Fitting the Gompertz equation to asymmetric breakthrough curves

Breakthrough curves of Cl and 3H2O were obtained during steady unsaturated flow in five lysimeters containing an undisturbed coarse sand (Orthic Haplohumod). The experimental data were analyzed in terms of the classical two-parameter convection-dispersion equation and a four-parameter two-region type physical nonequilibrium solute transport model. Model parameters were obtained by both curve fitting and time moment analysis. The four-parameter model provided a much better fit to the data for three soil columns, but performed only slightly better for the two remaining columns. The retardation factor for Cl was about 10 % less than for 3H2O, indicating some anion exclusion. For the four-parameter model the average immobile water fraction was 0.14 and the Peclet numbers of the mobile region varied between 50 and 200. Time moments analysis proved to be a useful tool for quantifying the break through curve (BTC) although the moments were found to be sensitive to experimental scattering in the measured data at larger times. Also, fitted parameters described the experimental data better than moment generated parameter values.

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Phosphorus transport in saturated slag columns: experiments and mathematical models

Water Science & Technology ◽

10.2166/wst.1996.0367 ◽

1996 ◽

Vol 34 (1-2) ◽

pp. 153-160 ◽

Cited By ~ 4

Author(s):

S. H. Lee ◽

S. Vigneswaran ◽

K. Bajracharya

Keyword(s):

Mathematical Models ◽

Sorption Capacity ◽

Algal Blooms ◽

Sandy Loam ◽

Dynamic Condition ◽

Water Environment ◽

Breakthrough Curves ◽

Column Experiments ◽

Phosphorus Transport ◽

Waste Products

Excessive phosphorus (P as orthophosphate) is one of the major pollutants in natural water that are responsible for algal blooms and eutrophication. P removal by slag is an attractive solution if the P sorption capacity of slag is significant. To design an efficient land treatment facility, basic information on the behaviour of P in the media-water environment is required. In this study, detailed column experiments were conducted to study the P transport under dynamic condition, and mathematical models were developed to describe this process. The column experiments conducted with dust and cake waste products (slag) from a steel industry as adsorbing indicated that they had higher sorption capacity of P than that of a sandy loam soil from North Sydney, Australia. P transport in the dust and cake columns exhibited characteristic S-shaped or curvilinear breakthrough curves. The simulated results from a dynamic physical nonequilibrium sorption model (DPNSM) and Freundlich isotherm constants satisfactorily matched the corresponding experimental breakthrough data. The mobility of P is restricted by the adsorbents and it is proportional to the sorption capacity of them.

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Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

Water Science & Technology ◽

10.2166/wst.1991.0080 ◽

1991 ◽

Vol 24 (2) ◽

pp. 309-314 ◽

Cited By ~ 16

Author(s):

G. Teutsch ◽

K. Herbold-Paschke ◽

D. Tougianidou ◽

T. Hahn ◽

K. Botzenhart

Keyword(s):

Simulation Models ◽

Mass Conservation ◽

Breakthrough Curves ◽

Conservation Equation ◽

Retardation Factor ◽

Natural Systems ◽

Laboratory Setup ◽

Preliminary Model ◽

Sand And Gravel ◽

Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

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Biochar caged zirconium ferrite nanocomposites for the adsorptive removal of Reactive Blue 19 dye in a batch and column reactors and conditions optimizaton

Zeitschrift für Physikalische Chemie ◽

10.1515/zpch-2020-1749 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Shazia Perveen ◽

Raziya Nadeem ◽

Shaukat Ali ◽

Yasir Jamil

Keyword(s):

Experimental Data ◽

Low Dose ◽

Fixed Bed ◽

Breakthrough Curves ◽

Adsorption Efficiency ◽

Fixed Bed Column ◽

Flow Rates ◽

Adsorptive Removal ◽

Reactive Blue 19 ◽

Pseudo Second Order

Abstract Biochar caged zirconium ferrite (BC-ZrFe2O5) nanocomposites were fabricated and their adsorption capacity for Reactive Blue 19 (RB19) dye was evaluated in a fixed-bed column and batch sorption mode. The adsorption of dye onto BC-ZrFe2O5 NCs followed pseudo-second-order kinetics (R 2 = 0.998) and among isotherms, the experimental data was best fitted to Sips model as compared to Freundlich and Langmuir isotherms models. The influence of flow-rate (3–5 mL min−1), inlet RB19 dye concentration (20–100 mg L−1) and quantity of BC-ZrFe2O5 NCs (0.5–1.5 g) on fixed-bed sorption was elucidated by Box-Behnken experimental design. The saturation times (C t /C o = 0.95) and breakthrough (C t /C o = 0.05) were higher at lower flow-rates and higher dose of BC-ZrFe2O5 NCs. The saturation times decreased, but breakthrough was increased with the initial RB19 dye concentration. The treated volume was higher at low sorbent dose and influent concentration. Fractional bed utilization (FBU) increased with RB19 dye concentration and flow rates at low dose of BC-ZrFe2O5 NCs. Yan model was fitted best to breakthrough curves data as compared to Bohart-Adams and Thomas models. Results revealed that BC-ZrFe2O5 nanocomposite has promising adsorption efficiency and could be used for the adsorption of dyes from textile effluents.

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Effective Separation of Prime Olefins from Gas Stream Using Anion Pillared Metal Organic Frameworks: Ideal Adsorbed Solution Theory Studies, Cyclic Application and Stability

Catalysts ◽

10.3390/catal11040510 ◽

2021 ◽

Vol 11 (4) ◽

pp. 510

Author(s):

Majeda Khraisheh ◽

Fares. Almomani ◽

Gavin Walker

Keyword(s):

Breakthrough Curves ◽

Isotherm Models ◽

Regeneration Ability ◽

Solution Theory ◽

Experimental Conditions ◽

Ideal Adsorbed Solution Theory ◽

Adsorbed Solution ◽

The Stability ◽

Adsorption Desorption ◽

Adsorbed Solution Theory

The separation of C3H4/C3H6 is one of the most energy intensive and challenging operations, requiring up to 100 theoretical stages, in traditional cryogenic distillation. In this investigation, the potential application of two MOFs (SIFSIX-3-Ni and NbOFFIVE-1-Ni) was tested by studying the adsorption–desorption behaviors at a range of operational temperatures (300–360 K) and pressures (1–100 kPa). Dynamic adsorption breakthrough tests were conducted and the stability and regeneration ability of the MOFs were established after eight consecutive cycles. In order to establish the engineering key parameters, the experimental data were fitted to four isotherm models (Langmuir, Freundlich, Sips and Toth) in addition to the estimation of the thermodynamic properties such as the isosteric heats of adsorption. The selectivity of the separation was tested by applying ideal adsorbed solution theory (IAST). The results revealed that SIFSIX-3-Ni is an effective adsorbent for the separation of 10/90 v/v C3H4/C3H6 under the range of experimental conditions used in this study. The maximum adsorption reported for the same combination was 3.2 mmolg−1. Breakthrough curves confirmed the suitability of this material for the separation with a 10-min gab before the lighter C3H4 is eluted from the column. The separated C3H6 was obtained with a 99.98% purity.

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Kinetic Studies of Cs+ and Sr2+ Ion Exchange Using Clinoptilolite in Static Columns and an Agitated Tubular Reactor (ATR)

ChemEngineering ◽

10.3390/chemengineering5010009 ◽

2021 ◽

Vol 5 (1) ◽

pp. 9

Author(s):

Muhammad Yusuf Prajitno ◽

Mohamad Taufiqurrakhman ◽

David Harbottle ◽

Timothy N. Hunter

Keyword(s):

Adsorption Capacity ◽

Tubular Reactor ◽

Process Intensification ◽

Kinetic Studies ◽

Breakthrough Curves ◽

Maximum Adsorption Capacity ◽

Batch Studies ◽

Shear Mixing ◽

Natural Clinoptilolite ◽

Kinetics Of

Natural clinoptilolite was studied to assess its performance in removing caesium and strontium ions, using both static columns and an agitated tube reactor (ATR) for process intensification. Kinetic breakthrough curves were fitted using the Thomas and Modified Dose Response (MDR) models. In the static columns, the clinoptilolite adsorption capacity (qe) for 200 ppm ion concentrations was found to be ~171 and 16 mg/g for caesium and strontium, respectively, highlighting the poor material ability to exchange strontium. Reducing the concentration of strontium to 100 ppm, however, led to a higher strontium qe of ~48 mg/g (close to the maximum adsorption capacity). Conversely, halving the column residence time to 15 min decreased the qe for 100 ppm strontium solutions to 13–14 mg/g. All the kinetic breakthrough data correlated well with the maximum adsorption capacities found in previous batch studies, where, in particular, the influence of concentration on the slow uptake kinetics of strontium was evidenced. For the ATR studies, two column lengths were investigated (of 25 and 34 cm) with the clinoptilolite embedded directly into the agitator bar. The 34 cm-length system significantly outperformed the static vertical columns, where the adsorption capacity and breakthrough time were enhanced by ~30%, which was assumed to be due to the heightened kinetics from shear mixing. Critically, the increase in performance was achieved with a relative process flow rate over twice that of the static columns.

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Experimental and modeling of competitive biosorption of benzene, toluene, ethylbenzene, xylenes, and naphthalene (BTEXN) in a packed-bed column with a macroalgae-based composite: Effect of dissolved organic matter and flow rate on breakthrough curves

Journal of Water Process Engineering ◽

10.1016/j.jwpe.2020.101874 ◽

2021 ◽

Vol 40 ◽

pp. 101874

Author(s):

Carlos E. Flores-Chaparro ◽

Mayra C. Rodriguez-Hernandez ◽

Luis F. Chazaro-Ruiz ◽

Ma. Catalina Alfaro-De la Torre ◽

Miguel A. Huerta-Diaz ◽

...

Keyword(s):

Organic Matter ◽

Dissolved Organic Matter ◽

Flow Rate ◽

Packed Bed ◽

Breakthrough Curves ◽

Composite Effect ◽

Packed Bed Column ◽

Competitive Biosorption ◽

Benzene Toluene

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Kinetics and Equilibrium of Radioactive Metal Adsorption onto Sugarcane Bagasse Waste: Comparison of Batch and Column Adsorption Modes

Zeitschrift für Physikalische Chemie ◽

10.1515/zpch-2019-1418 ◽

2021 ◽

Vol 235 (3) ◽

pp. 281-294

Author(s):

Abida Kausar ◽

Haq Nawaz Bhatti ◽

Munawar Iqbal

Keyword(s):

Sugarcane Bagasse ◽

Flow Rate ◽

Breakthrough Curves ◽

Quadratic Model ◽

Waste Biomass ◽

Initial Concentration ◽

Bed Height ◽

Column Adsorption ◽

Central Composite ◽

Bagasse Waste

Abstract Sugarcane bagasse waste biomass (SBWB) efficacy for the adsorption of Zr(IV) was investigated in batch and column modes. The process variables i.e. pH 1–4 (A), adsorbent dosage 0.0–0.3 g (B), and Zr(IV) ions initial concentration 25–200 mg/L (C) were studied. The experiments were run under central composite design (CCD) and data was analysed by response surface methodology (RSM) methodology. The factor A, B, C, AB interaction and square factor A2, C2 affected the Zr(IV) ions adsorption onto SBWB. The quadratic model fitted well to the adsorption data with high R2 values. The effect of bed height, flow rate and Zr(IV) ions initial concentration was also studied for column mode adsorption and efficiency was evaluated by breakthrough curves as well as Bed Depth Service and Thomas models. Bed height and Zr(IV) ions initial concentration enhanced the adsorption of capacity of Zr(IV) ions, whereas flow rate reduced the column efficiency.

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Use of a Modified Gompertz Equation to Predict the Effects of Temperature, pH, and NaCl on the Inactivation of Listeria monocytogenes Scott A Heated in Infant Formula

Journal of Food Protection ◽

10.4315/0362-028x-59.1.16 ◽

1996 ◽

Vol 59 (1) ◽

pp. 16-23 ◽

Cited By ~ 51

Author(s):

R. H. LINTON ◽

W. H. CARTER ◽

M. D. PIERSON ◽

C. R. HACKNEY ◽

J. D. EIFERT

Keyword(s):

Listeria Monocytogenes ◽

Infant Formula ◽

Nonlinear Regression ◽

Survival Curve ◽

Interactive Effects ◽

Parameter Estimates ◽

Survival Curves ◽

Gompertz Equation ◽

Nacl Concentration ◽

Effects Of Temperature

The heat resistance of Listeria monocytogenes was determined in infant formula for all possible combinations of temperature (50, 55, and 60°C), pH level (5, 6, and 7), and NaCl concentration (0, 2, and 4%). Survival curves were fit using nonlinear regression with a Gompertz equation. The Gompertz equation was flexible enough to fit the three most commonly observed survival curves: linear curves, those with an initial lag region followed by a linear region, and sigmoidal shaped. Parameter estimates obtained by the method of nonlinear least squares were used to describe the effect(s) of different heating treatments on the lag region, death rate, and tailing region of survival curves. These estimates were further used to predict single and interactive effects of temperature, pH, and percentage of NaCl on the log of the surviving fraction (LSF) of bacteria. Interactions among these variables significantly (P ≤ .05) affected the LSF. Generally, increased pH or NaCl concentration lead to an increased LSF, whereas increased time or temperature lead to a decreased LSF. All multiple-factor interactions significantly (P ≤ .05) affected the LSF. The correlation of observed LSF versus predicted LSF (R2 = .92) indicated that the estimated Gompertz equation was in close agreement with the observation. This study demonstrated that the Gompertz equation and nonlinear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes under many different environmental conditions.

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