Unsteady-state Model Research Articles

Modelling and advanced understanding of unsteady‐state gas transfer in shaking bioreactors

In shaken bioreactors equipped with a sterile closure (e.g. a cotton plug), a realistic understanding and estimation of gas transfer is advantageous to avoid oxygen limitation or carbon dioxide inhibition of a microbial culture. Therefore, in the present study, an unsteady-state gas-transfer model for shake flasks was developed and experimentally investigated for a wide range of gas-transfer resistances (k(plug)). The introduced approach is based on the model of Henzler and co-workers [Henzler and Schedel (1991) Bioprocess Eng. 7, 123-131; Mrotzek, Anderlei, Henzler and Büchs (2001) Biochem. Eng. J. 7, 107-112], which describe the spatially resolved gas partial pressures inside the sterile closure, affecting the local gas diffusion coefficients and convective Stefan flow. For further easy processing the resulting total mass-transfer resistance (k(plug)) is described as a function of the mass flow through the sterile plug (OTR(plug)) by an empirical equation. This equation is introduced into a simulation model which calculates the gas partial pressures in the head space of the flask. Additionally, the gas-transfer rates through the sterile closure and gas/liquid interface inside the flask is provided. Simulations indicate that neglecting the oxygen in the head space volume of the flask under initial conditions (simple steady-state assumption) may lead to an underestimation of the oxygen transfer into the liquid phase. The extension of error depends on the conditions. A good agreement between the introduced unsteady-state model and experimental results for the sulfite oxidation as a chemical model system confirmed the validity and usefulness of the proposed unsteady-state approach.

On the role of nighttime meteorology in modeling dispersion of near surface emissions in urban areas

This paper examines the role of meteorology in linking near surface emissions of particulate matter and associated ambient concentrations in urban areas. The examination is conducted with two models: a steady state model based on urban dispersion models developed earlier, and an unsteady state model that accounts for time varying meteorological and emission inputs. After conducting sensitivity studies with the models, they are applied in Pune, India to (a) check consistency between estimates of surface emissions of particulate matter (with aerodynamic diameters of less than 10 μ m, referred to as PM 10 ) and observed ambient concentrations and (b) identify the variables that govern air quality. Results from the modeling exercise indicate that (1) nighttime meteorology governs both hourly as well as 24 h averaged concentrations and (2) because the wind speeds in urban areas are typically low, concentration estimates from the steady state model differ substantially from those of the unsteady state model during the nighttime hours both in magnitude and in timing of the peaks; however, the difference between the 24 h averaged concentrations from the two models is less than 5% for the cases considered here. Because our understanding of nighttime meteorology in urban areas is limited, there is a need for experimental programs to relate the diurnal variation of concentrations with associated meteorology, especially during the night.

Effect of Pretreatments on Drying and Rehydration Kinetics and Color of Sweet Potato Slices

The effect of air temperature and pretreatments (KMS: citric acid) on drying kinetics of sweet potato slices was investigated. Drying experiments were performed in a tray dryer. In falling rate period, moisture transfer from sweet potato slices was described by applying the unsteady-state Fickian diffusion model, and the rate constant (k) were calculated. The effect of temperature on k could be interpreted according to Arrhenius law. Drying rate and therefore k values were found to be affected by pretreatments. Rehydration rates of dried sweet potato slices at 25, 40, 80°C were also determined and found to be independent of drying conditions and rehydration temperature. The ΔE value was found to be the highest for slices treated at 50°C with 0.5:1.0% KMS and citric acid.

Kinetic behavior of benzene hydrogenation and thiophene hydrogenolysis on sulfide Ni-Mo/Al2O3 catalyst

An unsteady-state kinetic model of both benzene hydrogenation (HDA) and thiophene hydrogenolysis (HDS) on a sulfide hydrotreating catalyst Ni-Mo/Al2O3 has been developed. The model adequately describes experimental data obtained at the pressure 2 MPa, temperature 573 K and at various contact times and ratios of benzene/thiophene. The model is based on the assumption that the catalyst surface contains only one type of active sites, i.e., Ni atoms in the sulfide bimetallic species, which are responsible for both hydrogenolysis and hydrogenation reactions.

06/01896 Challenges for PEM fuel cell membranes: Beuscher, U. et al. International Journal of Energy Research, 2005, 29, (12), 1103–1112

The dynamic performance of a PEM fuel cell is one of the most important criteria in the design of fuel cells, especially when the application of the fuel cell in mobile systems is concerned. To attack this issue, we extend the theoretical model developed by Okada (J. Electroanal. Chem. 465 (1999) 1,18) to an unsteady state model and investigate the transient behavior of water transport across the membrane as well as the influences of several physical parameters on the characteristic time to reach the steady state. We also consider the influence due to the presence of foreign impurity ions, which turn out to be a crucial factor affecting the unsteady state features of water transport across the membrane. The results suggest that a higher initial current density to start the operation, a higher water flux from the anode side, a smaller operational current density, and a lower level of contamination in the membrane (especially at the cathode side) can all result in a shorter time for the water transport to reach the steady state, and thus a better dynamic performance of the fuel cell can be obtained.

Model‐based analysis and design of a microchannel reactor for tissue engineering

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.

Drying of Lentil Including Shrinkage: A Numerical Simulation

This article presents a theoretical study about drying of lentil including shrinkage. The two-dimensional unsteady-state diffusion modeling written in the oblate spheroidal coordinates system considers the volume variation effect, convective boundary condition at the surface of the solid, and variable thermo-physical properties. The governing equation was discretized using the finite-volume method and the linear equations system was solved by Gauss-Siedel iterative method. To validate the model, numerical results of the average moisture content were compared with experimental data from eight experiments and a good agreement was obtained. The diffusion coefficients for all drying experiments are determined using the least square error technique.

Optimal control determination of MMA polymerization in non-isothermal batch reactor using bifunctional initiator

In this work, we determine the optimal control for free-radical methyl methacrylate polymerization using a bifunctional initiator in a non-isothermal batch reactor. A detailed unsteady-state model of the process is employed. Four different optimal control objectives are realized, each of which optimizes a given variable simultaneously with the specification of another. The first two objectives involve the maximization of monomer conversion in a specified operation time, and the minimization of operation time for a specified, final monomer conversion. The last two objectives involve the maximization of monomer conversion for specified, final number and weight average polymer molecular weights. The temperature of heat-exchange fluid inside reactor jacket is considered as a control function of an independent variable. To meet the specification of an optimization variable other than time, the differential model of batch process is derived in the range of specified variable. Equations are provided for Jacobian evaluations to help in the accurate solution of process model. A genetic algorithms-based optimal control method is applied to realize the four optimal control objectives. The results show that optimal control can significantly enhance the performance of the batch polymerization process.

Modeling of Deposit Formation from “Waxy” Mixtures via Moving Boundary Formulation: Radial Heat Transfer under Static and Laminar Flow Conditions

A mathematical formulation, based on heat transfer considerations, is presented for solids deposition from “waxy” or paraffinic mixtures. The proposed unsteady-state model uses the moving boundary problem approach for investigating the deposit-layer growth in a circular pipe from binary eutectic mixtures of n-C16H34 and n-C28H58. The model equations were solved numerically to explore the deposition behavior and the growth of deposit layer with time in the radial direction under both static and laminar flow conditions. The deposit-layer growth was predicted to be dependent on the rate of heat transfer at the liquid−deposit interface as well as in the liquid and deposit regions. For cooling under static conditions, complete pipe gelling was predicted to be faster for relatively lower values of mixture temperature, pipe-wall temperature, concentration of C28 in the mixture, and pipe diameter. For cooling under laminar flow conditions, higher values of mixture temperature, pipe-wall temperature and/or heat transfer coefficient yielded a thinner deposit layer with a faster approach to thermal steady state.

Diffusion of Nicotinamide Adenine Dinuncleotide in Calcium Alginate Hydrogel Beads Doped with Carbon and Silica Nanotubes

Alginate gel beads doped with nanotubes or nanoparticles were prepared using four kinds of dopants: carbon nanotubes (CNTs), silica nanotubes, graphite, or silica nanoparticles (SiO2). The effective diffusion coefficients (De) of reduced nicotinamide adenine dinuncleotide (NADH) in hybrid gels were calculated using an unsteady-state model developed by Nguyen and Luong. The maximum De values of NADH in the four kinds of hybrid gels obey the following sequence: De (CNTs-alginate) > De (silica nanotubes-alginate) > De (SiO2-alginate) > De (graphite-alginate). The effect of the dopant concentration on De was examined at five dopant concentration levels (0.3, 0.5, 0.9, and 1.25) g/L. For the CNTs-alginate and silica nanotubes-alginate gels, the maximum De values of NADH were obtained at 0.3 g/L and 0.9 g/L dopant concentrations, respectively. For the silica-alginate and graphite-alginate gels, the maximum De values of NADH were obtained at 0.5 g/L dopant concentration. The maximum De value of NADH in the CNT...

Dynamic modelling of periodically wetted catalyst particles

The design of periodically operated trickle-bed reactors requires extensive knowledge of the complex underlying processes occurring at various scales. The development of dynamic models offers detailed insights into system behaviour and allows quantitative investigations over a wide range of operating conditions without the expense of comprehensive experimental studies. The description of the dynamic behaviour of periodically wetted catalyst particles is an important element in the overall multi-scale model architecture. Unfortunately, very little information is available on the influence of various model assumptions to aid selection of appropriate unsteady-state models. A systematic evaluation of dynamic particle-scale modelling approaches based on various intra-particle concentration profiles and periodic wetting of the external particle surface is presented.

Development and experimental checking of an unsteady-state model for ultrafiltration continuous tank reactors

A mathematical model applicable to the analysis, design and simulation of homogeneous enzymatic processes reacting in a ultrafiltration membrane reactor has been formulated. The model develops the unsteady-state design equations, including a first-order model to represent enzyme deactivation kinetics. To check the model, the stereospecific hydrolysis of N-acetyl- DL-butyrine catalysed by L-aminoacylase to give L-butyrine and unmodified N-acetyl- D-butyrine was used as an experimental system. The experiments were carried out at pH 7.0 and 50 ∘ C , using two different flow rates (1.0 and 1.5 cm 3 min - 1 ), three different substrate concentrations at the reactor inlet (25, 50 and 100 mmol dm - 3 in N-acetyl- L-butyrine ( C SL 0 ) ) and two different start-up modes. When the experimental data were compared to those theoretically predicted, the statistical analysis underlined the goodness of the model and the accuracy of the constants calculated.

Numerical Modelling of Cuttings Transport With Foam in Vertical Wells

Abstract In this study, a 1D unsteady-state two-phase mechanistic model of cuttings transport with foam in vertical wells has been developed. The model is solved numerically to predict the optimum foam flow rate and rheological properties to maximize the cuttings transport efficiency in vertical wells. Comparisons of model predictions with the field test data have shown that model predictions are in close agreement with the field test results. The numerical solution allows analyzing the effects of borehole geometry, drilling rate, foam rheological properties, gas and liquid flowing rates, and reservoir fluid influx on the cuttings transport efficiency when drilling vertical wells. Results of sensitivity analysis study are presented. Introduction The Alberta Energy and Utilities Board defines underbalanced drilling (UBD) as, "when the hydrostatic head of a drilling fluid is intentionally designed to be lower than the pressure of the formation being drilled(1)." The benefits of UBD include increased productivity by reducing formation damage, increased rate of drilling bit penetration, minimization or elimination of lost circulation, improved formation evaluation while drilling, reduction or elimination of differential pipe sticking, reduced stimulation requirements, and earlier production. Four drilling methods are referred to as UBD:gas drilling- air, nitrogen, and some hydrocarbon gases can be used as a circulating medium;flow drilling-fluid with density below the formation's hydrostatic gradient is used as circulating fluid;gas/ liquid drilling-a gas-liquid two-phase drilling fluid is used in the drilling operation; and,foam drilling-stable foams are used as cuttings transport media. Because of its variable density and good cuttings transport ability, foam is often used in UBD operations. The use of foam as a drilling fluid in many drilling operations and the results from various field cases have been well documented in the literature(2–5). Field application of the foamed drilling fluids is very often complicated because of the difficulties encountered in controlling fluid hydraulic properties. In general, compared to conventional (incompressible) drilling fluids, much less is known about the hydraulic and rheological properties of foamed drilling fluids, and even less is known about their cuttings transport capabilities. The complex flow mechanism involving in compressible drilling fluid circulation makes the determination of the optimum combination of liquid and gas injection rates very difficult. Other questions also exist, such as how to predict the bottom-hole pressure and how to combine different controllable variables in order to obtain optimum cuttings transport performance and bit hydraulics. In order to realistically simulate the hydraulics of foam drilling, factors including foam rheological properties, drag coefficient of cuttings in foam, formation fluid influx, drillpipe eccentricity, and drilling rate need to be considered in any modelling study. An example of such a modelling study is presented in this article. Literature Review The following section provides a review of literature on cuttings transport in general, the rheology of foam, and of cuttings transport with foam. Cuttings Transport Hole cleaning (cuttings transport) is one of the major factors affecting cost, time, and quality of directional, horizontal, extended reach, and multilateral oil/gas wells.

Optimal Control of the Secondary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

: The problem of operating freeze drying of pharmaceutical products in vials loaded on trays of freeze dryer to obtain a desired final bound water content in minimum time is formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In the type I freeze dryer design, upper and lower plate temperatures were controlled together, while in the type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Only the scorch temperature was considered as a constraint on the system state variables during the secondary drying stage, because all the free water content (frozen water) is removed from the solid matrix during the primary drying stage of freeze drying. Necessary conditions of optimality for the secondary drying stage of freeze drying process in vials were derived and presented by using rigorous multidimensional unsteady-state mathematical models. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in drying times of the secondary drying stage of the freeze drying process in vials were observed and more uniform bound water and temperature distributions in the material being dried were obtained compared to the conventional operational policies.

Pure ice sublimation within vials in a laboratory lyophiliser; comparison of theory with experiment

A two-dimensional axisymmetric, unsteady state model was developed to simulate the coupled heat and mass transfer process that occurs during the sublimation of pure ice from within vials in a laboratory-scale lyophiliser. The theoretical model was solved numerically using an explicit finite difference method. The modified Euler method was used to discretise in time and an adaptive time step strategy was employed to ensure stability. Novel features of the model described here include a consideration of the varying, pressure dependent, insulating effect of the air gap under the curved base of a typical lyophilisation vial and the determination of the effects of radiative heating. The theoretical model was capable of predicting and describing the observed motion of the ice sublimation front, the ice temperature profile, the drying time and the influence of the total pressure. The model also gave a theoretical prediction of the improvement in drying rate that might be achieved by adding an extra energy source. The work provides insights into the understanding of the heat and mass transfer process during the primary drying stage of lyophilisation that can be applied to the optimisation of freeze-drying cycle design.

Step response analysis of phosphoric acid fuel cell (PAFC) cathode through a transient model

Transient state response analysis of phosphoric acid fuel cell (PAFC) cathode is important to understand various competitive processes like diffusion, reaction and product back diffusion occurring at various layers of the composite cathode. A two-dimensional unsteady state model for simulating PAFC cathode is developed as an extension of the previously developed steady-state model [S. Roy Choudhury, M.B. Deshmukh, R. Rengaswamy, A two-dimensional steady-state model for phosphoric acid fuel cells (PAFC), J. Power sources 112 (2002) 137–152]. The transient model is solved to study the impact of various parameters such as Tafel slope, diffusivity etc on the step response of the fuel cell. The effect of partial pressure variation in bulk gas for large sized PAFC cathode is also analysed. Trend analysis based on the model output is also experimentally verified using a small unit cell setup. The effect of various parameters on the settling time of the cathode, as revealed in this study, suggests possible development of a diagnostic tool employing such transient model.

A GIS-based multimedia watershed model: development and application

A multimedia model was developed using publicly available geographical information system (GIS) data, chemical release information and local monitoring networks to assess the fate of trichloroethene (TCE) within the Passaic River Watershed. Seven environmental media, air, water, sediment, surface soil, terrestrial vegetation, root zone soil and vadose zone soil, were modeled in this study along with their sub-compartments. The Passaic River Watershed is described using the NJDEP geographical information system (GIS) resources, the United States Geological Survey (USGS) and the United States Soil Conservation Services (US SCS) soil data. The introduction of spatial resolution to a multimedia, unsteady state model is performed in this work, and represents an important step in expanding the use of equilibrium models to provide far reaching information on the fate of toxic contaminants within a given environmental unit. The spatial representation of cross-boundary fluxes was successfully demonstrated with the use of sub-watershed as an environmental unit and the direct assessment of TCE for each of the 11 sub-watersheds that make up the Passaic River Basin in northern New Jersey. Important data gaps identified during the development of this model include the lack of comprehensive monitoring data on organic contaminants, and non-uniformity among available physical environmental data from different government agencies.

Transient behavior of water transport in the membrane of a PEM fuel cell

The dynamic performance of a PEM fuel cell is one of the most important criteria in the design of fuel cells, especially when the application of the fuel cell in mobile systems is concerned. To attack this issue, we extend the theoretical model developed by Okada (J. Electroanal. Chem. 465 (1999) 1,18) to an unsteady state model and investigate the transient behavior of water transport across the membrane as well as the influences of several physical parameters on the characteristic time to reach the steady state. We also consider the influence due to the presence of foreign impurity ions, which turn out to be a crucial factor affecting the unsteady state features of water transport across the membrane. The results suggest that a higher initial current density to start the operation, a higher water flux from the anode side, a smaller operational current density, and a lower level of contamination in the membrane (especially at the cathode side) can all result in a shorter time for the water transport to reach the steady state, and thus a better dynamic performance of the fuel cell can be obtained.

Application of Transition State Theory for Thermal Stability Prediction

Estimations of thermal hazards based on calorimetric experiments can be resource consuming. Therefore, reactive hazard predictions using computational techniques are an attractive option. Typically, prior to detailed experimentation, a screening test is performed on the set of potential reactive chemicals using a differential scanning calorimeter (DSC). The screening tests help to focus the resources on the more reactive systems. The onset temperature (To) and the energy of reaction (−ΔHrxn) are two important parameters obtained from a DSC run. Prediction of thermal stability requires the knowledge of both the thermodynamics and kinetics for the given system. In this paper, the energy of reaction (−ΔHrxn) is approximated by the maximum enthalpy of decomposition (as calculated by the CHETAH program) and transition state theory is employed to estimate the decomposition kinetics of aromatic nitro compounds. The activation energy is approximated as a fraction of the bond dissociation energy (BDE), calculated for the C−NO2 bond, at the B3P86 level of theory with the cc-pVDZ basis set. BDE values are also reported from the semiempirical AM1 theory. These quantum mechanical calculations are combined with an unsteady-state model for a batch reactor to predict onset temperatures for nineteen nitro compounds, which are compared with experimental values.

Sorption of volatile organic compounds on typical carpet fibers

Measurements of adsorption isotherms for three volatile organic compounds (VOCs) (toluene, 1,2-dichlorobenzene and 1,1,1-trichloroethane) on polyacrylonitrile carpet fibers over the temperature range 25–45 °C were carried out in a thermogravimetric analyzer (TGA). Linear isotherms were observed in all cases with values of the Henry coefficient ranging from 0.063 to 0.941 mm. The results of additional experiments carried out in a simple test chamber containing a single source of VOC showed that the carpet fibers acted as a significant sink causing a prolonged elevation of VOC concentration in the air within the chamber. An unsteady-state model is presented, which adequately described the adsorption and desorption phenomena occurring in the test chamber and yielded realistic values of the adsorption and desorption rate constants. There was good agreement between the equilibrium and kinetic constants obtained in the TGA and test chamber experiments.