Siddharth G. Chatterjee

Modeling xylan solubilization during autohydrolysis of sugar maple wood meal: reaction kinetics.

Abstract The objective of this work was to study the kinetics of hemicelluloses extraction during hydrothermal pretreatment of sugar maple wood meal. Pretreatment was conducted in a batch reactor at 145–185°C with reaction times up to 8 h and with liquor to solid ratio of 20:1. Under these conditions, hemicelluloses were selectively solubilized and little degradation (approximately 6–9% of the initial amount) of cellulose and lignin was observed. A kinetic model was developed. It was supposed that there are no diffusion limitations and that the reaction rate constants have first-order kinetics with Arrhenius-type temperature dependence. The model proposes the formation of xylose directly from wood xylan as well as from xylooligomers formed in the liquid phase by the hydrolysis of xylan. The model is able to correlate satisfactorily experimentally measured yields of residual xylan, xylooligomers, xylose, and furfural obtained during the pretreatment.

Evaporative Cooling of Water in a Small Vessel Under Varying Ambient Humidity

Evaporative cooling of water in a small porous clay vessel was studied under controlled humidity conditions. In steady-state experiments performed at an ambient temperature of 23 °C, the cooling effect increased from 4.7 to 8.3 °C as the ambient relative humidity decreased from 60 to 15%. External heat and mass transfer coefficients, estimated from the steady-state measurements, were used in mathematical models to predict the experimentally observed transient temperature variation of the water under ramp changes of the ambient relative humidity. With a prototypical cool chamber containing water tested in Kolkata, India under an ambient temperature of 34.5–35 °C, the cooling effect reached a maximum of 7 °C between 3 and 3:30 PM and then declined to 4.5 °C around 6 PM.

A SURFACE-RENEWAL MODEL OF CROSS-FLOW MICROFILTRATION

A mathematical model using classical cake-filtration theory and the surface-renewal concept is formulated for describing cross-flow microfiltration under dynamic and steady-state conditions. The model can predict the permeate flux and cake buildup in the filter. The three basic parameters of the model are the membrane resistance, specific cake resistance and rate of surface renewal. The model is able to correlate experimental permeate flow rate data in the microfiltration of fermentation broths in laboratory- and pilot- scale units with an average root-mean-square (RMS) error of 4.6%. The experimental data are also compared against the critical-flux model of cross-flow microfiltration, which has average RMS errors of 6.3, 5.5 and 6.1% for the cases of cake filtration, intermediate blocking and complete blocking mechanisms, respectively.

Analytical Expressions for the Adsorbate Breakthrough Curve from a Fixed Bed of Adsorbent with First-order and Second-order Kinetic Models

Abstract In many batch studies, the kinetics of adsorption have demonstrated adherence to first-order (Lagergren) or second-order (Ho and McKay) models. Since practical adsorption systems generally operate in the fixed-bed mode, in this work, the first- and second-order kinetic models describing adsorbate uptake are combined with an overall adsorbate material balance to obtain simple analytical expressions for the adsorbate breakthrough curve from a fixed bed of adsorbent. These expressions can correlate some fixed-bed experimental data reported in the literature with an average error of 18%. The equations describing the breakthrough behaviour can be used for the rapid scale-up and design of fixed-bed adsorption columns for removing contaminants from water and wastewater.

On the Use of the Surface-Renewal Concept to Describe Cross-Flow Ultrafiltration

Abstract A theoretical model using the surface-renewal concept is developed for describing cross-flow ultrafiltration under dynamic and steady-state conditions. The model can predict the local permeate flux and concentration profile of dissolved solute in the filter. The rate of surface renewal (S) at the membrane surface and the diffusion coefficient (D) of the solute in the solvent are the two parameters of the model. The model is able to correlate literature data of transient permeate flux in the ultrafiltration of skim milk with an average root-mean-square error of 9.9%. The values of S and D, estimated from the model, are 0.84 − 1.74×10−3 s−1 and 0.55 − 2.07×10−9 m2/s, respectively.

A Theoretical Analysis of Dissolved-Gas Transfer to the Bulk Liquid in Gas Absorption with a First-Order Reaction

Abstract A theoretical analysis using the surface-renewal and film-penetration models, which includes gas-phase resistance to mass transfer, is presented for the rate of absorption of a gas and its transfer to the bulk liquid in the case where the solute gas undergoes a first-order chemical reaction in the liquid phase. It reveals that: a. The fraction of absorbed gas transported to the bulk liquid depends upon the Hatta number Ha in case of the surface-renewal model and on Ha as well as a dimensionless hydrodynamic parameter in case of the film-penetration model. b. The widely assumed law of addition of resistances is valid for the surface-renewal and film-penetration models. c. The reaction influences both the overall mass-transfer coefficient and the nature of the driving force, i.e. the increased rate of absorption due to the reaction is not solely due to the enhancement factor multiplying the liquid-phase mass-transfer coefficient for physical absorption as has been conventionally assumed in the literature. It is also shown that in a gas-liquid reactor the film and surface-renewal models give close predictions for both the rate of absorption and concentration of dissolved gas in the liquid leaving the reactor. For values of Ha ⩾ 0.5, the bulk-liquid concentration of dissolved gas predicted by both models is negligible compared to its interfacial concentration.

A time-lag model for biogas production by anaerobic digestion

This work presents a simple time-lag model for biogas production from anaerobic digestion of organic wastes (biomass) in a batch digester. The model has the ability of predicting the S-shaped nature of the cumulative biogas yield with retention time that is commonly observed experimentally. The model is calibrated against biogas production data from anaerobic digestion of three types of organic waste: OFMSW (organic fraction of municipal solid waste), FVW (fruit and vegetable waste) and RH (rice husk). For these three wastes, the fit of the model to the experimental data has an average root-mean-square deviation of 9%. The time-lag model leads to the formulation of two measures or indexes of biodegradability of a particular waste. The values of these indexes are much higher for FVW compared to those for OFMSW and RH showing that the susceptibility of FVW to anaerobic digestion far exceeds that of the other two wastes.

A frequency quantum interpretation of the surface renewal model of mass transfer

The surface of a turbulent liquid is visualized as consisting of a large number of chaotic eddies or liquid elements. Assuming that surface elements of a particular age have renewal frequencies that are integral multiples of a fundamental frequency quantum, and further assuming that the renewal frequency distribution is of the Boltzmann type, performing a population balance for these elements leads to the Danckwerts surface age distribution. The basic quantum is what has been traditionally called the rate of surface renewal. The Higbie surface age distribution follows if the renewal frequency distribution of such elements is assumed to be continuous. Four age distributions, which reflect different start-up conditions of the absorption process, are then used to analyse transient physical gas absorption into a large volume of liquid, assuming negligible gas-side mass-transfer resistance. The first two are different versions of the Danckwerts model, the third one is based on the uniform and Higbie distributions, while the fourth one is a mixed distribution. For the four cases, theoretical expressions are derived for the rates of gas absorption and dissolved-gas transfer to the bulk liquid. Under transient conditions, these two rates are not equal and have an inverse relationship. However, with the progress of absorption towards steady state, they approach one another. Assuming steady-state conditions, the conventional one-parameter Danckwerts age distribution is generalized to a two-parameter age distribution. Like the two-parameter logarithmic normal distribution, this distribution can also capture the bell-shaped nature of the distribution of the ages of surface elements observed experimentally in air–sea gas and heat exchange. Estimates of the liquid-side mass-transfer coefficient made using these two distributions for the absorption of hydrogen and oxygen in water are very close to one another and are comparable to experimental values reported in the literature.

A surface renewal model for unsteady-state mass transfer using the generalized Danckwerts age distribution function

The recently derived steady-state generalized Danckwerts age distribution is extended to unsteady-state conditions. For three different wind speeds used by researchers on air–water heat exchange on the Heidelberg Aeolotron, calculations reveal that the distribution has a sharp peak during the initial moments, but flattens out and acquires a bell-shaped character with process time, with the time taken to attain a steady-state profile being a strong and inverse function of wind speed. With increasing wind speed, the age distribution narrows significantly, its skewness decreases and its peak becomes larger. The mean eddy renewal time increases linearly with process time initially but approaches a final steady-state value asymptotically, which decreases dramatically with increased wind speed. Using the distribution to analyse the transient absorption of a gas into a large body of liquid, assuming negligible gas-side mass-transfer resistance, estimates are made of the gas-absorption and dissolved-gas transfer coefficients for oxygen absorption in water at 25°C for the three different wind speeds. Under unsteady-state conditions, these two coefficients show an inverse behaviour, indicating a heightened accumulation of dissolved gas in the surface elements, especially during the initial moments of absorption. However, the two mass-transfer coefficients start merging together as the steady state is approached. Theoretical predictions of the steady-state mass-transfer coefficient or transfer velocity are in fair agreement (average absolute error of prediction = 18.1%) with some experimental measurements of the same for the nitrous oxide–water system at 20°C that were made in the Heidelberg Aeolotron.