Instantaneous Balance Research Articles

Mass balance and thermodynamic description of solid state fermentation of lignocellulosics byPleurotus ostreatus for animal feed production

This study was focused primarily on the degradation of lignin in water hyacinth and barley straw for animal-feed production. The experiment was performed in a 1.5-L Applikon fermenter for 30 days, varying the air flow rate from 0.022 VVM/0.047 VMM to 0.048 VVM/0.102 VMM. A novel approach was introduced for prediction of a kinetic model by using instantaneous respiratory quotient (RQ) measurements and steady state elemental balances. Growth kinetics were determined for the fungus in a 30-day fermentation with a mixture of barley straw and water hyacinth as the substrate. The instantaneous heat-interaction profile was predicted from steady state balances. Fermentation data were checked for consistency using the entropy balance inequality, and thermodynamic efficiency was calculated to show that degradation of lignocellulosics byPleurotus ostreatus followed more than one metabolic pathway during the course of the fermentation. Growth ofP. ostreatus on lignocellulosics, such as water hyacinth and barley straw, was di-auxic or possibly tri-auxic during the 30 days of fermentation.

Use of remote sensing and reference site measurements to estimate instantaneous surface energy balance components over a semiarid rangeland watershed

A primary motivation for using remotely sensed data to estimate components of the surface energy balance is to quantify surface energy fluxes in a spatially distributed manner over various spatial scales. However, all models which utilize remotely sensed data to estimate surface fluxes also require input variables and parameters which cannot be estimated on a spatially distributed basis with remotely sensed data. In this analysis, data from the Monsoon '90 experiment were used to evaluate the limitations in spatially extending a relatively simple energy balance model with remotely sensed data over a semiarid rangeland watershed. Using one ground‐based meteorological and flux station as a reference site, aircraft‐based remotely sensed data (surface temperatures and reflectances) were used to compute energy balance components for seven other locations within the watershed. The results indicated that for clear sky conditions, all components of the surface energy balance could be estimated to within approximately the same level of uncertainty with which the fluxes were measured with ground‐based flux instrumentation. However, under partly cloudy conditions the variability in incoming solar radiation across the watershed significantly degraded the estimation of distributed values of net radiation (Rnet). If ground‐based estimates of incoming solar radiation are used to calculate Rnet from remotely sensed data, then the spatial extent over which that measurement is valid limits the area over which accurate spatially distributed values of Rnet can be estimated. Additionally, the results of sensitivity analyses indicate that the level of uncertainty to which the roughness length for momentum, or z0m, is typically known for spatially distributed values in an area of naturally variable vegetation can give rise to significant uncertainties in the estimation of sensible heat flux. For areas where the spatial variation in roughness parameters is of the order of several centimeters, the error associated with assuming constant values for the roughness length for momentum is similar in size to the errors associated with temperature variations of the order of several degrees. In order to utilize radiometric temperatures to reliably estimate spatially distributed values of sensible heat flux, techniques such as those explored by Menenti and Ritchie (this issue) are needed to provide spatially distributed information on surface roughness parameters.

Modeling of Compressible Cake Filtration

The transport of suspended solid particles in a liquid through porous media has importance from the viewpoint of engineering practice and industrial applications. Deposition of solid particles on a filter cloth or on a pervious porous medium forms the filter cakes. Following a literature survey, a governing equation for the cake thickness is obtained by considering an instantaneous material balance. In addition to the conservation of mass equations for the liquid, and for suspended and captured solid particles, functional relations among porosity, permeability, and pressure are obtained from literature and solved simultaneously. Later, numerical solutions for cake porosity, pore pressure, cake permeability, velocity of solid particles, concentration of suspended solid particles, and net rate of deposition are obtained. At each instant of time, the porosity decreases throughout the cake from the surface to the filter septum where it has the smallest value. As the cake thickness increases, the trends in pressure variation are similar to data obtained by other researchers. This comparison shows the validity of the theory and the associated solution presented. A sensitivity analysis shows higher pressure values at the filter septum for a less pervious membrane. Finally, a reduction in compressibility parameter provides a thicker cake, causes more particles to be captured inside the cake, and reduces the volumetric filtrate rate. The increase of solid velocity with the reduction in compressibility parameter shows that more rigid cakes compress less.

Balance equations for fluid lines, sheets, filaments and membranes

Fluid structures can be classified into two categories: fluid filaments and fluid membranes. If the cross section of a fluid filament vanishes, the fluid filament is called a fluid line, whereas if the thickness of a fluid membrane vanishes, the fluid membrane is called a fluid sheet. In this paper, the local instantaneous balance equations are derived for a line and a sheet of fluid moving in a three-dimensional geometrical space. For a filament, the balance equations are obtained by using quantities averaged over the cross section of the filament. For a membrane, the balance equations are obtained by using quantities averaged over the height of the membrane. It is shown that the local and averaged formulations are consistent. All these balance equations have been rigorously derived by applying original mathematical theorems given in the appendices to the paper. Such balance equations can be used to model single-phase flow in bends or coils, the dynamic centering of thin liquid shells in capillary oscillations and the instability of an annular jet.

FORMATION OF FILTER CAKES WITH PARTICLE PENETRATION AT THE FILTER SEPTUM

The mass of solid particles entering the formation is an important factor in industrial cake filtration operations. Predictions of the concentration at the filter septum require the ability to predict the mass transport of solid particles under variety of conditions. This study analyzes cake formation, including particle penetration at the filter septum. In addition to the total instantaneous mass balance equation, mass balance equations for captured and suspended particles and the fluid phase are averaged along the cake thickness taking into account conditions at the surface and the septum. Capture mechanisms, such as surface straining, and internal cake erosion and particle capture are included in the analysis. The results are ordinary differential equations in terms of thickness, concentration of suspended particles in the filtrate, average particle concentration, average porosity, and such operational parameters, as slurry concentration, injection rate, and volumetric solid fraction. To test tbe validity of the analysis presented here, the numerical results are compared to results for a simplified case. The conclusions from the sensitivity analysis conducted in this study agree with earlier conclusions. Results show that the concentration of suspended particles in the filtrate increases rapidly and then decreases gradually until it reaches zero after 13 hours. This yields that after 13 hours we have a clear filtrate.

Numerical solution and sensitivity analysis of filter cake permeability and resistance to model parameters

The migration and capture of solid particles in porous media occur in fields as diverse as water and wastewater treatment, well drilling, and in various liquid-solid separation processes. Filter cakes are formed when a liquid containing solid particles is forced through a pervious surface which allows the liquid transport while retaining solid particles. Following a literature survey, a governing equation for the cake thickness is obtained by considering the instantaneous mass balance. Later, numerical solutions for the cake thickness, cake permeability, cake resistance, solid particle velocity (cake compression rate) and concentration of suspended particles are obtained and a sensitivity analysis is conducted. The sensitivity analysis shows that the cake permeability and cake resistance are more sensitive to the rate constant of cake erosion than they are to the rate constant of particle capture. However, the concentration of suspended solid particles, and the solid velocity are mostly sensitive to the slurry parameter and the rate constant of particle trapping. Moreover, cake permeability, compressibility, concentration of suspended particles, and the solid velocity are very sensitive to the concentration at the filter septum. Finally, as expected, with a thicker slurry, more particles are captured inside the cake, thus forming a thicker and more resistant cake. Also, as more particles are being filtered at the filter septum, a thinner cake is formed and a smaller effluent concentration is achieved.

A single-phase converter with a high-frequency current-sourced link

Duality relationships that have proved useful in the development of DC-DC converter topologies are applied to existing voltage stiff high-frequency link force-commutated converters. This new area of application of the duality concept results in the development of new current stiff link converters that retain the advantages of current fed DC-DC converters. The requirements on the converters enforced by the need for instantaneous balance of input and output powers are examined. A current control technique has been developed that controls the charge delivered to the load during each switching cycle. This allows a wide bandwidth voltage regulator to be applied. Finally, the results obtained with a low-power prototype and a reactive load are presented. The new converter requires only four power MOSFETs and relatively simple controls and is reversible. >

Optimal Control of Evaporator and Washer Plants

Tests with radioactive tracers were used for experimental analysis of a multiple-effect evaporator plant. The residence time distribution of the liquor in each evaporator was described by one or two perfect mixers with time delay and by-pass flow terms. The theoretical model of a single evaporator unit was set up on the basis of its instantaneous heat and mass balances and such models were fitted to the test data. The results were interpreted in terms of physical structures of the evaporators. Further model parameters were evaluated by conventional step tests and by measurements of process variables at one or more steady states. Computer simulation and comparison with the experimental results showed that the model produces a satisfactory response to solids concentration input and could be extended to cover the steam feed and liquor flow inputs. An optimal feedforward control algorithm was then derived for a two unit, co-current evaporator plant. Because the operation of such a plant is affected by the out...

Application of adaptive estimation in microbial fermentation processes

This paper aims at the estimation of biomass concentration of fed-batch fermentation processes by simultaneous measurement of substrate consumption, oxygen uptake and carbon dioxide production. On the basis of chemical stoichiometry and elemental balance describing intracellular biochemical reactions, the instantaneous conservation balance equations for Saccharomyces cerevisiae and Streptomyces ambofaciens are derived for the present purpose. Application of these equations is disturbed by process random errors. The process is also affected by random disturbance commonly regarded as white noise. Extended Kalman filter is used for estimating state variables. Two white noise matrices are obtained according to the intensity of random errors and that of disturbance. Computer simulation of the above mentioned two processes agrees well with the experimental data showing the cell growth versus time.

A model of the energy fluxes in a solar heated swimming pool and its experimental validation

In the present work, a theoretical model is presented concerning the various energy fluxes in a solar heated outdoor swimming pool, with a bare or covered surface. The analysis considers the instantaneous energy balance using actual climatological data, special attention being focussed on setting up equations for the calculation of the turbulent heat-mass transfer energy fluxes. Thus, the net heat loss can be calculated under constant water temperature conditions, paving the way for the determination of the needed solar collector heat power and/or conventional heating. A computer program is written and developed to implement the analysis. To check the validity of the model, experimental work has been carried out at the Athens Olympic (25 × 50 m) swimming pool, which is heated by a solar collector array consisting of flat plate plastic panels. A vast monitoring campaign is undertaken, involving the installation of the sensing instruments and the data acquisition and reduction system. All the relevant parameters were continuously recorded and conveniently averaged over 1 h intervals. For the first year of operation, the agreement between experimental results and theoretical calculations (on an hourly basis) is promising for the days tested. From a comparison of the magnitudes of the individual flux losses, it is concluded that the higher loss contributor is the evaporative one.

Magnetically pulsed crystal monochromators on a pulsed neutron source

For some crystal neutron monochromators a Bragg reflection can be found for which the structure factor for nuclear scattering is negligible, while that for magnetic scattering is large. Manipulation of the direction of the magnetisation within the crystal with respect to the scattering vector thus enables the reflectivity of the crystal to be switched on or off. On a pulsed neutron source such switching can be phased to the neutron pulse from the moderator, the duration of the magnetic “on” pulse defining the resolution of the monochromating device, and its exact phasing defining, within limits, the monochromated energy. This paper examines the principles of magnetically pulsed monochromation on a pulsed neutron source, and considers the performance of certain magnetic ferrites as pulsed monochromators. Comparisons are made between an inelastic scattering spectrometer based on ferrite monochromation and spectrometers using conventional (copper) crystal monochromators and choppers. It is shown that ferrite monochromation provides a comparible neutron flux at a given energy and resolution, with the additional flexibility that electronic control of the resolution permits an instantaneous balance to be made between resolution and neutron flux. It is also shown that magnetically pulsed monochromator techniques are well suited to crosscorrelation spectroscopy on pulsed neutron sources.

Drag measurements for first‐year sea ice over a shallow sea

For a free‐drift case a method is developed for simultaneously determining air (Ca) and water (Cw) drag coefficients by solving the vertically integrated stress balance equation for sea ice. The method allows the algebraic determination of Ca and Cw from measurements of relative wind and relative current at single reference levels, from estimates of the densities of all three fluids and ice thickness, and from estimates of the accelerations caused by the nonsurface stress terms derived from position measurements. The method treats the ice as a natural drag plate and therefore includes contributions from both skin and form drag. One shortcoming of the technique is that if the relative wind and current are colinear, then only the ratio of Ca and Cw can be determined. Another is that the accelerations caused by other forces need to be independently determined. An experiment was conducted on a single floe in the eastern Bering Sea over the continental shelf during March 1981. The site was about 80 km from the ice edge and was occupied for approximately 3 days following the passage of a storm which had broken the pack into 10–20 m diameter floes. Both profile and slab inversion estimates of drag were made from the current meter and anemometer measurements at the site: Ca at 3 m was 4.55×10−3 by the profile method, compared to 3.63–4.39×10−3 for slab, depending on assumptions; Cw at 1.1 m by profile was 24.2×10−3, compared to 18.3–22.0×10−3 for slab. The two methods gave results which were not statistically separable and which were among the highest drags observed for sea ice. The instantaneous stress balance on the floe included contributions from material acceleration, Coriolis force, the two surface stresses, and sea‐surface tilt relative to mean current and tide.

A Study of Tidal Energy Dissipation and Bottom Stress in an Estuary

Abstract A Method for inferring an area-averaged bottom stress and energy dissipation rate in a tidal estuarine channel is presented. The one-dimensional continuity and momentum relations are developed using simplifying assumptions appropriate for a well-mixed shallow and narrow estuary. The finite-difference form of these relations is derived for a section of the Great Bay Estuary, New Hampshire, an estuary which has been shown to have a relatively large energy dissipation rate. A set of current, bottom-pressure and sea-level measurements from the Estuary is used to estimate time series of all important first- and second-order terms in the momentum equation. Except near slack water, we find that the instantaneous first-order balance must be between the surface-slope-induced pressure gradient and bottom-stress forces. Important second-order contributions to the balance come from the inertial and convective acceleration terms. Time series of bottom stress are inferred by summing the estimated terms. For th...

Instantaneous global ozone balance including observed nitrogen dioxide

The catalytic destruction of stratospheric ozone by the oxides of nitrogen is believed to be an important part of the global ozone balance. The lack of sufficient measurements of NO x concentrations has impeded efforts to quantify this process. Recent measurements of stratospheric nitrogen dioxide from ground-based stations as well as aircraft and balloons have provided a first approximation to a global distribution of NO2 vertical columns at sunset. These observed vertical columns have been translated into time-dependent vertical NO2 profiles by means of a one-dimensional atmospheric photochemical model. Using recent observations of air temperature and ozone along with this information, the independent instantaneous (one second) rates of ozone production from oxygen photolysis P(O3), of ozone destruction from pure oxygen species (Chapman reactions) L(O x ), and of ozone destruction by nitrogen oxides L(NO x ) were estimated over the three-dimensional atmosphere. These quantities are displayed as zonal average contour maps, summed over various latitude zones, summed over various altitude bands, and integrated globally between 15 and 45 km. Although the global summation between 15 and 45 km by no means tells the complete story, these numbers are of some interest, and the relative values are: P(O3), 100; L(O x ), 15; L(NO x ), 45±15. It is to be emphasized that this relative NO x contribution to the integrated ozone balance is not a measure of the sensitivity of ozone to possible perturbations of stratospheric NO x ; recent model results must be examined for current estimates of this sensitivity.

Energy balance and wind effects in a shallow sound

Tidal energetics and wind effects in an extensive (3000 km2) shallow (∼3.5 m) sound with two widely separated entrances were studied numerically with a two‐dimensional vertically averaged model. A comparison of current predictions with observations from 15 current meter stations under differing tidal regimes proved the reliability of the model. Evaluation of the instantaneous energy balance equation showed the change in energy content to be nearly balanced by input energy flux, frictional energy dissipation being of secondary importance. In contrast to the equipartition of energy in classical long waves, there is on the average eight times more potential energy than kinetic energy. Input energy flow shows preferential pathways; the wide northern entrance mainly shows energy gain to the Sound, the southern entrance shows equal amounts of gain and loss, while small cuts through the barrier island chain serve mainly as conduits for energy loss. When real tidal input is used, the energy balance time‐averaged over a diurnal tidal cycle is not in a steady state (〈∂E/∂t〉 is 25% of the other terms), and frictional dissipation is the dominant term. Experiments showed that with winds in the 8‐ to 9‐m/s range, extensive setup can occur (20 cm), strongly dependent on wind direction. Increased speeds through the passages can significantly reduce the residence time in the Sound. Relaxation time of the wind perturbations is only about 3 hours.

The Tidal energetics of Narragansett Bay

The average tidal energy budget of Narragansett Bay, a weakly stratified estuary, has been determined from observations of tidal height and current. For average conditions the tidal energy influx to the bay is balanced by the bay's energy sinks, and within the error limits the energy budget balances completely. The average energy inputs to the three bay channels, the West Passage, the East Passage, and the Sakonnet River, are 4.3, 6.4, and 1.1×1013 ergs/s, respectively. Tidal energy is dissipated on the bottom of the bay at the average rate of 8.8×1013 ergs/s, mostly in a few localized areas of high dissipation. The bay does work on the moon at an average rate of 1.8×1013 ergs/s. The energy required for vertical mixing is 0.3×1013 ergs/s. Phase adjustment between tidal height and current is suggested as a mechanism contributing to the instantaneous balance of the tidal energy budget over the lunar cycle.

AN EVALUATION OP MIXING IN THE TAY ESTUARY

The authors consider the derivation of an expression for salinity distribution in an estuary, from an instantaneous mass balance equation for a solute in a continuum. The expression is compatible with existing field instrumentation and limited economic resources. Details are given of a prototype survey which included continuous monitoring of the salinity distribution of the Firth of Tay, an estuary subject to a wide range of fluvial and marine influences. The survey results enabled an apparent dispersion coefficient to be evaluated and an estimate to be made of the net mixing.

Calibration of Infrasonic Microphones at WSMR

This paper describes a technique for the rapid calibration of high-sensitivity, low-frequency microphones in the presence of relatively high ambient noise. Because of the uncertain volume displacement and the physical configuration of the microphones, normal pistonphone calibrations cannot be made. This technique entails calibration of a reference microphone in an electrodynamically driven pistonphone, comparison of the test microphone with this reference to determine the sensitivity magnitude, and the use of an electrostatic actuator to determine the relative response at ambient pressure. All voltage comparisons made are instantaneous amplitude and phase balances of single-frequency components referenced to the dc voltage input of the displacement control in the pistonphone calibration. This method minimizes the error contributions from voltage-transfer (dc to ac) distortion and noise. Microphone circuit modifications are described that allow field system calibration from a remote location. The estimated uncertainty of the calibration is 0.75 dB. Plans for the improvement of the method are presented.

Kinetics of hydrogen reduction of ferrous oxide in a batch fluidized bed: Effects of mass velocity and pressure

AbstractThe kinetics of reduction of ferrous oxide with hydrogen were studied in a 1½‐in. diameter isothermal batch fluidized reactor. The effects of mass velocity and pressure on the reduction path were investigated over the ranges 5.3 to 19.2 moles/sq.ft.hr. and 1.3 to 5.4 atm. at 1,000° and 1,300°F. The results are correlated by means of instantaneous oxygen balances on the assumptions that there are no oxygen concentration gradients in the solid phase, that the distribution of residence times for the gas flow is represented closely by assuming complete mixing, and that the reduction rate is controlled at the oxide‐metal interface. The rate of reduction increased with increasing pressure and mass velocity. An excellent correlation was obtained for the program at 1,000°F. At 1,300°F. sintering and grain growth of the product layer complicated the reduction process, and a correlation was not obtained. Application of the results to the design of commercial fluidized‐reduction processes is discussed qualitatively.