Mass Balance Relationships Research Articles

Infrared spectra of phthalic acid, the hydrogen phthalate ion, and the phthalate ion in aqueous solution

The infrared spectra of a series of aqueous solutions containing phthalic acid (1,2-benzenedicarboxylic acid) and varying pH were examined using attenuated total reflection Fourier transform infrared spectroscopy and potentiometry. The basis spectra of phthalic acid, the hydrogen phthalate ion, and the phthalate ion were isolated using a factor analysis in which the absorbance of these species varies with pH and total phthalate concentration according to equilibrium and mass balance relations. Assignments of these basis spectra were made by comparison with spectra calculated ab initio. The conditional formation constants of phthalic acid and the hydrogen phthalate ion were determined at 25.0±0.1°C in 0.6 M NaCl ionic media using infrared spectroscopy and in 1.5 M NaCl ionic media using both infrared spectroscopy and potentiometry.

Comparison of continuous and stepwise control of CO2 supply into outdoor open thin-layer algal culture units

Using CO 2 mass balance, kinetic and equilibrium relationships for CO 2 dissolved in algal culture and the course of irradiance and culture temperature, mathematical relationship was derived for the rate G of CO 2 supply per unit area of outdoor open thin-layer (thickness 6 mm) growth surface. In the case of stepwise control of the CO 2 supply in the light period T L of growth, G exponentially decreased with increasing number n of time subintervals (into which T L had been divided) and in which G had been changed stepwise. In the limit (n→ ∞), G approached the values of continuous control of CO 2 supply. For practical use, a correlation was worked out where G was a function of culture temperature, irradiance and the length of growth surface.

Multi‐stage pseudomorphic replacement of garnet during polymetamorphism: 2. Algebraic analysis of mineral assemblages

Chemical relationships among four metapelites have been studied by investigation of mineral and bulk chemistry data and by singular value decomposition analysis of single and composite assemblage matrices. Bulk rock compositions cluster close together in an AFM diagram, all within the intersection space defined by the four sample assemblages. The similarity of bulk compositions normalized on a silica‐free, anhydrous basis indicates that sample chemistries differ mainly as a result of inhomogeneous distribution of quartz layers. The existence of mass balance relationships among samples indicates that assemblages also overlap in the Si–Ti–Al–Fe–Mg–Mn–Ca–Na–K multisystem. Analysis of single and composite matrices helps in defining possible mass balances linking sample mineral facies to one another during progressive contact metamorphism. The assemblage in sample A can form as the result of the model reaction 5.000 Ky+0.269 Grt+0.965 Bt+0.314 Pl=0.049 Ilm+1.115 Ms+0.849 Chl+0.306 St and react to assemblage B via reaction 0.97 Chl+0.52 Grt+0.66 Ms+0.14 Ilm+1.26 Ky=0.42 St+0.63 Bt+0.22 Pl coupled with the Ky→And transition. Assemblage B can transform into C by initial progress of Ky+Ilm+Chl+Grt+Ms=And+St+Bt+Pl followed by 0.142 Ilm+0.175 St+1.089 Chl+1.533 Ms+0.003 Grt=5.000 And+1.266 Bt+0.551 Pl Matrix analysis cannot satisfactorily model the C–D transition, because it predicts a net production of staurolite, which is in disagreement with petrographic evidence. All mass balances in the C–D composite matrix indicate net consumption of muscovite; this is integrated with the contrasting evidence of prograde pseudomorphs of muscovite after staurolite, observed in the nodules of sample D, within a model involving the progress of ionic reaction cycles.

ANALYTICAL EQUATIONS OF STORAGE RESERVOIR WATER QUALITY

Distribution system water quality protection is an integral aspect of public water supply management. Effective regulatory compliance requires a thorough understanding of the transport and mixing processes in storage reservoirs and their impacts on effluent water quality. This paper presents the development and verification of an explicit mathematical model of distribution storage water quality. The mathematical model is based on a compartmental representation of the reservoir continuum and is formulated analytically from mass balance relationships. The equations are applicable to separate inlet and outlet configuration reservoirs with simultaneous dual-directional flow. Previous models considered a common inlet/outlet reservoir configuration with unidirectional flow. The performance of the proposed model is illustrated by application to actual reservoir data taken from previous papers. The developed model should prove to be a valuable tool for assessing the effects of alternative designs or operational policies for optimizing distribution water quality.

Advanced Control of an Industrial Closed-Loop Grinding Circuit

This paper gives an industrial application of advanced control strategies using basic functions available in distributed control systems (DCS). The process under study is an industrial full-scale closed-loop grinding circuit where pulp solid mass fraction is to be controlled at the mill and at the cyclones. An algebraic implementation of a Kalman filter is used to evaluate the unmeasured pulp solid mass fraction at the mill discharge using mass balance relations. A static decoupler is used to eliminate the interaction between the two controlled variables. Open-loop adaptation is used to take into account the non-linearity of the process in conjunction with an internal model controller.

Numerical modelling of floodplain hydraulics and suspended sediment transport and deposition

A numerical model is presented for the prediction of floodplain inundation extents, flow depths and velocities, and patterns of suspended sediment dispersion and deposition. The model employs a simplified and novel treatment of fluid flow and a conventional convection–diffusion mass balance relationship for suspended sediment transport and deposition. These relationships are solved over a finite difference grid with a relatively fine nodal spacing, which enables a detailed representation of complex floodplain topography. The model is applied to a 600 m reach of the River Culm, Devon, UK. Continuous records of river stage and suspended sediment concentration monitored at the upstream boundary of the study reach provide the data needed to operate the model. These data are supplemented by measurements of the in situ settling characteristics of the suspended sediment load. Model predictions of overbank flow depths and velocities and patterns of suspended sediment concentrations and deposition amounts are presented. Predicted patterns of overbank deposition are described and compared with field measurements obtained with the aid of astroturf sedimentation traps. Grain size distributions obtained for samples of deposited sediment retrieved from the sedimentation traps are also examined and compared with model predictions. The results of both the field measurement programme and modelling work are shown to have significant implications for the representation of floodplain topography and suspended sediment particle size and settling properties in numerical simulations of overbank processes. © 1998 John Wiley & Sons, Ltd.

Monitoring Anhydride and Acid Conversion in Supercritical/Hydrothermal Water by in Situ Fiber-Optic Raman Spectroscopy

The hydrolysis of acetic anhydride to acetic acid in a hydrothermal/supercritical water reactor is monitored via in situ fiber-optic Raman spectroscopy to demonstrate the use of in situ spectroscopy to gain understanding of reaction kinetics and thermodynamics. We discuss the instrumentation used to make measurements in this harsh, corrosive medium, the multivariate mathematical methods used to interpret the spectroscopy, and the mass balance relationships used to convert the result into kinetic and thermodynamic information. From the intensity relationships and temperature information, Ea for the hydrolysis reaction is estimated and compared to literature values. Also, ΔH and ΔS are estimated for a change in solvation environment of acetic acid at high temperatures.

Applying mass transfer models for controlling organic compounds in ozonation process

Mass transfer plays a significant role in the ozonation process. The prediction models associated with the volumetric overall mass transfer coefficient (K La) and initial fractional ozone absorption (FOA 0) during the ozonation process were developed through the use of dimensional analysis. It was found that the volumetric overall mass transfer coefficient is the function of diffusivity, agitation speed, and gas flow rate, and the parameters in the K La equation are determined. Application of the prediction models for K La and FOA 0 would yield information to choose the most practically feasible operating parameters. The removability of total organic carbon (TOC) can be estimated based on the mass balance relationship and kinetic expression of TOC oxidation, during continuous laboratory ozonation of humic acid solution. The reaction rate constant averaged 0.0291 L/mg·min. The developed model in combination with the mass transfer and reaction kinetics can be used successfully in forecasting the most efficient agitation speed to control the formation of organic compounds. Also, the critical value of ozone partial pressure to achieve the highest TOC removability can be determined through the use of the above developed model.

Normal flow boundary conditions in 3D circulation models

SUMMARY The problem of enforcing normal transport conditions on 3D velocity fields is considered in the context of ‘wave equation’ finite element models. A procedure for strong enforcement of the transport constraint is given. The procedure is identical for Neumann (transport known) and Dirichlet (pressure known) problems, which are treated reversibly. All local mass and force balance relations are retained in the FEM system. A global mass conservation property is proven for the general 3D, discrete-time case. Examples demonstrate the quality of the solutions and the practicality of the approach.# 1997 John Wiley & Sons, Ltd.

On the dissipation of internal solitons in coastal seas

Previous descriptions of the turbulent decay of an internal soliton have been based on an adiabatic assumption in which the soliton parameters continuously change in time in response to the dissipation. A complete leading order description of a decaying internal soliton including both horizontal and vertical dissipation is given. It is shown that the adiabatic ansatz fails to fully describe a decaying internal soliton under the influence of weak dissipation. Physically, the breakdown is the consequence of the fact that an adiabatically decaying internal soliton is unable to simultaneously satisfy averaged energy and mass balance relations. An extended region with vertical momentum flux develops behind the decaying soliton in order to compensate for the additional mass lost in the adiabatically decaying internal soliton. The leading order evolution of this extended region is described as is its connection to the stream function field associated with the internal soliton. The magnitude of the vertical flux associated with this region scales linearly with the dissipation parameters. The transition of this extended region back to zero is accomplished through the formation of a spatially decaying packet of linear internal gravity waves.

A lung retention model based on Michaelis-Menten-like kinetics.

A Michaelis-Menten (MM)-like kinetic model for pulmonary clearance and retention of insoluble dusts was developed and validated by comparing our predictions with experimental data from F344 rats. Published data from inhalation studies involving accumulation and elimination of photocopy test toner, antimony trioxide, carbon black, and diesel exhaust particles were investigated. Numerical integration techniques were used to solve mass balance relationships based upon dust retention in a single lung compartment and clearance via an MM-like kinetic process. The model fit most of the experimental data well. The parameters of MM-like clearance kinetics, which had been derived strictly from the elimination phase, accurately predicted dust retention during the elimination as well as accumulation phases. Furthermore, parameters estimated from one study could accurately predict retention of the same dust in other studies. Particle density and gender of the animals had no effect on the goodness of fit of model predictions. This study suggests that MM-like kinetics offer a reasonable description of particle clearance from the pulmonary region of the rat lung that is more parsimonious than existing particle-clearance models and therefore more suitable for use with small amounts of data.

A state model for the drying paper in the paper product industry

The purpose of this paper is to present a state variable model for the drying section of a paper-making machine. This model is based on the mass and energy balance relationships written for steam, paper, cylindrical heater wall, and moisture. These relationships give a set of six nonlinear partial derivative equations. The form of these equations changes somewhat from one cylindrical heater to another. The solution for this model yields the operating parameters needed to achieve the desired steam temperature while obtaining good paper drying. Boundary conditions are specified by a stochastic generator, and initial conditions are obtained by solving the static model. In this paper, the authors present only the state variable model for the paper drying, as well as comparing the obtained results with dynamic model results. Solving the set of differential equations with respect to the boundary conditions, they obtain the standard form of the state representation, which represents the dynamic version of the model used for process control. In conclusion, it can be said that the consistency of the model with experimental results seems to be reasonably good and can be used for process control.

MODELLING FLOOD HYDRAULICS AND OVERBANK DEPOSITION ON RIVER FLOODPLAINS

This paper outlines a numerical model for the prediction of floodplain inundation sequences, overbank deposition rates and deposit grain size distributions. The model has two main components: first, a simplified hydraulic scheme which predicts floodwater flow depths and velocities, and second, a sediment transport element which employs a mass balance relation describing suspended sediment dispersion by convective and diffusive processes and sediment deposition as a function of particle settling rates. These relationships are solved numerically on a finite difference grid that accurately replicates the complex topographic features typical of natural river floodplains. The model is applied to a 600 m reach of the River Culm, Devon, U.K. using data derived from a range of field and laboratory techniques. Continuous records of river stage and suspended sediment concentration provide the model's upstream boundary input requirements. These are supplemented by measurements of the in situ settling characteristics of the suspended sediment load. The model's sediment transport component is calibrated with the aid of a dataset of measured overbank deposition amounts derived from flood events over a 16 month period. The model is shown to predict complicated floodwater inundation sequences and patterns of suspended sediment dispersion and deposition, which are largely a product of the complex topography of the floodplain. These results compare favourably with observations of overbank processes and are an improvement over those of previous models which have employed relatively simple representations of floodplain geometry. © 1997 by John Wiley & Sons, Ltd.

Kinetics of the reaction: H+HI?H2+I at 298 K and very low pressures

The reaction \scriptfont4=\seveni \scriptscriptfont4=\fivei $\rm H+HI\mathop\rightarrow\limits ^{1}H_{2}+I$ was studied at 298 K and millitorr pressures employing the “Very Low Pressure Reactor” (VLPR) kinetic technique. H-atoms were generated by dissociating H2 molecules (of a H2/Ar mixture) in a microwave discharge cavity that preceded the very low pressure well-mixed reaction vessel. Quadrupole mass spectrometry was used to analyze molecules and atoms. The mass signal intensities of I and HI were measured at both 20 and 40 eV ionizing potentials while those of H and H2 were measured at 40 eV due to the very weak signal of these species at lower ionization potentials. Three different exit flow orifices were utilized in the reported VLPR experiments of about 2, 3, and 5 mm inner diameter to vary the species concentration under steady-state reaction conditions. A rate constant of k1=(2.1±0.2)×10−11 cm3/molecule.s was determined for the forward reaction at 298 K, which lies between the two previously reported values directly measured at 298 K. Satisfactory mass balance relations were obtained for the iodine atoms (from the HI and I species) which were better than 90% for most of the experiments. The value of the reported rate constant (k1) is 14.3% higher than the value measured by Umemoto et al. [6], and 33.3% lower than the value measured by Lorenz et al. [4]. Based on this comparison, the activation energy E1 of the forward reaction probably lies between those two previously reported values of 580 and 720 cal/mol. Transition State Calculations of A1 and A2 for the reaction of \scriptfont4=\seveni \scriptscriptfont4=\fivei $\rm H+I_{2}\mathop\rightarrow\limits ^{2}HI+I$ are in good agreement with the data on both reactions and suggest an activation energy of about 500±100 cal/mol for E2.© 1997 John Wiley & Sons, Inc. Int J Chem Kinet: 29: 915–925, 1997.

Modeling and parametric study of the activated sludge process at Doha treatment plant

Abstract For the secondary treatment stage of Doha Municipal Wastewater Treatment Plant, the activated sludge process was represented by mass balance relationships for substrate and micro‐organisms. The substrate utilisation rate was assumed to follow the Monod model. Kinetic coefficients were determined using steady and unsteady‐state analyses. The non‐linear governing equations in the unsteady‐state analysis were solved using the fourth order Rung‐Kutta method. The steady‐state approach was observed to give better results. For the final settling tank, a performance equation was obtained for the determination of the suspended solids in the effluent.

Shock slip-relations for thermal and chemical nonequilibrium flows

This paper appears to be the first where the multi-temperature shock slip-relations for the thermal and chemical nonequilibrium flows are derived. The derivation is based on analysis of the influences of thermal nonequilibrium and viscous effects on the mass, momentum and energy flux balance relations at the shock wave. When the relaxation times for all internal energy modes tend to sere, the multi-temperature shock slip-relations are converted into single-temperature ones for thermal equilibrium hows. The present results can be applied to flows over vehicles of different geometries with or without angles of attack. In addition, the present single-temperature shock slip-relations are compared with those in the literature, and Some defects and limitations in the latter are clarified.

Setting reactions in dental amalgam. Part 2. The kinetics of amalgamation.

The literature on the setting mechanisms of dental amalgams made from powders of silver-rich alloys of tin and/or copper has been critically reviewed. Part 2 is a review of the kinetics of the reactions that convert the mixture of alloy powder and liquid mercury to hardened amalgam containing the phases and microstructures described in Part 1. It is emphasized that amalgamation is a non-equilbrium process in which hardened microstructures are determined as much by kinetics as by chemistry. The setting reaction begins with dissolution of silver and tin into liquid mercury; most of the product phases precipitate in the liquid mercury. The processes that produce supersaturation in the liquid mercury and the subsequent nucleation and growth of solid phases are considered. Mass balance relationships that provide insight into the factors that control the volume fraction of the undesirable gamma 2 Sn-Hg phase are described. The nucleation and growth of eta' Cu-Sn crystals are also discussed; it is found that these crystals nucleate on copper-rich phases and grow into the liquid mercury. Finally, aspects of the setting reaction that are controlled by intergranular and interphase diffusion in the solid are discussed. These aspects include: the supersaturation of silver and tin within the liquid mercury, nucleation and growth of the beta 1 Ag-Hg phase in the surfaces of alloy particles, and the decomposition of initially formed gamma 2 Sn-Hg.

Hexavalent Chromium Removal in Two-Stage Bioreactor System

A two-stage bioreactor system was used to reduce Cr(VI). Escherichia coli ATCC 33456 cells were aerobically grown in a first-stage chemostat, and then pumped to a second-stage plug-flow reactor where anaerobic Cr(VI) reduction occurred. Experimental results demonstrated that near complete removal of Cr(VI) was achieved in the plug-flow reactor under appropriate operating conditions. The removal efficiency in the plug-flow reactor was significantly affected by the influent Cr(VI) concentration, Cr(VI) loading rate, liquid detention time, and a consumed Cr(VI) reduction capacity factor. The consumed Cr(VI) reduction capacity factor was directly related to the toxicity effect of Cr(VI) on cells. To illustrate the influence of the consumed reduction capacity factor on Cr(VI) reduction in the plug-flow reactor, a mathematical model was developed by incorporating Cr(VI) reduction kinetics into the mass balance relationship of Cr(VI) for a plug-flow reactor. Analyses of Cr(VI) concentration profiles along the plug-flow reactor using both model simulations and experimental data indicated that the rate of Cr(VI) reduction decreased with the depletion of the reduction capacity of cells and Cr(VI) reduction ceased after the reduction capacity was exhausted.

Quantitative determination of metamorphic reaction history : mass balance relations between groundmass and mineral inclusion assemblages in metamorphic rocks

Quantitative determination of metamorphic reaction history : mass balance relations between groundmass and mineral inclusion assemblages in metamorphic rocks

Quantitative determination of metamorphic reaction history: mass balance relations between groundmass and mineral inclusion assemblages in metamorphic rocks

Qualitative and quantitative information about metamorphic reaction history and PT paths may be obtained from mineral inclusions in garnet by comparing the mineralogy, distribution, and compositions of paragenetically-related inclusions with minerals in the groundmass assemblage. Using the algebraic technique of singular value decomposition (SVD), we document mass balance relations between inclusion and groundmass assemblages in metapelitic rocks from two metamorphic terranes that experienced different peak metamorphic conditions, and whose transition from inclusion to groundmass assemblage records different PT path segments relative to peak conditions. We calculate mass balances relating an inclusion assemblage consisting in part of armored relics of chloritoid to groundmass mineral assemblages in a kyanite-staurolite mica schist from the Solitude Range, British Columbia, and an inclusion assemblage of kyanite, staurolite, and rutile to groundmass minerals in a sillimanite-cordierite gneiss from the Skagit Gneiss, North Cascade Range, Washington. Mass balances for each rock are consistent with reaction histories inferred from petrographic observations. In the Solitude Range schist, the results of mass balance calculations are consistent with the growth of staurolite and garnet at the expense of chloritoid during prograde metamorphism and suggest that chlorite, although not preserved as an inclusion, was involved in initial staurolite growth. In the Skagit sillimanite gneiss, mass balance relations exist between the inclusion suite, which formed during high pressure metamorphism, and the associated groundmass assemblage, which equilibrated at high temperature but much lower pressure. Mass balance does not exist between the groundmass of the Skagit sillimanite gneiss and the groundmass of a nearby kyanite-staurolite schist that has been proposed as a possible lower-grade equivalent of the sillimanite-bearing rocks. These results indicate that, although compositional modification and selective preservation of minerals must be taken into account, mineral inclusion suites may nevertheless preserve enough compositional information to allow reconstruction of complete or nearly complete pre-existing assemblages. This information may not be retrievable from any other source if no lower-grade equivalents of the rocks of interest are exposed.