumed that equilibrium concentrations in the mobile phase are proportional to the instantaneous fraction of solute mass sorbed in the fixed phase. Such assumption, which is thought of as representative of large-scale transport volumes, is derived from the theory of two-component convection-dispersion in soils and is aimed at endowing the model with predictive characters. It is seen that the use of generalized MRF's poses serious computational problems, which are partly related to the conditional behavior of the instantaneous response of solutes on the impulse time. The conditionality of the transfer functions on the injection time is related in a rational manner to the combined effects of convection-dispersion during the hydrological cycle and of sorption processes that occur between fixed and mobile phases. The relevance of the problem addressed lies in the ability of solute generation and movement over large scales to predict the dominant modes of the phenomena on the basis of the knowledge of parameters with a clear physical significance. In this paper, this ability is tested with reference to suitable field experiments. The results show that a number of characteristic residence times are the most important properties for basin-scale transport processes and for the evolution of resident and flux solute concentrations. An MRF model of solute NO 3 N concentrations in river waters is constructed, the architecture of which is tailored to solute generation and transport processes occurring in a gauged watershed. The theoretical results are compared with the experimental observations and are found to agree with them well. It is argued that MRF's are rational models of the complex chain of events occurring in large-sclae solute sorption and transport, and may be validly employed for quantitative studies of environmental impacts due to the release of chemical species in surface or subsurface waters.

Amorphous Cr5Si3 thin films— morphology and kinetics of crystallization

The changes in morphology and the crystallization kinetics of amorphous Cr5Si3 were studied by means ofin situ resistivity measurements and hot stage transmission electron microscopy (TEM). The crystallization process is controlled by nucleation and growth during the continuous heating as well as in the isothermal annealing. Initially the growth is isotropic. In the later stages it becomes anisotropic due to impingement. The growth characteristics and nucleation rates were deduced from the changes in linear dimension of a growing particle with time and from the number of nucleation points as a function of time. Growth rates were found to remain constant for most of the total transformation time while nucleation rates initially increase, subsequently peak, and then rapidly decrease. The determined nucleation and growth rates were used to calculate the transformed volume fractions. The results were compared with data obtained by assuming a linear relationship between instantaneous resistivity and volume fraction and with data based on measurements of projected crystallized areas in transmission (image analysis). Kinetics studies showed that the isothermal crys-tallization follows a sigmoidal curve. The apparent activation energy was found to be ∼2.4 eV. The transformation mode parameter was found to be ∼3 which, given that the crystallization reaction is interface controlled and the nucleation may be approximated as instantaneous, suggests a three-dimensional mode of crystallization.

Inexpensive Performance Monitoring of Solar Domestic Water Heating Systems

Performance monitoring is essential in order to conclusively demonstrate the cost effectiveness of a solar heating system. Unfortunately, this “last step” is an aspect which has received little engineering consideration. The monitoring programs in progress typically use instrumentation which is much too expensive and complex for use by individual operators of domestic water heating systems. Hence, few systems are monitored, and the average owner knows little about the performance characteristics of his system. Even malfunctions go undetected. An inexpensive performance monitoring system is described in this paper. It could probably be mass-produced for under 15 dollars or built by the typical homeowner for under 30 dollars. The monitor indicates the instantaneous solar fraction. Overall system performance can be improved with this monitor, since it enables the user to correlate load with the availability of solar heated water. Methodology, performance parameters, and some performance data are presented.

The diffuse fraction of instantaneous solar radiation

Nearly all diffuse fraction correlations have been based on integrated hourly or daily data. Solar collectors, however, see instantaneous solar radiation. Measurements of the terrestrial instantaneous diffuse fraction are shown to depend on both clearness index and air mass. The resulting instantaneous diffuse fraction correlation differs markedly from the correlations obtained for integrated diffuse fractions. A model for the instantaneous diffuse fraction is developed, which describes the generation and transmission of diffuse solar radiation in the atmosphere. The measurements of instantaneous diffuse fraction are used to explain the scatter inherent in daily diffuse fraction data. It is shown that measurements of the instantaneous diffuse fraction together with the frequency distribution of instantaneous radiation may be used to determine monthly average daily diffuse fractions.

Microvessel hematocrit: measurement and implications for capillary oxygen transport.

Microvascular preparations of the hamster cheek pouch and cremaster muscle were used to establish the relationship among three measures of red cell distribution: 1) the systemic hematocrit defined as the volume percentage of red cells sampled from a toe clip; 2) the tube hematocrit defined as the instantaneous volume fraction of red cells in a microvessel segment of measured length and diameter; and 3) the discharge hematocrit defined as the volume percentage of red cells that flowed into micropipettes inserted into microvessels. The results show the tube hematocrit is low and highly variable in the presence of a nearly constant systemic hematocrit. The discharge hematocrit, in contrast, consistently approximated systemic values in blood taken from arterioles or venules with diameters of 6-98 micron. Indeed, the mean ratio of the discharge to the systemic hematocrit did not differ from unity (P greater than 0.25). The observed similarity between the discharge and systemic hematocrit indicates that red cells are distributed uniformly across capillary networks. Differences between the absolute value and variance of the tube hematocrit compared with the discharge hematocrit imply that the anatomical volume of a microvessel can differ from the volume available to cells and plasma within a microvessel. Thus moment-to-moment variation in the tube hematocrit or capillary red cell spacing may be indicative of a change in the effective capillary flow cross section and not solely on the inflow hematocrit.

Thermal Expansion of Elastic-Plastic Composite Materials

Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stiffness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also, the local instantaneous thermal strain and stress concentration factors are related in an exact way to the corresponding mechanical concentration factors. The results depend on instantaneous thermoelastic constants and volume fractions of the phases. They are found for fibrous composites with two distinct elastically isotropic or transversely isotropic phases, and for any binary composite with elastically isotropic phases. The results indicate that in the plastic range the thermal and mechanical loading effects are coupled even if the phase properties do not depend on changes in temperature. The derivation is based on a novel decomposition procedure which shows that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase eigenstrains with local strains, caused by piecewise uniform stress fields which are in equilibrium with prescribed surface tractions. The method is extended to discretized microstructures, and also to the analysis of moisture absorption and phase transformation effects on overall response and on local fields in the two composite materials.

Seasonal estimates of global oceanic whitecap coverage

Seasonal estimates of oceanic whitecap coverage are presented on global contour maps. The instantaneous fraction of the sea surface covered by whitecaps as a function of wind speed has been described previously using a power law fitting technique [Monahan and Muircheartaigh, 1980]. This relationship, coupled with a Gaussian wind speed frequency distribution, allows us to calculate the oceanic whitecap coverage accounting for the variance about mean wind speeds. We use monthly mean wind speed and variance information in 5° latitude × 5° longitude areas over the world ocean to estimate the global oceanic whitecap coverage distribution. The whitecap coverage in the northern hemisphere oceans displays a substantial seasonal dependence. The boreal summer average whitecap coverage in the high‐latitude North Atlantic is about 0.5% and increases by a factor of roughly 6 to over 3.0% for a boreal winter average. The whitecap coverage in the high‐latitude southern hemisphere oceans exhibits only a factor of 3 difference for the same seasons, from about 1% in the austral summer to over 3% for the austral winter. There are several high‐latitude areas with greater than 3% average whitecap coverage over several months of the year. The monsoonal winds in the Indian Ocean result in over 3% mean whitecap coverage for the June‐July‐August period.

Isotopic tracer studies of the further reactions of pentenes in the combusion of pentane

Detailed studies have been made of the mechanisms by which products other than the conjugate alkenes are formed when pentane undergoes combustion in the presence of small quantities of isotopically labelled pent-1-ene and pent-2-ene. Seven pentenes, specifically labelled with 14 C in different skeletal positions, have been synthesized and the fate of the labelled carbon atoms during combustion has been determined. Special attention has been paid to the formation and destruction of the pentadienes, acrolein and ethylene, as products derived from pent-1-ene. In particular, measurements have been made of the instantaneous fraction of the original pentene converted into each of these compounds and of the percentages have been shown to be derived exclusively from the pentenes, whilst acrolein and ethylene, which are complementary products resulting simultaneously from the same pentene molecule, are formed principally from the alkenes. It has also been possible to determine the distribution of the points of abstractive attack in the pentenes and the reactivity rations of pent-1-ene to secondary products. There are sharply defined changes in the relative rates for the pentadienes and pent-1-ene before and after the passage of cool flames; the results suggest that penta-1, 2-diene is oxidized to acrolein and ethylene. A significant amount of 2, 4-dimethyloxetan is formed from both pent-1-ene and pent-2-ene; this compound appears to be produced by a somewhat unusual route, involving the isomerization of one hydroperoxy radical to another through a peroxy radical. The majority of these compounds result from reactions involving free radial addition to the alkene molecule. However, abstractive modes of attack, although leading almost exclusively to the pentadienes, acrolein and ethylene, are quantitatively very important in terms of the total amount of attack on the pentenes. The principal products formed from the pentenes are only minor constituents of the combustion products of pentane. This shows that the coujugate alkenes do not play nearly as important a part in the combustion of pentane as they do in the case of alkanes of lower molecular mass.

Estimation of molecular weight distribution based on chain length dependence of termination rate

AbstractWhen a chain length dependence of polymer‐polymer termination is given by kt,ns = const. (n−2a + s−2a) where n and s are the chain lengths for the polymer radicals and a is parameter, an instantaneous weight fraction of the non‐reacting polymers is derived as: where h and k̄ are the kinetic parameters, p is a parameter depending on a, and pn is instantaneous number‐average chain length. Such a weight fraction corresponds to the experimental one over a wide range of conversion in the polymerization of styrene. On the scope of this correspondence, the polymer‐polymer termination rate is estimated as: k̄t = 8πR0D1/100 ( = 4πRsDs) where R0 is reaction radius between monomer radicals and D1 is the diffusion coefficient of the monomer; Rs is reaction radius between segment radicals with n ≅ 100 and Ds is the diffusion coefficient of the segment. The Fujita‐Doolittle theory applies to such a rate. Further, the rate also yields 1.5 × 1071./mole‐sec, which is the observable extent at conversions less than 0.2.

Stereocontrol. VII. The relation between instantaneous and final diad and triad fractions in one‐way polymerization mechanism

AbstractThe relationships between isotactic and syndiotactic diads and triads resp., on one hand, and the rate constants of the different propagation steps in MARKOV 1st and 2nd order processes have been calculated under the assumption of a steady state condition for the concentration of free radicals. Instantaneous and final diad fractions are equal only if i and s stand for the formation of an isotactic or a syndiotactic diad at an existing diad A or B. A and B stand for i and s in a MARKOV 1st order process and for ii, is, si, and ss in a MARKOV 2nd order process.

Miscible Displacement in a Controlled Natural System

Abstract Three confined five-spot miscible displacements at unity, favorable, and unfavorable mobility ratios were conducted in a shallow, water-saturated sandstone of Pennsylvanian age near Chandler, Okla. These studies, plus associated laboratory experiments, were designed to measure-miscible displacement performance in a controlled natural system, using known scaling criteria to develop an approach to modeling the heterogeneous field system. We have concluded from these studies that: displacement efficiency in the field is a pronounced function of mobility ratio, indicating that miscible fingering observed in simple laboratory models occurs in the field field displacements can be quantitatively predicted by scaled laboratory models if the degree and location of field permeability variations are preserved in the models and arbitrary simplifications of heterogeneity will net necessarily predict observed displacement efficiency, and the simpler the model, the more optimistic the prediction. Introduction Many processes to achieve miscible displacement of reservoir oil by injected fluids have been conceived and field tested by the oil industry. Among the better known are high-pressure gas, enriched gas, and LPG banks. The simplest form of miscible displacement one fluid miscible, displacing another fluid of different viscosity but the same density has been studied extensively in homogeneous laboratory models. Observations of unstable fingering have been made which explain the significant decrease in displacement efficiency as the mobility ratio (ratio of displacing fluid mobility to displaced fluid mobility) increases. General industry experience with field tests of miscible displacement projects, mostly LPG banks, has been premature solvent breakthrough and lower than predicted production rate increases. These results have been attributed to either unstable fingering, unusual or unexpected permeability stratification, or both. Miscible displacement data in a controlled natural system have never been reported, however. Also, it has not been shown that properly designed and constructed laboratory models quantitatively predict field-scale behavior. The purpose of the combined field and laboratory experiments reported in this paper is twofold. The first was to measure miscible displacement performance at different mobility ratios in natural rock approaching field size under precise, controlled conditions. The second purpose was to utilize known scaling criteria plus several approaches to heterogeneity to model the field. Comparison of model and actual field results should then determine whether or not the laboratory phenomena (manifested by miscible displacement efficiency) are exhibited in large, natural rock systems. We carried out our program by first locating a shallow, water-saturated reservoir whose rock properties were representative of oil-bearing reservoirs. Detailed reservoir description by core analysis and interference testing showed the field site to be heterogeneous." A sequence of controlled, aqueous-phase miscible displacements was conducted at unity, favorable and unfavorable mobility ratios. A central, confined pattern was used to obtain the displacement data. A laboratory program using sand-packed models was conducted to determine the modeling criteria necessary to simulate field behavior of miscible displacement in a heterogeneous system. SCALING THEORY The detailed derivations and descriptions of the scaling laws that apply to laboratory models of reservoirs are adequately described elsewhere, so the following discussion will be restricted to facets of importance in this study. For a displacement in which one liquid miscibly displaces another, the following dimensionless groups are required to have the same numerical value in the model as in the field: ........................................(1) The model also must be geometrically similar to the field, be spatially oriented the same as the field (same dip angle), and have the same initial and boundary conditions as the field (same initial fluid saturations and same injection-production well arrangement). When these conditions are satisfied, the theory predicts that at any dimensionless time (pore volumes of produced fluids) the dimensionless flow potential and dimensionless fluid concentrations will be identical at all dimensionless spatial locations within the model and the field. If this prediction is correct, then the local dimensionless velocities must be identical, thus the instantaneous fraction of displaced fluid produced and the cumulative recovery expressed as fraction of original fluids in place must be identical at all dimensionless times. JPT P. 1329ˆ